Finite Group Databasebeta

← #7710998

Subgroups — #7710998

Order 512.

4656 conjugacy classes of subgroups.

The subgroup lattice has 1133 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59871C211yesmaximal, characteristic, complemented
3#59864C211yesmaximal, characteristic, complemented
4#59821C211yesmaximal, characteristic, complemented
5#59258C212yesmaximal, complemented
6#59065C212yesmaximal, complemented
7#45965C214yesmaximal, complemented
8#45715C214yesmaximal, complemented
9#39245C214yesmaximal, complemented
10#39216C214yesmaximal, complemented
11#39203C212yesmaximal, complemented
12#39147C212yesmaximal
13#38966C212yesmaximal, complemented
14#38931C212yesmaximal, complemented
15#38225C214yesmaximal, complemented
16#38048C214yesmaximal, complemented
17#37637C212yesmaximal, complemented
18#37167C214yesmaximal, complemented
19#36635C211yesmaximal, characteristic, complemented
20#36631C211yesmaximal, characteristic
21#36459C212yesmaximal, complemented
22#36447C212yesmaximal, complemented
23#36300C212yesmaximal, complemented
24#36272C212yesmaximal, complemented
25#35116C214yesmaximal, complemented
26#34481C212yesmaximal, complemented
27C4×#533C211yesmaximal, characteristic, complemented
28C2×#556C2212yes—
29C2×#552C2214yes—
30C2×#533C2211yescharacteristic
31C2×#529C2212yes—
32#2864C2212yes—
33#2863C2212yes—
34#2863C2212yes—
35#2862C2211yescharacteristic
36#2861C2212yes—
37#2860C2212yes—
38#2860C2212yes—
39#2860C2214yes—
40#2859C2211yescharacteristic
41#2859C2211yescharacteristic
42#2859C2214yes—
43#2858C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2856C2211yescharacteristic
48#2855C2212yes—
49#2855C2212yes—
50#2854C2212yes—
51#2854C2212yes—
52#2851C2212yes—
53#2850C2212yes—
54#2831C2218yes—
55#2806C2214yes—
56#2806C2214yes—
57#2804C2214yes—
58#2798C2218yes—
59#2790C2218yes—
60#2773C2218yes—
61#2770C2218yes—
62#2768C2218yes—
63#2758C2218yes—
64#2757C2218yes—
65#2754C2218yes—
66#2727C2214yes—
67#2724C2218yes—
68#2723C2218yes—
69#2718C2218yes—
70#2701C2218yes—
71#2698C2218yes—
72#2695C2218yes—
73#2654C2218yes—
74#2647C2214yes—
75#2644C2214yes—
76#2637C2218yes—
77#2629C2214yes—
78#2625C2214yes—
79#2611C2218yes—
80#2584C2214yes—
81#2584C2214yes—
82#2582C2214yes—
83#2582C2214yes—
84#2580C2214yes—
85#2580C2214yes—
86#2571C2212yes—
87#2571C2214yes—
88#2570C2214yes—
89#2567C2212yes—
90#2567C2212yes—
91#2566C2214yes—
92#2563C2212yes—
93#2563C2212yes—
94#2560C2218yes—
95#2553C2218yes—
96#2552C2212yes—
97#2552C2214yes—
98#2552C2212yes—
99#2552C2212yes—
100#2552C2212yes—
101#2548C2212yes—
102#2542C2212yes—
103#2538C2212yes—
104#2532C2218yes—
105#2521C2218yes—
106#2519C2218yes—
107#2513C2214yes—
108#2513C2214yes—
109#2512C2214yes—
110#2512C2214yes—
111#2508C2214yes—
112#2508C2214yes—
113#2508C2218yes—
114#2507C2214yes—
115#2507C2214yes—
116#2506C2214yes—
117#2506C2218yes—
118#2496C2214yes—
119#2496C2214yes—
120#2496C2214yes—
121#2495C2214yes—
122#2490C2214yes—
123#2489C2214yes—
124#2489C2214yes—
125#2487C2214yes—
126#2485C2214yes—
127#2478C2218yes—
128#2475C2218yes—
129#2474C2218yes—
130#2469C2218yes—
131#2454C2214yes—
132#2448C2214yes—
133#2448C2214yes—
134#2442C2214yes—
135#2441C2214yes—
