Finite Group Databasebeta

← D3×#6499855 #72272012

Subgroups — D3×#6499855 #72272012

Order 3072.

Only the 4613 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 1191 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72272006C212yesmaximal, complemented
2#72272001C212yesmaximal, complemented
3#72271999C211yesmaximal, characteristic, complemented
4D3×#21778C211yesmaximal, characteristic, complemented
5#72271996C211yesmaximal, characteristic, complemented
6#72271992C211yesmaximal, characteristic, complemented
7C3×#6499855C211yesmaximal, characteristic, complemented
8#72271988C214yesmaximal, complemented
9#72271985C214yesmaximal, complemented
10D3×#23990C214yesmaximal, complemented
11#72258088C214yesmaximal, complemented
12D3×#23994C214yesmaximal, complemented
13#72258048C214yesmaximal, complemented
14D3×#21782C212yesmaximal, complemented
15#72258014C212yesmaximal, complemented
16#72258005C212yesmaximal, complemented
17D3×#23998C214yesmaximal, complemented
18#72257991C214yesmaximal, complemented
19D3×#23906C212yesmaximal, complemented
20D3×#60399C211yesmaximal, characteristic, complemented
21D3×#23897C212yesmaximal, complemented
22D3×#60388C212yesmaximal, complemented
23D3×#62832C211yesmaximal, characteristic, complemented
24D3×#23872C214yesmaximal, complemented
25D3×#23882C214yesmaximal, complemented
26D3×H(7,𝔽2)C2211yescharacteristic, complemented
27D3×#3585C2214yescomplemented
28#11704069C2211yescharacteristic, complemented
29#11704068C2212yescomplemented
30#11704067C2212yescomplemented
31#11704067C2212yescomplemented
32#11704066C2212yescomplemented
33#11704066C2212yescomplemented
34#11704065C2212yescomplemented
35#11704065C2211yescharacteristic, complemented
36#11704065C2211yescharacteristic, complemented
37D3×#3508C2212yescomplemented
38D3×#3508C2212yescomplemented
39D3×#3498C2212yes—
40D3×#3498C2212yescomplemented
41D3×#3484C2211yescharacteristic
42D3×#3484C2212yescomplemented
43D3×#3484C2211yescharacteristic, complemented
44D3×#3484C2212yescomplemented
45D3×#3444C2212yescomplemented
46C22×D3×#127C2211yescharacteristic, complemented
47#11661941C2212yescomplemented
48#11661941C2211yescharacteristic, complemented
49#11661940C2214yescomplemented
50#11661938C2211yescharacteristic, complemented
51#11661937C2211yescharacteristic, complemented
52#11661937C2212yescomplemented
53#11661936C2214yescomplemented
54D3×#3027C2214yescomplemented
55D3×#3025C2214yescomplemented
56#11661870C2212yescomplemented
57#11661869C2214yescomplemented
58#11661868C2212yescomplemented
59#11661867C2212yescomplemented
60#11661866C2214yescomplemented
61#11661865C2214yescomplemented
62#11661864C2214yescomplemented
63#11661863C2214yescomplemented
64#11661862C2214yescomplemented
65D3×#3021C2214yescomplemented
66D3×#3019C2214yescomplemented
67D3×#3019C2214yescomplemented
68D3×#3018C2214yescomplemented
69C2×D3×#453C2214yescomplemented
70D3×#3003C2214yescomplemented
71D3×#2901C2214yescomplemented
72D3×#2888C2212yescomplemented
73D3×#2883C2212yescomplemented
74D3×#2883C2211yescharacteristic, complemented
75#10827781C2214yescomplemented
76#10827780C2218yescomplemented
77#10827779C2214yescomplemented
78#10827778C2214yescomplemented
79#10827777C2218yescomplemented
80#10827776C2214yescomplemented
81#10827775C2214yescomplemented
82#10827774C2218yescomplemented
83#10827773C2214yescomplemented
84#10827772C2214yescomplemented
85#10827771C2218yescomplemented
86#10827737C2214yescomplemented
87#10827736C2218yescomplemented
88#10827735C2214yescomplemented
89#10827734C2214yescomplemented
90#10827733C2218yescomplemented
91#10827732C2214yescomplemented
92#10827731C2214yescomplemented
93#10827730C2218yescomplemented
94#10827729C2214yescomplemented
95#10827728C2214yescomplemented
96#10827727C2218yescomplemented
97#10827693C2214yescomplemented
98#10827692C2218yescomplemented
99#10827691C2214yescomplemented
100#10827690C2214yescomplemented
101#10827689C2218yescomplemented
102#10827688C2214yescomplemented
103#10827687C2214yescomplemented
104#10827686C2218yescomplemented
105#10827685C2214yescomplemented
106#10827684C2214yescomplemented
107#10827683C2218yescomplemented
108#10826824C2214yescomplemented
109#10826823C2212yescomplemented
110#10826822C2212yescomplemented
111#10826821C2214yescomplemented
112#10826820C2214yescomplemented
113#10826819C2214yescomplemented
114#10826818C2212yescomplemented
115#10826817C2218yescomplemented
116#10826749C2212yescomplemented
117#10826748C2214yescomplemented
118#10826748C2214yescomplemented
119#10826747C2214yescomplemented
120#10826747C2214yescomplemented
121#10826746C2212yescomplemented
122#10826746C2212yescomplemented
123#10826745C2218yescomplemented
124#10826602C2214yescomplemented
125#10826601C2214yescomplemented
126#10826600C2214yescomplemented
127#10826599C2214yescomplemented
128#10826598C2214yescomplemented
129#10826597C2218yescomplemented
130#10826596C2214yescomplemented
131#10826595C2218yescomplemented
132#10826594C2218yescomplemented
133#10826593C2214yescomplemented
134#10826592C2218yescomplemented
135#10826484C2214yescomplemented
136#10826483C2214yescomplemented
137#10826482C2214yescomplemented
138#10826481C2214yescomplemented
139#10826480C2214yescomplemented
140#10826479C2218yescomplemented
141#10826478C2214yescomplemented
142#10826477C2218yescomplemented
143#10826476C2218yescomplemented
144#10826475C2214yescomplemented
145#10826474C2218yescomplemented
146D3×#2031C2218yescomplemented
147D3×#2010C2218yescomplemented
148D3×#2008C2218yescomplemented
149D3×#2002C2218yescomplemented
150#10804378C2212yescomplemented
151#10804377C2212yescomplemented
152#10804376C2214yescomplemented
153#10804375C2214yescomplemented
154#10804374C2214yescomplemented
155#10804373C2214yescomplemented
156#10804372C2214yescomplemented
157#10804371C2212yescomplemented
158#10804370C2214yescomplemented
159#10804351C2211yescharacteristic, complemented
160#10804350C2212yescomplemented
161#10804349C2212yescomplemented
162#10804348C2214yescomplemented
163#10804347C2212yescomplemented
164#10804346C2214yescomplemented
165D3×#1914C2214yescomplemented
166D3×#1911C2214yescomplemented
167D3×#1911C2214yescomplemented
168D3×#1910C2214yescomplemented
169D3×#1906C2218yescomplemented
170D3×#1904C2218yescomplemented
171D3×#1896C2214yescomplemented
172D3×#1891C2214yescomplemented
173D3×#1887C2214yescomplemented
174D3×#1884C2214yescomplemented
175D3×#1829C2212yescomplemented
176D3×#1827C2214yescomplemented
177D3×#1795C2214yescomplemented
178D3×#1783C2212yescomplemented
179C3×#62832C2211yescharacteristic, complemented
180C3×#60399C2211yescharacteristic, complemented
181C3×#60388C2212yescomplemented
182C3×#23998C2214yescomplemented
183C3×#23994C2214yescomplemented
184C3×#23990C2214yescomplemented
185C3×#23906C2212yescomplemented
186C3×#23897C2212yescomplemented
187C3×#23882C2214yescomplemented
188C3×#23872C2214yescomplemented
189C3×#21782C2212yescomplemented
