Finite Group Databasebeta

← #7696400

Subgroups — #7696400

Order 512.

4894 conjugacy classes of subgroups.

The subgroup lattice has 1438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60019C212yesmaximal, complemented
2#59782C214yesmaximal, complemented
3#59421C212yesmaximal, complemented
4#59379C211yesmaximal, characteristic, complemented
5#52300C212yesmaximal, complemented
6#52275C211yesmaximal, characteristic, complemented
7#45418C211yesmaximal, characteristic, complemented
8#45351C211yesmaximal, characteristic, complemented
9#45320C212yesmaximal, complemented
10#45268C212yesmaximal, complemented
11#44821C214yesmaximal, complemented
12#44814C212yesmaximal, complemented
13#44675C214yesmaximal, complemented
14#44671C212yesmaximal, complemented
15#39673C212yesmaximal, complemented
16#39261C212yesmaximal, complemented
17#39188C212yesmaximal, complemented
18#38851C214yesmaximal, complemented
19#38587C214yesmaximal, complemented
20#38558C214yesmaximal, complemented
21#36582C211yesmaximal, characteristic, complemented
22#36484C212yesmaximal, complemented
23#36077C212yesmaximal, complemented
24#36062C211yesmaximal, characteristic
25#36050C212yesmaximal, complemented
26#35985C211yesmaximal, characteristic, complemented
27#34326C212yesmaximal, complemented
28#34311C212yesmaximal, complemented
29#34291C212yesmaximal, complemented
30C2×#556C2212yes—
31C2×#555C2211yescharacteristic
32C2×#553C2211yescharacteristic
33C2×D4×Q8C2212yes—
34C2×D4×Q8C2212yes—
35C2×#519C2211yescharacteristic
36C2×#519C2212yes—
37C22×C4×Q8C2211yescharacteristic
38#2865C2214yes—
39#2864C2212yes—
40#2854C2211yescharacteristic
41#2854C2212yes—
42#2807C2211yescharacteristic
43#2803C2214yes—
44#2803C2214yes—
45#2803C2212yes—
46#2799C2212yes—
47#2798C2214yes—
48#2798C2212yes—
49#2797C2212yes—
50#2795C2214yes—
51#2792C2214yes—
52#2791C2214yes—
53#2777C2214yes—
54#2777C2214yes—
55#2774C2214yes—
56#2773C2212yes—
57#2771C2211yescharacteristic
58#2764C2212yes—
59#2758C2214yes—
60#2755C2214yes—
61#2755C2214yes—
62#2754C2212yes—
63#2754C2214yes—
64#2752C2211yescharacteristic
65#2741C2214yes—
66#2739C2214yes—
67#2722C2212yes—
68#2718C2214yes—
69#2717C2212yes—
70#2716C2214yes—
71#2716C2214yes—
72#2712C2211yescharacteristic
73#2710C2212yes—
74#2702C2214yes—
75#2702C2214yes—
76#2701C2214yes—
77#2692C2214yes—
78#2692C2214yes—
79#2677C2212yes—
80#2677C2212yes—
81#2677C2214yes—
82#2661C2212yes—
83#2660C2211yescharacteristic
84#2651C2214yes—
85#2647C2212yes—
86#2637C2212yes—
87#2632C2214yes—
88#2624C2211yescharacteristic
89#2624C2212yes—
90#2605C2214yes—
91#2604C2212yes—
92#2599C2214yes—
93#2596C2214yes—
94#2596C2214yes—
95#2595C2214yes—
96#2595C2214yes—
97#2593C2214yes—
98#2593C2214yes—
99#2592C2214yes—
100#2591C2212yes—
101#2590C2214yes—
102#2588C2214yes—
103#2588C2214yes—
104#2586C2212yes—
105#2586C2214yes—
106#2585C2214yes—
107#2582C2212yes—
108#2581C2212yes—
109#2580C2212yes—
110#2579C2212yes—
111#2577C2214yes—
112#2577C2214yes—
113#2562C2211yescharacteristic
114#2560C2214yes—
115#2560C2214yes—
116#2559C2214yes—
117#2555C2214yes—
118#2547C2211yescharacteristic
119#2543C2212yes—
120#2537C2212yes—
121#2536C2212yes—
122#2536C2212yes—
123#2535C2212yes—
124#2532C2214yes—
125#2532C2214yes—
126#2532C2214yes—
127#2530C2214yes—
128#2529C2214yes—
129#2524C2214yes—
130#2524C2214yes—
131#2523C2212yes—
132#2522C2214yes—
133#2522C2214yes—
134#2521C2214yes—
135#2521C2214yes—
