Finite Group Databasebeta

← #8926399

Subgroups — #8926399

Order 512.

4315 conjugacy classes of subgroups.

The subgroup lattice has 1415 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58849C211yesmaximal, characteristic, complemented
2#58460C211yesmaximal, characteristic, complemented
3#58274C213yesmaximal, complemented
4#58260C211yesmaximal, characteristic, complemented
5#58238C213yesmaximal, complemented
6#58174C213yesmaximal, complemented
7#58002C213yesmaximal, complemented
8#57474C213yesmaximal, complemented
9#57369C213yesmaximal, complemented
10#56577C213yesmaximal, complemented
11#47392C213yesmaximal, complemented
12#47312C213yesmaximal, complemented
13#47169C213yesmaximal, complemented
14#47103C213yesmaximal, complemented
15#46791C213yesmaximal, complemented
16#46619C213yesmaximal, complemented
17#37365C213yesmaximal, complemented
18#37207C213yesmaximal, complemented
19#37204C213yesmaximal, complemented
20#37112C213yesmaximal, complemented
21#37054C213yesmaximal, complemented
22#37038C213yesmaximal, complemented
23#35473C213yesmaximal, complemented
24#2863C2213yescomplemented
25#2861C2213yescomplemented
26#2861C2213yescomplemented
27#2860C2213yescomplemented
28#2838C2213yescomplemented
29#2837C2213yescomplemented
30#2836C2213yescomplemented
31#2829C2213yes—
32#2829C2213yes—
33#2828C2213yescomplemented
34#2825C2213yescomplemented
35#2818C2211yescharacteristic, complemented
36#2818C2211yescharacteristic, complemented
37#2813C2213yescomplemented
38#2812C2213yes—
39#2812C2211yescharacteristic
40#2806C2213yescomplemented
41#2803C2213yes—
42#2803C2213yescomplemented
43#2803C2213yescomplemented
44#2803C2213yescomplemented
45#2803C2213yescomplemented
46#2803C2213yescomplemented
47#2801C2213yescomplemented
48#2800C2213yescomplemented
49#2800C2213yescomplemented
50#2798C2213yescomplemented
51#2797C2213yes—
52#2797C2213yescomplemented
53#2797C2213yescomplemented
54#2796C2213yescomplemented
55#2795C2213yescomplemented
56#2787C2213yescomplemented
57#2787C2213yescomplemented
58#2785C2211yescharacteristic, complemented
59#2783C2213yescomplemented
60#2783C2213yescomplemented
61#2778C2213yescomplemented
62#2778C2213yescomplemented
63#2777C2213yescomplemented
64#2777C2213yescomplemented
65#2777C2213yescomplemented
66#2777C2213yescomplemented
67#2772C2213yescomplemented
68#2762C2213yescomplemented
69#2759C2213yescomplemented
70#2759C2213yescomplemented
71#2759C2213yescomplemented
72#2759C2213yescomplemented
73#2756C2213yes—
74#2756C2213yes—
75#2756C2213yescomplemented
76#2754C2213yescomplemented
77#2753C2213yes—
78#2752C2213yes—
79#2749C2213yescomplemented
80#2746C2213yescomplemented
81#2741C2213yescomplemented
82#2740C2213yescomplemented
83#2737C2213yescomplemented
84#2736C2211yescharacteristic
85#2735C2213yes—
86#2735C2213yes—
87#2735C2213yes—
88#2735C2213yescomplemented
89#2735C2213yescomplemented
90#2733C2213yes—
91#2732C2213yescomplemented
92#2730C2213yescomplemented
93#2730C2213yescomplemented
94#2730C2213yescomplemented
95#2727C2213yescomplemented
96#2727C2213yescomplemented
97#2727C2213yescomplemented
98#2723C2213yescomplemented
99#2720C2213yescomplemented
100#2715C2213yescomplemented
101#2715C2213yescomplemented
102#2715C2213yescomplemented
103#2715C2213yescomplemented
104#2712C2213yescomplemented
105#2711C2213yescomplemented
106#2710C2213yes—
107#2710C2213yescomplemented
108#2707C2213yescomplemented
109#2706C2213yescomplemented
110#2705C2213yes—
111#2705C2213yescomplemented
112#2704C2213yescomplemented
113#2703C2213yes—
114#2702C2213yescomplemented
115#2701C2213yescomplemented
116#2701C2213yescomplemented
117#2697C2213yescomplemented
118#2697C2213yescomplemented
119#2695C2213yescomplemented
120#2692C2213yescomplemented
121#2689C2213yescomplemented
122#2687C2213yescomplemented
123#2686C2213yescomplemented
124#2685C2213yes—
125#2685C2213yescomplemented
126#2685C2213yescomplemented
127#2685C2213yescomplemented
128#2685C2213yescomplemented
129#2684C2213yes—
130#2681C2213yescomplemented
131#2678C2213yescomplemented
132#2678C2213yescomplemented
133#2672C2213yescomplemented
134#2670C2213yes—
135#2670C2213yescomplemented
