Finite Group Databasebeta

← #61867

Subgroups — #61867

Order 256.

814 conjugacy classes of subgroups.

The subgroup lattice has 793 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3557C211yesmaximal, characteristic, complemented
2#3504C211yesmaximal, characteristic, complemented
3#3390C211yesmaximal, characteristic, complemented
4#3389C211yesmaximal, characteristic, complemented
5#3388C211yesmaximal, characteristic, complemented
6#3388C211yesmaximal, characteristic, complemented
7#3383C211yesmaximal, characteristic, complemented
8#3381C211yesmaximal, characteristic, complemented
9#3381C211yesmaximal, characteristic, complemented
10#3380C211yesmaximal, characteristic, complemented
11#3377C211yesmaximal, characteristic, complemented
12#3376C211yesmaximal, characteristic, complemented
13#3371C211yesmaximal, characteristic, complemented
14#3370C211yesmaximal, characteristic, complemented
15#3365C211yesmaximal, characteristic, complemented
16#3364C211yesmaximal, characteristic, complemented
17#3361C211yesmaximal, characteristic, complemented
18#3360C211yesmaximal, characteristic, complemented
19#3244C211yesmaximal, characteristic, complemented
20#3243C211yesmaximal, characteristic, complemented
21#3242C211yesmaximal, characteristic, complemented
22#3241C211yesmaximal, characteristic, complemented
23#3232C211yesmaximal, characteristic, complemented
24#3232C211yesmaximal, characteristic, complemented
25#3125C211yesmaximal, characteristic, complemented
26#3124C211yesmaximal, characteristic, complemented
27#3120C211yesmaximal, characteristic, complemented
28#3119C211yesmaximal, characteristic
29#3102C211yesmaximal, characteristic, complemented
30#3102C211yesmaximal, characteristic, complemented
31#2986C211yesmaximal, characteristic, complemented
32#563—21no—
33#563—21no—
34#559C2211yescharacteristic
35#559C2211yescharacteristic
36#557C2211yescharacteristic
37#557C2211yescharacteristic
38#557C2211yescharacteristic
39#557C2211yescharacteristic
40#557C2211yescharacteristic
41#557C2211yescharacteristic
42#556C2211yescharacteristic
43#556C2211yescharacteristic
44#554—21no—
45#554—21no—
46#554—21no—
47#554—21no—
48#554C2211yescharacteristic
49#554C2211yescharacteristic
50#554C2211yescharacteristic
51#554C2211yescharacteristic
52#554C2211yescharacteristic
53#554C2211yescharacteristic
54#552—21no—
55#552—21no—
56#544—21no—
57#544—21no—
58#544C2211yescharacteristic
59#544C2211yescharacteristic
60#542—21no—
61#542—21no—
62#542C2211yescharacteristic
63#542C2211yescharacteristic
64#541C2211yescharacteristic
65#540C2211yescharacteristic
66#539—21no—
67#539—21no—
68#533—21no—
69#533C2211yescharacteristic
70#529C2211yescharacteristic
71#529C2211yescharacteristic
72C2×#125—21no—
73C2×#125C2211yescharacteristic
74#520C2211yescharacteristic
75#520C2211yescharacteristic
76C4×#41C2211yescharacteristic
77#501C2211yescharacteristic
78#501C2211yescharacteristic
79#501C2211yescharacteristic
80#501C2211yescharacteristic
81#500C2211yescharacteristic
82#499C2211yescharacteristic
83#499C2211yescharacteristic
84#499C2211yescharacteristic
85#499C2211yescharacteristic
86#499C2211yescharacteristic
87#499C2211yescharacteristic
88#498C2211yescharacteristic
89#491C2211yescharacteristic
90#490C2211yescharacteristic
91#489C2211yescharacteristic
92#489C2211yescharacteristic
93#488C2211yescharacteristic
94#488C2211yescharacteristic
