Finite Group Databasebeta

← #8746512

Subgroups — #8746512

Order 512.

4388 conjugacy classes of subgroups.

The subgroup lattice has 1461 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59201C211yesmaximal, characteristic, complemented
2#59027C212yesmaximal, complemented
3#58319C212yesmaximal, complemented
4#57921C214yesmaximal, complemented
5#55523C214yesmaximal, complemented
6#54521C214yesmaximal, complemented
7#54464C214yesmaximal, complemented
8#53052C212yesmaximal, complemented
9#53017C211yesmaximal, characteristic, complemented
10#52751C212yesmaximal, complemented
11#52366C214yesmaximal, complemented
12#47183C212yesmaximal, complemented
13#45375C211yesmaximal, characteristic, complemented
14#45339C212yesmaximal, complemented
15#45320C212yesmaximal, complemented
16#45261C212yesmaximal, complemented
17#44972C212yesmaximal, complemented
18#42906C212yesmaximal, complemented
19#42887C211yesmaximal, characteristic, complemented
20#42781C212yesmaximal, complemented
21#42557C212yesmaximal, complemented
22#42450C212yesmaximal, complemented
23#41650C212yesmaximal, complemented
24#40792C214yesmaximal, complemented
25#39909C212yesmaximal, complemented
26#39133C211yesmaximal, characteristic, complemented
27#36676C211yesmaximal, characteristic, complemented
28#35996C211yesmaximal, characteristic, complemented
29#35772C212yesmaximal, complemented
30C2×#556C2211yescharacteristic, complemented
31C2×#552C2212yes—
32C2×#548C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C2×#520C2211yescharacteristic, complemented
35#2847C2211yescharacteristic
36#2842C2211yescharacteristic
37#2841C2212yes—
38#2837C2214yes—
39#2837C2214yes—
40#2837C2214yescomplemented
41#2836C2214yes—
42#2834C2211yescharacteristic
43#2831C2214yescomplemented
44#2830C2214yes—
45#2829C2214yes—
46#2828C2214yes—
47#2827C2212yes—
48#2827C2212yes—
49#2827C2212yes—
50#2827C2214yescomplemented
51#2826C2212yes—
52#2826C2211yescharacteristic
53#2825C2212yes—
54#2822C2212yescomplemented
55#2819C2212yescomplemented
56#2812C2211yescharacteristic
57#2812C2212yes—
58#2807C2214yescomplemented
59#2807C2214yescomplemented
60#2803C2214yes—
61#2803C2214yescomplemented
62#2802C2214yescomplemented
63#2800C2214yes—
64#2798C2214yescomplemented
65#2797C2214yes—
66#2783C2214yescomplemented
67#2777C2214yes—
68#2777C2214yescomplemented
69#2775C2214yescomplemented
70#2773C2214yes—
71#2772C2214yescomplemented
72#2772C2214yescomplemented
73#2771C2212yes—
74#2771C2212yescomplemented
75#2770C2214yescomplemented
76#2770C2214yescomplemented
77#2769C2212yescomplemented
78#2766C2214yescomplemented
79#2764C2212yes—
80#2758C2214yescomplemented
81#2757C2214yes—
82#2757C2214yes—
83#2757C2214yes—
84#2756C2214yes—
85#2756C2214yescomplemented
86#2755C2214yescomplemented
87#2752C2214yes—
88#2751C2214yes—
89#2750C2214yes—
90#2741C2214yes—
91#2738C2214yescomplemented
92#2736C2212yes—
93#2732C2214yes—
94#2730C2214yes—
95#2727C2214yes—
96#2725C2214yes—
97#2724C2214yes—
98#2723C2214yescomplemented
99#2721C2214yes—
100#2721C2214yescomplemented
101#2718C2214yes—
102#2714C2214yes—
103#2711C2214yes—
104#2710C2214yes—
105#2707C2214yes—
106#2698C2214yes—
107#2697C2212yes—
108#2694C2214yes—
109#2687C2214yes—
110#2685C2214yes—
111#2678C2214yes—
112#2652C2214yescomplemented
113#2651C2214yescomplemented
114#2651C2214yescomplemented
115#2649C2214yes—
116#2648C2214yes—
117#2644C2214yes—
118#2640C2211yescharacteristic, complemented