136#2426C2214yes—
137#2422C2214yes—
138#2422C2214yes—
139#2421C2214yes—
140#2421C2214yes—
141#2415C2214yes—
142#2415C2214yes—
143#2383C2218yes—
144#2369C2212yes—
145#2369C2212yes—
146#2367C2214yes—
147#2366C2212yes—
148#2365C2212yes—
149#2365C2212yes—
150#2360C2214yes—
151#2354C2212yes—
152#2354C2214yes—
153#2354C2214yes—
154#2351C2214yes—
155Q8×C4⋊C4C2212yes—
156Q8×C4⋊C4C2214yes—
157Q8×C4⋊C4C2212yes—
158Q8×C4⋊C4C2212yes—
159D4×C4⋊C4C2212yes—
160D4×C4⋊C4C2212yes—
161#2347C2214yes—
162#2334C2218yes—
163#2334C2218yes—
164#2326C2214yes—
165#2323C2214yes—
166#2320C2214yes—
167#2317C2214yes—
168C4×C4⋊Q8C2211yescharacteristic
169C4×C4⋊Q8C2211yescharacteristic
170C4×C4⋊Q8C2211yescharacteristic
171C4×C4⋊Q8C2211yescharacteristic
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2211yescharacteristic
175C4×#127C2211yescharacteristic
176C4×#125C2212yes—
177C4×#125C2212yes—
178C4×#125C2214yes—
179C4×#125C2212yes—
180C4×#124C2212yes—
181C4×C22⋊Q8C2212yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×#121C2212yes—
188C4×#121C2212yes—
189#2296C2212yes—
190#2295C2212yes—
191#2295C2212yes—
192#2295C2212yes—
193#2295C2212yes—
194#2293C2212yes—
195#2293C2212yes—
196#2293C2214yes—
197#2285C2211yescharacteristic
198#2283C2212yes—
199C42×Q8C2212yes—
200C42×Q8C2212yes—
201C4×#117C2212yes—
202C2×C43C2211yescharacteristic
203#556—216no—
204#552—416no—
205#533—28no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212#529—48no—
213C2×#126C2318yes—
214C2×#126C2318yes—
215C2×#126C2314yes—
216C2×#126C2318yes—
217C2×#125C2312yes—
218C2×#125C2314yes—
219C2×#125C2312yes—
220C2×#125C2314yes—
221C2×#125C2312yes—
222C2×#125C2318yes—
223C2×#124C2314yes—
224C2×#124C2312yes—
225C2×#124C2312yes—
226C2×#123C2314yes—
227C2×#123C2318yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2314yes—
235C2×#121C2312yes—
236C2×#121C2312yes—
237C2×#121C2312yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×#117C2314yes—
257C2×#117C2312yes—
258C2×#117C2312yes—
259C2×#117C2314yes—
260C2×#117C2318yes—
261C22×C4⋊C4C2314yes—
262C22×C42C2311yescharacteristic
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#399C2318yes—
277#399C2318yes—
278#399C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2318yes—
301#396C2318yes—
302#395C2318yes—
303#395C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#393C2318yes—
308#393C2318yes—
309#391C2318yes—
310#391C2312yes—
311#391C2312yes—
312#391C2312yes—
313#391C2312yes—
314#391C2312yes—
315#391C2312yes—
316#391C2312yes—
317#391C2314yes—
318#391C2314yes—
319#391C2312yes—
320#391C2318yes—
321#391C2312yes—
322#391C2312yes—
323#391C2312yes—
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#390C2318yes—
328#390C2312yes—
329#390C2312yes—
330#390C2312yes—
331#390C2314yes—
332#390C2314yes—
333#390C2312yes—
334#390C2314yes—
335#390C2312yes—
336#390C2312yes—
337#390C2312yes—
338#390C2312yes—
339#390C2312yes—
340#390C2312yes—
341#390C2314yes—
342#390C2314yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2312yes—
365#389C2312yes—
366#389C2314yes—
367#389C2318yes—
368#389C2314yes—
369#389C2314yes—
370#389C2312yes—
371#389C2314yes—
372#389C2314yes—
373#389C2312yes—
374#389C2318yes—
375#389C2318yes—
376#389C2314yes—
