Finite Group Databasebeta

← #8429474

Subgroups — #8429474

Order 512.

3889 conjugacy classes of subgroups.

The subgroup lattice has 1528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59709C212yesmaximal, complemented
2#59459C211yesmaximal, characteristic, complemented
3#59443C212yesmaximal, complemented
4#59259C211yesmaximal, characteristic, complemented
5#59248C211yesmaximal, characteristic, complemented
6#56201C214yesmaximal, complemented
7#54771C214yesmaximal, complemented
8#53093C212yesmaximal, complemented
9#53086C212yesmaximal, complemented
10#53075C212yesmaximal
11#53070C212yesmaximal
12#52871C214yesmaximal
13#42870C212yesmaximal
14#42766C212yesmaximal
15#42764C212yesmaximal, complemented
16#42717C212yesmaximal, complemented
17#42199C214yesmaximal, complemented
18#39754C211yesmaximal, characteristic, complemented
19#39734C211yesmaximal, characteristic, complemented
20#39681C212yesmaximal, complemented
21#39293C212yesmaximal, complemented
22#39182C211yesmaximal, characteristic, complemented
23#39159C211yesmaximal, characteristic, complemented
24#39011C212yesmaximal, complemented
25#39003C212yesmaximal, complemented
26#37630C211yesmaximal, characteristic, complemented
27#37624C211yesmaximal, characteristic, complemented
28#37598C212yesmaximal, complemented
29#37580C212yesmaximal, complemented
30#36481C211yesmaximal, characteristic, complemented
31#36314C211yesmaximal, characteristic, complemented
32#36209C211yesmaximal, characteristic
33#34978C211yesmaximal, characteristic, complemented
34#34803C211yesmaximal, characteristic
35#34793C211yesmaximal, characteristic
36#2864C2212yes—
37#2863C2212yes—
38#2859C2211yescharacteristic
39#2857C2211yescharacteristic
40#2857C2211yescharacteristic
41#2841C2214yes—
42#2839C2214yes—
43#2839C2214yes—
44#2839C2214yes—
45#2838C2214yes—
46#2838C2214yes—
47#2838C2214yes—
48#2837C2214yes—
49#2837C2214yes—
50#2836C2214yes—
51#2833C2214yes—
52#2832C2214yes—
53#2831C2214yes—
54#2831C2214yes—
55#2806C2214yes—
56#2805C2214yes—
57#2805C2214yes—
58#2802C2214yes—
59#2799C2214yes—
60#2798C2214yes—
61#2795C2214yes—
62#2792C2214yes—
63#2791C2214yes—
64#2789C2214yes—
65#2789C2214yes—
66#2783C2214yes—
67#2777C2214yes—
68#2777C2214yes—
69#2776C2214yes—
70#2776C2214yes—
71#2776C2214yes—
72#2774C2214yes—
73#2774C2214yes—
74#2773C2214yes—
75#2772C2214yes—
76#2769C2214yes—
77#2768C2214yes—
78#2766C2214yes—
79#2766C2214yes—
80#2762C2214yes—
81#2762C2214yes—
82#2759C2214yes—
83#2759C2214yes—
84#2758C2214yes—
85#2758C2214yes—
86#2758C2214yes—
87#2755C2214yes—
88#2754C2214yes—
89#2754C2214yes—
90#2747C2214yes—
91#2745C2214yes—
92#2666C2214yes—
93#2666C2214yes—
94#2660C2212yes—
95#2660C2212yes—
96#2655C2214yes—
97#2655C2214yes—
98#2655C2214yes—
99#2655C2214yes—
100#2655C2214yes—
101#2654C2214yes—
102#2654C2214yes—
103#2650C2214yes—
104#2650C2214yes—
105#2647C2212yes—
106#2647C2212yes—
107#2647C2212yes—
108#2645C2212yes—
109#2645C2212yes—
110#2645C2212yes—
111#2642C2212yes—
112#2629C2212yes—
113#2628C2212yes—
114#2621C2212yes—
115#2612C2214yes—
116#2606C2214yes—
117#2604C2214yes—
118#2599C2214yes—
119#2594C2214yes—
120#2586C2214yes—
121#2585C2214yes—
122#2584C2212yes—
123#2584C2212yes—
124#2582C2211yescharacteristic
125#2581C2214yes—
126#2581C2212yes—
127#2571C2212yes—
