Finite Group Databasebeta

← #7986735

Subgroups — #7986735

Order 512.

4759 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic, complemented
2#59652C212yesmaximal, complemented
3#59243C212yesmaximal, complemented
4#59050C212yesmaximal, complemented
5#51743C218yesmaximal, complemented
6#46083C214yesmaximal, complemented
7#45396C214yesmaximal, complemented
8#45067C214yesmaximal, complemented
9#42624C214yesmaximal, complemented
10#42620C214yesmaximal, complemented
11#39763C212yesmaximal, complemented
12#39194C214yesmaximal, complemented
13#39194C212yesmaximal, complemented
14#38942C212yesmaximal, complemented
15#38922C212yesmaximal, complemented
16#36563C211yesmaximal, characteristic, complemented
17#36302C212yesmaximal, complemented
18#36301C212yesmaximal, complemented
19#36187C211yesmaximal, characteristic, complemented
20#36134C211yesmaximal, characteristic, complemented
21#35202C212yesmaximal, complemented
22#35201C212yesmaximal, complemented
23#34945C211yesmaximal, characteristic, complemented
24#34934C211yesmaximal, characteristic, complemented
25#34484C212yesmaximal, complemented
26C4×#555C211yesmaximal, characteristic, complemented
27C2×#555C2211yescharacteristic
28C2×#555C2212yes—
29C2×#554C2212yes—
30C2×#533C2212yes—
31C2×#529C2212yes—
32#2868C2211yescharacteristic
33#2864C2214yes—
34#2861C2214yes—
35#2859C2212yes—
36#2859C2214yes—
37#2857C2212yes—
38#2856C2212yes—
39#2829C2218yes—
40#2801C2218yes—
41#2801C2218yes—
42#2800C2218yes—
43#2800C2218yes—
44#2800C2218yes—
45#2800C2218yes—
46#2786C2218yes—
47#2783C2218yes—
48#2756C2218yes—
49#2741C2218yes—
50#2740C2218yes—
51#2732C2214yes—
52#2730C2218yes—
53#2730C2218yes—
54#2715C2218yes—
55#2699C2218yes—
56#2672C2218yes—
57#2667C2218yes—
58#2663C2218yes—
59#2641C2214yes—
60#2624C2214yes—
61#2624C2218yes—
62#2606C2218yes—
63#2604C2218yes—
64#2594C2218yes—
65#2582C2212yes—
66#2573C2214yes—
67#2571C2211yescharacteristic
68#2568C2211yescharacteristic
69#2567C2212yes—
70#2563C2212yes—
71#2554C2214yes—
72#2552C2212yes—
73#2552C2212yes—
74#2552C2212yes—
75#2552C2211yescharacteristic
76#2550C2214yes—
77#2548C2211yescharacteristic
78#2547C2211yescharacteristic
79#2542C2212yes—
80#2542C2212yes—
81#2541C2211yescharacteristic
82#2540C2214yes—
83#2538C2214yes—
84#2538C2212yes—
85#2538C2211yescharacteristic
86#2538C2212yes—
87#2538C2211yescharacteristic
88#2537C2212yes—
89#2537C2214yes—
90#2537C2212yes—
91#2531C2218yes—
92#2527C2218yes—
93#2514C2212yes—
94#2513C2214yes—
95#2513C2214yes—
96#2512C2212yes—
97#2507C2214yes—
98#2500C2214yes—
99#2500C2214yes—
100#2500C2214yes—
101#2499C2214yes—
102#2494C2218yes—
103#2494C2214yes—
104#2494C2212yes—
105#2494C2214yes—
106#2494C2214yes—
107#2491C2214yes—
108#2491C2214yes—
109#2490C2214yes—
110#2490C2214yes—
111#2490C2212yes—
112#2490C2214yes—
113#2485C2214yes—
114#2485C2214yes—
115#2477C2218yes—
116#2476C2218yes—
117#2454C2214yes—
118#2451C2214yes—
119#2448C2218yes—
120#2447C2212yes—
121#2445C2212yes—
122#2441C2214yes—
123#2441C2214yes—
124#2441C2214yes—
125#2441C2214yes—
126#2441C2214yes—
127#2429C2214yes—
128#2428C2214yes—
129#2427C2214yes—
130#2426C2212yes—
131#2426C2218yes—
132#2426C2214yes—
133#2423C2214yes—
134#2421C2212yes—
135#2420C2214yes—
136#2417C2214yes—
137#2416C2214yes—
138#2415C2214yes—
139#2415C2214yes—
140#2415C2214yes—
141#2415C2214yes—
142#2414C2214yes—
143#2401C2214yes—
144#2392C2214yes—
145#2378C2218yes—
146#2372C2214yes—
147#2370C2214yes—
148#2369C2211yescharacteristic