190C3×#21778C2211yescharacteristic, complemented
191#6499855D311yescharacteristic, direct product factor
192C3×H(7,𝔽2)C2311yescharacteristic, complemented
193#87574C2314yescomplemented
194D3×#585C2314yes—
195#87568C2312yescomplemented
196#87568C2311yescharacteristic, complemented
197C2×D3×H(5,𝔽2)C2311yescharacteristic
198C2×D3×H(5,𝔽2)C2312yes—
199C2×D3×H(5,𝔽2)C2312yes—
200C2×D3×H(5,𝔽2)C2311yescharacteristic, complemented
201C23×D3×D4C2311yescharacteristic
202C23×D3×D4C2311yescharacteristic, complemented
203C3×#3585C2314yescomplemented
204C3×#3508C2312yescomplemented
205C3×#3508C2312yescomplemented
206C3×#3498C2312yes—
207C3×#3498C2312yescomplemented
208C3×#3484C2311yescharacteristic
209C3×#3484C2312yescomplemented
210C3×#3484C2311yescharacteristic, complemented
211C3×#3484C2312yescomplemented
212C3×#3444C2312yescomplemented
213C22×C3×#127C2311yescharacteristic, complemented
214#87298C2314yescomplemented
215#87284C2311yescharacteristic
216#87284C2312yescomplemented
217#87284C2311yescharacteristic, complemented
218#87284C2312yescomplemented
219#87282C2312yes—
220#87282C2312yes—
221#87282C2312yescomplemented
222#87282C2312yescomplemented
223#87277C2314yescomplemented
224#87239C2311yescharacteristic
225#87239C2312yescomplemented
226#87239C2312yescomplemented
227#87239C2311yescharacteristic, complemented
228C22×#940C2311yescharacteristic, complemented
229C22×#940C2311yescharacteristic, complemented
230#87200C2318yescomplemented
231D3×#575C2318yes—
232#87192C2318yescomplemented
233C2×D3×AGL(1,ℤ/8)C2318yes—
234#87167C2314yescomplemented
235D3×#568C2314yes—
236#86330C2312yes—
237#86330C2314yescomplemented
238#86330C2312yescomplemented
239#86330C2312yescomplemented
240#86330C2312yescomplemented
241D3×#535D414yescomplemented
242D3×#535D414yescomplemented
243D3×#535C2312yes—
244D3×#535C2312yes—
245D3×#535C2312yes—
246D3×#535C2314yes—
247D3×#535C2312yescomplemented
248#86319C2312yescomplemented
249#86319C2312yescomplemented
250#86319C2312yescomplemented
251#86319C2312yescomplemented
252#86316D414yescomplemented
253#86316D414yescomplemented
254#86316C2312yes—
255#86316C2312yes—
256#86316C2312yescomplemented
257#86316C2312yescomplemented
258#86308D414yes—
259D3×#534D414yes—
260D3×#533C2312yescomplemented
261#86261C2312yescomplemented
262#86261C2312yescomplemented
263#86257C2312yescomplemented
264#86242D414yescomplemented
265#86242C2312yes—
266#86242C2312yescomplemented
267D3×#532D414yescomplemented
268D3×#532C2312yes—
269#86219C2312yescomplemented
270#86195D414yescomplemented
271#86195C2312yes—
272#86195C2312yescomplemented
273C2×D3×#127D414yescomplemented
274C2×D3×#127C2312yes—
275C2×D3×#127C2312yescomplemented
276C2×D3×#127C2312yescomplemented
277C2×D3×#127C2312yescomplemented
278#86190C2312yescomplemented
279#86190C2312yescomplemented
280#86039C2312yes—
281#86039C2314yescomplemented
282#86039C2312yescomplemented
283#86039C2312yescomplemented
284#86039C2312yescomplemented
285D3×#525C2312yes—
286D3×#525C2314yes—
287D3×#525C2312yescomplemented
288#86018C2312yescomplemented
289#86018C2312yescomplemented
290#85919D414yes—
291C2×D3×#120D414yes—
292#85867C2311yescharacteristic
293#85867C2312yescomplemented
294#85867C2311yescharacteristic, complemented
295#85867C2312yescomplemented
296D3×#518C2311yescharacteristic
297D3×#518C2312yes—
298D3×#518C2312yescomplemented
299D3×#518C2311yescharacteristic, complemented
300#85862C2312yescomplemented
301#85862C2312yescomplemented
302#85862C2312yescomplemented
303#85862C2312yescomplemented
304#85848C2312yescomplemented
305#85848C2312yescomplemented
306#85846C2312yes—
307#85846C2312yescomplemented
308#85836C2312yescomplemented
309#85836C2312yescomplemented
310C4×D3×#41C2312yes—
311C4×D3×#41C2312yescomplemented
312#85680C2312yescomplemented
313C22×#874C2311yescharacteristic, complemented
314C22×C42×D3C2311yescharacteristic, complemented
315C3×#3027C2314yescomplemented
316C3×#3025C2314yescomplemented
317C3×#3021C2314yescomplemented
318C3×#3019C2314yescomplemented
319C3×#3019C2314yescomplemented
320C3×#3018C2314yescomplemented
321C2×C3×#453C2314yescomplemented
322C3×#3003C2314yescomplemented
323C3×#2901C2314yescomplemented
324C3×#2888C2312yescomplemented
325C3×#2883C2312yescomplemented
326C3×#2883C2311yescharacteristic, complemented
327#84126C2314yescomplemented
328#84125C2314yescomplemented
329#84122C2314yescomplemented
330#84121C2314yescomplemented
331#84120C2314yescomplemented
332#84107C2312yescomplemented
333#84107C2311yescharacteristic, complemented
334#84104C2314yescomplemented
335#84104C2314yescomplemented
336C2×#5241C2314yescomplemented
337#84100C2312yescomplemented
338#84038C2314yescomplemented
339#84005C2318yescomplemented
340#84005C2318yescomplemented
341#84004C2318yescomplemented
342#83957C2318yescomplemented
343C2×#5198C2318yescomplemented
344#83944C2318yescomplemented
345#83817C2314yescomplemented
346#83813C2314yescomplemented
347#83396C2318yescomplemented
348#83396C2314yescomplemented
349#83395C2314yescomplemented
350#83394C2314yescomplemented
351#83394C2314yescomplemented
352#83322C2314yescomplemented
353C2×#5077C2314yescomplemented
354#82936C2318yescomplemented
355#82936C2314yescomplemented
356#82927C2314yescomplemented
357#82546C2312yescomplemented
358#82546C2312yescomplemented
359#82546C2312yescomplemented
360#82536C2314yescomplemented
361#78994C2318yescomplemented
362#78993C2318yescomplemented
363#78993C2318yescomplemented
364#78992C2318yescomplemented
365D3×#421C2318yes—
366D3×#421C2318yescomplemented
367#78986C2318yescomplemented
368C2×#4822C2318yescomplemented
369#78983C2318yescomplemented
370C2×D3×#104C2318yes—
371#78926C2318yescomplemented
372D3×#418C2318yescomplemented
373#78717C2314yescomplemented
374#78716C2314yescomplemented
375#78714C2314yescomplemented
376D3×#413C2314yes—
377#78700C2314yescomplemented
378#78700C2314yescomplemented
379C2×#4747C2314yescomplemented
380#78697C2314yescomplemented
381C2×D3×#100C2314yes—
382C2×D3×#100C2314yescomplemented
383#78694C2318yescomplemented
384#78694C2314yescomplemented
385D3×#410C2318yes—
386D3×#410C2314yes—
387#78691C2318yescomplemented
388#78691C2314yescomplemented
389#78690C2318yescomplemented
390#78690C2314yescomplemented
391#78637C2314yescomplemented
392D3×#407C2314yescomplemented
393C3×#2031C2318yescomplemented
394C3×#2010C2318yescomplemented
395C3×#2008C2318yescomplemented
396C3×#2002C2318yescomplemented
397C3×#1914C2314yescomplemented
398C3×#1911C2314yescomplemented
399C3×#1911C2314yescomplemented
400C3×#1910C2314yescomplemented
401C3×#1906C2318yescomplemented
402C3×#1904C2318yescomplemented
403C3×#1896C2314yescomplemented
404C3×#1891C2314yescomplemented
405C3×#1887C2314yescomplemented
406C3×#1884C2314yescomplemented
407C3×#1829C2312yescomplemented
408C3×#1827C2314yescomplemented
409C3×#1795C2314yescomplemented
410C3×#1783C2312yescomplemented
411#72141C2314yescomplemented
412#72129C2312yescomplemented
413#72119C2318yescomplemented
