Finite Group Databasebeta

← #61862

Subgroups — #61862

Order 256.

807 conjugacy classes of subgroups.

The subgroup lattice has 785 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3555C211yesmaximal, characteristic, complemented
2#3504C211yesmaximal, characteristic, complemented
3#3390C211yesmaximal, characteristic, complemented
4#3389C211yesmaximal, characteristic, complemented
5#3388C211yesmaximal, characteristic, complemented
6#3388C211yesmaximal, characteristic, complemented
7#3387C211yesmaximal, characteristic, complemented
8#3385C211yesmaximal, characteristic, complemented
9#3383C211yesmaximal, characteristic, complemented
10#3381C211yesmaximal, characteristic, complemented
11#3377C211yesmaximal, characteristic, complemented
12#3377C211yesmaximal, characteristic, complemented
13#3376C211yesmaximal, characteristic, complemented
14#3376C211yesmaximal, characteristic, complemented
15#3374C211yesmaximal, characteristic, complemented
16#3372C211yesmaximal, characteristic, complemented
17#3364C211yesmaximal, characteristic, complemented
18#3360C211yesmaximal, characteristic, complemented
19#3244C211yesmaximal, characteristic, complemented
20#3243C211yesmaximal, characteristic, complemented
21#3242C211yesmaximal, characteristic, complemented
22#3242C211yesmaximal, characteristic, complemented
23#3236C211yesmaximal, characteristic, complemented
24#3232C211yesmaximal, characteristic, complemented
25#3125C211yesmaximal, characteristic
26#3124C211yesmaximal, characteristic
27#3120C211yesmaximal, characteristic, complemented
28#3120C211yesmaximal, characteristic, complemented
29#3111C211yesmaximal, characteristic
30#3107C211yesmaximal, characteristic, complemented
31#2985C211yesmaximal, characteristic, complemented
32#563—21no—
33#563—21no—
34Q82C2211yescharacteristic
35#557C2211yescharacteristic
36#557C2211yescharacteristic
37#557C2211yescharacteristic
38#557C2211yescharacteristic
39#557C2211yescharacteristic
40#557C2211yescharacteristic
41#557C2211yescharacteristic
42#556—21no—
43#556C2211yescharacteristic
44#556C2211yescharacteristic
45#556C2211yescharacteristic
46#554—21no—
47#554—21no—
48#554—21no—
49#554—21no—
50#554C2211yescharacteristic
51#554C2211yescharacteristic
52#554C2211yescharacteristic
53#554C2211yescharacteristic
54#554C2211yescharacteristic
55#552—21no—
56#544—21no—
57#544—21no—
58#544—21no—
59#544C2211yescharacteristic
60#544C2211yescharacteristic
61#542C2211yescharacteristic
62#542C2211yescharacteristic
63#541—21no—
64#541—21no—
65#541—21no—
66#541C2211yescharacteristic
67#541C2211yescharacteristic
68#533—21no—
69#533C2211yescharacteristic
70#533C2211yescharacteristic
71#529C2211yescharacteristic
72C2×#125—21no—
73C2×#125C2211yescharacteristic
74#520C2211yescharacteristic
75#520C2211yescharacteristic
76C4×#41C2211yescharacteristic
77#501C2211yescharacteristic
78#501C2211yescharacteristic
79#501C2211yescharacteristic
80#501C2211yescharacteristic
81#501C2211yescharacteristic
82#501C2211yescharacteristic
83#500C2211yescharacteristic
84#499C2211yescharacteristic
85#499C2211yescharacteristic
86#499C2211yescharacteristic
87#499C2211yescharacteristic
88#498C2211yescharacteristic
89#491C2211yescharacteristic
90#491C2211yescharacteristic
91#491C2211yescharacteristic
92#491C2211yescharacteristic
93#489C2211yescharacteristic
94#489C2211yescharacteristic
95#488C2211yescharacteristic
96#488C2211yescharacteristic
97#488C2211yescharacteristic
98#488C2211yescharacteristic
99#487C2211yescharacteristic
100#487C2211yescharacteristic
101#485C2211yescharacteristic
102#485C2211yescharacteristic
103#485C2211yescharacteristic
104#484C2211yescharacteristic
105#484C2211yescharacteristic
106#484C2211yescharacteristic
107#483C2211yescharacteristic
108#483C2211yescharacteristic
109#483C2211yescharacteristic
110#482C2211yescharacteristic
111#481C2211yescharacteristic
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#479C2211yescharacteristic
126#479C2211yescharacteristic
127#479C2211yescharacteristic
128#478C2211yescharacteristic
129#478C2211yescharacteristic
130#478C2211yescharacteristic
131#478C2211yescharacteristic
132#478C2211yescharacteristic
133#478C2211yescharacteristic
134#478C2211yescharacteristic
135#477C2211yescharacteristic
136#477C2211yescharacteristic
137#477C2211yescharacteristic
138#477C2211yescharacteristic
139#476C2211yescharacteristic
140#476C2211yescharacteristic
141#475C2211yescharacteristic