377#389C2318yes—
378#389C2314yes—
379#389C2318yes—
380#389C2314yes—
381#389C2318yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#389C2312yes—
386#389C2312yes—
387#389C2318yes—
388#389C2312yes—
389#389C2312yes—
390#389C2314yes—
391#389C2318yes—
392#389C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2314yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2314yes—
401#388C2314yes—
402#388C2318yes—
403#388C2318yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#387C2318yes—
415#387C2314yes—
416#387C2314yes—
417#387C2318yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2314yes—
422#387C2318yes—
423#387C2318yes—
424#387C2314yes—
425#387C2318yes—
426#387C2314yes—
427#387C2314yes—
428#387C2318yes—
429#387C2318yes—
430#387C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2318yes—
434#386C2314yes—
435#386C2314yes—
436#386C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2314yes—
445#385C2314yes—
446#385C2314yes—
447#385C2314yes—
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#384C2311yescharacteristic
451#384C2311yescharacteristic
452#384C2311yescharacteristic
453#384C2311yescharacteristic
454#384C2314yes—
455#384C2314yes—
456#384C2314yes—
457#384C2314yes—
458#384C2318yes—
459#384C2314yes—
460#383C2318yes—
461#383C2314yes—
462#382C2312yes—
463#382C2314yes—
464#382C2312yes—
465#382C2314yes—
466#382C2312yes—
467#382C2312yes—
468#382C2318yes—
469#382C2318yes—
470#382C2318yes—
471#382C2312yes—
472#381C2314yes—
473#380C2314yes—
474#380C2314yes—
475#380C2314yes—
476#380C2312yes—
477#380C2312yes—
478#380C2312yes—
479#380C2312yes—
480#380C2312yes—
481#380C2312yes—
482#380C2314yes—
483#380C2318yes—
484#380C2312yes—
485#380C2312yes—
486C4×C4⋊C4C2318yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2318yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2314yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2314yes—
515C4×C4⋊C4C2312yes—
516C4×C4⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2318yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2314yes—
523#376C2314yes—
524#376C2314yes—
525C43C2311yescharacteristic
526C43C2311yescharacteristic
527C43C2311yescharacteristic
528C43C2314yes—
529C43C2311yescharacteristic
530C43C2311yescharacteristic
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2311yescharacteristic
534C22×Q8C2412yes—
535C22×Q8C2412yes—
536C22×Q8C2412yes—
537C22×Q8C2412yes—
538C22×Q8C2412yes—
539C22×D4C2412yes—
540C22×D4C2412yes—
541C22×D4C2414yes—
542C22×D4C2412yes—
543C23×C4C2414yes—
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2418yes—
552C4⋊Q8—24no—
553C4⋊Q8—24no—
554C4⋊Q8—24no—
555C4⋊Q8—24no—
556C4⋊Q8#4118yes—
557#127—24no—
558#126—232no—
559#126—416no—
560#126—48no—
561#126—416no—
562#125—28no—
563#125—44no—
564#125—48no—
565#125—44no—
566#125—416no—
567#125—48no—
568#124—216no—
569#124—44no—
570#124—44no—
571#123—416no—
572#123—48no—
573C22⋊Q8—28no—
574C22⋊Q8—28no—
575C22⋊Q8—28no—
576C22⋊Q8—216no—
577C22⋊Q8—44no—
578C22⋊Q8—44no—
579C22⋊Q8—48no—
580#121—44no—
581#121—44no—
582#121—44no—
583C4×Q8—28no—
584C4×Q8—216no—
585C4×Q8—28no—
586C4×Q8—28no—
587C4×Q8—28no—
588C4×Q8—44no—
589C4×Q8—44no—
590C4×Q8—44no—
591C4×Q8—44no—
592C4×Q8—44no—