128#2571C2211yescharacteristic
129#2571C2211yescharacteristic
130#2571C2212yes—
131#2570C2212yes—
132#2570C2212yes—
133#2570C2212yes—
134#2568C2212yes—
135#2568C2212yes—
136#2568C2211yescharacteristic
137#2567C2212yes—
138#2567C2212yes—
139#2565C2214yes—
140#2565C2212yes—
141#2552C2211yescharacteristic
142#2552C2211yescharacteristic
143#2552C2211yescharacteristic
144#2551C2211yescharacteristic
145#2551C2211yescharacteristic
146#2550C2212yes—
147#2550C2212yes—
148#2550C2212yes—
149#2550C2212yes—
150#2546C2211yescharacteristic
151#2536C2212yes—
152#2533C2214yes—
153#2533C2214yes—
154#2533C2214yes—
155#2533C2212yes—
156#2530C2214yes—
157#2530C2212yes—
158#2528C2214yes—
159#2528C2214yes—
160#2528C2212yes—
161#2527C2212yes—
162#2525C2214yes—
163#2523C2212yes—
164#2522C2214yes—
165#2520C2214yes—
166#2517C2212yes—
167#2514C2214yes—
168#2514C2211yescharacteristic
169#2514C2212yes—
170#2514C2212yes—
171#2514C2212yes—
172#2514C2212yes—
173#2511C2214yes—
174#2511C2212yes—
175#2511C2212yes—
176#2511C2211yescharacteristic
177#2509C2212yes—
178#2509C2214yes—
179#2509C2211yescharacteristic
180#2508C2212yes—
181#2508C2212yes—
182#2508C2212yes—
183#2508C2212yes—
184#2508C2212yes—
185#2507C2212yes—
186#2507C2212yes—
187#2507C2212yes—
188#2506C2211yescharacteristic
189#2499C2212yes—
190#2499C2211yescharacteristic
191#2499C2211yescharacteristic
192#2497C2212yes—
193#2496C2211yescharacteristic
194#2495C2212yes—
195#2495C2212yes—
196#2495C2212yes—
197#2495C2212yes—
198#2495C2212yes—
199#2494C2212yes—
200#2494C2212yes—
201#2494C2211yescharacteristic
202#2494C2212yes—
203#2492C2212yes—
204#2492C2212yes—
205#2492C2212yes—
206#2492C2212yes—
207#2492C2211yescharacteristic
208#2489C2211yescharacteristic
209#2489C2212yes—
210#2489C2212yes—
211#2485C2212yes—
212#2485C2211yescharacteristic
213#2485C2212yes—
214#2485C2211yescharacteristic
215#2469C2214yes—
216#2466C2212yes—
217#2462C2214yes—
218#2460C2212yes—
219#2453C2212yes—
220#2453C2212yes—
221#2453C2212yes—
222#2451C2212yes—
223#2451C2212yes—
224#2446C2212yes—
225#2446C2212yes—
226#2441C2211yescharacteristic
227#2441C2212yes—
228#2441C2212yes—
229#2441C2212yes—
230#2441C2212yes—
231#2441C2212yes—
232#2439C2212yes—
233#2439C2212yes—
234#2439C2212yes—
235#2439C2211yescharacteristic
236#2429C2212yes—
237#2423C2212yes—
238#2423C2212yes—
239#2421C2212yes—
240#2421C2212yes—
241#2415C2211yescharacteristic
242#2415C2211yescharacteristic
243#2401C2212yes—
244#2401C2212yes—
245#2398C2212yes—
246#2396C2214yes—
247#2395C2212yes—
248#2370C2212yes—
249#2370C2212yes—
250#2365C2212yes—
251#2365C2211yescharacteristic
252#2365C2211yescharacteristic
253#2365C2212yes—
254#2362C2212yes—
255#2362C2212yes—
256#2356C2214yes—
257#2356C2212yes—
258#2356C2212yes—
259#2355C2211yescharacteristic
260#2355C2212yes—
261#2355C2211yescharacteristic
262Q8×C4⋊C4C2211yescharacteristic
263Q8×C4⋊C4C2212yes—
264Q8×C4⋊C4C2211yescharacteristic
265#2347C2212yes—
266#2346C2212yes—
267#2346C2212yes—
268#2331C2212yes—
269#2331C2212yes—
270#2330C2212yes—
271#2323C2212yes—
272#2320C2214yes—
273C4×C4⋊Q8C2212yes—
274C4×C4⋊Q8C2212yes—
275C4×C4⋊Q8C2212yes—
276C4×C4⋊Q8C2211yescharacteristic
277C4×C4⋊Q8C2211yescharacteristic
278C4×#125C2211yescharacteristic
279C4×#125C2212yes—
280C4×#125C2212yes—
281C4×#125C2212yes—
282C4×#126C2212yes—
