Finite Group Databasebeta

← #11900187

Subgroups — #11900187

Order 1152.

3475 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64307C211yesmaximal, characteristic
2#10595993C211yesmaximal, characteristic, complemented
3C3×#5523C211yesmaximal, characteristic, complemented
4C3×#5521C211yesmaximal, characteristic, complemented
5#10594990C211yesmaximal, characteristic, complemented
6#10594958C211yesmaximal, characteristic, complemented
7C2×#63898C211yesmaximal, characteristic, complemented
8#10594604C212yesmaximal, complemented
9D3×#893C212yesmaximal, complemented
10#10594359C212yesmaximal, complemented
11#10594358C212yesmaximal, complemented
12#10594254C214yesmaximal, complemented
13D3×#67⋊C4C214yesmaximal, complemented
14#10593996C212yesmaximal, complemented
15C4×#3802C212yesmaximal, complemented
16#10593889C212yesmaximal, complemented
17C4×#3796C212yesmaximal, complemented
18#85886—31nomaximal
19#85857—31nomaximal
20C2×#3828C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic
23C2×D3×#67C2214yes—
24C22×D3×Dic3C2212yescomplemented
25#64307C4116yescomplemented
26C2×#3802C2212yes—
27C2×D3×D12C2212yes—
28C2×C4×D32C2214yescomplemented
29C2×#3796C2212yes—
30C2×#3795C2212yes—
31C32×#117C2211yescharacteristic, complemented
32C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
33#64102C2211yescharacteristic, complemented
34#64102C2211yescharacteristic, complemented
35#64096C2211yescharacteristic, complemented
36#64096C2211yescharacteristic, complemented
37#64090C2212yescomplemented
38#64090C2212yescomplemented
39#64081C2212yescomplemented
40C42×C3⋊D3C2212yescomplemented
41C3×#926C2211yescharacteristic, complemented
42C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
43C3×#893C2212yescomplemented
44C3×#893C2212yescomplemented
45C3×#892C2212yescomplemented
46C3×D3×C4⋊C4C2212yescomplemented
47C3×#67⋊C4C2214yescomplemented
48C3×D3×C22⋊C4C2214yescomplemented
49C3×C4×D12C2212yescomplemented
50C3×C4×D12C2212yescomplemented
51C3×C4×D12C2212yescomplemented
52C3×C4×Dic6C2212yescomplemented
53#67⋊Dic3C2212yescomplemented
54#67⋊Dic3C2212yescomplemented
55C2×(C2×D3)⋊Dic3C2212yescomplemented
56#63952C2214yescomplemented
57#63921C2214yescomplemented
58D3×(C2×D3)⋊C4C2214yescomplemented
59D3×(C2×D3)⋊C4C2214yescomplemented
60#63904C2214yescomplemented
61C4×#626C2214yescomplemented
62#63902C2214yescomplemented
63C4×#625C2214yescomplemented
64#63900C2212yescomplemented
65#63898C2212yescomplemented
66#63898C2212yescomplemented
67#63898C2212yescomplemented
68#63898C2212yescomplemented
69#63898C2211yescharacteristic, complemented
70#63898C2211yescharacteristic, complemented
71#63894C2212yescomplemented
72#63881C2214yescomplemented
73#63880C2214yescomplemented
74#63879C2214yescomplemented
75#63879C2214yescomplemented
76#63878C2214yescomplemented
77#63877C2214yescomplemented
78D3×Dic3⋊C4C2214yescomplemented
79C4×D3×Dic3C2212yescomplemented
80C4×D3×Dic3C2214yescomplemented
81#63855C2212yescomplemented
82#63849C2212yescomplemented
83#63844C2212yescomplemented
84#63843C2211yescharacteristic, complemented
85#63843C2211yescharacteristic, complemented
86C2×#1009—31no—
87C2×#1004—31no—
88C3×#520—31no—
89C3×#518—31no—
90Dic3×#41—31no—
91C2×D4×Dic3—31no—
92#5574—32no—
93C4×#239—32no—