119#2636C2214yes—
120#2635C2214yes—
121#2633C2214yescomplemented
122#2632C2212yescomplemented
123#2631C2212yes—
124#2630C2214yes—
125#2629C2212yescomplemented
126#2625C2211yescharacteristic, complemented
127#2625C2212yescomplemented
128#2624C2212yescomplemented
129#2618C2212yes—
130#2609C2214yescomplemented
131#2606C2214yescomplemented
132#2603C2214yes—
133#2601C2214yes—
134#2600C2212yes—
135#2600C2212yescomplemented
136#2597C2214yes—
137#2595C2214yescomplemented
138#2587C2214yescomplemented
139#2585C2214yescomplemented
140#2580C2212yes—
141#2572C2214yes—
142#2566C2212yescomplemented
143#2563C2211yescharacteristic
144#2562C2212yes—
145#2562C2212yescomplemented
146#2559C2214yes—
147#2556C2214yes—
148#2552C2212yescomplemented
149#2550C2212yescomplemented
150#2540C2211yescharacteristic, complemented
151#2539C2212yes—
152#2538C2212yes—
153#2537C2212yes—
154#2536C2212yes—
155#2534C2212yes—
156#2532C2214yescomplemented
157#2530C2214yes—
158#2527C2214yescomplemented
159#2524C2214yescomplemented
160#2523C2212yes—
161#2522C2214yes—
162#2519C2214yes—
163#2518C2214yes—
164#2515C2214yes—
165#2513C2212yescomplemented
166#2507C2212yescomplemented
167#2506C2212yescomplemented
168#2506C2214yescomplemented
169#2502C2211yescharacteristic, complemented
170#2502C2212yescomplemented
171#2501C2211yescharacteristic
172#2499C2212yes—
173#2497C2212yes—
174#2496C2212yes—
175#2495C2212yes—
176#2495C2212yescomplemented
177#2490C2212yes—
178#2489C2212yes—
179#2487C2212yescomplemented
180#2486C2211yescharacteristic
181#2486C2211yescharacteristic
182#2486C2212yes—
183#2485C2212yes—
184#2485C2212yes—
185#2480C2214yes—
186#2478C2214yescomplemented
187#2477C2214yes—
188#2474C2214yescomplemented
189#2473C2214yes—
190#2473C2214yescomplemented
191#2469C2214yes—
192#2460C2214yescomplemented
193#2460C2214yescomplemented
194#2456C2214yes—
195#2455C2214yes—
196#2455C2214yes—
197#2454C2214yescomplemented
198#2453C2212yescomplemented
199#2453C2212yescomplemented
200#2453C2214yescomplemented
201#2447C2212yescomplemented
202#2447C2214yescomplemented
203#2443C2214yes—
204#2442C2212yes—
205#2441C2212yes—
206#2441C2212yescomplemented
207#2439C2212yes—
208#2426C2212yes—
209#2423C2212yes—
210#2423C2212yes—
211#2423C2212yescomplemented
212#2422C2214yes—
213#2422C2212yes—
214#2421C2212yescomplemented
215#2418C2214yes—
216#2417C2212yes—
217#2415C2212yes—
218#2415C2212yescomplemented
219#2414C2212yes—
220#2414C2212yes—
221#2409C2212yes—
222#2407C2212yes—
223#2407C2212yescomplemented
224#2401C2212yes—
225#2397C2211yescharacteristic
226#2395C2212yes—
227#2395C2212yes—
228#2395C2211yescharacteristic
229#2392C2212yes—
230#2392C2212yes—
231#2392C2212yes—
232#2392C2214yescomplemented
233#2374C2212yes—
234#2363C2212yes—
235#2362C2212yes—
236#2361C2212yescomplemented
237#2356C2212yescomplemented
238#2355C2212yescomplemented
239#2354C2212yes—
240#2352C2212yes—
241#2352C2214yes—
242Q8×C4⋊C4C2212yescomplemented
243D4×C4⋊C4C2212yes—
244D4×C4⋊C4C2212yescomplemented
245#2347C2212yes—
246#2341C2211yescharacteristic, complemented
247Q8×C22⋊C4C2211yescharacteristic
248Q8×C22⋊C4C2212yes—
249#2335C2214yes—
250#2330C2212yescomplemented
251#2323C2212yescomplemented
252#2323C2212yescomplemented
253#2322C2212yes—
254#2320C2211yescharacteristic, complemented
255#2317C2212yescomplemented
256C4×#120C2211yescharacteristic
257C4×#120C2212yes—
258#2280C2212yes—
