Finite Group Databasebeta

← #8459227

Subgroups — #8459227

Order 512.

3941 conjugacy classes of subgroups.

The subgroup lattice has 1518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59436C211yesmaximal, characteristic
3#59435C211yesmaximal, characteristic
4#58813C214yesmaximal, complemented
5#57102C214yesmaximal, complemented
6#56754C214yesmaximal, complemented
7#53086C212yesmaximal, complemented
8#52996C212yesmaximal, complemented
9#52047C214yesmaximal, complemented
10#46343C212yesmaximal
11#46116C212yesmaximal, complemented
12#45414C212yesmaximal, complemented
13#44956C212yesmaximal, complemented
14#42830C212yesmaximal
15#42667C212yesmaximal, complemented
16#42626C212yesmaximal
17#42573C212yesmaximal, complemented
18#40075C212yesmaximal, complemented
19#39974C212yesmaximal, complemented
20#39753C211yesmaximal, characteristic, complemented
21#39633C211yesmaximal, characteristic
22#39498C211yesmaximal, characteristic
23#39296C212yesmaximal, complemented
24#38978C211yesmaximal, characteristic
25#38225C212yesmaximal
26#37638C211yesmaximal, characteristic, complemented
27#37413C212yesmaximal, complemented
28#37313C212yesmaximal, complemented
29#36584C211yesmaximal, characteristic, complemented
30#36563C211yesmaximal, characteristic, complemented
31#36285C211yesmaximal, characteristic, complemented
32#35208C211yesmaximal, characteristic, complemented
33#35185C211yesmaximal, characteristic
34#34951C211yesmaximal, characteristic, complemented
35#34902C211yesmaximal, characteristic
36#2868C2211yescharacteristic
37#2864C2212yes—
38#2863C2212yes—
39#2863C2212yes—
40#2860C2212yes—
41#2859C2212yes—
42#2859C2211yescharacteristic
43#2859C2211yescharacteristic
44#2859C2212yes—
45#2839C2214yes—
46#2839C2214yes—
47#2839C2214yes—
48#2839C2214yes—
49#2838C2214yes—
50#2836C2214yes—
51#2833C2214yes—
52#2831C2214yes—
53#2810C2214yes—
54#2807C2214yes—
55#2807C2214yes—
56#2806C2214yes—
57#2805C2214yes—
58#2802C2214yes—
59#2798C2214yes—
60#2792C2214yes—
61#2791C2214yes—
62#2791C2214yes—
63#2790C2214yes—
64#2788C2214yes—
65#2787C2214yes—
66#2777C2214yes—
67#2776C2214yes—
68#2776C2214yes—
69#2775C2214yes—
70#2774C2214yes—
71#2773C2214yes—
72#2772C2214yes—
73#2770C2214yes—
74#2769C2214yes—
75#2768C2214yes—
76#2766C2214yes—
77#2766C2214yes—
78#2766C2214yes—
79#2765C2214yes—
80#2764C2214yes—
81#2762C2214yes—
82#2762C2214yes—
83#2759C2214yes—
84#2758C2214yes—
85#2758C2214yes—
86#2754C2214yes—
87#2745C2214yes—
88#2744C2214yes—
89#2729C2214yes—
90#2726C2214yes—
91#2725C2214yes—
92#2722C2214yes—
93#2721C2214yes—
94#2720C2214yes—
95#2719C2214yes—
96#2719C2214yes—
97#2716C2214yes—
98#2713C2214yes—
99#2713C2214yes—
100#2704C2214yes—
101#2689C2214yes—
102#2666C2214yes—
103#2666C2214yes—
104#2664C2214yes—
105#2660C2212yes—
106#2654C2214yes—
107#2654C2214yes—
108#2650C2214yes—
109#2647C2212yes—
110#2647C2212yes—
111#2647C2212yes—
112#2645C2212yes—
113#2645C2212yes—
114#2644C2212yes—
115#2634C2214yes—
116#2628C2212yes—
117#2625C2214yes—
118#2612C2214yes—
119#2611C2214yes—
120#2606C2214yes—
121#2606C2214yes—
122#2605C2214yes—
123#2604C2214yes—
124#2599C2214yes—
125#2596C2214yes—
126#2596C2212yes—
127#2594C2212yes—
128#2592C2211yescharacteristic
129#2590C2214yes—
130#2585C2212yes—
131#2585C2212yes—
132#2584C2214yes—
133#2584C2212yes—
134#2582C2211yescharacteristic
135#2582C2212yes—
136#2582C2212yes—
137#2582C2211yescharacteristic
138#2582C2211yescharacteristic
139#2582C2212yes—
140#2581C2211yescharacteristic
141#2580C2212yes—
142#2571C2212yes—
143#2571C2211yescharacteristic
144#2571C2211yescharacteristic
145#2571C2212yes—
146#2571C2212yes—
