Finite Group Databasebeta

← #7658887

Subgroups — #7658887

Order 512.

4940 conjugacy classes of subgroups.

The subgroup lattice has 1564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42990C212yesmaximal, complemented
2#42923C212yesmaximal, complemented
3#42693C212yesmaximal, complemented
4#42688C212yesmaximal, complemented
5#42473C212yesmaximal, complemented
6#42471C212yesmaximal, complemented
7#42407C214yesmaximal, complemented
8#42065C214yesmaximal, complemented
9#41057C214yesmaximal, complemented
10#41036C214yesmaximal, complemented
11#40966C214yesmaximal, complemented
12#40951C214yesmaximal, complemented
13#37639C211yesmaximal, characteristic, complemented
14#37610C212yesmaximal, complemented
15#37604C212yesmaximal, complemented
16#37599C212yesmaximal, complemented
17#37561C211yesmaximal, characteristic, complemented
18#37554C211yesmaximal, characteristic, complemented
19#36694C212yesmaximal, complemented
20#36687C211yesmaximal, characteristic, complemented
21#36083C212yesmaximal, complemented
22#35947C212yesmaximal, complemented
23#35923C212yesmaximal, complemented
24#35770C212yesmaximal, complemented
25#35768C212yesmaximal, complemented
26#35682C212yesmaximal, complemented
27#34242C211yesmaximal, characteristic, complemented
28#34232C211yesmaximal, characteristic, complemented
29#34208C211yesmaximal, characteristic, complemented
30C2×#553C2212yes—
31C2×#547C2212yes—
32C2×#532C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#520C2211yescharacteristic
37#2845C2212yes—
38#2844C2212yes—
39#2832C2214yes—
40#2832C2214yes—
41#2832C2214yes—
42#2828C2214yes—
43#2828C2214yes—
44#2828C2214yes—
45#2821C2212yes—
46#2820C2211yescharacteristic
47#2820C2211yescharacteristic
48#2820C2212yes—
49#2819C2212yes—
50#2819C2212yes—
51#2819C2211yescharacteristic
52#2819C2211yescharacteristic
53#2819C2212yes—
54#2818C2212yes—
55#2816C2212yes—
56#2815C2212yes—
57#2813C2212yes—
58#2813C2212yes—
59#2797C2214yes—
60#2797C2214yes—
61#2786C2214yes—
62#2778C2214yes—
63#2767C2214yes—
64#2754C2214yes—
65#2753C2214yes—
66#2751C2214yes—
67#2747C2214yes—
68#2745C2214yes—
69#2741C2214yes—
70#2740C2214yes—
71#2714C2214yes—
72#2714C2214yes—
73#2709C2214yes—
74#2705C2214yes—
75#2703C2214yes—
76#2703C2214yes—
77#2699C2214yes—
78#2696C2214yes—
79#2691C2214yes—
80#2686C2214yes—
81#2676C2214yes—
82#2673C2214yes—
83#2666C2214yes—
84#2665C2214yes—
85#2663C2214yes—
86#2662C2214yes—
87#2661C2214yes—
88#2661C2214yes—
89#2661C2214yes—
90#2660C2212yes—
91#2659C2212yes—
92#2656C2212yes—
93#2653C2214yes—
94#2653C2214yes—
95#2653C2214yes—
96#2651C2214yes—
97#2651C2214yes—
98#2650C2214yes—
99#2649C2214yes—
100#2648C2214yes—
101#2647C2212yes—
102#2646C2212yes—
103#2639C2212yes—
104#2637C2214yes—
105#2637C2214yes—
106#2636C2214yes—
107#2630C2214yes—
108#2630C2214yes—
109#2628C2212yes—
110#2619C2214yes—
