Finite Group Databasebeta

← #62564

Subgroups — #62564

Order 256.

890 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3565C211yesmaximal, characteristic, complemented
2#3543C211yesmaximal, characteristic, complemented
3#3371C211yesmaximal, characteristic, complemented
4#3370C211yesmaximal, characteristic, complemented
5#3368C211yesmaximal, characteristic, complemented
6#3366C211yesmaximal, characteristic, complemented
7#3325C211yesmaximal, characteristic, complemented
8#3324C211yesmaximal, characteristic, complemented
9#3323C211yesmaximal, characteristic, complemented
10#3322C211yesmaximal, characteristic, complemented
11#3319C211yesmaximal, characteristic, complemented
12#3318C211yesmaximal, characteristic, complemented
13#3318C211yesmaximal, characteristic, complemented
14#3317C211yesmaximal, characteristic, complemented
15#3311C211yesmaximal, characteristic, complemented
16#3310C211yesmaximal, characteristic, complemented
17#3310C211yesmaximal, characteristic, complemented
18#3309C211yesmaximal, characteristic, complemented
19#3241C211yesmaximal, characteristic, complemented
20#3241C211yesmaximal, characteristic, complemented
21#3240C211yesmaximal, characteristic, complemented
22#3224C211yesmaximal, characteristic, complemented
23#3224C211yesmaximal, characteristic, complemented
24#3217C211yesmaximal, characteristic, complemented
25#3183C211yesmaximal, characteristic, complemented
26#3179C211yesmaximal, characteristic, complemented
27#3179C211yesmaximal, characteristic, complemented
28#3138C211yesmaximal, characteristic, complemented
29#3136C211yesmaximal, characteristic, complemented
30#3136C211yesmaximal, characteristic, complemented
31#2967C211yesmaximal, characteristic, complemented
32#563—21no—
33#562—21no—
34#560—21no—
35#560—21no—
36#559C2211yescharacteristic
37#557C2211yescharacteristic, complemented
38#556—21no—
39#556C2211yescharacteristic, complemented
40#555C2211yescharacteristic, complemented
41#554C2211yescharacteristic, complemented
42#553C2211yescharacteristic, complemented
43#553C2211yescharacteristic, complemented
44#552—21no—
45#552C2211yescharacteristic, complemented
46#552C2211yescharacteristic, complemented
47#550C2211yescharacteristic
48#550C2211yescharacteristic
49#546—21no—
50#546C2211yescharacteristic
51#546C2211yescharacteristic
52D42—21no—
53D42C2211yescharacteristic
54D42C2211yescharacteristic
55D42C2211yescharacteristic
56#544C2211yescharacteristic, complemented
57#544C2211yescharacteristic, complemented
58#542—21no—
59#542—21no—
60#542C2211yescharacteristic, complemented
61#542C2211yescharacteristic, complemented
62#541—21no—
63#540—21no—
64#540C2211yescharacteristic
65#540C2211yescharacteristic
66#539—21no—
67#535—21no—
68#535C2211yescharacteristic
69#535C2211yescharacteristic
70#534—21no—
71#534—21no—
72#533C2211yescharacteristic, complemented
73C2×#127C2211yescharacteristic
74#529C2211yescharacteristic
75#529C2211yescharacteristic
76#529C2211yescharacteristic, complemented
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#499C2211yescharacteristic, complemented
80#496C2211yescharacteristic, complemented
81#496C2211yescharacteristic, complemented
82#495C2211yescharacteristic, complemented
83#490C2211yescharacteristic
84#490C2211yescharacteristic
85#490C2211yescharacteristic, complemented
86#490C2211yescharacteristic, complemented
87#490C2211yescharacteristic, complemented
88#490C2211yescharacteristic, complemented
89#490C2211yescharacteristic, complemented
90#490C2211yescharacteristic, complemented
91#489C2211yescharacteristic, complemented
92#489C2211yescharacteristic, complemented
93#489C2211yescharacteristic, complemented
94#489C2211yescharacteristic, complemented
