Finite Group Databasebeta

← #11906219

Subgroups — #11906219

Order 1152.

2361 conjugacy classes of subgroups.

The subgroup lattice has 955 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64133C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic
3C2×C3×#924C211yesmaximal, characteristic, complemented
4#10595521C212yesmaximal, complemented
5#10595506C212yesmaximal
6#10594993C212yesmaximal, complemented
7#10594988C212yesmaximal, complemented
8#10594971C212yesmaximal, complemented
9#10594959C214yesmaximal, complemented
10#10594951C214yesmaximal, complemented
11#10594915C212yesmaximal, complemented
12Dic6×#67C212yesmaximal, complemented
13D3×#924C212yesmaximal, complemented
14#10594812C212yesmaximal, complemented
15#10594808C212yesmaximal, complemented
16#85986—31nomaximal
17#85766—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C22×#634C2211yescharacteristic, complemented
20C22×C3×#67C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic, complemented
23C2×D3×Dic6C2212yescomplemented
24C2×#3757C2212yes—
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
26#64133C2212yes—
27#64133C2212yes—
28#64133C2212yescomplemented
29#64133C2212yescomplemented
30C2×#3750C2212yescomplemented
31C2×C3×#217C2212yes—
32C2×C3×#217C2211yescharacteristic
33C3×C4×#67C2212yes—
34C3×C4×#67C2212yes—
35C3×C4×#67C2212yes—
36C3×C4×#67C2212yes—
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
39C3×#924C2212yes—
40C3×#924C2212yes—
41C3×#924C2212yescomplemented
42C3×#924C2212yescomplemented
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2212yescomplemented
45C2×C3×C4×Dic3C2211yescharacteristic
46#63982C2214yescomplemented
47#63982C2214yescomplemented
48#67⋊Dic3C2214yes—
49#67⋊Dic3C2214yes—
50Dic3×#67C2214yes—
51Dic3×#67C2214yes—
52D3×#217C2214yes—
53#63964C2214yes—
54#63964C2214yes—
55#63964C2214yescomplemented
56#63964C2214yescomplemented
57#63955C2214yes—
58#63918C2212yescomplemented
59#63899C2214yescomplemented
60#63896C2214yescomplemented
61#63893C2214yescomplemented
62D3×C4⋊Dic3C2212yescomplemented
63#63887C2214yescomplemented
64D3×Dic3⋊C4C2214yescomplemented
65#63867C2214yescomplemented
66#63866C2212yescomplemented
67#63857C2212yescomplemented
68#63856C2212yescomplemented
69#63851C2214yescomplemented
70#63846C2214yescomplemented
71#63845C2214yescomplemented
72#63844C2212yescomplemented
73Dic3×Dic6C2212yescomplemented
74#63840C2214yescomplemented
75#63839C2214yescomplemented
76#63837C2214yescomplemented
77C2×C3×C22⋊Q8—31no—
78C2×C3×C4×D4—31no—
79Q8×#67—32no—
80#5798—32no—
81C2×C4×#67D311yescharacteristic
82C2×#924—31no—
83C2×#924—31no—
84C2×#924—32no—
85C2×#924—61no—
86C2×#924D311yescharacteristic, complemented
87#5636—34no—
88#5635—32no—