111#2619C2212yes—
112#2615C2214yes—
113#2615C2212yes—
114#2615C2212yes—
115#2603C2214yes—
116#2602C2214yes—
117#2602C2214yes—
118#2595C2214yes—
119#2580C2212yes—
120#2574C2214yes—
121#2574C2214yes—
122#2570C2212yes—
123#2564C2214yes—
124#2563C2212yes—
125#2563C2212yes—
126#2563C2212yes—
127#2562C2212yes—
128#2560C2214yes—
129#2559C2214yes—
130#2554C2214yes—
131#2554C2214yes—
132#2553C2214yes—
133#2553C2214yes—
134#2553C2214yes—
135#2550C2212yes—
136#2541C2212yes—
137#2541C2212yes—
138#2537C2212yes—
139#2537C2212yes—
140#2537C2212yes—
141#2535C2214yes—
142#2535C2212yes—
143#2535C2212yes—
144#2530C2214yes—
145#2528C2214yes—
146#2521C2214yes—
147#2517C2214yes—
148#2516C2214yes—
149#2505C2214yes—
150#2504C2212yes—
151#2500C2212yes—
152#2497C2212yes—
153#2496C2212yes—
154#2496C2212yes—
155#2494C2212yes—
156#2491C2212yes—
157#2490C2212yes—
158#2486C2212yes—
159#2485C2212yes—
160#2485C2212yes—
161#2485C2212yes—
162#2469C2214yes—
163#2467C2214yes—
164#2465C2214yes—
165#2464C2214yes—
166#2464C2214yes—
167#2464C2214yes—
168#2464C2214yes—
169#2464C2214yes—
170#2463C2214yes—
171#2461C2214yes—
172#2458C2214yes—
173#2458C2214yes—
174#2458C2214yes—
175#2457C2214yes—
176#2457C2214yes—
177#2456C2214yes—
178#2445C2214yes—
179#2442C2212yes—
180#2442C2212yes—
181#2440C2212yes—
182#2439C2212yes—
183#2438C2214yes—
184#2431C2214yes—
185#2430C2214yes—
186#2430C2214yes—
187#2425C2214yes—
188#2422C2212yes—
189#2422C2212yes—
190#2416C2212yes—
191#2416C2212yes—
192#2416C2212yes—
193#2414C2212yes—
194#2414C2212yes—
195#2414C2212yes—
196#2407C2214yes—
197#2398C2214yes—
198#2398C2212yes—
199#2398C2214yes—
200#2398C2214yes—
201#2397C2212yes—
202#2392C2212yes—
203#2392C2212yes—
204#2388C2214yes—
205#2388C2212yes—
206#2388C2212yes—
207#2388C2214yes—
208#2388C2214yes—
209#2373C2214yes—
210#2366C2211yescharacteristic
211#2366C2211yescharacteristic
212#2365C2211yescharacteristic
213#2365C2211yescharacteristic
214#2364C2214yes—
215#2364C2214yes—
216#2363C2212yes—
217#2363C2212yes—
218#2363C2212yes—
219#2363C2212yes—
220#2362C2212yes—
221#2361C2212yes—
222#2355C2211yescharacteristic
223#2354C2212yes—
224#2354C2211yescharacteristic
225#2353C2214yes—
226#2352C2212yes—
227#2352C2212yes—
228#2352C2212yes—
229#2352C2212yes—
230#2352C2212yes—
231#2352C2212yes—
232Q8×C4⋊C4C2211yescharacteristic
233D4×C4⋊C4C2211yescharacteristic
234D4×C4⋊C4C2212yes—
235#2346C2212yes—
236#2345C2212yes—
237#2341C2212yes—
238#2339C2212yes—
239#2335C2214yes—
240#2333C2214yes—
241#2328C2212yes—
242#2327C2212yes—
243#2319C2212yes—
244#2314C2212yes—
245#2311C2211yescharacteristic
246#2311C2211yescharacteristic
247C4×#125C2212yes—
248C4×#124C2212yes—
249C4×#124C2212yes—
250C4×#124C2212yes—
251C4×#124C2212yes—
252C4×#124C2212yes—
253#2285C2211yescharacteristic
254#2283C2211yescharacteristic
255C2×#382C2211yescharacteristic
256#2275C2212yes—
