Finite Group Databasebeta

← #7696309

Subgroups — #7696309

Order 512.

5145 conjugacy classes of subgroups.

The subgroup lattice has 1492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59903C212yesmaximal, complemented
2#59878C212yesmaximal, complemented
3#59822C211yesmaximal, characteristic, complemented
4#59156C214yesmaximal, complemented
5#52267C211yesmaximal, characteristic, complemented
6#52160C212yesmaximal, complemented
7#45393C212yesmaximal, complemented
8#44967C212yesmaximal, complemented
9#44905C212yesmaximal, complemented
10#44291C214yesmaximal, complemented
11#44123C214yesmaximal, complemented
12#43206C214yesmaximal, complemented
13#39818C212yesmaximal, complemented
14#39756C211yesmaximal, characteristic, complemented
15#39572C212yesmaximal, complemented
16#39483C211yesmaximal, characteristic, complemented
17#38747C214yesmaximal, complemented
18#38475C212yesmaximal, complemented
19#38317C214yesmaximal, complemented
20#38089C212yesmaximal, complemented
21#36285C211yesmaximal, characteristic, complemented
22#36117C212yesmaximal, complemented
23#35865C212yesmaximal, complemented
24#35844C212yesmaximal, complemented
25#35785C212yesmaximal, complemented
26#34331C211yesmaximal, characteristic, complemented
27#34313C211yesmaximal, characteristic, complemented
28#34305C212yesmaximal, complemented
29#34252C212yesmaximal, complemented
30C2×#559C2211yescharacteristic
31C2×#555C2212yes—
32C2×#553C2212yes—
33C2×#550C2211yescharacteristic
34C2×#529C2214yes—
35C2×#520C2212yes—
36#2863C2212yes—
37#2859C2211yescharacteristic
38#2856C2212yes—
39#2854C2214yes—
40#2808C2212yes—
41#2808C2212yes—
42#2807C2212yes—
43#2806C2211yescharacteristic
44#2805C2211yescharacteristic
45#2804C2211yescharacteristic
46#2803C2214yes—
47#2802C2212yes—
48#2793C2214yes—
49#2790C2212yes—
50#2788C2212yes—
51#2780C2212yes—
52#2773C2214yes—
53#2770C2214yes—
54#2768C2214yes—
55#2768C2214yes—
56#2756C2214yes—
57#2748C2214yes—
58#2741C2214yes—
59#2733C2212yes—
60#2733C2212yes—
61#2732C2211yescharacteristic
62#2730C2214yes—
63#2729C2212yes—
64#2727C2212yes—
65#2727C2212yes—
66#2727C2212yes—
67#2727C2212yes—
68#2721C2214yes—
69#2714C2214yes—
70#2706C2214yes—
71#2705C2214yes—
72#2701C2214yes—
73#2695C2214yes—
74#2694C2214yes—
75#2688C2214yes—
76#2682C2212yes—
77#2682C2212yes—
78#2673C2214yes—
79#2673C2214yes—
80#2671C2214yes—
81#2671C2214yes—
82#2648C2214yes—
83#2648C2214yes—
84#2641C2212yes—
85#2631C2214yes—
86#2619C2212yes—
87#2619C2212yes—
88#2611C2214yes—
89#2611C2214yes—
90#2610C2214yes—
91#2606C2214yes—
92#2604C2214yes—
93#2603C2214yes—
94#2602C2214yes—
95#2602C2214yes—
96#2598C2214yes—
97#2595C2214yes—
98#2593C2214yes—
99#2590C2214yes—
100#2582C2211yescharacteristic
101#2582C2211yescharacteristic
102#2580C2212yes—
103#2570C2212yes—
104#2570C2212yes—
105#2566C2212yes—
106#2565C2212yes—
107#2559C2214yes—
108#2559C2214yes—
109#2557C2214yes—
110#2554C2214yes—
111#2554C2214yes—
112#2553C2214yes—
113#2553C2214yes—
114#2552C2212yes—
115#2548C2212yes—
116#2548C2212yes—
117#2541C2212yes—
118#2541C2212yes—
119#2537C2212yes—
120#2531C2214yes—
121#2529C2214yes—
122#2525C2214yes—
123#2521C2214yes—
124#2518C2214yes—
125#2513C2212yes—
126#2513C2212yes—
127#2512C2212yes—
128#2512C2212yes—
129#2512C2212yes—
130#2512C2212yes—
131#2507C2212yes—
132#2501C2212yes—
133#2501C2212yes—
134#2500C2212yes—
135#2500C2212yes—
136#2479C2214yes—
137#2479C2214yes—
138#2478C2214yes—
139#2476C2214yes—
140#2474C2214yes—
141#2470C2214yes—
142#2468C2214yes—