89#5634—32no—
90#5632—32no—
91D3×C22⋊Q8—32no—
92#5623—32no—
93#5622—32no—
94#5543—32no—
95#5543—32no—
96#5539—34no—
97#5539—34no—
98D4×Dic6—32no—
99D4×Dic6—32no—
100#5511—34no—
101#5511—32no—
102#5500—32no—
103#5486—32no—
104#5483—32no—
105#5483—32no—
106#5483—32no—
107#5470—32no—
108C24×C32C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C22×C32×C4—42no—
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C22×C32×C4C2311yescharacteristic
115C22×C32×C4C2311yescharacteristic
116C22×C32×C4C2311yescharacteristic
117C22×C3⋊Dic3C2312yes—
118C22×C3⋊Dic3C2312yes—
119C2×#634—42no—
120C2×#634C2312yes—
121C2×#634C2312yes—
122C2×C3×#67Q818yescomplemented
123C2×C3×#67C2312yes—
124C2×C3×#67C2312yes—
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2312yes—
128C22×C3×Dic3C2312yes—
129C22×C3×Dic3C2311yescharacteristic
130C2×C3×C4×D3—42no—
131C2×C3×C4×D3C2312yes—
132C2×C3×C4×D3C2312yes—
133C2×C3×Dic6—42no—
134C2×C3×Dic6C2312yes—
135C2×C3×Dic6C2312yes—
136C2×#627C2314yes—
137C2×#627C2314yes—
138C2×D3×Dic3C2314yes—
139C2×D3×Dic3C2314yes—
140D3×Dic6—44no—
141#3757C2314yes—
142#3757C2314yes—
143C4⋊(C3⋊Dic3)C2312yes—
144C4⋊(C3⋊Dic3)C2312yes—
145#3750C2314yes—
146#3750C2314yes—
147C3×#217C2314yes—
148C3×#217C2314yes—
149C3×#217C2312yes—
150C3×#217C2312yes—
151C3×(C2×D3)⋊C4C2312yes—
152C3×(C2×D3)⋊C4C2312yes—
153C3×C4⋊Dic3C2312yes—
154C3×C4⋊Dic3C2312yes—
155C3×Dic3⋊C4C2312yes—
156C3×Dic3⋊C4C2312yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×C4×Dic3C2312yes—
160C3×C4×Dic3C2312yes—
161#3724C2314yes—
162#3724C2314yes—
163Dic3⋊Dic3C2314yes—
164Dic3⋊Dic3C2314yes—
165Dic3⋊Dic3C2314yes—
166Dic3⋊Dic3C2314yes—
167Dic3⋊Dic3C2314yes—
168Dic3⋊Dic3C2314yes—
169(C2×D3)⋊Dic3C2314yes—
170(C2×D3)⋊Dic3C2314yes—
171Dic32C2314yes—
172Dic32C2314yes—
173#3501—91noSylow
174C22×C3×Q8—31no—
175C22×C3×D4—31no—
176C23×C3×C4—21no—
177C23×C3×C4—31no—
178C23×C3×C4C2×D311yescharacteristic
179C23×C3×C4C2×D311yescharacteristic
180C22×#67C2×D311yescharacteristic
181C2×D3×Q8—32no—
182C22×C4×D3C2×D311yescharacteristic
183C22×Dic6—31no—
184C22×Dic6—31no—
185C22×Dic6—32no—
186C22×Dic6—61no—
187C22×Dic6C2×D311yescharacteristic, complemented
188C3×C22⋊Q8—32no—
189C3×C22⋊Q8—32no—
190C3×C22⋊Q8—32no—
191C3×C22⋊Q8—32no—
192C3×C4×D4—32no—
193C3×C4×D4—32no—
194C3×C4×D4—32no—
195C3×C4×D4—32no—
196C2×C3×C4⋊C4—31no—
197C2×C3×C4⋊C4—32no—
198C2×C3×C4⋊C4—31no—
199C2×C3×C22⋊C4—31no—
200C2×C3×C22⋊C4—32no—
201C2×C3×C22⋊C4—31no—
202C2×C3×C42—31no—
203C2×#217—32no—
204C2×#217—32no—
205C2×#217—34no—
206C2×#217—62no—
207C2×#217C2×D311yescharacteristic
208C2×#217C2×D312yes—
209#946—32no—
210#946—34no—
211Q8×Dic3—32no—
212#944—34no—
213#944—32no—
214D4×Dic3—34no—
215D4×Dic3—34no—
216D4×Dic3—34no—
217D4×Dic3—34no—