283C4×C22⋊Q8C2211yescharacteristic
284C4×C22⋊Q8C2211yescharacteristic
285C4×C22⋊Q8C2211yescharacteristic
286C4×C22⋊Q8C2211yescharacteristic
287#2298C2212yes—
288#2295C2212yes—
289#2295C2211yescharacteristic
290#2295C2212yes—
291#2295C2211yescharacteristic
292#2285C2211yescharacteristic
293#2285C2211yescharacteristic
294#2285C2211yescharacteristic
295#2283C2211yescharacteristic
296C42×D4C2211yescharacteristic
297C4×#117C2211yescharacteristic
298C4×#117C2211yescharacteristic
299C2×C4⋊Q8C2311yescharacteristic
300C2×C4⋊Q8C2312yes—
301C2×C4⋊Q8C2312yes—
302C2×C4⋊Q8C2312yes—
303C2×C4⋊Q8C2311yescharacteristic
304C2×C4⋊Q8C2312yes—
305C2×C4⋊Q8C2312yes—
306C2×#126C2312yes—
307C2×#125C2311yescharacteristic
308C2×#125C2312yes—
309C2×#125C2312yes—
310C2×#125C2312yes—
311C2×#125C2312yes—
312C2×#125C2312yes—
313C2×C22⋊Q8C2311yescharacteristic
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2311yescharacteristic
317C2×C22⋊Q8C2311yescharacteristic
318C2×C22⋊Q8C2311yescharacteristic
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2314yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2314yes—
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2311yescharacteristic
331C2×C4×D4C2311yescharacteristic
332C2×#117C2311yescharacteristic
333C2×#117C2312yes—
334C2×#117C2312yes—
335C2×#117C2312yes—
336C2×#117C2311yescharacteristic
337C2×#117C2311yescharacteristic
338C2×#117C2311yescharacteristic
339C22×C42C2311yescharacteristic
340C22×C42C2311yescharacteristic
341#401C2314yes—
342#401C2314yes—
343#401C2314yes—
344#401C2314yes—
345#401C2314yes—
346#401C2312yes—
347#401C2312yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2312yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2312yes—
374#400C2312yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2314yes—
380#400C2314yes—
381#400C2314yes—
382#400C2314yes—
383#400C2314yes—
384#400C2314yes—
385#400C2314yes—
386#400C2312yes—
387#400C2312yes—
388#400C2312yes—
389#400C2312yes—
390#400C2312yes—
391#400C2312yes—
392#399C2314yes—
393#399C2314yes—
394#399C2314yes—
395#399C2314yes—
396#399C2312yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2312yes—
426#397C2312yes—
427#397C2312yes—
428#397C2314yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2312yes—
434#397C2314yes—
435#397C2314yes—
436#397C2312yes—
437#397C2312yes—
438#397C2314yes—
439#397C2312yes—
440#397C2312yes—
441#397C2312yes—
442#397C2312yes—
443#397C2312yes—
444#397C2312yes—
445#396C2312yes—
446#396C2312yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#395C2314yes—
454#395C2314yes—
455#395C2314yes—
456#395C2314yes—
457#395C2314yes—
458#395C2314yes—
459#395C2314yes—
460#395C2314yes—
461#395C2314yes—
462#395C2314yes—
463#395C2314yes—
464#394C2312yes—
465#394C2312yes—
466#394C2314yes—
467#394C2312yes—
468#394C2312yes—
469#393C2314yes—
470#393C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2312yes—
474#393C2312yes—
475#391C2311yescharacteristic
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2314yes—
480#391C2314yes—
481#391C2311yescharacteristic
482#391C2314yes—
483#391C2314yes—
484#391C2312yes—
485#391C2314yes—
486#391C2312yes—
487#391C2312yes—
488#391C2311yescharacteristic
489#391C2312yes—
490#391C2312yes—
491#391C2314yes—
492#391C2314yes—
493#391C2312yes—
494#391C2312yes—
495#391C2314yes—
