Finite Group Databasebeta

← #61919

Subgroups — #61919

Order 256.

862 conjugacy classes of subgroups.

The subgroup lattice has 847 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3557C211yesmaximal, characteristic, complemented
2#3506C211yesmaximal, characteristic, complemented
3#3403C211yesmaximal, characteristic, complemented
4#3402C211yesmaximal, characteristic, complemented
5#3401C211yesmaximal, characteristic, complemented
6#3401C211yesmaximal, characteristic, complemented
7#3399C211yesmaximal, characteristic, complemented
8#3397C211yesmaximal, characteristic, complemented
9#3396C211yesmaximal, characteristic, complemented
10#3394C211yesmaximal, characteristic, complemented
11#3377C211yesmaximal, characteristic, complemented
12#3376C211yesmaximal, characteristic, complemented
13#3371C211yesmaximal, characteristic, complemented
14#3370C211yesmaximal, characteristic, complemented
15#3368C211yesmaximal, characteristic, complemented
16#3366C211yesmaximal, characteristic, complemented
17#3365C211yesmaximal, characteristic, complemented
18#3361C211yesmaximal, characteristic, complemented
19#3224C211yesmaximal, characteristic, complemented
20#3224C211yesmaximal, characteristic, complemented
21#3222C211yesmaximal, characteristic, complemented
22#3220C211yesmaximal, characteristic, complemented
23#3219C211yesmaximal, characteristic, complemented
24#3212C211yesmaximal, characteristic, complemented
25#3125C211yesmaximal, characteristic, complemented
26#3124C211yesmaximal, characteristic, complemented
27#3120C211yesmaximal, characteristic, complemented
28#3119C211yesmaximal, characteristic, complemented
29#3114C211yesmaximal, characteristic, complemented
30#3105C211yesmaximal, characteristic, complemented
31#2985C211yesmaximal, characteristic, complemented
32#563—21no—
33#563—21no—
34#559C2211yescharacteristic
35#559C2211yescharacteristic
36#559C2211yescharacteristic
37#559C2211yescharacteristic
38#559C2211yescharacteristic, complemented
39#559C2211yescharacteristic, complemented
40#557C2211yescharacteristic, complemented
41#557C2211yescharacteristic, complemented
42#556C2211yescharacteristic
43#556C2211yescharacteristic
44#556C2211yescharacteristic, complemented
45#556C2211yescharacteristic, complemented
46#555—21no—
47#554C2211yescharacteristic, complemented
48#554C2211yescharacteristic, complemented
49#553—21no—
50#553—21no—
51#552—21no—
52#552—21no—
53#550C2211yescharacteristic
54#550C2211yescharacteristic
55#547—21no—
56#542—21no—
57#542—21no—
58#542C2211yescharacteristic
59#542C2211yescharacteristic
60#541C2211yescharacteristic
61#540C2211yescharacteristic
62#539—21no—
63#539—21no—
64#538—21no—
65#538—21no—
66#535C2211yescharacteristic
67#535C2211yescharacteristic
68#533C2211yescharacteristic
69#532C2211yescharacteristic
70#529C2211yescharacteristic
71#529C2211yescharacteristic
72#525—21no—
73#525—21no—
74#520C2211yescharacteristic
75#520C2211yescharacteristic
76C2×C4×D4C2211yescharacteristic
77#497C2211yescharacteristic
78#497C2211yescharacteristic, complemented
79#496C2211yescharacteristic
80#496C2211yescharacteristic
81#496C2211yescharacteristic
82#496C2211yescharacteristic, complemented
83#495C2211yescharacteristic
84#495C2211yescharacteristic
85#495C2211yescharacteristic, complemented
86#495C2211yescharacteristic, complemented
87#493C2211yescharacteristic
88#492C2211yescharacteristic
89#491C2211yescharacteristic, complemented
90#490C2211yescharacteristic
91#490C2211yescharacteristic
92#490C2211yescharacteristic, complemented
93#489C2211yescharacteristic
94#489C2211yescharacteristic
95#488C2211yescharacteristic
96#488C2211yescharacteristic
97#488C2211yescharacteristic, complemented