218C4×#67—34no—
219C4×#67—34no—
220C4×#67C2×D312yes—
221C4×#67C2×D312yes—
222C4×#67C2×D312yes—
223C4×#67C2×D312yes—
224C2×(C2×D3)⋊C4C2×D311yescharacteristic
225#926—34no—
226C2×C4⋊Dic3—31no—
227C2×C4⋊Dic3—31no—
228C2×C4⋊Dic3—32no—
229C2×C4⋊Dic3—61no—
230C2×C4⋊Dic3C2×D311yescharacteristic, complemented
231#924—32no—
232#924—32no—
233#924—32no—
234#924—32no—
235#924—32no—
236#924—32no—
237#924—32no—
238#924—32no—
239#924—32no—
240#924—34no—
241#924—34no—
242#924—34no—
243#924—34no—
244#924—32no—
245#924—34no—
246#924—62no—
247#924—62no—
248#924—62no—
249#924—62no—
250#924C2×D312yes—
251#924C2×D312yes—
252#924C2×D312yescomplemented
253#924C2×D312yescomplemented
254C2×Dic3⋊C4—32no—
255C2×Dic3⋊C4—32no—
256C2×Dic3⋊C4—34no—
257C2×Dic3⋊C4—62no—
258C2×Dic3⋊C4C2×D311yescharacteristic
259C2×Dic3⋊C4C2×D312yescomplemented
260C2×C4×Dic3C2×D311yescharacteristic
261#897—32no—
262#897—34no—
263#896—34no—
264#896—34no—
265#896—34no—
266D3×C4⋊C4—32no—
267D3×C4⋊C4—34no—
268#890—34no—
269#890—34no—
270#889—34no—
271#889—34no—
272#889—34no—
273#888—34no—
274#888—34no—
275#888—34no—
276#888—32no—
277#887—32no—
278#887—34no—
279#67⋊C4—34no—
280#67⋊C4—34no—
281D3×C22⋊C4—34no—
282#878—34no—
283#878—34no—
284#878—34no—
285#878—34no—
286#878—34no—
287#878—34no—
288#878—34no—
289#878—34no—
290#878—34no—
291#878—34no—
292#878—34no—
293#878—34no—
294#877—34no—
295#870—34no—
296#869—32no—
297#869—32no—
298C4×Dic6—32no—
299C4×Dic6—32no—
300C4×Dic6—34no—
301C23×C32—41no—
302C23×C32—41no—
303C23×C32C2×Q814yescomplemented
304C23×C32C2411yescharacteristic
305C23×C32C2411yescharacteristic
306C23×C32C2411yescharacteristic
307C22×C3×D3—41no—
308C22×C3×D3—41no—
309C22×C3×D3C2×Q814yescomplemented
310C22×C3×D3C2412yes—
311C2×C32×C4—22no—
312C2×C32×C4—22no—
313C2×C32×C4—22no—
314C2×C32×C4—41no—
315C2×C32×C4—41no—
316C2×C32×C4—41no—
317C2×C32×C4C2411yescharacteristic
318C2×C32×C4C2411yescharacteristic
319C2×C32×C4C2411yescharacteristic
320C2×C32×C4C2411yescharacteristic
321C2×C3⋊Dic3—42no—
322C2×C3⋊Dic3—42no—
323C2×C3⋊Dic3C2414yes—
324C2×C3⋊Dic3C2414yes—
325#634—24no—
326#634—42no—
327C3×#67C2×Q818yescomplemented
328C3×#67C2×Q818yescomplemented
329C2×C3×Dic3—42no—
330C2×C3×Dic3—41no—
331C2×C3×Dic3—42no—
332C2×C3×Dic3—41no—
333C2×C3×Dic3C2×Q814yescomplemented
334C2×C3×Dic3C2414yes—
335C2×C3×Dic3C2414yes—
336C2×C3×Dic3C2412yes—
337C2×C3×Dic3C2412yes—
338C2×C3×Dic3C2412yes—
339C3×C4×D3—24no—
340C3×C4×D3—42no—
341C3×Dic6—24no—
342C3×Dic6—42no—
343#627—44no—
344#627—44no—
345D3×Dic3—44no—
346D3×Dic3—44no—
347#554—94no—
348#554—92no—
349#554—92no—
350#554—94no—
351D4×Q8—92no—
352D4×Q8—92no—
353#544—92no—
354#543—92no—
355#543—92no—
356#533—92no—
357C2×C22⋊Q8—31no—
358C2×C22⋊Q8—92no—