414#72118C2318yescomplemented
415#72114C2318yescomplemented
416#72099C2318yescomplemented
417#72094C2318yescomplemented
418#72089C2318yescomplemented
419#72030C2314yescomplemented
420#72029C2314yescomplemented
421#72025C2314yescomplemented
422#72021C2314yescomplemented
423#71858C2318yescomplemented
424#71856C2318yescomplemented
425#71855C2314yescomplemented
426#71854C2314yescomplemented
427#71853C2314yescomplemented
428#71853C2314yescomplemented
429#71842C2318yescomplemented
430#71817C2314yescomplemented
431#71769C2318yescomplemented
432#71763C2314yescomplemented
433#71715C2318yescomplemented
434#71715C2318yescomplemented
435#71714C2314yescomplemented
436#71711C2314yescomplemented
437#71652C2314yescomplemented
438#71652C2314yescomplemented
439#71651C2318yescomplemented
440#71650C2314yescomplemented
441#71648C2312yescomplemented
442#71645C2318yescomplemented
443#71644C2314yescomplemented
444#71532C2314yescomplemented
445#70417C2318yescomplemented
446#70414C2318yescomplemented
447#70409C2318yescomplemented
448#70408C2318yescomplemented
449#70408C2318yescomplemented
450#70407C2318yescomplemented
451#70406C2318yescomplemented
452#70406C2318yescomplemented
453#70395C2318yescomplemented
454#70394C2318yescomplemented
455#70391C2318yescomplemented
456#70385C2318yescomplemented
457#70382C2318yescomplemented
458#70368C2318yescomplemented
459#70331C2318yescomplemented
460#70330C2318yescomplemented
461#70327C2318yescomplemented
462#70324C2318yescomplemented
463#70323C2318yescomplemented
464#70314C2318yescomplemented
465#70139C2314yescomplemented
466#70137C2314yescomplemented
467#70136C2314yescomplemented
468#70131C2314yescomplemented
469#70089C2318yescomplemented
470#70082C2318yescomplemented
471#70079C2314yescomplemented
472#70079C2314yescomplemented
473#70071C2314yescomplemented
474#70071C2314yescomplemented
475#70070C2314yescomplemented
476#70067C2314yescomplemented
477#70055C2318yescomplemented
478#70050C2318yescomplemented
479#70049C2318yescomplemented
480#70048C2314yescomplemented
481#70047C2314yescomplemented
482#70045C2314yescomplemented
483#70039C2314yescomplemented
484#70038C2318yescomplemented
485#69993C2318yescomplemented
486#69992C2318yescomplemented
487#69988C2314yescomplemented
488#69965C2314yescomplemented
489#69042C2318yescomplemented
490#69040C2318yescomplemented
491#69039C2318yescomplemented
492#69036C2318yescomplemented
493#69028C2318yescomplemented
494#69027C2318yescomplemented
495#69026C2318yescomplemented
496D3×#344C2318yescomplemented
497#68779C2318yescomplemented
498#68778C2318yescomplemented
499#68777C2318yescomplemented
500#68761C2318yescomplemented
501#68760C2318yescomplemented
502#68756C2318yescomplemented
503D3×#339C2318yescomplemented
504#68737C2318yescomplemented
505#68714C2318yescomplemented
506#68713C2318yescomplemented
507#68711C2318yescomplemented
508#68705C2318yescomplemented
509#68705C2318yescomplemented
510#68704C2318yescomplemented
511#68703C2318yescomplemented
512D3×H(3,ℤ/4)C2318yescomplemented
513#62832C2×D311yescharacteristic, complemented
514#60399C2×D311yescharacteristic, complemented
515#60388C2×D312yescomplemented
516#23998C2×D314yescomplemented
517#23994C2×D314yescomplemented
518#23990C2×D314yescomplemented
519#23906C2×D312yescomplemented
520#23897C2×D312yescomplemented
521#23882C2×D314yescomplemented
522#23872C2×D314yescomplemented
523#21782C2×D312yescomplemented
524#21778C2×D311yescharacteristic, complemented
525C25×D3C2×D412yes—
526C3×#585C2414yes—
527C2×C3×H(5,𝔽2)C2411yescharacteristic
528C2×C3×H(5,𝔽2)C2412yes—
529C2×C3×H(5,𝔽2)C2412yes—
530C2×C3×H(5,𝔽2)C2411yescharacteristic, complemented
531C23×C3×D4C2411yescharacteristic
532C23×C3×D4C2411yescharacteristic, complemented
533C23×#67C2×D412yes—
534#5964C2418yes—
535#5964C2414yes—
536C2×#1009C2×D414yes—
537C2×#1009C2×D414yescomplemented
538C2×#1009C2412yes—
539C2×#1009C2412yes—
540C2×#1009C2412yes—
541C2×#1009C2414yes—
542C2×#1009C2412yescomplemented
543C2×D3×#41C2×D414yes—
544C2×D3×#41C2×D414yescomplemented
545C2×D3×#41C2412yes—
546C2×D3×#41C2412yes—
547C2×D3×#41C2414yes—
548C2×#1004C2×D414yes—
549C2×#1004C2×D414yes—
550C2×#1004C2×D414yescomplemented
551C2×#1004C2411yescharacteristic
552C2×#1004C2412yes—
553C2×#1004C2412yes—
554C2×#1004C2411yescharacteristic, complemented
555C22×D3×D4C2×D414yes—
556C22×D3×D4C2×D414yes—
557C22×D3×D4C2×D412yes—
558C22×D3×D4C2×D412yes—
559C22×D3×D4C2×D414yescomplemented
560C22×D3×D4C2411yescharacteristic
561C22×D3×D4C2412yes—
562C22×D3×D4C2411yescharacteristic
563C22×D3×D4C2411yescharacteristic
564C22×D3×D4C2411yescharacteristic
565C22×D3×D4C2412yescomplemented
566C23×D12C2411yescharacteristic
567C23×D12C2411yescharacteristic, complemented
568C23×C4×D3C2411yescharacteristic
569C3×#575C2418yes—
570C2×C3×AGL(1,ℤ/8)C2418yes—
571C3×#568C2414yes—
572C3×#535C2×D414yescomplemented
573C3×#535C2×D414yescomplemented
574C3×#535C2412yes—
575C3×#535C2412yes—
576C3×#535C2412yes—
577C3×#535C2414yes—
578C3×#535C2412yescomplemented
579C3×#534C2×D414yes—
580C3×#533C2412yescomplemented
581C3×#532C2×D414yescomplemented
582C3×#532C2412yes—
583C2×C3×#127C2×D414yescomplemented
584C2×C3×#127C2412yes—
585C2×C3×#127C2412yescomplemented
586C3×#525C2412yes—
587C3×#525C2414yes—
588C3×#525C2412yescomplemented
589C2×C3×#120C2×D414yes—
590C3×#518C2411yescharacteristic
591C3×#518C2412yes—
592C3×#518C2412yescomplemented
593C3×#518C2411yescharacteristic, complemented
594C3×C4×#41C2412yes—
595C3×C4×#41C2412yescomplemented
596C22×C3×C42C2411yescharacteristic, complemented
597C2×#953C2×D414yes—
598#5832C2×D414yescomplemented
599#5832C2×D414yescomplemented
600#5832C2412yes—
601#5832C2412yes—
602#5830C2×D414yescomplemented
603#5830C2×D414yescomplemented
604#5830C2412yes—
605#5830C2412yes—
606#5830C2412yes—
607#5830C2414yes—
608#5830C2412yescomplemented
609#5828C2412yes—
610#5828C2414yes—
611#5828C2412yescomplemented
612Dic3×#41C2412yes—
613Dic3×#41C2412yescomplemented
614#5822C2418yes—
615#5822C2418yes—
616C2×#949C2418yes—
617#5819C2414yes—
618#5805C2×D414yescomplemented
619#5805C2×D414yescomplemented
620#5805C2412yes—
621#5805C2412yes—
622#5805C2412yes—
623#5805C2414yes—
624#5805C2412yescomplemented
625#5804C2×D414yes—
626#5804C2×D414yes—
627C2×#940C2×D414yescomplemented
628C2×#940C2×D414yescomplemented
629C2×#940C2412yes—
630C2×#940C2412yes—
631C2×#940C2412yescomplemented
632C2×#940C2412yescomplemented
633C2×#937C2×D414yes—
634#5798C2411yescharacteristic
635#5798C2412yes—
636#5798C2412yescomplemented
637#5798C2411yescharacteristic, complemented
638C2×#932C2418yes—
639#5791C2412yes—
640#5791C2414yes—
641#5791C2412yescomplemented
642C22×C4×Dic3C2411yescharacteristic, complemented
643#5748C2418yes—
644C2×#908C2418yes—
645#5745C2418yes—
646C2×D3×M16C2418yes—
647#5725C2×D412yescomplemented
648#5725C2×D414yescomplemented
649D3×C4⋊Q8C2×D412yescomplemented
650#5716C2×D412yescomplemented
651#5716C2×D414yescomplemented
652#5715C2×D414yes—
