Finite Group Databasebeta

← #7895401

Subgroups — #7895401

Order 512.

4779 conjugacy classes of subgroups.

The subgroup lattice has 1498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59856C212yesmaximal, complemented
2#59823C211yesmaximal, characteristic, complemented
3#52160C211yesmaximal, characteristic, complemented
4#49133C214yesmaximal, complemented
5#48805C214yesmaximal, complemented
6#48217C214yesmaximal, complemented
7#46698C214yesmaximal, complemented
8#45800C212yesmaximal, complemented
9#45375C212yesmaximal, complemented
10#45228C212yesmaximal, complemented
11#44978C212yesmaximal, complemented
12#43375C214yesmaximal, complemented
13#42679C212yesmaximal, complemented
14#42591C212yesmaximal, complemented
15#41107C214yesmaximal, complemented
16#40148C212yesmaximal, complemented
17#39757C211yesmaximal, characteristic, complemented
18#39631C212yesmaximal, complemented
19#39580C212yesmaximal, complemented
20#39509C211yesmaximal, characteristic, complemented
21#39271C212yesmaximal, complemented
22#38040C212yesmaximal, complemented
23#37141C212yesmaximal, complemented
24#36468C211yesmaximal, characteristic, complemented
25#35701C212yesmaximal, complemented
26#35521C212yesmaximal, complemented
27#35176C211yesmaximal, characteristic, complemented
28#34461C212yesmaximal, complemented
29#34308C211yesmaximal, characteristic, complemented
30C2×#554C2212yes—
31C2×#553C2212yes—
32C2×#547C2211yescharacteristic
33C2×#529C2212yes—
34C2×#520C2212yes—
35#2859C2211yescharacteristic
36#2857C2212yes—
37#2855C2212yes—
38#2855C2212yes—
39#2854C2212yes—
40#2826C2214yes—
41#2813C2214yes—
42#2810C2212yes—
43#2810C2212yes—
44#2810C2212yes—
45#2808C2212yes—
46#2807C2214yes—
47#2807C2214yes—
48#2807C2214yes—
49#2805C2212yes—
50#2805C2212yes—
51#2805C2212yes—
52#2802C2214yes—
53#2796C2214yes—
54#2796C2214yes—
55#2795C2214yes—
56#2794C2214yes—
57#2783C2214yes—
58#2781C2214yes—
59#2780C2214yes—
60#2773C2214yes—
61#2772C2214yes—
62#2771C2214yes—
63#2771C2214yes—
64#2770C2214yes—
65#2769C2214yes—
66#2761C2214yes—
67#2756C2214yes—
68#2750C2214yes—
69#2743C2214yes—
70#2743C2214yes—
71#2741C2214yes—
72#2733C2211yescharacteristic
73#2732C2212yes—
74#2732C2212yes—
75#2732C2211yescharacteristic
76#2730C2212yes—
77#2727C2211yescharacteristic
78#2727C2212yes—
79#2721C2214yes—
80#2721C2212yes—
81#2719C2214yes—
82#2718C2214yes—
83#2718C2214yes—
84#2718C2214yes—
85#2714C2212yes—
86#2705C2212yes—
87#2703C2214yes—
88#2703C2214yes—
89#2703C2214yes—
90#2694C2212yes—
91#2689C2214yes—
92#2688C2214yes—
93#2682C2211yescharacteristic
94#2674C2214yes—
95#2673C2212yes—
96#2667C2214yes—
97#2646C2214yes—
98#2642C2212yes—
99#2636C2214yes—
100#2635C2214yes—
101#2633C2214yes—
102#2630C2214yes—
103#2628C2212yes—
104#2625C2212yes—
105#2623C2214yes—
106#2611C2214yes—
107#2602C2214yes—
108#2602C2214yes—
109#2600C2214yes—
110#2600C2214yes—
111#2598C2214yes—
112#2596C2214yes—
113#2596C2214yes—
114#2587C2214yes—
115#2581C2212yes—
116#2579C2214yes—
117#2575C2214yes—
118#2570C2214yes—
119#2569C2214yes—
120#2562C2212yes—
121#2562C2212yes—
122#2562C2212yes—
123#2562C2212yes—
124#2559C2214yes—
125#2552C2211yescharacteristic
126#2552C2212yes—
127#2546C2211yescharacteristic
128#2542C2212yes—
129#2542C2211yescharacteristic
130#2538C2214yes—
131#2538C2211yescharacteristic
132#2538C2212yes—
133#2537C2211yescharacteristic
134#2537C2211yescharacteristic
135#2535C2212yes—
136#2533C2214yes—
137#2533C2214yes—
138#2531C2214yes—
139#2529C2214yes—
140#2522C2214yes—
141#2522C2214yes—