95#488C2211yescharacteristic
96#488C2211yescharacteristic
97#488C2211yescharacteristic
98#488C2211yescharacteristic
99#487C2211yescharacteristic
100#486C2211yescharacteristic
101#485C2211yescharacteristic
102#485C2211yescharacteristic
103#484C2211yescharacteristic
104#484C2211yescharacteristic
105#483C2211yescharacteristic
106#483C2211yescharacteristic
107#482C2211yescharacteristic
108#482C2211yescharacteristic
109#481C2211yescharacteristic
110#481C2211yescharacteristic
111#480C2211yescharacteristic
112#480C2211yescharacteristic
113#479C2211yescharacteristic
114#479C2211yescharacteristic
115#479C2211yescharacteristic
116#479C2211yescharacteristic
117#479C2211yescharacteristic
118#479C2211yescharacteristic
119#479C2211yescharacteristic
120#479C2211yescharacteristic
121#479C2211yescharacteristic
122#479C2211yescharacteristic
123#479C2211yescharacteristic
124#479C2211yescharacteristic
125#478C2211yescharacteristic
126#478C2211yescharacteristic
127#478C2211yescharacteristic
128#478C2211yescharacteristic
129#478C2211yescharacteristic
130#478C2211yescharacteristic
131#478C2211yescharacteristic
132#478C2211yescharacteristic
133#478C2211yescharacteristic
134#478C2211yescharacteristic
135#478C2211yescharacteristic
136#478C2211yescharacteristic
137#477C2211yescharacteristic
138#477C2211yescharacteristic
139#477C2211yescharacteristic
140#476C2211yescharacteristic
141#476C2211yescharacteristic
142#476C2211yescharacteristic
143#475C2211yescharacteristic
144#475C2211yescharacteristic
145#475C2211yescharacteristic
146#474C2211yescharacteristic
147#474C2211yescharacteristic
148#474C2211yescharacteristic
149#464C2211yescharacteristic
150#464C2211yescharacteristic
151#464C2211yescharacteristic
152#464C2211yescharacteristic
153#463C2211yescharacteristic
154#463C2211yescharacteristic
155#463C2211yescharacteristic
156#463C2211yescharacteristic
157#462C2211yescharacteristic
158#461C2211yescharacteristic
159#460C2211yescharacteristic
160#459C2211yescharacteristic
161#452C2211yescharacteristic
162#452C2211yescharacteristic
163#449C2211yescharacteristic
164#449C2211yescharacteristic
165#446C2211yescharacteristic
166#446C2211yescharacteristic
167#446C2211yescharacteristic
168#446C2211yescharacteristic
169C8×Q8C2211yescharacteristic
170C8×Q8C2211yescharacteristic
171C8×Q8C2211yescharacteristic
172C8×Q8C2211yescharacteristic
173#442C2211yescharacteristic
174#442C2211yescharacteristic
175#441C2211yescharacteristic
176#441C2211yescharacteristic
177#440C2211yescharacteristic
178#440C2211yescharacteristic
179#440C2211yescharacteristic
180#440C2211yescharacteristic
181C4×Q16C2211yescharacteristic
182C4×Q16C2211yescharacteristic
183C4×Q16C2211yescharacteristic
184C4×Q16C2211yescharacteristic
185C4×SD16C2211yescharacteristic
186C4×SD16C2211yescharacteristic
187C4×SD16C2211yescharacteristic
188C4×SD16C2211yescharacteristic
189C4×SD16C2211yescharacteristic
190C4×SD16C2211yescharacteristic
191C4×SD16C2211yescharacteristic
192C4×SD16C2211yescharacteristic
193C4×D8C2211yescharacteristic
194C4×D8C2211yescharacteristic
195C4×D8C2211yescharacteristic
196C4×D8C2211yescharacteristic
197#433C2211yescharacteristic
198#433C2211yescharacteristic
199#433C2211yescharacteristic
200#433C2211yescharacteristic
201#431C2211yescharacteristic
202#431C2211yescharacteristic
203C2×#41C2311yescharacteristic
204C2×Q16C2311yescharacteristic
205C2×Q16C2311yescharacteristic