257#2274C2212yes—
258C4×#117C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C22×#41C2312yes—
262C22×#41C2314yes—
263#553—48no—
264#547—48no—
265#532—28no—
266#532—28no—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×#127C2311yescharacteristic
271C2×#127C2311yescharacteristic
272C2×#127C2314yes—
273#529—28no—
274C2×#126C2312yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125C2311yescharacteristic
279C2×#125C2312yes—
280C2×#124C2311yescharacteristic
281C2×#124C2311yescharacteristic
282C2×#124C2312yes—
283C2×#124C2311yescharacteristic
284C2×#124C2314yes—
285C2×#123C2312yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×C22⋊Q8C2311yescharacteristic
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×#121C2312yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2311yescharacteristic
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2314yes—
307C2×#121C2314yes—
308C2×#121C2314yes—
309C2×#121C2314yes—
310C2×#121C2314yes—
311C2×#121C2314yes—
312C2×#121C2314yes—
313#520—44no—
314#520—44no—
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2314yes—
342C2×C4×D4C2314yes—
343C2×#117C2312yes—
344C2×#117C2312yes—
345C2×#117C2311yescharacteristic
346C2×#117C2311yescharacteristic
347C2×#117C2312yes—
348C2×#117C2312yes—
349C2×#117C2312yes—
350C22×C4⋊C4C2312yes—
351C22×C4⋊C4C2312yes—
352C22×C4⋊C4C2311yescharacteristic
353C22×C4⋊C4C2311yescharacteristic
354C22×C4⋊C4C2312yes—
355C22×C42C2311yescharacteristic
356#401C2314yes—
357#400C2314yes—
358#400C2312yes—
359#400C2312yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#399C2312yes—
370#399C2312yes—
371#399C2312yes—
372#399C2314yes—
373#399C2312yes—
374#399C2314yes—
375#398C2312yes—
376#398C2312yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2312yes—
390#397C2312yes—
391#397C2312yes—
392#397C2312yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#396C2312yes—
406#396C2314yes—
407#396C2314yes—
408#396C2312yes—
409#396C2312yes—
410#396C2312yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#395C2314yes—
415#395C2312yes—
416#395C2312yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#394C2314yes—
422#394C2312yes—
423#394C2312yes—
424#394C2312yes—
425#394C2312yes—
426#394C2312yes—
427#394C2312yes—
428#394C2314yes—
429#394C2312yes—
430#394C2312yes—
431#394C2312yes—
432#394C2312yes—
433#394C2312yes—
434#394C2314yes—
435#394C2314yes—
436#394C2312yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2312yes—
442#394C2312yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#393C2314yes—
460#393C2312yes—
461#393C2312yes—
462#393C2314yes—
463#393C2314yes—
464#393C2314yes—
465#393C2314yes—
466#393C2314yes—
467#393C2314yes—
468#393C2312yes—
469#393C2312yes—
470#393C2314yes—
471#393C2314yes—
472#393C2314yes—
473#392C2312yes—
474#392C2312yes—
475#392C2312yes—
476#392C2312yes—
477#392C2312yes—
478#392C2312yes—