142#2518C2214yes—
143#2516C2214yes—
144#2515C2214yes—
145#2511C2212yes—
146#2511C2212yes—
147#2507C2212yes—
148#2507C2214yes—
149#2505C2214yes—
150#2497C2212yes—
151#2497C2214yes—
152#2496C2212yes—
153#2496C2212yes—
154#2489C2212yes—
155#2489C2212yes—
156#2488C2214yes—
157#2487C2212yes—
158#2487C2212yes—
159#2487C2214yes—
160#2487C2214yes—
161#2486C2212yes—
162#2486C2212yes—
163#2481C2214yes—
164#2475C2214yes—
165#2471C2214yes—
166#2469C2214yes—
167#2468C2214yes—
168#2467C2214yes—
169#2466C2214yes—
170#2463C2214yes—
171#2463C2214yes—
172#2461C2214yes—
173#2457C2214yes—
174#2456C2214yes—
175#2455C2214yes—
176#2455C2214yes—
177#2454C2212yes—
178#2454C2214yes—
179#2449C2214yes—
180#2449C2214yes—
181#2449C2214yes—
182#2444C2214yes—
183#2443C2214yes—
184#2440C2214yes—
185#2429C2212yes—
186#2428C2212yes—
187#2423C2212yes—
188#2423C2212yes—
189#2423C2212yes—
190#2419C2214yes—
191#2417C2212yes—
192#2417C2212yes—
193#2417C2212yes—
194#2417C2212yes—
195#2415C2212yes—
196#2415C2212yes—
197#2407C2212yes—
198#2407C2212yes—
199#2407C2212yes—
200#2407C2212yes—
201#2397C2212yes—
202#2397C2214yes—
203#2392C2212yes—
204#2392C2212yes—
205#2383C2214yes—
206#2376C2214yes—
207#2370C2212yes—
208#2366C2212yes—
209#2365C2211yescharacteristic
210#2364C2214yes—
211#2361C2212yes—
212#2361C2214yes—
213#2361C2212yes—
214#2361C2212yes—
215#2360C2212yes—
216#2359C2214yes—
217#2356C2212yes—
218#2354C2211yescharacteristic
219#2352C2212yes—
220D4×C4⋊C4C2211yescharacteristic
221D4×C4⋊C4C2211yescharacteristic
222D4×C4⋊C4C2212yes—
223D4×C4⋊C4C2212yes—
224D4×C4⋊C4C2212yes—
225D4×C4⋊C4C2211yescharacteristic
226D4×C4⋊C4C2214yes—
227#2347C2212yes—
228#2345C2212yes—
229#2344C2212yes—
230#2339C2212yes—
231#2334C2214yes—
232#2330C2212yes—
233#2330C2212yes—
234#2325C2214yes—
235#2325C2214yes—
236#2324C2212yes—
237#2323C2212yes—
238#2323C2212yes—
239#2322C2214yes—
240#2322C2214yes—
241#2319C2212yes—
242#2318C2214yes—
243#2317C2212yes—
244#2314C2212yes—
245C4×C4⋊Q8C2211yescharacteristic
246C4×C4⋊Q8C2211yescharacteristic
247C4×#127C2211yescharacteristic
248C4×C22⋊Q8C2212yes—
249C4×#121C2212yes—
250C4×#121C2212yes—
251C4×#121C2212yes—
252C4×#121C2212yes—
253#2295C2211yescharacteristic
254#2293C2211yescharacteristic
255C2×#389C2212yes—
256C2×#389C2212yes—
257#2290C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260#554—48no—
261#553—216no—
262#547—28no—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×#127C2311yescharacteristic
267#529—48no—
268C2×#126C2314yes—
269C2×#126C2312yes—
270C2×#126C2312yes—
271C2×#126C2314yes—
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2314yes—
275C2×#125C2312yes—
276C2×#124C2312yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2312yes—
280C2×#123C2312yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2314yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302#520—48no—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2311yescharacteristic
310C2×C4×D4C2314yes—
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2314yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2311yescharacteristic
332C2×#117C2312yes—
333C2×#117C2312yes—
334C2×#117C2312yes—
335C2×#117C2314yes—
336C22×C4⋊C4C2312yes—
337C22×C4⋊C4C2312yes—
338C22×C4⋊C4C2312yes—
339C22×C4⋊C4C2314yes—
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2312yes—
343C22×C4⋊C4C2314yes—
344C22×C42C2312yes—
345C22×C42C2312yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#399C2314yes—
368#399C2314yes—
369#399C2314yes—
370#399C2314yes—
371#399C2314yes—