359C2×C22⋊Q8—91no—
360#518—92no—
361C2×C4×D4—31no—
362C24×C3—21no—
363C24×C3—31no—
364C24×C3C22×D311yescharacteristic
365C24×C3C22×D311yescharacteristic
366C23×D3C22×D311yescharacteristic
367C2×C3×Q8—32no—
368C2×C3×Q8—32no—
369C2×C3×Q8—122no—
370C2×C3×D4—38no—
371C2×C3×D4—32no—
372C2×C3×D4—32no—
373C22×C3×C4—21no—
374C22×C3×C4—21no—
375C22×C3×C4—21no—
376C22×C3×C4—21no—
377C22×C3×C4—21no—
378C22×C3×C4—21no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—32no—
383C22×C3×C4—32no—
384C22×C3×C4—32no—
385C22×C3×C4—32no—
386C22×C3×C4—42no—
387C22×C3×C4—42no—
388C22×C3×C4—44no—
389C22×C3×C4—122no—
390C22×C3×C4C22×D311yescharacteristic
391C22×C3×C4C22×D311yescharacteristic
392C22×C3×C4C22×D311yescharacteristic
393C22×C3×C4C22×D311yescharacteristic
394C22×C3×C4C22×D311yescharacteristic
395C22×C3×C4C22×D311yescharacteristic
396C22×C3×C4C22×D311yescharacteristic
397C22×C3×C4C22×D311yescharacteristic
398C22×C3×C4C22×D311yescharacteristic
399C22×C3×C4C22×D311yescharacteristic
400C22×C3×C4C22×D311yescharacteristic
401C22×C3×C4C22×D311yescharacteristic
402C2×#67Dic618yescomplemented
403C2×#67C22×D312yes—
404C2×#67C22×D312yes—
405C22×Dic3—32no—
406C22×Dic3—32no—
407C22×Dic3—32no—
408C22×Dic3—32no—
409C22×Dic3—34no—
410C22×Dic3—34no—
411C22×Dic3—62no—
412C22×Dic3—62no—
413C22×Dic3C22×D311yescharacteristic
414C22×Dic3C22×D311yescharacteristic
415C22×Dic3C22×D312yes—
416C22×Dic3C22×D312yes—
417C22×Dic3C22×D311yescharacteristic
418D3×Q8—124no—
419C2×C4×D3—34no—
420C2×C4×D3—34no—
421C2×C4×D3—42no—
422C2×C4×D3C22×D312yes—
423C2×C4×D3C22×D312yes—
424C2×Dic6—32no—
425C2×Dic6—32no—
426C2×Dic6—32no—
427C2×Dic6—32no—
428C2×Dic6—34no—
429C2×Dic6—34no—
430C2×Dic6—34no—
431C2×Dic6—34no—
432C2×Dic6—42no—
433C2×Dic6—62no—
434C2×Dic6—62no—
435C2×Dic6—124no—
436C2×Dic6—122no—
437C2×Dic6—122no—
438C2×Dic6—124no—
439C2×Dic6C22×D312yes—
440C2×Dic6C22×D312yes—
441C3×C4⋊C4—32no—
442C3×C4⋊C4—34no—
443C3×C4⋊C4—32no—
444C3×C4⋊C4—32no—
445C3×C4⋊C4—34no—
446C3×C4⋊C4—32no—
447C3×C22⋊C4—34no—
448C3×C22⋊C4—32no—
449C3×C22⋊C4—32no—
450C3×C22⋊C4—34no—
451C3×C22⋊C4—32no—
452C3×C22⋊C4—32no—
453C3×C42—32no—
454C3×C42—32no—
455#217—34no—
456#217—34no—
457#217—34no—
458#217—34no—
459#217—34no—
460#217—34no—
461#217—64no—
462#217—64no—
463#217C22×D312yes—
464#217C22×D314yes—
465#217C22×D312yes—
466#217C22×D314yes—
467(C2×D3)⋊C4—34no—
468(C2×D3)⋊C4—34no—
469(C2×D3)⋊C4C22×D312yes—
470(C2×D3)⋊C4C22×D312yes—
471C4⋊Dic3—32no—
472C4⋊Dic3—32no—
473C4⋊Dic3—32no—
474C4⋊Dic3—32no—
475C4⋊Dic3—34no—
476C4⋊Dic3—34no—
477C4⋊Dic3—34no—
478C4⋊Dic3—34no—
479C4⋊Dic3—34no—
480C4⋊Dic3—34no—
481C4⋊Dic3—62no—
482C4⋊Dic3—62no—
483C4⋊Dic3C22×D312yes—
484C4⋊Dic3C22×D312yes—
485Dic3⋊C4—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4—34no—
