Finite Group Databasebeta

← #7712565

Subgroups — #7712565

Order 512.

4862 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59291C214yesmaximal, complemented
2#59113C214yesmaximal, complemented
3#46153C212yesmaximal, complemented
4#46152C212yesmaximal, complemented
5#46006C212yesmaximal, complemented
6#46005C212yesmaximal, complemented
7#39749C212yesmaximal, complemented
8#39662C214yesmaximal, complemented
9#39661C214yesmaximal, complemented
10#39639C212yesmaximal, complemented
11#39631C212yesmaximal
12#39623C212yesmaximal, complemented
13#39614C212yesmaximal
14#39365C212yesmaximal, complemented
15#37687C214yesmaximal, complemented
16#37561C212yesmaximal, complemented
17#37313C214yesmaximal, complemented
18#36645C211yesmaximal, characteristic, complemented
19C2×#2859C211yesmaximal, characteristic, complemented
20#36563C212yesmaximal, complemented
21#36189C212yesmaximal, complemented
22#36189C212yesmaximal, complemented
23#36180C212yesmaximal, complemented
24#35284C212yesmaximal, complemented
25#35275C212yesmaximal, complemented
26#34382C212yesmaximal
27C4×#529C211yesmaximal, characteristic
28C2×#554C2214yes—
29C2×#544C2214yes—
30C2×#533C2212yes—
31C2×#529C2211yescharacteristic
32C22×#125C2212yes—
33#2868C2211yescharacteristic
34#2868C2211yescharacteristic
35#2868C2212yes—
36#2862C2212yes—
37#2859C2212yes—
38#2859C2212yes—
39#2859C2212yes—
40#2859C2212yes—
41#2859C2212yes—
42#2859C2212yes—
43#2859C2212yes—
44#2859C2212yes—
45#2859C2212yes—
46#2859C2212yes—
47#2859C2212yes—
48#2857C2212yes—
49#2857C2212yes—
50#2857C2212yes—
51#2857C2212yes—
52#2857C2212yes—
53#2857C2212yes—
54#2845C2214yes—
55#2844C2214yes—
56#2809C2214yes—
57#2807C2218yes—
58#2806C2214yes—
59#2805C2214yes—
60#2802C2218yes—
61#2792C2218yes—
62#2774C2218yes—
63#2768C2218yes—
64#2734C2214yes—
65#2732C2214yes—
66#2726C2218yes—
67#2726C2214yes—
68#2726C2218yes—
69#2726C2214yes—
70#2720C2218yes—
71#2720C2218yes—
72#2713C2218yes—
73#2704C2218yes—
74#2704C2218yes—
75#2683C2214yes—
76#2666C2218yes—
77#2660C2214yes—
78#2660C2214yes—
79#2659C2214yes—
80#2647C2214yes—
81#2646C2214yes—
82#2629C2214yes—
83#2590C2218yes—
84#2582C2214yes—
85#2570C2214yes—
86#2570C2214yes—
87#2567C2214yes—
88#2567C2214yes—
89#2556C2218yes—
90#2552C2214yes—
91#2552C2214yes—
92#2552C2214yes—
93#2552C2214yes—
94#2552C2214yes—
95#2551C2214yes—
96#2551C2214yes—
97#2550C2214yes—
98#2550C2214yes—
99#2511C2214yes—
100#2511C2214yes—
101#2507C2214yes—
102#2507C2214yes—
103#2507C2214yes—
104#2507C2214yes—
105#2507C2214yes—
106#2507C2214yes—
107#2502C2214yes—
108#2502C2214yes—
109#2497C2214yes—
110#2497C2214yes—
111#2497C2214yes—
112#2497C2214yes—
113#2487C2214yes—
114#2487C2214yes—
115#2473C2218yes—
116#2462C2218yes—
117#2451C2214yes—
118#2451C2214yes—
119#2449C2218yes—
120#2446C2214yes—
121#2446C2214yes—
122#2442C2214yes—
123#2442C2214yes—
124#2441C2214yes—
125#2441C2214yes—
126#2440C2214yes—
127#2440C2218yes—
128#2440C2214yes—
129#2440C2214yes—
130#2440C2214yes—
131#2440C2214yes—
132#2440C2214yes—
133#2440C2214yes—
134#2440C2214yes—
135#2438C2218yes—
136#2429C2214yes—
137#2429C2214yes—
138#2429C2218yes—
139#2423C2214yes—
140#2423C2214yes—
141#2417C2218yes—
142#2417C2214yes—
143#2417C2214yes—
144#2382C2214yes—
145#2379C2214yes—
146#2369C2214yes—
147#2360C2214yes—
148#2360C2214yes—
149#2359C2218yes—
150#2355C2214yes—
151#2352C2214yes—
152#2352C2214yes—
153Q8×C4⋊C4C2214yes—