149#2369C2212yes—
150#2366C2212yes—
151#2365C2212yes—
152#2363C2214yes—
153#2363C2212yes—
154#2363C2212yes—
155#2362C2214yes—
156#2355C2212yes—
157#2354C2211yescharacteristic
158#2354C2214yes—
159#2354C2212yes—
160#2354C2211yescharacteristic
161#2354C2212yes—
162#2354C2212yes—
163#2354C2214yes—
164#2352C2214yes—
165Q8×C4⋊C4C2212yes—
166Q8×C4⋊C4C2212yes—
167D4×C4⋊C4C2212yes—
168#2346C2212yes—
169#2346C2212yes—
170#2344C2214yes—
171#2330C2214yes—
172#2330C2214yes—
173#2323C2218yes—
174#2323C2214yes—
175#2323C2214yes—
176#2319C2214yes—
177#2316C2214yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×#127C2212yes—
182C4×#127C2211yescharacteristic
183C4×#124C2214yes—
184C4×#124C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×#121C2212yes—
187C4×#121C2212yes—
188C4×#121C2212yes—
189#2295C2212yes—
190#2293C2212yes—
191#2293C2214yes—
192#2285C2212yes—
193#2283C2212yes—
194C42×Q8C2211yescharacteristic
195C42×D4C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C4×#117C2212yes—
198C4×#117C2212yes—
199#555—28no—
200#555—48no—
201#554—216no—
202#533—48no—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2311yescharacteristic
208C2×#127C2311yescharacteristic
209C2×#127C2312yes—
210#529—48no—
211C2×#126C2314yes—
212C2×#125C2314yes—
213C2×#125C2314yes—
214C2×#125C2312yes—
215C2×#125C2314yes—
216C2×#124C2314yes—
217C2×#124C2312yes—
218C2×#124C2318yes—
219C2×#124C2312yes—
220C2×#123C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2314yes—
229C2×#121C2312yes—
230C2×#121C2312yes—
231C2×#121C2314yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×#121C2312yes—
235C2×#121C2312yes—
236C2×#121C2314yes—
237C2×#121C2318yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2312yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2314yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×#117C2312yes—
261C2×#117C2312yes—
262C2×#117C2314yes—
263C2×#117C2314yes—
264C2×#117C2314yes—
265C2×#117C2312yes—
266C2×#117C2312yes—
267C2×#117C2314yes—
268C2×#117C2318yes—
269C22×C4⋊C4C2314yes—
270C22×C42C2312yes—
271C22×C42C2312yes—
272#401C2318yes—
273#401C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#399C2318yes—
278#399C2318yes—
279#399C2318yes—
280#399C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2314yes—
284#398C2318yes—
285#398C2318yes—
286#397C2314yes—
287#397C2314yes—
288#397C2318yes—
289#397C2318yes—
290#397C2314yes—
291#397C2318yes—
292#397C2318yes—
293#397C2314yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#396C2314yes—
298#396C2318yes—
299#396C2318yes—
300#396C2314yes—
301#396C2314yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#395C2318yes—
306#394C2314yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2314yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2314yes—
318#394C2318yes—
319#394C2318yes—
320#393C2318yes—
321#392C2318yes—
322#392C2314yes—
323#391C2314yes—
324#391C2312yes—
325#391C2312yes—
326#391C2314yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#391C2314yes—
331#391C2314yes—
332#391C2312yes—
333#391C2318yes—
334#390C2312yes—
335#390C2314yes—
336#390C2314yes—
337#390C2312yes—
338#390C2312yes—
339#390C2312yes—
340#390C2312yes—
341#390C2314yes—
342#390C2314yes—
343#390C2312yes—
344#390C2314yes—
345#390C2314yes—
346#390C2314yes—
347#390C2312yes—
348#390C2312yes—
349#390C2312yes—
350#390C2318yes—
351#390C2314yes—
352#390C2318yes—
353#390C2314yes—
354#390C2312yes—
355#390C2318yes—
356#390C2312yes—
357#389C2314yes—