372#399C2312yes—
373#399C2314yes—
374#399C2314yes—
375#399C2314yes—
376#399C2312yes—
377#399C2312yes—
378#399C2312yes—
379#399C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#398C2312yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2312yes—
406#397C2312yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2312yes—
414#396C2312yes—
415#396C2312yes—
416#396C2312yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#395C2314yes—
421#395C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2312yes—
427#394C2314yes—
428#394C2314yes—
429#394C2312yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2312yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2312yes—
438#394C2312yes—
439#394C2312yes—
440#393C2314yes—
441#392C2314yes—
442#392C2314yes—
443#392C2312yes—
444#392C2312yes—
445#392C2312yes—
446#392C2314yes—
447#392C2314yes—
448#392C2314yes—
449#392C2312yes—
450#392C2312yes—
451#392C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2311yescharacteristic
459#391C2312yes—
460#391C2312yes—
461#391C2311yescharacteristic
462#390C2311yescharacteristic
463#390C2312yes—
464#390C2311yescharacteristic
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2314yes—
469#390C2312yes—
470#390C2311yescharacteristic
471#390C2314yes—
472#390C2314yes—
473#390C2311yescharacteristic
474#390C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2312yes—
500#389C2312yes—
501#389C2311yescharacteristic
502#389C2312yes—
503#389C2311yescharacteristic
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#389C2312yes—
512#389C2314yes—
513#389C2314yes—
514#389C2311yescharacteristic
515#389C2314yes—
516#389C2312yes—
517#389C2311yescharacteristic
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#388C2312yes—
534#388C2312yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2312yes—
543#388C2314yes—
544#388C2314yes—
545#388C2312yes—
546#388C2312yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2312yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2312yes—
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#387C2312yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2312yes—
587#387C2312yes—
588#387C2314yes—
589#387C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2312yes—
595#386C2314yes—
596#386C2312yes—
597#386C2312yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2312yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2312yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2312yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#384C2311yescharacteristic
640#384C2311yescharacteristic
641#384C2311yescharacteristic
642#384C2314yes—
643#384C2314yes—
644#384C2312yes—
645#384C2312yes—
646#384C2311yescharacteristic
647#384C2311yescharacteristic
648#383C2314yes—
649#383C2314yes—
650#382C2312yes—
651#382C2314yes—
652#382C2314yes—
653#382C2314yes—
654#381C2314yes—
655#381C2314yes—
656#381C2314yes—
657#381C2314yes—
658#381C2314yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2314yes—
672#380C2314yes—
673#380C2312yes—
674#380C2314yes—
675#380C2314yes—
676#380C2314yes—
677#380C2312yes—
678#380C2312yes—
679#380C2314yes—
680#380C2312yes—
681#380C2314yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2311yescharacteristic
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2311yescharacteristic
700C4×C4⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712#376C2312yes—
713#376C2314yes—
714C2×#95C2314yes—
715C2×#95C2314yes—
716C43C2311yescharacteristic
717C2×#41—28no—
718C2×#41—44no—
719C2×#41—44no—
720C22×Q8C2412yes—