492Dic3⋊C4—34no—
493Dic3⋊C4—34no—
494Dic3⋊C4—34no—
495Dic3⋊C4—34no—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—64no—
500Dic3⋊C4—64no—
501Dic3⋊C4C22×D314yes—
502Dic3⋊C4C22×D314yes—
503Dic3⋊C4C22×D312yes—
504Dic3⋊C4C22×D312yes—
505C4×Dic3—34no—
506C4×Dic3—34no—
507C4×Dic3—34no—
508C4×Dic3—34no—
509C4×Dic3C22×D312yes—
510C4×Dic3C22×D312yes—
511C22×C32—21no—
512C22×C32—21no—
513C22×C32—21no—
514C22×C32—21no—
515C22×C32—21no—
516C22×C32—21no—
517C22×C32—44no—
518C22×C32C22×Q812yes—
519C22×C32C22×Q812yes—
520C22×C32C22×Q812yes—
521C22×C32C2511yescharacteristic
522C2×C3×D3—22no—
523C2×C3×D3—22no—
524C2×C3×D3—44no—
525C2×C3×D3C22×Q814yes—
526C32×C4—21no—
527C32×C4—21no—
528C32×C4—21no—
529C32×C4H(5,𝔽2)12yes—
530C3⋊Dic3—24no—
531C3⋊Dic3—24no—
532C3×Dic3—24no—
533C3×Dic3—22no—
534C3×Dic3—24no—
535C3×Dic3—22no—
536C3×Dic3C22×Q814yes—
537C22×Q8—31no—
538C22×Q8—92no—
539C22×Q8—91no—
540C22×D4—31no—
541C23×C4—31no—
542C23×C4D3211yescharacteristic
543C4⋊Q8—92no—
544C4⋊Q8—92no—
545C4⋊Q8—94no—
546C4⋊Q8—94no—
547#125—94no—
548#125—94no—
549#125—94no—
550C22⋊Q8—32no—
551C22⋊Q8—32no—
552C22⋊Q8—32no—
553C22⋊Q8—32no—
554C22⋊Q8—94no—
555C22⋊Q8—94no—
556C22⋊Q8—94no—
557C22⋊Q8—94no—
558C22⋊Q8—94no—
559C22⋊Q8—94no—
560C22⋊Q8—94no—
561C22⋊Q8—94no—
562C22⋊Q8—94no—
563C22⋊Q8—94no—
564C22⋊Q8—92no—
565C22⋊Q8—94no—
566C22⋊Q8—92no—
567C22⋊Q8—92no—
568C22⋊Q8—92no—
569C22⋊Q8—92no—
570C22⋊Q8—92no—
571C4×Q8—92no—
572C4×Q8—94no—
573C4×Q8—92no—
574C4×D4—32no—
575C4×D4—32no—
576C4×D4—32no—
577C4×D4—32no—
578C4×D4—94no—
579C4×D4—94no—
580C4×D4—94no—
581C4×D4—94no—
582#117—94no—
583C2×C4⋊C4—31no—
584C2×C4⋊C4—32no—
585C2×C4⋊C4—31no—
586C2×C4⋊C4—94no—
587C2×C4⋊C4—92no—
588C2×C4⋊C4—92no—
589C2×C4⋊C4—91no—
590C2×C22⋊C4—31no—
591C2×C22⋊C4—32no—
592C2×C22⋊C4—31no—
593C2×C22⋊C4—94no—
594C2×C22⋊C4—92no—
595C2×C42—31no—
596C23×C3—21no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—24no—
600C23×C3—32no—
601C23×C3—34no—
602C23×C3—41no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3—41no—
606C23×C3—42no—
607C23×C3—42no—
608C23×C3—121no—
609C23×C3—121no—
610C23×C3C2×Dic614yescomplemented
611C23×C3D3×Q814yescomplemented
612C23×C3C23×D311yescharacteristic
613C23×C3C23×D311yescharacteristic
614C23×C3C23×D311yescharacteristic
615C23×C3C23×D311yescharacteristic
616C23×C3C23×D311yescharacteristic
617C23×C3C23×D311yescharacteristic
618C22×D3—41no—
619C22×D3—41no—
620C22×D3C2×Dic614yescomplemented
621C22×D3C23×D312yes—
622C3×Q8—64no—
623C3×Q8—122no—
624C3×D4—38no—
625C3×D4—38no—
626C2×C3×C4—24no—
627C2×C3×C4—22no—
628C2×C3×C4—22no—
629C2×C3×C4—22no—
630C2×C3×C4—22no—
631C2×C3×C4—22no—
632C2×C3×C4—22no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—34no—
