Finite Group Databasebeta

← #7688930

Subgroups — #7688930

Order 512.

4985 conjugacy classes of subgroups.

The subgroup lattice has 1467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60038C212yesmaximal, complemented
2#59998C214yesmaximal, complemented
3#59982C214yesmaximal, complemented
4#59951C211yesmaximal, characteristic, complemented
5#59894C212yesmaximal, complemented
6#59050C212yesmaximal, complemented
7#45410C211yesmaximal, characteristic, complemented
8#45364C211yesmaximal, characteristic, complemented
9#44897C212yesmaximal, complemented
10#44716C212yesmaximal, complemented
11#44657C212yesmaximal, complemented
12#44605C214yesmaximal, complemented
13#38830C214yesmaximal, complemented
14#38824C214yesmaximal, complemented
15#38291C212yesmaximal, complemented
16#37773C212yesmaximal, complemented
17#36496C211yesmaximal, characteristic, complemented
18#36413C214yesmaximal, complemented
19#36373C212yesmaximal, complemented
20#36269C212yesmaximal, complemented
21#36268C212yesmaximal, complemented
22#36051C211yesmaximal, characteristic, complemented
23#35959C211yesmaximal, characteristic, complemented
24#35773C212yesmaximal, complemented
25#34954C212yesmaximal, complemented
26#34874C211yesmaximal, characteristic, complemented
27#34306C212yesmaximal, complemented
28#34285C212yesmaximal, complemented
29#34154C212yesmaximal, complemented
30C2×#559C2211yescharacteristic
31C2×#556C2211yescharacteristic
32C2×#555C2212yes—
33C2×#555C2211yescharacteristic
34C2×#554C2211yescharacteristic
35C2×#552C2212yes—
36C2×#542C2212yes—
37C2×#533C2212yes—
38#2861C2212yes—
39#2861C2212yes—
40#2861C2214yes—
41#2860C2214yes—
42#2858C2211yescharacteristic
43#2850C2212yes—
44#2811C2212yes—
45#2808C2214yes—
46#2806C2214yes—
47#2803C2214yes—
48#2795C2212yes—
49#2792C2212yes—
50#2785C2212yes—
51#2783C2214yes—
52#2775C2214yes—
53#2775C2214yes—
54#2769C2212yes—
55#2744C2214yes—
56#2737C2214yes—
57#2733C2214yes—
58#2732C2214yes—
59#2731C2212yes—
60#2730C2214yes—
61#2730C2214yes—
62#2730C2214yes—
63#2730C2214yes—
64#2721C2214yes—
65#2714C2214yes—
66#2694C2214yes—
67#2673C2214yes—
68#2663C2212yes—
69#2663C2214yes—
70#2661C2212yes—
71#2658C2211yescharacteristic
72#2640C2211yescharacteristic
73#2621C2212yes—
74#2612C2211yescharacteristic
75#2612C2212yes—
76#2611C2214yes—
77#2610C2214yes—
78#2610C2212yes—
79#2610C2214yes—
80#2610C2214yes—
81#2609C2211yescharacteristic
82#2602C2214yes—
83#2601C2214yes—
84#2601C2214yes—
85#2593C2214yes—
86#2593C2212yes—
87#2593C2211yescharacteristic
88#2593C2214yes—
89#2592C2211yescharacteristic
90#2586C2212yes—
91#2584C2212yes—
92#2582C2212yes—
93#2574C2212yes—
94#2574C2214yes—
95#2571C2212yes—
96#2568C2211yescharacteristic
97#2567C2211yescharacteristic
98#2566C2212yes—
99#2564C2212yes—
100#2560C2214yes—
101#2559C2214yes—
102#2557C2214yes—
103#2557C2214yes—
104#2556C2214yes—
105#2556C2214yes—
106#2555C2211yescharacteristic
107#2554C2214yes—
108#2553C2214yes—
109#2550C2212yes—
110#2550C2212yes—
111#2548C2214yes—
112#2547C2212yes—
113#2546C2211yescharacteristic
114#2544C2212yes—
115#2544C2212yes—
116#2543C2212yes—
117#2542C2212yes—
118#2541C2211yescharacteristic