94#5546—32no—
95#5546—32no—
96#5545—32no—
97#5545—34no—
98#5545—32no—
99#5545—32no—
100C4×D3×D4—32no—
101C4×D3×D4—34no—
102C4×D3×D4—32no—
103C4×D3×D4—32no—
104C4×#237—32no—
105C4×#237—32no—
106#5523—31no—
107#5523D311yescharacteristic, complemented
108#5522—31no—
109#5522—31no—
110#5522—31no—
111#5522—32no—
112#5522—61no—
113#5521—32no—
114#5521D311yescharacteristic, complemented
115#5504—31no—
116#5504—32no—
117C2×#893—31no—
118C2×#893—32no—
119#5486—34no—
120C2×#67⋊C4—34no—
121C23×C3×D3C2312yes—
122C22×D32C2314yes—
123C22×C32×C4C2311yescharacteristic
124C2×#638C2312yes—
125C22×C3⋊Dic3C2311yescharacteristic
126C22×C3⋊Dic3C2311yescharacteristic
127#3828C2×C418yescomplemented
128C2×C4⋊(C3⋊D3)C2311yescharacteristic
129C2×C4×C3⋊D3C2312yes—
130C2×C4×C3⋊D3C2312yes—
131C2×C4×C3⋊D3C2312yes—
132C2×#634C2311yescharacteristic
133C2×C3×#67C2312yes—
134C22×C3×Dic3C2312yes—
135C3×#235C2×C418yescomplemented
136C2×C3×D12C2×C418yescomplemented
137C2×C3×D12C2312yes—
138C2×C3×D12C2312yes—
139C2×C3×D12C2311yescharacteristic
140C2×C3×C4×D3C2314yes—
141C2×C3×C4×D3C2314yes—
142C2×C3×C4×D3C2314yes—
143C2×C3×C4×D3C2312yes—
144C2×C3×Dic6C2311yescharacteristic
145D3×#67C2×C4132yescomplemented
146C2×#626C2314yes—
147C2×#625C2314yes—
148C2×#624C2314yes—
149C2×D3×Dic3—44no—
150C2×D3×Dic3C2312yes—
151C2×D3×Dic3C2314yes—
152C2×D3×Dic3C2314yes—
153C2×D3×Dic3C2312yes—
154C2×D3×Dic3C2314yes—
155#3802C2×C4116yescomplemented
156D3×D12C2×C4116yescomplemented
157C4×D32—48no—
158#3796C2×C4116yescomplemented
159#3795C2×C4116yescomplemented
160C32×C4⋊C4C2311yescharacteristic
161C32×C4⋊C4C2311yescharacteristic
162C32×C22⋊C4C2312yes—
163C32×C42C2312yes—
164#3752C2312yes—
165#3752C2312yes—
166#3750C2312yes—
167#3750C2312yes—
168C4×C3⋊Dic3C2311yescharacteristic
169C4×C3⋊Dic3C2312yes—
170C4×C3⋊Dic3C2312yes—
171C4×C3⋊Dic3C2311yescharacteristic
172C4×C3⋊Dic3C2311yescharacteristic
173C4×C3⋊Dic3C2311yescharacteristic
174C3×#217C2312yes—
175C3×(C2×D3)⋊C4C2314yes—
176C3×(C2×D3)⋊C4C2314yes—
177C3×(C2×D3)⋊C4C2314yes—
178C3×C4⋊Dic3C2312yes—
179C3×C4⋊Dic3C2312yes—
180C3×C4⋊Dic3C2311yescharacteristic
181C3×C4⋊Dic3C2311yescharacteristic
182C3×Dic3⋊C4C2314yes—
183C3×C4×Dic3C2314yes—
184C3×C4×Dic3C2312yes—
185#3724C2314yes—
186Dic3⋊Dic3C2312yes—
187Dic3⋊Dic3C2312yes—
188#3722C2314yes—
189(C2×D3)⋊Dic3C2312yes—
190(C2×D3)⋊Dic3C2312yes—
191(C2×D3)⋊Dic3C2314yes—
192(C2×D3)⋊Dic3C2314yes—
193Dic32C2312yes—
194Dic32C2312yes—
195Dic32C2314yes—
196C4×H(5,𝔽2)—91noSylow
197C2×C3×#41—31no—
198C22×C3×D4—31no—
199C22×#67—34no—
200C23×Dic3—32no—
201#1009—316no—
202C2×#239—32no—
203#1004—316no—
204C2×#237—32no—
205C2×#237—32no—
206C2×D3×D4—34no—
207C2×D3×D4—32no—
208C2×D3×D4—32no—
209C2×D3×D4—32no—
210C2×#235—31no—
211C2×#235—31no—
212C2×#235—32no—
213C2×#235—61no—
214C2×#235C2×D311yescharacteristic
215C22×D12—32no—
216C22×D12C2×D311yescharacteristic
217C22×C4×D3—32no—
218C22×C4×D3—34no—
219C22×C4×D3—34no—
220C3×C4×Q8—32no—
221C3×C4×D4—32no—
222C3×C4×D4—32no—
223C3×C4×D4—34no—
224C3×C4×D4—32no—
225C3×C4×D4—32no—
226C3×C4×D4—32no—
227C3×#117—21no—
228C3×#117—31no—
229C3×#117—32no—
230C3×#117C2×D311yescharacteristic, complemented
231C3×#117C2×D311yescharacteristic, complemented
232C2×C3×C4⋊C4—31no—
233C2×C3×C4⋊C4—32no—
234C2×C3×C22⋊C4—34no—
