Finite Group Databasebeta

← #7895415

Subgroups — #7895415

Order 512.

5045 conjugacy classes of subgroups.

The subgroup lattice has 1526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59826C212yesmaximal, complemented
2#59815C211yesmaximal, characteristic, complemented
3#52160C211yesmaximal, characteristic, complemented
4#49539C214yesmaximal, complemented
5#49478C214yesmaximal, complemented
6#48677C214yesmaximal, complemented
7#47172C214yesmaximal, complemented
8#45962C212yesmaximal, complemented
9#45386C214yesmaximal, complemented
10#45356C212yesmaximal, complemented
11#45064C212yesmaximal, complemented
12#44975C212yesmaximal, complemented
13#42752C212yesmaximal, complemented
14#42688C212yesmaximal, complemented
15#40743C214yesmaximal, complemented
16#40175C212yesmaximal, complemented
17#39637C211yesmaximal, characteristic, complemented
18#39372C211yesmaximal, characteristic, complemented
19#39258C212yesmaximal, complemented
20#38770C212yesmaximal, complemented
21#38433C212yesmaximal, complemented
22#38043C212yesmaximal, complemented
23#37152C212yesmaximal, complemented
24#36270C211yesmaximal, characteristic, complemented
25#35699C212yesmaximal, complemented
26#35567C212yesmaximal, complemented
27#35186C211yesmaximal, characteristic, complemented
28#34460C212yesmaximal, complemented
29#34317C211yesmaximal, characteristic, complemented
30C2×#554C2211yescharacteristic
31C2×#553C2214yes—
32C2×#552C2212yes—
33C2×#550C2212yes—
34C2×#547C2212yes—
35C2×#540C2212yes—
36C2×#529C2212yes—
37#2861C2212yes—
38#2860C2212yes—
39#2860C2212yes—
40#2859C2211yescharacteristic
41#2855C2212yes—
42#2829C2214yes—
43#2828C2214yes—
44#2809C2212yes—
45#2806C2212yes—
46#2805C2212yes—
47#2800C2214yes—
48#2800C2214yes—
49#2786C2214yes—
50#2786C2214yes—
51#2782C2214yes—
52#2781C2214yes—
53#2748C2214yes—
54#2747C2214yes—
55#2741C2214yes—
56#2740C2214yes—
57#2740C2214yes—
58#2740C2214yes—
59#2733C2211yescharacteristic
60#2732C2214yes—
61#2732C2214yes—
62#2732C2211yescharacteristic
63#2730C2212yes—
64#2727C2211yescharacteristic
65#2726C2212yes—
66#2726C2214yes—
67#2725C2214yes—
68#2725C2214yes—
69#2724C2212yes—
70#2724C2212yes—
71#2722C2214yes—
72#2721C2212yes—
73#2715C2214yes—
74#2714C2214yes—
75#2714C2212yes—
76#2707C2214yes—
77#2705C2214yes—
78#2705C2212yes—
79#2703C2214yes—
80#2703C2214yes—
81#2701C2214yes—
82#2701C2214yes—
83#2699C2214yes—
84#2699C2214yes—
85#2694C2214yes—
86#2694C2214yes—
87#2694C2214yes—
88#2694C2212yes—
89#2691C2214yes—
90#2691C2214yes—
91#2682C2212yes—
92#2682C2211yescharacteristic
93#2682C2212yes—
94#2682C2212yes—
95#2682C2212yes—
96#2673C2214yes—
97#2673C2212yes—
98#2661C2214yes—
99#2654C2214yes—
100#2652C2214yes—
101#2651C2214yes—
102#2651C2214yes—
103#2648C2214yes—
104#2647C2212yes—
105#2630C2214yes—
106#2629C2212yes—
107#2625C2212yes—
108#2601C2214yes—
109#2601C2214yes—
110#2595C2214yes—
111#2587C2214yes—
112#2587C2214yes—
113#2585C2214yes—
114#2585C2214yes—
115#2584C2212yes—
116#2582C2211yescharacteristic
117#2579C2214yes—
118#2569C2214yes—
119#2562C2212yes—
120#2559C2214yes—
121#2558C2214yes—
122#2558C2214yes—
123#2555C2214yes—
124#2554C2214yes—
125#2552C2211yescharacteristic
126#2548C2211yescharacteristic
127#2548C2211yescharacteristic
