Finite Group Databasebeta

← #7806583

Subgroups — #7806583

Order 512.

4528 conjugacy classes of subgroups.

The subgroup lattice has 1051 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C212yesmaximal, complemented
2#59871C212yesmaximal, complemented
3#59828C212yesmaximal, complemented
4#59672C212yesmaximal, complemented
5#59668C212yesmaximal, complemented
6#59667C212yesmaximal, complemented
7#59666C212yesmaximal, complemented
8#59665C212yesmaximal, complemented
9#59467C212yesmaximal, complemented
10#59467C212yesmaximal, complemented
11#59459C212yesmaximal, complemented
12#59456C212yesmaximal, complemented
13#47816C218yesmaximal, complemented
14#42816C214yesmaximal
15#42492C214yesmaximal
16#42489C214yesmaximal
17#37643C211yesmaximal, characteristic
18#35843C214yesmaximal
19#35786C214yesmaximal
20#35708C214yesmaximal
21#34978C211yesmaximal, characteristic
22#34978C211yesmaximal, characteristic
23#34978C211yesmaximal, characteristic
24#34216C211yesmaximal, characteristic
25#34216C211yesmaximal, characteristic
26#34209C211yesmaximal, characteristic
27C2×#557C2214yes—
28C22×C4⋊Q8C2211yescharacteristic
29C2×#519C2212yes—
30#2845C2214yes—
31#2841C2218yes—
32#2809C2218yes—
33#2806C2218yes—
34#2806C2218yes—
35#2806C2218yes—
36#2802C2218yes—
37#2799C2218yes—
38#2792C2218yes—
39#2791C2218yes—
40#2791C2218yes—
41#2755C2218yes—
42#2726C2218yes—
43#2713C2218yes—
44#2667C2218yes—
45#2665C2218yes—
46#2629C2214yes—
47#2629C2214yes—
48#2629C2214yes—
49#2629C2218yes—
50#2612C2214yes—
51#2612C2214yes—
52#2612C2214yes—
53#2608C2218yes—
54#2590C2218yes—
55#2590C2218yes—
56#2586C2218yes—
57#2585C2218yes—
58#2584C2214yes—
59#2584C2214yes—
60#2584C2214yes—
61#2584C2214yes—
62#2582C2214yes—
63#2582C2214yes—
64#2582C2218yes—
65#2581C2214yes—
66#2571C2211yescharacteristic
67#2571C2211yescharacteristic
68#2571C2211yescharacteristic
69#2567C2214yes—
70#2567C2214yes—
71#2565C2214yes—
72#2565C2218yes—
73#2565C2214yes—
74#2552C2212yes—
75#2552C2212yes—
76#2552C2212yes—
77#2552C2212yes—
78#2552C2212yes—
79#2552C2212yes—
80#2552C2211yescharacteristic
81#2552C2214yes—
82#2552C2214yes—
83#2552C2211yescharacteristic
84#2552C2211yescharacteristic
85#2552C2214yes—
86#2552C2211yescharacteristic
87#2552C2211yescharacteristic
88#2552C2211yescharacteristic
89#2551C2214yes—
90#2551C2211yescharacteristic
91#2551C2211yescharacteristic
92#2551C2211yescharacteristic
93#2550C2214yes—
94#2550C2214yes—
95#2546C2214yes—
96#2520C2218yes—
97#2509C2214yes—
98#2509C2214yes—
99#2508C2214yes—
100#2508C2214yes—
101#2507C2214yes—
102#2507C2214yes—
103#2507C2214yes—
104#2507C2214yes—
105#2507C2218yes—
106#2506C2214yes—
107#2506C2214yes—
108#2506C2214yes—
109#2506C2214yes—
110#2462C2218yes—
111#2453C2218yes—
112#2453C2214yes—
113#2453C2214yes—
114#2453C2214yes—
115#2453C2214yes—
116#2451C2214yes—
117#2451C2218yes—
118#2451C2214yes—
119#2446C2218yes—
120#2441C2212yes—
121#2441C2212yes—
122#2441C2212yes—
123#2441C2218yes—
124#2441C2212yes—
125#2441C2212yes—
126#2441C2212yes—
127#2439C2212yes—
128#2439C2212yes—
129#2439C2218yes—
130#2439C2212yes—
131#2439C2212yes—
132#2439C2212yes—
133#2439C2212yes—
134#2396C2218yes—
135#2396C2214yes—
136#2396C2214yes—
137#2396C2214yes—
138#2370C2214yes—
139#2370C2214yes—
140#2370C2214yes—
141#2370C2214yes—
142#2369C2214yes—
143#2369C2212yes—
144#2369C2212yes—
145#2369C2212yes—
146#2369C2212yes—
147#2365C2214yes—
148#2365C2212yes—
149#2365C2212yes—
150#2365C2212yes—
151#2365C2212yes—
152#2365C2212yes—
153#2365C2212yes—
154#2365C2212yes—
155#2365C2212yes—
156#2355C2214yes—
157#2351C2214yes—
158Q8×C4⋊C4C2214yes—
159Q8×C4⋊C4C2214yes—