235C2×#217—32no—
236Q8×Dic3—31no—
237Q8×Dic3—31no—
238D4×Dic3—32no—
239D4×Dic3—32no—
240D4×Dic3—32no—
241D4×Dic3—32no—
242D4×Dic3—32no—
243D4×Dic3—32no—
244D4×Dic3—31no—
245D4×Dic3—31no—
246C4×#67—34no—
247C4×#67—34no—
248C4×#67—34no—
249C4×#67—34no—
250C4×#67—34no—
251C4×#67—34no—
252C4×#67—34no—
253C2×(C2×D3)⋊C4—32no—
254C2×(C2×D3)⋊C4—34no—
255C2×(C2×D3)⋊C4—34no—
256#926—32no—
257#926C2×D311yescharacteristic, complemented
258C2×C4⋊Dic3C2×D311yescharacteristic, complemented
259C2×Dic3⋊C4—34no—
260C2×C4×Dic3—31no—
261C2×C4×Dic3—31no—
262C2×C4×Dic3—34no—
263C2×C4×Dic3—32no—
264C2×C4×Dic3—61no—
265#893—32no—
266#893—32no—
267#893—32no—
268#893—32no—
269#893—31no—
270#893—31no—
271#893—34no—
272#893—31no—
273#893—31no—
274#893—31no—
275#893—31no—
276#893—34no—
277#893—32no—
278#893—61no—
279#893—61no—
280#893C2×D312yescomplemented
281#893C2×D312yescomplemented
282#892—34no—
283#892—32no—
284#892—32no—
285#892C2×D312yescomplemented
286D3×C4⋊C4—34no—
287D3×C4⋊C4—32no—
288D3×C4⋊C4—32no—
289D3×C4⋊C4C2×D312yescomplemented
290#887—31no—
291#887—31no—
292#887—31no—
293#887—31no—
294#887—31no—
295#887—31no—
296#887—32no—
297#887—61no—
298#887—61no—
299#67⋊C4—32no—
300#67⋊C4—32no—
301#67⋊C4—34no—
302#67⋊C4—34no—
303#67⋊C4—34no—
304#67⋊C4—32no—
305#67⋊C4—32no—
306#67⋊C4—32no—
307#67⋊C4—32no—
308#67⋊C4—34no—
309#67⋊C4—34no—
310#67⋊C4—34no—
311#67⋊C4—34no—
312#67⋊C4—62no—
313#67⋊C4—62no—
314#67⋊C4C2×D314yescomplemented
315D3×C22⋊C4—34no—
316D3×C22⋊C4—34no—
317D3×C22⋊C4—34no—
318D3×C22⋊C4—34no—
319D3×C22⋊C4C2×D314yescomplemented
320#877—34no—
321#877—34no—
322C4×D12—34no—
323C4×D12—34no—
324C4×D12—32no—
325C4×D12C2×D312yescomplemented
326C4×D12C2×D312yescomplemented
327C4×D12C2×D312yescomplemented
328#872—32no—
329#872—32no—
330#872—32no—
331#872—34no—
332#872—62no—
333C42×D3—32no—
334C42×D3—34no—
335C42×D3—32no—
336C42×D3—32no—
337C42×D3—62no—
338C4×Dic6—32no—
339C4×Dic6C2×D312yescomplemented
340C23×C32C2411yescharacteristic
341C22×C3⋊D3C2412yes—
342C22×C3×D3—42no—
343C22×C3×D3—42no—
344C22×C3×D3C22×C418yescomplemented
345C22×C3×D3C2412yes—
346C22×C3×D3C2414yes—
347C2×D32—44no—
348C2×D32—44no—
349C2×D32C22×C4116yescomplemented
350C2×C32×C4C22×C414yescomplemented
351C2×C32×C4C2412yes—
352C2×C32×C4C2412yes—
353C2×C32×C4C2411yescharacteristic
354C2×C32×C4C2411yescharacteristic
355#638C22×C418yescomplemented
356C2×C3⋊Dic3—22no—
357C2×C3⋊Dic3—41no—
358C2×C3⋊Dic3C2411yescharacteristic
359C2×C3⋊Dic3C2411yescharacteristic
360C2×C3⋊Dic3C2411yescharacteristic
361C2×C3⋊Dic3C2412yes—
362C2×C3⋊Dic3C2411yescharacteristic
363C4⋊(C3⋊D3)C22×C414yescomplemented
364C4×C3⋊D3—24no—
365C4×C3⋊D3—42no—
366C4×C3⋊D3C22×C418yescomplemented
367#634C22×C414yescomplemented
368C3×#67C22×C418yescomplemented
369C2×C3×Dic3—42no—
370C2×C3×Dic3C2412yes—
371C2×C3×Dic3C2414yes—
372C2×C3×Dic3C2412yes—
373C2×C3×Dic3C2412yes—
374C3×D12C22×C418yescomplemented
375C3×D12C22×C418yescomplemented
376C3×D12C22×C414yescomplemented
377C3×C4×D3—44no—
378C3×C4×D3—44no—
379C3×C4×D3—44no—
380C3×C4×D3C22×C418yescomplemented
381C3×Dic6C22×C414yescomplemented
382#626C22×C4116yescomplemented
383#625C22×C4116yescomplemented
384#624—44no—
385D3×Dic3—24no—
386D3×Dic3—28no—
387D3×Dic3—44no—
388D3×Dic3—42no—
389D3×Dic3C22×C4116yescomplemented