128#2541C2212yes—
129#2540C2212yes—
130#2540C2212yes—
131#2538C2211yescharacteristic
132#2538C2212yes—
133#2538C2211yescharacteristic
134#2537C2212yes—
135#2536C2212yes—
136#2535C2212yes—
137#2522C2214yes—
138#2516C2214yes—
139#2512C2212yes—
140#2507C2212yes—
141#2506C2212yes—
142#2506C2212yes—
143#2497C2212yes—
144#2496C2212yes—
145#2490C2214yes—
146#2490C2214yes—
147#2486C2214yes—
148#2486C2212yes—
149#2485C2212yes—
150#2485C2212yes—
151#2485C2212yes—
152#2475C2214yes—
153#2471C2214yes—
154#2471C2214yes—
155#2470C2214yes—
156#2468C2214yes—
157#2468C2214yes—
158#2468C2214yes—
159#2466C2214yes—
160#2466C2214yes—
161#2464C2214yes—
162#2461C2214yes—
163#2460C2214yes—
164#2457C2214yes—
165#2456C2214yes—
166#2456C2214yes—
167#2454C2212yes—
168#2453C2214yes—
169#2448C2212yes—
170#2447C2212yes—
171#2445C2214yes—
172#2445C2214yes—
173#2445C2212yes—
174#2445C2214yes—
175#2444C2214yes—
176#2444C2214yes—
177#2444C2214yes—
178#2438C2214yes—
179#2428C2214yes—
180#2427C2212yes—
181#2427C2212yes—
182#2425C2214yes—
183#2425C2214yes—
184#2425C2214yes—
185#2422C2212yes—
186#2422C2212yes—
187#2417C2212yes—
188#2417C2212yes—
189#2416C2212yes—
190#2416C2212yes—
191#2416C2212yes—
192#2416C2212yes—
193#2416C2212yes—
194#2414C2212yes—
195#2414C2214yes—
196#2414C2212yes—
197#2414C2214yes—
198#2414C2212yes—
199#2413C2214yes—
200#2407C2214yes—
201#2407C2214yes—
202#2407C2214yes—
203#2397C2212yes—
204#2392C2212yes—
205#2392C2212yes—
206#2392C2214yes—
207#2378C2214yes—
208#2376C2214yes—
209#2370C2212yes—
210#2370C2212yes—
211#2369C2211yescharacteristic
212#2363C2212yes—
213#2362C2212yes—
214#2362C2214yes—
215#2361C2212yes—
216#2359C2214yes—
217#2357C2212yes—
218#2355C2211yescharacteristic
219#2354C2211yescharacteristic
220#2354C2211yescharacteristic
221#2352C2212yes—
222#2349C2212yes—
223D4×C4⋊C4C2212yes—
224D4×C4⋊C4C2212yes—
225D4×C4⋊C4C2212yes—
226D4×C4⋊C4C2211yescharacteristic
227#2345C2212yes—
228#2344C2212yes—
229#2344C2212yes—
230#2339C2214yes—
231#2335C2214yes—
232#2332C2214yes—
233#2331C2212yes—
234#2329C2214yes—
235#2326C2212yes—
236#2324C2212yes—
237#2324C2214yes—
238#2324C2212yes—
239#2323C2212yes—
240#2322C2214yes—
241#2319C2212yes—
242#2316C2212yes—
243#2311C2214yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×#127C2211yescharacteristic
246C4×#127C2211yescharacteristic
247C4×#125C2212yes—
248C4×#121C2212yes—
249C4×#121C2212yes—
250C4×#121C2212yes—
251#2295C2211yescharacteristic
252#2293C2212yes—
253#2293C2211yescharacteristic
254#2293C2212yes—
255C2×#389C2212yes—
256#2290C2212yes—
257#2274C2212yes—
258C42×Q8C2211yescharacteristic
259C22×#41C2314yes—
260#554—28no—
261#553—416no—
262#552—48no—
263#550—48no—
264#547—216no—
265#540—48no—
266C2×C4⋊Q8C2311yescharacteristic
267C2×#127C2311yescharacteristic
268C2×#127C2311yescharacteristic
269C2×#127C2314yes—
270#529—48no—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2312yes—
274C2×#126C2312yes—
275C2×#126C2314yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#125C2312yes—
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2312yes—
289C2×#123C2312yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×#121C2312yes—
302C2×#121C2314yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2314yes—
