Finite Group Databasebeta

← #8726388

Subgroups — #8726388

Order 512.

4470 conjugacy classes of subgroups.

The subgroup lattice has 1465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59855C212yesmaximal, complemented
2#59237C212yesmaximal, complemented
3#59209C212yesmaximal, complemented
4#59201C211yesmaximal, characteristic, complemented
5#59027C212yesmaximal, complemented
6#56169C214yesmaximal, complemented
7#56042C214yesmaximal, complemented
8#55994C212yesmaximal, complemented
9#54019C214yesmaximal, complemented
10#53093C212yesmaximal, complemented
11#52993C211yesmaximal, characteristic, complemented
12#52292C211yesmaximal, characteristic, complemented
13#47665C214yesmaximal, complemented
14#47452C212yesmaximal, complemented
15#45308C211yesmaximal, characteristic, complemented
16#45157C212yesmaximal, complemented
17#45115C212yesmaximal, complemented
18#44568C214yesmaximal, complemented
19#42944C211yesmaximal, characteristic, complemented
20#42620C212yesmaximal, complemented
21#41620C214yesmaximal, complemented
22#41204C212yesmaximal, complemented
23#39933C212yesmaximal, complemented
24#39906C212yesmaximal, complemented
25#39722C211yesmaximal, characteristic, complemented
26#39238C212yesmaximal, complemented
27#38950C212yesmaximal, complemented
28#36055C212yesmaximal, complemented
29#35923C211yesmaximal, characteristic, complemented
30C2×#553C2211yescharacteristic
31C2×#552C2212yes—
32C2×#547C2211yescharacteristic, complemented
33C2×#544C2211yescharacteristic, complemented
34C22×C22⋊Q8C2211yescharacteristic
35#2850C2212yescomplemented
36#2847C2211yescharacteristic
37#2841C2214yescomplemented
38#2841C2212yescomplemented
39#2838C2214yes—
40#2836C2214yes—
41#2834C2212yes—
42#2833C2214yescomplemented
43#2831C2214yes—
44#2829C2214yes—
45#2821C2212yescomplemented
46#2807C2211yescharacteristic
47#2804C2214yescomplemented
48#2800C2214yes—
49#2800C2214yescomplemented
50#2799C2214yescomplemented
51#2796C2212yes—
52#2789C2214yescomplemented
53#2789C2212yescomplemented
54#2786C2214yes—
55#2780C2212yes—
56#2778C2212yes—
57#2778C2214yes—
58#2776C2214yescomplemented
59#2776C2214yescomplemented
60#2770C2214yes—
61#2769C2214yescomplemented
62#2766C2214yescomplemented
63#2761C2214yes—
64#2760C2214yes—
65#2760C2212yescomplemented
66#2759C2214yes—
67#2759C2214yescomplemented
68#2759C2214yescomplemented
69#2756C2214yes—
70#2750C2214yes—
71#2746C2212yes—
72#2742C2212yes—
73#2740C2214yescomplemented
74#2740C2214yescomplemented
75#2738C2214yescomplemented
76#2737C2214yes—
77#2736C2212yes—
78#2735C2211yescharacteristic
79#2723C2214yes—
80#2719C2214yescomplemented
81#2716C2214yes—
82#2707C2214yescomplemented
83#2705C2214yes—
84#2704C2214yescomplemented
85#2702C2214yes—
86#2702C2214yes—
87#2699C2214yes—
88#2698C2214yes—
89#2697C2212yes—
90#2696C2214yes—
91#2696C2214yes—
92#2693C2214yes—
93#2693C2212yes—
94#2693C2211yescharacteristic
95#2688C2214yes—
96#2688C2212yes—
97#2687C2214yes—
98#2687C2214yescomplemented
99#2684C2214yes—
100#2678C2212yes—
101#2678C2214yes—
102#2672C2214yes—
103#2668C2211yescharacteristic
104#2667C2214yescomplemented
105#2664C2212yescomplemented
106#2663C2212yescomplemented
107#2660C2211yescharacteristic, complemented
108#2653C2214yes—
109#2650C2214yescomplemented
110#2649C2214yes—
111#2648C2214yes—
112#2645C2212yescomplemented
113#2633C2212yes—
114#2624C2214yes—
115#2624C2211yescharacteristic, complemented
116#2618C2214yes—
117#2617C2212yes—
118#2612C2212yescomplemented
119#2606C2214yescomplemented
120#2595C2214yes—
121#2594C2214yescomplemented
122#2591C2214yes—
123#2576C2214yes—