390C2×H(5,𝔽2)—91no—
391#520—31no—
392#520—91no—
393#520—92no—
394#520—92no—
395#518—31no—
396#518—94no—
397#518—92no—
398#518—92no—
399C4×#41—92no—
400C4×#41—91no—
401C4×#41—92no—
402C4×#41—91no—
403C2×C4×D4—94no—
404C2×C4×D4—92no—
405C2×C4×D4—91no—
406C2×C4×D4—92no—
407C24×C3—32no—
408C23×D3—34no—
409C23×D3—34no—
410C23×D3C22×D312yes—
411C3×#41—38no—
412C2×C3×Q8—31no—
413C2×C3×D4—32no—
414C2×C3×D4—38no—
415C2×C3×D4—31no—
416C2×C3×D4—32no—
417C2×C3×D4—32no—
418C22×C3×C4—21no—
419C22×C3×C4—32no—
420C22×C3×C4—32no—
421C22×C3×C4—34no—
422C22×C3×C4—34no—
423C22×C3×C4—34no—
424C22×C3×C4C22×D311yescharacteristic
425C22×C3×C4C22×D311yescharacteristic
426C2×#67—32no—
427C2×#67—32no—
428C2×#67—34no—
429C2×#67—34no—
430C2×#67—332no—
431C2×#67—34no—
432C2×#67—62no—
433C2×#67C22×D312yes—
434C22×Dic3—34no—
435C22×Dic3—31no—
436C22×Dic3—31no—
437C22×Dic3—31no—
438C22×Dic3—31no—
439C22×Dic3—32no—
440C22×Dic3—34no—
441C22×Dic3—32no—
442C22×Dic3—34no—
443C22×Dic3—61no—
444C22×Dic3—61no—
445C22×Dic3—124no—
446C22×Dic3C22×D312yes—
447#239—316no—
448#237—316no—
449#237—316no—
450D3×D4—332no—
451D3×D4—316no—
452D3×D4—316no—
453D3×D4—316no—
454#235—38no—
455#235—38no—
456#235—316no—
457#235—68no—
458#235C4×D318yescomplemented
459C2×D12—34no—
460C2×D12—31no—
461C2×D12—31no—
462C2×D12—316no—
463C2×D12—61no—
464C2×D12C4×D318yescomplemented
465C2×D12C22×D312yes—
466C2×D12C22×D311yescharacteristic
467C2×D12C22×D312yes—
468C2×C4×D3—34no—
469C2×C4×D3—32no—
470C2×C4×D3—32no—
471C2×C4×D3—32no—
472C2×C4×D3—34no—
473C2×C4×D3—32no—
474C2×C4×D3—32no—
475C2×C4×D3—32no—
476C2×C4×D3—34no—
477C2×C4×D3—32no—
478C2×C4×D3—32no—
479C2×C4×D3—34no—
480C2×C4×D3—34no—
481C2×C4×D3—62no—
482C2×C4×D3—62no—
483C2×C4×D3—62no—
484C2×C4×D3—128no—
485C2×C4×D3—128no—
486C2×C4×D3—124no—
487C2×C4×D3C22×D314yes—
488C2×C4×D3C22×D314yes—
489C2×C4×D3C22×D314yes—
490C2×C4×D3C22×D312yes—
491C2×Dic6—31no—
492C2×Dic6—31no—
493C2×Dic6—61no—
494C2×Dic6C22×D311yescharacteristic
495C3×C4⋊C4—21no—
496C3×C4⋊C4—21no—
497C3×C4⋊C4—31no—
498C3×C4⋊C4—31no—
499C3×C4⋊C4—32no—
500C3×C4⋊C4—34no—
501C3×C4⋊C4—32no—
502C3×C4⋊C4C22×D311yescharacteristic
503C3×C4⋊C4C22×D311yescharacteristic
504C3×C4⋊C4C22×D311yescharacteristic
505C3×C4⋊C4C22×D311yescharacteristic
506C3×C22⋊C4—22no—
507C3×C22⋊C4—32no—
508C3×C22⋊C4—34no—
509C3×C22⋊C4—34no—
510C3×C22⋊C4—34no—
511C3×C22⋊C4C22×D312yes—
512C3×C22⋊C4C22×D312yes—
513C3×C42—22no—
514C3×C42—32no—
515C3×C42—34no—
516C3×C42C22×D312yes—
517C3×C42C22×D312yes—
518#217—34no—
519#217—34no—
520#217—32no—
521#217—32no—
522#217C22×D312yes—
523(C2×D3)⋊C4—32no—
524(C2×D3)⋊C4—32no—
525(C2×D3)⋊C4—34no—
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4—32no—
528(C2×D3)⋊C4—32no—
529(C2×D3)⋊C4—32no—
530(C2×D3)⋊C4—32no—
531(C2×D3)⋊C4—34no—
532(C2×D3)⋊C4—34no—
533(C2×D3)⋊C4—62no—
534(C2×D3)⋊C4—62no—
535(C2×D3)⋊C4C22×D314yes—
536(C2×D3)⋊C4C22×D314yes—
537(C2×D3)⋊C4C22×D314yes—
538C4⋊Dic3—32no—
539C4⋊Dic3—32no—
540C4⋊Dic3C22×D312yes—
541C4⋊Dic3C22×D312yes—
542C4⋊Dic3C22×D311yescharacteristic
543C4⋊Dic3C22×D311yescharacteristic
544Dic3⋊C4—32no—
545Dic3⋊C4—32no—
546Dic3⋊C4—32no—
547Dic3⋊C4—32no—
548Dic3⋊C4—34no—
549Dic3⋊C4—32no—
550Dic3⋊C4—32no—
551Dic3⋊C4—34no—
552Dic3⋊C4—62no—
553Dic3⋊C4—62no—
554Dic3⋊C4C22×D314yes—
