Finite Group Databasebeta

← #7986724

Subgroups — #7986724

Order 512.

4623 conjugacy classes of subgroups.

The subgroup lattice has 1125 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59228C212yesmaximal, complemented
3#59065C212yesmaximal, complemented
4#59050C212yesmaximal, complemented
5#51685C218yesmaximal, complemented
6#46083C214yesmaximal, complemented
7#45309C214yesmaximal, complemented
8#44983C214yesmaximal, complemented
9#42784C214yesmaximal, complemented
10#42783C214yesmaximal, complemented
11#39737C212yesmaximal, complemented
12#39156C212yesmaximal, complemented
13#39156C212yesmaximal, complemented
14#39136C212yesmaximal, complemented
15#38978C214yesmaximal, complemented
16#36315C212yesmaximal, complemented
17#36314C212yesmaximal, complemented
18#36188C211yesmaximal, characteristic, complemented
19#36134C211yesmaximal, characteristic, complemented
20#36134C211yesmaximal, characteristic, complemented
21#35202C212yesmaximal, complemented
22#35201C212yesmaximal, complemented
23#34943C211yesmaximal, characteristic, complemented
24#34932C211yesmaximal, characteristic, complemented
25#34394C212yesmaximal, complemented
26C4×#555C211yesmaximal, characteristic, complemented
27C2×#556C2212yes—
28C2×#555C2211yescharacteristic
29C2×#533C2212yes—
30C2×#533C2212yes—
31C2×#529C2212yes—
32#2868C2211yescharacteristic
33#2864C2214yes—
34#2861C2214yes—
35#2859C2214yes—
36#2857C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2829C2218yes—
40#2806C2214yes—
41#2800C2218yes—
42#2800C2218yes—
43#2783C2218yes—
44#2777C2218yes—
45#2777C2218yes—
46#2777C2218yes—
47#2772C2218yes—
48#2772C2218yes—
49#2756C2218yes—
50#2741C2218yes—
51#2740C2218yes—
52#2740C2218yes—
53#2730C2218yes—
54#2727C2218yes—
55#2723C2218yes—
56#2705C2218yes—
57#2667C2218yes—
58#2663C2218yes—
59#2644C2218yes—
60#2644C2214yes—
61#2620C2214yes—
62#2606C2218yes—
63#2604C2218yes—
64#2593C2218yes—
65#2584C2214yes—
66#2582C2214yes—
67#2572C2214yes—
68#2571C2211yescharacteristic
69#2568C2212yes—
70#2567C2212yes—
71#2563C2211yescharacteristic
72#2563C2211yescharacteristic
73#2562C2214yes—
74#2553C2214yes—
75#2552C2212yes—
76#2552C2212yes—
77#2552C2212yes—
78#2552C2212yes—
79#2552C2211yescharacteristic
80#2547C2212yes—
81#2547C2212yes—
82#2547C2211yescharacteristic
83#2542C2212yes—
84#2542C2212yes—
85#2542C2211yescharacteristic
86#2540C2214yes—
87#2538C2212yes—
88#2538C2212yes—
89#2538C2214yes—
90#2538C2214yes—
91#2537C2211yescharacteristic
92#2537C2211yescharacteristic
93#2533C2218yes—
94#2531C2218yes—
95#2530C2218yes—
96#2529C2218yes—
97#2511C2214yes—
98#2509C2218yes—
99#2507C2214yes—
100#2500C2214yes—
101#2499C2214yes—
102#2499C2214yes—
103#2499C2214yes—
104#2497C2214yes—
105#2497C2214yes—
106#2496C2214yes—
107#2496C2214yes—
108#2496C2212yes—
109#2495C2212yes—
110#2495C2214yes—
111#2495C2212yes—
112#2490C2214yes—
113#2490C2214yes—
114#2489C2212yes—
115#2489C2214yes—
116#2485C2214yes—
117#2469C2218yes—
118#2448C2214yes—
119#2448C2218yes—
120#2441C2214yes—
121#2441C2214yes—
122#2441C2214yes—
123#2441C2214yes—
124#2441C2214yes—
125#2441C2214yes—
126#2429C2214yes—
127#2429C2214yes—
128#2427C2212yes—
129#2426C2214yes—
130#2426C2214yes—
131#2423C2214yes—
132#2423C2214yes—
133#2422C2212yes—
134#2421C2214yes—
135#2421C2214yes—
136#2420C2212yes—
137#2420C2212yes—
138#2415C2214yes—
139#2415C2214yes—
140#2415C2214yes—
141#2414C2214yes—
142#2414C2214yes—
143#2398C2214yes—
144#2395C2214yes—
145#2378C2218yes—
146#2372C2214yes—
147#2369C2211yescharacteristic
148#2369C2212yes—
149#2365C2212yes—
150#2365C2212yes—
151#2365C2212yes—
152#2365C2212yes—
153#2365C2212yes—
154#2363C2212yes—
155#2363C2212yes—
156#2362C2214yes—
157#2356C2214yes—
158#2354C2212yes—
159#2354C2212yes—
160#2354C2211yescharacteristic
161#2354C2214yes—
162#2354C2211yescharacteristic
163#2354C2214yes—
164#2351C2214yes—
165Q8×C4⋊C4C2212yes—
166Q8×C4⋊C4C2212yes—
167Q8×C4⋊C4C2212yes—
168#2347C2214yes—
169#2346C2214yes—