638C2×C3×C4—32no—
639C2×C3×C4—34no—
640C2×C3×C4—34no—
641C2×C3×C4—32no—
642C2×C3×C4—32no—
643C2×C3×C4—42no—
644C2×C3×C4—42no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—41no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—42no—
652C2×C3×C4—42no—
653C2×C3×C4—42no—
654C2×C3×C4—64no—
655C2×C3×C4—122no—
656C2×C3×C4—121no—
657C2×C3×C4—122no—
658C2×C3×C4—121no—
659C2×C3×C4—122no—
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C23×D311yescharacteristic
662C2×C3×C4C23×D311yescharacteristic
663C2×C3×C4C23×D311yescharacteristic
664C2×C3×C4C23×D311yescharacteristic
665C2×C3×C4C23×D311yescharacteristic
666C2×C3×C4C23×D311yescharacteristic
667C2×C3×C4C23×D311yescharacteristic
668#67C2×Dic618yescomplemented
669#67C2×Dic618yescomplemented
670C2×Dic3—34no—
671C2×Dic3—34no—
672C2×Dic3—34no—
673C2×Dic3—34no—
674C2×Dic3—42no—
675C2×Dic3—41no—
676C2×Dic3—41no—
677C2×Dic3—42no—
678C2×Dic3—64no—
679C2×Dic3—64no—
680C2×Dic3—124no—
681C2×Dic3—124no—
682C2×Dic3—122no—
683C2×Dic3—122no—
684C2×Dic3—122no—
685C2×Dic3—122no—
686C2×Dic3—124no—
687C2×Dic3—124no—
688C2×Dic3C2×Dic614yescomplemented
689C2×Dic3C23×D314yes—
690C2×Dic3C23×D314yes—
691C2×Dic3C23×D312yes—
692C2×Dic3C23×D312yes—
693C2×Dic3C23×D312yes—
694C4×D3—24no—
695C4×D3—42no—
696C4×D3—124no—
697C4×D3—124no—
698Dic6—24no—
699Dic6—42no—
700Dic6—64no—
701Dic6—64no—
702Dic6—124no—
703Dic6—124no—
704Dic6—124no—
705Dic6—124no—
706Dic6—124no—
707Dic6—122no—
708Dic6—122no—
709Dic6—124no—
710C2×C32—22no—
711C2×C32—22no—
712C2×C32—22no—
713C2×C32C23×Q811yescharacteristic
714C2×C32C2×H(5,𝔽2)11yescharacteristic
715C2×C32#58511yescharacteristic
716C3×D3—24no—
717C24—31no—
718C24C2×D3211yescharacteristic
719C2×Q8—32no—
720C2×Q8—32no—
721C2×Q8—94no—
722C2×Q8—94no—
723C2×Q8—92no—
724C2×Q8—92no—
725C2×Q8—122no—
726C2×Q8—362no—
727C2×Q8—364no—
728C2×D4—32no—
729C2×D4—32no—
730C2×D4—38no—
731C22×C4—31no—
732C22×C4—31no—
733C22×C4—32no—
734C22×C4—32no—
735C22×C4—31no—
736C22×C4—32no—
737C22×C4—32no—
738C22×C4—42no—
739C22×C4—94no—
740C22×C4—94no—
741C22×C4—92no—
742C22×C4—92no—
743C22×C4—122no—
744C22×C4C2×D3211yescharacteristic
745C22×C4C2×D3211yescharacteristic
746C22×C4C2×D3211yescharacteristic
747C22×C4C2×D3211yescharacteristic
748C22×C4C2×D3211yescharacteristic
749C22×C4C2×D3211yescharacteristic
750C4⋊C4—34no—
751C4⋊C4—32no—
752C4⋊C4—32no—
753C4⋊C4—32no—
754C4⋊C4—32no—
755C4⋊C4—34no—
756C4⋊C4—94no—
757C4⋊C4—94no—
758C4⋊C4—94no—
759C4⋊C4—94no—
760C4⋊C4—94no—
761C4⋊C4—94no—
762C4⋊C4—94no—
763C4⋊C4—94no—
764C4⋊C4—94no—
765C4⋊C4—92no—
766C4⋊C4—92no—
767C4⋊C4—94no—
768C22⋊C4—34no—
769C22⋊C4—32no—
770C22⋊C4—32no—
771C22⋊C4—34no—
772C22⋊C4—32no—
773C22⋊C4—32no—
774C22⋊C4—94no—
775C22⋊C4—94no—
776C22⋊C4—94no—