653#5715C2×D414yescomplemented
654#5715C2×D414yescomplemented
655#5715C2×D414yescomplemented
656#5715C2×D414yescomplemented
657#5715C2×D414yescomplemented
658D3×#127C2×D414yes—
659D3×#127C2×D414yes—
660D3×#127C2×D414yes—
661D3×#127C2×D414yes—
662D3×#127C2×D414yes—
663D3×#127C2×D414yescomplemented
664D3×#127C2×D412yescomplemented
665D3×#127C2×D414yescomplemented
666D3×#127C2×D414yescomplemented
667D3×#127C2×D414yescomplemented
668D3×#127C2×D414yescomplemented
669#5674C2×D414yes—
670#5674C2×D414yescomplemented
671#5674C2×D414yescomplemented
672#5674C2×D414yescomplemented
673#5674C2×D414yescomplemented
674#5674C2×D414yescomplemented
675D3×#124C2×D414yes—
676D3×#124C2×D412yescomplemented
677D3×#124C2×D412yescomplemented
678D3×#124C2×D414yescomplemented
679#5668C2×D412yescomplemented
680#5668C2×D412yescomplemented
681#5668C2×D414yescomplemented
682#5668C2×D414yescomplemented
683#5656C2×D414yes—
684#5653C2×D418yes—
685D3×#123C2×D414yes—
686#5592C2×D418yes—
687#5589C2×D418yes—
688D3×#120C2×D414yes—
689D3×#120C2×D418yes—
690D3×#120C2×D418yes—
691D3×#120C2×D418yes—
692#5586C2×D414yes—
693#5525C2×D414yescomplemented
694#5525C2×D414yescomplemented
695#5525C2412yes—
696#5525C2412yes—
697#5525C2412yes—
698#5525C2414yes—
699#5525C2412yescomplemented
700#5524C2412yes—
701#5524C2414yes—
702#5524C2412yescomplemented
703#5522C2×D414yescomplemented
704#5522C2412yes—
705#5522C2412yescomplemented
706#5521C2412yes—
707#5521C2414yes—
708#5521C2412yescomplemented
709#5521C2412yescomplemented
710#5521C2412yescomplemented
711D3×#117C2×D414yescomplemented
712D3×#117C2412yes—
713D3×#117C2412yes—
714D3×#117C2414yes—
715#5517C2412yescomplemented
716#5517C2412yescomplemented
717#5493C2×D414yes—
718C2×#882C2×D414yes—
719#5486C2×D414yes—
720C2×D3×C22⋊C4C2×D414yes—
721#5477C2×D414yescomplemented
722#5477C2412yes—
723C2×#874C2×D414yescomplemented
724C2×#874C2412yes—
725C2×#874C2412yescomplemented
726C4×#235C2×D414yescomplemented
727C4×#235C2412yes—
728C4×#235C2412yescomplemented
729C2×C42×D3C2×D414yescomplemented
730C2×C42×D3C2412yes—
731C2×C42×D3C2412yescomplemented
732#5470C2412yescomplemented
733C3×#421C2418yes—
734C3×#421C2418yescomplemented
735C2×C3×#104C2418yes—
736C3×#418C2418yescomplemented
737C3×#413C2414yes—
738C2×C3×#100C2414yes—
739C2×C3×#100C2414yescomplemented
740C3×#410C2418yes—
741C3×#410C2414yes—
742C3×#407C2414yescomplemented
743#5240C2418yes—
744#5240C2414yes—
745#5237C2414yes—
746#5236C2418yes—
747#5236C2418yescomplemented
748C2×#837C2418yes—
749C2×#833C2414yes—
750C2×#833C2414yescomplemented
751#5215C2418yescomplemented
752#5207C2414yescomplemented
753#5139C2418yes—
754#5139C2418yescomplemented
755C2×#825C2418yes—
756#5132C2418yes—
757#5131C2418yescomplemented
758C2×#823C2418yes—
759C2×#823C2418yescomplemented
760#5126C2418yescomplemented
761#5006C2418yes—
762#5006C2418yes—
763#5006C2418yes—
764#5005C2418yes—
765#5005C2418yescomplemented
766#5001C2418yescomplemented
767C2×#805C2418yes—
768C3×#344C2418yescomplemented
769C3×#339C2418yescomplemented
770C3×H(3,ℤ/4)C2418yescomplemented
771#4559C2418yescomplemented
772#4557C2418yescomplemented
773#4556C2418yescomplemented
774#4555C2418yescomplemented
775#4533C2418yescomplemented
776#4532C2418yescomplemented
777#4531C2418yescomplemented
778#4531C2418yescomplemented
779#4523C2418yescomplemented
780H(7,𝔽2)C22×D311yescharacteristic, complemented
781#3585C22×D314yescomplemented
782#3508C22×D312yescomplemented
783#3508C22×D312yescomplemented
784#3498C22×D312yes—
785#3498C22×D312yescomplemented
786#3484C22×D311yescharacteristic
787#3484C22×D312yescomplemented
788#3484C22×D312yescomplemented
789#3484C22×D311yescharacteristic, complemented
790#3444C22×D312yescomplemented
791C22×#127C22×D311yescharacteristic, complemented
792#3027C22×D314yescomplemented
793#3025C22×D314yescomplemented
794#3021C22×D314yescomplemented
795#3019C22×D314yescomplemented
796#3019C22×D314yescomplemented
797#3018C22×D314yescomplemented
798C2×#453C22×D314yescomplemented
799#3003C22×D314yescomplemented
800#2901C22×D314yescomplemented
801#2888C22×D312yescomplemented
802#2883C22×D311yescharacteristic, complemented
803#2883C22×D312yescomplemented
804#2031C22×D318yescomplemented
805#2010C22×D318yescomplemented
806#2008C22×D318yescomplemented
807#2002C22×D318yescomplemented
808#1914C22×D314yescomplemented
809#1911C22×D314yescomplemented
810#1911C22×D314yescomplemented
811#1910C22×D314yescomplemented
812#1906C22×D318yescomplemented
813#1904C22×D318yescomplemented
814#1896C22×D314yescomplemented
815#1891C22×D314yescomplemented
816#1887C22×D314yescomplemented
817#1884C22×D314yescomplemented
818#1829C22×D312yescomplemented
819#1827C22×D314yescomplemented
820#1795C22×D314yescomplemented
821#1783C22×D312yescomplemented
822C25×C3C22×D412yes—
823C24×D3#12014yes—
824C24×D3C22×D412yes—
825C24×D3C22×D411yescharacteristic
826C24×D3C22×D412yes—
827C24×D3C22×D412yes—
828C24×D3C22×D412yes—
829C24×D3C22×D412yes—
830C2×C3×#41C22×D414yes—
831C2×C3×#41C22×D414yescomplemented
832C2×C3×#41C2512yes—
833C2×C3×#41C2512yes—
834C2×C3×#41C2514yes—
835C22×C3×D4C22×D414yes—
836C22×C3×D4C22×D414yes—
837C22×C3×D4C22×D412yes—
838C22×C3×D4C22×D414yescomplemented
839C22×C3×D4C2512yes—
840C22×C3×D4C2511yescharacteristic
841C22×C3×D4C2511yescharacteristic
842C23×C3×C4C2511yescharacteristic
843C22×#67#12014yes—
844C22×#67#12018yes—
845C22×#67C22×D414yes—
846C22×#67C22×D412yes—
847C22×#67C22×D412yes—
848C22×#67C22×D412yes—
849C22×#67C22×D412yes—
850C23×Dic3C22×D411yescharacteristic
851C2×#239C22×D414yes—
852C2×#239C22×D412yes—
853C2×#239C22×D412yes—
854C2×#239C22×D414yescomplemented
855C2×#239H(5,𝔽2)14yescomplemented
856C2×D3×Q8C22×D412yes—
857C2×D3×Q8C22×D412yes—
858C2×D3×Q8H(5,𝔽2)14yescomplemented
859C2×#237#12018yes—
860C2×#237C22×D414yes—
861C2×#237C22×D412yes—
862C2×#237C22×D414yes—
863C2×#237C22×D412yes—
864C2×#237C22×D414yescomplemented
865C2×#237H(5,𝔽2)14yescomplemented
866C2×D3×D4#12018yes—
867C2×D3×D4#12018yes—
868C2×D3×D4#12018yes—
869C2×D3×D4C22×D414yes—
870C2×D3×D4C22×D418yes—
871C2×D3×D4C22×D414yes—
872C2×D3×D4C22×D412yes—
873C2×D3×D4C22×D414yes—
874C2×D3×D4C22×D414yes—
875C2×D3×D4C22×D414yes—
876C2×D3×D4C22×D412yes—
877C2×D3×D4C22×D414yes—
878C2×D3×D4C22×D414yes—
879C2×D3×D4C22×D414yescomplemented
880C2×D3×D4C22×D414yescomplemented
881C2×D3×D4H(5,𝔽2)14yescomplemented
882C2×#235#12018yes—
883C2×#235C22×D414yes—
884C2×#235C22×D414yes—
885C2×#235C22×D414yescomplemented
886C2×#235C2512yes—
887C2×#235C2512yes—
888C2×#235C2514yes—
889C22×D12#12014yes—
890C22×D12C22×D414yes—
891C22×D12C22×D412yes—
892C22×D12C22×D414yescomplemented
893C22×D12C2511yescharacteristic
894C22×D12C2512yes—
895C22×D12C2511yescharacteristic
896C22×C4×D3#12014yes—
897C22×C4×D3C22×D414yes—
898C22×C4×D3C22×D411yescharacteristic
899C22×C4×D3C22×D411yescharacteristic
900C22×C4×D3C2511yescharacteristic
901C22×C4×D3C2511yescharacteristic
902C2×C3×M16C2518yes—
903C3×C4⋊Q8C22×D412yescomplemented
