Finite Group Databasebeta

← #62412

Subgroups — #62412

Order 256.

807 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3557C211yesmaximal, characteristic, complemented
2#3555C211yesmaximal, characteristic, complemented
3#3401C211yesmaximal, characteristic, complemented
4#3401C211yesmaximal, characteristic, complemented
5#3398C211yesmaximal, characteristic, complemented
6#3393C211yesmaximal, characteristic, complemented
7#3390C211yesmaximal, characteristic, complemented
8#3389C211yesmaximal, characteristic, complemented
9#3387C211yesmaximal, characteristic, complemented
10#3381C211yesmaximal, characteristic, complemented
11#3377C211yesmaximal, characteristic, complemented
12#3377C211yesmaximal, characteristic, complemented
13#3376C211yesmaximal, characteristic, complemented
14#3376C211yesmaximal, characteristic, complemented
15#3375C211yesmaximal, characteristic, complemented
16#3372C211yesmaximal, characteristic, complemented
17#3365C211yesmaximal, characteristic, complemented
18#3364C211yesmaximal, characteristic, complemented
19#3262C211yesmaximal, characteristic, complemented
20#3260C211yesmaximal, characteristic, complemented
21#3258C211yesmaximal, characteristic, complemented
22#3258C211yesmaximal, characteristic, complemented
23#3250C211yesmaximal, characteristic, complemented
24#3248C211yesmaximal, characteristic, complemented
25#3183C211yesmaximal, characteristic, complemented
26#3179C211yesmaximal, characteristic
27#3178C211yesmaximal, characteristic, complemented
28#3177C211yesmaximal, characteristic, complemented
29#3173C211yesmaximal, characteristic, complemented
30#3172C211yesmaximal, characteristic, complemented
31#2962C211yesmaximal, characteristic, complemented
32#563—21no—
33#563—21no—
34#563—21no—
35#563—21no—
36#559C2211yescharacteristic
37#559C2211yescharacteristic
38Q82C2211yescharacteristic
39#557C2211yescharacteristic
40#557C2211yescharacteristic
41#557C2211yescharacteristic
42#557C2211yescharacteristic
43#557C2211yescharacteristic
44#556—21no—
45#556C2211yescharacteristic
46#556C2211yescharacteristic
47#556C2211yescharacteristic
48#556C2211yescharacteristic
49#556C2211yescharacteristic
50#554C2211yescharacteristic
51#554C2211yescharacteristic
52#554C2211yescharacteristic
53#552—21no—
54#552—21no—
55#552—21no—
56#544—21no—
57#542—21no—
58#542—21no—
59#542C2211yescharacteristic
60#542C2211yescharacteristic
61#542C2211yescharacteristic
62#542C2211yescharacteristic
63#541—21no—
64#541—21no—
65#541—21no—
66#541C2211yescharacteristic
67#541C2211yescharacteristic
68#541C2211yescharacteristic
69#540C2211yescharacteristic
70#539—21no—
71#539—21no—
72#533C2211yescharacteristic
73#533C2211yescharacteristic
74#529C2211yescharacteristic
75#529C2211yescharacteristic
76#529C2211yescharacteristic
77#501C2211yescharacteristic
78#501C2211yescharacteristic
79#501C2211yescharacteristic
80#499C2211yescharacteristic
81#499C2211yescharacteristic
82#498C2211yescharacteristic
83#497C2211yescharacteristic
84#497C2211yescharacteristic
85#496C2211yescharacteristic
86#495C2211yescharacteristic
87#495C2211yescharacteristic
88#494C2211yescharacteristic
89#491C2211yescharacteristic
90#491C2211yescharacteristic
91#491C2211yescharacteristic
92#489C2211yescharacteristic
93#489C2211yescharacteristic
94#489C2211yescharacteristic
95#488C2211yescharacteristic
96#488C2211yescharacteristic
97#488C2211yescharacteristic
98#488C2211yescharacteristic
99#487C2211yescharacteristic
100#486C2211yescharacteristic
101#479C2211yescharacteristic
102#479C2211yescharacteristic
103#479C2211yescharacteristic
104#479C2211yescharacteristic
105#479C2211yescharacteristic
106#479C2211yescharacteristic
107#479C2211yescharacteristic
108#479C2211yescharacteristic
109#478C2211yescharacteristic
110#478C2211yescharacteristic
111#478C2211yescharacteristic
112#478C2211yescharacteristic
113#478C2211yescharacteristic
114#478C2211yescharacteristic
