Finite Group Databasebeta

← #8429384

Subgroups — #8429384

Order 512.

3885 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#59671C212yesmaximal, complemented
2#59666C211yesmaximal, characteristic, complemented
3#59508C212yesmaximal, complemented
4#59262C211yesmaximal, characteristic, complemented
5#59242C211yesmaximal, characteristic, complemented
6#58536C214yesmaximal, complemented
7#57817C214yesmaximal, complemented
8#53093C212yesmaximal, complemented
9#53086C212yesmaximal, complemented
10#53077C212yesmaximal
11#53072C212yesmaximal
12#52935C214yesmaximal
13#42901C212yesmaximal, complemented
14#42777C212yesmaximal
15#42766C212yesmaximal
16#42748C212yesmaximal, complemented
17#42323C214yesmaximal, complemented
18#39802C212yesmaximal, complemented
19#39626C211yesmaximal, characteristic, complemented
20#39609C211yesmaximal, characteristic, complemented
21#39535C212yesmaximal, complemented
22#39526C212yesmaximal, complemented
23#39296C212yesmaximal, complemented
24#39182C211yesmaximal, characteristic, complemented
25#39149C211yesmaximal, characteristic, complemented
26#37638C212yesmaximal, complemented
27#37630C211yesmaximal, characteristic, complemented
28#37624C211yesmaximal, characteristic, complemented
29#37592C212yesmaximal, complemented
30#36450C211yesmaximal, characteristic, complemented
31#36288C211yesmaximal, characteristic, complemented
32#36210C211yesmaximal, characteristic
33#34978C211yesmaximal, characteristic, complemented
34#34803C211yesmaximal, characteristic
35#34793C211yesmaximal, characteristic
36#2863C2212yes—
37#2862C2212yes—
38#2859C2211yescharacteristic
39#2857C2211yescharacteristic
40#2857C2211yescharacteristic
41#2841C2214yes—
42#2839C2214yes—
43#2839C2214yes—
44#2838C2214yes—
45#2838C2214yes—
46#2837C2214yes—
47#2837C2214yes—
48#2836C2214yes—
49#2836C2214yes—
50#2836C2214yes—
51#2833C2214yes—
52#2833C2214yes—
53#2832C2214yes—
54#2831C2214yes—
55#2810C2214yes—
56#2806C2214yes—
57#2805C2214yes—
58#2805C2214yes—
59#2802C2214yes—
60#2802C2214yes—
61#2802C2214yes—
62#2799C2214yes—
63#2798C2214yes—
64#2798C2214yes—
65#2795C2214yes—
66#2792C2214yes—
67#2789C2214yes—
68#2789C2214yes—
69#2787C2214yes—
70#2783C2214yes—
71#2776C2214yes—
72#2776C2214yes—
73#2775C2214yes—
74#2774C2214yes—
75#2773C2214yes—
76#2773C2214yes—
77#2772C2214yes—
78#2769C2214yes—
79#2767C2214yes—
80#2766C2214yes—
81#2766C2214yes—
82#2762C2214yes—
83#2762C2214yes—
84#2759C2214yes—
85#2759C2214yes—
86#2759C2214yes—
87#2758C2214yes—
88#2758C2214yes—
89#2755C2214yes—
90#2742C2214yes—
91#2739C2214yes—
92#2666C2214yes—
93#2666C2214yes—
94#2660C2212yes—
95#2660C2212yes—
96#2655C2214yes—
97#2654C2214yes—
98#2650C2214yes—
99#2650C2214yes—
100#2647C2212yes—
101#2647C2214yes—
102#2647C2212yes—
103#2647C2212yes—
104#2645C2212yes—
105#2645C2212yes—
106#2645C2214yes—
107#2645C2212yes—
108#2642C2212yes—
109#2637C2214yes—
110#2634C2214yes—
111#2634C2214yes—
112#2629C2212yes—
113#2628C2212yes—
114#2628C2212yes—
115#2612C2214yes—
116#2612C2214yes—
117#2611C2214yes—
118#2605C2214yes—
119#2596C2214yes—
120#2590C2214yes—
121#2588C2214yes—
122#2582C2212yes—
123#2582C2212yes—
124#2582C2211yescharacteristic
125#2581C2212yes—
126#2577C2214yes—
127#2574C2214yes—
128#2571C2212yes—
129#2571C2212yes—
130#2571C2211yescharacteristic
131#2571C2211yescharacteristic
132#2570C2212yes—
133#2570C2212yes—
134#2568C2212yes—
135#2568C2211yescharacteristic
136#2567C2212yes—
137#2567C2212yes—
138#2565C2212yes—
139#2562C2212yes—
140#2552C2211yescharacteristic
141#2552C2212yes—
142#2552C2211yescharacteristic