721C22×Q8C2412yes—
722C22×Q8C2411yescharacteristic
723C22×D4C2414yes—
724C22×D4C2412yes—
725C22×D4C2412yes—
726C22×D4C2411yescharacteristic
727C22×D4C2411yescharacteristic
728C22×D4C2412yes—
729C22×D4C2414yes—
730C22×D4C2414yes—
731C22×D4C2412yes—
732C22×D4C2411yescharacteristic
733C22×D4C2412yes—
734C22×D4C2412yes—
735C22×D4C2411yescharacteristic
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2414yes—
740C23×C4C2412yes—
741C23×C4C2414yes—
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2414yes—
745C23×C4C2414yes—
746C23×C4C2412yes—
747C23×C4C2414yes—
748C23×C4C2414yes—
749C23×C4C2412yes—
750C4⋊Q8—24no—
751C4⋊Q8—24no—
752C4⋊Q8—82no—
753#127—24no—
754#126—216no—
755#126—44no—
756#126—44no—
757#126—84no—
758#125—28no—
759#125—44no—
760#125—48no—
761#125—44no—
762#124—44no—
763#123—216no—
764#123—216no—
765#123—44no—
766#123—44no—
767#123—84no—
768#123—84no—
769C22⋊Q8—28no—
770C22⋊Q8—44no—
771C22⋊Q8—48no—
772C22⋊Q8—48no—
773C22⋊Q8—44no—
774C22⋊Q8—44no—
775C22⋊Q8—44no—
776C22⋊Q8—44no—
777C22⋊Q8—82no—
778C22⋊Q8—82no—
779C22⋊Q8—82no—
780#121—28no—
781#121—28no—
782#121—28no—
783#121—28no—
784#121—28no—
785#121—216no—
786#121—44no—
787#121—82no—
788C4×Q8—28no—
789C4×Q8—24no—
790C4×Q8—44no—
791C4×Q8—82no—
792C4×D4—216no—
793C4×D4—24no—
794C4×D4—28no—
795C4×D4—24no—
796C4×D4—28no—
797C4×D4—48no—
798C4×D4—42no—
799C4×D4—44no—
800C4×D4—48no—
801C4×D4—42no—
802C4×D4—42no—
803C4×D4—44no—
804C4×D4—44no—
805C4×D4—44no—
806C4×D4—44no—
807C4×D4—48no—
808C4×D4—82no—
809C4×D4—82no—
810C4×D4—84no—
811C4×D4—84no—
812C4×D4—84no—
813C4×D4—84no—
814C4×D4—84no—
815C4×D4—84no—
816C4×D4#4118yes—
817#117—28no—
818#117—28no—
819#117—44no—
820#117—48no—
821C2×C4⋊C4—28no—
822C2×C4⋊C4—28no—
823C2×C4⋊C4—44no—
824C2×C4⋊C4—48no—
825C2×C4⋊C4—44no—
826C2×C4⋊C4—44no—
827C2×C4⋊C4—82no—
828C2×C4⋊C4—84no—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2411yescharacteristic
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2412yes—
948C2×C42—44no—
949C2×C42—82no—
950C2×C42C2412yes—
951C2×C42C2414yes—
952C2×C42C2412yes—
953C2×C42C2414yes—
954C2×C42C2411yescharacteristic
955C2×C42C2412yes—
956C2×C42C2411yescharacteristic
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2414yes—
961C2×C42C2414yes—
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2411yescharacteristic
965C2×C42C2412yes—
966C2×C42C2412yes—
967C2×C42C2412yes—
968C2×C42C2411yescharacteristic
969C2×C42C2411yescharacteristic
970C2×C42C2414yes—
971C2×C42C2411yescharacteristic
972C2×C42C2411yescharacteristic
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2414yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030C24C2512yes—
1031C24C2512yes—
1032C24C2512yes—
1033C24C2512yes—
1034#41—432no—
1035C2×Q8—24no—
1036C2×Q8—24no—
1037C2×Q8—22no—
1038C2×Q8—24no—
1039C2×Q8—24no—
1040C2×Q8—42no—
1041C2×Q8—41no—
1042C2×Q8—42no—
1043C2×Q8—41no—
1044C2×D4—28no—
1045C2×D4—28no—
1046C2×D4—28no—
1047C2×D4—24no—
1048C2×D4—24no—
1049C2×D4—24no—
1050C2×D4—28no—
1051C2×D4—24no—
1052C2×D4—22no—
1053C2×D4—24no—
1054C2×D4—22no—
1055C2×D4—24no—
1056C2×D4—22no—
1057C2×D4—22no—
1058C2×D4—44no—
1059C2×D4—41no—
1060C2×D4—42no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—41no—
1064C2×D4—41no—
1065C2×D4—44no—
1066C2×D4—42no—
1067C2×D4—42no—
1068C2×D4—42no—
1069C2×D4—41no—
1070C2×D4—42no—
1071C2×D4—44no—
1072C2×D4—42no—
1073C2×D4—42no—
1074C2×D4—41no—
1075C2×D4—44no—
1076C2×D4—41no—
1077C2×D4—42no—
1078C2×D4—42no—
1079C2×D4—44no—
1080C2×D4—42no—
1081C2×D4C2×#4114yes—
1082C2×D42−1+414yes—