206C2×SD16C2311yescharacteristic
207C2×SD16C2311yescharacteristic
208C2×SD16C2311yescharacteristic
209C2×SD16C2311yescharacteristic
210C2×D8C2311yescharacteristic
211C2×D8C2311yescharacteristic
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8D411yescharacteristic
221C4⋊Q8D411yescharacteristic
222C4⋊Q8C2311yescharacteristic
223C4⋊Q8C2311yescharacteristic
224C4⋊Q8C2311yescharacteristic
225C4⋊Q8C2311yescharacteristic
226C4⋊Q8C2311yescharacteristic
227C4⋊Q8C2311yescharacteristic
228C4⋊Q8C2311yescharacteristic
229#127C2311yescharacteristic
230#126—21no—
231#126—21no—
232#126—21no—
233#126—21no—
234#126—21no—
235#126—21no—
236#126—21no—
237#126—21no—
238#126—21no—
239#126—21no—
240#125—21no—
241#125—21no—
242#125—21no—
243#125—21no—
244#125—21no—
245#125—21no—
246#125—21no—
247#125—21no—
248#125—21no—
249#125—21no—
250#125—21no—
251#125—21no—
252#125—21no—
253#125—21no—
254#125—21no—
255#125—21no—
256#125—21no—
257#125—21no—
258#125D411yescharacteristic
259#125D411yescharacteristic
260#125C2311yescharacteristic
261#125C2311yescharacteristic
262#125C2311yescharacteristic
263#125C2311yescharacteristic
264#125C2311yescharacteristic
265#125C2311yescharacteristic
266#125C2311yescharacteristic
267#125C2311yescharacteristic
268#125C2311yescharacteristic
269#125C2311yescharacteristic
270#125C2311yescharacteristic
271#125C2311yescharacteristic
272#124—21no—
273#124—21no—
274#124—21no—
275#124—21no—
276#124C2311yescharacteristic
277#124C2311yescharacteristic
278#124C2311yescharacteristic
279#124C2311yescharacteristic
280#123—21no—
281#123—21no—
282#123—21no—
283#123—21no—
284#123—21no—
285#123—21no—
286#123—21no—
287#123—21no—
288#123—21no—
289#123—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8—21no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C22⋊Q8D411yescharacteristic
317C22⋊Q8D411yescharacteristic
318C22⋊Q8D411yescharacteristic
319C22⋊Q8D411yescharacteristic
320C22⋊Q8C2311yescharacteristic
321C22⋊Q8C2311yescharacteristic
322#121—21no—
323#121—21no—
324#121C2311yescharacteristic
325#121C2311yescharacteristic
326C4×Q8—21no—
327C4×Q8—21no—
328C4×Q8—21no—
329C4×Q8—21no—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×Q8C2311yescharacteristic
333C4×Q8C2311yescharacteristic
334C4×Q8C2311yescharacteristic
335C4×Q8C2311yescharacteristic
336C4×Q8C2311yescharacteristic
337C4×Q8C2311yescharacteristic
338C4×Q8C2311yescharacteristic
339C4×Q8C2311yescharacteristic
340C4×Q8C2311yescharacteristic
341C4×Q8C2311yescharacteristic
342C4×Q8C2311yescharacteristic
343C4×Q8C2311yescharacteristic
344C4×Q8C2311yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4C2311yescharacteristic
359C4×D4C2311yescharacteristic
360C4×D4C2311yescharacteristic
361C4×D4C2311yescharacteristic
362C4×D4C2311yescharacteristic
363C4×D4C2311yescharacteristic
364C4×D4C2311yescharacteristic
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117C2311yescharacteristic
378#117C2311yescharacteristic
379#117C2311yescharacteristic
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4C2311yescharacteristic
391C2×C4⋊C4C2311yescharacteristic
392C2×C42—21no—
393C2×C42C2311yescharacteristic
394#107C2311yescharacteristic
395#107C2311yescharacteristic
396#107C2311yescharacteristic
397#107C2311yescharacteristic
398#107C2311yescharacteristic
399#107C2311yescharacteristic
400#107C2311yescharacteristic
401#107C2311yescharacteristic