115#477C2211yescharacteristic
116#477C2211yescharacteristic
117#477C2211yescharacteristic
118#477C2211yescharacteristic
119#475C2211yescharacteristic
120#475C2211yescharacteristic
121#475C2211yescharacteristic
122#474C2211yescharacteristic
123#474C2211yescharacteristic
124#474C2211yescharacteristic
125#470C2211yescharacteristic
126#470C2211yescharacteristic
127#470C2211yescharacteristic
128#469C2211yescharacteristic
129#468C2211yescharacteristic
130#468C2211yescharacteristic
131#468C2211yescharacteristic
132#468C2211yescharacteristic
133#467C2211yescharacteristic
134#467C2211yescharacteristic
135#467C2211yescharacteristic
136#466C2211yescharacteristic
137#465C2211yescharacteristic
138#465C2211yescharacteristic
139#465C2211yescharacteristic
140#465C2211yescharacteristic
141#464C2211yescharacteristic
142#464C2211yescharacteristic
143#464C2211yescharacteristic
144#464C2211yescharacteristic
145#464C2211yescharacteristic
146#464C2211yescharacteristic
147#464C2211yescharacteristic
148#464C2211yescharacteristic
149#464C2211yescharacteristic
150#464C2211yescharacteristic
151#463C2211yescharacteristic
152#463C2211yescharacteristic
153#463C2211yescharacteristic
154#463C2211yescharacteristic
155#462C2211yescharacteristic
156#462C2211yescharacteristic
157#462C2211yescharacteristic
158#461C2211yescharacteristic
159#461C2211yescharacteristic
160#461C2211yescharacteristic
161#461C2211yescharacteristic
162#461C2211yescharacteristic
163#460C2211yescharacteristic
164#460C2211yescharacteristic
165#446C2211yescharacteristic
166#446C2211yescharacteristic
167#446C2211yescharacteristic
168#446C2211yescharacteristic
169#446C2211yescharacteristic
170#446C2211yescharacteristic
171C8×Q8C2211yescharacteristic
172C8×Q8C2211yescharacteristic
173#442C2211yescharacteristic
174#442C2211yescharacteristic
175#442C2211yescharacteristic
176#441C2211yescharacteristic
177#441C2211yescharacteristic
178#441C2211yescharacteristic
179#441C2211yescharacteristic
180#441C2211yescharacteristic
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#424C2211yescharacteristic
198#424C2211yescharacteristic
199C2×C4⋊C8C2211yescharacteristic
200#405C2211yescharacteristic
201#405C2211yescharacteristic
202C4×M16C2211yescharacteristic
203C2×Q16C2311yescharacteristic
204C2×Q16C2311yescharacteristic
205C2×Q16C2311yescharacteristic
206C2×Q16C2311yescharacteristic
207C2×Q16C2311yescharacteristic
208C2×Q16C2311yescharacteristic
209C2×SD16C2311yescharacteristic
210C2×SD16C2311yescharacteristic
211C2×SD16C2311yescharacteristic
212C2×SD16C2311yescharacteristic
213C2×SD16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×D8C2311yescharacteristic
218C2×D8C2311yescharacteristic
219C2×M16C2311yescharacteristic
220C2×M16C2311yescharacteristic
221C22×C8C2311yescharacteristic
222C22×C8C2311yescharacteristic
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8D411yescharacteristic
231C4⋊Q8D411yescharacteristic
232C4⋊Q8C2311yescharacteristic
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
236C4⋊Q8C2311yescharacteristic
237C4⋊Q8C2311yescharacteristic
238C4⋊Q8C2311yescharacteristic
239C4⋊Q8C2311yescharacteristic
240C4⋊Q8C2311yescharacteristic
241#127C2311yescharacteristic
242#126—21no—
243#126—21no—
244#126—21no—
245#126—21no—
246#126—21no—
247#126—21no—
248#126—21no—
249#126—21no—
250#126—21no—
251#126—21no—
252#126—21no—
253#126—21no—
254#126—21no—
255#126—21no—
256#126—21no—
257#126—21no—
258#126—21no—
259#126—21no—
260#126—21no—
261#126—21no—
262#126—21no—
263#126—21no—
264#126—21no—
265#125—21no—
266#125—21no—
267#125—21no—
268#125—21no—
269#125—21no—
270#125—21no—
271#125—21no—
272#125—21no—
273#125—21no—
274#125—21no—
275#125—21no—
276#125—21no—
277#125—21no—
278#125—21no—
279#125—21no—
280#125—21no—
281#125—21no—
282#125—21no—
283#125D411yescharacteristic
284#125D411yescharacteristic
285#125C2311yescharacteristic
286#125C2311yescharacteristic