496#391C2314yes—
497#391C2312yes—
498#391C2312yes—
499#391C2311yescharacteristic
500#391C2314yes—
501#391C2314yes—
502#391C2312yes—
503#391C2312yes—
504#391C2311yescharacteristic
505#391C2312yes—
506#391C2314yes—
507#391C2314yes—
508#391C2311yescharacteristic
509#391C2312yes—
510#391C2311yescharacteristic
511#391C2311yescharacteristic
512#389C2311yescharacteristic
513#389C2312yes—
514#389C2311yescharacteristic
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2311yescharacteristic
523#389C2312yes—
524#389C2312yes—
525#389C2311yescharacteristic
526#389C2312yes—
527#389C2314yes—
528#389C2312yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2312yes—
533#389C2314yes—
534#389C2314yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2314yes—
540#389C2314yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2312yes—
550#389C2312yes—
551#389C2314yes—
552#389C2312yes—
553#389C2312yes—
554#389C2314yes—
555#389C2312yes—
556#389C2311yescharacteristic
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2314yes—
561#389C2314yes—
562#389C2314yes—
563#389C2311yescharacteristic
564#389C2312yes—
565#389C2312yes—
566#389C2312yes—
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2314yes—
571#389C2311yescharacteristic
572#389C2311yescharacteristic
573#389C2312yes—
574#389C2311yescharacteristic
575#389C2312yes—
576#389C2314yes—
577#389C2314yes—
578#389C2311yescharacteristic
579#389C2311yescharacteristic
580#389C2311yescharacteristic
581#388C2312yes—
582#388C2312yes—
583#388C2312yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2312yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2312yes—
602#388C2312yes—
603#388C2312yes—
604#387C2312yes—
605#387C2312yes—
606#387C2312yes—
607#387C2312yes—
608#387C2314yes—
609#387C2314yes—
610#387C2312yes—
611#387C2314yes—
612#387C2314yes—
613#387C2312yes—
614#387C2312yes—
615#387C2312yes—
616#387C2312yes—
617#387C2312yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2312yes—
636#387C2312yes—
637#387C2314yes—
638#387C2314yes—
639#387C2312yes—
640#387C2312yes—
641#387C2312yes—
642#387C2312yes—
643#387C2312yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2312yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2312yes—
670#387C2312yes—
671#387C2312yes—
672#387C2312yes—
673#387C2312yes—
674#387C2314yes—
675#387C2314yes—
676#387C2312yes—
677#387C2312yes—
678#385C2312yes—
679#385C2312yes—
680#385C2312yes—
681#385C2312yes—
682#384C2311yescharacteristic
683#384C2312yes—
684#384C2312yes—
685#384C2311yescharacteristic
686#384C2312yes—
687#384C2314yes—
688#384C2312yes—
689#384C2311yescharacteristic
690#384C2311yescharacteristic
691#384C2311yescharacteristic
692#384C2312yes—
693#384C2311yescharacteristic
694#383C2312yes—
695#383C2314yes—
696#383C2314yes—
697#383C2314yes—
698#383C2314yes—
699#383C2314yes—
700#383C2314yes—
701#383C2312yes—
702#382C2312yes—
703#382C2312yes—
704#382C2311yescharacteristic
705#382C2312yes—
706#382C2314yes—
707#382C2312yes—
708#382C2311yescharacteristic
709#382C2312yes—
710#382C2312yes—
711#382C2312yes—
712#382C2312yes—
713#382C2312yes—
714#382C2312yes—
715#382C2314yes—
716#382C2314yes—
717#382C2314yes—
718#382C2314yes—
719#382C2312yes—
720#382C2312yes—
721#382C2311yescharacteristic
722#381C2312yes—
723#380C2311yescharacteristic
724#380C2312yes—