98#488C2211yescharacteristic, complemented
99#486C2211yescharacteristic
100#486C2211yescharacteristic
101#484C2211yescharacteristic
102#483C2211yescharacteristic
103#481C2211yescharacteristic
104#480C2211yescharacteristic
105#479C2211yescharacteristic, complemented
106#479C2211yescharacteristic, complemented
107#478C2211yescharacteristic
108#478C2211yescharacteristic
109#478C2211yescharacteristic
110#478C2211yescharacteristic
111#478C2211yescharacteristic, complemented
112#478C2211yescharacteristic, complemented
113#477C2211yescharacteristic, complemented
114#476C2211yescharacteristic, complemented
115#475C2211yescharacteristic, complemented
116#474C2211yescharacteristic, complemented
117#464C2211yescharacteristic
118#464C2211yescharacteristic
119#464C2211yescharacteristic
120#464C2211yescharacteristic
121#464C2211yescharacteristic, complemented
122#464C2211yescharacteristic, complemented
123#464C2211yescharacteristic, complemented
124#464C2211yescharacteristic, complemented
125#463C2211yescharacteristic
126#463C2211yescharacteristic
127#463C2211yescharacteristic
128#463C2211yescharacteristic
129#463C2211yescharacteristic
130#463C2211yescharacteristic
131#463C2211yescharacteristic
132#463C2211yescharacteristic
133#463C2211yescharacteristic, complemented
134#463C2211yescharacteristic, complemented
135#463C2211yescharacteristic, complemented
136#463C2211yescharacteristic, complemented
137#462C2211yescharacteristic, complemented
138#462C2211yescharacteristic, complemented
139#461C2211yescharacteristic, complemented
140#461C2211yescharacteristic, complemented
141#460C2211yescharacteristic
142#460C2211yescharacteristic
143#460C2211yescharacteristic
144#460C2211yescharacteristic
145#460C2211yescharacteristic, complemented
146#460C2211yescharacteristic, complemented
147#459C2211yescharacteristic
148#459C2211yescharacteristic
149#459C2211yescharacteristic
150#459C2211yescharacteristic
151#459C2211yescharacteristic, complemented
152#459C2211yescharacteristic, complemented
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic
156#452C2211yescharacteristic
157#450C2211yescharacteristic
158#450C2211yescharacteristic
159#449C2211yescharacteristic
160#449C2211yescharacteristic
161#449C2211yescharacteristic
162#449C2211yescharacteristic
163#447C2211yescharacteristic
164#447C2211yescharacteristic
165#446C2211yescharacteristic, complemented
166#446C2211yescharacteristic, complemented
167#446C2211yescharacteristic, complemented
168#446C2211yescharacteristic, complemented
169#446C2211yescharacteristic, complemented
170#446C2211yescharacteristic, complemented
171C8×Q8C2211yescharacteristic, complemented
172C8×Q8C2211yescharacteristic, complemented
173#442C2211yescharacteristic
174#442C2211yescharacteristic
175#442C2211yescharacteristic, complemented
176#442C2211yescharacteristic, complemented
177#441C2211yescharacteristic, complemented
178#441C2211yescharacteristic, complemented
179#440C2211yescharacteristic
180#440C2211yescharacteristic
181#440C2211yescharacteristic, complemented
182#440C2211yescharacteristic, complemented
183#440C2211yescharacteristic, complemented
184#440C2211yescharacteristic, complemented
185C4×Q16C2211yescharacteristic, complemented
186C4×Q16C2211yescharacteristic, complemented
187C4×SD16C2211yescharacteristic
188C4×SD16C2211yescharacteristic
189C4×SD16C2211yescharacteristic, complemented
190C4×SD16C2211yescharacteristic, complemented
191C4×SD16C2211yescharacteristic, complemented
192C4×SD16C2211yescharacteristic, complemented
193C4×D8C2211yescharacteristic
194C4×D8C2211yescharacteristic
195C4×D8C2211yescharacteristic, complemented
196C4×D8C2211yescharacteristic, complemented