143#2467C2214yes—
144#2467C2214yes—
145#2467C2214yes—
146#2466C2214yes—
147#2466C2214yes—
148#2464C2214yes—
149#2464C2214yes—
150#2464C2214yes—
151#2459C2214yes—
152#2458C2214yes—
153#2457C2214yes—
154#2456C2214yes—
155#2456C2214yes—
156#2456C2214yes—
157#2455C2214yes—
158#2455C2214yes—
159#2454C2214yes—
160#2448C2212yes—
161#2448C2212yes—
162#2448C2214yes—
163#2446C2212yes—
164#2445C2212yes—
165#2445C2212yes—
166#2444C2214yes—
167#2443C2214yes—
168#2443C2214yes—
169#2431C2212yes—
170#2431C2212yes—
171#2425C2214yes—
172#2425C2214yes—
173#2425C2214yes—
174#2414C2214yes—
175#2414C2214yes—
176#2402C2212yes—
177#2397C2214yes—
178#2396C2212yes—
179#2396C2212yes—
180#2392C2214yes—
181#2392C2214yes—
182#2373C2214yes—
183#2372C2214yes—
184#2370C2212yes—
185#2367C2212yes—
186#2367C2212yes—
187#2366C2212yes—
188#2366C2212yes—
189#2366C2211yescharacteristic
190#2366C2212yes—
191#2366C2211yescharacteristic
192#2364C2214yes—
193#2361C2212yes—
194#2361C2212yes—
195#2361C2214yes—
196#2361C2212yes—
197#2359C2214yes—
198#2359C2214yes—
199#2357C2212yes—
200#2357C2212yes—
201#2356C2212yes—
202#2356C2212yes—
203#2355C2211yescharacteristic
204#2355C2212yes—
205#2355C2211yescharacteristic
206#2354C2212yes—
207#2354C2212yes—
208#2354C2212yes—
209#2354C2212yes—
210Q8×C4⋊C4C2211yescharacteristic
211Q8×C4⋊C4C2211yescharacteristic
212Q8×C4⋊C4C2211yescharacteristic
213#2349C2214yes—
214#2349C2212yes—
215D4×C4⋊C4C2211yescharacteristic
216D4×C4⋊C4C2212yes—
217#2347C2214yes—
218#2346C2212yes—
219#2346C2214yes—
220#2345C2212yes—
221#2345C2214yes—
222#2344C2214yes—
223#2341C2212yes—
224#2335C2214yes—
225#2335C2214yes—
226#2334C2214yes—
227#2330C2212yes—
228#2326C2212yes—
229#2324C2212yes—
230#2324C2214yes—
231#2324C2212yes—
232#2318C2214yes—
233#2318C2214yes—
234#2317C2212yes—
235#2311C2212yes—
236C4×C4⋊Q8C2211yescharacteristic
237C4×#127C2211yescharacteristic
238C4×#127C2212yes—
239C4×#127C2211yescharacteristic
240C4×#124C2212yes—
241C4×C22⋊Q8C2212yes—
242C4×#121C2212yes—
243C4×#121C2214yes—
244#2297C2212yes—
245#2296C2212yes—
246#2295C2211yescharacteristic
247#2295C2212yes—
248#2293C2211yescharacteristic
249#2293C2212yes—
250#2293C2212yes—
251#2290C2214yes—
252#2290C2212yes—
253#2290C2214yes—
254#2290C2214yes—
255#2275C2212yes—
256#2274C2212yes—
257C42×Q8C2211yescharacteristic
258C2×C4×C4⋊C4C2212yes—
259C22×#41C2312yes—
260#559—28no—
261#555—48no—
262#553—216no—
263#550—28no—
264C2×C4⋊Q8C2311yescharacteristic
265C2×#127C2311yescharacteristic
266C2×#127C2311yescharacteristic
267C2×#127C2312yes—
268C2×#127C2312yes—
269C2×#127C2312yes—
270#529—416no—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#124C2312yes—
279C2×#124C2312yes—
280C2×#124C2314yes—
281C2×#124C2314yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×C22⋊Q8C2312yes—
291C2×#121C2312yes—
292C2×#121C2312yes—
293C2×#121C2314yes—
294C2×#121C2312yes—
295C2×#121C2314yes—
296C2×#121C2314yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×#121C2314yes—
301C2×#121C2314yes—
302#520—216no—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×D4C2312yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2311yescharacteristic
336C2×#117C2312yes—
337C2×#117C2312yes—
338C2×#117C2314yes—
339C2×#117C2312yes—
340C2×#117C2314yes—
341C2×#117C2314yes—
342C2×#117C2314yes—
343C2×#117C2314yes—
344C22×C4⋊C4C2312yes—
345C22×C4⋊C4C2314yes—
346C22×C4⋊C4C2312yes—
347C22×C42C2314yes—
348C22×C42C2312yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2312yes—
353#400C2312yes—