259C22×#41C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261C24×C4C2311yescharacteristic
262#556—44no—
263#552—48no—
264#548—44no—
265C2×C4⋊Q8C2311yescharacteristic
266C2×#126C2314yes—
267C2×#126C2314yes—
268C2×#126C2314yes—
269C2×#125C2312yes—
270C2×#125C2312yes—
271C2×#125C2314yes—
272C2×#125C2314yes—
273C2×#125C2314yes—
274C2×#124C2312yes—
275C2×#124C2312yes—
276C2×#124C2311yescharacteristic
277C2×#123C2312yes—
278C2×#123C2314yes—
279C2×#123C2312yes—
280C2×#123C2314yes—
281C2×#123C2312yes—
282C2×#123C2312yes—
283C2×C22⋊Q8—44no—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2311yescharacteristic
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×#121C2312yes—
292C2×#121C2311yescharacteristic
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2314yes—
296C2×#120C2312yes—
297C2×#120C2311yescharacteristic
298C2×#120C2312yes—
299#520—44no—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2311yescharacteristic
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2311yescharacteristic
315C2×C4×D4C2312yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×#117C2312yes—
319C2×#117C2312yes—
320C2×#117C2312yes—
321C2×#117C2312yes—
322C2×#117C2314yes—
323C2×#117C2312yes—
324C2×#117C2311yescharacteristic
325C22×C4⋊C4C2312yes—
326C22×C4⋊C4C2312yes—
327C22×C4⋊C4C2311yescharacteristic
328C22×C4⋊C4C2311yescharacteristic
329C22×C4⋊C4C2312yes—
330C22×C22⋊C4C2312yes—
331#401C2312yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2312yes—
337#400C2312yes—
338#400C2312yes—
339#400C2311yescharacteristic
340#400C2312yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2312yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#399C2311yescharacteristic
352#399C2312yes—
353#399C2311yescharacteristic
354#399C2312yes—
355#399C2314yes—
356#399C2314yes—
357#399C2311yescharacteristic
358#399C2312yes—
359#399C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#399C2314yes—
364#399C2314yes—
365#398C2311yescharacteristic
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2312yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2312yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#398C2312yes—
390#398C2314yes—
391#397C2312yes—
392#397C2312yes—
393#397C2312yes—
394#397C2312yes—
395#397C2312yes—
396#397C2312yes—
397#397C2312yes—
398#397C2312yes—
399#397C2312yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2312yes—
409#397C2312yes—
410#397C2311yescharacteristic
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2312yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2312yes—
427#396C2312yes—
428#396C2312yes—
429#396C2312yes—
430#396C2312yes—
431#396C2312yes—
432#396C2312yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#395C2314yes—
444#395C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2312yes—
450#394C2312yes—
451#394C2312yes—
452#394C2312yes—
453#394C2312yes—
454#394C2312yes—
455#394C2312yes—
456#394C2312yes—
457#394C2312yes—
458#394C2312yes—
459#394C2312yes—
460#394C2312yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#393C2312yes—
476#393C2312yes—
477#393C2312yes—
478#393C2314yes—
479#393C2314yes—
480#393C2312yes—
481#392C2311yescharacteristic
482#392C2314yes—
483#392C2312yes—
484#392C2312yes—
485#392C2312yes—
486#392C2312yes—
487#392C2311yescharacteristic
488#392C2312yes—
489#392C2314yes—
490#392C2314yes—
491#392C2314yes—
492#391C2314yes—
493#391C2314yes—
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2314yes—