136#2521C2214yes—
137#2518C2214yes—
138#2518C2214yes—
139#2518C2214yes—
140#2517C2212yes—
141#2516C2214yes—
142#2516C2214yes—
143#2498C2212yes—
144#2497C2212yes—
145#2496C2212yes—
146#2495C2212yes—
147#2495C2212yes—
148#2492C2214yes—
149#2477C2214yes—
150#2477C2214yes—
151#2476C2214yes—
152#2476C2214yes—
153#2476C2214yes—
154#2474C2214yes—
155#2474C2214yes—
156#2470C2214yes—
157#2469C2214yes—
158#2467C2214yes—
159#2467C2214yes—
160#2463C2212yes—
161#2463C2214yes—
162#2463C2212yes—
163#2458C2214yes—
164#2453C2212yes—
165#2453C2212yes—
166#2451C2212yes—
167#2451C2212yes—
168#2439C2214yes—
169#2436C2211yescharacteristic
170#2436C2212yes—
171#2436C2211yescharacteristic
172#2427C2214yes—
173#2426C2212yes—
174#2426C2212yes—
175#2426C2212yes—
176#2426C2212yes—
177#2423C2212yes—
178#2423C2212yes—
179#2421C2212yes—
180#2421C2212yes—
181#2409C2212yes—
182#2409C2211yescharacteristic
183#2409C2211yescharacteristic
184#2402C2214yes—
185#2398C2212yes—
186#2398C2212yes—
187#2397C2211yescharacteristic
188#2396C2214yes—
189#2395C2212yes—
190#2395C2211yescharacteristic
191#2395C2212yes—
192#2373C2214yes—
193#2373C2214yes—
194#2372C2212yes—
195#2368C2214yes—
196#2367C2212yes—
197#2367C2212yes—
198#2365C2212yes—
199#2365C2214yes—
200#2365C2214yes—
201#2363C2214yes—
202#2362C2214yes—
203#2362C2214yes—
204#2362C2212yes—
205#2362C2212yes—
206#2362C2214yes—
207#2362C2212yes—
208#2360C2214yes—
209#2360C2212yes—
210#2357C2212yes—
211#2356C2212yes—
212#2355C2212yes—
213#2355C2212yes—
214#2354C2214yes—
215#2354C2212yes—
216#2352C2214yes—
217#2352C2212yes—
218#2351C2212yes—
219Q8×C4⋊C4C2212yes—
220#2347C2212yes—
221#2346C2211yescharacteristic
222#2345C2211yescharacteristic
223#2343C2214yes—
224Q8×C22⋊C4C2212yes—
225Q8×C22⋊C4C2212yes—
226Q8×C22⋊C4C2212yes—
227Q8×C22⋊C4C2212yes—
228#2334C2214yes—
229#2332C2214yes—
230#2327C2214yes—
231#2327C2212yes—
232#2327C2212yes—
233#2326C2212yes—
234#2323C2212yes—
235#2323C2214yes—
236#2323C2212yes—
237#2323C2214yes—
238#2323C2212yes—
239#2323C2214yes—
240C4×C4⋊Q8C2212yes—
241C4×C4⋊Q8C2214yes—
242C4×#126C2214yes—
243C4×#126C2214yes—
244C4×#124C2212yes—
245C4×#124C2212yes—
246C4×C22⋊Q8C2214yes—
247C4×C22⋊Q8C2212yes—
248C4×#123C2211yescharacteristic
249C4×#123C2212yes—
250#2298C2214yes—
251#2295C2212yes—
252#2293C2212yes—
253#2293C2214yes—
254#2290C2212yes—
255#2290C2214yes—
256#2276C2212yes—
257#2275C2211yescharacteristic
258C42×Q8C2212yes—
259C23×Q8C2311yescharacteristic
260C23×Q8C2312yes—
261C23×Q8C2311yescharacteristic
262#556—216no—
263#555—44no—
264#553—44no—
265D4×Q8—216no—
266D4×Q8—216no—
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2312yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#126C2312yes—
275C2×#125C2311yescharacteristic
276C2×#124C2312yes—
277C2×#124C2312yes—
278C2×#124C2314yes—
279C2×#124C2312yes—
280C2×#124C2312yes—
281C2×#123C2312yes—
282C2×#123C2311yescharacteristic
283C2×#123C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2312yes—
293C2×#121C2312yes—
294C2×#121C2311yescharacteristic
295C2×#121C2314yes—
296C2×#121C2311yescharacteristic
297C2×#121C2312yes—
298C2×#121C2312yes—
299#519—44no—
300#519—48no—
301C2×C4×Q8—44no—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2314yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2314yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2312yes—
326C2×C4×D4C2311yescharacteristic
327C2×#117C2314yes—
328C2×#117C2311yescharacteristic