136#2670C2213yescomplemented
137#2669C2213yes—
138#2669C2213yes—
139#2668C2213yescomplemented
140#2663C2213yescomplemented
141#2662C2213yescomplemented
142#2661C2213yescomplemented
143#2653C2213yescomplemented
144#2653C2213yescomplemented
145#2650C2213yescomplemented
146#2633C2213yescomplemented
147#2631C2213yes—
148#2630C2213yescomplemented
149#2630C2213yescomplemented
150#2624C2213yescomplemented
151#2620C2213yescomplemented
152#2609C2213yescomplemented
153#2601C2213yescomplemented
154#2600C2213yescomplemented
155#2597C2213yescomplemented
156#2596C2213yescomplemented
157#2595C2213yescomplemented
158#2594C2213yescomplemented
159#2594C2213yescomplemented
160#2578C2213yescomplemented
161#2576C2213yescomplemented
162#2558C2213yescomplemented
163#2557C2213yes—
164#2556C2213yescomplemented
165#2555C2213yes—
166#2554C2213yes—
167#2544C2213yescomplemented
168#2543C2213yes—
169#2540C2213yes—
170#2534C2213yescomplemented
171#2529C2213yescomplemented
172#2526C2213yescomplemented
173#2525C2213yescomplemented
174#2525C2213yescomplemented
175#2522C2213yescomplemented
176#2522C2213yescomplemented
177#2521C2213yescomplemented
178#2521C2213yescomplemented
179#2512C2213yescomplemented
180#2512C2213yescomplemented
181#2510C2213yescomplemented
182#2507C2213yescomplemented
183#2494C2213yescomplemented
184#2490C2213yescomplemented
185#2485C2213yescomplemented
186#2480C2213yescomplemented
187#2479C2213yescomplemented
188#2477C2213yescomplemented
189#2476C2213yescomplemented
190#2474C2213yescomplemented
191#2474C2213yescomplemented
192#2474C2213yescomplemented
193#2472C2213yescomplemented
194#2472C2213yescomplemented
195#2472C2213yescomplemented
196#2471C2213yes—
197#2471C2213yescomplemented
198#2471C2213yescomplemented
199#2470C2213yescomplemented
200#2470C2213yescomplemented
201#2467C2213yescomplemented
202#2467C2213yescomplemented
203#2466C2213yescomplemented
204#2466C2213yescomplemented
205#2464C2213yescomplemented
206#2462C2213yescomplemented
207#2461C2213yes—
208#2461C2213yescomplemented
209#2460C2213yescomplemented
210#2458C2213yescomplemented
211#2456C2213yescomplemented
212#2456C2213yescomplemented
213#2448C2213yescomplemented
214#2445C2213yescomplemented
215#2441C2213yescomplemented
216#2438C2213yescomplemented
217#2435C2213yes—
218#2426C2213yescomplemented
219#2425C2213yescomplemented
220#2418C2213yescomplemented
221#2418C2213yescomplemented
222#2415C2213yescomplemented
223#2414C2213yescomplemented
224#2412C2213yescomplemented
225#2411C2213yescomplemented
226#2410C2213yes—
227#2408C2213yes—
228#2405C2213yes—
229#2403C2213yes—
230#2337C2213yescomplemented
231#2336C2213yescomplemented
232#2335C2213yescomplemented
233#2333C2213yescomplemented
234#2333C2213yescomplemented
235#2332C2213yescomplemented
236#2323C2213yescomplemented
237#2323C2213yescomplemented
238#2321C2213yescomplemented
239#2321C2213yescomplemented
240#2309C2213yes—
241C4×#126C2213yescomplemented
242C4×#124C2213yescomplemented
243#2293C2213yescomplemented
244#2275C2211yescharacteristic, complemented
245C23×D4C2313yes—
246C2×#127C2311yescharacteristic
247C2×#127C2311yescharacteristic
248C2×#126C2313yes—
249C2×#126C2311yescharacteristic
250C2×#126C2311yescharacteristic
251C2×#126C2313yes—
252C2×#126C2313yes—
253C2×#126C2313yes—
254C2×#126C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#124C2313yes—
258C2×#124C2313yes—
259C2×#124C2313yes—
260C2×#124C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#123C2313yes—
265C2×#123C2313yes—
266C2×#123C2313yes—
267C2×#123C2313yes—
268C2×#123C2313yes—
269C2×#123C2313yes—
270C2×#123C2313yes—
271C2×C22⋊Q8C2313yes—
272C2×C22⋊Q8C2313yes—
273C2×C22⋊Q8C2313yes—
274C2×C22⋊Q8C2313yes—
275C2×C22⋊Q8C2313yes—
276C2×#121C2313yes—
277C2×#121C2313yes—
278C2×#121C2313yes—
279C2×#121C2313yes—
280C2×#121C2313yes—
281C2×#121C2313yes—
282C2×#120C2313yes—
283C2×#120C2313yes—
284C2×#120C2313yes—
285C2×#120C2313yes—
286C2×#120C2311yescharacteristic
287C2×#120C2313yes—
288C2×#120C2311yescharacteristic
289C2×#120C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×D4C2313yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×#117C2313yes—