354#400C2312yes—
355#400C2312yes—
356#400C2312yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2312yes—
361#399C2312yes—
362#399C2314yes—
363#399C2314yes—
364#399C2314yes—
365#399C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2312yes—
376#398C2312yes—
377#398C2312yes—
378#398C2312yes—
379#398C2312yes—
380#398C2314yes—
381#398C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2312yes—
395#396C2314yes—
396#396C2314yes—
397#396C2312yes—
398#396C2312yes—
399#396C2312yes—
400#396C2314yes—
401#396C2314yes—
402#395C2312yes—
403#395C2312yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#393C2314yes—
425#393C2312yes—
426#393C2312yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#392C2314yes—
436#392C2314yes—
437#392C2314yes—
438#392C2314yes—
439#391C2311yescharacteristic
440#391C2311yescharacteristic
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2311yescharacteristic
448#391C2312yes—
449#391C2311yescharacteristic
450#390C2311yescharacteristic
451#390C2312yes—
452#390C2312yes—
453#390C2314yes—
454#390C2312yes—
455#390C2314yes—
456#390C2312yes—
457#390C2312yes—
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2314yes—
464#390C2314yes—
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2314yes—
471#390C2314yes—
472#390C2314yes—
473#390C2314yes—
474#390C2314yes—
475#390C2314yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2311yescharacteristic
481#390C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2311yescharacteristic
510#389C2311yescharacteristic
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2311yescharacteristic
515#389C2311yescharacteristic
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2312yes—
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#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2312yes—
558#388C2314yes—
559#388C2312yes—
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#387C2312yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2312yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2312yes—
583#387C2312yes—
584#387C2312yes—
585#387C2312yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2312yes—
605#386C2314yes—
606#386C2314yes—
607#386C2312yes—
608#386C2314yes—
609#386C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2312yes—
615#385C2312yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2312yes—
628#385C2312yes—
629#385C2312yes—
630#385C2312yes—
631#385C2312yes—
632#385C2312yes—
633#384C2311yescharacteristic
634#384C2311yescharacteristic
635#384C2312yes—
636#384C2311yescharacteristic
637#384C2312yes—
638#384C2312yes—
639#384C2312yes—
640#384C2311yescharacteristic
641#384C2311yescharacteristic
642#383C2314yes—
643#383C2314yes—
644#382C2312yes—
645#382C2312yes—
646#382C2312yes—
647#382C2312yes—
648#382C2314yes—
649#382C2314yes—
650#381C2314yes—
651#381C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2314yes—
655#380C2314yes—
656#380C2312yes—
657#380C2314yes—
658#380C2314yes—
659#380C2314yes—
660#380C2312yes—
661#380C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
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⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710#376C2312yes—
711#376C2314yes—
712#376C2314yes—
713#376C2314yes—
714C2×#95C2314yes—
715C2×#95C2314yes—
716C43C2311yescharacteristic
717C43C2312yes—
718C2×#41—28no—
719C2×#41—28no—
720C2×#41—44no—
721C22×Q8C2411yescharacteristic
722C22×Q8C2411yescharacteristic
723C22×Q8C2411yescharacteristic
724C22×Q8C2411yescharacteristic
725C22×D4C2412yes—