329C2×#117C2312yes—
330C2×#117C2312yes—
331C2×#117C2311yescharacteristic
332C2×#117C2314yes—
333C2×#117C2314yes—
334C2×#117C2314yes—
335C2×#117C2312yes—
336C22×C4⋊C4C2311yescharacteristic
337C22×C4⋊C4C2312yes—
338C22×C42C2311yescharacteristic
339C22×C42C2312yes—
340#400C2312yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2311yescharacteristic
350#400C2314yes—
351#400C2312yes—
352#400C2312yes—
353#400C2314yes—
354#400C2312yes—
355#400C2314yes—
356#399C2311yescharacteristic
357#399C2312yes—
358#399C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2312yes—
362#399C2311yescharacteristic
363#399C2311yescharacteristic
364#399C2312yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2311yescharacteristic
372#398C2314yes—
373#398C2314yes—
374#398C2312yes—
375#398C2314yes—
376#398C2312yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2312yes—
384#397C2314yes—
385#397C2314yes—
386#397C2312yes—
387#397C2314yes—
388#397C2314yes—
389#397C2312yes—
390#397C2312yes—
391#397C2311yescharacteristic
392#397C2312yes—
393#397C2314yes—
394#397C2312yes—
395#397C2312yes—
396#397C2312yes—
397#397C2312yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2312yes—
408#395C2314yes—
409#395C2312yes—
410#394C2314yes—
411#394C2314yes—
412#394C2312yes—
413#394C2314yes—
414#394C2312yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2312yes—
423#394C2312yes—
424#394C2312yes—
425#394C2312yes—
426#394C2314yes—
427#393C2314yes—
428#393C2314yes—
429#393C2312yes—
430#393C2312yes—
431#393C2314yes—
432#393C2314yes—
433#393C2312yes—
434#393C2312yes—
435#393C2312yes—
436#393C2312yes—
437#392C2311yescharacteristic
438#392C2312yes—
439#392C2311yescharacteristic
440#392C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2314yes—
446#391C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2314yes—
450#391C2312yes—
451#391C2312yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2314yes—
459#391C2312yes—
460#391C2314yes—
461#391C2312yes—
462#391C2314yes—
463#391C2314yes—
464#391C2312yes—
465#390C2314yes—
466#390C2314yes—
467#390C2312yes—
468#390C2314yes—
469#390C2314yes—
470#390C2312yes—
471#390C2314yes—
472#390C2312yes—
473#390C2312yes—
474#390C2312yes—
475#389C2314yes—
476#389C2312yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
492#389C2314yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#389C2312yes—
500#389C2312yes—
501#388C2312yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2312yes—
508#388C2314yes—
509#388C2312yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2312yes—
514#388C2314yes—
515#388C2312yes—
516#388C2312yes—
517#388C2312yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2312yes—
549#388C2314yes—
550#388C2314yes—
551#388C2312yes—
552#388C2312yes—
553#388C2312yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#387C2312yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2312yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2312yes—
597#387C2314yes—
598#387C2312yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2312yes—
603#387C2314yes—
604#387C2312yes—
605#387C2312yes—
606#386C2312yes—
607#386C2314yes—
608#386C2312yes—
609#386C2311yescharacteristic
610#386C2312yes—
611#386C2312yes—
612#386C2314yes—
613#386C2312yes—
614#386C2314yes—
615#386C2312yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2312yes—
621#385C2312yes—
622#385C2314yes—
623#385C2311yescharacteristic
624#385C2314yes—