555C4×Dic3—32no—
556C4×Dic3—31no—
557C4×Dic3—31no—
558C4×Dic3—31no—
559C4×Dic3—32no—
560C4×Dic3—32no—
561C4×Dic3—32no—
562C4×Dic3—31no—
563C4×Dic3—31no—
564C4×Dic3—31no—
565C4×Dic3—31no—
566C4×Dic3—31no—
567C4×Dic3—34no—
568C4×Dic3—32no—
569C4×Dic3—32no—
570C4×Dic3—32no—
571C4×Dic3—34no—
572C4×Dic3—32no—
573C4×Dic3—61no—
574C4×Dic3—62no—
575C4×Dic3—62no—
576C4×Dic3—61no—
577C4×Dic3—61no—
578C4×Dic3—61no—
579C4×Dic3C22×D314yes—
580C4×Dic3C22×D312yes—
581C22×C32—21no—
582C22×C32—21no—
583C22×C32C23×C412yes—
584C22×C32C2511yescharacteristic
585C2×C3⋊D3—22no—
586C2×C3⋊D3—22no—
587C2×C3⋊D3C23×C414yes—
588C2×C3×D3—24no—
589C2×C3×D3—22no—
590C2×C3×D3—22no—
591C2×C3×D3—24no—
592C2×C3×D3—48no—
593C2×C3×D3C23×C418yes—
594C2×C3×D3C23×C414yes—
595D32—416no—
596C32×C4—22no—
597C32×C4—22no—
598C32×C4C23×C412yes—
599C32×C4C23×C412yes—
600C3⋊Dic3—21no—
601C3⋊Dic3—21no—
602C3⋊Dic3—21no—
603C3⋊Dic3C23×C414yes—
604C3⋊Dic3H(5,𝔽2)12yescomplemented
605C3×Dic3—24no—
606C3×Dic3—22no—
607C3×Dic3—22no—
608C3×Dic3C23×C414yes—
609H(5,𝔽2)—916no—
610C2×#41—31no—
611C2×#41—92no—
612C2×#41—92no—
613C2×#41—91no—
614C22×D4—31no—
615C22×D4—92no—
616C22×D4—92no—
617C22×D4—94no—
618C23×C4—94no—
619C23×C4—92no—
620C4×Q8—32no—
621C4×Q8—92no—
622C4×Q8—91no—
623C4×Q8—91no—
624C4×Q8—91no—
625C4×Q8—91no—
626C4×D4—32no—
627C4×D4—32no—
628C4×D4—34no—
629C4×D4—32no—
630C4×D4—32no—
631C4×D4—32no—
632C4×D4—94no—
633C4×D4—92no—
634C4×D4—94no—
635C4×D4—94no—
636C4×D4—94no—
637C4×D4—94no—
638C4×D4—94no—
639C4×D4—94no—
640C4×D4—92no—
641C4×D4—92no—
642C4×D4—94no—
643C4×D4—92no—
644C4×D4—92no—
645C4×D4—91no—
646C4×D4—92no—
647C4×D4—92no—
648C4×D4—91no—
649C4×D4—94no—
650C4×D4—91no—
651C4×D4—91no—
652C4×D4—92no—
653C4×D4—92no—
654#117—31no—
655#117—32no—
656#117—94no—
657#117—92no—
658#117—94no—
659#117—92no—
660#117—92no—
661#117D3211yescharacteristic, complemented
662C2×C4⋊C4—31no—
663C2×C4⋊C4—32no—
664C2×C4⋊C4—92no—
665C2×C4⋊C4—94no—
666C2×C22⋊C4—34no—
667C2×C22⋊C4—94no—
668C2×C22⋊C4—94no—
669C2×C22⋊C4—94no—
670C2×C22⋊C4—92no—
671C2×C42—92no—
672C2×C42—94no—
673C2×C42—91no—
674C2×C42—92no—
675C23×C3—21no—
676C23×C3—34no—
677C23×C3—32no—
678C23×C3—38no—
679C23×C3—122no—
680C23×C3—122no—
681C23×C3C23×D311yescharacteristic
682C23×C3C23×D311yescharacteristic
683C22×D3—32no—
684C22×D3—32no—
685C22×D3—316no—
686C22×D3—316no—
687C22×D3—42no—
688C22×D3—42no—
689C22×D3—62no—
690C22×D3—124no—
691C22×D3—124no—
692C22×D3—124no—
693C22×D3—124no—
694C22×D3C2×C4×D318yescomplemented
695C22×D3C23×D314yes—
696C22×D3C23×D312yes—
697C3×Q8—34no—
698C3×D4—38no—
699C3×D4—34no—
700C3×D4—38no—
701C3×D4—38no—
702C2×C3×C4—21no—
703C2×C3×C4—21no—
704C2×C3×C4—22no—
705C2×C3×C4—22no—
706C2×C3×C4—24no—
707C2×C3×C4—32no—
708C2×C3×C4—38no—
709C2×C3×C4—32no—
710C2×C3×C4—32no—
711C2×C3×C4—34no—
712C2×C3×C4—124no—
713C2×C3×C4—124no—
714C2×C3×C4—124no—
715C2×C3×C4—122no—
716C2×C3×C4C2×C4×D314yescomplemented
717C2×C3×C4C2×C4×D314yescomplemented
718C2×C3×C4C23×D312yes—
719C2×C3×C4C23×D312yes—
720C2×C3×C4C23×D312yes—
721C2×C3×C4C23×D312yes—
722C2×C3×C4C23×D311yescharacteristic
723C2×C3×C4C23×D311yescharacteristic
724C2×C3×C4C23×D311yescharacteristic
725C2×C3×C4C23×D311yescharacteristic
726#67—38no—
727#67—38no—
728#67—316no—
729#67—316no—
730#67—316no—
731#67—68no—