726C22×D4C2412yes—
727C22×D4C2414yes—
728C22×D4C2414yes—
729C22×D4C2412yes—
730C22×D4C2412yes—
731C22×D4C2412yes—
732C22×D4C2414yes—
733C22×D4C2414yes—
734C22×D4C2412yes—
735C22×D4C2414yes—
736C22×D4C2414yes—
737C22×D4C2414yes—
738C22×D4C2414yes—
739C22×D4C2411yescharacteristic
740C23×C4C2414yes—
741C23×C4C2412yes—
742C23×C4C2414yes—
743C23×C4C2414yes—
744C23×C4C2414yes—
745C23×C4C2414yes—
746C23×C4C2414yes—
747C23×C4C2414yes—
748C23×C4C2412yes—
749C23×C4C2414yes—
750C23×C4C2412yes—
751C4⋊Q8—24no—
752#127—28no—
753#127—24no—
754#127—24no—
755#127—44no—
756#127—44no—
757#126—216no—
758#126—48no—
759#126—48no—
760#126—84no—
761#126—84no—
762#125—28no—
763#125—48no—
764#124—28no—
765#124—216no—
766#124—28no—
767#124—48no—
768#123—216no—
769#123—216no—
770#123—48no—
771#123—48no—
772#123—84no—
773#123—84no—
774#123—84no—
775#123—84no—
776C22⋊Q8—28no—
777#121—216no—
778#121—28no—
779#121—28no—
780#121—28no—
781#121—216no—
782#121—48no—
783#121—48no—
784#121—48no—
785#121—84no—
786#121—84no—
787#121—84no—
788C4×Q8—28no—
789C4×Q8—28no—
790C4×Q8—24no—
791C4×Q8—24no—
792C4×Q8—42no—
793C4×Q8—42no—
794C4×Q8—42no—
795C4×Q8—82no—
796C4×Q8#4118yes—
797C4×D4—28no—
798C4×D4—216no—
799C4×D4—28no—
800C4×D4—28no—
801C4×D4—216no—
802C4×D4—216no—
803C4×D4—28no—
804C4×D4—28no—
805C4×D4—28no—
806C4×D4—48no—
807C4×D4—48no—
808C4×D4—44no—
809C4×D4—44no—
810C4×D4—44no—
811C4×D4—48no—
812C4×D4—82no—
813C4×D4—84no—
814C4×D4—82no—
815C4×D4—82no—
816C4×D4—84no—
817C4×D4—82no—
818C4×D4—82no—
819C4×D4—84no—
820C4×D4#4118yes—
821#117—28no—
822#117—216no—
823#117—28no—
824#117—44no—
825#117—48no—
826#117—48no—
827#117—48no—
828#117—48no—
829C2×C4⋊C4—28no—
830C2×C4⋊C4—28no—
831C2×C4⋊C4—216no—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2411yescharacteristic
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2411yescharacteristic
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2412yes—
946C2×C42—48no—
947C2×C42—44no—
948C2×C42C2412yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2412yes—
953C2×C42C2414yes—
954C2×C42C2412yes—
955C2×C42C2412yes—
956C2×C42C2411yescharacteristic
957C2×C42C2412yes—
958C2×C42C2412yes—
959C2×C42C2411yescharacteristic
960C2×C42C2412yes—
961C2×C42C2414yes—
962C2×C42C2414yes—
963C2×C42C2412yes—
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966C2×C42C2414yes—
967C2×C42C2412yes—
968C2×C42C2414yes—
969C2×C42C2414yes—
970C2×C42C2412yes—
971C2×C42C2414yes—
972C2×C42C2411yescharacteristic
973C2×C42C2412yes—
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2411yescharacteristic
977C2×C42C2411yescharacteristic
978#95C2412yes—
979#95C2414yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2414yes—
1033C24C2514yes—
1034C24C2514yes—
1035C24C2512yes—
1036#41—432no—
1037C2×Q8—22no—
1038C2×Q8—22no—
1039C2×Q8—22no—
1040C2×Q8—22no—
1041C2×Q8—41no—
1042C2×Q8—41no—
1043C2×Q8—41no—
1044C2×Q8—41no—
1045C2×Q8—41no—
1046C2×Q8—41no—
1047C2×Q8C2×#4114yes—
1048C2×Q8H(5,𝔽2)14yes—
1049C2×D4—28no—
1050C2×D4—28no—
1051C2×D4—28no—
1052C2×D4—28no—
1053C2×D4—28no—
1054C2×D4—24no—
1055C2×D4—24no—
1056C2×D4—24no—
1057C2×D4—24no—
1058C2×D4—24no—
1059C2×D4—24no—
1060C2×D4—24no—
1061C2×D4—24no—
1062C2×D4—28no—
1063C2×D4—24no—
1064C2×D4—24no—
1065C2×D4—41no—
1066C2×D4—42no—
1067C2×D4—42no—
1068C2×D4—44no—
1069C2×D4—41no—
1070C2×D4—42no—
1071C2×D4—42no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—42no—
1075C2×D4—42no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—44no—
1079C2×D4—42no—