904C3×#127C22×D414yes—
905C3×#127C22×D414yes—
906C3×#127C22×D414yes—
907C3×#127C22×D412yescomplemented
908C3×#127C22×D414yescomplemented
909C3×#124C22×D414yes—
910C3×#124C22×D414yescomplemented
911C3×#124C22×D412yescomplemented
912C3×#124C22×D412yescomplemented
913C3×#123C22×D414yes—
914C3×#120C22×D414yes—
915C3×#120C22×D418yes—
916C3×#117C22×D414yescomplemented
917C3×#117C2512yes—
918C3×#117C2512yes—
919C3×#117C2514yes—
920C2×C3×C22⋊C4C22×D414yes—
921C2×C3×C42C22×D414yescomplemented
922C2×C3×C42C2512yes—
923#953C22×D414yes—
924#953C22×D418yes—
925C2×#217C22×D414yes—
926#947C22×D414yes—
927#947C22×D412yescomplemented
928#947C22×D412yescomplemented
929#947C22×D414yescomplemented
930#944C22×D412yescomplemented
931#944C22×D412yescomplemented
932#940C22×D414yes—
933#940C22×D414yes—
934#940C22×D414yes—
935#940C22×D414yes—
936#940C22×D414yes—
937#940C22×D414yes—
938#940C22×D412yescomplemented
939#940C22×D412yescomplemented
940#940C22×D414yescomplemented
941#940C22×D414yescomplemented
942#937C22×D418yes—
943#937C22×D414yes—
944#936C22×D414yes—
945#936C22×D412yescomplemented
946#936C22×D412yescomplemented
947#936C22×D414yescomplemented
948#935C22×D414yes—
949#929C22×D414yes—
950#926C22×D414yescomplemented
951#926C2512yes—
952#926C2512yes—
953#926C2514yes—
954C2×C4×Dic3C22×D414yescomplemented
955C2×C4×Dic3C2512yes—
956C2×#208C2518yes—
957#886C22×D414yes—
958#882C22×D418yes—
959#882C22×D414yes—
960D3×C22⋊C4C22×D414yes—
961D3×C22⋊C4C22×D418yes—
962#877C22×D414yes—
963#875C22×D414yes—
964#875C22×D414yescomplemented
965#875C22×D412yescomplemented
966#875C22×D412yescomplemented
967#874C22×D414yes—
968#874C22×D414yes—
969#874C22×D414yes—
970#874C22×D414yescomplemented
971#874C22×D412yescomplemented
972#872C22×D414yes—
973#872C22×D414yescomplemented
974#872C22×D414yescomplemented
975C42×D3C22×D412yes—
976C42×D3C22×D414yes—
977C42×D3C22×D412yes—
978C42×D3C22×D412yes—
979C42×D3C22×D412yes—
980C42×D3C22×D414yescomplemented
981C42×D3C22×D414yescomplemented
982#869C22×D412yescomplemented
983#585C23×D314yes—
984C2×H(5,𝔽2)C23×D311yescharacteristic
985C2×H(5,𝔽2)C23×D312yes—
986C2×H(5,𝔽2)C23×D312yes—
987C2×H(5,𝔽2)C23×D311yescharacteristic, complemented
988C23×D4C23×D311yescharacteristic
989C23×D4C23×D311yescharacteristic, complemented
990#575C23×D318yes—
991C2×AGL(1,ℤ/8)C23×D318yes—
992#568C23×D314yes—
993#535D3×D414yescomplemented
994#535D3×D414yescomplemented
995#535C23×D312yes—
996#535C23×D312yes—
997#535C23×D312yes—
998#535C23×D314yes—
999#535C23×D312yescomplemented
1000#534D3×D414yes—
1001#533C23×D312yescomplemented
1002#532D3×D414yescomplemented
1003#532C23×D312yes—
1004C2×#127D3×D414yescomplemented
1005C2×#127C23×D312yes—
1006C2×#127C23×D312yescomplemented
1007#525C23×D312yes—
1008#525C23×D314yes—
1009#525C23×D312yescomplemented
1010C2×#120D3×D414yes—
1011#518C23×D311yescharacteristic
1012#518C23×D312yes—
1013#518C23×D312yescomplemented
1014#518C23×D311yescharacteristic, complemented
1015C4×#41C23×D312yes—
1016C4×#41C23×D312yescomplemented
1017C22×C42C23×D311yescharacteristic, complemented
1018#421C23×D318yes—
1019#421C23×D318yescomplemented
1020C2×#104C23×D318yes—
1021#418C23×D318yescomplemented
1022#413C23×D314yes—
1023C2×#100C23×D314yes—
1024C2×#100C23×D314yescomplemented
1025#410C23×D314yes—
1026#410C23×D318yes—
1027#407C23×D314yescomplemented
1028#344C23×D318yescomplemented
1029#339C23×D318yescomplemented
1030H(3,ℤ/4)C23×D318yescomplemented
1031C24×C3C2×#12014yes—
1032C24×C3C23×D411yescharacteristic
1033C24×C3C23×D412yes—
1034C24×C3C23×D412yes—
1035C23×D3C2×#12014yes—
1036C23×D3C2×#12014yes—
1037C23×D3C2×#12014yes—
1038C23×D3C2×#12014yes—
1039C23×D3C2×#12018yes—
1040C23×D3C23×D411yescharacteristic
1041C23×D3C23×D412yes—
1042C23×D3C23×D411yescharacteristic
1043C23×D3C23×D412yes—
1044C2×C3×Q8C23×D412yes—
1045C2×C3×Q8C23×D412yes—
1046C2×C3×Q8C2×H(5,𝔽2)14yescomplemented
1047C2×C3×D4C2×#12018yes—
1048C2×C3×D4C23×D414yes—
1049C2×C3×D4C23×D412yes—
1050C2×C3×D4C23×D414yes—
1051C2×C3×D4C23×D412yes—
1052C2×C3×D4C23×D414yes—
1053C2×C3×D4C2×H(5,𝔽2)14yescomplemented
1054C22×C3×C4C2×#12014yes—
1055C22×C3×C4C23×D414yes—
1056C22×C3×C4C23×D411yescharacteristic
1057C22×C3×C4C2611yescharacteristic
1058C2×#67C2×#12018yes—
1059C2×#67C2×#12018yes—
1060C2×#67C2×#12014yes—
1061C2×#67C2×#12014yes—
1062C2×#67C2×#12018yes—
1063C2×#67C23×D414yes—
1064C22×Dic3C2×#12014yes—
1065C22×Dic3C2×#12014yes—
1066C22×Dic3C23×D411yescharacteristic
1067C22×Dic3C23×D411yescharacteristic
1068C2×D12C2×#12014yes—
1069C2×D12C2×#12018yes—
1070C2×D12C23×D412yes—
1071C2×D12C23×D414yes—
1072C2×D12C23×D414yes—
1073C2×D12C23×D412yes—
1074C2×D12C2×H(5,𝔽2)14yescomplemented
1075C2×C4×D3C2×#12014yes—
1076C2×C4×D3C2×#12018yes—
1077C2×C4×D3C2×#12014yes—
1078C2×C4×D3C23×D412yes—
1079C2×C4×D3C23×D412yes—
1080C2×C4×D3C23×D414yes—
1081C2×C4×D3C2×H(5,𝔽2)14yes—
1082C2×C4×D3C2×H(5,𝔽2)14yes—
1083C2×Dic6C2×#12014yes—
1084C2×Dic6C23×D412yes—
1085C2×Dic6C23×D412yes—
1086C2×Dic6C2×H(5,𝔽2)14yescomplemented
1087C3×C22⋊C4C23×D414yes—
1088C3×C42C23×D412yes—
1089C3×C42C23×D412yes—
1090C3×C42C23×D414yes—
1091#217C23×D414yes—
1092C4×Dic3C23×D412yes—
1093C4×Dic3C23×D412yes—
1094C4×Dic3C23×D414yes—
1095C25C2×D3×D412yes—
1096C2×#41C2×D3×D414yes—
1097C2×#41C2×D3×D414yescomplemented
1098C2×#41C24×D312yes—
1099C2×#41C24×D312yes—
1100C2×#41C24×D314yes—
1101C22×D4C2×D3×D414yes—
1102C22×D4C2×D3×D412yes—
1103C22×D4C2×D3×D414yes—
1104C22×D4C2×D3×D414yescomplemented
1105C22×D4C24×D312yes—
1106C22×D4C24×D311yescharacteristic
1107C22×D4C24×D311yescharacteristic
1108C23×C4C24×D311yescharacteristic
1109C2×M16C24×D318yes—
1110C4⋊Q8C2×D3×D412yescomplemented
1111#127C2×D3×D414yes—
1112#127C2×D3×D414yes—
1113#127C2×D3×D414yes—
1114#127C2×D3×D412yescomplemented
1115#127C2×D3×D414yescomplemented
1116#124C2×D3×D414yes—
1117#124C2×D3×D414yescomplemented
1118#124C2×D3×D412yescomplemented
1119#124C2×D3×D412yescomplemented
1120#123C2×D3×D414yes—
1121#120C2×D3×D414yes—
1122#120C2×D3×D418yes—
1123#117C2×D3×D414yescomplemented
1124#117C24×D312yes—
1125#117C24×D312yes—
1126#117C24×D314yes—
1127C2×C22⋊C4C2×D3×D414yes—
1128C2×C42C2×D3×D414yescomplemented
1129C2×C42C24×D312yes—
1130C23×C3C22×#12014yes—
1131C23×C3C22×#12014yes—
1132C23×C3C24×D411yescharacteristic
1133C22×D3C22×#12011yescharacteristic
1134C22×D3C22×#12011yescharacteristic
1135C22×D3C22×#12014yes—
1136C22×D3C22×#12014yes—
1137C22×D3#348412yes—
1138C22×D3#348412yes—
1139C2×C3×C4C22×#12014yes—
1140C2×C3×C4C24×D412yes—
1141C2×C3×C4C22×H(5,𝔽2)14yes—
1142C2×Dic3C22×#12012yes—
1143C2×Dic3C22×#12014yes—
1144C2×Dic3#348414yes—
1145C4×D3#348414yes—
1146C4×D3#348414yes—
1147C4×D3#348418yes—
1148C24D3×#12014yes—
1149C24C22×D3×D411yescharacteristic
1150C24C22×D3×D412yes—
1151C24C22×D3×D412yes—
1152C2×Q8C22×D3×D412yes—
1153C2×Q8C22×D3×D412yes—
1154C2×Q8D3×H(5,𝔽2)14yescomplemented
1155C2×D4D3×#12018yes—
1156C2×D4C22×D3×D412yes—
1157C2×D4C22×D3×D414yes—
1158C2×D4C22×D3×D414yes—
1159C2×D4C22×D3×D412yes—