297C2×#117C2313yes—
298C2×#117C2313yes—
299C2×#117C2313yes—
300C22×C22⋊C4C2313yes—
301C22×C22⋊C4C2313yes—
302#401C2313yes—
303#401C2313yes—
304#401C2313yes—
305#400C2313yes—
306#400C2313yes—
307#400C2313yes—
308#400C2313yes—
309#400C2313yes—
310#400C2313yes—
311#400C2313yes—
312#400C2313yes—
313#399C2313yes—
314#399C2313yes—
315#399C2313yes—
316#399C2313yes—
317#399C2313yes—
318#399C2313yes—
319#399C2313yes—
320#399C2313yes—
321#399C2313yes—
322#399C2313yes—
323#399C2313yes—
324#398C2313yes—
325#398C2313yes—
326#398C2313yes—
327#398C2313yes—
328#398C2313yes—
329#398C2313yes—
330#398C2313yes—
331#398C2313yes—
332#398C2313yes—
333#398C2313yes—
334#398C2313yes—
335#398C2313yes—
336#397C2313yes—
337#397C2313yes—
338#397C2313yes—
339#397C2313yes—
340#397C2313yes—
341#397C2313yes—
342#397C2313yes—
343#397C2313yes—
344#397C2313yes—
345#397C2313yes—
346#397C2313yes—
347#397C2313yes—
348#397C2313yes—
349#397C2313yes—
350#397C2313yes—
351#397C2313yes—
352#397C2313yes—
353#397C2313yes—
354#397C2313yes—
355#397C2313yes—
356#397C2313yes—
357#397C2313yes—
358#397C2313yes—
359#397C2313yes—
360#397C2313yes—
361#397C2313yes—
362#397C2313yes—
363#397C2313yes—
364#397C2313yes—
365#397C2313yes—
366#397C2313yes—
367#396C2313yes—
368#396C2313yes—
369#396C2313yes—
370#396C2313yes—
371#396C2313yes—
372#396C2313yes—
373#396C2313yes—
374#396C2313yes—
375#396C2313yes—
376#396C2313yes—
377#396C2313yes—
378#396C2313yes—
379#396C2313yes—
380#396C2313yes—
381#396C2313yes—
382#396C2313yes—
383#396C2313yes—
384#396C2313yes—
385#396C2313yes—
386#396C2313yes—
387#396C2313yes—
388#395C2313yes—
389#395C2313yes—
390#395C2311yescharacteristic
391#395C2313yes—
392#395C2313yes—
393#395C2313yes—
394#394C2313yes—
395#394C2313yes—
396#394C2313yes—
397#394C2313yes—
398#394C2313yes—
399#394C2313yes—
400#394C2313yes—
401#394C2313yes—
402#394C2313yes—
403#394C2313yes—
404#394C2313yes—
405#394C2313yes—
406#394C2313yes—
407#394C2313yes—
408#394C2313yes—
409#394C2313yes—
410#394C2313yes—
411#394C2313yes—
412#394C2313yes—
413#394C2313yes—
414#394C2313yes—
415#394C2313yes—
416#394C2313yes—
417#394C2313yes—
418#394C2313yes—
419#394C2313yes—
420#394C2313yes—
421#394C2313yes—
422#394C2313yes—
423#394C2313yes—
424#394C2313yes—
425#394C2313yes—
426#394C2313yes—
427#394C2313yes—
428#394C2313yes—
429#394C2313yes—
430#394C2313yes—
431#394C2313yes—
432#394C2313yes—
433#394C2313yes—
434#394C2313yes—
435#394C2313yes—
436#394C2313yes—
437#394C2313yes—
438#394C2313yes—
439#393C2313yes—
440#393C2311yescharacteristic
441#393C2313yes—
442#393C2311yescharacteristic
443#393C2313yes—
444#393C2313yes—
445#393C2313yes—
446#393C2313yes—
447#392C2313yes—
448#392C2313yes—
449#392C2313yes—
450#392C2313yes—
451#392C2313yes—
452#392C2313yes—
453#392C2313yes—
454#392C2313yes—
455#392C2313yes—
456#392C2313yes—
457#392C2313yes—
458#392C2313yes—
459#392C2313yes—
460#392C2313yes—
461#392C2313yes—
462#392C2313yes—
463#392C2313yes—
464#391C2313yes—
465#391C2313yes—
466#391C2313yes—
467#391C2313yes—
468#391C2313yes—
469#391C2313yes—
470#391C2313yes—
471#391C2313yes—
472#391C2313yes—
473#391C2313yes—
474#390C2313yes—
475#390C2313yes—
476#390C2313yes—
477#390C2313yes—
478#390C2313yes—
479#390C2313yes—
480#390C2313yes—
481#390C2313yes—
482#390C2313yes—
483#390C2313yes—
484#390C2313yes—
485#390C2313yes—
486#390C2313yes—
487#390C2313yes—
488#390C2313yes—
489#390C2313yes—
490#390C2313yes—
491#390C2313yes—
492#390C2313yes—
493#390C2313yes—
494#390C2313yes—
495#390C2313yes—
496#390C2313yes—
497#390C2313yes—
498#390C2313yes—
499#389C2313yes—
500#389C2313yes—
501#389C2313yes—
502#389C2313yes—
503#389C2313yes—
504#389C2313yes—
505#389C2313yes—
506#389C2313yes—
507#389C2313yes—
508#389C2313yes—
509#389C2313yes—
510#389C2313yes—
511#389C2313yes—
512#389C2313yes—
513#389C2313yes—
514#389C2313yes—
515#389C2313yes—
516#389C2313yes—
517#389C2313yes—
518#389C2313yes—
519#389C2313yes—
520#388C2313yes—
521#388C2313yes—
522#388C2313yes—
523#388C2313yes—
524#388C2313yes—
525#388C2313yes—
526#388C2313yes—
527#388C2313yes—
528#388C2313yes—
529#388C2313yes—
530#388C2313yes—
531#388C2313yes—
532#388C2313yes—