402#107C2311yescharacteristic
403#107C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#106C2311yescharacteristic
407#106C2311yescharacteristic
408#106C2311yescharacteristic
409#106C2311yescharacteristic
410#106C2311yescharacteristic
411#106C2311yescharacteristic
412#106C2311yescharacteristic
413#106C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418C4⋊C8C2311yescharacteristic
419C4⋊C8C2311yescharacteristic
420C4⋊C8C2311yescharacteristic
421C4⋊C8C2311yescharacteristic
422C4⋊C8C2311yescharacteristic
423C4⋊C8C2311yescharacteristic
424C4⋊C8C2311yescharacteristic
425C4⋊C8C2311yescharacteristic
426C4⋊C8C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430#103C2311yescharacteristic
431#103C2311yescharacteristic
432#103C2311yescharacteristic
433#103C2311yescharacteristic
434#103C2311yescharacteristic
435#103C2311yescharacteristic
436#103C2311yescharacteristic
437#103C2311yescharacteristic
438#103C2311yescharacteristic
439#103C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#103C2311yescharacteristic
443#103C2311yescharacteristic
444#103C2311yescharacteristic
445#103C2311yescharacteristic
446#102C2311yescharacteristic
447#102C2311yescharacteristic
448#102C2311yescharacteristic
449#102C2311yescharacteristic
450#102C2311yescharacteristic
451#102C2311yescharacteristic
452#102C2311yescharacteristic
453#102C2311yescharacteristic
454#102C2311yescharacteristic
455#102C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462C22⋊C8C2311yescharacteristic
463C22⋊C8C2311yescharacteristic
464C22⋊C8C2311yescharacteristic
465C22⋊C8C2311yescharacteristic
466#97C2311yescharacteristic
467#97C2311yescharacteristic
468#97C2311yescharacteristic
469#97C2311yescharacteristic
470C4×C8C2311yescharacteristic
471C4×C8C2311yescharacteristic
472C4×C8C2311yescharacteristic
473C4×C8C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478#41—22no—
479#41—22no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8C2×D411yescharacteristic
487C2×Q8C2×D411yescharacteristic
488C2×Q8C2×D411yescharacteristic
489C2×Q8C2×D411yescharacteristic
490C2×Q8C2411yescharacteristic
491C2×Q8C2411yescharacteristic
492C2×Q8C2411yescharacteristic
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4C2411yescharacteristic
499C2×D4C2411yescharacteristic
500C2×D4C2411yescharacteristic
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4C2×D411yescharacteristic
517C22×C4C2×D411yescharacteristic
518C22×C4C2411yescharacteristic
519Q16—22no—
520Q16—22no—
521SD16—22no—
522SD16—22no—
523SD16—22no—
524SD16—22no—
525D8—22no—
526D8—22no—
527C2×C8C2411yescharacteristic
528C2×C8C2411yescharacteristic
529C2×C8C2411yescharacteristic
530C2×C8C2411yescharacteristic
531C2×C8C2411yescharacteristic
532C2×C8C2411yescharacteristic
533C2×C8C2411yescharacteristic
534C2×C8C2411yescharacteristic
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4C2×D411yescharacteristic
584C4⋊C4C2×D411yescharacteristic
585C4⋊C4C2×D411yescharacteristic
586C4⋊C4C2×D411yescharacteristic
587C4⋊C4C2×D411yescharacteristic
588C4⋊C4C2×D411yescharacteristic
589C4⋊C4C2×D411yescharacteristic
590C4⋊C4C2×D411yescharacteristic
591C4⋊C4C2×D411yescharacteristic
592C4⋊C4C2×D411yescharacteristic
593C4⋊C4C2×D411yescharacteristic
594C4⋊C4C2×D411yescharacteristic
595C4⋊C4C2×D411yescharacteristic
596C4⋊C4C2×D411yescharacteristic
597C4⋊C4C2×D411yescharacteristic
598C4⋊C4C2×D411yescharacteristic