1160C2×D4C22×D3×D414yes—
1161C2×D4D3×H(5,𝔽2)14yescomplemented
1162C22×C4D3×#12014yes—
1163C22×C4C22×D3×D414yes—
1164C22×C4C22×D3×D411yescharacteristic
1165C22×C4C25×D311yescharacteristic
1166C22⋊C4C22×D3×D414yes—
1167C42C22×D3×D412yes—
1168C42C22×D3×D414yes—
1169C42C22×D3×D412yes—
1170C22×C3C23×#12011yescharacteristic
1171C22×C3C2×#348412yes—
1172C2×D3#3534611yescharacteristic
1173C2×D3#3534611yescharacteristic
1174C2×D3#3534612yes—
1175C3×C4C2×#348414yes—
1176Dic3#3534614yes—
1177C23C2×D3×#12014yes—
1178C23C2×D3×#12014yes—
1179C23C23×D3×D411yescharacteristic
1180C2×C4C2×D3×#12014yes—
1181C2×C4C23×D3×D412yes—
1182C2×C4C2×D3×H(5,𝔽2)14yes—
1183C2×C3C2×#3534611yescharacteristic
1184D3#649985512yesdirect product factor
1185C22C22×D3×#12011yescharacteristic
1186C22D3×#348412yes—
1187C4D3×#348414yes—
1188C3C2×#649985511yescharacteristic, complemented, Sylow
1189C2D3×#3534611yescharacteristic
subgroupG/H
centerC2D3×#35346
commutator, cosocleC22×C3×C4C26
FrattiniC22×C4C25×D3
FittingC3×#6499855C2
socleC2×C3C2×#35346
hypercenter#6499855D3
hypocenterC3C2×#6499855
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C22×C4 ◁ #6499855

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #72272006C2semidirect
2. #72272001C2semidirect
3. #72271999C2semidirect
4. D3×#21778C2semidirect
5. #72271996C2semidirect
6. #72271992C2semidirect
7. C3×#6499855C2semidirect
8. #72271988C2semidirect
9. #72271985C2semidirect
10. D3×#23990C2semidirect
11. #72258088C2semidirect
12. D3×#23994C2semidirect
13. #72258048C2semidirect
14. D3×#21782C2semidirect
15. #72258014C2semidirect
16. #72258005C2semidirect
17. D3×#23998C2semidirect
18. #72257991C2semidirect
19. D3×#23906C2semidirect
20. D3×#60399C2semidirect
21. D3×#23897C2semidirect
22. D3×#60388C2semidirect
23. D3×#62832C2semidirect
24. D3×#23872C2semidirect
25. D3×#23882C2semidirect
26. D3×H(7,𝔽2)C22semidirect
27. D3×#3585C22semidirect
28. #11704069C22semidirect
29. #11704068C22semidirect
30. #11704067C22semidirect
31. #11704067C22semidirect
32. #11704066C22semidirect
33. #11704066C22semidirect
34. #11704065C22semidirect
35. #11704065C22semidirect
36. #11704065C22semidirect
37. D3×#3508C22semidirect
38. D3×#3508C22semidirect
40. D3×#3498C22semidirect
42. D3×#3484C22semidirect
43. D3×#3484C22semidirect
44. D3×#3484C22semidirect
45. D3×#3444C22semidirect
46. C22×D3×#127C22semidirect
47. #11661941C22semidirect
48. #11661941C22semidirect
49. #11661940C22semidirect
50. #11661938C22semidirect
51. #11661937C22semidirect
52. #11661937C22semidirect
53. #11661936C22semidirect
54. D3×#3027C22semidirect
55. D3×#3025C22semidirect
56. #11661870C22semidirect
57. #11661869C22semidirect
58. #11661868C22semidirect
59. #11661867C22semidirect
60. #11661866C22semidirect
61. #11661865C22semidirect
62. #11661864C22semidirect
63. #11661863C22semidirect
64. #11661862C22semidirect
65. D3×#3021C22semidirect
66. D3×#3019C22semidirect
67. D3×#3019C22semidirect
68. D3×#3018C22semidirect
69. C2×D3×#453C22semidirect
70. D3×#3003C22semidirect
71. D3×#2901C22semidirect
72. D3×#2888C22semidirect
73. D3×#2883C22semidirect
74. D3×#2883C22semidirect
75. #10827781C22semidirect
76. #10827780C22semidirect
77. #10827779C22semidirect
78. #10827778C22semidirect
79. #10827777C22semidirect
80. #10827776C22semidirect
81. #10827775C22semidirect
82. #10827774C22semidirect
83. #10827773C22semidirect
84. #10827772C22semidirect
85. #10827771C22semidirect
86. #10827737C22semidirect
87. #10827736C22semidirect
88. #10827735C22semidirect
89. #10827734C22semidirect
90. #10827733C22semidirect
91. #10827732C22semidirect
92. #10827731C22semidirect
93. #10827730C22semidirect
94. #10827729C22semidirect
95. #10827728C22semidirect
96. #10827727C22semidirect
97. #10827693C22semidirect
98. #10827692C22semidirect
99. #10827691C22semidirect
100. #10827690C22semidirect
101. #10827689C22semidirect
102. #10827688C22semidirect
103. #10827687C22semidirect
104. #10827686C22semidirect
105. #10827685C22semidirect
106. #10827684C22semidirect
107. #10827683C22semidirect
108. #10826824C22semidirect
109. #10826823C22semidirect
110. #10826822C22semidirect
111. #10826821C22semidirect
112. #10826820C22semidirect
113. #10826819C22semidirect
114. #10826818C22semidirect
115. #10826817C22semidirect
116. #10826749C22semidirect
117. #10826748C22semidirect
118. #10826748C22semidirect
119. #10826747C22semidirect
120. #10826747C22semidirect
121. #10826746C22semidirect
122. #10826746C22semidirect
123. #10826745C22semidirect
124. #10826602C22semidirect
125. #10826601C22semidirect
126. #10826600C22semidirect
127. #10826599C22semidirect
128. #10826598C22semidirect
129. #10826597C22semidirect
130. #10826596C22semidirect
131. #10826595C22semidirect
132. #10826594C22semidirect
133. #10826593C22semidirect
134. #10826592C22semidirect
135. #10826484C22semidirect
136. #10826483C22semidirect
137. #10826482C22semidirect
138. #10826481C22semidirect
139. #10826480C22semidirect
140. #10826479C22semidirect
141. #10826478C22semidirect
142. #10826477C22semidirect
143. #10826476C22semidirect
144. #10826475C22semidirect
145. #10826474C22semidirect
146. D3×#2031C22semidirect
147. D3×#2010C22semidirect
148. D3×#2008C22semidirect
149. D3×#2002C22semidirect
150. #10804378C22semidirect
151. #10804377C22semidirect
152. #10804376C22semidirect
153. #10804375C22semidirect
154. #10804374C22semidirect
155. #10804373C22semidirect
156. #10804372C22semidirect
157. #10804371C22semidirect
158. #10804370C22semidirect
159. #10804351C22semidirect
160. #10804350C22semidirect
161. #10804349C22semidirect
162. #10804348C22semidirect
163. #10804347C22semidirect
164. #10804346C22semidirect
165. D3×#1914C22semidirect
166. D3×#1911C22semidirect
167. D3×#1911C22semidirect
168. D3×#1910C22semidirect
169. D3×#1906C22semidirect
170. D3×#1904C22semidirect
171. D3×#1896C22semidirect
172. D3×#1891C22semidirect
173. D3×#1887C22semidirect
174. D3×#1884C22semidirect
175. D3×#1829C22semidirect
176. D3×#1827C22semidirect
177. D3×#1795C22semidirect
178. D3×#1783C22semidirect
179. C3×#62832C22semidirect
180. C3×#60399C22semidirect
181. C3×#60388C22semidirect
182. C3×#23998C22semidirect
183. C3×#23994C22semidirect
184. C3×#23990C22semidirect
185. C3×#23906C22semidirect
186. C3×#23897C22semidirect
187. C3×#23882C22semidirect
188. C3×#23872C22semidirect
189. C3×#21782C22semidirect
190. C3×#21778C22semidirect
191. #6499855D3direct (N × H)
192. C3×H(7,𝔽2)C23semidirect
193. #87574C23semidirect
195. #87568C23semidirect
196. #87568C23semidirect
200. C2×D3×H(5,𝔽2)C23semidirect
202. C23×D3×D4C23semidirect
203. C3×#3585C23semidirect
204. C3×#3508C23semidirect
205. C3×#3508C23semidirect
207. C3×#3498C23semidirect
209. C3×#3484C23semidirect
210. C3×#3484C23semidirect
211. C3×#3484C23semidirect
212. C3×#3444C23semidirect
213. C22×C3×#127C23semidirect
214. #87298C23semidirect
216. #87284C23semidirect
217. #87284C23semidirect
218. #87284C23semidirect