479#392C2312yes—
480#392C2314yes—
481#392C2314yes—
482#392C2314yes—
483#392C2314yes—
484#392C2314yes—
485#392C2314yes—
486#392C2312yes—
487#392C2314yes—
488#392C2314yes—
489#392C2314yes—
490#392C2314yes—
491#392C2314yes—
492#392C2314yes—
493#392C2314yes—
494#392C2314yes—
495#392C2312yes—
496#392C2312yes—
497#392C2312yes—
498#392C2312yes—
499#392C2314yes—
500#391C2314yes—
501#391C2312yes—
502#391C2312yes—
503#391C2312yes—
504#391C2312yes—
505#391C2312yes—
506#391C2314yes—
507#390C2314yes—
508#390C2314yes—
509#390C2314yes—
510#390C2312yes—
511#390C2312yes—
512#390C2312yes—
513#390C2312yes—
514#390C2312yes—
515#390C2312yes—
516#390C2312yes—
517#390C2312yes—
518#390C2314yes—
519#390C2314yes—
520#390C2314yes—
521#390C2312yes—
522#390C2314yes—
523#390C2314yes—
524#390C2314yes—
525#390C2314yes—
526#390C2314yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2312yes—
539#389C2312yes—
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#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#384C2312yes—
631#384C2312yes—
632#384C2311yescharacteristic
633#384C2311yescharacteristic
634#383C2312yes—
635#382C2312yes—
636#382C2314yes—
637#382C2314yes—
638#382C2311yescharacteristic
639#382C2312yes—
640#382C2311yescharacteristic
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#382C2314yes—
645#382C2312yes—
646#382C2312yes—
647#381C2312yes—
648#381C2314yes—
649#381C2314yes—
650#380C2312yes—
651#380C2312yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2314yes—
661#380C2314yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2314yes—
666#380C2314yes—
667#380C2312yes—
668#380C2311yescharacteristic
669#380C2311yescharacteristic
670#380C2312yes—
671#380C2314yes—
672#380C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712#376C2312yes—
713#376C2312yes—
714#376C2314yes—
715C2×#95C2314yes—
716C2×#95C2312yes—
717C2×#95C2312yes—
718C43C2312yes—
719C2×#41—24no—
720C2×#41—24no—
721C2×#41—28no—
722C2×#41—42no—
723C2×#41—42no—
724C2×#41—42no—
725C2×#41—42no—
726C2×#41—48no—
727C2×#41—82no—
728C2×#41—82no—
729C2×#41—84no—
730C2×#41—84no—
731C22×Q8C2411yescharacteristic
732C22×Q8C2411yescharacteristic
733C22×Q8C2411yescharacteristic
734C22×Q8C2412yes—
735C22×Q8C2414yes—
736C22×D4C2412yes—
737C22×D4C2411yescharacteristic
738C22×D4C2412yes—
739C22×D4C2412yes—
740C22×D4C2411yescharacteristic
741C22×D4C2411yescharacteristic
742C22×D4C2412yes—
743C22×D4C2412yes—
744C22×D4C2412yes—
745C22×D4C2412yes—
746C22×D4C2412yes—
747C22×D4C2414yes—
748C22×D4C2412yes—
749C22×D4C2414yes—
750C22×D4C2412yes—
751C22×D4C2412yes—
752C22×D4C2414yes—
753C22×D4C2412yes—
754C22×D4C2414yes—
755C22×D4C2414yes—
756C22×D4C2414yes—
757C22×D4C2414yes—
758C23×C4C2412yes—
759C23×C4C2412yes—
760C23×C4C2412yes—
761C23×C4C2411yescharacteristic
762C23×C4C2414yes—
763C23×C4C2414yes—
764C23×C4C2414yes—
765C23×C4C2414yes—