119#2540C2212yes—
120#2540C2212yes—
121#2540C2211yescharacteristic
122#2532C2214yes—
123#2532C2214yes—
124#2532C2214yes—
125#2531C2212yes—
126#2531C2214yes—
127#2531C2214yes—
128#2529C2214yes—
129#2529C2212yes—
130#2526C2214yes—
131#2521C2214yes—
132#2521C2214yes—
133#2519C2214yes—
134#2519C2214yes—
135#2518C2214yes—
136#2513C2214yes—
137#2513C2214yes—
138#2506C2214yes—
139#2499C2214yes—
140#2498C2212yes—
141#2498C2212yes—
142#2492C2212yes—
143#2492C2212yes—
144#2491C2214yes—
145#2490C2212yes—
146#2490C2214yes—
147#2489C2212yes—
148#2479C2214yes—
149#2479C2214yes—
150#2476C2214yes—
151#2476C2212yes—
152#2474C2214yes—
153#2474C2212yes—
154#2471C2214yes—
155#2471C2214yes—
156#2464C2214yes—
157#2461C2214yes—
158#2461C2214yes—
159#2461C2214yes—
160#2459C2214yes—
161#2451C2214yes—
162#2448C2214yes—
163#2448C2214yes—
164#2448C2214yes—
165#2441C2214yes—
166#2429C2212yes—
167#2429C2212yes—
168#2428C2212yes—
169#2427C2212yes—
170#2426C2212yes—
171#2426C2214yes—
172#2426C2212yes—
173#2426C2212yes—
174#2426C2212yes—
175#2423C2214yes—
176#2415C2212yes—
177#2415C2212yes—
178#2415C2212yes—
179#2414C2212yes—
180#2414C2214yes—
181#2399C2211yescharacteristic
182#2398C2211yescharacteristic
183#2395C2214yes—
184#2395C2212yes—
185#2395C2212yes—
186#2392C2212yes—
187#2374C2214yes—
188#2372C2214yes—
189#2372C2214yes—
190#2371C2214yes—
191#2371C2214yes—
192#2369C2212yes—
193#2369C2212yes—
194#2368C2214yes—
195#2367C2214yes—
196#2367C2212yes—
197#2367C2212yes—
198#2365C2212yes—
199#2365C2212yes—
200#2365C2212yes—
201#2365C2212yes—
202#2364C2214yes—
203#2363C2212yes—
204#2363C2214yes—
205#2363C2212yes—
206#2362C2212yes—
207#2362C2214yes—
208#2362C2214yes—
209#2362C2212yes—
210#2362C2214yes—
211#2362C2212yes—
212#2362C2212yes—
213#2362C2212yes—
214#2361C2212yes—
215#2361C2212yes—
216#2360C2212yes—
217#2359C2214yes—
218#2357C2212yes—
219#2354C2214yes—
220#2352C2212yes—
221#2347C2212yes—
222#2346C2212yes—
223#2346C2214yes—
224#2343C2214yes—
225#2337C2214yes—
226#2337C2214yes—
227#2334C2214yes—
228#2333C2214yes—
229#2331C2212yes—
230#2324C2212yes—
231#2320C2212yes—
232C4×#127C2212yes—
233C4×#126C2214yes—
234C4×#124C2214yes—
235C4×#124C2211yescharacteristic
236C4×#124C2212yes—
237C4×#124C2214yes—
238C4×#121C2212yes—
239C4×#121C2212yes—
240#2298C2214yes—
241#2298C2212yes—
242#2298C2214yes—
243#2298C2214yes—
244#2295C2212yes—
245#2295C2214yes—
246#2295C2212yes—
247#2293C2212yes—
248#2293C2214yes—
249#2293C2214yes—
250#2290C2212yes—
251#2275C2211yescharacteristic
252#2275C2211yescharacteristic
253#2274C2212yes—
254C42×Q8C2214yes—
255C42×Q8C2211yescharacteristic
256C42×Q8C2212yes—
257C4×#117C2212yes—
258C4×#117C2212yes—
259#559—44no—
260#556—44no—
261#555—216no—
262#555—44no—
263#554—44no—
264#552—48no—
265#542—216no—
266#533—216no—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2312yes—
273C2×#127C2312yes—
274C2×#127C2311yescharacteristic
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125C2314yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2314yes—
282C2×#124C2314yes—
283C2×#124C2314yes—
284C2×#124C2312yes—
285C2×#124C2314yes—
286C2×#124C2311yescharacteristic
287C2×#124C2314yes—
288C2×#124C2314yes—