625#385C2312yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2312yes—
630#385C2314yes—
631#385C2314yes—
632#385C2312yes—
633#384C2312yes—
634#384C2314yes—
635#384C2312yes—
636#383C2314yes—
637#383C2314yes—
638#383C2314yes—
639#383C2314yes—
640#382C2312yes—
641#382C2312yes—
642#382C2314yes—
643#382C2312yes—
644#382C2314yes—
645#382C2312yes—
646#382C2312yes—
647#381C2314yes—
648#381C2311yescharacteristic
649#380C2312yes—
650#380C2312yes—
651#380C2312yes—
652#380C2314yes—
653#380C2314yes—
654#380C2312yes—
655#380C2314yes—
656#380C2312yes—
657#380C2314yes—
658#380C2311yescharacteristic
659#380C2311yescharacteristic
660#380C2312yes—
661#380C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2311yescharacteristic
708C4×C22⋊C4C2311yescharacteristic
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712#376C2312yes—
713#376C2311yescharacteristic
714#376C2314yes—
715#376C2312yes—
716#376C2314yes—
717C2×#95C2312yes—
718C43C2314yes—
719C43C2312yes—
720C22×Q8—28no—
721C22×Q8—28no—
722C22×Q8—28no—
723C22×Q8—28no—
724C22×Q8—42no—
725C22×Q8—42no—
726C22×Q8—44no—
727C22×Q8C2412yes—
728C22×Q8C2414yes—
729C22×Q8C2412yes—
730C22×Q8C2412yes—
731C22×Q8C2412yes—
732C22×Q8C2412yes—
733C22×Q8C2412yes—
734C22×D4C2411yescharacteristic
735C22×D4C2412yes—
736C22×D4C2412yes—
737C22×D4C2412yes—
738C22×D4C2411yescharacteristic
739C22×D4C2411yescharacteristic
740C22×D4C2414yes—
741C22×D4C2412yes—
742C23×C4C2411yescharacteristic
743C23×C4C2411yescharacteristic
744C23×C4C2412yes—
745C23×C4C2412yes—
746C23×C4C2414yes—
747C23×C4C2412yes—
748C23×C4C2412yes—
749C23×C4C2412yes—
750C23×C4C2414yes—
751C23×C4C2411yescharacteristic
752C23×C4C2411yescharacteristic
753C4⋊Q8—216no—
754C4⋊Q8—216no—
755C4⋊Q8—42no—
756C4⋊Q8#41116yes—
757#126—216no—
758#126—216no—
759#126—44no—
760#126—48no—
761#125—42no—
762#124—28no—
763#124—28no—
764#124—48no—
765#124—44no—
766#124—44no—
767#123—44no—
768#123—42no—
769#123—44no—
770C22⋊Q8—28no—
771C22⋊Q8—28no—
772C22⋊Q8—28no—
773C22⋊Q8—28no—
774C22⋊Q8—216no—
775C22⋊Q8—216no—
776C22⋊Q8—216no—
777C22⋊Q8—216no—
778C22⋊Q8—216no—
779#121—44no—
780#121—44no—
781#121—48no—
782#121—42no—
783#121—42no—
784#121—44no—
785C4×Q8—28no—
786C4×Q8—28no—
787C4×Q8—28no—
788C4×Q8—28no—
789C4×Q8—28no—
790C4×Q8—28no—
791C4×Q8—28no—
792C4×Q8—48no—
793C4×Q8—44no—
794C4×Q8—48no—
795C4×Q8—48no—
796C4×Q8—44no—
797C4×Q8—44no—
798C4×Q8—44no—
799C4×Q8—44no—
800C4×Q8—44no—
801C4×D4—216no—
802C4×D4—216no—
803C4×D4—24no—
804C4×D4—28no—
805C4×D4—28no—
806C4×D4—28no—
807C4×D4—44no—
808C4×D4—42no—
809C4×D4—42no—
810#117—216no—
811#117—24no—
812#117—28no—
813#117—44no—
814#117—42no—
815#117—44no—
816#117—48no—
817#117—48no—
818#117—48no—
819C2×C4⋊C4—24no—
820C2×C4⋊C4—44no—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2411yescharacteristic
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2411yescharacteristic
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2411yescharacteristic
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2411yescharacteristic
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C42—42no—
927C2×C42—44no—
928C2×C42C2414yes—
929C2×C42C2412yes—
930C2×C42C2414yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2411yescharacteristic
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2414yes—
949C2×C42C2412yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2412yes—
957#95C2411yescharacteristic
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2411yescharacteristic