732#67C2×C4×D318yescomplemented
733C2×Dic3—31no—
734C2×Dic3—31no—
735C2×Dic3—32no—
736C2×Dic3—32no—
737C2×Dic3—316no—
738C2×Dic3—31no—
739C2×Dic3—31no—
740C2×Dic3—31no—
741C2×Dic3—31no—
742C2×Dic3—31no—
743C2×Dic3—31no—
744C2×Dic3—42no—
745C2×Dic3—61no—
746C2×Dic3—61no—
747C2×Dic3—62no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3—64no—
751C2×Dic3—68no—
752C2×Dic3—62no—
753C2×Dic3—62no—
754C2×Dic3—122no—
755C2×Dic3—122no—
756C2×Dic3—124no—
757C2×Dic3—121no—
758C2×Dic3—121no—
759C2×Dic3—122no—
760C2×Dic3C23×D312yes—
761C2×Dic3C23×D312yes—
762C2×Dic3C23×D314yes—
763C2×Dic3C23×D312yes—
764D12—316no—
765D12—34no—
766D12—34no—
767D12—64no—
768D12C2×C4×D318yescomplemented
769D12C2×C4×D318yescomplemented
770D12C2×C4×D314yescomplemented
771C4×D3—316no—
772C4×D3—38no—
773C4×D3—38no—
774C4×D3—44no—
775C4×D3—44no—
776C4×D3—44no—
777C4×D3—68no—
778C4×D3—64no—
779C4×D3—64no—
780C4×D3—68no—
781C4×D3—64no—
782C4×D3—124no—
783C4×D3—124no—
784C4×D3—124no—
785C4×D3—122no—
786C4×D3—122no—
787C4×D3—124no—
788C4×D3—122no—
789C4×D3—124no—
790C4×D3C2×C4×D318yescomplemented
791Dic6—34no—
792Dic6—34no—
793Dic6—64no—
794Dic6C2×C4×D314yescomplemented
795C2×C32—22no—
796C2×C32C24×C411yescharacteristic
797C2×C32C2×H(5,𝔽2)11yescharacteristic
798C2×C32#58511yescharacteristic
799C3⋊D3—24no—
800C3×D3—24no—
801C3×D3—28no—
802C24—32no—
803C24—94no—
804#41—38no—
805#41—916no—
806#41—916no—
807#41—98no—
808C2×Q8—31no—
809C2×Q8—91no—
810C2×D4—32no—
811C2×D4—32no—
812C2×D4—32no—
813C2×D4—31no—
814C2×D4—38no—
815C2×D4—916no—
816C2×D4—94no—
817C2×D4—916no—
818C2×D4—932no—
819C2×D4—94no—
820C2×D4—92no—
821C2×D4—91no—
822C22×C4—32no—
823C22×C4—32no—
824C22×C4—34no—
825C22×C4—34no—
826C22×C4—34no—
827C22×C4—94no—
828C22×C4—94no—
829C22×C4—92no—
830C22×C4—94no—
831C22×C4—92no—
832C22×C4—94no—
833C22×C4—92no—
834C22×C4—91no—
835C22×C4—91no—
836C22×C4—92no—
837C22×C4—92no—
838C22×C4—368no—
839C22×C4—364no—
840C22×C4C2×D3211yescharacteristic
841C4⋊C4—32no—
842C4⋊C4—34no—
843C4⋊C4—32no—
844C4⋊C4—31no—
845C4⋊C4—31no—
846C4⋊C4—94no—
847C4⋊C4—92no—
848C4⋊C4—92no—
849C4⋊C4—92no—
850C4⋊C4—92no—
851C4⋊C4C2×D3211yescharacteristic
852C4⋊C4C2×D3211yescharacteristic
853C22⋊C4—32no—
854C22⋊C4—34no—
855C22⋊C4—34no—
856C22⋊C4—34no—
857C22⋊C4—94no—
858C22⋊C4—92no—
859C22⋊C4—92no—
860C22⋊C4—94no—
861C22⋊C4—94no—
862C22⋊C4—92no—
863C22⋊C4—92no—
864C22⋊C4C2×D3212yes—
865C42—32no—
866C42—34no—
867C42—92no—
868C42—92no—
869C42—94no—
870C42—92no—
871C42—91no—
872C42—91no—
873C42—92no—
874C42—91no—
875C42—91no—
876C42C2×D3212yes—
877C22×C3—21no—
878C22×C3—21no—
879C22×C3—21no—
880C22×C3—21no—
881C22×C3—22no—
882C22×C3—21no—
883C22×C3—38no—
884C22×C3—34no—
885C22×C3—41no—
886C22×C3—41no—
887C22×C3—64no—
888C22×C3—62no—
889C22×C3—62no—
890C22×C3—64no—
891C22×C3—128no—
892C22×C3C22×C4×D312yes—
893C22×C3C22×C4×D312yes—
894C22×C3C24×D311yescharacteristic
895C22×C3C24×D311yescharacteristic
896C2×D3—22no—
897C2×D3—24no—
898C2×D3—24no—
899C2×D3—22no—
900C2×D3—34no—
901C2×D3—34no—
902C2×D3—48no—
903C2×D3—64no—
904C2×D3—62no—
905C2×D3—62no—
906C2×D3—62no—
907C2×D3—62no—
908C2×D3—122no—
909C2×D3—122no—
910C2×D3—1216no—
911C2×D3—1216no—
912C2×D3C22×C4×D318yes—
913C2×D3C22×C4×D314yes—
914C3×C4—22no—
915C3×C4—22no—
916C3×C4—22no—