777C22⋊C4—94no—
778C42—32no—
779C42—32no—
780C42—94no—
781C42—94no—
782C22×C3—22no—
783C22×C3—22no—
784C22×C3—21no—
785C22×C3—21no—
786C22×C3—21no—
787C22×C3—21no—
788C22×C3—21no—
789C22×C3—21no—
790C22×C3—21no—
791C22×C3—21no—
792C22×C3—21no—
793C22×C3—21no—
794C22×C3—21no—
795C22×C3—21no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—21no—
800C22×C3—34no—
801C22×C3—41no—
802C22×C3—41no—
803C22×C3—41no—
804C22×C3—41no—
805C22×C3—44no—
806C22×C3—44no—
807C22×C3—48no—
808C22×C3—62no—
809C22×C3—62no—
810C22×C3—124no—
811C22×C3C22×Dic612yes—
812C22×C3C22×Dic612yes—
813C22×C3C22×Dic612yes—
814C22×C3C2×D3×Q812yes—
815C22×C3C2×D3×Q812yes—
816C22×C3C2×D3×Q812yes—
817C22×C3C24×D311yescharacteristic
818C22×C3C24×D311yescharacteristic
819C2×D3—22no—
820C2×D3—22no—
821C2×D3—44no—
822C2×D3C22×Dic614yes—
823C3×C4—22no—
824C3×C4—21no—
825C3×C4—21no—
826C3×C4—21no—
827C3×C4—21no—
828C3×C4—21no—
829C3×C4—21no—
830C3×C4—22no—
831C3×C4—34no—
832C3×C4—41no—
833C3×C4—41no—
834C3×C4—62no—
835C3×C4—64no—
836C3×C4—62no—
837C3×C4—64no—
838C3×C4#100412yes—
839C3×C4#100412yes—
840Dic3—24no—
841Dic3—22no—
842Dic3—22no—
843Dic3—24no—
844Dic3—64no—
845Dic3—64no—
846Dic3—64no—
847Dic3—64no—
848Dic3—124no—
849Dic3—124no—
850Dic3C22×Dic614yes—
851C32#350111yescharacteristic, complemented, Sylow
852C23—32no—
853C23—34no—
854C23—41no—
855C23—41no—
856C23—121no—
857C23—121no—
858C23D3×Dic614yescomplemented
859C23C22×D3211yescharacteristic
860C23C22×D3211yescharacteristic
861C23C22×D3211yescharacteristic
862Q8—64no—
863Q8—122no—
864Q8—184no—
865Q8—362no—
866Q8—364no—
867Q8—364no—
868D4—38no—
869D4—38no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—34no—
874C2×C4—32no—
875C2×C4—32no—
876C2×C4—34no—
877C2×C4—34no—
878C2×C4—32no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—64no—
883C2×C4—94no—
884C2×C4—94no—
885C2×C4—122no—
886C2×C4—121no—
887C2×C4—122no—
888C2×C4—122no—
889C2×C4—121no—
890C2×C4—364no—
891C2×C4—364no—
892C2×C4—362no—
893C2×C4—362no—
894C2×C4C22×D3211yescharacteristic
895C2×C4C22×D3211yescharacteristic
896C2×C4C22×D3211yescharacteristic
897C2×C4C22×D3211yescharacteristic
898C2×C3—24no—
899C2×C3—22no—
900C2×C3—22no—
901C2×C3—22no—
902C2×C3—22no—
903C2×C3—22no—
904C2×C3—22no—
905C2×C3—21no—
906C2×C3—21no—
907C2×C3—21no—
908C2×C3—42no—
909C2×C3—42no—
910C2×C3—64no—
911C2×C3C23×Dic611yescharacteristic
912C2×C3C2×#100411yescharacteristic
913C2×C3C2×#100411yescharacteristic
914C2×C3C22×D3×Q811yescharacteristic
915C2×C3#596411yescharacteristic
916C2×C3#596411yescharacteristic
917D3—24no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—34no—
925C22—44no—
926C22—62no—
927C22—62no—
928C22—124no—
929C22C2×D3×Dic612yes—
930C22C2×D3×Dic612yes—