962#95C2412yes—
963#95C2414yes—
964#95C2411yescharacteristic
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2411yescharacteristic
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2414yes—
1026C24C2512yes—
1027C24C2511yescharacteristic
1028C24C2512yes—
1029C24C2511yescharacteristic
1030C2×Q8—24no—
1031C2×Q8—24no—
1032C2×Q8—28no—
1033C2×Q8—28no—
1034C2×Q8—28no—
1035C2×Q8—28no—
1036C2×Q8—24no—
1037C2×Q8—24no—
1038C2×Q8—24no—
1039C2×Q8—44no—
1040C2×Q8—42no—
1041C2×Q8—42no—
1042C2×Q8—42no—
1043C2×Q8—42no—
1044C2×Q8—42no—
1045C2×Q8—42no—
1046C2×Q8—42no—
1047C2×Q8—416no—
1048C2×Q8—416no—
1049C2×Q8—432no—
1050C2×Q8C2×#4118yes—
1051C2×Q8C2×#4118yes—
1052C2×D4—24no—
1053C2×D4—24no—
1054C2×D4—22no—
1055C2×D4—24no—
1056C2×D4—24no—
1057C2×D4—24no—
1058C2×D4—22no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—41no—
1064C2×D4—41no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D4—41no—
1068C2×D4—42no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C22×C4—22no—
1074C22×C4—28no—
1075C22×C4—28no—
1076C22×C4—28no—
1077C22×C4—28no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—24no—
1081C22×C4—24no—
1082C22×C4—22no—
1083C22×C4—22no—
1084C22×C4—24no—
1085C22×C4—28no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—41no—
1089C22×C4—42no—
1090C22×C4—44no—
1091C22×C4—42no—
1092C22×C4—41no—
1093C22×C4—41no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—42no—
1099C22×C4C2511yescharacteristic
1100C22×C4C2512yes—
1101C22×C4C2514yes—
1102C22×C4C2512yes—
1103C22×C4C2514yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2511yescharacteristic
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2514yes—
1110C22×C4C2514yes—
1111C22×C4C2511yescharacteristic
1112C22×C4C2512yes—
1113C22×C4C2511yescharacteristic
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2514yes—
1121C22×C4C2514yes—
1122C22×C4C2512yes—
1123C22×C4C2511yescharacteristic
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—28no—
1129C4⋊C4—28no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—28no—
1133C4⋊C4—28no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—28no—
1137C4⋊C4—28no—
1138C4⋊C4—28no—
1139C4⋊C4—28no—
1140C4⋊C4—22no—
1141C4⋊C4—24no—
1142C4⋊C4—28no—
1143C4⋊C4—22no—
1144C4⋊C4—24no—
1145C4⋊C4—28no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—41no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—42no—
1164C4⋊C4—41no—
1165C4⋊C4—41no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—41no—
1170C4⋊C4—44no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4C2×#41116yes—
1178C4⋊C4C2×#41116yes—
1179C4⋊C4H(5,𝔽2)14yes—
1180C22⋊C4—28no—
1181C22⋊C4—22no—
1182C22⋊C4—24no—
1183C22⋊C4—24no—
1184C22⋊C4—28no—
1185C22⋊C4—28no—
1186C22⋊C4—28no—
1187C22⋊C4—28no—
1188C22⋊C4—28no—
1189C22⋊C4—28no—
1190C22⋊C4—24no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—24no—
1194C22⋊C4—28no—
1195C22⋊C4—28no—
1196C22⋊C4—28no—
1197C22⋊C4—24no—
1198C22⋊C4—28no—
1199C22⋊C4—24no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—44no—
1207C22⋊C4—42no—
1208C22⋊C4—41no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—44no—
1218C22⋊C4—41no—
1219C22⋊C4—42no—
1220C22⋊C4—41no—
1221C22⋊C4—42no—
1222C22⋊C4—44no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—44no—
1226C22⋊C4—42no—
1227C22⋊C4—44no—
1228C22⋊C4—42no—
1229C42—28no—
1230C42—28no—
1231C42—28no—
1232C42—28no—
1233C42—24no—
1234C42—24no—
1235C42—28no—