124#2575C2214yescomplemented
125#2574C2214yescomplemented
126#2572C2214yes—
127#2572C2214yescomplemented
128#2572C2214yescomplemented
129#2570C2212yescomplemented
130#2568C2212yescomplemented
131#2564C2212yes—
132#2563C2211yescharacteristic
133#2563C2212yes—
134#2562C2211yescharacteristic, complemented
135#2558C2214yes—
136#2557C2214yes—
137#2557C2214yes—
138#2556C2214yes—
139#2553C2214yescomplemented
140#2550C2212yescomplemented
141#2547C2212yes—
142#2540C2212yes—
143#2537C2212yescomplemented
144#2536C2212yes—
145#2535C2212yes—
146#2532C2214yes—
147#2531C2214yes—
148#2531C2214yes—
149#2531C2214yescomplemented
150#2530C2214yes—
151#2526C2214yes—
152#2526C2214yes—
153#2525C2214yes—
154#2523C2212yes—
155#2523C2212yes—
156#2515C2214yes—
157#2514C2212yescomplemented
158#2510C2214yes—
159#2510C2214yes—
160#2510C2214yescomplemented
161#2509C2212yescomplemented
162#2507C2212yescomplemented
163#2504C2212yes—
164#2504C2211yescharacteristic, complemented
165#2499C2212yes—
166#2498C2214yescomplemented
167#2495C2212yes—
168#2495C2214yescomplemented
169#2494C2212yes—
170#2494C2212yes—
171#2493C2214yescomplemented
172#2493C2214yescomplemented
173#2492C2212yescomplemented
174#2491C2212yes—
175#2489C2212yes—
176#2489C2212yes—
177#2489C2214yescomplemented
178#2487C2212yes—
179#2486C2211yescharacteristic
180#2486C2212yes—
181#2486C2214yes—
182#2485C2212yes—
183#2484C2214yescomplemented
184#2480C2214yes—
185#2477C2214yes—
186#2477C2214yescomplemented
187#2476C2214yes—
188#2476C2214yescomplemented
189#2473C2214yes—
190#2464C2214yes—
191#2454C2212yescomplemented
192#2451C2212yescomplemented
193#2447C2212yescomplemented
194#2442C2212yes—
195#2442C2212yescomplemented
196#2439C2212yes—
197#2439C2212yes—
198#2439C2214yescomplemented
199#2436C2211yescharacteristic
200#2430C2214yes—
201#2430C2212yescomplemented
202#2427C2212yes—
203#2426C2212yescomplemented
204#2423C2212yes—
205#2421C2212yescomplemented
206#2420C2212yes—
207#2418C2214yes—
208#2417C2212yes—
209#2417C2212yescomplemented
210#2417C2212yescomplemented
211#2417C2212yescomplemented
212#2416C2212yes—
213#2415C2212yes—
214#2415C2212yes—
215#2414C2212yes—
216#2409C2211yescharacteristic
217#2409C2212yes—
218#2401C2212yes—
219#2401C2214yescomplemented
220#2397C2211yescharacteristic
221#2395C2211yescharacteristic
222#2392C2212yes—
223#2388C2212yes—
224#2374C2212yes—
225#2370C2212yescomplemented
226#2367C2212yescomplemented
227#2363C2212yes—
228#2362C2212yes—
229#2359C2214yes—
230#2356C2212yescomplemented
231#2352C2214yes—
232#2352C2212yes—
233#2352C2212yes—
234#2352C2212yescomplemented
235D4×C4⋊C4C2212yes—
236#2347C2212yes—
237#2347C2211yescharacteristic, complemented
238#2346C2214yescomplemented
239#2345C2211yescharacteristic
240#2345C2214yescomplemented
241#2344C2212yescomplemented
242Q8×C22⋊C4C2212yes—
243#2337C2214yes—
244#2333C2214yes—
245#2333C2214yescomplemented
246#2323C2212yescomplemented
247#2321C2212yes—
248#2311C2214yescomplemented
249C4×C22⋊Q8C2212yescomplemented
250C4×#123C2212yes—
251C4×#121C2212yes—
252C4×#121C2212yes—
253C4×#120C2211yescharacteristic
254C4×#120C2212yes—
255C2×#389C2212yescomplemented
256#2283C2212yescomplemented
257#2280C2212yes—
258#2275C2211yescharacteristic, complemented
259C22×#41C2312yes—
260C23×Q8C2311yescharacteristic
261C24×C4C2311yescharacteristic
262#553—44no—
263#552—48no—
264#547—44no—
265#544—44no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×#126C2312yes—
270C2×#126C2314yes—
271C2×#125C2312yes—
272C2×#125C2311yescharacteristic
273C2×#125C2312yes—
274C2×#125C2314yes—
275C2×#124C2314yes—