95#488C2211yescharacteristic, complemented
96#488C2211yescharacteristic, complemented
97#488C2211yescharacteristic, complemented
98#488C2211yescharacteristic, complemented
99#486C2211yescharacteristic, complemented
100#486C2211yescharacteristic, complemented
101#486C2211yescharacteristic, complemented
102#486C2211yescharacteristic, complemented
103#486C2211yescharacteristic, complemented
104#486C2211yescharacteristic, complemented
105#485C2211yescharacteristic, complemented
106#485C2211yescharacteristic, complemented
107#482C2211yescharacteristic
108#482C2211yescharacteristic
109#482C2211yescharacteristic, complemented
110#482C2211yescharacteristic, complemented
111#482C2211yescharacteristic, complemented
112#482C2211yescharacteristic, complemented
113#481C2211yescharacteristic, complemented
114#481C2211yescharacteristic, complemented
115#480C2211yescharacteristic, complemented
116#480C2211yescharacteristic, complemented
117#479C2211yescharacteristic, complemented
118#479C2211yescharacteristic, complemented
119#478C2211yescharacteristic, complemented
120#478C2211yescharacteristic, complemented
121#478C2211yescharacteristic, complemented
122#478C2211yescharacteristic, complemented
123#478C2211yescharacteristic, complemented
124#478C2211yescharacteristic, complemented
125#476C2211yescharacteristic, complemented
126#476C2211yescharacteristic, complemented
127#474C2211yescharacteristic, complemented
128#474C2211yescharacteristic, complemented
129#470C2211yescharacteristic, complemented
130#469C2211yescharacteristic
131#469C2211yescharacteristic, complemented
132#469C2211yescharacteristic, complemented
133#468C2211yescharacteristic
134#468C2211yescharacteristic, complemented
135#468C2211yescharacteristic, complemented
136#468C2211yescharacteristic, complemented
137#466C2211yescharacteristic, complemented
138#466C2211yescharacteristic, complemented
139#465C2211yescharacteristic, complemented
140#465C2211yescharacteristic, complemented
141#464C2211yescharacteristic, complemented
142#464C2211yescharacteristic, complemented
143#463C2211yescharacteristic, complemented
144#463C2211yescharacteristic, complemented
145#460C2211yescharacteristic
146#460C2211yescharacteristic, complemented
147#460C2211yescharacteristic, complemented
148#460C2211yescharacteristic, complemented
149#459C2211yescharacteristic
150#459C2211yescharacteristic, complemented
151#459C2211yescharacteristic, complemented
152#459C2211yescharacteristic, complemented
153#452C2211yescharacteristic, complemented
154#452C2211yescharacteristic, complemented
155#450C2211yescharacteristic, complemented
156#450C2211yescharacteristic, complemented
157#450C2211yescharacteristic, complemented
158#450C2211yescharacteristic, complemented
159#449C2211yescharacteristic, complemented
160#449C2211yescharacteristic, complemented
161#447C2211yescharacteristic, complemented
162#447C2211yescharacteristic, complemented
163#447C2211yescharacteristic, complemented
164#447C2211yescharacteristic, complemented
165#446C2211yescharacteristic, complemented
166#446C2211yescharacteristic, complemented
167#442C2211yescharacteristic, complemented
168#442C2211yescharacteristic, complemented
169#442C2211yescharacteristic, complemented
170#441C2211yescharacteristic, complemented
171#440C2211yescharacteristic, complemented
172#440C2211yescharacteristic, complemented
173#440C2211yescharacteristic, complemented
174#440C2211yescharacteristic, complemented
175C4×SD16C2211yescharacteristic, complemented
176C4×SD16C2211yescharacteristic, complemented
177C4×D8C2211yescharacteristic, complemented
178C4×D8C2211yescharacteristic, complemented
179#436C2211yescharacteristic, complemented