197#433C2211yescharacteristic
198#433C2211yescharacteristic
199#433C2211yescharacteristic
200#433C2211yescharacteristic
201#432C2211yescharacteristic
202#431C2211yescharacteristic
203C2×#41—21no—
204C2×#41—21no—
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×D4C2311yescharacteristic
208C23×C4—21no—
209C2×Q16C2311yescharacteristic
210C2×Q16C2311yescharacteristic
211C2×Q16C2311yescharacteristic
212C2×Q16C2311yescharacteristic
213C2×SD16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×SD16C2311yescharacteristic
221C2×SD16C2311yescharacteristic
222C2×SD16C2311yescharacteristic
223C2×SD16C2311yescharacteristic
224C2×SD16C2311yescharacteristic
225C2×D8C2311yescharacteristic
226C2×D8C2311yescharacteristic
227C2×D8C2311yescharacteristic
228C2×D8C2311yescharacteristic
229C2×D8C2311yescharacteristic
230C2×D8C2311yescharacteristic
231C2×D8C2311yescharacteristic
232C2×D8C2311yescharacteristic
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8D411yescharacteristic
236C4⋊Q8D411yescharacteristic
237C4⋊Q8C2311yescharacteristic
238C4⋊Q8C2311yescharacteristic
239C4⋊Q8C2311yescharacteristic
240C4⋊Q8C2311yescharacteristic
241#127C2311yescharacteristic
242#127C2311yescharacteristic
243#127C2311yescharacteristic
244#127C2311yescharacteristic
245#127C2311yescharacteristic
246#127C2311yescharacteristic
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#125—21no—
262#125—21no—
263#125—21no—
264#125—21no—
265#125—21no—
266#125—21no—
267#125D411yescharacteristic
268#125D411yescharacteristic
269#125C2311yescharacteristic
270#125C2311yescharacteristic
271#125C2311yescharacteristic
272#125C2311yescharacteristic
273#124—21no—
274#124—21no—
275#124—21no—
276#124—21no—
277#124—21no—
278#124—21no—
279#124—21no—
280#124—21no—
281#124C2311yescharacteristic
282#124C2311yescharacteristic
283#124C2311yescharacteristic
284#124C2311yescharacteristic
285#124C2311yescharacteristic
286#124C2311yescharacteristic
287#124C2311yescharacteristic
288#124C2311yescharacteristic
289#124C2311yescharacteristic
290#124C2311yescharacteristic
291#123—21no—
292#123—21no—
293#123—21no—
294#123—21no—
295#123—21no—
296#123—21no—
297#123—21no—
298#123—21no—
299#123—21no—
300#123—21no—
301#123—21no—
302#123—21no—
303#123—21no—
304#123—21no—
305#123—21no—
306#123—21no—
307#123—21no—
308#123—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⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8D411yescharacteristic
322C22⋊Q8D411yescharacteristic
323C22⋊Q8D411yescharacteristic
324C22⋊Q8D411yescharacteristic
325C22⋊Q8C2311yescharacteristic
326C22⋊Q8C2311yescharacteristic
327#121—21no—
328#121—21no—
329#121—21no—
330#121—21no—
331#121—21no—
332#121—21no—
333#121—21no—
334#121—21no—
335#121—21no—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340#121—21no—
341#121C2311yescharacteristic
342#121C2311yescharacteristic
343#120—21no—
344#120—21no—
345#120—21no—
346#120—21no—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8C2311yescharacteristic
350C4×Q8C2311yescharacteristic
351C4×Q8C2311yescharacteristic
352C4×Q8C2311yescharacteristic
353C4×Q8C2311yescharacteristic
354C4×Q8C2311yescharacteristic
355C4×Q8C2311yescharacteristic
356C4×Q8C2311yescharacteristic
357C4×Q8C2311yescharacteristic
358C4×Q8C2311yescharacteristic
359C4×Q8C2311yescharacteristic
360C4×Q8C2311yescharacteristic
361C4×Q8C2311yescharacteristic
362C4×Q8C2311yescharacteristic
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4C2311yescharacteristic
380C4×D4C2311yescharacteristic
381C4×D4C2311yescharacteristic
382C4×D4C2311yescharacteristic
383C4×D4C2311yescharacteristic
384C4×D4C2311yescharacteristic
385C4×D4C2311yescharacteristic
386C4×D4C2311yescharacteristic