276C2×#124C2312yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2312yes—
281C2×#123C2312yes—
282C2×#123C2312yes—
283C2×C22⋊Q8—44no—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×#121C2314yes—
293C2×#121C2314yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2311yescharacteristic
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2311yescharacteristic
300C2×#121C2312yes—
301C2×#120C2312yes—
302C2×#120C2311yescharacteristic
303C2×#120C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×D4C2311yescharacteristic
307C2×C4×D4C2311yescharacteristic
308C2×C4×D4C2312yes—
309C2×C4×D4C2311yescharacteristic
310C2×C4×D4C2312yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×#117C2311yescharacteristic
318C2×#117C2314yes—
319C2×#117C2311yescharacteristic
320C2×#117C2314yes—
321C2×#117C2312yes—
322C2×#117C2312yes—
323C22×C4⋊C4C2311yescharacteristic
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2314yes—
326C22×C4⋊C4C2312yes—
327C22×C4⋊C4C2312yes—
328C22×C4⋊C4C2311yescharacteristic
329C22×C22⋊C4C2312yes—
330C22×C42C2312yes—
331#401C2314yes—
332#401C2314yes—
333#401C2314yes—
334#401C2314yes—
335#401C2312yes—
336#400C2312yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2314yes—
345#400C2314yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2311yescharacteristic
351#400C2314yes—
352#400C2314yes—
353#400C2312yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#399C2311yescharacteristic
358#399C2314yes—
359#399C2314yes—
360#399C2311yescharacteristic
361#399C2312yes—
362#399C2312yes—
363#399C2311yescharacteristic
364#399C2314yes—
365#398C2311yescharacteristic
366#398C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2312yes—
383#397C2312yes—
384#397C2312yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2312yes—
393#397C2312yes—
394#397C2314yes—
395#397C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2312yes—
400#397C2314yes—
401#397C2314yes—
402#397C2312yes—
403#397C2311yescharacteristic
404#397C2312yes—
405#397C2314yes—
406#397C2312yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2312yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2312yes—
421#396C2312yes—
422#395C2312yes—
423#395C2314yes—
424#395C2314yes—
425#395C2312yes—
426#395C2312yes—
427#395C2314yes—
428#394C2312yes—
429#394C2314yes—
430#394C2314yes—
431#394C2312yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2312yes—
441#394C2314yes—
442#394C2314yes—
443#394C2312yes—
444#394C2314yes—
445#394C2312yes—
446#393C2312yes—
447#393C2312yes—
448#393C2314yes—
449#393C2314yes—
450#393C2314yes—
451#393C2314yes—
452#393C2314yes—
453#393C2314yes—
454#393C2314yes—
455#393C2314yes—
456#393C2312yes—
457#392C2314yes—
458#392C2311yescharacteristic
459#392C2314yes—
460#392C2312yes—
461#392C2314yes—
462#392C2312yes—
463#392C2311yescharacteristic
464#391C2314yes—
465#391C2314yes—
466#391C2314yes—
467#391C2314yes—
468#391C2312yes—
469#391C2312yes—
470#391C2314yes—
471#391C2314yes—
472#391C2314yes—
473#391C2312yes—
474#391C2312yes—
475#391C2314yes—
476#391C2312yes—
477#391C2312yes—
478#391C2314yes—
479#390C2314yes—
480#390C2312yes—
481#390C2314yes—
482#390C2314yes—
483#390C2314yes—
484#390C2314yes—
485#390C2314yes—
486#390C2312yes—
487#390C2312yes—
488#390C2312yes—
489#390C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2314yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2312yes—
504#389C2312yes—
505#389C2314yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#389C2312yes—
510#389C2314yes—
511#389C2312yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2312yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2312yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2312yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2312yes—