160Q8×C4⋊C4C2214yes—
161#2345C2214yes—
162#2345C2214yes—
163#2344C2214yes—
164#2344C2214yes—
165Q8×C22⋊C4C2214yes—
166Q8×C22⋊C4C2214yes—
167#2331C2214yes—
168#2331C2214yes—
169#2327C2214yes—
170#2316C2212yes—
171#2316C2212yes—
172#2310C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2212yes—
183C4×C4⋊Q8C2212yes—
184C4×C4⋊Q8C2212yes—
185C4×#125C2212yes—
186C4×#125C2212yes—
187C4×#125C2212yes—
188C4×#125C2212yes—
189C4×#125C2212yes—
190C4×#125C2212yes—
191#2285C2211yescharacteristic
192#2285C2211yescharacteristic
193#2285C2211yescharacteristic
194#2274C2212yes—
195#2274C2212yes—
196C4×#117C2211yescharacteristic
197C4×#117C2211yescharacteristic
198C4×#117C2211yescharacteristic
199C23×Q8C2312yes—
200#557—416no—
201C2×C4⋊Q8Q8116yescomplemented
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2318yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×#125C2312yes—
214C2×#125C2312yes—
215C2×#125C2312yes—
216C2×#125C2312yes—
217C2×#125C2312yes—
218C2×#125C2312yes—
219C2×#125C2314yes—
220C2×#125C2318yes—
221C2×#125C2314yes—
222C2×#125C2314yes—
223C2×#125C2318yes—
224#519—48no—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2318yes—
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2312yes—
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2312yes—
245C2×#117C2312yes—
246C2×#117C2318yes—
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2312yes—
249C22×C42C2311yescharacteristic
250#400C2314yes—
251#400C2314yes—
252#400C2314yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#399C2314yes—
259#399C2314yes—
260#399C2314yes—
261#398C2318yes—
262#398C2314yes—
263#398C2318yes—
264#398C2318yes—
265#398C2318yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2314yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2314yes—
281#398C2314yes—
282#398C2314yes—
283#398C2314yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#396C2314yes—
288#396C2318yes—
289#396C2314yes—
290#396C2314yes—
291#396C2314yes—
292#396C2318yes—
293#396C2314yes—
294#396C2314yes—
295#395C2318yes—
296#395C2318yes—
297#395C2318yes—
298#395C2318yes—
299#395C2318yes—
300#395C2314yes—
301#395C2314yes—
302#395C2314yes—
303#393C2314yes—
304#393C2314yes—
305#393C2314yes—
306#391C2314yes—
307#391C2314yes—
308#391C2314yes—
309#391C2314yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2314yes—
314#391C2314yes—
315#391C2314yes—
316#391C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2318yes—
320#391C2318yes—
321#391C2314yes—
322#391C2318yes—
323#391C2318yes—
324#391C2318yes—
325#391C2318yes—
326#391C2318yes—
327#391C2318yes—
328#389C2312yes—
329#389C2312yes—
330#389C2312yes—
331#389C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2314yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2312yes—
353#389C2314yes—
354#389C2314yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2312yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2312yes—
369#389C2312yes—
370#389C2314yes—
371#389C2318yes—
372#389C2314yes—
373#389C2318yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2318yes—
379#389C2318yes—
380#389C2318yes—
381#389C2318yes—
382#389C2318yes—
383#389C2314yes—
384#389C2318yes—
385#389C2318yes—
386#389C2318yes—
387#389C2314yes—
388#389C2314yes—
389#389C2318yes—
390#389C2318yes—
391#389C2318yes—
392#389C2318yes—
393#389C2314yes—
394#387C2314yes—
395#387C2314yes—
396#387C2314yes—
397#387C2314yes—
398#387C2314yes—
399#387C2314yes—
400#387C2314yes—
401#387C2314yes—
402#387C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2312yes—
433#384C2312yes—
434#384C2312yes—
435#384C2312yes—
436#384C2312yes—
437#384C2312yes—
438#384C2314yes—