147#2570C2211yescharacteristic
148#2570C2212yes—
149#2570C2212yes—
150#2570C2212yes—
151#2568C2211yescharacteristic
152#2567C2211yescharacteristic
153#2567C2211yescharacteristic
154#2567C2212yes—
155#2567C2211yescharacteristic
156#2565C2212yes—
157#2565C2212yes—
158#2563C2211yescharacteristic
159#2552C2212yes—
160#2552C2212yes—
161#2552C2211yescharacteristic
162#2552C2212yes—
163#2552C2211yescharacteristic
164#2552C2212yes—
165#2550C2212yes—
166#2550C2212yes—
167#2550C2212yes—
168#2546C2211yescharacteristic
169#2545C2211yescharacteristic
170#2538C2211yescharacteristic
171#2532C2214yes—
172#2528C2214yes—
173#2525C2212yes—
174#2524C2214yes—
175#2519C2214yes—
176#2514C2212yes—
177#2514C2212yes—
178#2514C2214yes—
179#2514C2211yescharacteristic
180#2514C2212yes—
181#2513C2212yes—
182#2512C2212yes—
183#2512C2211yescharacteristic
184#2511C2212yes—
185#2511C2212yes—
186#2509C2212yes—
187#2509C2212yes—
188#2509C2212yes—
189#2509C2212yes—
190#2509C2214yes—
191#2509C2212yes—
192#2509C2211yescharacteristic
193#2509C2214yes—
194#2509C2211yescharacteristic
195#2507C2212yes—
196#2507C2212yes—
197#2507C2212yes—
198#2507C2212yes—
199#2507C2212yes—
200#2507C2212yes—
201#2506C2212yes—
202#2506C2212yes—
203#2506C2212yes—
204#2506C2212yes—
205#2502C2212yes—
206#2499C2212yes—
207#2497C2212yes—
208#2496C2212yes—
209#2496C2212yes—
210#2495C2212yes—
211#2495C2212yes—
212#2495C2212yes—
213#2494C2212yes—
214#2492C2212yes—
215#2489C2212yes—
216#2478C2214yes—
217#2475C2214yes—
218#2469C2214yes—
219#2469C2212yes—
220#2462C2214yes—
221#2454C2212yes—
222#2453C2211yescharacteristic
223#2453C2212yes—
224#2453C2211yescharacteristic
225#2452C2212yes—
226#2451C2212yes—
227#2451C2212yes—
228#2451C2212yes—
229#2451C2212yes—
230#2448C2212yes—
231#2448C2212yes—
232#2448C2211yescharacteristic
233#2447C2212yes—
234#2446C2212yes—
235#2446C2211yescharacteristic
236#2446C2212yes—
237#2442C2212yes—
238#2442C2212yes—
239#2441C2212yes—
240#2441C2212yes—
241#2441C2212yes—
242#2440C2212yes—
243#2421C2212yes—
244#2402C2212yes—
245#2402C2212yes—
246#2401C2212yes—
247#2396C2212yes—
248#2383C2214yes—
249#2370C2212yes—
250#2369C2212yes—
251#2369C2212yes—
252#2365C2212yes—
253#2356C2212yes—
254#2356C2212yes—
255#2355C2211yescharacteristic
256#2355C2212yes—
257#2354C2211yescharacteristic
258#2354C2212yes—
259#2351C2212yes—
260#2351C2212yes—
261Q8×C4⋊C4C2211yescharacteristic
262Q8×C4⋊C4C2211yescharacteristic
263Q8×C4⋊C4C2212yes—
264Q8×C4⋊C4C2211yescharacteristic
265D4×C4⋊C4C2211yescharacteristic
266#2346C2212yes—
267#2344C2212yes—
268#2331C2212yes—
269#2330C2212yes—
270#2330C2214yes—
271#2326C2212yes—
272#2323C2212yes—
273#2320C2212yes—
274#2320C2212yes—
275#2317C2212yes—
276#2314C2212yes—
277C4×C4⋊Q8C2211yescharacteristic
278C4×C4⋊Q8C2212yes—
279C4×C4⋊Q8C2211yescharacteristic
280C4×C4⋊Q8C2211yescharacteristic
281C4×C4⋊Q8C2211yescharacteristic
282C4×C4⋊Q8C2211yescharacteristic
283C4×#125C2211yescharacteristic
284C4×#125C2211yescharacteristic
285C4×#125C2212yes—
286C4×#126C2212yes—
287C4×#124C2211yescharacteristic
288C4×#124C2211yescharacteristic
289#2298C2212yes—
290#2295C2211yescharacteristic
291#2295C2211yescharacteristic
292#2295C2212yes—
293#2295C2212yes—
294#2295C2211yescharacteristic
295#2293C2211yescharacteristic
296C42×Q8C2211yescharacteristic
297C42×Q8C2211yescharacteristic
298C42×Q8C2211yescharacteristic
299C2×C4⋊Q8C2311yescharacteristic
300C2×C4⋊Q8C2311yescharacteristic
301C2×C4⋊Q8C2311yescharacteristic
302C2×C4⋊Q8C2312yes—
303C2×C4⋊Q8C2312yes—
304C2×C4⋊Q8C2312yes—
305C2×C4⋊Q8C2312yes—
306C2×#126C2312yes—
307C2×#126C2314yes—
308C2×#126C2314yes—
309C2×#125C2312yes—