143#2552C2211yescharacteristic
144#2551C2211yescharacteristic
145#2551C2211yescharacteristic
146#2550C2212yes—
147#2550C2212yes—
148#2550C2212yes—
149#2550C2212yes—
150#2550C2212yes—
151#2546C2211yescharacteristic
152#2533C2212yes—
153#2532C2214yes—
154#2530C2212yes—
155#2529C2214yes—
156#2528C2214yes—
157#2528C2214yes—
158#2528C2214yes—
159#2528C2212yes—
160#2527C2212yes—
161#2524C2214yes—
162#2524C2214yes—
163#2524C2214yes—
164#2523C2212yes—
165#2520C2214yes—
166#2520C2214yes—
167#2519C2214yes—
168#2517C2212yes—
169#2514C2214yes—
170#2514C2212yes—
171#2514C2212yes—
172#2514C2212yes—
173#2514C2211yescharacteristic
174#2514C2212yes—
175#2511C2214yes—
176#2511C2212yes—
177#2511C2212yes—
178#2511C2211yescharacteristic
179#2509C2211yescharacteristic
180#2509C2212yes—
181#2509C2212yes—
182#2509C2212yes—
183#2509C2212yes—
184#2508C2212yes—
185#2508C2212yes—
186#2508C2212yes—
187#2507C2212yes—
188#2507C2212yes—
189#2506C2211yescharacteristic
190#2506C2214yes—
191#2506C2212yes—
192#2506C2212yes—
193#2499C2212yes—
194#2499C2212yes—
195#2499C2211yescharacteristic
196#2499C2211yescharacteristic
197#2497C2212yes—
198#2496C2211yescharacteristic
199#2495C2212yes—
200#2495C2212yes—
201#2495C2212yes—
202#2495C2212yes—
203#2494C2212yes—
204#2494C2212yes—
205#2494C2212yes—
206#2494C2212yes—
207#2494C2211yescharacteristic
208#2492C2212yes—
209#2492C2212yes—
210#2492C2211yescharacteristic
211#2489C2212yes—
212#2489C2212yes—
213#2489C2211yescharacteristic
214#2485C2211yescharacteristic
215#2485C2211yescharacteristic
216#2485C2212yes—
217#2466C2212yes—
218#2460C2212yes—
219#2453C2212yes—
220#2453C2212yes—
221#2451C2212yes—
222#2451C2212yes—
223#2446C2212yes—
224#2441C2212yes—
225#2441C2212yes—
226#2441C2212yes—
227#2441C2211yescharacteristic
228#2439C2212yes—
229#2439C2212yes—
230#2439C2212yes—
231#2439C2212yes—
232#2439C2211yescharacteristic
233#2429C2212yes—
234#2429C2212yes—
235#2423C2212yes—
236#2423C2212yes—
237#2423C2212yes—
238#2421C2212yes—
239#2421C2212yes—
240#2415C2212yes—
241#2415C2211yescharacteristic
242#2415C2211yescharacteristic
243#2401C2212yes—
244#2401C2212yes—
245#2398C2212yes—
246#2396C2214yes—
247#2395C2212yes—
248#2370C2212yes—
249#2370C2214yes—
250#2370C2212yes—
251#2370C2212yes—
252#2369C2212yes—
253#2365C2211yescharacteristic
254#2365C2211yescharacteristic
255#2362C2212yes—
256#2362C2212yes—
257#2356C2212yes—
258#2356C2212yes—
259#2355C2211yescharacteristic
260#2355C2212yes—
261#2355C2211yescharacteristic
262#2351C2212yes—
263Q8×C4⋊C4C2211yescharacteristic
264Q8×C4⋊C4C2211yescharacteristic
265#2347C2212yes—
266#2347C2212yes—
267#2346C2212yes—
268#2331C2212yes—
269#2331C2212yes—
270#2327C2212yes—
271#2323C2212yes—
272#2320C2214yes—
273C4×C4⋊Q8C2212yes—
274C4×C4⋊Q8C2211yescharacteristic
275C4×C4⋊Q8C2211yescharacteristic
276C4×C4⋊Q8C2212yes—
277C4×#125C2211yescharacteristic
278C4×#125C2212yes—
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#2295C2212yes—
290#2295C2211yescharacteristic
291#2295C2211yescharacteristic
292#2285C2211yescharacteristic
293#2285C2211yescharacteristic
294#2285C2211yescharacteristic
295#2283C2211yescharacteristic
296C42×D4C2211yescharacteristic
297C4×#117C2211yescharacteristic
298C4×#117C2211yescharacteristic
299C2×C4⋊Q8C2311yescharacteristic
300C2×C4⋊Q8C2311yescharacteristic
301C2×C4⋊Q8C2312yes—
302C2×C4⋊Q8C2312yes—
303C2×C4⋊Q8C2312yes—
304C2×C4⋊Q8C2312yes—
305C2×C4⋊Q8C2312yes—
306C2×#126C2312yes—
307C2×#125C2312yes—
308C2×#125C2311yescharacteristic
309C2×#125C2312yes—
310C2×#125C2312yes—
311C2×#125C2312yes—