499#391C2314yes—
500#391C2314yes—
501#391C2312yes—
502#390C2312yes—
503#390C2312yes—
504#390C2312yes—
505#390C2314yes—
506#390C2314yes—
507#390C2314yes—
508#390C2314yes—
509#390C2314yes—
510#390C2312yes—
511#390C2314yes—
512#390C2314yes—
513#390C2314yes—
514#390C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2312yes—
518#389C2314yes—
519#389C2314yes—
520#389C2312yes—
521#389C2312yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2312yes—
530#389C2312yes—
531#389C2314yes—
532#389C2314yes—
533#389C2312yes—
534#389C2314yes—
535#389C2312yes—
536#389C2314yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
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#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
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#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#386C2312yes—
611#386C2312yes—
612#386C2312yes—
613#386C2312yes—
614#386C2311yescharacteristic
615#386C2314yes—
616#386C2314yes—
617#386C2312yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2311yescharacteristic
628#385C2312yes—
629#385C2312yes—
630#385C2312yes—
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#384C2312yes—
648#384C2312yes—
649#384C2312yes—
650#384C2314yes—
651#384C2312yes—
652#383C2314yes—
653#383C2314yes—
654#383C2312yes—
655#383C2314yes—
656#383C2314yes—
657#382C2312yes—
658#382C2312yes—
659#382C2312yes—
660#382C2312yes—
661#382C2314yes—
662#382C2314yes—
663#381C2312yes—
664#381C2314yes—
665#381C2312yes—
666#381C2314yes—
667#380C2311yescharacteristic
668#380C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2311yescharacteristic
672#380C2312yes—
673#380C2312yes—
674#380C2312yes—
675#380C2312yes—
676#380C2314yes—
677#380C2314yes—
678#380C2312yes—
679#380C2312yes—
680#380C2314yes—
681#380C2312yes—
682#380C2312yes—
683#380C2314yes—
684#380C2312yes—
685#379C2312yes—
686#379C2311yescharacteristic
687#379C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2311yescharacteristic
710C4×C22⋊C4C2311yescharacteristic
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715#376C2311yescharacteristic
716#376C2314yes—
717C25C2411yescharacteristic
718C2×#41—24no—
719C2×#41—44no—
720C22×Q8—24no—
721C22×Q8—44no—
722C22×Q8C2411yescharacteristic
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2412yes—
726C22×D4C2411yescharacteristic
727C22×D4C2412yes—
728C22×D4C2412yes—
729C22×D4C2411yescharacteristic
730C22×D4C2412yes—
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2412yes—
735C22×D4C2414yes—
736C22×D4C2411yescharacteristic
737C22×D4C2414yes—
738C23×C4—42no—
739C23×C4—44no—
740C23×C4C2412yes—
741C23×C4C2411yescharacteristic
742C23×C4C2411yescharacteristic
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2412yes—
746C23×C4C2412yes—
747C23×C4C2411yescharacteristic
748C23×C4C2414yes—
749C23×C4C2412yes—
750C23×C4C2414yes—
751C23×C4C2412yes—
752C4⋊Q8—42no—
753#126—48no—
754#126—48no—
755#126—84no—
756#125—44no—
757#125—44no—
758#125—48no—
759#125—84no—
760#125—84no—
761#124—44no—
762#124—42no—
763#124—44no—
764#123—48no—
765#123—44no—
766#123—48no—
767#123—44no—
768#123—82no—
769#123—82no—
770C22⋊Q8—28no—
771C22⋊Q8—28no—
772C22⋊Q8—48no—
773C22⋊Q8—44no—
774C22⋊Q8—44no—
775C22⋊Q8—42no—
776C22⋊Q8—44no—
777#121—44no—
778#121—44no—
779#121—42no—
780#121—44no—
781#121—84no—
782#120—44no—
783#120—42no—
784#120—82no—
785C4×Q8—28no—
786C4×Q8—24no—
787C4×Q8—44no—
788C4×Q8—44no—
789C4×Q8—44no—