154D4×C4⋊C4C2214yes—
155D4×C4⋊C4C2214yes—
156#2345C2214yes—
157#2345C2214yes—
158#2334C2218yes—
159#2330C2214yes—
160#2329C2214yes—
161#2325C2214yes—
162#2317C2214yes—
163#2314C2214yes—
164C4×C4⋊Q8C2212yes—
165C4×C4⋊Q8C2212yes—
166C4×C4⋊Q8C2212yes—
167C4×C4⋊Q8C2212yes—
168C4×C4⋊Q8C2212yes—
169C4×C4⋊Q8C2212yes—
170C4×#125C2211yescharacteristic
171C4×#125C2211yescharacteristic
172C4×#126C2212yes—
173C4×#126C2212yes—
174C4×#124C2211yescharacteristic
175C4×#124C2211yescharacteristic
176C4×C22⋊Q8C2211yescharacteristic
177C4×C22⋊Q8C2211yescharacteristic
178C4×#123C2212yes—
179C4×#123C2212yes—
180C4×#121C2211yescharacteristic
181C4×#121C2211yescharacteristic
182#2298C2212yes—
183#2295C2211yescharacteristic
184#2293C2211yescharacteristic
185C2×#389C2212yes—
186C2×#389C2212yes—
187C2×#389C2212yes—
188C2×#389C2212yes—
189#2290C2212yes—
190#2285C2212yes—
191#2285C2212yes—
192#2285C2212yes—
193C2×#384C2211yescharacteristic
194C2×#384C2211yescharacteristic
195C2×#384C2212yes—
196#2283C2211yescharacteristic
197C2×#382C2212yes—
198C42×Q8C2211yescharacteristic
199C42×D4C2212yes—
200C42×D4C2211yescharacteristic
201C4×#117C2212yes—
202C2×C43C2211yescharacteristic
203#554—416no—
204#544—416no—
205#533—48no—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2318yes—
216#529Q8116yescomplemented
217C2×#126C2312yes—
218C2×#125—48no—
219C2×#125C2314yes—
220C2×#125C2314yes—
221C2×#125C2314yes—
222C2×#125C2314yes—
223C2×#125C2314yes—
224C2×#125C2314yes—
225C2×#125C2318yes—
226C2×#125C2318yes—
227C2×#125C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#123C2312yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2318yes—
235C2×C22⋊Q8C2318yes—
236C2×C22⋊Q8C2318yes—
237C2×C22⋊Q8C2318yes—
238C2×C22⋊Q8C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4C2312yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2318yes—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2312yes—
253C2×C4×D4C2311yescharacteristic
254C2×#117C2312yes—
255C2×#117C2314yes—
256C2×#117C2314yes—
257C2×#117C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2314yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2314yes—
267C22×C4⋊C4C2314yes—
268C22×C4⋊C4C2314yes—
269C22×C42C2311yescharacteristic
270C22×C42C2311yescharacteristic
271C22×C42C2312yes—
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#399C2318yes—
284#399C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#395C2318yes—
310#395C2318yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#395C2318yes—
316#395C2318yes—
317#391C2314yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2318yes—
324#391C2314yes—
325#391C2314yes—
326#391C2318yes—
327#391C2318yes—
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2318yes—
349#389C2318yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2318yes—
355#389C2318yes—
356#389C2314yes—
357#389C2314yes—
358#389C2318yes—
359#389C2318yes—
360#389C2318yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2318yes—
380#389C2318yes—
381#389C2318yes—
382#389C2318yes—
383#388C2312yes—
384#388C2312yes—
385#388C2312yes—
386#388C2312yes—
387#388C2312yes—
388#388C2312yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2312yes—
394#388C2312yes—
395#387C2312yes—
396#387C2312yes—
397#387C2312yes—
398#387C2312yes—
399#387C2312yes—
400#387C2312yes—
401#387C2312yes—
402#387C2312yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#386C2318yes—
418#386C2318yes—