310C2×#125C2311yescharacteristic
311C2×#125C2311yescharacteristic
312C2×#125C2312yes—
313C2×#125C2312yes—
314C2×#125C2314yes—
315C2×#125C2314yes—
316C2×#125C2314yes—
317C2×#125C2314yes—
318C2×#124C2311yescharacteristic
319C2×#124C2311yescharacteristic
320C2×C22⋊Q8C2312yes—
321C2×C22⋊Q8C2314yes—
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2311yescharacteristic
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2312yes—
336C2×C4×Q8C2311yescharacteristic
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2312yes—
339C2×C4×D4C2311yescharacteristic
340C2×C4×D4C2312yes—
341C2×#117C2312yes—
342C2×#117C2312yes—
343C2×#117C2314yes—
344C22×C4⋊C4C2312yes—
345#401C2314yes—
346#401C2314yes—
347#401C2312yes—
348#401C2314yes—
349#400C2312yes—
350#400C2312yes—
351#400C2312yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2312yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2312yes—
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#400C2312yes—
384#400C2312yes—
385#400C2312yes—
386#400C2314yes—
387#400C2312yes—
388#400C2312yes—
389#400C2314yes—
390#399C2314yes—
391#399C2314yes—
392#399C2312yes—
393#399C2314yes—
394#399C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2312yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2312yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2312yes—
412#398C2312yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2312yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2312yes—
427#398C2312yes—
428#398C2312yes—
429#398C2312yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2312yes—
434#398C2314yes—
435#398C2314yes—
436#397C2312yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2312yes—
442#397C2312yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2312yes—
452#396C2312yes—
453#396C2314yes—
454#396C2314yes—
455#396C2312yes—
456#396C2314yes—
457#395C2314yes—
458#395C2314yes—
459#395C2314yes—
460#395C2314yes—
461#395C2314yes—
462#395C2314yes—
463#395C2312yes—
464#395C2314yes—
465#395C2314yes—
466#395C2314yes—
467#393C2314yes—
468#393C2314yes—
469#393C2314yes—
470#393C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2311yescharacteristic
474#391C2311yescharacteristic
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2311yescharacteristic
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2312yes—
485#391C2314yes—
486#391C2312yes—
487#391C2311yescharacteristic
488#391C2311yescharacteristic
489#391C2312yes—
490#391C2314yes—
491#391C2311yescharacteristic
492#391C2312yes—
493#391C2312yes—
494#391C2311yescharacteristic
495#391C2314yes—
496#391C2314yes—
497#391C2311yescharacteristic
498#391C2311yescharacteristic
499#391C2314yes—
500#391C2314yes—
501#391C2311yescharacteristic
502#391C2314yes—
503#391C2314yes—
504#391C2312yes—
505#390C2312yes—
506#390C2311yescharacteristic
507#390C2312yes—
508#390C2312yes—
509#390C2311yescharacteristic
510#390C2311yescharacteristic
511#390C2311yescharacteristic
512#389C2311yescharacteristic
513#389C2312yes—
514#389C2311yescharacteristic
515#389C2312yes—
516#389C2311yescharacteristic
517#389C2311yescharacteristic
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2311yescharacteristic
532#389C2311yescharacteristic
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2311yescharacteristic
546#389C2311yescharacteristic
547#389C2314yes—
548#389C2314yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2314yes—
553#389C2314yes—
554#389C2314yes—
555#389C2312yes—
556#389C2312yes—
557#389C2312yes—
558#389C2314yes—
559#389C2311yescharacteristic
560#389C2311yescharacteristic
561#389C2314yes—
562#389C2314yes—
563#389C2312yes—