790C4×D4—48no—
791C4×D4—44no—
792C4×D4—44no—
793C4×D4—44no—
794C4×D4—44no—
795C4×D4—44no—
796C4×D4—42no—
797C4×D4—44no—
798C4×D4—44no—
799C4×D4—42no—
800C4×D4—48no—
801C4×D4—84no—
802C4×D4—84no—
803#117—44no—
804#117—44no—
805#117—42no—
806#117—48no—
807#117—44no—
808#117—44no—
809#117—44no—
810C2×C4⋊C4—42no—
811C2×C4⋊C4—44no—
812C2×C4⋊C4—42no—
813C2×C4⋊C4—44no—
814C2×C4⋊C4—44no—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C22⋊C4—44no—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2411yescharacteristic
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2411yescharacteristic
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2411yescharacteristic
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2411yescharacteristic
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2411yescharacteristic
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2412yes—
952C2×C42C2414yes—
953#95C2412yes—
954#95C2414yes—
955#95C2411yescharacteristic
956#95C2414yes—
957#95C2411yescharacteristic
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2411yescharacteristic
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2411yescharacteristic
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2412yes—
996#95C2414yes—
997#95C2412yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016C24—22no—
1017C24—41no—
1018C24—42no—
1019C24—41no—
1020C24—42no—
1021C24C2512yes—
1022C24C2512yes—
1023C24C2512yes—
1024C24C2511yescharacteristic
1025C24C2511yescharacteristic
1026#41—416no—
1027C2×Q8—22no—
1028C2×Q8—24no—
1029C2×Q8—24no—
1030C2×Q8—24no—
1031C2×Q8—42no—
1032C2×Q8—44no—
1033C2×Q8—44no—
1034C2×Q8—88no—
1035C2×Q8H(5,𝔽2)14yes—
1036C2×D4—24no—
1037C2×D4—22no—
1038C2×D4—24no—
1039C2×D4—24no—
1040C2×D4—22no—
1041C2×D4—24no—
1042C2×D4—42no—
1043C2×D4—42no—
1044C2×D4—42no—
1045C2×D4—42no—
1046C2×D4—42no—
1047C2×D4—44no—
1048C2×D4—42no—
1049C2×D4—41no—
1050C2×D4—42no—
1051C2×D4—41no—
1052C2×D4—42no—
1053C2×D4—42no—
1054C2×D4—44no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—42no—
1058C2×D4—42no—
1059C2×D4—44no—
1060C2×D4—42no—
1061C2×D4—41no—
1062C2×D4—42no—
1063C2×D4—44no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—44no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C22×C4—24no—
1070C22×C4—24no—
1071C22×C4—24no—
1072C22×C4—22no—
1073C22×C4—22no—
1074C22×C4—24no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—24no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—24no—
1081C22×C4—24no—
1082C22×C4—44no—
1083C22×C4—42no—
1084C22×C4—41no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—42no—
1089C22×C4—42no—
1090C22×C4—42no—
1091C22×C4—42no—
1092C22×C4—42no—
1093C22×C4—44no—
1094C22×C4—42no—
1095C22×C4—44no—
1096C22×C4—42no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—42no—
1100C22×C4—88no—
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2514yes—
1108C22×C4C2514yes—
1109C22×C4C2512yes—
1110C22×C4C2514yes—
1111C22×C4C2514yes—
1112C22×C4C2512yes—
1113C22×C4C2511yescharacteristic
1114C22×C4C2514yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2514yes—
1121C22×C4C2512yes—
1122C22×C4C2511yescharacteristic
1123C22×C4C2512yes—
1124C22×C4C2511yescharacteristic
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—28no—
1128C4⋊C4—28no—
1129C4⋊C4—22no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—28no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—42no—