1083C22×C4—28no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—28no—
1095C22×C4—24no—
1096C22×C4—24no—
1097C22×C4—42no—
1098C22×C4—44no—
1099C22×C4—42no—
1100C22×C4—44no—
1101C22×C4—42no—
1102C22×C4—42no—
1103C22×C4—42no—
1104C22×C4—42no—
1105C22×C4—42no—
1106C22×C4—44no—
1107C22×C4—42no—
1108C22×C4—42no—
1109C22×C4—42no—
1110C22×C4—44no—
1111C22×C4—42no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—44no—
1121C22×C4—44no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4C2×#4118yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2514yes—
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2514yes—
1131C22×C4C2512yes—
1132C22×C4C2514yes—
1133C22×C4C2512yes—
1134C22×C4C2511yescharacteristic
1135C22×C4C2514yes—
1136C22×C4C2514yes—
1137C22×C4C2512yes—
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2514yes—
1143C22×C4C2511yescharacteristic
1144C22×C4C2511yescharacteristic
1145C22×C4C2512yes—
1146C22×C4C2511yescharacteristic
1147C22×C4C2511yescharacteristic
1148C22×C4C2511yescharacteristic
1149C22×C4C2511yescharacteristic
1150C4⋊C4—22no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—28no—
1154C4⋊C4—28no—
1155C4⋊C4—24no—
1156C4⋊C4—28no—
1157C4⋊C4—24no—
1158C4⋊C4—28no—
1159C4⋊C4—24no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—22no—
1163C4⋊C4—24no—
1164C4⋊C4—28no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—22no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—22no—
1173C4⋊C4—24no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—41no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—42no—
1185C4⋊C4—41no—
1186C4⋊C4—44no—
1187C4⋊C4—42no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—42no—
1191C4⋊C4—41no—
1192C4⋊C4—41no—
1193C4⋊C4—42no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—42no—
1197C4⋊C4—42no—
1198C4⋊C4—42no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—42no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—41no—
1210C4⋊C4—41no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—42no—
1216C4⋊C4C2×#4114yes—
1217C22⋊C4—28no—
1218C22⋊C4—28no—
1219C22⋊C4—24no—
1220C22⋊C4—28no—
1221C22⋊C4—28no—
1222C22⋊C4—24no—
1223C22⋊C4—24no—
1224C22⋊C4—24no—
1225C22⋊C4—28no—
1226C22⋊C4—24no—
1227C22⋊C4—24no—
1228C22⋊C4—24no—
1229C22⋊C4—24no—
1230C22⋊C4—24no—
1231C22⋊C4—24no—
1232C22⋊C4—42no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—42no—
1237C22⋊C4—42no—
1238C22⋊C4—42no—
1239C22⋊C4—42no—
1240C22⋊C4—42no—
1241C22⋊C4—42no—
1242C22⋊C4—42no—
1243C22⋊C4—42no—
1244C22⋊C4—42no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—42no—
1248C22⋊C4—42no—
1249C22⋊C4—42no—
1250C22⋊C4—42no—
1251C22⋊C4—44no—
1252C22⋊C4—42no—
1253C22⋊C4—42no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—42no—
1268C22⋊C4C2×#4118yes—
1269C42—28no—
1270C42—24no—
1271C42—24no—
1272C42—28no—
1273C42—22no—
1274C42—22no—
1275C42—24no—
1276C42—42no—
1277C42—42no—
1278C42—41no—
1279C42—42no—
1280C42—42no—
1281C42—42no—
1282C42—41no—
1283C42—44no—
1284C42—44no—
1285C42—44no—
1286C42—44no—
1287C42—44no—
1288C42—44no—
1289C42—41no—
1290C42C2×#4114yes—
1291C42H(5,𝔽2)14yes—
1292C23—22no—
1293C23—22no—
1294C23—22no—
1295C23—22no—
1296C23—22no—
1297C23—22no—
1298C23—22no—
1299C23—22no—
1300C23—22no—
1301C23—22no—
1302C23—22no—
1303C23—22no—
1304C23—22no—
1305C23—22no—
1306C23—22no—
1307C23—22no—
1308C23—22no—
1309C23—22no—
1310C23—22no—
1311C23—22no—
1312C23—22no—
1313C23—22no—
1314C23—22no—
1315C23—22no—
1316C23—22no—
1317C23—22no—
1318C23C22×#4114yes—
1319C23C2×2−1+414yes—