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2311yescharacteristic
293C2×#124C2311yescharacteristic
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×#123C2312yes—
297C2×#123C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×#121C2312yes—
309C2×#121C2314yes—
310C2×#121C2312yes—
311C2×#121C2312yes—
312C2×#121C2312yes—
313C2×#121C2314yes—
314C2×#121C2312yes—
315C2×#121C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2314yes—
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2314yes—
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2314yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2311yescharacteristic
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2311yescharacteristic
337C2×C4×D4C2312yes—
338C2×C4×D4C2311yescharacteristic
339C2×#117C2312yes—
340C2×#117C2314yes—
341C2×#117C2312yes—
342C2×#117C2312yes—
343C2×#117C2312yes—
344C2×#117C2314yes—
345C2×#117C2312yes—
346C2×#117C2314yes—
347C2×#117C2314yes—
348C2×#117C2312yes—
349C2×#117C2312yes—
350C2×#117C2312yes—
351C22×C4⋊C4C2312yes—
352C22×C42C2312yes—
353#400C2312yes—
354#400C2312yes—
355#400C2311yescharacteristic
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2311yescharacteristic
360#399C2312yes—
361#399C2314yes—
362#399C2312yes—
363#399C2314yes—
364#399C2312yes—
365#399C2314yes—
366#399C2314yes—
367#399C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2311yescharacteristic
371#398C2314yes—
372#398C2312yes—
373#398C2314yes—
374#398C2311yescharacteristic
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2312yes—
380#398C2312yes—
381#397C2314yes—
382#397C2312yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2312yes—
387#397C2312yes—
388#397C2312yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2312yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2312yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2312yes—
404#395C2311yescharacteristic
405#395C2312yes—
406#395C2312yes—
407#395C2314yes—
408#395C2312yes—
409#395C2314yes—
410#395C2314yes—
411#395C2311yescharacteristic
412#394C2312yes—
413#394C2314yes—
414#394C2312yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2311yescharacteristic
423#394C2314yes—
424#394C2314yes—
425#394C2312yes—
426#394C2311yescharacteristic
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#393C2314yes—
431#393C2312yes—
432#393C2312yes—
433#393C2314yes—
434#393C2314yes—
435#392C2312yes—
436#392C2314yes—
437#392C2314yes—
438#392C2314yes—
439#392C2312yes—
440#392C2314yes—
441#392C2314yes—
442#391C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2311yescharacteristic
448#391C2314yes—
449#391C2312yes—
450#391C2314yes—
451#391C2314yes—
452#391C2312yes—
453#391C2314yes—
454#391C2312yes—
455#391C2314yes—
456#391C2314yes—
457#391C2312yes—
458#391C2314yes—
459#391C2314yes—
460#391C2312yes—
461#391C2312yes—
462#391C2314yes—
463#390C2314yes—
464#390C2311yescharacteristic
465#390C2312yes—
466#390C2314yes—
467#390C2314yes—
468#390C2312yes—
469#390C2312yes—
470#390C2314yes—
471#390C2312yes—
472#390C2314yes—
473#390C2312yes—
474#390C2314yes—
475#390C2312yes—
476#390C2314yes—
477#390C2314yes—
478#390C2312yes—
479#390C2314yes—
480#390C2314yes—