307C2×#121C2314yes—
308C2×#121C2314yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×#121C2312yes—
312C2×#121C2314yes—
313C2×#121C2314yes—
314C2×#121C2312yes—
315C2×#121C2314yes—
316C2×#121C2314yes—
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2312yes—
328C2×C4×D4C2311yescharacteristic
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2312yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2314yes—
344C2×#117C2312yes—
345C2×#117C2312yes—
346C2×#117C2312yes—
347C2×#117C2314yes—
348C2×#117C2314yes—
349C2×#117C2312yes—
350C2×#117C2314yes—
351C22×C4⋊C4C2312yes—
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2312yes—
354C22×C4⋊C4C2314yes—
355C22×C4⋊C4C2312yes—
356C22×C42C2312yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#399C2314yes—
365#399C2312yes—
366#399C2312yes—
367#399C2312yes—
368#399C2312yes—
369#399C2314yes—
370#399C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2312yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2312yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2312yes—
396#397C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2312yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2312yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2312yes—
418#396C2312yes—
419#396C2314yes—
420#396C2314yes—
421#395C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2312yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2312yes—
437#394C2312yes—
438#394C2312yes—
439#394C2312yes—
440#394C2312yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#392C2312yes—
450#392C2314yes—
451#392C2314yes—
452#392C2314yes—
453#392C2314yes—
454#392C2314yes—
455#392C2312yes—
456#392C2312yes—
457#392C2312yes—
458#392C2312yes—
459#392C2312yes—
460#392C2314yes—
461#392C2314yes—
462#392C2314yes—
463#391C2312yes—
464#391C2314yes—
465#391C2314yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2314yes—
470#391C2311yescharacteristic
471#391C2311yescharacteristic
472#390C2312yes—
473#390C2311yescharacteristic
474#390C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2311yescharacteristic
478#390C2312yes—
479#390C2314yes—
480#390C2314yes—
481#390C2312yes—
482#390C2312yes—
483#390C2312yes—
484#390C2312yes—
485#390C2312yes—
486#390C2314yes—
487#390C2314yes—
488#390C2314yes—
489#390C2314yes—
490#390C2312yes—
491#390C2312yes—
492#390C2312yes—
493#390C2312yes—
494#390C2312yes—
495#390C2311yescharacteristic
496#390C2314yes—
497#390C2314yes—
498#390C2314yes—
499#390C2311yescharacteristic
500#390C2314yes—
501#390C2312yes—
502#390C2314yes—
503#389C2311yescharacteristic
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#389C2312yes—
510#389C2314yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2312yes—
519#389C2314yes—
520#389C2314yes—
521#389C2312yes—
522#389C2314yes—
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2312yes—
528#389C2314yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2311yescharacteristic
535#389C2312yes—
536#389C2311yescharacteristic
537#389C2312yes—
538#389C2312yes—
539#389C2314yes—
540#389C2312yes—
541#389C2311yescharacteristic
542#389C2312yes—
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#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2312yes—
562#388C2314yes—