766C23×C4C2412yes—
767C23×C4C2412yes—
768C23×C4C2414yes—
769C23×C4C2414yes—
770C23×C4C2411yescharacteristic
771C23×C4C2411yescharacteristic
772C4⋊Q8—24no—
773C4⋊Q8—24no—
774C4⋊Q8—44no—
775#127—24no—
776#127—24no—
777#127—84no—
778#126—28no—
779#126—48no—
780#126—84no—
781#126—84no—
782#125—24no—
783#125—44no—
784#124—24no—
785#124—24no—
786#124—24no—
787#124—28no—
788#124—84no—
789#123—28no—
790#123—48no—
791#123—48no—
792#123—48no—
793#123—84no—
794#123—84no—
795#123—84no—
796C22⋊Q8—24no—
797C22⋊Q8—48no—
798C22⋊Q8—84no—
799#121—24no—
800#121—28no—
801#121—28no—
802#121—28no—
803#121—28no—
804#121—48no—
805#121—44no—
806#121—44no—
807#121—44no—
808#121—44no—
809#121—44no—
810#121—44no—
811#121—84no—
812#121—84no—
813#121—84no—
814#121—84no—
815#121—84no—
816#121—84no—
817C4×Q8—24no—
818C4×Q8—44no—
819C4×Q8—44no—
820C4×Q8—82no—
821C4×Q8—82no—
822C4×Q8—82no—
823C4×D4—28no—
824C4×D4—28no—
825C4×D4—24no—
826C4×D4—28no—
827C4×D4—28no—
828C4×D4—28no—
829C4×D4—28no—
830C4×D4—44no—
831C4×D4—48no—
832C4×D4—44no—
833C4×D4—44no—
834C4×D4—44no—
835C4×D4—44no—
836C4×D4—44no—
837C4×D4—48no—
838C4×D4—44no—
839C4×D4—48no—
840C4×D4—84no—
841C4×D4—82no—
842C4×D4—82no—
843C4×D4—84no—
844C4×D4—82no—
845#117—24no—
846#117—28no—
847#117—28no—
848#117—42no—
849#117—44no—
850#117—44no—
851#117—82no—
852C2×C4⋊C4—28no—
853C2×C4⋊C4—28no—
854C2×C4⋊C4—42no—
855C2×C4⋊C4—44no—
856C2×C4⋊C4—42no—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
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⋊C4C2411yescharacteristic
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2411yescharacteristic
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2411yescharacteristic
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2412yes—
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2412yes—
970C2×C42#4118yescomplemented
971C2×C42C2412yes—
972C2×C42C2414yes—
973C2×C42C2412yes—
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2414yes—
977C2×C42C2414yes—
978C2×C42C2412yes—
979C2×C42C2414yes—
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2414yes—
984C2×C42C2414yes—
985C2×C42C2414yes—
986C2×C42C2414yes—
987C2×C42C2412yes—
988C2×C42C2411yescharacteristic
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046C24C2512yes—
1047C24C2512yes—
1048C24C2514yes—
1049C24C2512yes—
1050C24C2511yescharacteristic
1051#41—416no—
1052#41—416no—
1053#41—816no—
1054#41—832no—
1055C2×Q8—22no—
1056C2×Q8—22no—
1057C2×Q8—22no—
1058C2×Q8—24no—
1059C2×Q8—41no—
1060C2×Q8—41no—
1061C2×Q8—41no—
1062C2×Q8—42no—
1063C2×Q8—42no—
1064C2×Q8—41no—
1065C2×Q8—41no—
1066C2×Q8—41no—
1067C2×Q8—44no—
1068C2×Q8—44no—
1069C2×Q8—44no—
1070C2×D4—24no—
1071C2×D4—24no—
1072C2×D4—24no—
1073C2×D4—28no—
1074C2×D4—22no—
1075C2×D4—24no—
1076C2×D4—22no—
1077C2×D4—22no—
1078C2×D4—24no—
1079C2×D4—24no—
1080C2×D4—24no—
1081C2×D4—24no—
1082C2×D4—24no—