533#388C2313yes—
534#388C2313yes—
535#388C2313yes—
536#388C2313yes—
537#388C2313yes—
538#388C2313yes—
539#388C2313yes—
540#388C2313yes—
541#388C2313yes—
542#388C2313yes—
543#388C2313yes—
544#388C2313yes—
545#388C2313yes—
546#388C2313yes—
547#388C2313yes—
548#388C2313yes—
549#388C2313yes—
550#388C2313yes—
551#388C2313yes—
552#388C2313yes—
553#388C2313yes—
554#388C2313yes—
555#388C2313yes—
556#388C2313yes—
557#388C2313yes—
558#388C2313yes—
559#388C2313yes—
560#388C2313yes—
561#388C2313yes—
562#388C2313yes—
563#388C2313yes—
564#388C2313yes—
565#388C2313yes—
566#388C2313yes—
567#388C2313yes—
568#388C2313yes—
569#388C2313yes—
570#388C2313yes—
571#388C2313yes—
572#388C2313yes—
573#388C2313yes—
574#388C2313yes—
575#388C2313yes—
576#388C2313yes—
577#388C2313yes—
578#388C2313yes—
579#388C2313yes—
580#388C2313yes—
581#388C2313yes—
582#388C2313yes—
583#388C2313yes—
584#388C2313yes—
585#388C2313yes—
586#388C2313yes—
587#388C2313yes—
588#388C2313yes—
589#388C2313yes—
590#388C2313yes—
591#388C2313yes—
592#388C2313yes—
593#387C2313yes—
594#387C2313yes—
595#387C2313yes—
596#387C2313yes—
597#387C2313yes—
598#387C2313yes—
599#387C2313yes—
600#387C2313yes—
601#387C2313yes—
602#387C2313yes—
603#387C2313yes—
604#387C2313yes—
605#387C2313yes—
606#387C2313yes—
607#387C2313yes—
608#387C2313yes—
609#387C2313yes—
610#387C2313yes—
611#387C2313yes—
612#387C2313yes—
613#387C2313yes—
614#387C2313yes—
615#387C2313yes—
616#387C2313yes—
617#387C2313yes—
618#387C2313yes—
619#387C2313yes—
620#387C2313yes—
621#387C2313yes—
622#387C2313yes—
623#387C2313yes—
624#386C2313yes—
625#386C2313yes—
626#386C2313yes—
627#386C2313yes—
628#386C2313yes—
629#386C2313yes—
630#386C2313yes—
631#386C2313yes—
632#386C2313yes—
633#386C2313yes—
634#386C2313yes—
635#386C2313yes—
636#386C2313yes—
637#386C2313yes—
638#386C2313yes—
639#386C2313yes—
640#386C2313yes—
641#386C2313yes—
642#386C2313yes—
643#386C2313yes—
644#386C2313yes—
645#386C2313yes—
646#386C2313yes—
647#386C2313yes—
648#386C2313yes—
649#386C2313yes—
650#386C2313yes—
651#386C2313yes—
652#386C2313yes—
653#385C2313yes—
654#385C2313yes—
655#385C2313yes—
656#385C2313yes—
657#385C2313yes—
658#385C2313yes—
659#385C2313yes—
660#385C2313yes—
661#385C2313yes—
662#385C2313yes—
663#385C2313yes—
664#385C2313yes—
665#385C2313yes—
666#385C2313yes—
667#385C2313yes—
668#384C2313yes—
669#383C2313yes—
670#383C2311yescharacteristic
671#383C2311yescharacteristic
672#383C2313yes—
673#383C2313yes—
674#382C2313yes—
675#382C2313yes—
676#381C2313yes—
677#381C2313yes—
678#381C2313yes—
679#380C2313yes—
680#380C2313yes—
681#380C2313yes—
682#380C2313yes—
683#380C2313yes—
684#380C2313yes—
685#380C2313yes—
686#380C2313yes—
687#380C2313yes—
688#379C2313yes—
689#379C2313yes—
690#379C2313yes—
691#379C2313yes—
692#379C2313yes—
693#379C2313yes—
694#379C2313yes—
695#379C2311yescharacteristic
696#379C2313yes—
697#379C2313yes—
698C4×C4⋊C4C2313yes—
699C4×C4⋊C4C2313yes—
700C4×C4⋊C4C2313yes—
701C4×C4⋊C4C2313yes—
702C4×C4⋊C4C2313yes—
703C4×C4⋊C4C2313yes—
704C4×C4⋊C4C2313yes—
705C4×C4⋊C4C2313yes—
706C4×C22⋊C4C2313yes—
707C4×C22⋊C4C2313yes—
708C4×C22⋊C4C2313yes—
709C4×C22⋊C4C2313yes—
710C4×C22⋊C4C2313yes—
711C4×C22⋊C4C2313yes—
712C4×C22⋊C4C2313yes—
713C4×C22⋊C4C2313yes—
714C4×C22⋊C4C2313yes—
715C4×C22⋊C4C2313yes—
716#376C2311yescharacteristic
717C2×#95C2311yescharacteristic
718C2×#95C2311yescharacteristic
719C43C2313yes—
720C25C2413yes—
721C25C2411yescharacteristic
722C22×Q8C2413yes—
723C22×Q8C2413yes—
724C22×Q8C2411yescharacteristic
725C22×D4—46no—
726C22×D4—83no—
727C22×D4—83no—
728C22×D4C2413yes—
729C22×D4C2413yes—
730C22×D4C2411yescharacteristic
731C22×D4C2413yes—
732C22×D4C2413yes—
733C22×D4C2413yes—
734C22×D4C2413yes—
735C22×D4C2413yes—
736C22×D4C2413yes—
737C22×D4C2413yes—
738C22×D4C2413yes—
739C22×D4C2413yes—
740C22×D4C2413yes—
741C22×D4C2413yes—
742C22×D4C2413yes—
743C23×C4C2413yes—
744C23×C4C2413yes—
745C23×C4C2413yes—
746C23×C4C2413yes—
747C23×C4C2413yes—
748C23×C4C2413yes—
749C23×C4C2413yes—
750#127—81no—
751#127—81no—
752#126—46no—
753#126—83no—
754#126—83no—
755#126—83no—
756#126—83no—
757#126—81no—
758#126—81no—
759#125—46no—
760#125—83no—