358#389C2312yes—
359#389C2314yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2318yes—
369#389C2318yes—
370#389C2314yes—
371#389C2312yes—
372#389C2318yes—
373#389C2318yes—
374#389C2318yes—
375#389C2314yes—
376#389C2314yes—
377#389C2312yes—
378#389C2318yes—
379#389C2318yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2318yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2318yes—
388#389C2312yes—
389#389C2312yes—
390#388C2314yes—
391#388C2314yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2314yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2314yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2318yes—
409#388C2318yes—
410#388C2314yes—
411#388C2314yes—
412#388C2318yes—
413#388C2318yes—
414#388C2314yes—
415#388C2314yes—
416#388C2318yes—
417#388C2318yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#386C2318yes—
433#386C2314yes—
434#386C2314yes—
435#386C2318yes—
436#386C2318yes—
437#386C2314yes—
438#385C2314yes—
439#385C2318yes—
440#384C2312yes—
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#384C2311yescharacteristic
444#384C2312yes—
445#384C2314yes—
446#384C2312yes—
447#384C2314yes—
448#384C2312yes—
449#384C2314yes—
450#384C2312yes—
451#383C2314yes—
452#382C2314yes—
453#382C2312yes—
454#382C2312yes—
455#382C2312yes—
456#382C2314yes—
457#382C2314yes—
458#381C2314yes—
459#381C2318yes—
460#380C2314yes—
461#380C2314yes—
462#380C2318yes—
463#380C2318yes—
464#380C2314yes—
465#380C2314yes—
466#380C2312yes—
467#380C2312yes—
468#380C2314yes—
469#380C2312yes—
470#380C2312yes—
471#380C2318yes—
472#380C2314yes—
473#380C2312yes—
474#380C2314yes—
475#380C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2318yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2311yescharacteristic
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518#376C2314yes—
519#376C2314yes—
520#376C2314yes—
521C43C2311yescharacteristic
522C43C2312yes—
523C43C2314yes—
524C22×Q8C2412yes—
525C22×Q8C2411yescharacteristic
526C22×Q8C2414yes—
527C22×Q8C2412yes—
528C22×D4C2411yescharacteristic
529C22×D4C2412yes—
530C22×D4C2412yes—
531C22×D4C2411yescharacteristic
532C22×D4C2414yes—
533C22×D4C2412yes—
534C22×D4C2414yes—
535C22×D4C2414yes—
536C22×D4C2418yes—
537C23×C4C2414yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2418yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C4⋊Q8—24no—
546C4⋊Q8—28no—
547C4⋊Q8—44no—
548C4⋊Q8—82no—
549C4⋊Q8#4118yes—
550#127—24no—
551#127—44no—
552#126—48no—
553#125—216no—
554#125—48no—
555#125—44no—
556#125—48no—
557#124—216no—
558#124—44no—
559#124—44no—
560#124—416no—
561#123—48no—
562C22⋊Q8—232no—
563C22⋊Q8—216no—
564C22⋊Q8—48no—
565C22⋊Q8—44no—
566C22⋊Q8—44no—
567C22⋊Q8—48no—
568C22⋊Q8—48no—
569C22⋊Q8—84no—
570#121—28no—
571#121—28no—
572#121—44no—
573#121—48no—
574#121—44no—
575#121—48no—
576#121—48no—
577#121—84no—
578#121—88no—
579C4×Q8—28no—
580C4×Q8—24no—
581C4×Q8—24no—
582C4×Q8—44no—
583C4×Q8—42no—
584C4×Q8—48no—
585C4×Q8—48no—
586C4×Q8—84no—
587C4×D4—216no—
588C4×D4—28no—
589C4×D4—24no—
590C4×D4—24no—
591C4×D4—28no—
592C4×D4—24no—
593C4×D4—24no—
594C4×D4—42no—
595C4×D4—48no—
596C4×D4—42no—
597C4×D4—44no—
598C4×D4—48no—
599C4×D4—48no—
600C4×D4—48no—
601#117—28no—
602#117—28no—
603#117—48no—
604#117—44no—
605#117—44no—
606#117—48no—
607#117—48no—
608#117—48no—
609#117—88no—
610C2×C4⋊C4—216no—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C42—28no—
697C2×C42—28no—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2414yes—