725#380C2312yes—
726#380C2312yes—
727#380C2312yes—
728#380C2312yes—
729#380C2312yes—
730#380C2311yescharacteristic
731#380C2312yes—
732#380C2311yescharacteristic
733#380C2311yescharacteristic
734#380C2311yescharacteristic
735#380C2312yes—
736#380C2312yes—
737#380C2311yescharacteristic
738#380C2311yescharacteristic
739#380C2311yescharacteristic
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2312yes—
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2314yes—
745C4×C4⋊C4C2311yescharacteristic
746C4×C4⋊C4C2311yescharacteristic
747C4×C4⋊C4C2311yescharacteristic
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2314yes—
751C4×C4⋊C4C2314yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2311yescharacteristic
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2311yescharacteristic
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2314yes—
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2314yes—
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2314yes—
780C4×C4⋊C4C2314yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2314yes—
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2311yescharacteristic
785C4×C22⋊C4C2311yescharacteristic
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2311yescharacteristic
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2311yescharacteristic
797C4×C22⋊C4C2311yescharacteristic
798C4×C22⋊C4C2311yescharacteristic
799C4×C22⋊C4C2311yescharacteristic
800#376C2314yes—
801#376C2312yes—
802#376C2312yes—
803#376C2312yes—
804#376C2314yes—
805#376C2312yes—
806#376C2312yes—
807C43C2312yes—
808C43C2312yes—
809C43C2311yescharacteristic
810C22×Q8C2411yescharacteristic
811C22×Q8C2412yes—
812C22×Q8C2411yescharacteristic
813C22×Q8C2414yes—
814C22×Q8C2414yes—
815C22×Q8C2412yes—
816C22×D4C2411yescharacteristic
817C23×C4C2411yescharacteristic
818C23×C4C2411yescharacteristic
819C23×C4C2411yescharacteristic
820C23×C4C2411yescharacteristic
821C23×C4C2411yescharacteristic
822C23×C4C2411yescharacteristic
823C4⋊Q8—28no—
824C4⋊Q8—24no—
825C4⋊Q8—44no—
826C4⋊Q8—44no—
827C4⋊Q8—44no—
828C4⋊Q8—42no—
829C4⋊Q8—44no—
830#126—44no—
831#125—24no—
832#125—44no—
833#125—44no—
834#125—44no—
835#125—44no—
836#125—44no—
837C22⋊Q8—24no—
838C22⋊Q8—42no—
839C22⋊Q8—44no—
840C22⋊Q8—44no—
841C22⋊Q8—42no—
842C22⋊Q8—42no—
843C4×Q8—24no—
844C4×Q8—24no—
845C4×Q8—48no—
846C4×Q8—44no—
847C4×Q8—48no—
848C4×Q8—44no—
849C4×Q8—44no—
850C4×Q8—44no—
851C4×Q8—44no—
852C4×Q8—44no—
853C4×D4—42no—
854C4×D4—42no—
855C4×D4—42no—
856#117—24no—
857#117—44no—
858#117—44no—
859#117—42no—
860#117—44no—
861#117—42no—
862#117—42no—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2414yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2412yes—
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2414yes—
933C2×C4⋊C4C2414yes—
934C2×C4⋊C4C2414yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2414yes—
944C2×C4⋊C4C2414yes—
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2411yescharacteristic
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2411yescharacteristic
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2411yescharacteristic
958C2×C22⋊C4C2411yescharacteristic
959C2×C22⋊C4C2411yescharacteristic
960C2×C22⋊C4C2411yescharacteristic
961C2×C22⋊C4C2411yescharacteristic
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2412yes—