593C4×Q8—48no—
594C4×Q8—48no—
595C4×D4—216no—
596C4×D4—28no—
597C4×D4—28no—
598C4×D4—48no—
599C4×D4—48no—
600C4×D4—44no—
601#117—28no—
602#117—28no—
603#117—216no—
604#117—48no—
605#117—416no—
606C2×C4⋊C4—48no—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2418yes—
684C2×C42—24no—
685C2×C42—24no—
686C2×C42—24no—
687C2×C42—24no—
688C2×C42—42no—
689C2×C42—42no—
690C2×C42—42no—
691C2×C42C2411yescharacteristic
692C2×C42C2414yes—
693C2×C42C2414yes—
694C2×C42C2414yes—
695C2×C42C2418yes—
696C2×C42C2411yescharacteristic
697C2×C42C2414yes—
698C2×C42C2414yes—
699C2×C42C2414yes—
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2414yes—
707C2×C42C2414yes—
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2418yes—
720C2×C42C2414yes—
721C2×C42C2418yes—
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771C24C2514yes—
772C24C2511yescharacteristic
773C2×Q8—24no—
774C2×Q8—24no—
775C2×Q8—24no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—24no—
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—42no—
782C2×Q8—42no—
783C2×Q8—42no—
784C2×Q8—42no—
785C2×Q8—42no—
786C2×Q8—42no—
787C2×Q8C2×#4118yes—
788C2×D4—28no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—24no—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—42no—
797C2×D4—44no—
798C2×D4—44no—
799C2×D4—42no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—28no—
807C22×C4—28no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—28no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—41no—
818C22×C4—41no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—48no—
824C22×C4—48no—
825C22×C4—48no—
826C22×C4H(5,𝔽2)14yes—
827C22×C4C2511yescharacteristic
828C22×C4C2511yescharacteristic
829C22×C4C2514yes—
830C22×C4C2511yescharacteristic
831C22×C4C2511yescharacteristic
832C22×C4C2514yes—
833C22×C4C2514yes—
834C22×C4C2514yes—
835C22×C4C2514yes—
836C22×C4C2514yes—
837C22×C4C2514yes—
838C22×C4C2514yes—
839C22×C4C2514yes—
840C22×C4C2511yescharacteristic
841C22×C4C2511yescharacteristic
842C22×C4C2514yes—
843C22×C4C2514yes—
844C22×C4C2511yescharacteristic
845C22×C4C2511yescharacteristic
846C22×C4C2511yescharacteristic
847C22×C4C2511yescharacteristic
848C22×C4C2511yescharacteristic
849C22×C4C2511yescharacteristic
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—216no—
858C4⋊C4—24no—
859C4⋊C4—28no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—24no—
866C4⋊C4—28no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—28no—
879C4⋊C4—24no—
880C4⋊C4—48no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—48no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—44no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—42no—
894C4⋊C4—48no—
895C4⋊C4—44no—
896C4⋊C4—42no—
897C4⋊C4—48no—
898C4⋊C4—48no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4C2×#4118yes—
906C4⋊C4C2×#4118yes—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—216no—
912C22⋊C4—28no—
913C22⋊C4—216no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—44no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C42—22no—
930C42—22no—
931C42—22no—
932C42—28no—
933C42—216no—
934C42—28no—
935C42—22no—
936C42—22no—
937C42—22no—
938C42—22no—
939C42—28no—
940C42—28no—