170#2346C2212yes—
171#2346C2212yes—
172#2330C2214yes—
173#2330C2214yes—
174#2330C2214yes—
175#2323C2214yes—
176#2323C2214yes—
177#2323C2214yes—
178#2320C2218yes—
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×#124C2214yes—
183C4×C22⋊Q8C2212yes—
184C4×#121C2212yes—
185C4×#121C2212yes—
186C4×#121C2212yes—
187C4×#121C2212yes—
188C4×#121C2212yes—
189#2295C2214yes—
190#2285C2212yes—
191#2285C2212yes—
192#2283C2212yes—
193#2283C2212yes—
194C42×D4C2211yescharacteristic
195C42×D4C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C4×#117C2212yes—
198C4×#117C2212yes—
199#556—48no—
200#555—28no—
201#533—216no—
202#533—48no—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2311yescharacteristic
209#529—48no—
210C2×#126C2314yes—
211C2×#126C2318yes—
212C2×#125C2314yes—
213C2×#125C2314yes—
214C2×#125C2312yes—
215C2×#125C2314yes—
216C2×#124C2314yes—
217C2×#124C2312yes—
218C2×#124C2314yes—
219C2×#123C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×#121C2312yes—
230C2×#121C2312yes—
231C2×#121C2312yes—
232C2×#121C2312yes—
233C2×#121C2312yes—
234C2×#121C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2314yes—
255C2×C4×D4C2311yescharacteristic
256C2×#117C2314yes—
257C2×#117C2312yes—
258C2×#117C2312yes—
259C2×#117C2314yes—
260C2×#117C2314yes—
261C2×#117C2312yes—
262C2×#117C2312yes—
263C2×#117C2314yes—
264C22×C42C2312yes—
265C22×C42C2312yes—
266C22×C42C2312yes—
267#400C2318yes—
268#400C2318yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2318yes—
273#400C2318yes—
274#399C2318yes—
275#399C2318yes—
276#399C2314yes—
277#399C2318yes—
278#399C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2314yes—
283#398C2318yes—
284#398C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2314yes—
288#397C2314yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2314yes—
294#397C2314yes—
295#397C2314yes—
296#397C2318yes—
297#397C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2318yes—
301#396C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#395C2318yes—
306#394C2318yes—
307#394C2314yes—
308#394C2314yes—
309#394C2314yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#394C2314yes—
314#394C2318yes—
315#393C2314yes—
316#393C2314yes—
317#392C2318yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2318yes—
327#391C2314yes—
328#391C2314yes—
329#391C2312yes—
330#390C2312yes—
331#390C2312yes—
332#390C2314yes—
333#390C2318yes—
334#390C2314yes—
335#390C2312yes—
336#390C2312yes—
337#390C2318yes—
338#390C2314yes—
339#390C2318yes—
340#390C2312yes—
341#390C2318yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#389C2314yes—
349#389C2314yes—
350#389C2312yes—
351#389C2312yes—
352#389C2318yes—
353#389C2318yes—
354#389C2312yes—
355#389C2318yes—
356#389C2318yes—
357#389C2314yes—
358#389C2314yes—
359#389C2318yes—
360#389C2314yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2318yes—
367#389C2318yes—
368#389C2318yes—
369#389C2318yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2318yes—
375#389C2318yes—
376#389C2318yes—
377#389C2312yes—
378#389C2314yes—
379#388C2318yes—
380#388C2318yes—
381#388C2314yes—
382#388C2314yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2314yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#388C2318yes—
397#388C2318yes—
398#388C2314yes—
399#388C2314yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2314yes—
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#387C2318yes—
418#387C2314yes—
419#387C2318yes—
420#387C2318yes—
421#386C2314yes—
422#386C2314yes—
423#386C2314yes—
424#386C2314yes—
425#386C2314yes—
426#385C2314yes—
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2314yes—
431#384C2312yes—
432#384C2312yes—
433#384C2314yes—
434#384C2312yes—
435#384C2314yes—
436#384C2312yes—
437#384C2312yes—
438#384C2314yes—
439#384C2312yes—
440#383C2314yes—
441#383C2314yes—
442#383C2318yes—
443#382C2312yes—
444#382C2312yes—
445#382C2314yes—
446#382C2312yes—
447#382C2312yes—
448#382C2314yes—
449#382C2318yes—