1080C2×D4—42no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C2×D4—44no—
1084C2×D4—44no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—44no—
1088C2×D4—44no—
1089C2×D4—44no—
1090C2×D4—44no—
1091C2×D4—44no—
1092C2×D4—44no—
1093C2×D4C2×#4114yes—
1094C22×C4—24no—
1095C22×C4—24no—
1096C22×C4—28no—
1097C22×C4—28no—
1098C22×C4—28no—
1099C22×C4—24no—
1100C22×C4—28no—
1101C22×C4—28no—
1102C22×C4—28no—
1103C22×C4—28no—
1104C22×C4—28no—
1105C22×C4—42no—
1106C22×C4—42no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—42no—
1111C22×C4—44no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—42no—
1119C22×C4—44no—
1120C22×C4—44no—
1121C22×C4—42no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4C2×#4118yes—
1127C22×C4C2512yes—
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2514yes—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2514yes—
1137C22×C4C2514yes—
1138C22×C4C2512yes—
1139C22×C4C2514yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2511yescharacteristic
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2511yescharacteristic
1146C22×C4C2511yescharacteristic
1147C22×C4C2512yes—
1148C22×C4C2511yescharacteristic
1149C22×C4C2511yescharacteristic
1150C22×C4C2512yes—
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C4⋊C4—28no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—28no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—28no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—22no—
1163C4⋊C4—28no—
1164C4⋊C4—24no—
1165C4⋊C4—22no—
1166C4⋊C4—24no—
1167C4⋊C4—28no—
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—24no—
1173C4⋊C4—28no—
1174C4⋊C4—24no—
1175C4⋊C4—22no—
1176C4⋊C4—42no—
1177C4⋊C4—41no—
1178C4⋊C4—41no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—42no—
1190C4⋊C4—41no—
1191C4⋊C4—41no—
1192C4⋊C4—42no—
1193C4⋊C4—42no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—41no—
1197C4⋊C4—41no—
1198C4⋊C4—42no—
1199C4⋊C4—42no—
1200C4⋊C4—42no—
1201C4⋊C4—44no—
1202C4⋊C4—42no—
1203C4⋊C4—42no—
1204C4⋊C4—44no—
1205C4⋊C4—42no—
1206C4⋊C4—42no—
1207C4⋊C4—42no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—42no—
1211C4⋊C4—42no—
1212C4⋊C4—42no—
1213C4⋊C4C2×#4114yes—
1214C4⋊C4C2×#4118yes—
1215C4⋊C4C2×#4114yes—
1216C22⋊C4—28no—
1217C22⋊C4—28no—
1218C22⋊C4—24no—
1219C22⋊C4—24no—
1220C22⋊C4—28no—
1221C22⋊C4—28no—
1222C22⋊C4—28no—
1223C22⋊C4—28no—
1224C22⋊C4—28no—
1225C22⋊C4—28no—
1226C22⋊C4—28no—
1227C22⋊C4—28no—
1228C22⋊C4—28no—
1229C22⋊C4—28no—
1230C22⋊C4—28no—
1231C22⋊C4—24no—
1232C22⋊C4—24no—
1233C22⋊C4—28no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—42no—
1238C22⋊C4—42no—
1239C22⋊C4—42no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—42no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—42no—
1261C22⋊C4—42no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4C2×#4118yes—
1267C42—28no—
1268C42—24no—
1269C42—28no—
1270C42—24no—
1271C42—24no—
1272C42—28no—
1273C42—28no—
1274C42—24no—
1275C42—22no—
1276C42—24no—
1277C42—24no—
1278C42—24no—
1279C42—22no—
1280C42—42no—
1281C42—42no—
1282C42—44no—
1283C42—44no—
1284C42—41no—
1285C42—44no—
1286C42—42no—
1287C42—41no—
1288C42—41no—
1289C42—44no—
1290C42—42no—
1291C42—44no—
1292C42—42no—
1293C42—44no—
1294C42C2×#4118yes—
1295C42C2×#4114yes—
1296C42C2×#4114yes—
1297C23—22no—
1298C23—22no—
1299C23—22no—
1300C23—22no—
1301C23—22no—
1302C23—22no—
1303C23—24no—
1304C23—24no—
1305C23—24no—
1306C23—24no—
1307C23—24no—
1308C23—24no—
1309C23—24no—
1310C23—24no—
1311C23—24no—
1312C23—24no—
1313C23—24no—