387C4×D4C2311yescharacteristic
388C4×D4C2311yescharacteristic
389C4×D4C2311yescharacteristic
390C4×D4C2311yescharacteristic
391C4×D4C2311yescharacteristic
392C4×D4C2311yescharacteristic
393#117—21no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—21no—
399#117—21no—
400#117—21no—
401#117C2311yescharacteristic
402#117C2311yescharacteristic
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4C2311yescharacteristic
408C2×C22⋊C4—21no—
409C2×C42C2311yescharacteristic
410#107C2311yescharacteristic
411#107C2311yescharacteristic
412#107C2311yescharacteristic
413#107C2311yescharacteristic
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#102C2311yescharacteristic
443#102C2311yescharacteristic
444#102C2311yescharacteristic
445#102C2311yescharacteristic
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
470#97C2311yescharacteristic
471#97C2311yescharacteristic
472C4×C8C2311yescharacteristic
473C4×C8C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479#41—41no—
480#41—41no—
481#41—41no—
482#41—41no—
483#41—82no—
484#41—82no—
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×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4C2411yescharacteristic
515C2×D4C2411yescharacteristic
516C2×D4C2411yescharacteristic
517C2×D4C2411yescharacteristic
518C2×D4C2411yescharacteristic
519C2×D4C2411yescharacteristic
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—82no—
538C22×C4C2×D411yescharacteristic
539C22×C4C2×D411yescharacteristic
540C22×C4C2411yescharacteristic
541Q16—41no—
542Q16—41no—
543Q16—41no—
544Q16—41no—
545SD16—41no—
546SD16—41no—
547SD16—41no—
548SD16—41no—
549SD16—41no—
550SD16—41no—
551SD16—41no—
552SD16—41no—
553SD16—41no—
554SD16—41no—
555SD16—41no—
556SD16—41no—
557D8—41no—
558D8—41no—
559D8—41no—
560D8—41no—
561D8—41no—
562D8—41no—
563D8—41no—
564D8—41no—
565C2×C8C2411yescharacteristic
566C2×C8C2411yescharacteristic
567C2×C8C2411yescharacteristic
568C2×C8C2411yescharacteristic
569C2×C8C2411yescharacteristic
570C2×C8C2411yescharacteristic
571C2×C8C2411yescharacteristic
572C2×C8C2411yescharacteristic
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⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4C2×D411yescharacteristic
601C4⋊C4C2×D411yescharacteristic
602C4⋊C4C2×D411yescharacteristic
603C4⋊C4C2×D411yescharacteristic
604C4⋊C4C2×D411yescharacteristic
605C4⋊C4C2×D411yescharacteristic
606C4⋊C4C2×D411yescharacteristic
607C4⋊C4C2×D411yescharacteristic
608C4⋊C4C2×D411yescharacteristic
609C4⋊C4C2×D411yescharacteristic
610C4⋊C4C2×D411yescharacteristic
611C4⋊C4C2×D411yescharacteristic
612C4⋊C4C2×D411yescharacteristic
613C4⋊C4C2×D411yescharacteristic
614C4⋊C4C2×D411yescharacteristic
615C4⋊C4C2×D411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C4⋊C4C2411yescharacteristic
620C4⋊C4C2411yescharacteristic
621C4⋊C4C2411yescharacteristic
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⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C22⋊C4C2×D411yescharacteristic
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42C2×D411yescharacteristic
675C42C2×D411yescharacteristic
676C42C2411yescharacteristic
677C42C2411yescharacteristic
678C42C2411yescharacteristic
679C42C2411yescharacteristic
680C42C2411yescharacteristic
681C42C2411yescharacteristic
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—42no—
689C23—81no—
690C23—81no—
691C23C22×D411yescharacteristic
692Q8—21no—
693Q8—21no—
694Q8—21no—
695Q8—21no—
696Q8—21no—
697Q8—21no—
698Q8—21no—
699Q8—21no—
700Q8—41no—
701Q8—41no—
702Q8—41no—
703Q8—41no—
704Q8—81no—
705Q8—81no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—21no—
714D4—21no—
715D4—21no—
716D4—21no—
717D4—21no—
718D4—42no—
719D4—42no—
720D4—42no—