1137C4⋊C4—41no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—41no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—44no—
1158C4⋊C4—41no—
1159C4⋊C4—42no—
1160C4⋊C4—41no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—42no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—42no—
1184C22⋊C4—28no—
1185C22⋊C4—22no—
1186C22⋊C4—24no—
1187C22⋊C4—28no—
1188C22⋊C4—28no—
1189C22⋊C4—44no—
1190C22⋊C4—42no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C4—44no—
1197C22⋊C4—42no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—42no—
1203C22⋊C4—42no—
1204C22⋊C4—44no—
1205C22⋊C4—42no—
1206C22⋊C4—44no—
1207C22⋊C4—42no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—44no—
1219C22⋊C4—41no—
1220C22⋊C4—42no—
1221C22⋊C4—41no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—42no—
1229C22⋊C4—42no—
1230C22⋊C4—42no—
1231C22⋊C4—42no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—42no—
1236C22⋊C4—42no—
1237C22⋊C4—42no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—42no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—41no—
1244C22⋊C4—42no—
1245C42—28no—
1246C42—24no—
1247C42—22no—
1248C42—24no—
1249C42—24no—
1250C42—24no—
1251C42—24no—
1252C42—44no—
1253C42—44no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C42—44no—
1258C42—44no—
1259C42—44no—
1260C42—44no—
1261C42—42no—
1262C23—21no—
1263C23—22no—
1264C23—21no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—21no—
1270C23—22no—
1271C23—22no—
1272C23—22no—
1273C23—22no—
1274C23—22no—
1275C23—22no—
1276C23—22no—
1277C23—21no—
1278C23—24no—
1279C23—22no—
1280C23—22no—
1281C23—21no—
1282C23—22no—
1283C23—22no—
1284C23—22no—
1285C23—24no—
1286C23—22no—
1287C23—22no—
1288C23—22no—
1289C23—22no—
1290C23—44no—
1291C23—82no—
1292C23—84no—
1293C23—82no—
1294C23—84no—
1295C23#58512yes—
1296C23C2611yescharacteristic
1297Q8—28no—
1298Q8—44no—
1299Q8—84no—
1300Q8—84no—
1301D4—48no—
1302D4—48no—
1303D4—48no—
1304D4—44no—
1305D4—82no—
1306D4—84no—
1307D4—88no—
1308D4—82no—
1309D4—84no—
1310D4—84no—
1311D4—84no—
1312D4—164no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—21no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—21no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—21no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—21no—
1357C2×C4—24no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—48no—
1377C2×C4—48no—
1378C2×C4—48no—
1379C2×C4—44no—
1380C2×C4—44no—
1381C2×C4—84no—
1382C2×C4—84no—
1383C2×C4—88no—
1384C2×C4—82no—
1385C2×C4—84no—
1386C2×C4—162no—
1387C2×C4—164no—
1388C2×C4C2×H(5,𝔽2)14yes—
1389C2×C4C2×H(5,𝔽2)12yes—
1390C2×C4#58514yes—
1391C22—22no—
1392C22—24no—
1393C22—41no—
1394C22—42no—
1395C22—41no—
1396C22—42no—
1397C22—42no—
1398C22—41no—
1399C22—42no—
1400C22—42no—
1401C22—42no—
1402C22—42no—
1403C22—44no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—41no—
1408C22—42no—
1409C22—42no—
1410C22—42no—
1411C22—42no—
1412C22—41no—
1413C22—42no—
1414C22—42no—
1415C22—42no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—44no—
1420C22—88no—
1421C22C22×H(5,𝔽2)11yescharacteristic
1422C22C2×#58512yes—
1423C22C2×#58511yescharacteristic
1424C22H(7,𝔽2)11yescharacteristic
1425C222−1+612yes—
1426C4—24no—
1427C4—42no—
1428C4—41no—
1429C4—42no—
1430C4—41no—
1431C4—42no—
1432C4—42no—
1433C4—42no—
1434C4—42no—
1435C4—44no—
1436C4—44no—
1437C4—42no—
1438C4—41no—
1439C4—44no—
1440C4—44no—
1441C4—44no—
1442C4—42no—
1443C4—42no—
1444C4—41no—
1445C4—44no—