917C3×C4—22no—
918C3×C4—22no—
919C3×C4—22no—
920C3×C4—34no—
921C3×C4—42no—
922C3×C4—42no—
923C3×C4—64no—
924C3×C4—62no—
925C3×C4—62no—
926C3×C4C22×C4×D312yes—
927C3×C4C22×C4×D312yes—
928C3×C4C22×C4×D312yes—
929C3×C4C22×C4×D312yes—
930Dic3—22no—
931Dic3—24no—
932Dic3—22no—
933Dic3—34no—
934Dic3—34no—
935Dic3—32no—
936Dic3—32no—
937Dic3—64no—
938Dic3—62no—
939Dic3—62no—
940Dic3—61no—
941Dic3—61no—
942Dic3—61no—
943Dic3—61no—
944Dic3—61no—
945Dic3—61no—
946Dic3—121no—
947Dic3—121no—
948Dic3C22×C4×D314yes—
949C32C4×H(5,𝔽2)11yescharacteristic, complemented, Sylow
950C23—32no—
951C23—34no—
952C23—38no—
953C23—916no—
954C23—92no—
955C23—122no—
956C23—122no—
957C23—364no—
958C23—364no—
959C23C22×D3211yescharacteristic
960Q8—34no—
961Q8—94no—
962D4—38no—
963D4—38no—
964D4—38no—
965D4—34no—
966D4—916no—
967D4—916no—
968D4—98no—
969D4—94no—
970C2×C4—32no—
971C2×C4—38no—
972C2×C4—32no—
973C2×C4—32no—
974C2×C4—34no—
975C2×C4—916no—
976C2×C4—91no—
977C2×C4—92no—
978C2×C4—98no—
979C2×C4—91no—
980C2×C4—91no—
981C2×C4—91no—
982C2×C4—124no—
983C2×C4—124no—
984C2×C4—124no—
985C2×C4—122no—
986C2×C4—184no—
987C2×C4—184no—
988C2×C4—188no—
989C2×C4—182no—
990C2×C4—362no—
991C2×C4—364no—
992C2×C4—364no—
993C2×C4—362no—
994C2×C4—361no—
995C2×C4C4×D3214yescomplemented
996C2×C4C22×D3212yes—
997C2×C4C22×D3212yes—
998C2×C4C22×D3211yescharacteristic
999C2×C4C22×D3211yescharacteristic
1000C2×C3—22no—
1001C2×C3—22no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—42no—
1006C2×C3—64no—
1007C2×C3—68no—
1008C2×C3C23×C4×D311yescharacteristic
1009C2×C3C23×C4×D311yescharacteristic
1010C2×C3D3×H(5,𝔽2)11yescharacteristic
1011C2×C3D3×H(5,𝔽2)11yescharacteristic
1012C2×C3#596611yescharacteristic
1013C2×C3#596811yescharacteristic
1014D3—28no—
1015D3—24no—
1016D3—64no—
1017D3—64no—
1018D3—124no—
1019C22—21no—
1020C22—21no—
1021C22—34no—
1022C22—38no—
1023C22—62no—
1024C22—64no—
1025C22—64no—
1026C22—62no—
1027C22—94no—
1028C22—128no—
1029C22—182no—
1030C22—182no—
1031C22—3616no—
1032C22C2×C4×D3212yes—
1033C22C23×D3211yescharacteristic
1034C4—22no—
1035C4—22no—
1036C4—34no—
1037C4—62no—
1038C4—64no—
1039C4—62no—
1040C4—94no—
1041C4—92no—
1042C4—181no—
1043C4—181no—
1044C4—181no—
1045C4C2×C4×D3212yes—
1046C4C2×C4×D3212yes—
1047C3—21no—
1048C3#8585711yescharacteristic, complemented
1049C3#8588611yescharacteristic, complemented
1050C2—22no—
1051C2—68no—
1052C2—64no—
1053C2—184no—
1054C2C22×C4×D3211yescharacteristic
1055C2#1059669211yescharacteristic
1056C2#1059669811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutatorC2×C32C24×C4
FittingC32×#117C22
socle, cosocleC22×C32C25
prime radicalC2×#64307C2
hypercenter#117D32
hypocenterC32C4×H(5,𝔽2)
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10595993C2semidirect
3. C3×#5523C2semidirect
4. C3×#5521C2semidirect
5. #10594990C2semidirect
6. #10594958C2semidirect
7. C2×#63898C2semidirect
8. #10594604C2semidirect
9. D3×#893C2semidirect
10. #10594359C2semidirect
11. #10594358C2semidirect
12. #10594254C2semidirect
13. D3×#67⋊C4C2semidirect
14. #10593996C2semidirect
15. C4×#3802C2semidirect
16. #10593889C2semidirect
17. C4×#3796C2semidirect
24. C22×D3×Dic3C22semidirect
25. #64307C4semidirect
28. C2×C4×D32C22semidirect
31. C32×#117C22semidirect
32. C2×C4×C3⋊Dic3C22semidirect