450#382C2314yes—
451#381C2314yes—
452#381C2314yes—
453#380C2312yes—
454#380C2312yes—
455#380C2314yes—
456#380C2314yes—
457#380C2312yes—
458#380C2312yes—
459#380C2312yes—
460#380C2312yes—
461#380C2312yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2312yes—
468#380C2312yes—
469#380C2312yes—
470#380C2312yes—
471#380C2314yes—
472#380C2314yes—
473#380C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2318yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2318yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2311yescharacteristic
502C4×C22⋊C4C2312yes—
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2312yes—
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518#376C2318yes—
519#376C2314yes—
520#376C2314yes—
521#376C2314yes—
522C43C2311yescharacteristic
523C43C2314yes—
524C22×Q8C2414yes—
525C22×Q8C2412yes—
526C22×Q8C2412yes—
527C22×Q8C2412yes—
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2414yes—
532C22×D4C2414yes—
533C22×D4C2414yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C4⋊Q8—28no—
544C4⋊Q8—24no—
545C4⋊Q8—28no—
546C4⋊Q8—24no—
547C4⋊Q8—44no—
548C4⋊Q8#4118yes—
549#126—48no—
550#126—416no—
551#125—216no—
552#125—48no—
553#125—44no—
554#125—48no—
555#124—216no—
556#124—44no—
557#124—48no—
558#123—48no—
559C22⋊Q8—216no—
560C22⋊Q8—216no—
561C22⋊Q8—48no—
562C22⋊Q8—44no—
563C22⋊Q8—48no—
564C22⋊Q8—44no—
565C22⋊Q8—48no—
566C22⋊Q8—48no—
567C22⋊Q8—48no—
568#121—28no—
569#121—28no—
570#121—44no—
571#121—44no—
572#121—44no—
573#121—44no—
574C4×Q8—216no—
575C4×Q8—216no—
576C4×Q8—28no—
577C4×Q8—44no—
578C4×Q8—44no—
579C4×Q8—48no—
580C4×Q8—48no—
581C4×Q8—48no—
582C4×Q8—48no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—24no—
587C4×D4—24no—
588C4×D4—24no—
589C4×D4—42no—
590C4×D4—42no—
591C4×D4—42no—
592C4×D4—48no—
593C4×D4—48no—
594C4×D4—48no—
595#117—216no—
596#117—28no—
597#117—28no—
598#117—48no—
599#117—44no—
600#117—44no—
601#117—48no—
602#117—48no—
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C42—28no—
688C2×C42—28no—
689C2×C42—28no—
690C2×C42C2412yes—
691C2×C42C2414yes—
692C2×C42C2414yes—
693C2×C42C2418yes—
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2414yes—
697C2×C42C2414yes—
698C2×C42C2411yescharacteristic
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2418yes—
708C2×C42C2418yes—
709C2×C42C2414yes—
710C2×C42C2414yes—
711C2×C42C2418yes—
712C2×C42C2414yes—
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717#95C2412yes—
718#95C2412yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2418yes—
731#95C2418yes—
732#95C2414yes—
733#95C2412yes—
734#95C2412yes—
735#95C2412yes—
736#95C2412yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2414yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2414yes—
753#95C2414yes—
754#95C2418yes—
755#95C2418yes—
756#95C2414yes—
757#95C2418yes—
758#95C2418yes—
759C24C2512yes—
760C24C2512yes—
761C24C2512yes—
762C2×Q8—28no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—28no—
766C2×Q8—24no—
767C2×Q8—24no—
768C2×Q8—28no—
769C2×Q8—42no—
770C2×Q8—42no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8C2×#4118yes—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—28no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4C2512yes—
820C22×C4C2512yes—
821C22×C4C2512yes—
822C22×C4C2512yes—
823C22×C4C2512yes—
824C22×C4C2512yes—
825C22×C4C2514yes—
826C22×C4C2514yes—
827C22×C4C2512yes—
828C22×C4C2511yescharacteristic
829C22×C4C2514yes—
830C22×C4C2514yes—
831C22×C4C2514yes—
832C22×C4C2512yes—
833C22×C4C2518yes—
834C22×C4C2512yes—
835C22×C4C2511yescharacteristic
836C22×C4C2514yes—
837C22×C4C2511yescharacteristic
838C22×C4C2511yescharacteristic
839C22×C4C2511yescharacteristic
840C22×C4C2511yescharacteristic
841C22×C4C2511yescharacteristic
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—28no—
845C4⋊C4—216no—
846C4⋊C4—216no—
847C4⋊C4—28no—
848C4⋊C4—24no—
849C4⋊C4—28no—
850C4⋊C4—24no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—28no—