312C2×#125C2312yes—
313C2×#125C2314yes—
314C2×C22⋊Q8C2311yescharacteristic
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2311yescharacteristic
318C2×C22⋊Q8C2311yescharacteristic
319C2×C22⋊Q8C2311yescharacteristic
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2314yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2312yes—
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#400C2312yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2312yes—
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2314yes—
380#400C2314yes—
381#400C2312yes—
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#398C2312yes—
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#398C2314yes—
426#397C2312yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2312yes—
433#397C2312yes—
434#397C2312yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2312yes—
439#397C2312yes—
440#397C2312yes—
441#397C2312yes—
442#397C2312yes—
443#397C2312yes—
444#397C2312yes—
445#396C2314yes—
446#396C2312yes—
447#396C2314yes—
448#396C2312yes—
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#394C2314yes—
465#394C2312yes—
466#394C2312yes—
467#394C2312yes—
468#394C2312yes—
469#393C2314yes—
470#393C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2312yes—
474#393C2312yes—
475#391C2314yes—
476#391C2312yes—
477#391C2314yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2314yes—
484#391C2311yescharacteristic
485#391C2314yes—
486#391C2312yes—
487#391C2314yes—
488#391C2312yes—
489#391C2312yes—
490#391C2314yes—
491#391C2314yes—
492#391C2314yes—
493#391C2314yes—
494#391C2311yescharacteristic
495#391C2314yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2314yes—
500#391C2311yescharacteristic
501#391C2312yes—
502#391C2312yes—
503#391C2311yescharacteristic
504#391C2314yes—
505#391C2311yescharacteristic
506#391C2314yes—
507#391C2312yes—
508#391C2312yes—
509#391C2314yes—
510#391C2311yescharacteristic
511#391C2311yescharacteristic
512#391C2311yescharacteristic
513#389C2311yescharacteristic
514#389C2312yes—
515#389C2311yescharacteristic
516#389C2312yes—
517#389C2311yescharacteristic
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2314yes—
526#389C2312yes—
527#389C2314yes—
528#389C2311yescharacteristic
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2311yescharacteristic
534#389C2311yescharacteristic
535#389C2314yes—
536#389C2312yes—
537#389C2314yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2311yescharacteristic
545#389C2314yes—
546#389C2312yes—
547#389C2312yes—
548#389C2314yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2314yes—
553#389C2314yes—
554#389C2314yes—
555#389C2314yes—
556#389C2314yes—
557#389C2312yes—
558#389C2314yes—
559#389C2314yes—
560#389C2312yes—
561#389C2314yes—
562#389C2314yes—
563#389C2312yes—
564#389C2312yes—
565#389C2312yes—
566#389C2312yes—
567#389C2312yes—
568#389C2314yes—
569#389C2314yes—
570#389C2312yes—
571#389C2312yes—
572#389C2312yes—
573#389C2311yescharacteristic
574#389C2314yes—
575#389C2314yes—
576#389C2312yes—
577#389C2311yescharacteristic
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#388C2312yes—
599#388C2314yes—
600#388C2314yes—
601#388C2312yes—
602#388C2312yes—
603#388C2314yes—
604#387C2312yes—
605#387C2312yes—
606#387C2312yes—
607#387C2314yes—
608#387C2314yes—
609#387C2312yes—
610#387C2312yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2312yes—
616#387C2312yes—
617#387C2312yes—
618#387C2312yes—
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#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2312yes—