142#475C2211yescharacteristic
143#475C2211yescharacteristic
144#475C2211yescharacteristic
145#475C2211yescharacteristic
146#474C2211yescharacteristic
147#474C2211yescharacteristic
148#474C2211yescharacteristic
149#464C2211yescharacteristic
150#464C2211yescharacteristic
151#464C2211yescharacteristic
152#463C2211yescharacteristic
153#463C2211yescharacteristic
154#463C2211yescharacteristic
155#462C2211yescharacteristic
156#462C2211yescharacteristic
157#462C2211yescharacteristic
158#461C2211yescharacteristic
159#461C2211yescharacteristic
160#461C2211yescharacteristic
161#452C2211yescharacteristic
162#452C2211yescharacteristic
163#452C2211yescharacteristic
164#449C2211yescharacteristic
165#446C2211yescharacteristic
166#446C2211yescharacteristic
167#446C2211yescharacteristic
168#446C2211yescharacteristic
169#446C2211yescharacteristic
170#446C2211yescharacteristic
171C8×Q8C2211yescharacteristic
172C8×Q8C2211yescharacteristic
173#442C2211yescharacteristic
174#442C2211yescharacteristic
175#441C2211yescharacteristic
176#441C2211yescharacteristic
177#441C2211yescharacteristic
178#441C2211yescharacteristic
179#440C2211yescharacteristic
180#440C2211yescharacteristic
181#440C2211yescharacteristic
182#440C2211yescharacteristic
183#440C2211yescharacteristic
184#440C2211yescharacteristic
185C4×Q16C2211yescharacteristic
186C4×Q16C2211yescharacteristic
187C4×Q16C2211yescharacteristic
188C4×Q16C2211yescharacteristic
189C4×Q16C2211yescharacteristic
190C4×SD16C2211yescharacteristic
191C4×SD16C2211yescharacteristic
192C4×SD16C2211yescharacteristic
193C4×SD16C2211yescharacteristic
194C4×SD16C2211yescharacteristic
195C4×SD16C2211yescharacteristic
196C4×D8C2211yescharacteristic
197#433C2211yescharacteristic
198#433C2211yescharacteristic
199#433C2211yescharacteristic
200#433C2211yescharacteristic
201#432C2211yescharacteristic
202#431C2211yescharacteristic
203C2×#41C2311yescharacteristic
204C2×Q16C2311yescharacteristic
205C2×Q16C2311yescharacteristic
206C2×Q16C2311yescharacteristic
207C2×SD16C2311yescharacteristic
208C2×SD16C2311yescharacteristic
209C2×SD16C2311yescharacteristic
210C2×SD16C2311yescharacteristic
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⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8D411yescharacteristic
224C4⋊Q8D411yescharacteristic
225C4⋊Q8C2311yescharacteristic
226C4⋊Q8C2311yescharacteristic
227C4⋊Q8C2311yescharacteristic
228C4⋊Q8C2311yescharacteristic
229C4⋊Q8C2311yescharacteristic
230C4⋊Q8C2311yescharacteristic
231C4⋊Q8C2311yescharacteristic
232C4⋊Q8C2311yescharacteristic
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235#126—21no—
236#126—21no—
237#126—21no—
238#126—21no—
239#126—21no—
240#126—21no—
241#126—21no—
242#126—21no—
243#126—21no—
244#126—21no—
245#126—21no—
246#126—21no—
247#126—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#125—21no—
259#125—21no—
260#125—21no—
261#125—21no—
262#125—21no—
263#125—21no—
264#125—21no—
265#125—21no—
266#125—21no—
267#125—21no—
268#125—21no—
269#125—21no—
270#125—21no—
271#125—21no—
272#125D411yescharacteristic
273#125D411yescharacteristic
274#125C2311yescharacteristic
275#125C2311yescharacteristic
276#125C2311yescharacteristic
277#125C2311yescharacteristic
278#125C2311yescharacteristic
279#125C2311yescharacteristic
280#125C2311yescharacteristic
281#125C2311yescharacteristic
282#125C2311yescharacteristic
283#125C2311yescharacteristic
284#125C2311yescharacteristic
285#124—21no—
286#124—21no—
287#124C2311yescharacteristic
288#124C2311yescharacteristic
289#124C2311yescharacteristic
290#123—21no—
291#123—21no—
292#123—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⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8D411yescharacteristic
319C22⋊Q8D411yescharacteristic
320C22⋊Q8D411yescharacteristic
321C22⋊Q8D411yescharacteristic
322C22⋊Q8C2311yescharacteristic
323C22⋊Q8C2311yescharacteristic
324C22⋊Q8C2311yescharacteristic
325#121C2311yescharacteristic
326C4×Q8—21no—
327C4×Q8—21no—
328C4×Q8—21no—
329C4×Q8—21no—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×Q8—21no—
333C4×Q8—21no—
334C4×Q8—21no—
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×Q8C2311yescharacteristic
349C4×Q8C2311yescharacteristic
350C4×Q8C2311yescharacteristic
351C4×Q8C2311yescharacteristic
352C4×Q8C2311yescharacteristic
353C4×Q8C2311yescharacteristic
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
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#117—21no—