761#124—46no—
762#124—46no—
763#124—83no—
764#124—83no—
765#124—83no—
766#124—83no—
767#124—83no—
768#123—46no—
769#123—83no—
770#123—83no—
771#123—83no—
772#123—83no—
773#123—83no—
774#123—83no—
775C22⋊Q8—46no—
776C22⋊Q8—46no—
777C22⋊Q8—46no—
778C22⋊Q8—83no—
779C22⋊Q8—83no—
780#121—46no—
781#121—46no—
782#121—83no—
783#121—83no—
784#121—83no—
785#121—83no—
786#120—46no—
787#120—46no—
788#120—81no—
789#120—83no—
790#120—83no—
791#120—83no—
792#120—83no—
793#120—81no—
794C4×Q8—83no—
795C4×D4—46no—
796C4×D4—46no—
797C4×D4—83no—
798C4×D4—83no—
799C4×D4—83no—
800#117—83no—
801#117—83no—
802#117—83no—
803#117—83no—
804C2×C4⋊C4C2413yes—
805C2×C4⋊C4C2413yes—
806C2×C4⋊C4C2413yes—
807C2×C4⋊C4C2413yes—
808C2×C4⋊C4C2413yes—
809C2×C4⋊C4C2413yes—
810C2×C4⋊C4C2413yes—
811C2×C4⋊C4C2413yes—
812C2×C4⋊C4C2413yes—
813C2×C4⋊C4C2413yes—
814C2×C4⋊C4C2413yes—
815C2×C4⋊C4C2413yes—
816C2×C4⋊C4C2413yes—
817C2×C4⋊C4C2413yes—
818C2×C4⋊C4C2413yes—
819C2×C4⋊C4C2413yes—
820C2×C4⋊C4C2413yes—
821C2×C4⋊C4C2413yes—
822C2×C4⋊C4C2413yes—
823C2×C4⋊C4C2413yes—
824C2×C4⋊C4C2413yes—
825C2×C4⋊C4C2413yes—
826C2×C4⋊C4C2413yes—
827C2×C4⋊C4C2413yes—
828C2×C4⋊C4C2413yes—
829C2×C4⋊C4C2413yes—
830C2×C4⋊C4C2413yes—
831C2×C4⋊C4C2413yes—
832C2×C4⋊C4C2413yes—
833C2×C4⋊C4C2413yes—
834C2×C4⋊C4C2413yes—
835C2×C4⋊C4C2413yes—
836C2×C4⋊C4C2413yes—
837C2×C4⋊C4C2413yes—
838C2×C4⋊C4C2413yes—
839C2×C4⋊C4C2413yes—
840C2×C4⋊C4C2413yes—
841C2×C4⋊C4C2413yes—
842C2×C4⋊C4C2413yes—
843C2×C4⋊C4C2413yes—
844C2×C4⋊C4C2413yes—
845C2×C4⋊C4C2413yes—
846C2×C4⋊C4C2413yes—
847C2×C4⋊C4C2413yes—
848C2×C22⋊C4—83no—
849C2×C22⋊C4—83no—
850C2×C22⋊C4C2413yes—
851C2×C22⋊C4C2413yes—
852C2×C22⋊C4C2413yes—
853C2×C22⋊C4C2413yes—
854C2×C22⋊C4C2413yes—
855C2×C22⋊C4C2413yes—
856C2×C22⋊C4C2413yes—
857C2×C22⋊C4C2413yes—
858C2×C22⋊C4C2413yes—
859C2×C22⋊C4C2413yes—
860C2×C22⋊C4C2413yes—
861C2×C22⋊C4C2413yes—
862C2×C22⋊C4C2413yes—
863C2×C22⋊C4C2413yes—
864C2×C22⋊C4C2413yes—
865C2×C22⋊C4C2413yes—
866C2×C22⋊C4C2413yes—
867C2×C22⋊C4C2413yes—
868C2×C22⋊C4C2413yes—
869C2×C22⋊C4C2413yes—
870C2×C22⋊C4C2413yes—
871C2×C22⋊C4C2413yes—
872C2×C22⋊C4C2413yes—
873C2×C22⋊C4C2413yes—
874C2×C22⋊C4C2413yes—
875C2×C22⋊C4C2413yes—
876C2×C22⋊C4C2413yes—
877C2×C22⋊C4C2413yes—
878C2×C22⋊C4C2413yes—
879C2×C22⋊C4C2413yes—
880C2×C22⋊C4C2413yes—
881C2×C22⋊C4C2413yes—
882C2×C22⋊C4C2413yes—
883C2×C22⋊C4C2413yes—
884C2×C22⋊C4C2413yes—
885C2×C22⋊C4C2413yes—
886C2×C22⋊C4C2413yes—
887C2×C22⋊C4C2413yes—
888C2×C22⋊C4C2413yes—
889C2×C22⋊C4C2413yes—
890C2×C22⋊C4C2413yes—
891C2×C22⋊C4C2413yes—
892C2×C22⋊C4C2413yes—
893C2×C22⋊C4C2413yes—
894C2×C22⋊C4C2413yes—
895C2×C22⋊C4C2413yes—
896C2×C22⋊C4C2413yes—
897C2×C22⋊C4C2413yes—
898C2×C22⋊C4C2413yes—
899C2×C22⋊C4C2413yes—
900C2×C22⋊C4C2413yes—
901C2×C22⋊C4C2413yes—
902C2×C22⋊C4C2413yes—
903C2×C22⋊C4C2413yes—
904C2×C22⋊C4C2413yes—
905C2×C22⋊C4C2413yes—
906C2×C22⋊C4C2413yes—
907C2×C22⋊C4C2413yes—
908C2×C22⋊C4C2413yes—
909C2×C22⋊C4C2413yes—
910C2×C22⋊C4C2413yes—
911C2×C22⋊C4C2413yes—
912C2×C22⋊C4C2413yes—
913C2×C22⋊C4C2413yes—
914C2×C22⋊C4C2413yes—
915C2×C22⋊C4C2413yes—
916C2×C22⋊C4C2413yes—
917C2×C22⋊C4C2413yes—
918C2×C22⋊C4C2413yes—
919C2×C22⋊C4C2413yes—
920C2×C22⋊C4C2413yes—
921C2×C22⋊C4C2413yes—
922C2×C22⋊C4C2413yes—
923C2×C22⋊C4C2413yes—
924C2×C42C2413yes—
925C2×C42C2413yes—
926C2×C42C2413yes—
927C2×C42C2413yes—
928C2×C42C2413yes—
929C2×C42C2413yes—
930C2×C42C2413yes—
931C2×C42C2413yes—
932C2×C42C2413yes—
933C2×C42C2413yes—
934C2×C42C2413yes—
935C2×C42C2413yes—
936C2×C42C2413yes—
937C2×C42C2413yes—
938C2×C42C2413yes—
939C2×C42C2411yescharacteristic
940C2×C42C2411yescharacteristic
941C2×C42C2413yes—
942#95C2411yescharacteristic
943#95C2413yes—
944#95C2413yes—
945#95C2413yes—
946#95C2413yes—
947#95C2413yes—
948#95C2413yes—
949#95C2413yes—
950#95C2413yes—
951#95C2413yes—
952#95C2413yes—
953#95C2413yes—
954#95C2413yes—
955#95C2413yes—
956#95C2413yes—
957#95C2413yes—
958#95C2413yes—
959#95C2413yes—
960#95C2413yes—
961#95C2413yes—
962#95C2413yes—
963#95C2413yes—
964#95C2413yes—
965#95C2413yes—
966#95C2413yes—
967#95C2413yes—
968#95C2413yes—
969#95C2413yes—
970#95C2413yes—
971#95C2413yes—
972#95C2413yes—