221. #87282C23semidirect
222. #87282C23semidirect
223. #87277C23semidirect
225. #87239C23semidirect
226. #87239C23semidirect
227. #87239C23semidirect
228. C22×#940C23semidirect
229. C22×#940C23semidirect
230. #87200C23semidirect
232. #87192C23semidirect
234. #87167C23semidirect
237. #86330C23semidirect
238. #86330C23semidirect
239. #86330C23semidirect
240. #86330C23semidirect
241. D3×#535D4semidirect
242. D3×#535D4semidirect
247. D3×#535C23semidirect
248. #86319C23semidirect
249. #86319C23semidirect
250. #86319C23semidirect
251. #86319C23semidirect
252. #86316D4semidirect
253. #86316D4semidirect
256. #86316C23semidirect
257. #86316C23semidirect
260. D3×#533C23semidirect
261. #86261C23semidirect
262. #86261C23semidirect
263. #86257C23semidirect
264. #86242D4semidirect
266. #86242C23semidirect
267. D3×#532D4semidirect
269. #86219C23semidirect
270. #86195D4semidirect
272. #86195C23semidirect
273. C2×D3×#127D4semidirect
275. C2×D3×#127C23semidirect
276. C2×D3×#127C23semidirect
277. C2×D3×#127C23semidirect
278. #86190C23semidirect
279. #86190C23semidirect
281. #86039C23semidirect
282. #86039C23semidirect
283. #86039C23semidirect
284. #86039C23semidirect
287. D3×#525C23semidirect
288. #86018C23semidirect
289. #86018C23semidirect
293. #85867C23semidirect
294. #85867C23semidirect
295. #85867C23semidirect
298. D3×#518C23semidirect
299. D3×#518C23semidirect
300. #85862C23semidirect
301. #85862C23semidirect
302. #85862C23semidirect
303. #85862C23semidirect
304. #85848C23semidirect
305. #85848C23semidirect
307. #85846C23semidirect
308. #85836C23semidirect
309. #85836C23semidirect
311. C4×D3×#41C23semidirect
312. #85680C23semidirect
313. C22×#874C23semidirect
314. C22×C42×D3C23semidirect
315. C3×#3027C23semidirect
316. C3×#3025C23semidirect
317. C3×#3021C23semidirect
318. C3×#3019C23semidirect
319. C3×#3019C23semidirect
320. C3×#3018C23semidirect
321. C2×C3×#453C23semidirect
322. C3×#3003C23semidirect
323. C3×#2901C23semidirect
324. C3×#2888C23semidirect
325. C3×#2883C23semidirect
326. C3×#2883C23semidirect
327. #84126C23semidirect
328. #84125C23semidirect
329. #84122C23semidirect
330. #84121C23semidirect
331. #84120C23semidirect
332. #84107C23semidirect
333. #84107C23semidirect
334. #84104C23semidirect
335. #84104C23semidirect
336. C2×#5241C23semidirect
337. #84100C23semidirect
338. #84038C23semidirect
339. #84005C23semidirect
340. #84005C23semidirect
341. #84004C23semidirect
342. #83957C23semidirect
343. C2×#5198C23semidirect
344. #83944C23semidirect
345. #83817C23semidirect
346. #83813C23semidirect
347. #83396C23semidirect
348. #83396C23semidirect
349. #83395C23semidirect
350. #83394C23semidirect
351. #83394C23semidirect
352. #83322C23semidirect
353. C2×#5077C23semidirect
354. #82936C23semidirect
355. #82936C23semidirect
356. #82927C23semidirect
357. #82546C23semidirect
358. #82546C23semidirect
359. #82546C23semidirect
360. #82536C23semidirect
361. #78994C23semidirect
362. #78993C23semidirect
363. #78993C23semidirect
364. #78992C23semidirect
366. D3×#421C23semidirect
367. #78986C23semidirect
368. C2×#4822C23semidirect
369. #78983C23semidirect
371. #78926C23semidirect
372. D3×#418C23semidirect
373. #78717C23semidirect
374. #78716C23semidirect
375. #78714C23semidirect
377. #78700C23semidirect
378. #78700C23semidirect
379. C2×#4747C23semidirect
380. #78697C23semidirect
382. C2×D3×#100C23semidirect
383. #78694C23semidirect
384. #78694C23semidirect
387. #78691C23semidirect
388. #78691C23semidirect
389. #78690C23semidirect
390. #78690C23semidirect
391. #78637C23semidirect
392. D3×#407C23semidirect
393. C3×#2031C23semidirect
394. C3×#2010C23semidirect
395. C3×#2008C23semidirect
396. C3×#2002C23semidirect
397. C3×#1914C23semidirect
398. C3×#1911C23semidirect
399. C3×#1911C23semidirect
400. C3×#1910C23semidirect
401. C3×#1906C23semidirect
402. C3×#1904C23semidirect
403. C3×#1896C23semidirect
404. C3×#1891C23semidirect
405. C3×#1887C23semidirect
406. C3×#1884C23semidirect
407. C3×#1829C23semidirect
408. C3×#1827C23semidirect
409. C3×#1795C23semidirect
410. C3×#1783C23semidirect
411. #72141C23semidirect
412. #72129C23semidirect
413. #72119C23semidirect
414. #72118C23semidirect
415. #72114C23semidirect
416. #72099C23semidirect
417. #72094C23semidirect
418. #72089C23semidirect
419. #72030C23semidirect
420. #72029C23semidirect
421. #72025C23semidirect
422. #72021C23semidirect
423. #71858C23semidirect
424. #71856C23semidirect
425. #71855C23semidirect
426. #71854C23semidirect
427. #71853C23semidirect
428. #71853C23semidirect
429. #71842C23semidirect
430. #71817C23semidirect
431. #71769C23semidirect
432. #71763C23semidirect
433. #71715C23semidirect
434. #71715C23semidirect
435. #71714C23semidirect
436. #71711C23semidirect
437. #71652C23semidirect
438. #71652C23semidirect
439. #71651C23semidirect
440. #71650C23semidirect
441. #71648C23semidirect
442. #71645C23semidirect
443. #71644C23semidirect
444. #71532C23semidirect
445. #70417C23semidirect
446. #70414C23semidirect
447. #70409C23semidirect
448. #70408C23semidirect
449. #70408C23semidirect
450. #70407C23semidirect
451. #70406C23semidirect
452. #70406C23semidirect
453. #70395C23semidirect
454. #70394C23semidirect
455. #70391C23semidirect
456. #70385C23semidirect
457. #70382C23semidirect
458. #70368C23semidirect
459. #70331C23semidirect
460. #70330C23semidirect
461. #70327C23semidirect
462. #70324C23semidirect
463. #70323C23semidirect
464. #70314C23semidirect
465. #70139C23semidirect
466. #70137C23semidirect
467. #70136C23semidirect
468. #70131C23semidirect
469. #70089C23semidirect
470. #70082C23semidirect
471. #70079C23semidirect
472. #70079C23semidirect
473. #70071C23semidirect
474. #70071C23semidirect
475. #70070C23semidirect
476. #70067C23semidirect
477. #70055C23semidirect
478. #70050C23semidirect
479. #70049C23semidirect
480. #70048C23semidirect
481. #70047C23semidirect
482. #70045C23semidirect
483. #70039C23semidirect
484. #70038C23semidirect
485. #69993C23semidirect
486. #69992C23semidirect
487. #69988C23semidirect
488. #69965C23semidirect
489. #69042C23semidirect
490. #69040C23semidirect
491. #69039C23semidirect
492. #69036C23semidirect
493. #69028C23semidirect
494. #69027C23semidirect
495. #69026C23semidirect
496. D3×#344C23semidirect
497. #68779C23semidirect
498. #68778C23semidirect
499. #68777C23semidirect
500. #68761C23semidirect
501. #68760C23semidirect
502. #68756C23semidirect
503. D3×#339C23semidirect
504. #68737C23semidirect
505. #68714C23semidirect
506. #68713C23semidirect
507. #68711C23semidirect
508. #68705C23semidirect
509. #68705C23semidirect
510. #68704C23semidirect
511. #68703C23semidirect
512. D3×H(3,ℤ/4)C23semidirect
513. #62832C2×D3semidirect
514. #60399C2×D3semidirect
515. #60388C2×D3semidirect
516. #23998C2×D3semidirect
517. #23994C2×D3semidirect
518. #23990C2×D3semidirect
519. #23906C2×D3semidirect
520. #23897C2×D3semidirect
521. #23882C2×D3semidirect
522. #23872C2×D3semidirect