180#436C2211yescharacteristic, complemented
181#435C2211yescharacteristic, complemented
182#435C2211yescharacteristic, complemented
183#435C2211yescharacteristic, complemented
184#435C2211yescharacteristic, complemented
185#433C2211yescharacteristic, complemented
186#433C2211yescharacteristic, complemented
187#432C2211yescharacteristic, complemented
188#418C2211yescharacteristic, complemented
189#418C2211yescharacteristic, complemented
190#418C2211yescharacteristic, complemented
191#418C2211yescharacteristic, complemented
192#418C2211yescharacteristic, complemented
193#418C2211yescharacteristic, complemented
194#417C2211yescharacteristic, complemented
195#417C2211yescharacteristic, complemented
196#416C2211yescharacteristic, complemented
197#416C2211yescharacteristic, complemented
198C2×#102C2211yescharacteristic, complemented
199C2×#102C2211yescharacteristic, complemented
200#405C2211yescharacteristic, complemented
201#405C2211yescharacteristic, complemented
202C4×M16C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C22×D4—21no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4C2311yescharacteristic
212C22×D4C2311yescharacteristic
213C22×D4C2311yescharacteristic
214C22×D4C2311yescharacteristic
215C2×Q16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×SD16C2311yescharacteristic
221C2×SD16C2311yescharacteristic
222C2×D8C2311yescharacteristic
223C2×D8C2311yescharacteristic
224C2×D8C2311yescharacteristic
225C2×D8C2311yescharacteristic
226C2×D8C2311yescharacteristic
227C2×M16C2311yescharacteristic
228C2×M16C2311yescharacteristic
229C2×M16C2311yescharacteristic
230C2×M16C2311yescharacteristic
231C22×C8C2311yescharacteristic
232C22×C8C2311yescharacteristic
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8C2311yescharacteristic
237C4⋊Q8C2311yescharacteristic
238C4⋊Q8C2311yescharacteristic
239C4⋊Q8C2311yescharacteristic
240#127—21no—
241#127—21no—
242#127—21no—
243#127C2311yescharacteristic
244#127C2311yescharacteristic
245#127C2311yescharacteristic
246#127C2311yescharacteristic
247#127C2311yescharacteristic
248#127C2311yescharacteristic
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#126D411yescharacteristic
260#126D411yescharacteristic
261#125—21no—
262#125—21no—
263#125—21no—
264#125—21no—
265#125—21no—
266#125—21no—
267#125D411yescharacteristic
268#125C2311yescharacteristic
269#125C2311yescharacteristic
270#125C2311yescharacteristic
271#125C2311yescharacteristic
272#125C2311yescharacteristic
273#125C2311yescharacteristic
274#124—21no—
275#124—21no—
276#124—21no—
277#124—21no—
278#124—21no—
279#124—21no—
280#124D411yescharacteristic
281#124C2311yescharacteristic
282#124C2311yescharacteristic
283#124C2311yescharacteristic
284#124C2311yescharacteristic
285#123—21no—
286#123—21no—
287#123—21no—
288#123—21no—
289#123—21no—
290#123—21no—
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#123D411yescharacteristic
302#123D411yescharacteristic
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⋊Q8D411yescharacteristic
315C22⋊Q8C2311yescharacteristic
316C22⋊Q8C2311yescharacteristic
317C22⋊Q8C2311yescharacteristic
318C22⋊Q8C2311yescharacteristic
319#121—21no—
320#121—21no—
321#121—21no—
322#121—21no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121—21no—
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#121D411yescharacteristic
341#121C2311yescharacteristic
342#121C2311yescharacteristic
343#121C2311yescharacteristic
344#121C2311yescharacteristic
345#121C2311yescharacteristic
346#121C2311yescharacteristic
347#121C2311yescharacteristic
348#121C2311yescharacteristic
349#120—21no—
350#120—21no—
351#120—21no—
352#120—21no—
353#120—21no—
354#120—21no—
355#120—21no—
356#120—21no—
357#120—21no—
