Finite Group Databasebeta

← #8429482

Subgroups — #8429482

Order 512.

4093 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59828C212yesmaximal
2#59828C211yesmaximal, characteristic
3#59681C212yesmaximal
4#59467C212yesmaximal
5#53734C218yesmaximal
6#53147C214yesmaximal
7#53146C214yesmaximal
8#52996C214yesmaximal
9#42850C214yesmaximal
10#42850C214yesmaximal
11#42710C214yesmaximal
12#39769C212yesmaximal
13#39641C212yesmaximal
14#39635C212yesmaximal
15#39183C212yesmaximal
16#39170C212yesmaximal
17#39170C212yesmaximal
18#37630C212yesmaximal
19#37630C212yesmaximal
20#37630C212yesmaximal
21#36598C211yesmaximal, characteristic
22#36593C211yesmaximal, characteristic
23#36560C211yesmaximal, characteristic
24#34951C211yesmaximal, characteristic
25#34951C211yesmaximal, characteristic
26#34951C211yesmaximal, characteristic
27C2×#557C2212yes—
28C2×#557C2212yes—
29C2×#557C2212yes—
30#2868C2212yes—
31#2868C2211yescharacteristic
32#2862C2212yes—
33#2859C2212yes—
34#2839C2218yes—
35#2839C2218yes—
36#2839C2218yes—
37#2839C2218yes—
38#2839C2218yes—
39#2839C2218yes—
40#2839C2218yes—
41#2810C2218yes—
42#2802C2218yes—
43#2802C2218yes—
44#2802C2218yes—
45#2802C2218yes—
46#2802C2218yes—
47#2794C2218yes—
48#2794C2218yes—
49#2794C2218yes—
50#2791C2218yes—
51#2791C2218yes—
52#2791C2218yes—
53#2791C2218yes—
54#2726C2218yes—
55#2726C2214yes—
56#2719C2218yes—
57#2719C2218yes—
58#2719C2218yes—
59#2719C2218yes—
60#2655C2218yes—
61#2655C2218yes—
62#2655C2218yes—
63#2655C2218yes—
64#2647C2214yes—
65#2647C2214yes—
66#2647C2214yes—
67#2645C2214yes—
68#2645C2214yes—
69#2645C2214yes—
70#2642C2214yes—
71#2642C2214yes—
72#2642C2214yes—
73#2590C2218yes—
74#2590C2218yes—
75#2585C2214yes—
76#2585C2214yes—
77#2585C2214yes—
78#2582C2211yescharacteristic
79#2582C2211yescharacteristic
80#2582C2211yescharacteristic
81#2582C2212yes—
82#2582C2212yes—
83#2571C2212yes—
84#2570C2214yes—
85#2570C2214yes—
86#2570C2214yes—
87#2568C2211yescharacteristic
88#2568C2212yes—
89#2568C2211yescharacteristic
90#2568C2212yes—
91#2568C2211yescharacteristic
92#2565C2214yes—
93#2565C2214yes—
94#2565C2214yes—
95#2552C2214yes—
96#2552C2211yescharacteristic
97#2552C2214yes—
98#2552C2214yes—
99#2552C2212yes—
100#2552C2211yescharacteristic
101#2552C2212yes—
102#2552C2211yescharacteristic
103#2552C2212yes—
104#2552C2214yes—
105#2546C2211yescharacteristic
106#2546C2214yes—
107#2546C2214yes—
108#2546C2212yes—
109#2546C2211yescharacteristic
110#2546C2212yes—
111#2546C2214yes—
112#2546C2211yescharacteristic
113#2546C2212yes—
114#2546C2214yes—
115#2546C2212yes—
116#2511C2214yes—
117#2511C2214yes—
118#2511C2214yes—
119#2511C2212yes—
120#2511C2214yes—
121#2511C2212yes—
122#2511C2212yes—
123#2511C2214yes—
124#2509C2212yes—
125#2509C2212yes—
126#2509C2214yes—
127#2509C2214yes—
128#2509C2214yes—
129#2509C2212yes—
130#2507C2214yes—
131#2507C2214yes—
132#2507C2214yes—
133#2506C2214yes—
134#2506C2214yes—
135#2506C2218yes—
136#2506C2214yes—
137#2453C2214yes—
138#2453C2214yes—
139#2453C2214yes—
140#2453C2214yes—
141#2453C2214yes—
142#2453C2214yes—
143#2453C2214yes—
144#2453C2212yes—
145#2453C2212yes—
146#2453C2212yes—
147#2453C2214yes—
148#2446C2214yes—
149#2446C2214yes—
150#2446C2214yes—
151#2446C2214yes—
152#2446C2214yes—