378#117C2311yescharacteristic
379#117C2311yescharacteristic
380#117C2311yescharacteristic
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#103C2311yescharacteristic
447#103C2311yescharacteristic
448#103C2311yescharacteristic
449#103C2311yescharacteristic
450#103C2311yescharacteristic
451#103C2311yescharacteristic
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
470#97C2311yescharacteristic
471#97C2311yescharacteristic
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×Q8—21no—
487C2×Q8C2×D411yescharacteristic
488C2×Q8C2×D411yescharacteristic
489C2×Q8C2×D411yescharacteristic
490C2×Q8C2×D411yescharacteristic
491C2×Q8C2411yescharacteristic
492C2×Q8C2411yescharacteristic
493C2×Q8C2411yescharacteristic
494C2×Q8C2411yescharacteristic
495C2×D4—21no—
496C2×D4—21no—
497C2×D4C2411yescharacteristic
498C2×D4C2411yescharacteristic
499C22×C4—21no—
500C22×C4—21no—
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×C4C2×D411yescharacteristic
512C22×C4C2×D411yescharacteristic
513C22×C4C2411yescharacteristic
514Q16—22no—
515Q16—22no—
516Q16—22no—
517SD16—22no—
518SD16—22no—
519SD16—22no—
520SD16—22no—
521D8—22no—
522C2×C8C2411yescharacteristic
523C2×C8C2411yescharacteristic
524C2×C8C2411yescharacteristic
525C2×C8C2411yescharacteristic
526C2×C8C2411yescharacteristic
527C2×C8C2411yescharacteristic
528C2×C8C2411yescharacteristic
529C2×C8C2411yescharacteristic
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
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⋊C4—21no—
584C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
600C4⋊C4C2×D411yescharacteristic
601C4⋊C4C2411yescharacteristic
602C4⋊C4C2411yescharacteristic
603C4⋊C4C2411yescharacteristic
604C4⋊C4C2411yescharacteristic
605C4⋊C4C2411yescharacteristic
606C4⋊C4C2411yescharacteristic
607C4⋊C4C2411yescharacteristic
608C4⋊C4C2411yescharacteristic
609C4⋊C4C2411yescharacteristic
610C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
632C22⋊C4C2×D411yescharacteristic
633C22⋊C4C2×D411yescharacteristic
634C22⋊C4C2×D411yescharacteristic
635C42—21no—
636C42—21no—
637C42—21no—
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—
661C23C22×D411yescharacteristic
662Q8—21no—
663Q8—21no—
664Q8—21no—
665Q8—21no—
666Q8—21no—
667Q8—21no—
668Q8—21no—
669Q8—41no—
670Q8—41no—
671Q8—41no—
672Q8—41no—
673Q8—81no—
674Q8—81no—
675Q8—81no—
676Q8—81no—
677Q8—81no—
678Q8—81no—
679Q8—81no—
680Q82−1+412yes—
681D4—24no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—81no—
686D42−1+412yes—
687C2×C4—24no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
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—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—81no—
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×C4C22×D411yescharacteristic
718C2×C4C22×D411yescharacteristic
719C2×C4C22×D411yescharacteristic
720C2×C4C22×D411yescharacteristic
721C2×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
731C8—21no—
732C8—21no—
733C8—21no—
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—22no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22C23×D411yescharacteristic
749C4—21no—
750C4—21no—
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—21no—
762C4—22no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—41no—
776C4C2×2−1+411yescharacteristic
777C4C2×2−1+411yescharacteristic
778C2—41no—
779C2—42no—
780C2—81no—
781C2#348611yescharacteristic
782C2#358411yescharacteristic
783C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
prime radical#449C22
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. #3555C2semidirect
2. #3504C2semidirect
3. #3390C2semidirect
4. #3389C2semidirect
5. #3388C2semidirect
6. #3388C2semidirect
7. #3387C2semidirect
8. #3385C2semidirect
9. #3383C2semidirect
10. #3381C2semidirect
11. #3377C2semidirect
12. #3377C2semidirect
13. #3376C2semidirect
14. #3376C2semidirect
15. #3374C2semidirect
16. #3372C2semidirect
17. #3364C2semidirect
18. #3360C2semidirect
19. #3244C2semidirect
20. #3243C2semidirect
21. #3242C2semidirect
22. #3242C2semidirect
23. #3236C2semidirect
24. #3232C2semidirect
27. #3120C2semidirect
28. #3120C2semidirect
30. #3107C2semidirect
31. #2985C2semidirect

Maximal subgroups

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

subgroupindex
#35552
#35042
#33902
#33892
#33882
#33872
#33852
#33832
#33812
#33772
#33762
#33742
#33722
#33642
#33602
#32442
#32432
#32422
#32362
#32322
#31252
#31242
#31202
#31112
#31072
#29852