973#95C2413yes—
974#95C2413yes—
975#95C2413yes—
976#95C2413yes—
977#95C2413yes—
978#95C2413yes—
979#95C2413yes—
980#95C2413yes—
981#95C2413yes—
982#95C2413yes—
983#95C2413yes—
984#95C2413yes—
985#95C2413yes—
986#95C2413yes—
987#95C2413yes—
988#95C2413yes—
989#95C2413yes—
990#95C2413yes—
991#95C2413yes—
992#95C2413yes—
993#95C2413yes—
994#95C2413yes—
995#95C2413yes—
996#95C2413yes—
997#95C2413yes—
998#95C2413yes—
999#95C2413yes—
1000C24—43no—
1001C24—43no—
1002C24—43no—
1003C24—43no—
1004C24—43no—
1005C24—43no—
1006C24—43no—
1007C24—43no—
1008C24—43no—
1009C24—41no—
1010C24C2513yes—
1011C24C2513yes—
1012C24C2513yes—
1013C24C2511yescharacteristic
1014C24C2511yescharacteristic
1015C2×Q8—26no—
1016C2×Q8—43no—
1017C2×Q8—43no—
1018C2×Q8—43no—
1019C2×Q8—43no—
1020C2×Q8—43no—
1021C2×Q8—43no—
1022C2×D4—26no—
1023C2×D4—26no—
1024C2×D4—43no—
1025C2×D4—43no—
1026C2×D4—43no—
1027C2×D4—43no—
1028C2×D4—43no—
1029C2×D4—43no—
1030C2×D4—43no—
1031C2×D4—43no—
1032C2×D4—43no—
1033C2×D4—43no—
1034C2×D4—43no—
1035C2×D4—43no—
1036C2×D4—43no—
1037C2×D4—43no—
1038C2×D4—43no—
1039C2×D4—43no—
1040C2×D4—43no—
1041C2×D4—43no—
1042C2×D4—43no—
1043C2×D4—43no—
1044C2×D4—43no—
1045C2×D4—43no—
1046C2×D4—43no—
1047C2×D4—43no—
1048C2×D4—43no—
1049C2×D4—43no—
1050C2×D4—43no—
1051C2×D4—43no—
1052C2×D4—43no—
1053C2×D4—43no—
1054C2×D4—43no—
1055C2×D4—43no—
1056C2×D4—43no—
1057C2×D4—43no—
1058C2×D4—43no—
1059C2×D4—43no—
1060C2×D4—43no—
1061C2×D4—43no—
1062C2×D4—43no—
1063C2×D4—43no—
1064C2×D4—43no—
1065C2×D4—824no—
1066C22×C4—26no—
1067C22×C4—26no—
1068C22×C4—43no—
1069C22×C4—43no—
1070C22×C4—43no—
1071C22×C4—43no—
1072C22×C4—43no—
1073C22×C4—43no—
1074C22×C4—43no—
1075C22×C4—43no—
1076C22×C4—43no—
1077C22×C4—43no—
1078C22×C4—43no—
1079C22×C4—43no—
1080C22×C4—43no—
1081C22×C4—43no—
1082C22×C4—43no—
1083C22×C4—43no—
1084C22×C4—43no—
1085C22×C4—43no—
1086C22×C4—43no—
1087C22×C4C2513yes—
1088C22×C4C2513yes—
1089C22×C4C2511yescharacteristic
1090C22×C4C2513yes—
1091C22×C4C2513yes—
1092C22×C4C2513yes—
1093C22×C4C2513yes—
1094C22×C4C2513yes—
1095C22×C4C2513yes—
1096C22×C4C2513yes—
1097C22×C4C2513yes—
1098C22×C4C2513yes—
1099C22×C4C2513yes—
1100C22×C4C2513yes—
1101C22×C4C2513yes—
1102C22×C4C2513yes—
1103C22×C4C2513yes—
1104C22×C4C2513yes—
1105C4⋊C4—26no—
1106C4⋊C4—26no—
1107C4⋊C4—26no—
1108C4⋊C4—26no—
1109C4⋊C4—43no—
1110C4⋊C4—43no—
1111C4⋊C4—43no—
1112C4⋊C4—43no—
1113C4⋊C4—43no—
1114C4⋊C4—43no—
1115C4⋊C4—43no—
1116C4⋊C4—43no—
1117C4⋊C4—43no—
1118C4⋊C4—43no—
1119C4⋊C4—43no—
1120C4⋊C4—43no—
1121C4⋊C4—43no—
1122C4⋊C4—43no—
1123C4⋊C4—43no—
1124C4⋊C4—43no—
1125C4⋊C4—43no—
1126C4⋊C4—43no—
1127C4⋊C4—43no—
1128C4⋊C4—43no—
1129C4⋊C4—43no—
1130C4⋊C4—43no—
1131C4⋊C4—43no—
1132C4⋊C4—43no—
1133C4⋊C4—43no—
1134C4⋊C4—43no—
1135C4⋊C4—43no—
1136C4⋊C4—43no—
1137C4⋊C4—43no—
1138C4⋊C4—43no—
1139C4⋊C4—43no—
1140C4⋊C4—43no—
1141C4⋊C4—43no—
1142C4⋊C4—43no—
1143C4⋊C4—43no—
1144C4⋊C4—43no—
1145C4⋊C4—43no—
1146C4⋊C4—43no—
1147C4⋊C4—43no—
1148C4⋊C4—43no—
1149C22⋊C4—26no—
1150C22⋊C4—26no—
1151C22⋊C4—26no—
1152C22⋊C4—26no—
1153C22⋊C4—26no—
1154C22⋊C4—43no—
1155C22⋊C4—43no—
1156C22⋊C4—43no—
1157C22⋊C4—43no—
1158C22⋊C4—43no—
1159C22⋊C4—43no—
1160C22⋊C4—43no—
1161C22⋊C4—43no—
1162C22⋊C4—43no—
1163C22⋊C4—43no—
1164C22⋊C4—43no—
1165C22⋊C4—43no—
1166C22⋊C4—43no—
1167C22⋊C4—43no—
1168C22⋊C4—43no—
1169C22⋊C4—43no—
1170C22⋊C4—43no—
1171C22⋊C4—43no—
1172C22⋊C4—43no—
1173C22⋊C4—43no—
1174C22⋊C4—43no—
1175C22⋊C4—43no—
1176C22⋊C4—43no—
1177C22⋊C4—43no—
1178C22⋊C4—43no—
1179C22⋊C4—43no—
1180C22⋊C4—43no—
1181C22⋊C4—43no—
1182C22⋊C4—43no—
1183C22⋊C4—43no—
1184C22⋊C4—43no—
1185C22⋊C4—43no—
1186C22⋊C4—43no—
1187C22⋊C4—43no—
1188C22⋊C4—43no—
1189C22⋊C4—43no—
1190C22⋊C4—43no—
1191C22⋊C4—43no—
1192C22⋊C4—43no—
1193C22⋊C4—43no—
1194C22⋊C4—43no—
1195C22⋊C4—43no—
1196C22⋊C4—43no—
1197C22⋊C4—43no—
1198C22⋊C4—43no—
1199C22⋊C4—43no—
1200C22⋊C4—43no—
1201C22⋊C4—43no—
1202C22⋊C4—43no—
1203C22⋊C4—43no—
1204C22⋊C4—43no—
1205C22⋊C4—43no—
1206C22⋊C4—43no—
1207C22⋊C4—43no—
1208C22⋊C4—43no—
1209C22⋊C4—43no—
1210C22⋊C4—43no—
1211C22⋊C4—43no—
1212C22⋊C4—43no—
1213C22⋊C4—43no—
1214C22⋊C4—43no—
1215C22⋊C4—43no—