153#2446C2212yes—
154#2446C2212yes—
155#2446C2214yes—
156#2446C2214yes—
157#2446C2214yes—
158#2446C2212yes—
159#2446C2214yes—
160#2402C2214yes—
161#2402C2214yes—
162#2402C2214yes—
163#2370C2214yes—
164#2365C2214yes—
165#2365C2212yes—
166#2365C2212yes—
167#2365C2212yes—
168#2365C2212yes—
169#2355C2212yes—
170#2355C2212yes—
171Q8×C4⋊C4C2212yes—
172Q8×C4⋊C4C2212yes—
173Q8×C4⋊C4C2214yes—
174Q8×C4⋊C4C2212yes—
175#2330C2214yes—
176#2327C2214yes—
177#2327C2214yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2212yes—
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2211yescharacteristic
185C4×C4⋊Q8C2211yescharacteristic
186C4×C4⋊Q8C2212yes—
187C4×#125C2212yes—
188C4×#125C2212yes—
189C4×#125C2212yes—
190#2295C2212yes—
191#2295C2212yes—
192#2295C2212yes—
193#2295C2212yes—
194#2295C2212yes—
195#2295C2212yes—
196C42×Q8C2211yescharacteristic
197C42×Q8C2211yescharacteristic
198C42×Q8C2211yescharacteristic
199#557—48no—
200#557—48no—
201#557—48no—
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×#125C2312yes—
216C2×#125C2312yes—
217C2×#125C2312yes—
218C2×#125C2314yes—
219C2×#125C2314yes—
220C2×#125C2314yes—
221C2×#125C2318yes—
222C2×#125C2318yes—
223C2×#125C2318yes—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2311yescharacteristic
243#401C2318yes—
244#400C2318yes—
245#400C2314yes—
246#400C2318yes—
247#400C2314yes—
248#400C2314yes—
249#400C2318yes—
250#400C2318yes—
251#400C2318yes—
252#400C2314yes—
253#400C2314yes—
254#400C2314yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2314yes—
277#400C2314yes—
278#400C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2318yes—
290#398C2314yes—
291#398C2314yes—
292#398C2318yes—
293#398C2314yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2314yes—
300#398C2314yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#398C2318yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2318yes—
313#398C2314yes—
314#391C2312yes—
315#391C2314yes—
316#391C2314yes—
317#391C2312yes—
318#391C2312yes—
319#391C2314yes—
320#391C2312yes—
321#391C2312yes—
322#391C2312yes—
323#391C2312yes—
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2312yes—
334#391C2312yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#391C2312yes—
339#391C2314yes—
340#391C2314yes—
341#391C2314yes—
342#391C2312yes—
343#391C2312yes—
344#391C2312yes—
345#391C2312yes—
346#391C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2312yes—
359#389C2312yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#389C2318yes—
382#389C2318yes—
383#389C2318yes—
384#389C2318yes—
385#389C2314yes—
386#389C2318yes—
387#389C2318yes—
388#389C2318yes—
389#389C2318yes—
390#389C2318yes—
391#389C2318yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2318yes—
397#389C2318yes—
398#389C2314yes—
399#389C2312yes—
400#389C2312yes—
401#389C2312yes—
402#389C2312yes—
403#389C2312yes—
404#389C2312yes—
405#389C2312yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
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#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2314yes—
434#387C2314yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2318yes—
446#387C2318yes—
447#387C2318yes—
448#387C2318yes—
449#387C2318yes—
450#384C2311yescharacteristic
451#384C2311yescharacteristic