973C2×C42—24no—
974C2×C42—24no—
975C2×C42C2414yes—
976C2×C42C2412yes—
977C2×C42C2412yes—
978C2×C42C2412yes—
979C2×C42C2411yescharacteristic
980C2×C42C2411yescharacteristic
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2411yescharacteristic
989C2×C42C2411yescharacteristic
990C2×C42C2412yes—
991C2×C42C2411yescharacteristic
992C2×C42C2411yescharacteristic
993C2×C42C2411yescharacteristic
994C2×C42C2411yescharacteristic
995C2×C42C2411yescharacteristic
996C2×C42C2411yescharacteristic
997C2×C42C2412yes—
998C2×C42C2412yes—
999C2×C42C2412yes—
1000C2×C42C2414yes—
1001C2×C42C2411yescharacteristic
1002C2×C42C2414yes—
1003C2×C42C2414yes—
1004C2×C42C2414yes—
1005C2×C42C2414yes—
1006C2×C42C2414yes—
1007C2×C42C2414yes—
1008C2×C42C2414yes—
1009C2×C42C2411yescharacteristic
1010C2×C42C2412yes—
1011C2×C42C2412yes—
1012C2×C42C2411yescharacteristic
1013#95C2411yescharacteristic
1014#95C2414yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2414yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2411yescharacteristic
1041#95C2411yescharacteristic
1042#95C2411yescharacteristic
1043#95C2411yescharacteristic
1044#95C2411yescharacteristic
1045#95C2412yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2412yes—
1055#95C2412yes—
1056#95C2412yes—
1057#95C2414yes—
1058#95C2412yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2412yes—
1062#95C2414yes—
1063#95C2412yes—
1064#95C2414yes—
1065#95C2412yes—
1066#95C2412yes—
1067#95C2412yes—
1068#95C2412yes—
1069#95C2412yes—
1070#95C2414yes—
1071#95C2412yes—
1072#95C2412yes—
1073#95C2412yes—
1074#95C2414yes—
1075#95C2414yes—
1076#95C2412yes—
1077#95C2414yes—
1078#95C2414yes—
1079#95C2414yes—
1080#95C2412yes—
1081#95C2414yes—
1082#95C2414yes—
1083#95C2414yes—
1084#95C2412yes—
1085#95C2414yes—
1086#95C2414yes—
1087#95C2414yes—
1088#95C2414yes—
1089#95C2412yes—
1090#95C2414yes—
1091#95C2414yes—
1092#95C2412yes—
1093#95C2412yes—
1094#95C2412yes—
1095#95C2414yes—
1096#95C2414yes—
1097#95C2414yes—
1098#95C2414yes—
1099#95C2412yes—
1100#95C2414yes—
1101#95C2414yes—
1102#95C2414yes—
1103#95C2414yes—
1104#95C2414yes—
1105#95C2414yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110#95C2414yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2414yes—
1115C24C2511yescharacteristic
1116C24C2511yescharacteristic
1117C2×Q8—22no—
1118C2×Q8—22no—
1119C2×Q8—22no—
1120C2×Q8—24no—
1121C2×Q8—28no—
1122C2×Q8—22no—
1123C2×Q8—22no—
1124C2×Q8—24no—
1125C2×Q8—24no—
1126C2×Q8—22no—
1127C2×Q8—44no—
1128C2×Q8—42no—
1129C2×Q8—44no—
1130C2×Q8—44no—
1131C2×Q8—44no—
1132C2×Q8—42no—
1133C2×Q8—44no—
1134C2×Q8—42no—
1135C2×D4—41no—
1136C2×D4—41no—
1137C2×D4—41no—
1138C22×C4—22no—
1139C22×C4—22no—
1140C22×C4—22no—
1141C22×C4—22no—
1142C22×C4—22no—
1143C22×C4—22no—
1144C22×C4—22no—
1145C22×C4—22no—
1146C22×C4—22no—
1147C22×C4—22no—
1148C22×C4—22no—
1149C22×C4—22no—
1150C22×C4—22no—
1151C22×C4—22no—
1152C22×C4—22no—
1153C22×C4—41no—
1154C22×C4—41no—
1155C22×C4—41no—
1156C22×C4C2511yescharacteristic
1157C22×C4C2511yescharacteristic
1158C22×C4C2512yes—
1159C22×C4C2512yes—
1160C22×C4C2511yescharacteristic
1161C22×C4C2511yescharacteristic
1162C22×C4C2511yescharacteristic
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2512yes—
1167C22×C4C2512yes—
1168C22×C4C2512yes—
1169C22×C4C2514yes—