547#388C2312yes—
548#388C2312yes—
549#388C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2312yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2312yes—
580#386C2314yes—
581#386C2312yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2312yes—
586#386C2314yes—
587#386C2314yes—
588#386C2312yes—
589#386C2312yes—
590#386C2314yes—
591#386C2312yes—
592#386C2314yes—
593#386C2314yes—
594#386C2312yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2312yes—
603#386C2314yes—
604#386C2312yes—
605#386C2312yes—
606#386C2312yes—
607#386C2312yes—
608#386C2314yes—
609#386C2311yescharacteristic
610#386C2312yes—
611#386C2312yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2312yes—
616#385C2312yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2312yes—
624#385C2312yes—
625#385C2311yescharacteristic
626#385C2312yes—
627#385C2312yes—
628#384C2312yes—
629#383C2312yes—
630#383C2314yes—
631#383C2314yes—
632#383C2314yes—
633#383C2314yes—
634#383C2314yes—
635#382C2314yes—
636#382C2312yes—
637#382C2312yes—
638#382C2312yes—
639#382C2312yes—
640#382C2314yes—
641#382C2314yes—
642#382C2312yes—
643#381C2312yes—
644#381C2314yes—
645#381C2312yes—
646#381C2314yes—
647#381C2314yes—
648#381C2314yes—
649#381C2314yes—
650#381C2314yes—
651#380C2312yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2312yes—
656#380C2312yes—
657#380C2312yes—
658#380C2314yes—
659#380C2314yes—
660#380C2314yes—
661#380C2314yes—
662#380C2314yes—
663#380C2312yes—
664#380C2314yes—
665#380C2314yes—
666#380C2314yes—
667#380C2311yescharacteristic
668#380C2314yes—
669#380C2312yes—
670#380C2312yes—
671#380C2311yescharacteristic
672#380C2314yes—
673#380C2312yes—
674#380C2312yes—
675#379C2311yescharacteristic
676#379C2314yes—
677#379C2312yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2311yescharacteristic
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2311yescharacteristic
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712#376C2314yes—
713#376C2314yes—
714#376C2311yescharacteristic
715C2×#95C2312yes—
716C2×#95C2314yes—
717C25C2411yescharacteristic
718C2×#41—44no—
719C2×#41—48no—
720C22×Q8—42no—
721C22×Q8—44no—
722C22×Q8C2412yes—
723C22×Q8C2412yes—
724C22×Q8C2414yes—
725C22×Q8C2412yes—
726C22×D4C2411yescharacteristic
727C22×D4C2412yes—
728C22×D4C2411yescharacteristic
729C22×D4C2412yes—
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2412yes—
736C22×D4C2414yes—
737C22×D4C2412yes—
738C23×C4—42no—
739C23×C4—44no—
740C23×C4C2412yes—
741C23×C4C2411yescharacteristic
742C23×C4C2411yescharacteristic
743C23×C4C2412yes—
744C23×C4C2414yes—
745C23×C4C2412yes—
746C23×C4C2414yes—
747C23×C4C2412yes—
748C23×C4C2412yes—
749C23×C4C2412yes—
750C23×C4C2411yescharacteristic
751C23×C4C2412yes—
752C23×C4C2414yes—
753C23×C4C2412yes—
754C23×C4C2412yes—
755C4⋊Q8—44no—
756C4⋊Q8—44no—
757C4⋊Q8—42no—
758#126—44no—
759#126—48no—
760#125—28no—
761#125—44no—
762#125—42no—
763#125—48no—
764#124—44no—
765#124—48no—
766#123—48no—
767#123—44no—
768#123—44no—
769#123—48no—
770#123—48no—
771#123—44no—
772C22⋊Q8—28no—
773C22⋊Q8—48no—
774C22⋊Q8—48no—
775C22⋊Q8—44no—
776C22⋊Q8—44no—
777C22⋊Q8—44no—
778C22⋊Q8—44no—
779C22⋊Q8—44no—
780#121—44no—
781#121—44no—
782#121—48no—
783#121—44no—
784#121—44no—
785#121—42no—
786#121—42no—
787#121—44no—
788#121—48no—
789#120—42no—
790#120—44no—
791#120—44no—
792C4×Q8—44no—
793C4×Q8—44no—
794C4×D4—24no—
795C4×D4—44no—
796C4×D4—44no—
797C4×D4—44no—
798C4×D4—44no—
799C4×D4—44no—
800C4×D4—42no—
801C4×D4—44no—