419#386C2312yes—
420#386C2312yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2312yes—
430#385C2312yes—
431#384C2312yes—
432#384C2312yes—
433#384C2312yes—
434#384C2312yes—
435#384C2312yes—
436#384C2312yes—
437#384C2312yes—
438#384C2318yes—
439#384C2314yes—
440#384C2312yes—
441#384C2312yes—
442#384C2314yes—
443#384C2312yes—
444#384C2314yes—
445#384C2314yes—
446#384C2312yes—
447#384C2312yes—
448#384C2312yes—
449#384C2312yes—
450#384C2312yes—
451#384C2312yes—
452#384C2314yes—
453#384C2314yes—
454#383C2312yes—
455#382C2311yescharacteristic
456#382C2311yescharacteristic
457#382C2314yes—
458#382C2314yes—
459#382C2314yes—
460#382C2314yes—
461#382C2314yes—
462#382C2314yes—
463#382C2314yes—
464#382C2314yes—
465#381C2312yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2318yes—
472#380C2318yes—
473#380C2314yes—
474#380C2314yes—
475#380C2314yes—
476#380C2311yescharacteristic
477#380C2311yescharacteristic
478#380C2314yes—
479#380C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2318yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2312yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2312yes—
522#376C2312yes—
523#376C2312yes—
524C2×#95C2314yes—
525C2×#95C2314yes—
526C43C2311yescharacteristic
527C43C2311yescharacteristic
528C43C2311yescharacteristic
529C43C2311yescharacteristic
530C43C2311yescharacteristic
531C43C2311yescharacteristic
532C43C2312yes—
533C43C2311yescharacteristic
534C43C2311yescharacteristic
535C22×Q8C2414yes—
536C22×Q8C2414yes—
537C22×Q8C2418yes—
538C22×Q8C2411yescharacteristic
539C22×D4C2412yes—
540C22×D4C2411yescharacteristic
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C23×C4C2412yes—
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550C23×C4C2414yes—
551C23×C4C2414yes—
552C23×C4C2418yes—
553C23×C4C2411yescharacteristic
554C4⋊Q8—28no—
555C4⋊Q8—28no—
556C4⋊Q8—44no—
557C4⋊Q8—48no—
558C4⋊Q8—44no—
559C4⋊Q8—48no—
560C4⋊Q8—48no—
561C4⋊Q8—44no—
562C4⋊Q8—44no—
563C4⋊Q8—416no—
564#126C2×Q8116yes—
565#125—216no—
566#125—48no—
567#125—48no—
568#125—48no—
569#125—48no—
570#125—48no—
571#125—416no—
572#125—416no—
573#125C2×Q818yes—
574#124C2×Q818yes—
575#123C2×Q8116yes—
576C22⋊Q8—216no—
577C22⋊Q8—48no—
578C22⋊Q8—416no—
579C22⋊Q8—416no—
580C22⋊Q8—416no—
581C22⋊Q8—416no—
582C22⋊Q8—48no—
583C22⋊Q8—48no—
584C22⋊Q8C2×Q818yes—
585#121C2×Q818yes—
586C4×Q8—42no—
587C4×Q8—42no—
588C4×Q8—48no—
589C4×Q8—48no—
590C4×Q8—48no—
591C4×Q8—48no—
592C4×Q8C2×Q818yes—
593C4×D4—28no—
594C4×D4—28no—
595C4×D4—42no—
596C4×D4—42no—
597C4×D4—416no—
598C4×D4C2×Q818yes—
599C4×D4C2×Q8116yes—
600#117—28no—
601#117—48no—
602#117—48no—
603#117C2×Q8116yes—
604C2×C4⋊C4—28no—
605C2×C4⋊C4—28no—
606C2×C4⋊C4—44no—
607C2×C4⋊C4—48no—
608C2×C4⋊C4—44no—
609C2×C4⋊C4—44no—
610C2×C4⋊C4—44no—
611C2×C4⋊C4—48no—
612C2×C4⋊C4—48no—
613C2×C4⋊C4—48no—
614C2×C4⋊C4—48no—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2412yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2412yes—
690C2×C42—24no—
691C2×C42—24no—
692C2×C42—24no—
693C2×C42—24no—
694C2×C42—28no—
695C2×C42—42no—
696C2×C42—42no—
697C2×C42C2×Q818yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2412yes—
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2418yes—
725C2×C42C2418yes—
726C2×C42C2418yes—
727C2×C42C2418yes—
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2412yes—
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2412yes—
744#95C2412yes—