1236C42—24no—
1237C42—28no—
1238C42—24no—
1239C42—28no—
1240C42—24no—
1241C42—22no—
1242C42—44no—
1243C42—42no—
1244C42—44no—
1245C42—42no—
1246C42—44no—
1247C42—44no—
1248C42—42no—
1249C42—42no—
1250C42—44no—
1251C42—44no—
1252C42—44no—
1253C42—44no—
1254C42—42no—
1255C42—42no—
1256C42—44no—
1257C42C2×#4118yes—
1258C23—22no—
1259C23—21no—
1260C23—22no—
1261C23—21no—
1262C23—24no—
1263C23—22no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—21no—
1268C23—22no—
1269C23—21no—
1270C23—22no—
1271C23—22no—
1272C23—22no—
1273C23—24no—
1274C23—22no—
1275C23—22no—
1276C23—21no—
1277C23—22no—
1278C23—22no—
1279C23#58512yes—
1280C23C2611yescharacteristic
1281Q8—216no—
1282Q8—216no—
1283Q8—416no—
1284Q8—48no—
1285Q8—48no—
1286Q8—84no—
1287Q8—162no—
1288D4—48no—
1289D4—48no—
1290D4—44no—
1291D4—84no—
1292D4—82no—
1293D4—82no—
1294D4—162no—
1295D4—164no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—21no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—21no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—21no—
1358C2×C4—48no—
1359C2×C4—416no—
1360C2×C4—48no—
1361C2×C4—44no—
1362C2×C4—44no—
1363C2×C4—44no—
1364C2×C4—48no—
1365C2×C4—88no—
1366C2×C4—84no—
1367C2×C4—84no—
1368C2×C4—82no—
1369C2×C4C22×#4114yes—
1370C2×C4C22×#4114yes—
1371C2×C4C22×#4118yes—
1372C2×C4C22×#4118yes—
1373C2×C4C22×#4114yes—
1374C2×C4C2×H(5,𝔽2)14yes—
1375C2×C4C2×H(5,𝔽2)12yes—
1376C22—24no—
1377C22—22no—
1378C22—41no—
1379C22—42no—
1380C22—41no—
1381C22—44no—
1382C22—42no—
1383C22—42no—
1384C22—42no—
1385C22—42no—
1386C22—42no—
1387C22—41no—
1388C22—42no—
1389C22—42no—
1390C22—44no—
1391C22—42no—
1392C22—42no—
1393C22—41no—
1394C22—42no—
1395C22—42no—
1396C22—41no—
1397C22—42no—
1398C22C23×#4112yes—
1399C22C22×H(5,𝔽2)11yescharacteristic
1400C22C2×#58511yescharacteristic
1401C222−1+612yes—
1402C222−1+611yescharacteristic
1403C4—24no—
1404C4—24no—
1405C4—24no—
1406C4—28no—
1407C4—28no—
1408C4—44no—
1409C4—44no—
1410C4—42no—
1411C4—42no—
1412C4—42no—
1413C4—42no—
1414C4—41no—
1415C4—42no—
1416C4—42no—
1417C4—42no—
1418C4—44no—
1419C4—42no—
1420C4—42no—
1421C4—42no—
1422C4—41no—
1423C4—44no—
1424C4—42no—
1425C4—41no—
1426C4—41no—
1427C4#348114yes—
1428C2—42no—
1429C2—82no—
1430C2—82no—
1431C2—81no—
1432C2C2×#348111yescharacteristic
1433C2#6285012yes—
1434C2#6291911yescharacteristic
1435C2#6300512yes—
1436C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36062C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60019C2semidirect
2. #59782C2semidirect
3. #59421C2semidirect
4. #59379C2semidirect
5. #52300C2semidirect
6. #52275C2semidirect
7. #45418C2semidirect
8. #45351C2semidirect
9. #45320C2semidirect
10. #45268C2semidirect
11. #44821C2semidirect
12. #44814C2semidirect
13. #44675C2semidirect
14. #44671C2semidirect
15. #39673C2semidirect
16. #39261C2semidirect
17. #39188C2semidirect
18. #38851C2semidirect
19. #38587C2semidirect
20. #38558C2semidirect
21. #36582C2semidirect
22. #36484C2semidirect
23. #36077C2semidirect
25. #36050C2semidirect
26. #35985C2semidirect
27. #34326C2semidirect
28. #34311C2semidirect
29. #34291C2semidirect

Maximal subgroups

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

subgroupindex
#600192
#597822
#594212
#593792
#523002
#522752
#454182
#453512
#453202
#452682
#448212
#448142
#446752
#446712
#396732
#392612
#391882
#388512
#385872
#385582
#365822
#364842
#360772
#360622
#360502
#359852
#343262
#343112
#342912