481#390C2314yes—
482#390C2312yes—
483#390C2314yes—
484#390C2312yes—
485#390C2314yes—
486#390C2314yes—
487#390C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2312yes—
504#389C2314yes—
505#389C2312yes—
506#389C2314yes—
507#389C2312yes—
508#389C2314yes—
509#389C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2312yes—
517#388C2314yes—
518#388C2312yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2312yes—
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#388C2312yes—
544#388C2314yes—
545#388C2312yes—
546#388C2314yes—
547#388C2312yes—
548#388C2312yes—
549#388C2314yes—
550#388C2314yes—
551#388C2312yes—
552#388C2312yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2312yes—
567#388C2312yes—
568#388C2312yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2312yes—
573#388C2312yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2312yes—
581#387C2314yes—
582#387C2312yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2312yes—
589#387C2314yes—
590#387C2312yes—
591#387C2314yes—
592#387C2314yes—
593#387C2312yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2312yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2312yes—
615#386C2314yes—
616#386C2312yes—
617#386C2312yes—
618#386C2314yes—
619#386C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2312yes—
625#385C2312yes—
626#385C2314yes—
627#385C2314yes—
628#384C2312yes—
629#384C2314yes—
630#383C2314yes—
631#383C2314yes—
632#382C2311yescharacteristic
633#382C2312yes—
634#382C2314yes—
635#382C2314yes—
636#382C2312yes—
637#382C2314yes—
638#382C2312yes—
639#381C2314yes—
640#380C2314yes—
641#380C2312yes—
642#380C2314yes—
643#380C2312yes—
644#380C2312yes—
645#380C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2311yescharacteristic
651C4×C4⋊C4C2311yescharacteristic
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2312yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705#376C2311yescharacteristic
706#376C2311yescharacteristic
707#376C2314yes—
708#376C2314yes—
709#376C2314yes—
710#376C2312yes—
711#376C2314yes—
712#376C2312yes—
713C2×#95C2312yes—
714C2×#95C2312yes—
715C43C2314yes—
716C43C2312yes—
717C43C2311yescharacteristic
718C43C2314yes—
719C43C2312yes—
720C22×Q8C2412yes—
721C22×Q8C2411yescharacteristic
722C22×Q8C2411yescharacteristic
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2412yes—
726C22×Q8C2414yes—
727C22×D4C2411yescharacteristic
728C22×D4C2411yescharacteristic
729C22×D4C2411yescharacteristic
730C22×D4C2414yes—
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2414yes—
734C22×D4C2414yes—
735C22×D4C2411yescharacteristic
736C22×D4C2412yes—
737C22×D4C2414yes—
738C22×D4C2412yes—
739C23×C4C2412yes—
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2414yes—
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2412yes—
746C23×C4C2414yes—
747C23×C4C2414yes—
748C4⋊Q8—28no—
749C4⋊Q8—42no—
750C4⋊Q8—42no—
751C4⋊Q8—42no—
752C4⋊Q8—44no—
753C4⋊Q8#41116yes—
754#127—44no—
755#127—42no—
756#126—216no—
757#126—48no—
758#126—48no—
759#125—216no—
760#125—48no—
761#125—44no—
762#125—44no—
763#124—216no—
764#124—216no—
765#124—216no—
766#124—28no—
767#124—44no—
768#124—48no—
769#124—48no—