439#384C2318yes—
440#384C2318yes—
441#384C2314yes—
442#384C2314yes—
443#382C2312yes—
444#382C2312yes—
445#382C2312yes—
446#382C2312yes—
447#382C2312yes—
448#382C2312yes—
449#382C2318yes—
450#382C2312yes—
451#382C2312yes—
452#382C2312yes—
453#381C2318yes—
454#380C2318yes—
455#380C2318yes—
456#380C2312yes—
457#380C2312yes—
458#380C2312yes—
459#380C2312yes—
460#380C2312yes—
461#380C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2318yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2318yes—
505C4×C4⋊C4C2318yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2314yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2312yes—
516#376C2312yes—
517#376C2312yes—
518#376C2312yes—
519C43C2312yes—
520C43C2312yes—
521C43C2312yes—
522C22×Q8—44no—
523C22×Q8—44no—
524C22×Q8C2×Q8116yes—
525C22×Q8C2414yes—
526C22×Q8C2414yes—
527C22×Q8C2414yes—
528C22×Q8C2414yes—
529C22×Q8C2414yes—
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C23×C4C2414yes—
534C4⋊Q8—28no—
535C4⋊Q8—28no—
536C4⋊Q8—28no—
537C4⋊Q8—44no—
538C4⋊Q8—44no—
539C4⋊Q8—44no—
540C4⋊Q8—416no—
541C4⋊Q8C2×Q8116yes—
542C4⋊Q8C2×Q8116yes—
543C4⋊Q8C2×Q8116yes—
544C4⋊Q8C2×Q8116yes—
545#125—28no—
546#125—28no—
547#125—28no—
548#125—48no—
549#125—48no—
550#125—44no—
551#125—44no—
552#125—44no—
553#125—48no—
554#125—416no—
555#125—416no—
556C4×Q8—216no—
557C4×Q8—48no—
558C4×Q8—48no—
559C4×Q8—48no—
560C4×Q8—48no—
561C4×Q8—48no—
562C4×Q8—48no—
563C4×Q8—48no—
564C4×Q8—48no—
565C4×Q8—416no—
566C4×Q8—48no—
567C4×Q8—48no—
568#117—24no—
569#117—24no—
570#117—24no—
571#117—44no—
572#117—44no—
573#117—44no—
574#117—416no—
575#117—42no—
576#117—42no—
577#117—42no—
578C2×C4⋊C4C2×Q8116yes—
579C2×C4⋊C4C2×Q8116yes—
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2412yes—
662C2×C42C2×Q818yes—
663C2×C42C2412yes—
664C2×C42C2414yes—
665C2×C42C2418yes—
666C2×C42C2414yes—
667C2×C42C2414yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2418yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2418yes—
687C2×C42C2418yes—
688C2×C42C2418yes—
689C2×C42C2418yes—
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694#95C2412yes—
695#95C2412yes—
696#95C2412yes—
697#95C2412yes—
698#95C2412yes—
699#95C2412yes—
700#95C2412yes—
701#95C2412yes—
702#95C2412yes—
703#95C2412yes—
704#95C2412yes—
705#95C2412yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2414yes—
743#95C2418yes—
744C24C2511yescharacteristic
745C2×Q8—28no—
746C2×Q8—28no—
747C2×Q8—28no—
748C2×Q8—28no—
749C2×Q8—28no—
750C2×Q8—44no—
751C2×Q8—44no—
752C2×Q8—44no—
753C2×Q8—44no—
754C2×Q8—44no—
755C2×Q8—44no—
756C2×Q8—44no—
757C2×Q8—44no—
758C2×Q8—432no—
759C2×Q8C22×Q8116yes—
760C2×Q8C22×Q8116yes—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4C22×Q814yes—
770C22×C4C22×Q814yes—
771C22×C4C22×Q814yes—
772C22×C4C22×Q8116yes—
773C22×C4C2512yes—
774C22×C4C2512yes—
775C22×C4C2512yes—
776C22×C4C2512yes—
777C22×C4C2512yes—
778C22×C4C2514yes—
779C22×C4C2514yes—
780C22×C4C2514yes—
781C22×C4C2512yes—
782C22×C4C2512yes—
783C22×C4C2514yes—
784C22×C4C2512yes—
785C22×C4C2514yes—
786C22×C4C2514yes—
787C22×C4C2512yes—
788C22×C4C2511yescharacteristic
789C22×C4C2511yescharacteristic
790C22×C4C2511yescharacteristic
791C22×C4C2518yes—
792C22×C4C2512yes—
793C22×C4C2512yes—
794C22×C4C2512yes—
795C22×C4C2511yescharacteristic
796C22×C4C2511yescharacteristic
797C22×C4C2511yescharacteristic
798C4⋊C4—22no—
799C4⋊C4—216no—
800C4⋊C4—28no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—28no—
804C4⋊C4—28no—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—28no—
810C4⋊C4—28no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—28no—