452#384C2312yes—
453#384C2312yes—
454#384C2311yescharacteristic
455#384C2312yes—
456#384C2312yes—
457#384C2312yes—
458#384C2312yes—
459#384C2314yes—
460#384C2314yes—
461#384C2312yes—
462#384C2314yes—
463#384C2314yes—
464#384C2318yes—
465#384C2314yes—
466#382C2312yes—
467#382C2312yes—
468#382C2312yes—
469#382C2314yes—
470#382C2314yes—
471#382C2314yes—
472#382C2314yes—
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2318yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2311yescharacteristic
515#376C2314yes—
516#376C2314yes—
517#376C2314yes—
518C43C2312yes—
519C43C2312yes—
520C43C2312yes—
521C43C2311yescharacteristic
522C22×Q8C2412yes—
523C22×Q8C2411yescharacteristic
524C22×Q8C2414yes—
525C22×Q8C2412yes—
526C22×Q8C2412yes—
527C22×Q8C2411yescharacteristic
528C22×Q8C2411yescharacteristic
529C4⋊Q8—28no—
530C4⋊Q8—28no—
531C4⋊Q8—24no—
532C4⋊Q8—28no—
533C4⋊Q8—24no—
534C4⋊Q8—28no—
535C4⋊Q8—24no—
536C4⋊Q8—44no—
537C4⋊Q8—44no—
538C4⋊Q8—48no—
539C4⋊Q8—48no—
540C4⋊Q8—48no—
541C4⋊Q8—48no—
542#125—28no—
543#125—28no—
544#125—44no—
545#125—48no—
546#125—48no—
547#125—48no—
548#125—416no—
549#125—416no—
550#125—416no—
551C4×Q8—24no—
552C4×Q8—24no—
553C4×Q8—24no—
554C4×Q8—28no—
555C4×Q8—28no—
556C4×Q8—24no—
557C4×Q8—24no—
558C4×Q8—28no—
559C4×Q8—24no—
560C4×Q8—24no—
561C4×Q8—24no—
562C4×Q8—48no—
563C4×Q8—42no—
564C4×Q8—48no—
565C4×Q8—48no—
566C4×Q8—48no—
567C4×Q8—48no—
568C4×Q8—48no—
569C4×Q8—48no—
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2411yescharacteristic
643C2×C42C2412yes—
644C2×C42C2414yes—
645C2×C42C2414yes—
646C2×C42C2412yes—
647C2×C42C2412yes—
648C2×C42C2411yescharacteristic
649C2×C42C2412yes—
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2411yescharacteristic
653C2×C42C2412yes—
654C2×C42C2411yescharacteristic
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2414yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2418yes—
664C2×C42C2418yes—
665C2×C42C2418yes—
666C2×C42C2412yes—
667C2×C42C2418yes—
668C2×C42C2411yescharacteristic
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2412yes—
688#95C2412yes—
689#95C2412yes—
690#95C2412yes—
691#95C2412yes—
692#95C2412yes—
693#95C2412yes—
694#95C2414yes—
695#95C2412yes—
696#95C2412yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2418yes—
701#95C2414yes—
702#95C2414yes—
703#95C2418yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2418yes—
720#95C2414yes—
721#95C2418yes—
722#95C2418yes—
723#95C2414yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735C2×Q8—22no—
736C2×Q8—24no—
737C2×Q8—24no—
738C2×Q8—22no—
739C2×Q8—24no—
740C2×Q8—28no—
741C2×Q8—22no—
742C2×Q8—24no—
743C2×Q8—22no—
744C2×Q8—22no—
745C2×Q8—22no—
746C2×Q8—22no—
747C2×Q8—24no—
748C2×Q8—24no—
749C2×Q8—24no—
750C2×Q8—24no—
751C2×Q8—28no—
752C2×Q8—22no—
753C2×Q8—28no—
754C2×Q8—24no—
755C2×Q82−1+414yes—
756C22×C4C2512yes—
757C22×C4C2512yes—
758C22×C4C2512yes—
759C22×C4C2512yes—
760C22×C4C2511yescharacteristic
761C22×C4C2512yes—
762C22×C4C2512yes—
763C22×C4C2512yes—
764C22×C4C2514yes—
765C22×C4C2514yes—
766C22×C4C2514yes—
767C22×C4C2512yes—
768C22×C4C2514yes—
769C22×C4C2514yes—
770C22×C4C2512yes—
771C22×C4C2514yes—
772C22×C4C2512yes—
773C22×C4C2518yes—
774C22×C4C2511yescharacteristic
775C22×C4C2511yescharacteristic