941C42—22no—
942C42—22no—
943C42—22no—
944C42—22no—
945C42—22no—
946C42—22no—
947C42—28no—
948C42—22no—
949C42—22no—
950C42—22no—
951C42—22no—
952C42—22no—
953C42—22no—
954C42—28no—
955C42—28no—
956C42—28no—
957C42—41no—
958C42—41no—
959C42—41no—
960C42—41no—
961C42—41no—
962C42—41no—
963C42—48no—
964C42—44no—
965C42—48no—
966C42C2×#4114yes—
967C422−1+414yes—
968C422−1+414yes—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23C2×H(5,𝔽2)12yes—
983C23C2611yescharacteristic
984Q8—216no—
985Q8—48no—
986Q8—48no—
987Q8—84no—
988Q8—84no—
989D4—48no—
990D4—48no—
991D4—84no—
992D4—88no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—24no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—24no—
1004C2×C4—21no—
1005C2×C4—28no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—44no—
1055C2×C4—44no—
1056C2×C4—44no—
1057C2×C4—44no—
1058C2×C4—44no—
1059C2×C4—416no—
1060C2×C4—44no—
1061C2×C4—816no—
1062C2×C4C22×#4118yes—
1063C2×C4C22×#4112yes—
1064C2×C4C22×#4112yes—
1065C2×C4C22×#4112yes—
1066C2×C4C2×H(5,𝔽2)12yes—
1067C2×C4C2×H(5,𝔽2)12yes—
1068C2×C4C2×2−1+412yes—
1069C2×C4C2×2−1+412yes—
1070C2×C4C2×2−1+412yes—
1071C2×C4C2×2−1+412yes—
1072C2×C4C2×2−1+412yes—
1073C2×C4C2×2−1+412yes—
1074C2×C4#58512yes—
1075C2×C4#58512yes—
1076C2×C4#58512yes—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—41no—
1081C22—41no—
1082C22—41no—
1083C22—41no—
1084C22—44no—
1085C22—44no—
1086C22—44no—
1087C22—44no—
1088C22—44no—
1089C22—44no—
1090C22—44no—
1091C22C23×#4111yescharacteristic
1092C22C22×H(5,𝔽2)11yescharacteristic
1093C22C22×2−1+411yescharacteristic
1094C22C22×2−1+411yescharacteristic
1095C22C2×#58511yescharacteristic
1096C22C2×#58511yescharacteristic
1097C22C2×#58511yescharacteristic
1098C4—28no—
1099C4—22no—
1100C4—22no—
1101C4—22no—
1102C4—22no—
1103C4—22no—
1104C4—41no—
1105C4—41no—
1106C4—41no—
1107C4—44no—
1108C4—44no—
1109C4—44no—
1110C4—41no—
1111C4—44no—
1112C4—44no—
1113C4—44no—
1114C4—41no—
1115C4—44no—
1116C4—44no—
1117C4—44no—
1118C4—41no—
1119C4—44no—
1120C4#351514yes—
1121C4#352214yes—
1122C4#355514yes—
1123C2—42no—
1124C2—84no—
1125C2C2×#355511yescharacteristic
1126C2#6275911yescharacteristic
1127C2C2×#351511yescharacteristic
1128C2C2×#352211yescharacteristic
1129C2#6279311yescharacteristic
1130C2#6283111yescharacteristic
1131C2#6283511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2856C22
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. #59864C2semidirect
4. #59821C2semidirect
5. #59258C2semidirect
6. #59065C2semidirect
7. #45965C2semidirect
8. #45715C2semidirect
9. #39245C2semidirect
10. #39216C2semidirect
11. #39203C2semidirect
13. #38966C2semidirect
14. #38931C2semidirect
15. #38225C2semidirect
16. #38048C2semidirect
17. #37637C2semidirect
18. #37167C2semidirect
19. #36635C2semidirect
21. #36459C2semidirect
22. #36447C2semidirect
23. #36300C2semidirect
24. #36272C2semidirect
25. #35116C2semidirect
26. #34481C2semidirect
27. C4×#533C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#598642
#598212
#592582
#590652
#459652
#457152
#392452
#392162
#392032
#391472
#389662
#389312
#382252
#380482
#376372
#371672
#366352
#366312
#364592
#364472
#363002
#362722
#351162
#344812
C4×#5332