1083C2×D4—24no—
1084C2×D4—41no—
1085C2×D4—41no—
1086C2×D4—42no—
1087C2×D4—42no—
1088C2×D4—42no—
1089C2×D4—42no—
1090C2×D4—41no—
1091C2×D4—42no—
1092C2×D4—42no—
1093C2×D4—42no—
1094C2×D4—41no—
1095C2×D4—42no—
1096C2×D4—41no—
1097C2×D4—41no—
1098C2×D4—42no—
1099C2×D4—42no—
1100C2×D4—42no—
1101C2×D4—42no—
1102C2×D4—42no—
1103C2×D4—44no—
1104C2×D4—42no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C2×D4—44no—
1109C2×D4—42no—
1110C2×D4—42no—
1111C2×D4—42no—
1112C2×D4—42no—
1113C2×D4—42no—
1114C2×D4—44no—
1115C2×D4—42no—
1116C2×D4—44no—
1117C2×D4—44no—
1118C2×D4—44no—
1119C2×D4—44no—
1120C2×D4—44no—
1121C2×D4—44no—
1122C2×D4—42no—
1123C2×D4—42no—
1124C2×D4—42no—
1125C2×D4—44no—
1126C2×D4—42no—
1127C2×D4—42no—
1128C2×D4—42no—
1129C2×D4—44no—
1130C2×D4—44no—
1131C2×D4—44no—
1132C2×D4—44no—
1133C2×D4—44no—
1134C2×D4—44no—
1135C2×D4—44no—
1136C22×C4—22no—
1137C22×C4—22no—
1138C22×C4—24no—
1139C22×C4—24no—
1140C22×C4—24no—
1141C22×C4—24no—
1142C22×C4—24no—
1143C22×C4—24no—
1144C22×C4—24no—
1145C22×C4—24no—
1146C22×C4—24no—
1147C22×C4—28no—
1148C22×C4—28no—
1149C22×C4—28no—
1150C22×C4—28no—
1151C22×C4—41no—
1152C22×C4—41no—
1153C22×C4—41no—
1154C22×C4—41no—
1155C22×C4—44no—
1156C22×C4—44no—
1157C22×C4—44no—
1158C22×C4—44no—
1159C22×C4—44no—
1160C22×C4—44no—
1161C22×C4—44no—
1162C22×C4—44no—
1163C22×C4—44no—
1164C22×C4—42no—
1165C22×C4—42no—
1166C22×C4—44no—
1167C22×C4—44no—
1168C22×C4—42no—
1169C22×C4—42no—
1170C22×C4—44no—
1171C22×C4—44no—
1172C22×C4—42no—
1173C22×C4—44no—
1174C22×C4—42no—
1175C22×C4C2×#4114yes—
1176C22×C4C2×#4114yes—
1177C22×C4C2×#4114yes—
1178C22×C4C2512yes—
1179C22×C4C2512yes—
1180C22×C4C2512yes—
1181C22×C4C2512yes—
1182C22×C4C2514yes—
1183C22×C4C2514yes—
1184C22×C4C2512yes—
1185C22×C4C2512yes—
1186C22×C4C2512yes—
1187C22×C4C2512yes—
1188C22×C4C2512yes—
1189C22×C4C2514yes—
1190C22×C4C2514yes—
1191C22×C4C2514yes—
1192C22×C4C2512yes—
1193C22×C4C2512yes—
1194C22×C4C2512yes—
1195C22×C4C2511yescharacteristic
1196C22×C4C2511yescharacteristic
1197C22×C4C2511yescharacteristic
1198C22×C4C2511yescharacteristic
1199C22×C4C2511yescharacteristic
1200C22×C4C2512yes—
1201C22×C4C2511yescharacteristic
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—24no—
1208C4⋊C4—22no—
1209C4⋊C4—24no—
1210C4⋊C4—22no—
1211C4⋊C4—24no—
1212C4⋊C4—24no—
1213C4⋊C4—28no—
1214C4⋊C4—24no—
1215C4⋊C4—28no—
1216C4⋊C4—22no—
1217C4⋊C4—24no—
1218C4⋊C4—22no—
1219C4⋊C4—22no—
1220C4⋊C4—24no—
1221C4⋊C4—42no—
1222C4⋊C4—42no—
1223C4⋊C4—44no—
1224C4⋊C4—42no—
1225C4⋊C4—42no—
1226C4⋊C4—42no—
1227C4⋊C4—42no—
1228C4⋊C4—42no—
1229C4⋊C4—44no—
1230C4⋊C4—42no—
1231C4⋊C4—41no—
1232C4⋊C4—41no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—41no—
1236C4⋊C4—41no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—44no—
1240C4⋊C4—44no—
1241C4⋊C4—42no—
1242C4⋊C4—42no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4H(5,𝔽2)14yes—