1216C22⋊C4—43no—
1217C22⋊C4—43no—
1218C22⋊C4—43no—
1219C22⋊C4—43no—
1220C22⋊C4—43no—
1221C22⋊C4—43no—
1222C22⋊C4—43no—
1223C42—26no—
1224C42—43no—
1225C42—43no—
1226C42—43no—
1227C42—43no—
1228C42—43no—
1229C42—43no—
1230C42—43no—
1231C42—43no—
1232C42—43no—
1233C42—43no—
1234C42—43no—
1235C42—43no—
1236C42—43no—
1237C42—43no—
1238C42—43no—
1239C42—41no—
1240C42—41no—
1241C23—23no—
1242C23—23no—
1243C23—23no—
1244C23—23no—
1245C23—23no—
1246C23—23no—
1247C23—23no—
1248C23—23no—
1249C23—23no—
1250C23—23no—
1251C23—23no—
1252C23—21no—
1253C23—23no—
1254C23—23no—
1255C23—23no—
1256C23—23no—
1257C23—23no—
1258C23—23no—
1259C23—23no—
1260C23—23no—
1261C23—23no—
1262C23—23no—
1263C23—23no—
1264C23—23no—
1265C23—23no—
1266C23—23no—
1267C23—21no—
1268C23—86no—
1269C23—86no—
1270C23—86no—
1271C23—86no—
1272C23—163no—
1273C23—161no—
1274C23—163no—
1275C23—163no—
1276C23—163no—
1277C23—163no—
1278C23C2611yescharacteristic
1279Q8—86no—
1280Q8—161no—
1281Q8—163no—
1282D4—44no—
1283D4—86no—
1284D4—86no—
1285D4—86no—
1286D4—86no—
1287D4—86no—
1288D4—86no—
1289D4—86no—
1290D4—86no—
1291D4—163no—
1292D4—163no—
1293D4—163no—
1294D4—163no—
1295D4—163no—
1296D4—163no—
1297C2×C4—23no—
1298C2×C4—23no—
1299C2×C4—23no—
1300C2×C4—23no—
1301C2×C4—23no—
1302C2×C4—23no—
1303C2×C4—23no—
1304C2×C4—23no—
1305C2×C4—23no—
1306C2×C4—23no—
1307C2×C4—23no—
1308C2×C4—23no—
1309C2×C4—23no—
1310C2×C4—23no—
1311C2×C4—23no—
1312C2×C4—23no—
1313C2×C4—23no—
1314C2×C4—23no—
1315C2×C4—23no—
1316C2×C4—23no—
1317C2×C4—23no—
1318C2×C4—23no—
1319C2×C4—23no—
1320C2×C4—23no—
1321C2×C4—23no—
1322C2×C4—23no—
1323C2×C4—23no—
1324C2×C4—23no—
1325C2×C4—23no—
1326C2×C4—23no—
1327C2×C4—23no—
1328C2×C4—23no—
1329C2×C4—23no—
1330C2×C4—23no—
1331C2×C4—23no—
1332C2×C4—23no—
1333C2×C4—23no—
1334C2×C4—23no—
1335C2×C4—23no—
1336C2×C4—23no—
1337C2×C4—23no—
1338C2×C4—23no—
1339C2×C4—23no—
1340C2×C4—23no—
1341C2×C4—23no—
1342C2×C4—23no—
1343C2×C4—23no—
1344C2×C4—23no—
1345C2×C4—23no—
1346C2×C4—23no—
1347C2×C4—23no—
1348C2×C4—412no—
1349C2×C4—86no—
1350C2×C4—86no—
1351C2×C4—163no—
1352C2×C4—163no—
1353C2×C4—163no—
1354C2×C4—163no—
1355C2×C4#58516yes—
1356C22—41no—
1357C22—41no—
1358C22—43no—
1359C22—43no—
1360C22—43no—
1361C22—43no—
1362C22—43no—
1363C22—43no—
1364C22—43no—
1365C22—43no—
1366C22—43no—
1367C22—43no—
1368C22—43no—
1369C22—43no—
1370C22—43no—
1371C22—43no—
1372C22—43no—
1373C22—43no—
1374C22—43no—
1375C22—43no—
1376C22—43no—
1377C22—43no—
1378C22—43no—
1379C22—43no—
1380C22—43no—
1381C22—43no—
1382C22—43no—
1383C22—1612no—
1384C22—164no—
1385C22C2×#58513yes—
1386C22H(7,𝔽2)13yes—
1387C22H(7,𝔽2)11yescharacteristic
1388C4—26no—
1389C4—41no—
1390C4—43no—
1391C4—43no—
1392C4—43no—
1393C4—43no—
1394C4—43no—
1395C4—43no—
1396C4—43no—
1397C4—43no—
1398C4—43no—
1399C4—43no—
1400C4—43no—
1401C4—43no—
1402C4—43no—
1403C4—43no—
1404C4—43no—
1405C4—43no—
1406C2—81no—
1407C2—81no—
1408C2—83no—
1409C2—83no—
1410C2—83no—
1411C2#6284111yescharacteristic
1412C2#6286713yes—
1413C2#6288313yes—
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. #58849C2semidirect
2. #58460C2semidirect
3. #58274C2semidirect
4. #58260C2semidirect
5. #58238C2semidirect
6. #58174C2semidirect
7. #58002C2semidirect
8. #57474C2semidirect
9. #57369C2semidirect
10. #56577C2semidirect
11. #47392C2semidirect
12. #47312C2semidirect
13. #47169C2semidirect
14. #47103C2semidirect
15. #46791C2semidirect
16. #46619C2semidirect
17. #37365C2semidirect
18. #37207C2semidirect
19. #37204C2semidirect
20. #37112C2semidirect
21. #37054C2semidirect
22. #37038C2semidirect
23. #35473C2semidirect
24. #2863C22semidirect
25. #2861C22semidirect
26. #2861C22semidirect
27. #2860C22semidirect
28. #2838C22semidirect
29. #2837C22semidirect
30. #2836C22semidirect
33. #2828C22semidirect
34. #2825C22semidirect
35. #2818C22semidirect
36. #2818C22semidirect
37. #2813C22semidirect
40. #2806C22semidirect
42. #2803C22semidirect
43. #2803C22semidirect
44. #2803C22semidirect
45. #2803C22semidirect
46. #2803C22semidirect
47. #2801C22semidirect
48. #2800C22semidirect
49. #2800C22semidirect
50. #2798C22semidirect
52. #2797C22semidirect
53. #2797C22semidirect