770#124—44no—
771#124—42no—
772#124—44no—
773#124—42no—
774#124—42no—
775#123—216no—
776#123—48no—
777#123—44no—
778#123—44no—
779C22⋊Q8—216no—
780C22⋊Q8—216no—
781C22⋊Q8—28no—
782C22⋊Q8—28no—
783C22⋊Q8—28no—
784C22⋊Q8—48no—
785C22⋊Q8—44no—
786C22⋊Q8—44no—
787C22⋊Q8—44no—
788C22⋊Q8—44no—
789#121—28no—
790#121—216no—
791#121—28no—
792#121—28no—
793#121—44no—
794#121—44no—
795#121—48no—
796#121—44no—
797C4×Q8—216no—
798C4×Q8—28no—
799C4×Q8—28no—
800C4×Q8—28no—
801C4×Q8—28no—
802C4×Q8—24no—
803C4×Q8—42no—
804C4×Q8—42no—
805C4×Q8—48no—
806C4×Q8—48no—
807C4×D4—28no—
808C4×D4—24no—
809C4×D4—24no—
810C4×D4—28no—
811C4×D4—28no—
812C4×D4—48no—
813C4×D4—48no—
814C4×D4—44no—
815C4×D4—44no—
816C4×D4—42no—
817C4×D4—42no—
818C4×D4—44no—
819C4×D4—48no—
820#117—216no—
821#117—216no—
822#117—28no—
823#117—28no—
824#117—28no—
825#117—28no—
826#117—48no—
827#117—44no—
828#117—44no—
829#117—48no—
830#117—44no—
831#117—44no—
832C2×C4⋊C4—28no—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2411yescharacteristic
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2412yes—
940C2×C42—28no—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2412yes—
944C2×C42C2411yescharacteristic
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2412yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2411yescharacteristic
953C2×C42C2414yes—
954C2×C42C2412yes—
955C2×C42C2411yescharacteristic
956C2×C42C2411yescharacteristic
957C2×C42C2412yes—
958C2×C42C2412yes—
959C2×C42C2412yes—
960C2×C42C2414yes—
961C2×C42C2412yes—
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2414yes—
965C2×C42C2414yes—
966C2×C42C2414yes—
967C2×C42C2414yes—
968C2×C42C2414yes—
969C2×C42C2414yes—
970C2×C42C2412yes—
971C2×C42C2411yescharacteristic
972C2×C42C2412yes—
973C2×C42C2414yes—
974C2×C42C2412yes—
975C2×C42C2412yes—
976#95C2411yescharacteristic
977#95C2411yescharacteristic
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2411yescharacteristic
987#95C2412yes—
988#95C2414yes—
989#95C2411yescharacteristic
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2412yes—
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2412yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2412yes—
1035C24C2512yes—
1036C24C2512yes—
1037C24C2512yes—
1038C24C2512yes—
1039C2×Q8—24no—
1040C2×Q8—24no—
1041C2×Q8—24no—
1042C2×Q8—22no—
1043C2×Q8—24no—
1044C2×Q8—22no—
1045C2×Q8—44no—
1046C2×Q8—44no—
1047C2×Q8—41no—
1048C2×Q8—41no—
1049C2×Q8—42no—
1050C2×Q8—41no—
1051C2×Q8—42no—
1052C2×Q8—42no—
1053C2×Q8—44no—
1054C2×Q8—42no—
1055C2×Q8—42no—
1056C2×Q8C2×#41116yes—
1057C2×D4—24no—
1058C2×D4—24no—
1059C2×D4—24no—
1060C2×D4—28no—
1061C2×D4—28no—
1062C2×D4—28no—
1063C2×D4—22no—
1064C2×D4—22no—
1065C2×D4—22no—
1066C2×D4—24no—
1067C2×D4—41no—
1068C2×D4—41no—
1069C2×D4—41no—
1070C2×D4—42no—
1071C2×D4—42no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—42no—
1077C2×D4—42no—
1078C2×D4—42no—
1079C2×D4—42no—
1080C2×D4—44no—
1081C2×D4—44no—
1082C2×D4—42no—
1083C2×D4—42no—
1084C2×D4—44no—
1085C2×D4—44no—
1086C2×D4—42no—
1087C2×D4—44no—
1088C2×D4—44no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—24no—
1095C22×C4—24no—
1096C22×C4—24no—
1097C22×C4—24no—