1170C22×C4C2514yes—
1171C22×C4C2511yescharacteristic
1172C22×C4C2511yescharacteristic
1173C22×C4C2511yescharacteristic
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2512yes—
1178C22×C4C2512yes—
1179C22×C4C2514yes—
1180C22×C4C2514yes—
1181C22×C4C2511yescharacteristic
1182C22×C4C2512yes—
1183C22×C4C2512yes—
1184C22×C4C2511yescharacteristic
1185C22×C4C2512yes—
1186C22×C4C2511yescharacteristic
1187C22×C4C2511yescharacteristic
1188C22×C4C2511yescharacteristic
1189C4⋊C4—22no—
1190C4⋊C4—22no—
1191C4⋊C4—22no—
1192C4⋊C4—24no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—24no—
1196C4⋊C4—24no—
1197C4⋊C4—22no—
1198C4⋊C4—28no—
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—22no—
1203C4⋊C4—24no—
1204C4⋊C4—22no—
1205C4⋊C4—22no—
1206C4⋊C4—22no—
1207C4⋊C4—22no—
1208C4⋊C4—24no—
1209C4⋊C4—22no—
1210C4⋊C4—22no—
1211C4⋊C4—24no—
1212C4⋊C4—24no—
1213C4⋊C4—22no—
1214C4⋊C4—24no—
1215C4⋊C4—24no—
1216C4⋊C4—24no—
1217C4⋊C4—22no—
1218C4⋊C4—22no—
1219C4⋊C4—42no—
1220C4⋊C4—42no—
1221C4⋊C4—42no—
1222C4⋊C4—44no—
1223C4⋊C4—44no—
1224C4⋊C4—42no—
1225C4⋊C4—44no—
1226C4⋊C4—42no—
1227C4⋊C4—44no—
1228C4⋊C4—42no—
1229C4⋊C4—42no—
1230C4⋊C4—42no—
1231C4⋊C4—42no—
1232C4⋊C4—42no—
1233C4⋊C4—41no—
1234C4⋊C4—41no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—42no—
1238C4⋊C4—42no—
1239C4⋊C4—44no—
1240C4⋊C4—44no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—42no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—42no—
1248C4⋊C4—42no—
1249C4⋊C4—42no—
1250C4⋊C4—44no—
1251C4⋊C4—44no—
1252C4⋊C4—42no—
1253C4⋊C4—42no—
1254C4⋊C4—44no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—42no—
1258C4⋊C4—42no—
1259C4⋊C4—44no—
1260C4⋊C4—44no—
1261C4⋊C4—44no—
1262C4⋊C4—44no—
1263C4⋊C4—44no—
1264C4⋊C4—42no—
1265C4⋊C4—42no—
1266C4⋊C4—44no—
1267C4⋊C4—44no—
1268C4⋊C4—44no—
1269C4⋊C4—42no—
1270C4⋊C4—44no—
1271C4⋊C4—44no—
1272C4⋊C42−1+414yes—
1273C22⋊C4—24no—
1274C22⋊C4—24no—
1275C22⋊C4—22no—
1276C22⋊C4—42no—
1277C22⋊C4—42no—
1278C22⋊C4—42no—
1279C22⋊C4—42no—
1280C22⋊C4—42no—
1281C22⋊C4—44no—
1282C22⋊C4—42no—
1283C22⋊C4—42no—
1284C22⋊C4—44no—
1285C22⋊C4—42no—
1286C22⋊C4—42no—
1287C22⋊C4—41no—
1288C22⋊C4—41no—
1289C22⋊C4—41no—
1290C22⋊C4—41no—
1291C22⋊C4—41no—
1292C22⋊C4—42no—
1293C22⋊C4—42no—
1294C22⋊C4—44no—
1295C22⋊C4—44no—
1296C22⋊C4—42no—
1297C22⋊C4—42no—
1298C22⋊C4—42no—
1299C42—22no—
1300C42—22no—
1301C42—22no—
1302C42—22no—
1303C42—22no—
1304C42—22no—
1305C42—24no—
1306C42—24no—
1307C42—24no—
1308C42—22no—
1309C42—24no—
1310C42—28no—
1311C42—24no—
1312C42—24no—
1313C42—22no—
1314C42—22no—
1315C42—24no—
1316C42—24no—
1317C42—24no—
1318C42—24no—
1319C42—24no—
1320C42—22no—
1321C42—42no—
1322C42—42no—
1323C42—41no—
1324C42—44no—
1325C42—42no—
1326C42—42no—
1327C42—42no—
1328C42—41no—
1329C42—44no—
1330C42—44no—
1331C42—44no—
1332C42—44no—
1333C42—44no—
1334C42—44no—
1335C42—44no—
1336C422−1+414yes—
1337C23—21no—
1338C23—21no—
1339C23—21no—
1340C23—21no—
1341C23—21no—
1342C23—21no—
1343C23—21no—
1344C23—21no—
1345C23—21no—
1346C23—21no—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23C2611yescharacteristic
1352Q8—44no—
1353Q8—44no—
1354Q8—48no—
1355Q8—88no—
1356Q8—88no—
1357Q8—84no—
1358D4—44no—
1359C2×C4—21no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—22no—