563#388C2312yes—
564#388C2314yes—
565#388C2312yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2312yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2312yes—
578#388C2314yes—
579#388C2312yes—
580#387C2314yes—
581#387C2314yes—
582#387C2312yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2312yes—
592#387C2314yes—
593#387C2314yes—
594#387C2312yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2312yes—
607#386C2312yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2312yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2312yes—
619#386C2314yes—
620#386C2314yes—
621#386C2312yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2312yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2312yes—
648#384C2311yescharacteristic
649#384C2311yescharacteristic
650#384C2311yescharacteristic
651#384C2312yes—
652#384C2311yescharacteristic
653#384C2311yescharacteristic
654#382C2312yes—
655#382C2312yes—
656#381C2314yes—
657#381C2314yes—
658#381C2314yes—
659#381C2314yes—
660#381C2314yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2312yes—
674#380C2312yes—
675#380C2314yes—
676#380C2312yes—
677#380C2312yes—
678#380C2312yes—
679#380C2312yes—
680#380C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2311yescharacteristic
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2311yescharacteristic
703C4×C4⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2314yes—
714#376C2312yes—
715C2×#95C2314yes—
716C2×#95C2314yes—
717C43C2312yes—
718C43C2311yescharacteristic
719C2×#41—216no—
720C2×#41—48no—
721C2×#41—84no—
722C22×Q8C2411yescharacteristic
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×D4C2412yes—
726C22×D4C2412yes—
727C22×D4C2414yes—
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2414yes—
733C22×D4C2411yescharacteristic
734C22×D4C2412yes—
735C22×D4C2412yes—
736C22×D4C2414yes—
737C22×D4C2412yes—
738C22×D4C2412yes—
739C22×D4C2414yes—
740C22×D4C2414yes—
741C22×D4C2414yes—
742C22×D4C2411yescharacteristic
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2412yes—
746C23×C4C2414yes—
747C23×C4C2414yes—
748C23×C4C2412yes—
749C23×C4C2414yes—
750C23×C4C2414yes—
751C23×C4C2414yes—
752C23×C4C2414yes—
753C23×C4C2412yes—
754C23×C4C2414yes—
755C4⋊Q8#4118yes—
756#127—24no—
757#127—24no—
758#127—48no—
759#126—48no—
760#126—48no—
761#126—48no—
762#126—44no—
763#126—44no—
764#125—28no—
765#125—28no—
766#125—44no—
767#125—48no—
768#125—48no—
769#125—82no—
770#124—44no—
771#124—44no—
772#124—82no—
773#123—216no—
774#123—216no—
775#123—44no—
776#123—48no—
777#123—48no—
778#123—44no—
779#123—48no—
780#123—48no—
781#123—48no—
782#123—84no—
783C22⋊Q8—216no—
784C22⋊Q8—216no—
785C22⋊Q8—28no—
786C22⋊Q8—44no—
787C22⋊Q8—44no—
788C22⋊Q8—44no—
789#121—216no—
790#121—28no—
791#121—28no—
792#121—28no—
793#121—44no—
794#121—48no—
795#121—48no—
796#121—48no—
797#121—48no—
798#121—48no—
799#121—44no—
800#121—44no—
801#121—44no—
802#121—44no—
803#121—48no—
804#121—84no—
805C4×Q8—24no—
806C4×Q8—24no—
807C4×Q8—24no—
808C4×Q8—44no—
809C4×Q8—42no—
810C4×D4—28no—
811C4×D4—28no—
812C4×D4—28no—
813C4×D4—28no—
814C4×D4—24no—
815C4×D4—28no—
816C4×D4—44no—
817C4×D4—44no—
818C4×D4—44no—
819C4×D4—42no—
820C4×D4—42no—
821C4×D4—44no—
822C4×D4—44no—
823C4×D4—44no—