1098C22×C4—28no—
1099C22×C4—28no—
1100C22×C4—28no—
1101C22×C4—24no—
1102C22×C4—24no—
1103C22×C4—42no—
1104C22×C4—42no—
1105C22×C4—42no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—44no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4C2514yes—
1115C22×C4C2512yes—
1116C22×C4C2511yescharacteristic
1117C22×C4C2511yescharacteristic
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2514yes—
1121C22×C4C2511yescharacteristic
1122C22×C4C2511yescharacteristic
1123C22×C4C2511yescharacteristic
1124C22×C4C2512yes—
1125C22×C4C2514yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2514yes—
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2514yes—
1133C22×C4C2512yes—
1134C22×C4C2514yes—
1135C22×C4C2512yes—
1136C22×C4C2511yescharacteristic
1137C22×C4C2512yes—
1138C22×C4C2511yescharacteristic
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—28no—
1143C4⋊C4—24no—
1144C4⋊C4—28no—
1145C4⋊C4—28no—
1146C4⋊C4—28no—
1147C4⋊C4—28no—
1148C4⋊C4—28no—
1149C4⋊C4—28no—
1150C4⋊C4—28no—
1151C4⋊C4—24no—
1152C4⋊C4—28no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—28no—
1156C4⋊C4—28no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—28no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—41no—
1165C4⋊C4—41no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—41no—
1173C4⋊C4—41no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—41no—
1179C4⋊C4—41no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—42no—
1186C4⋊C4—44no—
1187C4⋊C4C2×#41116yes—
1188C4⋊C4C2×#4118yes—
1189C4⋊C4C2×#4118yes—
1190C4⋊C4H(5,𝔽2)14yes—
1191C22⋊C4—28no—
1192C22⋊C4—28no—
1193C22⋊C4—28no—
1194C22⋊C4—28no—
1195C22⋊C4—28no—
1196C22⋊C4—28no—
1197C22⋊C4—24no—
1198C22⋊C4—24no—
1199C22⋊C4—28no—
1200C22⋊C4—24no—
1201C22⋊C4—24no—
1202C22⋊C4—28no—
1203C22⋊C4—28no—
1204C22⋊C4—28no—
1205C22⋊C4—28no—
1206C22⋊C4—28no—
1207C22⋊C4—28no—
1208C22⋊C4—24no—
1209C22⋊C4—24no—
1210C22⋊C4—28no—
1211C22⋊C4—24no—
1212C22⋊C4—24no—
1213C22⋊C4—24no—
1214C22⋊C4—28no—
1215C22⋊C4—24no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—44no—
1221C22⋊C4—42no—
1222C22⋊C4—44no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—42no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—42no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—42no—
1239C22⋊C4—42no—
1240C22⋊C4—42no—
1241C22⋊C4—42no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—42no—
1245C22⋊C4—42no—
1246C42—24no—
1247C42—24no—
1248C42—24no—
1249C42—28no—
1250C42—28no—
1251C42—24no—
1252C42—28no—
1253C42—28no—
1254C42—28no—
1255C42—28no—
1256C42—28no—
1257C42—22no—
1258C42—22no—
1259C42—24no—
1260C42—24no—
1261C42—22no—
1262C42—24no—
1263C42—22no—
1264C42—24no—
1265C42—28no—
1266C42—24no—
1267C42—41no—
1268C42—44no—
1269C42—42no—
1270C42—42no—
1271C42—44no—
1272C42—42no—
1273C42—42no—
1274C42—44no—
1275C42—44no—
1276C42—44no—
1277C42—44no—
1278C42—44no—
1279C42—42no—
1280C42C2×#4118yes—
1281C23—22no—
1282C23—24no—
1283C23—22no—
1284C23—24no—
1285C23—22no—
1286C23—22no—
1287C23—22no—
1288C23—22no—
1289C23—22no—
1290C23—22no—
1291C23—24no—
1292C23—22no—
1293C23—24no—
1294C23—22no—
1295C23—22no—
1296C23—22no—
1297C23—22no—
1298C23—22no—
1299C23—22no—