802C4×D4—44no—
803C4×D4—42no—
804C4×D4—48no—
805#117—24no—
806#117—42no—
807#117—48no—
808#117—44no—
809#117—44no—
810#117—48no—
811C2×C4⋊C4—24no—
812C2×C4⋊C4—28no—
813C2×C4⋊C4—44no—
814C2×C4⋊C4—44no—
815C2×C4⋊C4—42no—
816C2×C4⋊C4—48no—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C22⋊C4—44no—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2411yescharacteristic
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2411yescharacteristic
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2411yescharacteristic
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2411yescharacteristic
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C42—44no—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2411yescharacteristic
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2412yes—
944C2×C42C2412yes—
945C2×C42C2414yes—
946C2×C42C2412yes—
947#95C2411yescharacteristic
948#95C2412yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2412yes—
956#95C2411yescharacteristic
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2414yes—
965#95C2412yes—
966#95C2411yescharacteristic
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2414yes—
978#95C2412yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2411yescharacteristic
989#95C2412yes—
990#95C2414yes—
991#95C2412yes—
992#95C2414yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
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—41no—
1019C24—42no—
1020C24—42no—
1021C24C2512yes—
1022C24C2511yescharacteristic
1023C24C2512yes—
1024C24C2511yescharacteristic
1025C24C2512yes—
1026#41—816no—
1027C2×Q8—24no—
1028C2×Q8—24no—
1029C2×Q8—24no—
1030C2×Q8—42no—
1031C2×Q8—42no—
1032C2×Q8—44no—
1033C2×Q8—44no—
1034C2×Q8—44no—
1035C2×Q8—44no—
1036C2×Q8—44no—
1037C2×Q8—88no—
1038C2×D4—24no—
1039C2×D4—24no—
1040C2×D4—24no—
1041C2×D4—24no—
1042C2×D4—24no—
1043C2×D4—22no—
1044C2×D4—24no—
1045C2×D4—24no—
1046C2×D4—28no—
1047C2×D4—22no—
1048C2×D4—24no—
1049C2×D4—42no—
1050C2×D4—41no—
1051C2×D4—41no—
1052C2×D4—42no—
1053C2×D4—42no—
1054C2×D4—42no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—42no—
1058C2×D4—44no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—41no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4—44no—
1066C2×D4—44no—
1067C2×D4—42no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C22×C4—28no—
1072C22×C4—24no—
1073C22×C4—28no—
1074C22×C4—28no—
1075C22×C4—24no—
1076C22×C4—22no—
1077C22×C4—22no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—24no—
1081C22×C4—24no—
1082C22×C4—24no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—44no—
1088C22×C4—42no—
1089C22×C4—42no—
1090C22×C4—42no—
1091C22×C4—41no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—42no—
1095C22×C4—42no—
1096C22×C4—42no—
1097C22×C4—44no—
1098C22×C4—42no—
1099C22×C4—42no—
1100C22×C4—42no—
1101C22×C4—42no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4—42no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—42no—
1108C22×C4—44no—
1109C22×C4—42no—
1110C22×C4—88no—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2511yescharacteristic
1114C22×C4C2511yescharacteristic
1115C22×C4C2512yes—
1116C22×C4C2514yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2514yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2514yes—
1125C22×C4C2514yes—
1126C22×C4C2514yes—
1127C22×C4C2514yes—
1128C22×C4C2511yescharacteristic
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2511yescharacteristic
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2511yescharacteristic
1135C4⋊C4—24no—
1136C4⋊C4—22no—
1137C4⋊C4—24no—
1138C4⋊C4—28no—
1139C4⋊C4—28no—