745#95C2412yes—
746#95C2412yes—
747#95C2412yes—
748#95C2412yes—
749#95C2412yes—
750#95C2412yes—
751#95C2412yes—
752#95C2412yes—
753#95C2412yes—
754#95C2412yes—
755#95C2412yes—
756#95C2412yes—
757#95C2412yes—
758#95C2412yes—
759#95C2412yes—
760#95C2418yes—
761#95C2418yes—
762#95C2418yes—
763#95C2412yes—
764#95C2412yes—
765#95C2412yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774#95C2418yes—
775#95C2418yes—
776#95C2418yes—
777#95C2418yes—
778#95C2418yes—
779C24C2512yes—
780C24C2511yescharacteristic
781C2×Q8—28no—
782C2×Q8—28no—
783C2×Q8—28no—
784C2×Q8—28no—
785C2×Q8—41no—
786C2×Q8—41no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—48no—
790C2×Q8—48no—
791C2×Q8—48no—
792C2×Q8C22×Q814yes—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—41no—
796C2×D4—41no—
797C2×D4C22×Q818yes—
798C2×D4C22×Q814yes—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—24no—
803C22×C4—22no—
804C22×C4—24no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—28no—
812C22×C4—28no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4C22×Q814yes—
833C22×C4C22×Q814yes—
834C22×C4C22×Q818yes—
835C22×C4C22×Q814yes—
836C22×C4H(5,𝔽2)14yes—
837C22×C42−1+414yes—
838C22×C4C2512yes—
839C22×C4C2511yescharacteristic
840C22×C4C2518yes—
841C22×C4C2518yes—
842C22×C4C2512yes—
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2518yes—
846C22×C4C2518yes—
847C22×C4C2511yescharacteristic
848C22×C4C2511yescharacteristic
849C22×C4C2511yescharacteristic
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2511yescharacteristic
853C22×C4C2511yescharacteristic
854C22×C4C2512yes—
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C22×C4C2511yescharacteristic
862C22×C4C2511yescharacteristic
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—28no—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—216no—
870C4⋊C4—216no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—216no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—28no—
878C4⋊C4—24no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—48no—
887C4⋊C4—48no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4—48no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—41no—
896C4⋊C4—41no—
897C4⋊C4—48no—
898C4⋊C4—42no—
899C4⋊C4—41no—
900C4⋊C4—41no—
901C4⋊C4—42no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—44no—
906C4⋊C4—48no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—48no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—48no—
915C4⋊C4C22×Q818yes—
916C4⋊C4C22×Q818yes—
917C4⋊C4C22×Q814yes—
918C4⋊C4C22×Q818yes—
919C4⋊C4C22×Q814yes—
920C4⋊C4C22×Q818yes—
921C22⋊C4—216no—
922C22⋊C4—24no—
923C22⋊C4—24no—
924C22⋊C4—24no—
925C22⋊C4—24no—
926C22⋊C4—24no—
927C22⋊C4—24no—
928C22⋊C4—48no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4C22×Q818yes—
934C22⋊C4C22×Q818yes—
935C22⋊C4C22×Q818yes—
936C22⋊C4C22×Q818yes—
937C22⋊C4C22×Q818yes—
938C42—22no—
939C42—22no—
940C42—22no—
941C42—22no—
942C42—22no—
943C42—22no—
944C42—22no—
945C42—24no—
946C42—24no—
947C42—22no—
948C42—22no—
949C42—22no—
950C42—22no—
951C42—22no—
952C42—22no—
953C42—24no—
954C42—22no—
955C42—24no—
956C42—24no—
957C42—24no—
958C42—22no—
959C42—22no—
960C42—22no—
961C42—22no—
962C42—24no—
963C42—24no—
964C42—41no—
965C42—41no—
966C42—41no—
967C42—41no—
968C42—48no—
969C42—48no—
970C42—48no—
971C42—48no—
972C42C22×Q814yes—
973C42C22×Q814yes—
974C42C22×Q814yes—
975C42C22×Q814yes—
976C42C22×Q818yes—