523. #21782C2×D3semidirect
524. #21778C2×D3semidirect
530. C2×C3×H(5,𝔽2)C24semidirect
532. C23×C3×D4C24semidirect
537. C2×#1009C2×D4semidirect
542. C2×#1009C24semidirect
544. C2×D3×#41C2×D4semidirect
550. C2×#1004C2×D4semidirect
554. C2×#1004C24semidirect
559. C22×D3×D4C2×D4semidirect
565. C22×D3×D4C24semidirect
567. C23×D12C24semidirect
572. C3×#535C2×D4semidirect
573. C3×#535C2×D4semidirect
578. C3×#535C24semidirect
580. C3×#533C24semidirect
581. C3×#532C2×D4semidirect
583. C2×C3×#127C2×D4semidirect
585. C2×C3×#127C24semidirect
588. C3×#525C24semidirect
592. C3×#518C24semidirect
593. C3×#518C24semidirect
595. C3×C4×#41C24semidirect
596. C22×C3×C42C24semidirect
598. #5832C2×D4semidirect
599. #5832C2×D4semidirect
602. #5830C2×D4semidirect
603. #5830C2×D4semidirect
608. #5830C24semidirect
611. #5828C24semidirect
613. Dic3×#41C24semidirect
618. #5805C2×D4semidirect
619. #5805C2×D4semidirect
624. #5805C24semidirect
627. C2×#940C2×D4semidirect
628. C2×#940C2×D4semidirect
631. C2×#940C24semidirect
632. C2×#940C24semidirect
636. #5798C24semidirect
637. #5798C24semidirect
641. #5791C24semidirect
642. C22×C4×Dic3C24semidirect
647. #5725C2×D4semidirect
648. #5725C2×D4semidirect
649. D3×C4⋊Q8C2×D4semidirect
650. #5716C2×D4semidirect
651. #5716C2×D4semidirect
653. #5715C2×D4semidirect
654. #5715C2×D4semidirect
655. #5715C2×D4semidirect
656. #5715C2×D4semidirect
657. #5715C2×D4semidirect
663. D3×#127C2×D4semidirect
664. D3×#127C2×D4semidirect
665. D3×#127C2×D4semidirect
666. D3×#127C2×D4semidirect
667. D3×#127C2×D4semidirect
668. D3×#127C2×D4semidirect
670. #5674C2×D4semidirect
671. #5674C2×D4semidirect
672. #5674C2×D4semidirect
673. #5674C2×D4semidirect
674. #5674C2×D4semidirect
676. D3×#124C2×D4semidirect
677. D3×#124C2×D4semidirect
678. D3×#124C2×D4semidirect
679. #5668C2×D4semidirect
680. #5668C2×D4semidirect
681. #5668C2×D4semidirect
682. #5668C2×D4semidirect
693. #5525C2×D4semidirect
694. #5525C2×D4semidirect
699. #5525C24semidirect
702. #5524C24semidirect
703. #5522C2×D4semidirect
705. #5522C24semidirect
708. #5521C24semidirect
709. #5521C24semidirect
710. #5521C24semidirect
711. D3×#117C2×D4semidirect
715. #5517C24semidirect
716. #5517C24semidirect
721. #5477C2×D4semidirect
723. C2×#874C2×D4semidirect
725. C2×#874C24semidirect
726. C4×#235C2×D4semidirect
728. C4×#235C24semidirect
729. C2×C42×D3C2×D4semidirect
731. C2×C42×D3C24semidirect
732. #5470C24semidirect
734. C3×#421C24semidirect
736. C3×#418C24semidirect
739. C2×C3×#100C24semidirect
742. C3×#407C24semidirect
747. #5236C24semidirect
750. C2×#833C24semidirect
751. #5215C24semidirect
752. #5207C24semidirect
754. #5139C24semidirect
757. #5131C24semidirect
759. C2×#823C24semidirect
760. #5126C24semidirect
765. #5005C24semidirect
766. #5001C24semidirect
768. C3×#344C24semidirect
769. C3×#339C24semidirect
770. C3×H(3,ℤ/4)C24semidirect
771. #4559C24semidirect
772. #4557C24semidirect
773. #4556C24semidirect
774. #4555C24semidirect
775. #4533C24semidirect
776. #4532C24semidirect
777. #4531C24semidirect
778. #4531C24semidirect
779. #4523C24semidirect
780. H(7,𝔽2)C22×D3semidirect
781. #3585C22×D3semidirect
782. #3508C22×D3semidirect
783. #3508C22×D3semidirect
785. #3498C22×D3semidirect
787. #3484C22×D3semidirect
788. #3484C22×D3semidirect
789. #3484C22×D3semidirect
790. #3444C22×D3semidirect
791. C22×#127C22×D3semidirect
792. #3027C22×D3semidirect
793. #3025C22×D3semidirect
794. #3021C22×D3semidirect
795. #3019C22×D3semidirect
796. #3019C22×D3semidirect
797. #3018C22×D3semidirect
798. C2×#453C22×D3semidirect
799. #3003C22×D3semidirect
800. #2901C22×D3semidirect
801. #2888C22×D3semidirect
802. #2883C22×D3semidirect
803. #2883C22×D3semidirect
804. #2031C22×D3semidirect
805. #2010C22×D3semidirect
806. #2008C22×D3semidirect
807. #2002C22×D3semidirect
808. #1914C22×D3semidirect
809. #1911C22×D3semidirect
810. #1911C22×D3semidirect
811. #1910C22×D3semidirect
812. #1906C22×D3semidirect
813. #1904C22×D3semidirect
814. #1896C22×D3semidirect
815. #1891C22×D3semidirect
816. #1887C22×D3semidirect
817. #1884C22×D3semidirect
818. #1829C22×D3semidirect
819. #1827C22×D3semidirect
820. #1795C22×D3semidirect
821. #1783C22×D3semidirect
831. C2×C3×#41C22×D4semidirect
838. C22×C3×D4C22×D4semidirect
854. C2×#239C22×D4semidirect
855. C2×#239H(5,𝔽2)semidirect
858. C2×D3×Q8H(5,𝔽2)semidirect
864. C2×#237C22×D4semidirect
865. C2×#237H(5,𝔽2)semidirect
879. C2×D3×D4C22×D4semidirect
880. C2×D3×D4C22×D4semidirect
881. C2×D3×D4H(5,𝔽2)semidirect
885. C2×#235C22×D4semidirect
892. C22×D12C22×D4semidirect
903. C3×C4⋊Q8C22×D4semidirect
907. C3×#127C22×D4semidirect
908. C3×#127C22×D4semidirect
910. C3×#124C22×D4semidirect
911. C3×#124C22×D4semidirect
912. C3×#124C22×D4semidirect
916. C3×#117C22×D4semidirect
921. C2×C3×C42C22×D4semidirect
927. #947C22×D4semidirect
928. #947C22×D4semidirect
929. #947C22×D4semidirect
930. #944C22×D4semidirect
931. #944C22×D4semidirect
938. #940C22×D4semidirect
939. #940C22×D4semidirect
940. #940C22×D4semidirect
941. #940C22×D4semidirect
945. #936C22×D4semidirect
946. #936C22×D4semidirect
947. #936C22×D4semidirect
950. #926C22×D4semidirect
954. C2×C4×Dic3C22×D4semidirect
964. #875C22×D4semidirect
965. #875C22×D4semidirect
966. #875C22×D4semidirect
970. #874C22×D4semidirect
971. #874C22×D4semidirect
973. #872C22×D4semidirect
974. #872C22×D4semidirect
980. C42×D3C22×D4semidirect
981. C42×D3C22×D4semidirect
982. #869C22×D4semidirect
987. C2×H(5,𝔽2)C23×D3semidirect
989. C23×D4C23×D3semidirect
993. #535D3×D4semidirect
994. #535D3×D4semidirect
999. #535C23×D3semidirect
1001. #533C23×D3semidirect
1002. #532D3×D4semidirect
1004. C2×#127D3×D4semidirect
1006. C2×#127C23×D3semidirect
1009. #525C23×D3semidirect
1013. #518C23×D3semidirect
1014. #518C23×D3semidirect
1016. C4×#41C23×D3semidirect
1017. C22×C42C23×D3semidirect
1019. #421C23×D3semidirect
1021. #418C23×D3semidirect
1024. C2×#100C23×D3semidirect
1027. #407C23×D3semidirect
1028. #344C23×D3semidirect
1029. #339C23×D3semidirect
1030. H(3,ℤ/4)C23×D3semidirect
1046. C2×C3×Q8C2×H(5,𝔽2)semidirect
1053. C2×C3×D4C2×H(5,𝔽2)semidirect
1074. C2×D12C2×H(5,𝔽2)semidirect
1086. C2×Dic6C2×H(5,𝔽2)semidirect
1097. C2×#41C2×D3×D4semidirect
1104. C22×D4C2×D3×D4semidirect
1110. C4⋊Q8C2×D3×D4semidirect
1114. #127C2×D3×D4semidirect
1115. #127C2×D3×D4semidirect
1117. #124C2×D3×D4semidirect
1118. #124C2×D3×D4semidirect
1119. #124C2×D3×D4semidirect
1123. #117C2×D3×D4semidirect
1128. C2×C42C2×D3×D4semidirect
1154. C2×Q8D3×H(5,𝔽2)semidirect
1161. C2×D4D3×H(5,𝔽2)semidirect
1184. D3#6499855direct (N × H)
1188. C3C2×#6499855semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#722720062
#722720012
#722719992
D3×#217782
#722719962
#722719922
C3×#64998552
#722719882
#722719852
D3×#239902
#722580882
D3×#239942
#722580482
D3×#217822
#722580142
#722580052
D3×#239982
#722579912
D3×#239062
D3×#603992
D3×#238972
C2×#64998553
D3×#603882
D3×#628322
D3×#238722
D3×#238822