776C22×C4C2512yes—
777C22×C4C2511yescharacteristic
778C22×C4C2512yes—
779C22×C4C2511yescharacteristic
780C22×C4C2511yescharacteristic
781C22×C4C2511yescharacteristic
782C4⋊C4—22no—
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—28no—
788C4⋊C4—28no—
789C4⋊C4—22no—
790C4⋊C4—28no—
791C4⋊C4—24no—
792C4⋊C4—24no—
793C4⋊C4—28no—
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—22no—
797C4⋊C4—22no—
798C4⋊C4—24no—
799C4⋊C4—22no—
800C4⋊C4—22no—
801C4⋊C4—22no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—28no—
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—28no—
816C4⋊C4—28no—
817C4⋊C4—24no—
818C4⋊C4—28no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—28no—
823C4⋊C4—24no—
824C4⋊C4—22no—
825C4⋊C4—42no—
826C4⋊C4—42no—
827C4⋊C4—42no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—48no—
835C4⋊C4—48no—
836C4⋊C4—42no—
837C4⋊C4—48no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C4⋊C4—48no—
842C4⋊C4—48no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—48no—
846C4⋊C4—48no—
847C4⋊C4—48no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—48no—
853C4⋊C4—48no—
854C4⋊C42−1+414yes—
855C42—24no—
856C42—28no—
857C42—28no—
858C42—24no—
859C42—24no—
860C42—22no—
861C42—22no—
862C42—24no—
863C42—24no—
864C42—24no—
865C42—24no—
866C42—28no—
867C42—24no—
868C42—24no—
869C42—24no—
870C42—24no—
871C42—24no—
872C42—24no—
873C42—22no—
874C42—24no—
875C42—41no—
876C42—42no—
877C42—42no—
878C42—42no—
879C42—48no—
880C42—42no—
881C42—48no—
882C42—48no—
883C42—48no—
884C42H(5,𝔽2)14yes—
885C422−1+414yes—
886C422−1+414yes—
887C23C2611yescharacteristic
888Q8—28no—
889Q8—48no—
890Q8—48no—
891Q8—48no—
892Q8—44no—
893Q8—416no—
894Q8—44no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—28no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—28no—
941C2×C4—21no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—28no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4C2×H(5,𝔽2)12yes—
960C2×C4C2×H(5,𝔽2)12yes—
961C2×C4C2×H(5,𝔽2)12yes—
962C2×C4C2×2−1+414yes—
963C2×C4C2×2−1+414yes—
964C2×C4C2×2−1+412yes—
965C2×C4C2×2−1+412yes—
966C2×C4C2×2−1+412yes—
967C2×C4C2×2−1+412yes—
968C2×C4C2×2−1+412yes—
969C2×C4C2×2−1+412yes—
970C2×C4C2×2−1+412yes—
971C2×C4C2×2−1+412yes—
972C2×C4#58512yes—
973C22C22×H(5,𝔽2)11yescharacteristic
974C22C22×2−1+411yescharacteristic
975C22C22×2−1+411yescharacteristic
976C22C22×2−1+411yescharacteristic
977C22C22×2−1+411yescharacteristic
978C22C2×#58511yescharacteristic
979C222−1+611yescharacteristic
980C4—24no—
981C4—24no—
982C4—22no—
983C4—22no—
984C4—22no—
985C4—44no—
986C4—44no—
987C4—44no—
988C4—42no—
989C4—48no—
990C4—42no—
991C4—41no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—44no—
996C4—44no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—44no—
1003C4#355214yes—
1004C4#355414yes—
1005C4#355614yes—
1006C2C2×#355211yescharacteristic
1007C2C2×#355411yescharacteristic
1008C2C2×#355611yescharacteristic
1009C2#6294611yescharacteristic
1010C2#6294711yescharacteristic
1011C2#6295611yescharacteristic
1012C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#598282
#596812
#594672
#537342
#531472
#531462
#529962
#428502
#427102
#397692
#396412
#396352
#391832
#391702
#376302
#365982
#365932
#365602
#349512