1446C4—42no—
1447C4—42no—
1448C4—42no—
1449C4#353314yes—
1450C2—42no—
1451C2—81no—
1452C2—82no—
1453C2—82no—
1454C2—82no—
1455C2C2×#353311yescharacteristic
1456C2#6289911yescharacteristic
1457C2#6290712yes—
1458C2#6304312yes—
1459C2#6304411yescharacteristic
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. #59201C2semidirect
2. #59027C2semidirect
3. #58319C2semidirect
4. #57921C2semidirect
5. #55523C2semidirect
6. #54521C2semidirect
7. #54464C2semidirect
8. #53052C2semidirect
9. #53017C2semidirect
10. #52751C2semidirect
11. #52366C2semidirect
12. #47183C2semidirect
13. #45375C2semidirect
14. #45339C2semidirect
15. #45320C2semidirect
16. #45261C2semidirect
17. #44972C2semidirect
18. #42906C2semidirect
19. #42887C2semidirect
20. #42781C2semidirect
21. #42557C2semidirect
22. #42450C2semidirect
23. #41650C2semidirect
24. #40792C2semidirect
25. #39909C2semidirect
26. #39133C2semidirect
27. #36676C2semidirect
28. #35996C2semidirect
29. #35772C2semidirect
30. C2×#556C22semidirect
34. C2×#520C22semidirect
40. #2837C22semidirect
43. #2831C22semidirect
50. #2827C22semidirect
54. #2822C22semidirect
55. #2819C22semidirect
58. #2807C22semidirect
59. #2807C22semidirect
61. #2803C22semidirect
62. #2802C22semidirect
64. #2798C22semidirect
66. #2783C22semidirect
68. #2777C22semidirect
69. #2775C22semidirect
71. #2772C22semidirect
72. #2772C22semidirect
74. #2771C22semidirect
75. #2770C22semidirect
76. #2770C22semidirect
77. #2769C22semidirect
78. #2766C22semidirect
80. #2758C22semidirect
85. #2756C22semidirect
86. #2755C22semidirect
91. #2738C22semidirect
98. #2723C22semidirect
100. #2721C22semidirect
112. #2652C22semidirect
113. #2651C22semidirect
114. #2651C22semidirect
118. #2640C22semidirect
121. #2633C22semidirect
122. #2632C22semidirect
125. #2629C22semidirect
126. #2625C22semidirect
127. #2625C22semidirect
128. #2624C22semidirect
130. #2609C22semidirect
131. #2606C22semidirect
135. #2600C22semidirect
137. #2595C22semidirect
138. #2587C22semidirect
139. #2585C22semidirect
142. #2566C22semidirect
145. #2562C22semidirect
148. #2552C22semidirect
149. #2550C22semidirect
150. #2540C22semidirect
156. #2532C22semidirect
158. #2527C22semidirect
159. #2524C22semidirect
165. #2513C22semidirect
166. #2507C22semidirect
167. #2506C22semidirect
168. #2506C22semidirect
169. #2502C22semidirect
170. #2502C22semidirect
176. #2495C22semidirect
179. #2487C22semidirect
186. #2478C22semidirect
188. #2474C22semidirect
190. #2473C22semidirect
192. #2460C22semidirect
193. #2460C22semidirect
197. #2454C22semidirect
198. #2453C22semidirect
199. #2453C22semidirect
200. #2453C22semidirect
201. #2447C22semidirect
202. #2447C22semidirect
206. #2441C22semidirect
211. #2423C22semidirect
214. #2421C22semidirect
218. #2415C22semidirect
223. #2407C22semidirect
232. #2392C22semidirect
236. #2361C22semidirect
237. #2356C22semidirect
238. #2355C22semidirect
242. Q8×C4⋊C4C22semidirect
244. D4×C4⋊C4C22semidirect
246. #2341C22semidirect
250. #2330C22semidirect
251. #2323C22semidirect
252. #2323C22semidirect
254. #2320C22semidirect
255. #2317C22semidirect

Maximal subgroups

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

subgroupindex
#592012
#590272
#583192
#579212
#555232
#545212
#544642
#530522
#530172
#527512
#523662
#471832
#453752
#453392
#453202
#452612
#449722
#429062
#428872
#427812
#425572
#424502
#416502
#407922
#399092
#391332
#366762
#359962
#357722