1372C2×C4—21no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—21no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—21no—
1383C2×C4—24no—
1384C2×C4—24no—
1385C2×C4—21no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—21no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—21no—
1398C2×C4—22no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—24no—
1409C2×C4—22no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—21no—
1418C2×C4—24no—
1419C2×C4—21no—
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—21no—
1429C2×C4—24no—
1430C2×C4—21no—
1431C2×C4—24no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—21no—
1435C2×C4—22no—
1436C2×C4—21no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—21no—
1440C2×C4—22no—
1441C2×C4—22no—
1442C2×C4—21no—
1443C2×C4—22no—
1444C2×C4—22no—
1445C2×C4—22no—
1446C2×C4—22no—
1447C2×C4—24no—
1448C2×C4—21no—
1449C2×C4—44no—
1450C2×C4—44no—
1451C2×C4—44no—
1452C2×C4—44no—
1453C2×C4—44no—
1454C2×C4—82no—
1455C2×C4C2×2−1+412yes—
1456C2×C4C2×2−1+414yes—
1457C2×C4C2×2−1+412yes—
1458C2×C4C2×2−1+412yes—
1459C2×C4C2×2−1+412yes—
1460C2×C4#58512yes—
1461C2×C4#58512yes—
1462C2×C4#58512yes—
1463C2×C4#58512yes—
1464C22—41no—
1465C22—41no—
1466C22—41no—
1467C22—41no—
1468C22—41no—
1469C22—41no—
1470C22—41no—
1471C22—41no—
1472C22—41no—
1473C22—41no—
1474C22—41no—
1475C22—41no—
1476C22—41no—
1477C22—41no—
1478C22C22×2−1+411yescharacteristic
1479C22C22×2−1+411yescharacteristic
1480C22C2×#58511yescharacteristic
1481C22C2×#58511yescharacteristic
1482C22C2×#58511yescharacteristic
1483C22C2×#58511yescharacteristic
1484C222−1+611yescharacteristic
1485C4—24no—
1486C4—22no—
1487C4—22no—
1488C4—41no—
1489C4—41no—
1490C4—42no—
1491C4—44no—
1492C4—41no—
1493C4—41no—
1494C4—42no—
1495C4—42no—
1496C4—42no—
1497C4—41no—
1498C4—44no—
1499C4—42no—
1500C4—42no—
1501C4—41no—
1502C4—44no—
1503C4—42no—
1504C4—42no—
1505C4—42no—
1506C4—41no—
1507C4—42no—
1508C4—41no—
1509C4—42no—
1510C4—42no—
1511C4—42no—
1512C4—44no—
1513C4—42no—
1514C4—42no—
1515C4—41no—
1516C4#355514yes—
1517C4#356514yes—
1518C2—81no—
1519C2—81no—
1520C2C2×#356511yescharacteristic
1521C2C2×#355511yescharacteristic
1522C2#6276211yescharacteristic
1523C2#6292811yescharacteristic
1524C2#6295311yescharacteristic
1525C2#6296711yescharacteristic
1526C2#6302511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59709C2semidirect
2. #59459C2semidirect
3. #59443C2semidirect
4. #59259C2semidirect
5. #59248C2semidirect
6. #56201C2semidirect
7. #54771C2semidirect
8. #53093C2semidirect
9. #53086C2semidirect
15. #42764C2semidirect
16. #42717C2semidirect
17. #42199C2semidirect
18. #39754C2semidirect
19. #39734C2semidirect
20. #39681C2semidirect
21. #39293C2semidirect
22. #39182C2semidirect
23. #39159C2semidirect
24. #39011C2semidirect
25. #39003C2semidirect
26. #37630C2semidirect
27. #37624C2semidirect
28. #37598C2semidirect
29. #37580C2semidirect
30. #36481C2semidirect
31. #36314C2semidirect
33. #34978C2semidirect

Maximal subgroups

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

subgroupindex
#597092
#594592
#594432
#592592
#592482
#562012
#547712
#530932
#530862
#530752
#530702
#528712
#428702
#427662
#427642
#427172
#421992
#397542
#397342
#396812
#392932
#391822
#391592
#390112
#390032
#376302
#376242
#375982
#375802
#364812
#363142
#362092
#349782
#348032
#347932