1314C23—24no—
1315C23—24no—
1316C23—24no—
1317C23C22×#4114yes—
1318C23C2611yescharacteristic
1319Q8—28no—
1320Q8—44no—
1321Q8—44no—
1322Q8—82no—
1323D4—44no—
1324D4—416no—
1325D4—48no—
1326D4—48no—
1327D4—416no—
1328D4—48no—
1329D4—48no—
1330D4—84no—
1331D4—84no—
1332D4—88no—
1333D4—88no—
1334D4—88no—
1335D4—88no—
1336D4—164no—
1337D4—164no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—22no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—22no—
1356C2×C4—216no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—24no—
1367C2×C4—24no—
1368C2×C4—24no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—21no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—24no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—24no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—24no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—416no—
1406C2×C4—48no—
1407C2×C4—88no—
1408C2×C4—88no—
1409C2×C4—88no—
1410C2×C4—88no—
1411C2×C4—88no—
1412C2×C4—88no—
1413C2×C4—84no—
1414C2×C4—164no—
1415C2×C4C22×#4112yes—
1416C2×C4C22×#4114yes—
1417C2×C4C22×#4114yes—
1418C2×C4C22×#4112yes—
1419C2×C4C22×#4114yes—
1420C2×C4C22×#4112yes—
1421C2×C4C22×#4112yes—
1422C2×C4C22×#4112yes—
1423C2×C4C22×#4112yes—
1424C2×C4C2×H(5,𝔽2)14yes—
1425C2×C4C2×H(5,𝔽2)12yes—
1426C2×C4#58512yes—
1427C22—24no—
1428C22—24no—
1429C22—24no—
1430C22—42no—
1431C22—42no—
1432C22—42no—
1433C22—42no—
1434C22—44no—
1435C22—44no—
1436C22—44no—
1437C22—44no—
1438C22—44no—
1439C22—44no—
1440C22—44no—
1441C22—44no—
1442C22—44no—
1443C22—44no—
1444C22—44no—
1445C22—44no—
1446C22—44no—
1447C22—44no—
1448C22C23×#4111yescharacteristic
1449C22C23×#4111yescharacteristic
1450C22C22×H(5,𝔽2)11yescharacteristic
1451C22C2×#58511yescharacteristic
1452C22H(7,𝔽2)11yescharacteristic
1453C22H(7,𝔽2)11yescharacteristic
1454C222−1+611yescharacteristic
1455C4—24no—
1456C4—22no—
1457C4—22no—
1458C4—22no—
1459C4—22no—
1460C4—24no—
1461C4—22no—
1462C4—24no—
1463C4—24no—
1464C4—42no—
1465C4—44no—
1466C4—42no—
1467C4—44no—
1468C4—44no—
1469C4—42no—
1470C4—41no—
1471C4—42no—
1472C4—42no—
1473C4—42no—
1474C4—42no—
1475C4—44no—
1476C4—42no—
1477C4—42no—
1478C4—42no—
1479C4—42no—
1480C4#347514yes—
1481C2—44no—
1482C2—84no—
1483C2—84no—
1484C2C2×#347511yescharacteristic
1485C2#6284511yescharacteristic
1486C2#6285111yescharacteristic
1487C2#6290111yescharacteristic
1488C2#6298611yescharacteristic
1489C2#6298611yescharacteristic
1490C2#6305111yescharacteristic
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. #59903C2semidirect
2. #59878C2semidirect
3. #59822C2semidirect
4. #59156C2semidirect
5. #52267C2semidirect
6. #52160C2semidirect
7. #45393C2semidirect
8. #44967C2semidirect
9. #44905C2semidirect
10. #44291C2semidirect
11. #44123C2semidirect
12. #43206C2semidirect
13. #39818C2semidirect
14. #39756C2semidirect
15. #39572C2semidirect
16. #39483C2semidirect
17. #38747C2semidirect
18. #38475C2semidirect
19. #38317C2semidirect
20. #38089C2semidirect
21. #36285C2semidirect
22. #36117C2semidirect
23. #35865C2semidirect
24. #35844C2semidirect
25. #35785C2semidirect
26. #34331C2semidirect
27. #34313C2semidirect
28. #34305C2semidirect
29. #34252C2semidirect

Maximal subgroups

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

subgroupindex
#599032
#598782
#598222
#591562
#522672
#521602
#453932
#449672
#449052
#442912
#441232
#432062
#398182
#397562
#395722
#394832
#387472
#384752
#383172
#380892
#362852
#361172
#358652
#358442
#357852
#343312
#343132
#343052
#342522