977C42H(5,𝔽2)14yes—
978C422−1+414yes—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23C23×Q814yes—
990C23C23×Q812yes—
991C23C2×H(5,𝔽2)12yes—
992C23C2×2−1+412yes—
993C23C2611yescharacteristic
994Q8—44no—
995Q8—416no—
996Q8—88no—
997Q8—168no—
998D4—216no—
999D4—44no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—22no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—28no—
1025C2×C4—28no—
1026C2×C4—216no—
1027C2×C4—28no—
1028C2×C4—28no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—28no—
1036C2×C4—28no—
1037C2×C4—28no—
1038C2×C4—28no—
1039C2×C4—28no—
1040C2×C4—22no—
1041C2×C4—28no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—28no—
1048C2×C4—28no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—28no—
1054C2×C4—28no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—28no—
1058C2×C4—28no—
1059C2×C4—44no—
1060C2×C4—44no—
1061C2×C4—44no—
1062C2×C4—48no—
1063C2×C4—48no—
1064C2×C4—88no—
1065C2×C4—88no—
1066C2×C4—168no—
1067C2×C4C23×Q812yes—
1068C2×C4C23×Q812yes—
1069C2×C4C23×Q812yes—
1070C2×C4C23×Q812yes—
1071C2×C4C23×Q812yes—
1072C2×C4C23×Q814yes—
1073C2×C4C23×Q814yes—
1074C2×C4C23×Q814yes—
1075C2×C4C23×Q812yes—
1076C2×C4C2×H(5,𝔽2)12yes—
1077C2×C4C2×H(5,𝔽2)12yes—
1078C2×C4C2×H(5,𝔽2)12yes—
1079C2×C4C2×H(5,𝔽2)12yes—
1080C2×C4C2×H(5,𝔽2)12yes—
1081C2×C4C2×2−1+412yes—
1082C2×C4C2×2−1+412yes—
1083C2×C4C2×2−1+412yes—
1084C2×C4C2×2−1+412yes—
1085C2×C4C2×2−1+412yes—
1086C2×C4#58512yes—
1087C2×C4#58512yes—
1088C22—22no—
1089C22—22no—
1090C22—22no—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—24no—
1095C22—24no—
1096C22—24no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22#350314yes—
1102C22C24×Q811yescharacteristic
1103C22C22×H(5,𝔽2)11yescharacteristic
1104C22C22×H(5,𝔽2)11yescharacteristic
1105C22C22×2−1+411yescharacteristic
1106C22C22×2−1+411yescharacteristic
1107C22C2×#58511yescharacteristic
1108C22C2×#58511yescharacteristic
1109C4—22no—
1110C4—22no—
1111C4—22no—
1112C4—22no—
1113C4—22no—
1114C4—24no—
1115C4—24no—
1116C4—22no—
1117C4—22no—
1118C4—24no—
1119C4—22no—
1120C4—22no—
1121C4—42no—
1122C4—48no—
1123C4—42no—
1124C4—41no—
1125C4—48no—
1126C4—48no—
1127C4—42no—
1128C4—42no—
1129C4—41no—
1130C4—48no—
1131C4#350314yes—
1132C4#355914yes—
1133C4#356314yes—
1134C2—24no—
1135C2—44no—
1136C2C2×#355911yescharacteristic
1137C2C2×#356311yescharacteristic
1138C2C2×#350311yescharacteristic
1139C2C2×#350311yescharacteristic
1140C2#6281311yescharacteristic
1141C2#6283411yescharacteristic
1142C2#6283511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59291C2semidirect
2. #59113C2semidirect
3. #46153C2semidirect
4. #46152C2semidirect
5. #46006C2semidirect
6. #46005C2semidirect
7. #39749C2semidirect
8. #39662C2semidirect
9. #39661C2semidirect
10. #39639C2semidirect
12. #39623C2semidirect
14. #39365C2semidirect
15. #37687C2semidirect
16. #37561C2semidirect
17. #37313C2semidirect
18. #36645C2semidirect
19. C2×#2859C2semidirect
20. #36563C2semidirect
21. #36189C2semidirect
22. #36189C2semidirect
23. #36180C2semidirect
24. #35284C2semidirect
25. #35275C2semidirect
216. #529Q8semidirect

Maximal subgroups

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

subgroupindex
#592912
#591132
#461532
#461522
#460062
#460052
#397492
#396622
#396612
#396392
#396312
#396232
#396142
#393652
#376872
#375612
#373132
#366452
C2×#28592
#365632
#361892
#361802
#352842
#352752
#343822
C4×#5292