1252C22⋊C4—24no—
1253C22⋊C4—24no—
1254C22⋊C4—24no—
1255C22⋊C4—28no—
1256C22⋊C4—24no—
1257C22⋊C4—24no—
1258C22⋊C4—28no—
1259C22⋊C4—24no—
1260C22⋊C4—24no—
1261C22⋊C4—24no—
1262C22⋊C4—24no—
1263C22⋊C4—24no—
1264C22⋊C4—28no—
1265C22⋊C4—28no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—42no—
1270C22⋊C4—42no—
1271C22⋊C4—42no—
1272C22⋊C4—44no—
1273C22⋊C4—42no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—42no—
1278C22⋊C4—44no—
1279C22⋊C4—42no—
1280C22⋊C4—42no—
1281C22⋊C4—42no—
1282C22⋊C4—42no—
1283C22⋊C4—44no—
1284C22⋊C4—42no—
1285C22⋊C4—42no—
1286C22⋊C4—42no—
1287C22⋊C4—42no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—44no—
1294C22⋊C4—44no—
1295C22⋊C4—44no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—44no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—42no—
1308C22⋊C4—42no—
1309C22⋊C4—42no—
1310C22⋊C4—44no—
1311C22⋊C4—42no—
1312C22⋊C4—44no—
1313C22⋊C4—42no—
1314C22⋊C4—42no—
1315C42—24no—
1316C42—24no—
1317C42—28no—
1318C42—24no—
1319C42—24no—
1320C42—42no—
1321C42—42no—
1322C42—44no—
1323C42—44no—
1324C42—44no—
1325C42—42no—
1326C42—42no—
1327C42—44no—
1328C42—44no—
1329C42—42no—
1330C42—44no—
1331C42—44no—
1332C42C2×#4114yes—
1333C42C2×#4114yes—
1334C42C2×#4114yes—
1335C42C2×#4114yes—
1336C23—21no—
1337C23—21no—
1338C23—21no—
1339C23—21no—
1340C23—21no—
1341C23—21no—
1342C23—22no—
1343C23—24no—
1344C23—22no—
1345C23—22no—
1346C23—22no—
1347C23—24no—
1348C23—22no—
1349C23—22no—
1350C23—22no—
1351C23—24no—
1352C23—22no—
1353C23—22no—
1354C23—22no—
1355C23—22no—
1356C23—22no—
1357C23—22no—
1358C23—22no—
1359C23—22no—
1360C23—22no—
1361C23—24no—
1362C23—24no—
1363C23—22no—
1364C23—22no—
1365C23—24no—
1366C23—22no—
1367C23—24no—
1368C23—22no—
1369C23—22no—
1370C23C22×#4112yes—
1371C23C2611yescharacteristic
1372Q8—44no—
1373Q8—44no—
1374Q8—44no—
1375Q8—48no—
1376Q8—88no—
1377D4—44no—
1378D4—44no—
1379D4—44no—
1380D4—48no—
1381D4—48no—
1382D4—48no—
1383D4—48no—
1384D4—48no—
1385D4—48no—
1386D4—84no—
1387D4—84no—
1388D4—84no—
1389D4—84no—
1390D4—88no—
1391D4—84no—
1392D4—88no—
1393D4—88no—
1394D4—84no—
1395D4—88no—
1396D4—88no—
1397D4—164no—
1398D4—164no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—28no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—24no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—24no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—24no—
1425C2×C4—22no—
1426C2×C4—24no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—24no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—22no—
1440C2×C4—22no—
1441C2×C4—24no—
1442C2×C4—22no—
1443C2×C4—22no—
1444C2×C4—24no—
1445C2×C4—24no—
1446C2×C4—24no—
1447C2×C4—24no—
1448C2×C4—22no—
1449C2×C4—24no—
1450C2×C4—22no—
1451C2×C4—24no—
1452C2×C4—24no—
1453C2×C4—22no—
1454C2×C4—22no—
1455C2×C4—24no—
1456C2×C4—22no—
1457C2×C4—22no—
1458C2×C4—22no—