645#387C2312yes—
646#387C2312yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2312yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2312yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2312yes—
667#387C2312yes—
668#387C2312yes—
669#387C2312yes—
670#387C2312yes—
671#387C2314yes—
672#387C2312yes—
673#387C2312yes—
674#387C2312yes—
675#387C2312yes—
676#385C2312yes—
677#385C2312yes—
678#385C2312yes—
679#385C2312yes—
680#384C2312yes—
681#384C2312yes—
682#384C2311yescharacteristic
683#384C2311yescharacteristic
684#384C2311yescharacteristic
685#384C2312yes—
686#384C2314yes—
687#384C2312yes—
688#384C2311yescharacteristic
689#384C2312yes—
690#384C2311yescharacteristic
691#384C2311yescharacteristic
692#383C2312yes—
693#383C2314yes—
694#383C2314yes—
695#383C2314yes—
696#383C2314yes—
697#383C2314yes—
698#383C2312yes—
699#383C2314yes—
700#382C2312yes—
701#382C2312yes—
702#382C2312yes—
703#382C2311yescharacteristic
704#382C2312yes—
705#382C2312yes—
706#382C2312yes—
707#382C2311yescharacteristic
708#382C2311yescharacteristic
709#382C2312yes—
710#382C2312yes—
711#382C2312yes—
712#382C2314yes—
713#382C2314yes—
714#382C2314yes—
715#382C2314yes—
716#382C2314yes—
717#382C2312yes—
718#382C2314yes—
719#382C2312yes—
720#382C2312yes—
721#381C2312yes—
722#380C2312yes—
723#380C2312yes—
724#380C2312yes—
725#380C2312yes—
726#380C2312yes—
727#380C2312yes—
728#380C2312yes—
729#380C2312yes—
730#380C2311yescharacteristic
731#380C2311yescharacteristic
732#380C2311yescharacteristic
733#380C2311yescharacteristic
734#380C2312yes—
735#380C2311yescharacteristic
736#380C2311yescharacteristic
737#380C2311yescharacteristic
738#380C2311yescharacteristic
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2314yes—
743C4×C4⋊C4C2311yescharacteristic
744C4×C4⋊C4C2311yescharacteristic
745C4×C4⋊C4C2311yescharacteristic
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2314yes—
750C4×C4⋊C4C2314yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2311yescharacteristic
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2314yes—
758C4×C4⋊C4C2314yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2314yes—
775C4×C4⋊C4C2314yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2314yes—
781C4×C4⋊C4C2314yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2311yescharacteristic
785C4×C22⋊C4C2311yescharacteristic
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2311yescharacteristic
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×Q8C2412yes—
814C22×Q8C2414yes—
815C22×Q8C2414yes—
816C22×D4C2411yescharacteristic
817C23×C4C2411yescharacteristic
818C23×C4C2411yescharacteristic
819C23×C4C2411yescharacteristic
820C23×C4C2411yescharacteristic
821C23×C4C2411yescharacteristic
822C23×C4C2411yescharacteristic
823C4⋊Q8—24no—
824C4⋊Q8—24no—
825C4⋊Q8—44no—
826C4⋊Q8—44no—
827C4⋊Q8—44no—
828C4⋊Q8—44no—
829C4⋊Q8—44no—
830#126—44no—
831#125—28no—
832#125—48no—
833#125—44no—
834#125—44no—
835#125—42no—
836#125—44no—
837#125—44no—
838C22⋊Q8—24no—
839C22⋊Q8—42no—
840C22⋊Q8—44no—
841C22⋊Q8—42no—
842C22⋊Q8—44no—
843C22⋊Q8—42no—
844C4×Q8—24no—
845C4×Q8—24no—
846C4×Q8—48no—
847C4×Q8—44no—
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⋊C4C2412yes—
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2414yes—
928C2×C4⋊C4C2414yes—
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2412yes—
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2414yes—
934C2×C4⋊C4C2414yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2414yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