599C4⋊C4C2411yescharacteristic
600C4⋊C4C2411yescharacteristic
601C4⋊C4C2411yescharacteristic
602C4⋊C4C2411yescharacteristic
603C4⋊C4C2411yescharacteristic
604C4⋊C4C2411yescharacteristic
605C4⋊C4C2411yescharacteristic
606C4⋊C4C2411yescharacteristic
607C4⋊C4C2411yescharacteristic
608C4⋊C4C2411yescharacteristic
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4C2×D411yescharacteristic
635C22⋊C4C2×D411yescharacteristic
636C22⋊C4C2×D411yescharacteristic
637C22⋊C4C2×D411yescharacteristic
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42C2×D411yescharacteristic
652C42C2×D411yescharacteristic
653C42C2411yescharacteristic
654C42C2411yescharacteristic
655C42C2411yescharacteristic
656C42C2411yescharacteristic
657C42C2411yescharacteristic
658C42C2411yescharacteristic
659C23—21no—
660C23—21no—
661C23—21no—
662C23C22×D411yescharacteristic
663Q8—21no—
664Q8—21no—
665Q8—21no—
666Q8—21no—
667Q8—21no—
668Q8—41no—
669Q8—41no—
670Q8—41no—
671Q8—41no—
672Q8—81no—
673Q8—81no—
674Q8—81no—
675Q8—81no—
676Q8—81no—
677Q8—81no—
678Q82−1+412yes—
679D4—24no—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—81no—
686D4—81no—
687D4—81no—
688D4—81no—
689D42−1+412yes—
690C2×C4—24no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4C22×D411yescharacteristic
723C2×C4C22×D411yescharacteristic
724C2×C4C22×D411yescharacteristic
725C2×C4C22×D411yescharacteristic
726C2×C4C22×D411yescharacteristic
727C2×C4C22×D411yescharacteristic
728C2×C4C22×D411yescharacteristic
729C2×C4C22×D411yescharacteristic
730C2×C4C22×D411yescharacteristic
731C2×C4C22×D411yescharacteristic
732C2×C4C22×D411yescharacteristic
733C2×C4C22×D411yescharacteristic
734C2×C4C22×D411yescharacteristic
735C2×C4C2511yescharacteristic
736C8—21no—
737C8—21no—
738C8—21no—
739C8—21no—
740C8—21no—
741C8—21no—
742C8—21no—
743C8—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—22no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22C23×D411yescharacteristic
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—21no—
768C4—21no—
769C4—21no—
770C4—22no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4C2×2−1+411yescharacteristic
784C4C2×2−1+411yescharacteristic
785C2—41no—
786C2—42no—
787C2—81no—
788C2—81no—
789C2#348611yescharacteristic
790C2#358411yescharacteristic
791C2#358411yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
prime radical#3119C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #533 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3557C2semidirect
2. #3504C2semidirect
3. #3390C2semidirect
4. #3389C2semidirect
5. #3388C2semidirect
6. #3388C2semidirect
7. #3383C2semidirect
8. #3381C2semidirect
9. #3381C2semidirect
10. #3380C2semidirect
11. #3377C2semidirect
12. #3376C2semidirect
13. #3371C2semidirect
14. #3370C2semidirect
15. #3365C2semidirect
16. #3364C2semidirect
17. #3361C2semidirect
18. #3360C2semidirect
19. #3244C2semidirect
20. #3243C2semidirect
21. #3242C2semidirect
22. #3241C2semidirect
23. #3232C2semidirect
24. #3232C2semidirect
25. #3125C2semidirect
26. #3124C2semidirect
27. #3120C2semidirect
29. #3102C2semidirect
30. #3102C2semidirect
31. #2986C2semidirect

Maximal subgroups

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

subgroupindex
#35572
#35042
#33902
#33892
#33882
#33832
#33812
#33802
#33772
#33762
#33712
#33702
#33652
#33642
#33612
#33602
#32442
#32432
#32422
#32412
#32322
#31252
#31242
#31202
#31192
#31022
#29862