54. #2796C22semidirect
55. #2795C22semidirect
56. #2787C22semidirect
57. #2787C22semidirect
58. #2785C22semidirect
59. #2783C22semidirect
60. #2783C22semidirect
61. #2778C22semidirect
62. #2778C22semidirect
63. #2777C22semidirect
64. #2777C22semidirect
65. #2777C22semidirect
66. #2777C22semidirect
67. #2772C22semidirect
68. #2762C22semidirect
69. #2759C22semidirect
70. #2759C22semidirect
71. #2759C22semidirect
72. #2759C22semidirect
75. #2756C22semidirect
76. #2754C22semidirect
79. #2749C22semidirect
80. #2746C22semidirect
81. #2741C22semidirect
82. #2740C22semidirect
83. #2737C22semidirect
88. #2735C22semidirect
89. #2735C22semidirect
91. #2732C22semidirect
92. #2730C22semidirect
93. #2730C22semidirect
94. #2730C22semidirect
95. #2727C22semidirect
96. #2727C22semidirect
97. #2727C22semidirect
98. #2723C22semidirect
99. #2720C22semidirect
100. #2715C22semidirect
101. #2715C22semidirect
102. #2715C22semidirect
103. #2715C22semidirect
104. #2712C22semidirect
105. #2711C22semidirect
107. #2710C22semidirect
108. #2707C22semidirect
109. #2706C22semidirect
111. #2705C22semidirect
112. #2704C22semidirect
114. #2702C22semidirect
115. #2701C22semidirect
116. #2701C22semidirect
117. #2697C22semidirect
118. #2697C22semidirect
119. #2695C22semidirect
120. #2692C22semidirect
121. #2689C22semidirect
122. #2687C22semidirect
123. #2686C22semidirect
125. #2685C22semidirect
126. #2685C22semidirect
127. #2685C22semidirect
128. #2685C22semidirect
130. #2681C22semidirect
131. #2678C22semidirect
132. #2678C22semidirect
133. #2672C22semidirect
135. #2670C22semidirect
136. #2670C22semidirect
139. #2668C22semidirect
140. #2663C22semidirect
141. #2662C22semidirect
142. #2661C22semidirect
143. #2653C22semidirect
144. #2653C22semidirect
145. #2650C22semidirect
146. #2633C22semidirect
148. #2630C22semidirect
149. #2630C22semidirect
150. #2624C22semidirect
151. #2620C22semidirect
152. #2609C22semidirect
153. #2601C22semidirect
154. #2600C22semidirect
155. #2597C22semidirect
156. #2596C22semidirect
157. #2595C22semidirect
158. #2594C22semidirect
159. #2594C22semidirect
160. #2578C22semidirect
161. #2576C22semidirect
162. #2558C22semidirect
164. #2556C22semidirect
167. #2544C22semidirect
170. #2534C22semidirect
171. #2529C22semidirect
172. #2526C22semidirect
173. #2525C22semidirect
174. #2525C22semidirect
175. #2522C22semidirect
176. #2522C22semidirect
177. #2521C22semidirect
178. #2521C22semidirect
179. #2512C22semidirect
180. #2512C22semidirect
181. #2510C22semidirect
182. #2507C22semidirect
183. #2494C22semidirect
184. #2490C22semidirect
185. #2485C22semidirect
186. #2480C22semidirect
187. #2479C22semidirect
188. #2477C22semidirect
189. #2476C22semidirect
190. #2474C22semidirect
191. #2474C22semidirect
192. #2474C22semidirect
193. #2472C22semidirect
194. #2472C22semidirect
195. #2472C22semidirect
197. #2471C22semidirect
198. #2471C22semidirect
199. #2470C22semidirect
200. #2470C22semidirect
201. #2467C22semidirect
202. #2467C22semidirect
203. #2466C22semidirect
204. #2466C22semidirect
205. #2464C22semidirect
206. #2462C22semidirect
208. #2461C22semidirect
209. #2460C22semidirect
210. #2458C22semidirect
211. #2456C22semidirect
212. #2456C22semidirect
213. #2448C22semidirect
214. #2445C22semidirect
215. #2441C22semidirect
216. #2438C22semidirect
218. #2426C22semidirect
219. #2425C22semidirect
220. #2418C22semidirect
221. #2418C22semidirect
222. #2415C22semidirect
223. #2414C22semidirect
224. #2412C22semidirect
225. #2411C22semidirect
230. #2337C22semidirect
231. #2336C22semidirect
232. #2335C22semidirect
233. #2333C22semidirect
234. #2333C22semidirect
235. #2332C22semidirect
236. #2323C22semidirect
237. #2323C22semidirect
238. #2321C22semidirect
239. #2321C22semidirect
241. C4×#126C22semidirect
242. C4×#124C22semidirect
243. #2293C22semidirect
244. #2275C22semidirect

Maximal subgroups

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

subgroupindex
#588492
#584602
#582742
#582602
#582382
#581742
#580022
#574742
#573692
#565772
#473922
#473122
#471692
#471032
#467912
#466192
#373652
#372072
#372042
#371122
#370542
#370382
#354732