1140C4⋊C4—24no—
1141C4⋊C4—22no—
1142C4⋊C4—28no—
1143C4⋊C4—28no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—41no—
1159C4⋊C4—41no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—44no—
1165C4⋊C4—41no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—41no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—42no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—42no—
1184C4⋊C4—44no—
1185C4⋊C4—42no—
1186C4⋊C4H(5,𝔽2)14yes—
1187C22⋊C4—24no—
1188C22⋊C4—28no—
1189C22⋊C4—22no—
1190C22⋊C4—24no—
1191C22⋊C4—28no—
1192C22⋊C4—24no—
1193C22⋊C4—28no—
1194C22⋊C4—24no—
1195C22⋊C4—24no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—41no—
1200C22⋊C4—44no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—42no—
1208C22⋊C4—42no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—44no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—44no—
1217C22⋊C4—41no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—41no—
1221C22⋊C4—42no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—44no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—44no—
1228C22⋊C4—42no—
1229C22⋊C4—44no—
1230C22⋊C4—42no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—42no—
1234C22⋊C4—44no—
1235C22⋊C4—42no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—42no—
1239C22⋊C4—42no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C42—24no—
1246C42—24no—
1247C42—22no—
1248C42—24no—
1249C42—24no—
1250C42—24no—
1251C42—42no—
1252C42—42no—
1253C42—42no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C42—44no—
1258C42—44no—
1259C42—44no—
1260C42—44no—
1261C42—44no—
1262C42—44no—
1263C23—22no—
1264C23—21no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—21no—
1273C23—22no—
1274C23—21no—
1275C23—22no—
1276C23—22no—
1277C23—24no—
1278C23—22no—
1279C23—22no—
1280C23—22no—
1281C23—22no—
1282C23—22no—
1283C23—22no—
1284C23—21no—
1285C23—22no—
1286C23—24no—
1287C23—22no—
1288C23—22no—
1289C23—21no—
1290C23—44no—
1291C23—84no—
1292C23—82no—
1293C23—82no—
1294C23—84no—
1295C23#58512yes—
1296C23#58514yes—
1297C23C2611yescharacteristic
1298Q8—48no—
1299Q8—84no—
1300Q8—84no—
1301Q8—164no—
1302D4—48no—
1303D4—44no—
1304D4—44no—
1305D4—84no—
1306D4—84no—
1307D4—84no—
1308D4—82no—
1309D4—84no—
1310D4—88no—
1311D4—84no—
1312D4—162no—
1313D4—164no—
1314C2×C4—24no—
1315C2×C4—21no—
1316C2×C4—22no—
1317C2×C4—21no—
1318C2×C4—22no—
1319C2×C4—21no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—21no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—21no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—21no—
1372C2×C4—24no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—416no—
1378C2×C4—48no—
1379C2×C4—44no—
1380C2×C4—48no—
1381C2×C4—44no—
1382C2×C4—84no—
1383C2×C4—84no—
1384C2×C4—84no—
1385C2×C4—88no—
1386C2×C4—84no—
1387C2×C4—82no—
1388C2×C4—84no—
1389C2×C4—84no—
1390C2×C4—164no—
1391C2×C4—162no—
1392C2×C4C2×H(5,𝔽2)14yes—
1393C2×C4C2×H(5,𝔽2)12yes—
1394C2×C4#58514yes—
1395C22—24no—
1396C22—24no—
1397C22—24no—
1398C22—24no—
1399C22—22no—
1400C22—41no—
1401C22—42no—
1402C22—41no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—42no—
1408C22—41no—
1409C22—42no—
1410C22—42no—
1411C22—42no—
1412C22—41no—
1413C22—42no—
1414C22—42no—
1415C22—42no—
1416C22—44no—
1417C22—44no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—41no—
1422C22—42no—
1423C22—42no—
1424C22—88no—
1425C22C22×H(5,𝔽2)11yescharacteristic
1426C22C2×#58512yes—
1427C22C2×#58512yes—
1428C22C2×#58511yescharacteristic
1429C222−1+611yescharacteristic
1430C4—24no—
1431C4—41no—
1432C4—42no—
1433C4—42no—
1434C4—41no—
1435C4—44no—
1436C4—44no—