33. #64102C22semidirect
34. #64102C22semidirect
35. #64096C22semidirect
36. #64096C22semidirect
37. #64090C22semidirect
38. #64090C22semidirect
39. #64081C22semidirect
40. C42×C3⋊D3C22semidirect
41. C3×#926C22semidirect
42. C2×C3×C4⋊Dic3C22semidirect
43. C3×#893C22semidirect
44. C3×#893C22semidirect
45. C3×#892C22semidirect
46. C3×D3×C4⋊C4C22semidirect
47. C3×#67⋊C4C22semidirect
48. C3×D3×C22⋊C4C22semidirect
49. C3×C4×D12C22semidirect
50. C3×C4×D12C22semidirect
51. C3×C4×D12C22semidirect
52. C3×C4×Dic6C22semidirect
53. #67⋊Dic3C22semidirect
54. #67⋊Dic3C22semidirect
55. C2×(C2×D3)⋊Dic3C22semidirect
56. #63952C22semidirect
57. #63921C22semidirect
58. D3×(C2×D3)⋊C4C22semidirect
59. D3×(C2×D3)⋊C4C22semidirect
60. #63904C22semidirect
61. C4×#626C22semidirect
62. #63902C22semidirect
63. C4×#625C22semidirect
64. #63900C22semidirect
65. #63898C22semidirect
66. #63898C22semidirect
67. #63898C22semidirect
68. #63898C22semidirect
69. #63898C22semidirect
70. #63898C22semidirect
71. #63894C22semidirect
72. #63881C22semidirect
73. #63880C22semidirect
74. #63879C22semidirect
75. #63879C22semidirect
76. #63878C22semidirect
77. #63877C22semidirect
78. D3×Dic3⋊C4C22semidirect
79. C4×D3×Dic3C22semidirect
80. C4×D3×Dic3C22semidirect
81. #63855C22semidirect
82. #63849C22semidirect
83. #63844C22semidirect
84. #63843C22semidirect
85. #63843C22semidirect
107. #5523D3semidirect
114. #5521D3semidirect
127. #3828C2×C4semidirect
135. C3×#235C2×C4semidirect
136. C2×C3×D12C2×C4semidirect
145. D3×#67C2×C4semidirect
155. #3802C2×C4semidirect
156. D3×D12C2×C4semidirect
158. #3796C2×C4semidirect
159. #3795C2×C4semidirect
230. C3×#117C2×D3semidirect
231. C3×#117C2×D3semidirect
257. #926C2×D3semidirect
258. C2×C4⋊Dic3C2×D3semidirect
280. #893C2×D3semidirect
281. #893C2×D3semidirect
285. #892C2×D3semidirect
289. D3×C4⋊C4C2×D3semidirect
314. #67⋊C4C2×D3semidirect
319. D3×C22⋊C4C2×D3semidirect
325. C4×D12C2×D3semidirect
326. C4×D12C2×D3semidirect
327. C4×D12C2×D3semidirect
339. C4×Dic6C2×D3semidirect
344. C22×C3×D3C22×C4semidirect
349. C2×D32C22×C4semidirect
350. C2×C32×C4C22×C4semidirect
355. #638C22×C4semidirect
363. C4⋊(C3⋊D3)C22×C4semidirect
366. C4×C3⋊D3C22×C4semidirect
367. #634C22×C4semidirect
368. C3×#67C22×C4semidirect
374. C3×D12C22×C4semidirect
375. C3×D12C22×C4semidirect
376. C3×D12C22×C4semidirect
380. C3×C4×D3C22×C4semidirect
381. C3×Dic6C22×C4semidirect
382. #626C22×C4semidirect
383. #625C22×C4semidirect
389. D3×Dic3C22×C4semidirect
458. #235C4×D3semidirect
464. C2×D12C4×D3semidirect
604. C3⋊Dic3H(5,𝔽2)semidirect
661. #117D32semidirect
694. C22×D3C2×C4×D3semidirect
716. C2×C3×C4C2×C4×D3semidirect
717. C2×C3×C4C2×C4×D3semidirect
732. #67C2×C4×D3semidirect
768. D12C2×C4×D3semidirect
769. D12C2×C4×D3semidirect
770. D12C2×C4×D3semidirect
790. C4×D3C2×C4×D3semidirect
794. Dic6C2×C4×D3semidirect
949. C32C4×H(5,𝔽2)semidirect
995. C2×C4C4×D32semidirect
1048. C3#85857semidirect
1049. C3#85886semidirect

Maximal subgroups

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

subgroupindex
C2×#643072
#105959932
C3×#55232
C3×#55212
#105949902
#105949582
C2×#638982
#105946042
D3×#8932
#105943592
#105943582
#105942542
D3×#67⋊C42
#105939962
C4×#38022
#105938892
C4×#37962
#858863
#858573