1300C23—22no—
1301C23—22no—
1302C23—22no—
1303C23—22no—
1304C23—22no—
1305C23C2611yescharacteristic
1306Q8—416no—
1307Q8—48no—
1308Q8—44no—
1309Q8—82no—
1310Q8—82no—
1311Q8—162no—
1312Q8—162no—
1313D4—44no—
1314D4—44no—
1315D4—44no—
1316D4—84no—
1317D4—88no—
1318D4—88no—
1319D4—88no—
1320D4—84no—
1321D4—82no—
1322D4—84no—
1323D4—162no—
1324D4—164no—
1325C2×C4—22no—
1326C2×C4—21no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—21no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—22no—
1361C2×C4—24no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—24no—
1370C2×C4—21no—
1371C2×C4—22no—
1372C2×C4—24no—
1373C2×C4—24no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—21no—
1379C2×C4—24no—
1380C2×C4—21no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—24no—
1384C2×C4—21no—
1385C2×C4—48no—
1386C2×C4—48no—
1387C2×C4—48no—
1388C2×C4—48no—
1389C2×C4—88no—
1390C2×C4—84no—
1391C2×C4—84no—
1392C2×C4—88no—
1393C2×C4—88no—
1394C2×C4C22×#4118yes—
1395C2×C4C22×#4118yes—
1396C2×C4C22×#4114yes—
1397C2×C4C22×#4114yes—
1398C2×C4C22×#4114yes—
1399C2×C4C2×H(5,𝔽2)14yes—
1400C2×C4C2×H(5,𝔽2)12yes—
1401C2×C4#58514yes—
1402C2×C4#58512yes—
1403C22—42no—
1404C22—44no—
1405C22—42no—
1406C22—42no—
1407C22—44no—
1408C22—42no—
1409C22—42no—
1410C22—42no—
1411C22—42no—
1412C22—42no—
1413C22—42no—
1414C22—44no—
1415C22—42no—
1416C22—44no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—42no—
1425C22—42no—
1426C22—42no—
1427C22C23×#4112yes—
1428C22C22×H(5,𝔽2)11yescharacteristic
1429C22C2×#58512yes—
1430C22C2×#58511yescharacteristic
1431C222−1+611yescharacteristic
1432C4—24no—
1433C4—24no—
1434C4—24no—
1435C4—24no—
1436C4—28no—
1437C4—28no—
1438C4—22no—
1439C4—42no—
1440C4—44no—
1441C4—41no—
1442C4—41no—
1443C4—44no—
1444C4—42no—
1445C4—41no—
1446C4—42no—
1447C4—42no—
1448C4—42no—
1449C4—44no—
1450C4—41no—
1451C4—41no—
1452C4—42no—
1453C4—42no—
1454C4—44no—
1455C4—42no—
1456C4#348314yes—
1457C2—82no—
1458C2—82no—
1459C2—82no—
1460C2—82no—
1461C2C2×#348311yescharacteristic
1462C2#6278112yes—
1463C2#6291911yescharacteristic
1464C2#6300512yes—
1465C2#6302111yescharacteristic
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. #60038C2semidirect
2. #59998C2semidirect
3. #59982C2semidirect
4. #59951C2semidirect
5. #59894C2semidirect
6. #59050C2semidirect
7. #45410C2semidirect
8. #45364C2semidirect
9. #44897C2semidirect
10. #44716C2semidirect
11. #44657C2semidirect
12. #44605C2semidirect
13. #38830C2semidirect
14. #38824C2semidirect
15. #38291C2semidirect
16. #37773C2semidirect
17. #36496C2semidirect
18. #36413C2semidirect
19. #36373C2semidirect
20. #36269C2semidirect
21. #36268C2semidirect
22. #36051C2semidirect
23. #35959C2semidirect
24. #35773C2semidirect
25. #34954C2semidirect
26. #34874C2semidirect
27. #34306C2semidirect
28. #34285C2semidirect
29. #34154C2semidirect

Maximal subgroups

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

subgroupindex
#600382
#599982
#599822
#599512
#598942
#590502
#454102
#453642
#448972
#447162
#446572
#446052
#388302
#388242
#382912
#377732
#364962
#364132
#363732
#362692
#362682
#360512
#359592
#357732
#349542
#348742
#343062
#342852
#341542