358#120—21no—
359#120—21no—
360#120—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8C2311yescharacteristic
366C4×Q8C2311yescharacteristic
367C4×Q8C2311yescharacteristic
368C4×Q8C2311yescharacteristic
369C4×Q8C2311yescharacteristic
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4C2311yescharacteristic
377C4×D4C2311yescharacteristic
378C4×D4C2311yescharacteristic
379C4×D4C2311yescharacteristic
380C4×D4C2311yescharacteristic
381C4×D4C2311yescharacteristic
382C4×D4C2311yescharacteristic
383C4×D4C2311yescharacteristic
384C4×D4C2311yescharacteristic
385C4×D4C2311yescharacteristic
386C4×D4C2311yescharacteristic
387#117—21no—
388#117—21no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117C2311yescharacteristic
393#117C2311yescharacteristic
394#117C2311yescharacteristic
395#117C2311yescharacteristic
396#117C2311yescharacteristic
397#117C2311yescharacteristic
398C2×C4⋊C4—21no—
399C2×C4⋊C4C2311yescharacteristic
400C2×C4⋊C4C2311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C42C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#106C2311yescharacteristic
411#106C2311yescharacteristic
412#106C2311yescharacteristic
413#106C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416C4⋊C8C2311yescharacteristic
417C4⋊C8C2311yescharacteristic
418C4⋊C8C2311yescharacteristic
419C4⋊C8C2311yescharacteristic
420C4⋊C8C2311yescharacteristic
421C4⋊C8C2311yescharacteristic
422#103C2311yescharacteristic
423#103C2311yescharacteristic
424#103C2311yescharacteristic
425#103C2311yescharacteristic
426#103C2311yescharacteristic
427#103C2311yescharacteristic
428#103C2311yescharacteristic
429#103C2311yescharacteristic
430#102C2311yescharacteristic
431#102C2311yescharacteristic
432#102C2311yescharacteristic
433#102C2311yescharacteristic
434#102C2311yescharacteristic
435#102C2311yescharacteristic
436#102C2311yescharacteristic
437#102C2311yescharacteristic
438#102C2311yescharacteristic
439#102C2311yescharacteristic
440#102C2311yescharacteristic
441#102C2311yescharacteristic
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
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468#97C2311yescharacteristic
469#97C2311yescharacteristic
470#97C2311yescharacteristic
471#97C2311yescharacteristic
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479C24—21no—
480C24—21no—
481C24—21no—
482#41—41no—
483#41—41no—
484#41—41no—
485#41—41no—
486#41—82no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8C2×D411yescharacteristic
492C2×Q8C2411yescharacteristic
493C2×Q8C2411yescharacteristic
494C2×D4—21no—
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—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—41no—
523C2×D4—41no—
524C2×D4—41no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—82no—
529C2×D4—82no—
530C2×D4—82no—
531C2×D4—82no—
532C2×D4—82no—
533C2×D4C2×D411yescharacteristic
534C2×D4C2×D411yescharacteristic
535C2×D4C2×D411yescharacteristic
536C2×D4C2411yescharacteristic
537C2×D4C2411yescharacteristic
538C2×D4C2411yescharacteristic
539C2×D4C2411yescharacteristic
540C2×D4C2411yescharacteristic
541C2×D4C2411yescharacteristic
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4C2×D411yescharacteristic
555C22×C4C2×D411yescharacteristic
556C22×C4C2411yescharacteristic
557C22×C4C2411yescharacteristic
558C22×C4C2411yescharacteristic
559Q16—41no—
560SD16—41no—
561SD16—41no—
562SD16—41no—
563SD16—41no—
564SD16—41no—
565SD16—41no—
566D8—41no—
567D8—41no—
568D8—41no—
569D8—41no—
570D8—41no—
571M16—41no—
572M16—41no—
573M16—41no—
574M16—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8C2411yescharacteristic
578C2×C8C2411yescharacteristic
579C2×C8C2411yescharacteristic
580C2×C8C2411yescharacteristic
581C2×C8C2411yescharacteristic