701C2×C42C2411yescharacteristic
702C2×C42C2414yes—
703C2×C42C2412yes—
704C2×C42C2414yes—
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2418yes—
715C2×C42C2414yes—
716C2×C42C2418yes—
717C2×C42C2418yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726#95C2412yes—
727#95C2412yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2412yes—
740#95C2412yes—
741#95C2412yes—
742#95C2412yes—
743#95C2414yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2412yes—
751#95C2412yes—
752#95C2412yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756#95C2414yes—
757#95C2418yes—
758#95C2414yes—
759#95C2418yes—
760#95C2418yes—
761#95C2414yes—
762#95C2418yes—
763#95C2418yes—
764C24C2514yes—
765C24C2512yes—
766C24C2512yes—
767C2×Q8—24no—
768C2×Q8—22no—
769C2×Q8—24no—
770C2×Q8—28no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—24no—
774C2×Q8—42no—
775C2×Q8—42no—
776C2×Q8—44no—
777C2×Q8—44no—
778C2×Q8C2×#4118yes—
779C2×D4—24no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—28no—
783C2×D4—22no—
784C2×D4—24no—
785C2×D4—22no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—24no—
793C2×D4—44no—
794C2×D4—42no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4—44no—
799C2×D4—42no—
800C2×D4—44no—
801C2×D4—44no—
802C2×D4—44no—
803C2×D4—48no—
804C2×D4—48no—
805C2×D4—48no—
806C22×C4—28no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—28no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—28no—
820C22×C4—24no—
821C22×C4—216no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—48no—
825C22×C4—42no—
826C22×C4—48no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2512yes—
833C22×C4C2512yes—
834C22×C4C2512yes—
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2511yescharacteristic
839C22×C4C2514yes—
840C22×C4C2512yes—
841C22×C4C2514yes—
842C22×C4C2518yes—
843C22×C4C2512yes—
844C22×C4C2514yes—
845C22×C4C2512yes—
846C22×C4C2514yes—
847C22×C4C2511yescharacteristic
848C22×C4C2511yescharacteristic
849C22×C4C2511yescharacteristic
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C22×C4C2511yescharacteristic
853C4⋊C4—24no—
854C4⋊C4—216no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—24no—
858C4⋊C4—28no—
859C4⋊C4—216no—
860C4⋊C4—22no—
861C4⋊C4—24no—
862C4⋊C4—28no—
863C4⋊C4—24no—
864C4⋊C4—28no—
865C4⋊C4—22no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—24no—
871C4⋊C4—22no—
872C4⋊C4—22no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—22no—
877C4⋊C4—28no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—48no—
882C4⋊C4—42no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—42no—
887C4⋊C4—44no—
888C4⋊C4—42no—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—48no—
895C4⋊C4—44no—
896C4⋊C4—42no—
897C4⋊C4—48no—
898C4⋊C4—48no—
899C4⋊C4—44no—
900C4⋊C4C2×#4118yes—
901C4⋊C4C2×#4118yes—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—216no—
905C22⋊C4—28no—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—28no—
909C22⋊C4—24no—
910C22⋊C4—24no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—44no—
916C22⋊C4—48no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—48no—
920C22⋊C4—42no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C22⋊C4—42no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—48no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C42—28no—
939C42—28no—
940C42—24no—
941C42—24no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—24no—
947C42—24no—
948C42—22no—
949C42—28no—
950C42—24no—