824C4×D4—44no—
825C4×D4—48no—
826C4×D4—48no—
827C4×D4—48no—
828C4×D4—48no—
829C4×D4—84no—
830C4×D4—84no—
831C4×D4—82no—
832#117—28no—
833#117—44no—
834#117—48no—
835#117—48no—
836#117—44no—
837#117—44no—
838#117—84no—
839C2×C4⋊C4—28no—
840C2×C4⋊C4—28no—
841C2×C4⋊C4—28no—
842C2×C4⋊C4—44no—
843C2×C4⋊C4—48no—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2411yescharacteristic
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2412yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2412yes—
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C42—44no—
967C2×C42C2412yes—
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2412yes—
971C2×C42C2411yescharacteristic
972C2×C42C2411yescharacteristic
973C2×C42C2412yes—
974C2×C42C2412yes—
975C2×C42C2414yes—
976C2×C42C2414yes—
977C2×C42C2414yes—
978C2×C42C2414yes—
979C2×C42C2414yes—
980C2×C42C2414yes—
981C2×C42C2411yescharacteristic
982C2×C42C2414yes—
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2411yescharacteristic
988C2×C42C2412yes—
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041C24C2512yes—
1042C24C2514yes—
1043C24C2512yes—
1044C24C2512yes—
1045#41—832no—
1046C2×Q8—22no—
1047C2×Q8—22no—
1048C2×Q8—22no—
1049C2×Q8—22no—
1050C2×Q8—42no—
1051C2×Q8—42no—
1052C2×Q8—41no—
1053C2×Q8—41no—
1054C2×Q8C2×#4118yes—
1055C2×D4—24no—
1056C2×D4—24no—
1057C2×D4—28no—
1058C2×D4—24no—
1059C2×D4—28no—
1060C2×D4—24no—
1061C2×D4—22no—
1062C2×D4—24no—
1063C2×D4—24no—
1064C2×D4—28no—
1065C2×D4—28no—
1066C2×D4—24no—
1067C2×D4—24no—
1068C2×D4—22no—
1069C2×D4—24no—
1070C2×D4—24no—
1071C2×D4—24no—
1072C2×D4—41no—
1073C2×D4—42no—
1074C2×D4—42no—
1075C2×D4—42no—
1076C2×D4—44no—
1077C2×D4—41no—
1078C2×D4—41no—
1079C2×D4—41no—
1080C2×D4—42no—
1081C2×D4—42no—
1082C2×D4—42no—
1083C2×D4—42no—
1084C2×D4—42no—
1085C2×D4—42no—
1086C2×D4—42no—
1087C2×D4—41no—
1088C2×D4—42no—
1089C2×D4—44no—
1090C2×D4—44no—
1091C2×D4—42no—
1092C2×D4—44no—
1093C2×D4—41no—
1094C2×D4—42no—
1095C2×D4—42no—
1096C2×D4—42no—
1097C2×D4—44no—
1098C2×D4—42no—
1099C2×D4—44no—
1100C2×D4—44no—
1101C2×D4—44no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C2×D4H(5,𝔽2)14yes—
1109C22×C4—28no—
1110C22×C4—24no—
1111C22×C4—28no—
1112C22×C4—24no—
1113C22×C4—24no—
1114C22×C4—24no—
1115C22×C4—28no—
1116C22×C4—24no—
1117C22×C4—24no—
1118C22×C4—24no—
1119C22×C4—24no—
1120C22×C4—24no—
1121C22×C4—24no—
1122C22×C4—28no—
1123C22×C4—28no—
1124C22×C4—28no—
1125C22×C4—44no—
1126C22×C4—42no—
1127C22×C4—42no—
1128C22×C4—44no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—42no—
1133C22×C4—44no—
1134C22×C4—44no—
1135C22×C4—44no—
1136C22×C4—44no—
1137C22×C4—42no—
1138C22×C4—42no—
1139C22×C4—44no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—44no—
1144C22×C4—44no—
1145C22×C4C2512yes—
1146C22×C4C2512yes—
1147C22×C4C2514yes—
1148C22×C4C2512yes—
1149C22×C4C2512yes—
1150C22×C4C2512yes—
1151C22×C4C2511yescharacteristic
1152C22×C4C2512yes—
1153C22×C4C2514yes—
1154C22×C4C2514yes—
1155C22×C4C2514yes—
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2512yes—
1160C22×C4C2512yes—
1161C22×C4C2512yes—
1162C22×C4C2512yes—
1163C22×C4C2511yescharacteristic
1164C22×C4C2511yescharacteristic
1165C22×C4C2514yes—
1166C22×C4C2511yescharacteristic
1167C22×C4C2511yescharacteristic