582C2×C8C2411yescharacteristic
583C2×C8C2411yescharacteristic
584C2×C8C2411yescharacteristic
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⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4C2×D411yescharacteristic
612C4⋊C4C2×D411yescharacteristic
613C4⋊C4C2×D411yescharacteristic
614C4⋊C4C2×D411yescharacteristic
615C4⋊C4C2×D411yescharacteristic
616C4⋊C4C2×D411yescharacteristic
617C4⋊C4C2×D411yescharacteristic
618C4⋊C4C2×D411yescharacteristic
619C4⋊C4C2×D411yescharacteristic
620C4⋊C4C2×D411yescharacteristic
621C4⋊C4C2411yescharacteristic
622C4⋊C4C2411yescharacteristic
623C4⋊C4C2411yescharacteristic
624C4⋊C4C2411yescharacteristic
625C4⋊C4C2411yescharacteristic
626C4⋊C4C2411yescharacteristic
627C4⋊C4C2411yescharacteristic
628C4⋊C4C2411yescharacteristic
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⋊C4—21no—
661C22⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C22⋊C4C2×D411yescharacteristic
664C22⋊C4C2×D411yescharacteristic
665C22⋊C4C2×D411yescharacteristic
666C22⋊C4C2×D411yescharacteristic
667C22⋊C4C2×D411yescharacteristic
668C22⋊C4C2×D411yescharacteristic
669C22⋊C4C2×D411yescharacteristic
670C22⋊C4C2×D411yescharacteristic
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42C2×D411yescharacteristic
680C42C2×D411yescharacteristic
681C42C2411yescharacteristic
682C42C2411yescharacteristic
683C42C2411yescharacteristic
684C42C2411yescharacteristic
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—42no—
692C23—42no—
693C23—81no—
694C23—81no—
695C23—81no—
696C23—81no—
697C23—81no—
698C23—81no—
699C23—81no—
700C23—81no—
701C23—81no—
702C23—81no—
703C23C22×D411yescharacteristic
704C23C22×D411yescharacteristic
705C23C22×D411yescharacteristic
706Q8—21no—
707Q8—21no—
708Q8—21no—
709Q8—21no—
710Q8—41no—
711Q8—81no—
712Q8—81no—
713Q8—81no—
714Q8—81no—
715D4—21no—
716D4—21no—
717D4—21no—
718D4—21no—
719D4—21no—
720D4—21no—
721D4—21no—
722D4—21no—
723D4—21no—
724D4—21no—
725D4—21no—
726D4—21no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—42no—
731D4—42no—
732D4—42no—
733D4—81no—
734D4—81no—
735D4—81no—
736D4—81no—
737D4—81no—
738D4—81no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—81no—
749D4—81no—
750D4—81no—
751D4—81no—
752D4—81no—
753D4—81no—
754D4—81no—
755D4—81no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4C22×D411yescharacteristic
787C2×C4C22×D411yescharacteristic
788C2×C4C22×D411yescharacteristic
789C2×C4C22×D411yescharacteristic
790C2×C4C22×D411yescharacteristic
791C2×C4C22×D411yescharacteristic
792C2×C4C22×D411yescharacteristic
793C2×C4C22×D411yescharacteristic
794C2×C4C22×D411yescharacteristic
795C2×C4C22×D411yescharacteristic
796C2×C4C22×D411yescharacteristic
797C2×C4C2511yescharacteristic
798C8—21no—
799C8—21no—
800C8—21no—
801C8—21no—
802C8—21no—
803C8—21no—
804C8—21no—
805C8—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—162no—
834C22—162no—
835C22—162no—
836C22—162no—
837C22C23×D411yescharacteristic
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—21no—
847C4—21no—
848C4—21no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4#58511yescharacteristic
860C4#58511yescharacteristic
861C2—41no—
862C2—41no—
863C2—41no—
864C2—81no—
865C2—81no—
866C2—81no—
867C2—81no—
868C2—81no—
869C2—81no—
870C2#350011yescharacteristic
871C2#358511yescharacteristic
872C2#358511yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #529 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3565C2semidirect
2. #3543C2semidirect
3. #3371C2semidirect
4. #3370C2semidirect
5. #3368C2semidirect
6. #3366C2semidirect
7. #3325C2semidirect
8. #3324C2semidirect
9. #3323C2semidirect
10. #3322C2semidirect
11. #3319C2semidirect
12. #3318C2semidirect
13. #3318C2semidirect