287#125C2311yescharacteristic
288#125C2311yescharacteristic
289#125C2311yescharacteristic
290#125C2311yescharacteristic
291#125C2311yescharacteristic
292#124—21no—
293#124—21no—
294#124—21no—
295#124—21no—
296#124—21no—
297#124—21no—
298#124C2311yescharacteristic
299#124C2311yescharacteristic
300#124C2311yescharacteristic
301#124C2311yescharacteristic
302#124C2311yescharacteristic
303#124C2311yescharacteristic
304#124C2311yescharacteristic
305#123—21no—
306#123—21no—
307#123—21no—
308#123—21no—
309#123—21no—
310#123—21no—
311#123—21no—
312#123—21no—
313#123—21no—
314#123—21no—
315#123—21no—
316#123—21no—
317#123—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C22⋊Q8D411yescharacteristic
338C22⋊Q8D411yescharacteristic
339C22⋊Q8D411yescharacteristic
340C22⋊Q8D411yescharacteristic
341C22⋊Q8C2311yescharacteristic
342C22⋊Q8C2311yescharacteristic
343C22⋊Q8C2311yescharacteristic
344C22⋊Q8C2311yescharacteristic
345C22⋊Q8C2311yescharacteristic
346#121—21no—
347#121—21no—
348#121C2311yescharacteristic
349#121C2311yescharacteristic
350#121C2311yescharacteristic
351C4×Q8—21no—
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8—21no—
358C4×Q8C2311yescharacteristic
359C4×Q8C2311yescharacteristic
360C4×Q8C2311yescharacteristic
361C4×Q8C2311yescharacteristic
362C4×Q8C2311yescharacteristic
363C4×Q8C2311yescharacteristic
364C4×Q8C2311yescharacteristic
365C4×Q8C2311yescharacteristic
366C4×Q8C2311yescharacteristic
367C4×Q8C2311yescharacteristic
368C4×Q8C2311yescharacteristic
369C4×Q8C2311yescharacteristic
370C4×Q8C2311yescharacteristic
371C4×Q8C2311yescharacteristic
372C4×Q8C2311yescharacteristic
373C4×Q8C2311yescharacteristic
374C4×Q8C2311yescharacteristic
375C4×Q8C2311yescharacteristic
376C4×Q8C2311yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4C2311yescharacteristic
383C4×D4C2311yescharacteristic
384C4×D4C2311yescharacteristic
385C4×D4C2311yescharacteristic
386C4×D4C2311yescharacteristic
387C4×D4C2311yescharacteristic
388C4×D4C2311yescharacteristic
389C4×D4C2311yescharacteristic
390C4×D4C2311yescharacteristic
391#117—21no—
392#117—21no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—21no—
399#117—21no—
400#117C2311yescharacteristic
401#117C2311yescharacteristic
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C42C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#107C2311yescharacteristic
411#107C2311yescharacteristic
412#107C2311yescharacteristic
413#107C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418#106C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422C4⋊C8C2311yescharacteristic
423C4⋊C8C2311yescharacteristic
424C4⋊C8C2311yescharacteristic
425C4⋊C8C2311yescharacteristic
426C4⋊C8C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430C4⋊C8C2311yescharacteristic
431C4⋊C8C2311yescharacteristic
432C4⋊C8C2311yescharacteristic
433C4⋊C8C2311yescharacteristic
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#103C2311yescharacteristic
453#103C2311yescharacteristic
454#102C2311yescharacteristic
455#102C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462#102C2311yescharacteristic
463#102C2311yescharacteristic
464#102C2311yescharacteristic
465#102C2311yescharacteristic
466#97C2311yescharacteristic
467#97C2311yescharacteristic
468#97C2311yescharacteristic
469#97C2311yescharacteristic
470#97C2311yescharacteristic
471#97C2311yescharacteristic
472C4×C8C2311yescharacteristic
473C4×C8C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8C2×D411yescharacteristic
484C2×Q8C2×D411yescharacteristic
485C2×Q8C2×D411yescharacteristic
486C2×Q8C2×D411yescharacteristic
487C2×Q8C2411yescharacteristic
488C2×Q8C2411yescharacteristic
489C2×Q8C2411yescharacteristic
490C2×Q8C2411yescharacteristic
491C2×Q8C2411yescharacteristic
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4C2411yescharacteristic
498C2×D4C2411yescharacteristic
499C2×D4C2411yescharacteristic