1459C2×C4—22no—
1460C2×C4—22no—
1461C2×C4—22no—
1462C2×C4—24no—
1463C2×C4—44no—
1464C2×C4—44no—
1465C2×C4—48no—
1466C2×C4—48no—
1467C2×C4—48no—
1468C2×C4—88no—
1469C2×C4—88no—
1470C2×C4—88no—
1471C2×C4—88no—
1472C2×C4—162no—
1473C2×C4—164no—
1474C2×C4—164no—
1475C2×C4—162no—
1476C2×C4C22×#4112yes—
1477C2×C4C22×#4112yes—
1478C2×C4C22×#4112yes—
1479C2×C4C22×#4112yes—
1480C2×C4C22×#4112yes—
1481C2×C4C22×#4112yes—
1482C2×C4C2×H(5,𝔽2)14yes—
1483C2×C4C2×H(5,𝔽2)12yes—
1484C2×C4#58512yes—
1485C22—22no—
1486C22—22no—
1487C22—22no—
1488C22—41no—
1489C22—41no—
1490C22—41no—
1491C22—41no—
1492C22—42no—
1493C22—42no—
1494C22—44no—
1495C22—42no—
1496C22—42no—
1497C22—42no—
1498C22—44no—
1499C22—42no—
1500C22—44no—
1501C22—42no—
1502C22—42no—
1503C22—42no—
1504C22—42no—
1505C22—42no—
1506C22—44no—
1507C22—42no—
1508C22—44no—
1509C22—42no—
1510C22—42no—
1511C22—42no—
1512C22—42no—
1513C22—42no—
1514C22—42no—
1515C22—44no—
1516C22—42no—
1517C22—42no—
1518C22—42no—
1519C22—44no—
1520C22C23×#4111yescharacteristic
1521C22C22×H(5,𝔽2)11yescharacteristic
1522C22C2×#58511yescharacteristic
1523C22H(7,𝔽2)11yescharacteristic
1524C22H(7,𝔽2)11yescharacteristic
1525C22H(7,𝔽2)11yescharacteristic
1526C222−1+611yescharacteristic
1527C4—24no—
1528C4—22no—
1529C4—22no—
1530C4—22no—
1531C4—22no—
1532C4—22no—
1533C4—42no—
1534C4—44no—
1535C4—44no—
1536C4—42no—
1537C4—42no—
1538C4—42no—
1539C4—42no—
1540C4—44no—
1541C4—42no—
1542C4—44no—
1543C4—42no—
1544C4—44no—
1545C4—42no—
1546C4—42no—
1547C4—42no—
1548C4—42no—
1549C4—42no—
1550C4#346014yes—
1551C2—42no—
1552C2—82no—
1553C2—82no—
1554C2—84no—
1555C2—82no—
1556C2C2×#346011yescharacteristic
1557C2#6285511yescharacteristic
1558C2#6285611yescharacteristic
1559C2#6304511yescharacteristic
1560C2#6304711yescharacteristic
1561C2#6305111yescharacteristic
1562C2#6305211yescharacteristic
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. #42990C2semidirect
2. #42923C2semidirect
3. #42693C2semidirect
4. #42688C2semidirect
5. #42473C2semidirect
6. #42471C2semidirect
7. #42407C2semidirect
8. #42065C2semidirect
9. #41057C2semidirect
10. #41036C2semidirect
11. #40966C2semidirect
12. #40951C2semidirect
13. #37639C2semidirect
14. #37610C2semidirect
15. #37604C2semidirect
16. #37599C2semidirect
17. #37561C2semidirect
18. #37554C2semidirect
19. #36694C2semidirect
20. #36687C2semidirect
21. #36083C2semidirect
22. #35947C2semidirect
23. #35923C2semidirect
24. #35770C2semidirect
25. #35768C2semidirect
26. #35682C2semidirect
27. #34242C2semidirect
28. #34232C2semidirect
29. #34208C2semidirect
970. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#429902
#429232
#426932
#426882
#424732
#424712
#424072
#420652
#410572
#410362
#409662
#409512
#376392
#376102
#376042
#375992
#375612
#375542
#366942
#366872
#360832
#359472
#359232
#357702
#357682
#356822
#342422
#342322
#342082