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×C42C2411yescharacteristic
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2412yes—
989C2×C42C2412yes—
990C2×C42C2411yescharacteristic
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×C42C2411yescharacteristic
1008C2×C42C2412yes—
1009C2×C42C2412yes—
1010C2×C42C2414yes—
1011C2×C42C2414yes—
1012C2×C42C2411yescharacteristic
1013#95C2412yes—
1014#95C2412yes—
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#95C2414yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2411yescharacteristic
1042#95C2411yescharacteristic
1043#95C2411yescharacteristic
1044#95C2411yescharacteristic
1045#95C2411yescharacteristic
1046#95C2411yescharacteristic
1047#95C2412yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2412yes—
1055#95C2412yes—
1056#95C2414yes—
1057#95C2412yes—
1058#95C2412yes—
1059#95C2412yes—
1060#95C2414yes—
1061#95C2412yes—
1062#95C2414yes—
1063#95C2414yes—
1064#95C2412yes—
1065#95C2412yes—
1066#95C2414yes—
1067#95C2412yes—
1068#95C2412yes—
1069#95C2412yes—
1070#95C2412yes—
1071#95C2412yes—
1072#95C2412yes—
1073#95C2414yes—
1074#95C2414yes—
1075#95C2414yes—
1076#95C2414yes—
1077#95C2414yes—
1078#95C2412yes—
1079#95C2414yes—
1080#95C2414yes—
1081#95C2414yes—
1082#95C2414yes—
1083#95C2414yes—
1084#95C2414yes—
1085#95C2412yes—
1086#95C2414yes—
1087#95C2414yes—
1088#95C2414yes—
1089#95C2412yes—
1090#95C2412yes—
1091#95C2412yes—
1092#95C2414yes—
1093#95C2414yes—
1094#95C2412yes—
1095#95C2412yes—
1096#95C2412yes—
1097#95C2414yes—
1098#95C2414yes—
1099#95C2414yes—
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—24no—
1122C2×Q8—22no—
1123C2×Q8—22no—
1124C2×Q8—24no—
1125C2×Q8—24no—
1126C2×Q8—22no—
1127C2×Q8—42no—
1128C2×Q8—44no—
1129C2×Q8—44no—
1130C2×Q8—44no—
1131C2×Q8—42no—
1132C2×Q8—44no—
1133C2×Q8—44no—
1134C2×Q8—44no—
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×C4C2512yes—
1158C22×C4C2511yescharacteristic
1159C22×C4C2511yescharacteristic
1160C22×C4C2512yes—
1161C22×C4C2511yescharacteristic
1162C22×C4C2512yes—
1163C22×C4C2511yescharacteristic
1164C22×C4C2511yescharacteristic
1165C22×C4C2512yes—
1166C22×C4C2512yes—
1167C22×C4C2512yes—
1168C22×C4C2514yes—
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2512yes—
1172C22×C4C2511yescharacteristic
1173C22×C4C2512yes—
1174C22×C4C2514yes—
1175C22×C4C2514yes—
1176C22×C4C2512yes—
1177C22×C4C2512yes—
1178C22×C4C2511yescharacteristic
1179C22×C4C2512yes—
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—28no—
1196C4⋊C4—28no—
1197C4⋊C4—24no—
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—22no—
1202C4⋊C4—22no—
1203C4⋊C4—24no—
1204C4⋊C4—22no—
1205C4⋊C4—24no—
1206C4⋊C4—22no—
1207C4⋊C4—22no—
1208C4⋊C4—22no—
1209C4⋊C4—22no—
1210C4⋊C4—22no—
1211C4⋊C4—22no—
1212C4⋊C4—24no—
1213C4⋊C4—24no—
1214C4⋊C4—22no—
1215C4⋊C4—24no—
1216C4⋊C4—24no—
1217C4⋊C4—24no—
1218C4⋊C4—22no—
1219C4⋊C4—42no—
1220C4⋊C4—42no—
1221C4⋊C4—42no—
1222C4⋊C4—42no—
1223C4⋊C4—42no—
1224C4⋊C4—44no—
1225C4⋊C4—42no—
1226C4⋊C4—42no—
1227C4⋊C4—42no—
1228C4⋊C4—42no—
1229C4⋊C4—42no—
1230C4⋊C4—41no—
1231C4⋊C4—41no—
1232C4⋊C4—42no—
1233C4⋊C4—42no—
1234C4⋊C4—44no—
1235C4⋊C4—42no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—44no—
1240C4⋊C4—44no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—42no—
1244C4⋊C4—42no—
1245C4⋊C4—42no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—42no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—44no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—44no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—42no—
1258C4⋊C4—42no—