1320C23C2611yescharacteristic
1321Q8—48no—
1322Q8—82no—
1323Q8—84no—
1324D4—28no—
1325D4—44no—
1326D4—48no—
1327D4—48no—
1328D4—44no—
1329D4—416no—
1330D4—48no—
1331D4—416no—
1332D4—48no—
1333D4—82no—
1334D4—88no—
1335D4—84no—
1336D4—84no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—22no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—21no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—24no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—24no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—22no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—21no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—24no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—24no—
1399C2×C4—24no—
1400C2×C4—21no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—48no—
1404C2×C4—416no—
1405C2×C4—48no—
1406C2×C4—48no—
1407C2×C4—48no—
1408C2×C4—88no—
1409C2×C4—84no—
1410C2×C4—84no—
1411C2×C4—84no—
1412C2×C4—84no—
1413C2×C4—164no—
1414C2×C4—164no—
1415C2×C4—164no—
1416C2×C4—164no—
1417C2×C4C22×#4114yes—
1418C2×C4C22×#4112yes—
1419C2×C4C22×#4112yes—
1420C2×C4C22×#4112yes—
1421C2×C4C2×H(5,𝔽2)12yes—
1422C2×C4C2×H(5,𝔽2)12yes—
1423C2×C4C2×H(5,𝔽2)12yes—
1424C2×C4C2×2−1+412yes—
1425C2×C4#58512yes—
1426C22—24no—
1427C22—24no—
1428C22—24no—
1429C22—24no—
1430C22—24no—
1431C22—24no—
1432C22—42no—
1433C22—42no—
1434C22—42no—
1435C22—42no—
1436C22—42no—
1437C22—42no—
1438C22—42no—
1439C22—42no—
1440C22—42no—
1441C22—42no—
1442C22—42no—
1443C22—42no—
1444C22—42no—
1445C22—42no—
1446C22—42no—
1447C22—42no—
1448C22—42no—
1449C22—42no—
1450C22—42no—
1451C22—42no—
1452C22—42no—
1453C22—42no—
1454C22C23×#4111yescharacteristic
1455C22C22×H(5,𝔽2)11yescharacteristic
1456C22C22×2−1+411yescharacteristic
1457C22C2×#58511yescharacteristic
1458C22H(7,𝔽2)11yescharacteristic
1459C22H(7,𝔽2)11yescharacteristic
1460C222−1+611yescharacteristic
1461C4—22no—
1462C4—22no—
1463C4—24no—
1464C4—22no—
1465C4—22no—
1466C4—22no—
1467C4—44no—
1468C4—42no—
1469C4—42no—
1470C4—42no—
1471C4—44no—
1472C4—41no—
1473C4—44no—
1474C4—42no—
1475C4—44no—
1476C4—42no—
1477C4—42no—
1478C4—42no—
1479C4—44no—
1480C4—44no—
1481C4—42no—
1482C4—42no—
1483C4—42no—
1484C4—42no—
1485C4#350614yes—
1486C2—44no—
1487C2—44no—
1488C2—82no—
1489C2—82no—
1490C2C2×#350611yescharacteristic
1491C2#6284711yescharacteristic
1492C2#6288011yescharacteristic
1493C2#6290211yescharacteristic
1494C2#6294211yescharacteristic
1495C2#6300011yescharacteristic
1496C2#6304711yescharacteristic
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. #59856C2semidirect
2. #59823C2semidirect
3. #52160C2semidirect
4. #49133C2semidirect
5. #48805C2semidirect
6. #48217C2semidirect
7. #46698C2semidirect
8. #45800C2semidirect
9. #45375C2semidirect
10. #45228C2semidirect
11. #44978C2semidirect
12. #43375C2semidirect
13. #42679C2semidirect
14. #42591C2semidirect
15. #41107C2semidirect
16. #40148C2semidirect
17. #39757C2semidirect
18. #39631C2semidirect
19. #39580C2semidirect
20. #39509C2semidirect
21. #39271C2semidirect
22. #38040C2semidirect
23. #37141C2semidirect
24. #36468C2semidirect
25. #35701C2semidirect
26. #35521C2semidirect
27. #35176C2semidirect
28. #34461C2semidirect
29. #34308C2semidirect

Maximal subgroups

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

subgroupindex
#598562
#598232
#521602
#491332
#488052
#482172
#466982
#458002
#453752
#452282
#449782
#433752
#426792
#425912
#411072
#401482
#397572
#396312
#395802
#395092
#392712
#380402
#371412
#364682
#357012
#355212
#351762
#344612
#343082