951C42—22no—
952C42—22no—
953C42—24no—
954C42—44no—
955C42—44no—
956C42—48no—
957C42—48no—
958C42—44no—
959C42—48no—
960C42—42no—
961C42—42no—
962C42—41no—
963C42C2×#4114yes—
964C42H(5,𝔽2)14yes—
965C422−1+414yes—
966C23—24no—
967C23—22no—
968C23—22no—
969C23—24no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—24no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—24no—
979C23—24no—
980C23—22no—
981C23—22no—
982C23—24no—
983C23—22no—
984C23—22no—
985C23—24no—
986C23—22no—
987C23C2611yescharacteristic
988Q8—48no—
989Q8—48no—
990Q8—44no—
991Q8—88no—
992D4—44no—
993D4—48no—
994D4—44no—
995D4—48no—
996D4—88no—
997D4—84no—
998D4—88no—
999D4—88no—
1000D4—168no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—24no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—24no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—28no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—28no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—28no—
1056C2×C4—24no—
1057C2×C4—416no—
1058C2×C4—48no—
1059C2×C4—48no—
1060C2×C4—48no—
1061C2×C4—48no—
1062C2×C4—816no—
1063C2×C4—84no—
1064C2×C4—84no—
1065C2×C4C22×#4118yes—
1066C2×C4C22×#4112yes—
1067C2×C4C22×#4112yes—
1068C2×C4C22×#4112yes—
1069C2×C4C2×H(5,𝔽2)12yes—
1070C2×C4C2×H(5,𝔽2)12yes—
1071C2×C4C2×H(5,𝔽2)12yes—
1072C2×C4C2×2−1+412yes—
1073C2×C4C2×2−1+412yes—
1074C2×C4C2×2−1+412yes—
1075C2×C4#58512yes—
1076C2×C4#58512yes—
1077C2×C4#58512yes—
1078C22—44no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—44no—
1084C22—42no—
1085C22—44no—
1086C22—42no—
1087C22—44no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—44no—
1092C22—42no—
1093C22—42no—
1094C22—44no—
1095C22—42no—
1096C22—42no—
1097C22—44no—
1098C22—42no—
1099C22C23×#4111yescharacteristic
1100C22C22×H(5,𝔽2)11yescharacteristic
1101C22C22×2−1+411yescharacteristic
1102C22C2×#58511yescharacteristic
1103C22C2×#58511yescharacteristic
1104C22C2×#58511yescharacteristic
1105C22H(7,𝔽2)11yescharacteristic
1106C4—28no—
1107C4—22no—
1108C4—22no—
1109C4—22no—
1110C4—44no—
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—41no—
1115C4—44no—
1116C4—42no—
1117C4—42no—
1118C4—44no—
1119C4—44no—
1120C4—42no—
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—48no—
1126C4#351714yes—
1127C4#351814yes—
1128C4#354714yes—
1129C2—84no—
1130C2—82no—
1131C2—82no—
1132C2C2×#354711yescharacteristic
1133C2C2×#351711yescharacteristic
1134C2C2×#351811yescharacteristic
1135C2#6292911yescharacteristic
1136C2#6295511yescharacteristic
1137C2#6299211yescharacteristic
1138C2#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. #59823C2semidirect
2. #59652C2semidirect
3. #59243C2semidirect
4. #59050C2semidirect
5. #51743C2semidirect
6. #46083C2semidirect
7. #45396C2semidirect
8. #45067C2semidirect
9. #42624C2semidirect
10. #42620C2semidirect
11. #39763C2semidirect
12. #39194C2semidirect
13. #39194C2semidirect
14. #38942C2semidirect
15. #38922C2semidirect
16. #36563C2semidirect
17. #36302C2semidirect
18. #36301C2semidirect
19. #36187C2semidirect
20. #36134C2semidirect
21. #35202C2semidirect
22. #35201C2semidirect
23. #34945C2semidirect
24. #34934C2semidirect
25. #34484C2semidirect
26. C4×#555C2semidirect

Maximal subgroups

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

subgroupindex
#598232
#596522
#592432
#590502
#517432
#460832
#453962
#450672
#426242
#426202
#397632
#391942
#389422
#389222
#365632
#363022
#363012
#361872
#361342
#352022
#352012
#349452
#349342
#344842
C4×#5552