1437C4—41no—
1438C4—42no—
1439C4—42no—
1440C4—42no—
1441C4—44no—
1442C4—42no—
1443C4—44no—
1444C4—42no—
1445C4—42no—
1446C4—42no—
1447C4—44no—
1448C4—42no—
1449C4—44no—
1450C4—41no—
1451C4—42no—
1452C4—42no—
1453C4#355114yes—
1454C2—44no—
1455C2—42no—
1456C2—81no—
1457C2—82no—
1458C2—82no—
1459C2C2×#355111yescharacteristic
1460C2#6291112yes—
1461C2#6291911yescharacteristic
1462C2#6301711yescharacteristic
1463C2#6302712yes—
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. #59855C2semidirect
2. #59237C2semidirect
3. #59209C2semidirect
4. #59201C2semidirect
5. #59027C2semidirect
6. #56169C2semidirect
7. #56042C2semidirect
8. #55994C2semidirect
9. #54019C2semidirect
10. #53093C2semidirect
11. #52993C2semidirect
12. #52292C2semidirect
13. #47665C2semidirect
14. #47452C2semidirect
15. #45308C2semidirect
16. #45157C2semidirect
17. #45115C2semidirect
18. #44568C2semidirect
19. #42944C2semidirect
20. #42620C2semidirect
21. #41620C2semidirect
22. #41204C2semidirect
23. #39933C2semidirect
24. #39906C2semidirect
25. #39722C2semidirect
26. #39238C2semidirect
27. #38950C2semidirect
28. #36055C2semidirect
29. #35923C2semidirect
32. C2×#547C22semidirect
33. C2×#544C22semidirect
35. #2850C22semidirect
37. #2841C22semidirect
38. #2841C22semidirect
42. #2833C22semidirect
45. #2821C22semidirect
47. #2804C22semidirect
49. #2800C22semidirect
50. #2799C22semidirect
52. #2789C22semidirect
53. #2789C22semidirect
58. #2776C22semidirect
59. #2776C22semidirect
61. #2769C22semidirect
62. #2766C22semidirect
65. #2760C22semidirect
67. #2759C22semidirect
68. #2759C22semidirect
73. #2740C22semidirect
74. #2740C22semidirect
75. #2738C22semidirect
80. #2719C22semidirect
82. #2707C22semidirect
84. #2704C22semidirect
98. #2687C22semidirect
104. #2667C22semidirect
105. #2664C22semidirect
106. #2663C22semidirect
107. #2660C22semidirect
109. #2650C22semidirect
112. #2645C22semidirect
115. #2624C22semidirect
118. #2612C22semidirect
119. #2606C22semidirect
121. #2594C22semidirect
124. #2575C22semidirect
125. #2574C22semidirect
127. #2572C22semidirect
128. #2572C22semidirect
129. #2570C22semidirect
130. #2568C22semidirect
134. #2562C22semidirect
139. #2553C22semidirect
140. #2550C22semidirect
143. #2537C22semidirect
149. #2531C22semidirect
157. #2514C22semidirect
160. #2510C22semidirect
161. #2509C22semidirect
162. #2507C22semidirect
164. #2504C22semidirect
166. #2498C22semidirect
168. #2495C22semidirect
171. #2493C22semidirect
172. #2493C22semidirect
173. #2492C22semidirect
177. #2489C22semidirect
183. #2484C22semidirect
186. #2477C22semidirect
188. #2476C22semidirect
191. #2454C22semidirect
192. #2451C22semidirect
193. #2447C22semidirect
195. #2442C22semidirect
198. #2439C22semidirect
201. #2430C22semidirect
203. #2426C22semidirect
205. #2421C22semidirect
209. #2417C22semidirect
210. #2417C22semidirect
211. #2417C22semidirect
219. #2401C22semidirect
225. #2370C22semidirect
226. #2367C22semidirect
230. #2356C22semidirect
234. #2352C22semidirect
237. #2347C22semidirect
238. #2346C22semidirect
240. #2345C22semidirect
241. #2344C22semidirect
245. #2333C22semidirect
246. #2323C22semidirect
248. #2311C22semidirect
249. C4×C22⋊Q8C22semidirect
255. C2×#389C22semidirect
256. #2283C22semidirect
258. #2275C22semidirect

Maximal subgroups

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

subgroupindex
#598552
#592372
#592092
#592012
#590272
#561692
#560422
#559942
#540192
#530932
#529932
#522922
#476652
#474522
#453082
#451572
#451152
#445682
#429442
#426202
#416202
#412042
#399332
#399062
#397222
#392382
#389502
#360552
#359232