1168C22×C4C2511yescharacteristic
1169C22×C4C2511yescharacteristic
1170C4⋊C4—24no—
1171C4⋊C4—22no—
1172C4⋊C4—28no—
1173C4⋊C4—28no—
1174C4⋊C4—28no—
1175C4⋊C4—24no—
1176C4⋊C4—22no—
1177C4⋊C4—24no—
1178C4⋊C4—28no—
1179C4⋊C4—22no—
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—24no—
1183C4⋊C4—24no—
1184C4⋊C4—28no—
1185C4⋊C4—28no—
1186C4⋊C4—24no—
1187C4⋊C4—24no—
1188C4⋊C4—24no—
1189C4⋊C4—24no—
1190C4⋊C4—22no—
1191C4⋊C4—24no—
1192C4⋊C4—28no—
1193C4⋊C4—22no—
1194C4⋊C4—24no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—41no—
1201C4⋊C4—41no—
1202C4⋊C4—42no—
1203C4⋊C4—42no—
1204C4⋊C4—41no—
1205C4⋊C4—42no—
1206C4⋊C4—42no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—42no—
1211C4⋊C4—42no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—41no—
1215C4⋊C4—41no—
1216C4⋊C4—42no—
1217C4⋊C4—42no—
1218C4⋊C4—42no—
1219C4⋊C4—42no—
1220C4⋊C4—44no—
1221C4⋊C4—42no—
1222C4⋊C4—44no—
1223C4⋊C4—44no—
1224C4⋊C4—42no—
1225C4⋊C4—44no—
1226C4⋊C4—42no—
1227C4⋊C4—42no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C4⋊C4—42no—
1231C4⋊C4—41no—
1232C4⋊C4C2×#4118yes—
1233C4⋊C4C2×#4118yes—
1234C22⋊C4—28no—
1235C22⋊C4—24no—
1236C22⋊C4—28no—
1237C22⋊C4—28no—
1238C22⋊C4—24no—
1239C22⋊C4—24no—
1240C22⋊C4—24no—
1241C22⋊C4—28no—
1242C22⋊C4—28no—
1243C22⋊C4—28no—
1244C22⋊C4—24no—
1245C22⋊C4—24no—
1246C22⋊C4—24no—
1247C22⋊C4—24no—
1248C22⋊C4—24no—
1249C22⋊C4—28no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—42no—
1254C22⋊C4—42no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—42no—
1258C22⋊C4—44no—
1259C22⋊C4—42no—
1260C22⋊C4—44no—
1261C22⋊C4—42no—
1262C22⋊C4—44no—
1263C22⋊C4—42no—
1264C22⋊C4—42no—
1265C22⋊C4—42no—
1266C22⋊C4—42no—
1267C22⋊C4—42no—
1268C22⋊C4—42no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—42no—
1275C22⋊C4—44no—
1276C22⋊C4—42no—
1277C22⋊C4—42no—
1278C22⋊C4—42no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C22⋊C4—44no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—42no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C42—24no—
1293C42—24no—
1294C42—24no—
1295C42—24no—
1296C42—24no—
1297C42—22no—
1298C42—22no—
1299C42—24no—
1300C42—42no—
1301C42—42no—
1302C42—41no—
1303C42—42no—
1304C42—41no—
1305C42—44no—
1306C42—44no—
1307C42—44no—
1308C42—44no—
1309C42—44no—
1310C42—44no—
1311C42—44no—
1312C42—41no—
1313C42—42no—
1314C42—42no—
1315C42C2×#4114yes—
1316C42H(5,𝔽2)14yes—
1317C23—22no—
1318C23—22no—
1319C23—22no—
1320C23—22no—
1321C23—22no—
1322C23—22no—
1323C23—22no—
1324C23—24no—
1325C23—22no—
1326C23—22no—
1327C23—22no—
1328C23—22no—
1329C23—24no—
1330C23—24no—
1331C23—22no—
1332C23—22no—
1333C23—24no—
1334C23—22no—
1335C23—22no—
1336C23—24no—
1337C23—22no—
1338C23—22no—
1339C23—24no—
1340C23—22no—
1341C23—24no—
1342C23—22no—
1343C23—22no—
1344C23C2×H(5,𝔽2)14yes—
1345C23C2611yescharacteristic
1346Q8—48no—
1347Q8—44no—
1348Q8—82no—
1349D4—44no—
1350D4—48no—
1351D4—416no—
1352D4—48no—
1353D4—44no—
1354D4—48no—
1355D4—48no—
1356D4—48no—
1357D4—84no—
1358D4—82no—
1359D4—84no—
1360D4—88no—
1361D4—88no—
1362D4—84no—
1363D4—84no—
1364D4—164no—
1365D4—164no—
1366D4—164no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—24no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—24no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—24no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—24no—