931C22C2×D3×Dic612yes—
932C22C23×D3211yescharacteristic
933C4—21no—
934C4—21no—
935C4—21no—
936C4—34no—
937C4—64no—
938C4—62no—
939C4—62no—
940C4—64no—
941C4—184no—
942C4—184no—
943C4#6433012yes—
944C3—21no—
945C3#8576611yescharacteristic, complemented
946C3#8598611yescharacteristic, complemented
947C2—22no—
948C2—22no—
949C2—22no—
950C2—64no—
951C2C22×D3×Dic611yescharacteristic
952C2#1059666911yescharacteristic
953C2C2×#6433011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC23×C32×C4C22
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#3501
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64133C2semidirect
3. C2×C3×#924C2semidirect
4. #10595521C2semidirect
6. #10594993C2semidirect
7. #10594988C2semidirect
8. #10594971C2semidirect
9. #10594959C2semidirect
10. #10594951C2semidirect
11. #10594915C2semidirect
12. Dic6×#67C2semidirect
13. D3×#924C2semidirect
14. #10594812C2semidirect
15. #10594808C2semidirect
19. C22×#634C22semidirect
22. C22×C3×Dic6C22semidirect
23. C2×D3×Dic6C22semidirect
25. C2×C4⋊(C3⋊Dic3)C22semidirect
28. #64133C22semidirect
29. #64133C22semidirect
30. C2×#3750C22semidirect
38. C2×C3×C4⋊Dic3C22semidirect
41. C3×#924C22semidirect
42. C3×#924C22semidirect
44. C2×C3×Dic3⋊C4C22semidirect
46. #63982C22semidirect
47. #63982C22semidirect
55. #63964C22semidirect
56. #63964C22semidirect
58. #63918C22semidirect
59. #63899C22semidirect
60. #63896C22semidirect
61. #63893C22semidirect
62. D3×C4⋊Dic3C22semidirect
63. #63887C22semidirect
64. D3×Dic3⋊C4C22semidirect
65. #63867C22semidirect
66. #63866C22semidirect
67. #63857C22semidirect
68. #63856C22semidirect
69. #63851C22semidirect
70. #63846C22semidirect
71. #63845C22semidirect
72. #63844C22semidirect
73. Dic3×Dic6C22semidirect
74. #63840C22semidirect
75. #63839C22semidirect
76. #63837C22semidirect
86. C2×#924D3semidirect
122. C2×C3×#67Q8semidirect
187. C22×Dic6C2×D3semidirect
230. C2×C4⋊Dic3C2×D3semidirect
252. #924C2×D3semidirect
253. #924C2×D3semidirect
259. C2×Dic3⋊C4C2×D3semidirect
303. C23×C32C2×Q8semidirect
309. C22×C3×D3C2×Q8semidirect
327. C3×#67C2×Q8semidirect
328. C3×#67C2×Q8semidirect
333. C2×C3×Dic3C2×Q8semidirect
402. C2×#67Dic6semidirect
610. C23×C3C2×Dic6semidirect
611. C23×C3D3×Q8semidirect
620. C22×D3C2×Dic6semidirect
668. #67C2×Dic6semidirect
669. #67C2×Dic6semidirect
688. C2×Dic3C2×Dic6semidirect
851. C32#3501semidirect
858. C23D3×Dic6semidirect
945. C3#85766semidirect
946. C3#85986semidirect

Maximal subgroups

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

subgroupindex
C2×#641332
C2×C3×C4×#672
C2×C3×#9242
#105955212
#105955062
#105949932
#105949882
#105949712
#105949592
#105949512
#105949152
Dic6×#672
D3×#9242
#105948122
#105948082
#859863
#857663