721D4—42no—
722D4—81no—
723D4—81no—
724D4—81no—
725D4—81no—
726D4—81no—
727D4—81no—
728D4—81no—
729D4—81no—
730D4—81no—
731D4—81no—
732D4—81no—
733D4—81no—
734D4—81no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4C22×D411yescharacteristic
767C2×C4C22×D411yescharacteristic
768C2×C4C22×D411yescharacteristic
769C2×C4C22×D411yescharacteristic
770C2×C4C22×D411yescharacteristic
771C2×C4C22×D411yescharacteristic
772C2×C4C22×D411yescharacteristic
773C2×C4C22×D411yescharacteristic
774C2×C4C22×D411yescharacteristic
775C2×C4C22×D411yescharacteristic
776C2×C4C22×D411yescharacteristic
777C2×C4C22×D411yescharacteristic
778C2×C4C22×D411yescharacteristic
779C2×C4C2511yescharacteristic
780C8—21no—
781C8—21no—
782C8—21no—
783C8—21no—
784C8—21no—
785C8—21no—
786C8—21no—
787C8—21no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—84no—
810C22C23×D411yescharacteristic
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4#58511yescharacteristic
835C4#58511yescharacteristic
836C2—41no—
837C2—81no—
838C2—81no—
839C2—81no—
840C2—81no—
841C2—81no—
842C2—81no—
843C2#348711yescharacteristic
844C2#358411yescharacteristic
845C2#358511yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
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. #3506C2semidirect
3. #3403C2semidirect
4. #3402C2semidirect
5. #3401C2semidirect
6. #3401C2semidirect
7. #3399C2semidirect
8. #3397C2semidirect
9. #3396C2semidirect
10. #3394C2semidirect
11. #3377C2semidirect
12. #3376C2semidirect
13. #3371C2semidirect
14. #3370C2semidirect
15. #3368C2semidirect
16. #3366C2semidirect
17. #3365C2semidirect
18. #3361C2semidirect
19. #3224C2semidirect
20. #3224C2semidirect
21. #3222C2semidirect
22. #3220C2semidirect
23. #3219C2semidirect
24. #3212C2semidirect
25. #3125C2semidirect
26. #3124C2semidirect
27. #3120C2semidirect
28. #3119C2semidirect
29. #3114C2semidirect
30. #3105C2semidirect
31. #2985C2semidirect
38. #559C22semidirect
39. #559C22semidirect
40. #557C22semidirect
41. #557C22semidirect
44. #556C22semidirect
45. #556C22semidirect
47. #554C22semidirect
48. #554C22semidirect
78. #497C22semidirect
82. #496C22semidirect
85. #495C22semidirect
86. #495C22semidirect
89. #491C22semidirect
92. #490C22semidirect
97. #488C22semidirect
98. #488C22semidirect
105. #479C22semidirect
106. #479C22semidirect
111. #478C22semidirect
112. #478C22semidirect
113. #477C22semidirect
114. #476C22semidirect
115. #475C22semidirect
116. #474C22semidirect
121. #464C22semidirect
122. #464C22semidirect
123. #464C22semidirect
124. #464C22semidirect
133. #463C22semidirect
134. #463C22semidirect
135. #463C22semidirect
136. #463C22semidirect
137. #462C22semidirect
138. #462C22semidirect
139. #461C22semidirect
140. #461C22semidirect
145. #460C22semidirect
146. #460C22semidirect
151. #459C22semidirect
152. #459C22semidirect
165. #446C22semidirect
166. #446C22semidirect
167. #446C22semidirect
168. #446C22semidirect
169. #446C22semidirect
170. #446C22semidirect
171. C8×Q8C22semidirect
172. C8×Q8C22semidirect
175. #442C22semidirect
176. #442C22semidirect
177. #441C22semidirect
178. #441C22semidirect
181. #440C22semidirect
182. #440C22semidirect
183. #440C22semidirect
184. #440C22semidirect
185. C4×Q16C22semidirect
186. C4×Q16C22semidirect
189. C4×SD16C22semidirect
190. C4×SD16C22semidirect
191. C4×SD16C22semidirect
192. C4×SD16C22semidirect
195. C4×D8C22semidirect
196. C4×D8C22semidirect

Maximal subgroups

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

subgroupindex
#35572
#35062
#34032
#34022
#34012
#33992
#33972
#33962
#33942
#33772
#33762
#33712
#33702
#33682
#33662
#33652
#33612
#32242
#32222
#32202
#32192
#32122
#31252
#31242
#31202
#31192
#31142
#31052
#29852