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×C4C2×D411yescharacteristic
510C22×C4C2×D411yescharacteristic
511C22×C4C2411yescharacteristic
512Q16—22no—
513Q16—22no—
514Q16—41no—
515Q16—41no—
516Q16—41no—
517Q16—41no—
518SD16—22no—
519SD16—41no—
520SD16—41no—
521SD16—41no—
522SD16—41no—
523SD16—41no—
524SD16—41no—
525SD16—41no—
526D8—22no—
527D8—41no—
528M16—22no—
529M16—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8C2411yescharacteristic
533C2×C8C2411yescharacteristic
534C2×C8C2411yescharacteristic
535C2×C8C2411yescharacteristic
536C2×C8C2411yescharacteristic
537C2×C8C2411yescharacteristic
538C2×C8C2411yescharacteristic
539C2×C8C2411yescharacteristic
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⋊C4—21no—
586C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
602C4⋊C4C2×D411yescharacteristic
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⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4C2×D411yescharacteristic
643C22⋊C4C2×D411yescharacteristic
644C22⋊C4C2×D411yescharacteristic
645C22⋊C4C2×D411yescharacteristic
646C42—21no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42C2×D411yescharacteristic
662C42C2×D411yescharacteristic
663C42C2411yescharacteristic
664C42C2411yescharacteristic
665C42C2411yescharacteristic
666C42C2411yescharacteristic
667C42C2411yescharacteristic
668C42C2411yescharacteristic
669C23—21no—
670C23—21no—
671C23—21no—
672C23C22×D411yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—21no—
676Q8—21no—
677Q8—21no—
678Q8—21no—
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—21no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687Q8—81no—
688Q8—81no—
689Q8—81no—
690Q8—81no—
691Q8—81no—
692D4—21no—
693D4—21no—
694D4—21no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—81no—
699D4—81no—
700D4—81no—
701D4—81no—
702D4—81no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4C22×D411yescharacteristic
730C2×C4C22×D411yescharacteristic
731C2×C4C22×D411yescharacteristic
732C2×C4C22×D411yescharacteristic
733C2×C4C22×D411yescharacteristic
734C2×C4C22×D411yescharacteristic
735C2×C4C22×D411yescharacteristic
736C2×C4C22×D411yescharacteristic
737C2×C4C22×D411yescharacteristic
738C2×C4C22×D411yescharacteristic
739C2×C4C22×D411yescharacteristic
740C2×C4C22×D411yescharacteristic
741C2×C4C22×D411yescharacteristic
742C2×C4C2511yescharacteristic
743C8—21no—
744C8—21no—
745C8—21no—
746C8—21no—
747C8—21no—
748C8—21no—
749C8—21no—
750C82−1+412yes—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22C23×D411yescharacteristic
764C4—21no—
765C4—21no—
766C4—21no—
767C4—21no—
768C4—21no—
769C4—21no—
770C4—21no—
771C4—21no—
772C4—21no—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4C2×2−1+411yescharacteristic
791C4#58511yescharacteristic
792C2—41no—
793C2—81no—
794C2—81no—
795C2—81no—
796C2#349711yescharacteristic
797C2#358411yescharacteristic
798C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
prime radical#3179C2
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. #3555C2semidirect
3. #3401C2semidirect
4. #3401C2semidirect
5. #3398C2semidirect
6. #3393C2semidirect
7. #3390C2semidirect
8. #3389C2semidirect
9. #3387C2semidirect
10. #3381C2semidirect
11. #3377C2semidirect
12. #3377C2semidirect
13. #3376C2semidirect
14. #3376C2semidirect
15. #3375C2semidirect
16. #3372C2semidirect
17. #3365C2semidirect
18. #3364C2semidirect
19. #3262C2semidirect
20. #3260C2semidirect
21. #3258C2semidirect
22. #3258C2semidirect
23. #3250C2semidirect
24. #3248C2semidirect
25. #3183C2semidirect
27. #3178C2semidirect
28. #3177C2semidirect
29. #3173C2semidirect
30. #3172C2semidirect
31. #2962C2semidirect

Maximal subgroups

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

subgroupindex
#35572
#35552
#34012
#33982
#33932
#33902
#33892
#33872
#33812
#33772
#33762
#33752
#33722
#33652
#33642
#32622
#32602
#32582
#32502
#32482
#31832
#31792
#31782
#31772
#31732
#31722
#29622