814C4⋊C4—28no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—22no—
818C4⋊C4—22no—
819C4⋊C4—22no—
820C4⋊C4—22no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—24no—
829C4⋊C4—42no—
830C4⋊C4—42no—
831C4⋊C4—42no—
832C4⋊C4—42no—
833C4⋊C4—42no—
834C4⋊C4—42no—
835C4⋊C4—48no—
836C4⋊C4—44no—
837C4⋊C4—44no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—48no—
846C4⋊C4—44no—
847C4⋊C4—48no—
848C4⋊C4—44no—
849C4⋊C4—48no—
850C4⋊C4—44no—
851C4⋊C4—48no—
852C4⋊C4—48no—
853C4⋊C4—48no—
854C4⋊C4—48no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—48no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4C22×Q8116yes—
865C4⋊C4C22×Q8116yes—
866C4⋊C4C22×Q8116yes—
867C4⋊C4C22×Q8116yes—
868C4⋊C4H(5,𝔽2)14yes—
869C4⋊C42−1+414yes—
870C4⋊C42−1+414yes—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—24no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—42no—
877C22⋊C4—42no—
878C22⋊C4—42no—
879C22⋊C4—44no—
880C42—24no—
881C42—216no—
882C42—28no—
883C42—24no—
884C42—24no—
885C42—24no—
886C42—24no—
887C42—24no—
888C42—24no—
889C42—24no—
890C42—24no—
891C42—28no—
892C42—28no—
893C42—24no—
894C42—24no—
895C42—24no—
896C42—24no—
897C42—24no—
898C42—24no—
899C42—42no—
900C42—42no—
901C42—42no—
902C42—48no—
903C42—48no—
904C42—48no—
905C42—48no—
906C42—48no—
907C42C22×Q814yes—
908C42C22×Q814yes—
909C42C22×Q814yes—
910C42C22×Q814yes—
911C23—21no—
912C23—21no—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23C23×Q812yes—
918C23C2611yescharacteristic
919Q8—232no—
920Q8—416no—
921Q8—416no—
922Q8—88no—
923Q8—88no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—28no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—28no—
937C2×C4—21no—
938C2×C4—28no—
939C2×C4—28no—
940C2×C4—28no—
941C2×C4—24no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—416no—
987C2×C4C23×Q812yes—
988C2×C4C23×Q812yes—
989C2×C4C23×Q812yes—
990C2×C4C23×Q8116yes—
991C2×C4C23×Q812yes—
992C2×C4C23×Q812yes—
993C2×C4C23×Q812yes—
994C2×C4C2×H(5,𝔽2)14yes—
995C2×C4C2×H(5,𝔽2)12yes—
996C2×C4C2×2−1+414yes—
997C2×C4C2×2−1+414yes—
998C2×C4C2×2−1+412yes—
999C2×C4C2×2−1+412yes—
1000C2×C4#58512yes—
1001C2×C4#58512yes—
1002C2×C4#58512yes—
1003C22—22no—
1004C22—22no—
1005C22—22no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22C24×Q811yescharacteristic
1011C22C22×H(5,𝔽2)11yescharacteristic
1012C22C22×2−1+411yescharacteristic
1013C22C22×2−1+411yescharacteristic
1014C22C2×#58511yescharacteristic
1015C22C2×#58511yescharacteristic
1016C22C2×#58511yescharacteristic
1017C4—24no—
1018C4—24no—
1019C4—22no—
1020C4—216no—
1021C4—24no—
1022C4—22no—
1023C4—22no—
1024C4—44no—
1025C4—44no—
1026C4—42no—
1027C4—44no—
1028C4—42no—
1029C4—44no—
1030C4—42no—
1031C4—42no—
1032C4—42no—
1033C4—42no—
1034C4—44no—
1035C4—42no—
1036C4—42no—
1037C4—42no—
1038C4—44no—
1039C4#350114yes—
1040C4#350214yes—
1041C4#350214yes—
1042C2—42no—
1043C2C2×#350111yescharacteristic
1044C2C2×#350211yescharacteristic
1045C2C2×#350211yescharacteristic
1046C2#6301311yescharacteristic
1047C2#6303111yescharacteristic
1048C2#6303211yescharacteristic
1049C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59871C2semidirect
2. #59871C2semidirect
3. #59828C2semidirect
4. #59672C2semidirect
5. #59668C2semidirect
6. #59667C2semidirect
7. #59666C2semidirect
8. #59665C2semidirect
9. #59467C2semidirect
10. #59467C2semidirect
11. #59459C2semidirect
12. #59456C2semidirect
13. #47816C2semidirect
201. C2×C4⋊Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#598712
#598282
#596722
#596682
#596672
#596662
#596652
#594672
#594592
#594562
#478162
#428162
#424922
#424892
#376432
#358432
#357862
#357082
#349782
#342162
#342092