1399C2×C4—24no—
1400C2×C4—24no—
1401C2×C4—22no—
1402C2×C4—24no—
1403C2×C4—22no—
1404C2×C4—21no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—24no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—21no—
1417C2×C4—22no—
1418C2×C4—24no—
1419C2×C4—22no—
1420C2×C4—24no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—21no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—24no—
1430C2×C4—24no—
1431C2×C4—24no—
1432C2×C4—22no—
1433C2×C4—416no—
1434C2×C4—48no—
1435C2×C4—48no—
1436C2×C4—48no—
1437C2×C4—88no—
1438C2×C4—88no—
1439C2×C4—88no—
1440C2×C4—88no—
1441C2×C4—84no—
1442C2×C4—84no—
1443C2×C4—164no—
1444C2×C4—164no—
1445C2×C4C22×#4112yes—
1446C2×C4C22×#4112yes—
1447C2×C4C22×#4118yes—
1448C2×C4C22×#4112yes—
1449C2×C4C2×H(5,𝔽2)12yes—
1450C2×C4C2×H(5,𝔽2)12yes—
1451C2×C4C2×H(5,𝔽2)12yes—
1452C2×C4C2×H(5,𝔽2)12yes—
1453C2×C4#58512yes—
1454C22—24no—
1455C22—24no—
1456C22—24no—
1457C22—42no—
1458C22—42no—
1459C22—42no—
1460C22—42no—
1461C22—42no—
1462C22—42no—
1463C22—44no—
1464C22—42no—
1465C22—42no—
1466C22—44no—
1467C22—42no—
1468C22—42no—
1469C22—44no—
1470C22—42no—
1471C22—44no—
1472C22—42no—
1473C22—44no—
1474C22—42no—
1475C22—42no—
1476C22—42no—
1477C22—42no—
1478C22—44no—
1479C22—44no—
1480C22—42no—
1481C22—42no—
1482C22C23×#4111yescharacteristic
1483C22C22×H(5,𝔽2)11yescharacteristic
1484C22C22×H(5,𝔽2)11yescharacteristic
1485C22C2×#58511yescharacteristic
1486C22H(7,𝔽2)11yescharacteristic
1487C222−1+611yescharacteristic
1488C222−1+611yescharacteristic
1489C4—28no—
1490C4—22no—
1491C4—22no—
1492C4—22no—
1493C4—22no—
1494C4—22no—
1495C4—44no—
1496C4—42no—
1497C4—42no—
1498C4—42no—
1499C4—42no—
1500C4—42no—
1501C4—41no—
1502C4—42no—
1503C4—42no—
1504C4—42no—
1505C4—42no—
1506C4—44no—
1507C4—42no—
1508C4—44no—
1509C4—42no—
1510C4—42no—
1511C4—44no—
1512C4—42no—
1513C4#351714yes—
1514C2—44no—
1515C2—82no—
1516C2—82no—
1517C2—84no—
1518C2C2×#351711yescharacteristic
1519C2#6285011yescharacteristic
1520C2#6287811yescharacteristic
1521C2#6290111yescharacteristic
1522C2#6291411yescharacteristic
1523C2#6298311yescharacteristic
1524C2#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. #59826C2semidirect
2. #59815C2semidirect
3. #52160C2semidirect
4. #49539C2semidirect
5. #49478C2semidirect
6. #48677C2semidirect
7. #47172C2semidirect
8. #45962C2semidirect
9. #45386C2semidirect
10. #45356C2semidirect
11. #45064C2semidirect
12. #44975C2semidirect
13. #42752C2semidirect
14. #42688C2semidirect
15. #40743C2semidirect
16. #40175C2semidirect
17. #39637C2semidirect
18. #39372C2semidirect
19. #39258C2semidirect
20. #38770C2semidirect
21. #38433C2semidirect
22. #38043C2semidirect
23. #37152C2semidirect
24. #36270C2semidirect
25. #35699C2semidirect
26. #35567C2semidirect
27. #35186C2semidirect
28. #34460C2semidirect
29. #34317C2semidirect

Maximal subgroups

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

subgroupindex
#598262
#598152
#521602
#495392
#494782
#486772
#471722
#459622
#453862
#453562
#450642
#449752
#427522
#426882
#407432
#401752
#396372
#393722
#392582
#387702
#384332
#380432
#371522
#362702
#356992
#355672
#351862
#344602
#343172