854C4⋊C4—24no—
855C4⋊C4—28no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—22no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—42no—
869C4⋊C4—48no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—44no—
880C4⋊C4—48no—
881C4⋊C4—48no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—44no—
885C4⋊C4—48no—
886C4⋊C4—48no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4C2×#4118yes—
892C4⋊C4C2×#4118yes—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—216no—
896C22⋊C4—24no—
897C22⋊C4—24no—
898C22⋊C4—24no—
899C22⋊C4—24no—
900C22⋊C4—24no—
901C22⋊C4—24no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—48no—
908C22⋊C4—44no—
909C22⋊C4—48no—
910C22⋊C4—42no—
911C22⋊C4—42no—
912C22⋊C4—44no—
913C22⋊C4—42no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C42—24no—
927C42—24no—
928C42—24no—
929C42—28no—
930C42—216no—
931C42—24no—
932C42—24no—
933C42—24no—
934C42—28no—
935C42—24no—
936C42—24no—
937C42—24no—
938C42—28no—
939C42—22no—
940C42—22no—
941C42—28no—
942C42—22no—
943C42—41no—
944C42—44no—
945C42—44no—
946C42—44no—
947C42—48no—
948C42—48no—
949C42—48no—
950C42C2×#4114yes—
951C42H(5,𝔽2)14yes—
952C422−1+414yes—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23C2611yescharacteristic
975Q8—48no—
976Q8—48no—
977Q8—416no—
978Q8—48no—
979D4—44no—
980D4—44no—
981D4—44no—
982D4—88no—
983D4—88no—
984D4—88no—
985C2×C4—24no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—24no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—28no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—28no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—21no—
1015C2×C4—24no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—28no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—48no—
1042C2×C4—48no—
1043C2×C4—48no—
1044C2×C4—48no—
1045C2×C4—48no—
1046C2×C4—48no—
1047C2×C4—84no—
1048C2×C4—84no—
1049C2×C4—84no—
1050C2×C4C22×#4118yes—
1051C2×C4C22×#4112yes—
1052C2×C4C22×#4112yes—
1053C2×C4C22×#4112yes—
1054C2×C4C2×H(5,𝔽2)12yes—
1055C2×C4C2×H(5,𝔽2)12yes—
1056C2×C4C2×H(5,𝔽2)12yes—
1057C2×C4C2×2−1+412yes—
1058C2×C4C2×2−1+412yes—
1059C2×C4C2×2−1+412yes—
1060C2×C4#58512yes—
1061C2×C4#58512yes—
1062C2×C4#58512yes—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22C23×#4111yescharacteristic
1085C22C22×H(5,𝔽2)11yescharacteristic
1086C22C22×2−1+411yescharacteristic
1087C22C2×#58511yescharacteristic
1088C22C2×#58511yescharacteristic
1089C22C2×#58511yescharacteristic
1090C222−1+611yescharacteristic
1091C4—22no—
1092C4—28no—
1093C4—22no—
1094C4—22no—
1095C4—42no—
1096C4—42no—
1097C4—42no—
1098C4—44no—
1099C4—41no—
1100C4—44no—
1101C4—44no—
1102C4—42no—
1103C4—42no—
1104C4—48no—
1105C4—42no—
1106C4—42no—
1107C4—42no—
1108C4—44no—
1109C4—44no—
1110C4—42no—
1111C4#351714yes—
1112C4#351814yes—
1113C4#354714yes—
1114C2—82no—
1115C2—82no—
1116C2—82no—
1117C2C2×#354711yescharacteristic
1118C2C2×#351711yescharacteristic
1119C2C2×#351811yescharacteristic
1120C2#6292511yescharacteristic
1121C2#6295911yescharacteristic
1122C2#6299111yescharacteristic
1123C2#6303111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
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. #59228C2semidirect
3. #59065C2semidirect
4. #59050C2semidirect
5. #51685C2semidirect
6. #46083C2semidirect
7. #45309C2semidirect
8. #44983C2semidirect
9. #42784C2semidirect
10. #42783C2semidirect
11. #39737C2semidirect
12. #39156C2semidirect
13. #39156C2semidirect
14. #39136C2semidirect
15. #38978C2semidirect
16. #36315C2semidirect
17. #36314C2semidirect
18. #36188C2semidirect
19. #36134C2semidirect
20. #36134C2semidirect
21. #35202C2semidirect
22. #35201C2semidirect
23. #34943C2semidirect
24. #34932C2semidirect
25. #34394C2semidirect
26. C4×#555C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#592282
#590652
#590502
#516852
#460832
#453092
#449832
#427842
#427832
#397372
#391562
#391362
#389782
#363152
#363142
#361882
#361342
#352022
#352012
#349432
#349322
#343942
C4×#5552