14. #3317C2semidirect
15. #3311C2semidirect
16. #3310C2semidirect
17. #3310C2semidirect
18. #3309C2semidirect
19. #3241C2semidirect
20. #3241C2semidirect
21. #3240C2semidirect
22. #3224C2semidirect
23. #3224C2semidirect
24. #3217C2semidirect
25. #3183C2semidirect
26. #3179C2semidirect
27. #3179C2semidirect
28. #3138C2semidirect
29. #3136C2semidirect
30. #3136C2semidirect
31. #2967C2semidirect
37. #557C22semidirect
39. #556C22semidirect
40. #555C22semidirect
41. #554C22semidirect
42. #553C22semidirect
43. #553C22semidirect
45. #552C22semidirect
46. #552C22semidirect
56. #544C22semidirect
57. #544C22semidirect
60. #542C22semidirect
61. #542C22semidirect
72. #533C22semidirect
76. #529C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #499C22semidirect
80. #496C22semidirect
81. #496C22semidirect
82. #495C22semidirect
85. #490C22semidirect
86. #490C22semidirect
87. #490C22semidirect
88. #490C22semidirect
89. #490C22semidirect
90. #490C22semidirect
91. #489C22semidirect
92. #489C22semidirect
93. #489C22semidirect
94. #489C22semidirect
95. #488C22semidirect
96. #488C22semidirect
97. #488C22semidirect
98. #488C22semidirect
99. #486C22semidirect
100. #486C22semidirect
101. #486C22semidirect
102. #486C22semidirect
103. #486C22semidirect
104. #486C22semidirect
105. #485C22semidirect
106. #485C22semidirect
109. #482C22semidirect
110. #482C22semidirect
111. #482C22semidirect
112. #482C22semidirect
113. #481C22semidirect
114. #481C22semidirect
115. #480C22semidirect
116. #480C22semidirect
117. #479C22semidirect
118. #479C22semidirect
119. #478C22semidirect
120. #478C22semidirect
121. #478C22semidirect
122. #478C22semidirect
123. #478C22semidirect
124. #478C22semidirect
125. #476C22semidirect
126. #476C22semidirect
127. #474C22semidirect
128. #474C22semidirect
129. #470C22semidirect
131. #469C22semidirect
132. #469C22semidirect
134. #468C22semidirect
135. #468C22semidirect
136. #468C22semidirect
137. #466C22semidirect
138. #466C22semidirect
139. #465C22semidirect
140. #465C22semidirect
141. #464C22semidirect
142. #464C22semidirect
143. #463C22semidirect
144. #463C22semidirect
146. #460C22semidirect
147. #460C22semidirect
148. #460C22semidirect
150. #459C22semidirect
151. #459C22semidirect
152. #459C22semidirect
153. #452C22semidirect
154. #452C22semidirect
155. #450C22semidirect
156. #450C22semidirect
157. #450C22semidirect
158. #450C22semidirect
159. #449C22semidirect
160. #449C22semidirect
161. #447C22semidirect
162. #447C22semidirect
163. #447C22semidirect
164. #447C22semidirect
165. #446C22semidirect
166. #446C22semidirect
167. #442C22semidirect
168. #442C22semidirect
169. #442C22semidirect
170. #441C22semidirect
171. #440C22semidirect
172. #440C22semidirect
173. #440C22semidirect
174. #440C22semidirect
175. C4×SD16C22semidirect
176. C4×SD16C22semidirect
177. C4×D8C22semidirect
178. C4×D8C22semidirect
179. #436C22semidirect
180. #436C22semidirect
181. #435C22semidirect
182. #435C22semidirect
183. #435C22semidirect
184. #435C22semidirect
185. #433C22semidirect
186. #433C22semidirect
187. #432C22semidirect
188. #418C22semidirect
189. #418C22semidirect
190. #418C22semidirect
191. #418C22semidirect
192. #418C22semidirect
193. #418C22semidirect
194. #417C22semidirect
195. #417C22semidirect
196. #416C22semidirect
197. #416C22semidirect
198. C2×#102C22semidirect
199. C2×#102C22semidirect
200. #405C22semidirect
201. #405C22semidirect
202. C4×M16C22semidirect

Maximal subgroups

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

subgroupindex
#35652
#35432
#33712
#33702
#33682
#33662
#33252
#33242
#33232
#33222
#33192
#33182
#33172
#33112
#33102
#33092
#32412
#32402
#32242
#32172
#31832
#31792
#31382
#31362
#29672