1259C4⋊C4—42no—
1260C4⋊C4—44no—
1261C4⋊C4—44no—
1262C4⋊C4—42no—
1263C4⋊C4—42no—
1264C4⋊C4—42no—
1265C4⋊C4—42no—
1266C4⋊C4—44no—
1267C4⋊C4—44no—
1268C4⋊C4—44no—
1269C4⋊C4—44no—
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—42no—
1282C22⋊C4—44no—
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—44no—
1294C22⋊C4—42no—
1295C22⋊C4—42no—
1296C22⋊C4—44no—
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—24no—
1309C42—22no—
1310C42—28no—
1311C42—24no—
1312C42—24no—
1313C42—22no—
1314C42—22no—
1315C42—24no—
1316C42—22no—
1317C42—24no—
1318C42—24no—
1319C42—24no—
1320C42—24no—
1321C42—42no—
1322C42—42no—
1323C42—44no—
1324C42—41no—
1325C42—44no—
1326C42—44no—
1327C42—42no—
1328C42—42no—
1329C42—42no—
1330C42—41no—
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—84no—
1356Q8—88no—
1357Q8—164no—
1358D4—44no—
1359C2×C4—21no—
1360C2×C4—22no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—22no—
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—22no—
1373C2×C4—21no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—21no—
1380C2×C4—22no—
1381C2×C4—24no—
1382C2×C4—21no—
1383C2×C4—24no—
1384C2×C4—22no—
1385C2×C4—21no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—22no—
1392C2×C4—24no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—21no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—21no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—22no—
1413C2×C4—24no—
1414C2×C4—22no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—22no—
1418C2×C4—24no—
1419C2×C4—22no—
1420C2×C4—24no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—24no—
1425C2×C4—21no—
1426C2×C4—24no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—24no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—22no—
1440C2×C4—22no—
1441C2×C4—24no—
1442C2×C4—22no—
1443C2×C4—21no—
1444C2×C4—22no—
1445C2×C4—21no—
1446C2×C4—22no—
1447C2×C4—22no—
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—22no—
1486C4—22no—
1487C4—24no—
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—42no—
1502C4—41no—
1503C4—42no—
1504C4—44no—
1505C4—42no—
1506C4—42no—
1507C4—41no—
1508C4—42no—
1509C4—42no—
1510C4—41no—
1511C4—41no—
1512C4—42no—
1513C4—44no—
1514C4—42no—
1515C4—42no—
1516C4#355514yes—
1517C4#356514yes—
1518C2—81no—
1519C2—81no—
1520C2C2×#356511yescharacteristic
1521C2C2×#355511yescharacteristic
1522C2#6276211yescharacteristic
1523C2#6292811yescharacteristic
1524C2#6295011yescharacteristic
1525C2#6296811yescharacteristic
1526C2#6303411yescharacteristic
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. #59671C2semidirect
2. #59666C2semidirect
3. #59508C2semidirect
4. #59262C2semidirect
5. #59242C2semidirect
6. #58536C2semidirect
7. #57817C2semidirect
8. #53093C2semidirect
9. #53086C2semidirect
13. #42901C2semidirect
16. #42748C2semidirect
17. #42323C2semidirect
18. #39802C2semidirect
19. #39626C2semidirect
20. #39609C2semidirect
21. #39535C2semidirect
22. #39526C2semidirect
23. #39296C2semidirect
24. #39182C2semidirect
25. #39149C2semidirect
26. #37638C2semidirect
27. #37630C2semidirect
28. #37624C2semidirect
29. #37592C2semidirect
30. #36450C2semidirect
31. #36288C2semidirect
33. #34978C2semidirect

Maximal subgroups

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

subgroupindex
#596712
#596662
#595082
#592622
#592422
#585362
#578172
#530932
#530862
#530772
#530722
#529352
#429012
#427772
#427662
#427482
#423232
#398022
#396262
#396092
#395352
#395262
#392962
#391822
#391492
#376382
#376302
#376242
#375922
#364502
#362882
#362102
#349782
#348032
#347932