564#389C2312yes—
565#389C2312yes—
566#389C2312yes—
567#389C2312yes—
568#389C2312yes—
569#389C2314yes—
570#389C2312yes—
571#389C2314yes—
572#389C2314yes—
573#389C2314yes—
574#389C2314yes—
575#389C2314yes—
576#389C2314yes—
577#389C2314yes—
578#389C2314yes—
579#389C2314yes—
580#389C2314yes—
581#389C2314yes—
582#389C2314yes—
583#389C2312yes—
584#389C2314yes—
585#389C2314yes—
586#389C2311yescharacteristic
587#389C2312yes—
588#389C2314yes—
589#389C2314yes—
590#389C2312yes—
591#389C2314yes—
592#389C2314yes—
593#389C2311yescharacteristic
594#389C2312yes—
595#389C2311yescharacteristic
596#389C2311yescharacteristic
597#388C2312yes—
598#388C2312yes—
599#388C2312yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2312yes—
609#388C2312yes—
610#388C2312yes—
611#388C2312yes—
612#388C2312yes—
613#388C2314yes—
614#388C2314yes—
615#388C2312yes—
616#388C2312yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2312yes—
623#388C2312yes—
624#388C2312yes—
625#387C2312yes—
626#387C2312yes—
627#387C2312yes—
628#387C2312yes—
629#387C2312yes—
630#387C2312yes—
631#387C2312yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2312yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2312yes—
652#387C2312yes—
653#387C2314yes—
654#387C2314yes—
655#387C2312yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2312yes—
662#387C2312yes—
663#387C2312yes—
664#387C2312yes—
665#387C2312yes—
666#387C2312yes—
667#387C2312yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2314yes—
674#387C2314yes—
675#387C2312yes—
676#387C2314yes—
677#387C2314yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2314yes—
682#387C2314yes—
683#387C2314yes—
684#387C2314yes—
685#387C2314yes—
686#387C2312yes—
687#387C2312yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2314yes—
692#385C2314yes—
693#385C2314yes—
694#385C2314yes—
695#385C2314yes—
696#384C2311yescharacteristic
697#384C2311yescharacteristic
698#384C2311yescharacteristic
699#384C2311yescharacteristic
700#384C2311yescharacteristic
701#384C2312yes—
702#384C2312yes—
703#384C2312yes—
704#384C2312yes—
705#384C2312yes—
706#384C2312yes—
707#384C2314yes—
708#384C2312yes—
709#384C2312yes—
710#384C2312yes—
711#384C2312yes—
712#384C2312yes—
713#383C2312yes—
714#383C2314yes—
715#383C2314yes—
716#383C2314yes—
717#383C2314yes—
718#383C2314yes—
719#383C2314yes—
720#382C2311yescharacteristic
721#382C2311yescharacteristic
722#382C2312yes—
723#382C2312yes—
724#382C2312yes—
725#382C2312yes—
726#382C2311yescharacteristic
727#382C2311yescharacteristic
728#382C2312yes—
729#382C2312yes—
730#382C2312yes—
731#382C2312yes—
732#382C2314yes—
733#382C2314yes—
734#382C2314yes—
735#382C2314yes—
736#382C2314yes—
737#381C2314yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2312yes—
743#380C2314yes—
744#380C2314yes—
745C4×C4⋊C4C2311yescharacteristic
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2311yescharacteristic
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2311yescharacteristic
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2314yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2314yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2314yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2314yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2314yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2311yescharacteristic
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800#376C2312yes—
801#376C2312yes—
802#376C2314yes—
803#376C2312yes—
804#376C2314yes—
805C43C2312yes—
806C43C2311yescharacteristic
807C43C2311yescharacteristic
808C43C2311yescharacteristic
809C43C2312yes—
810C22×Q8C2411yescharacteristic
811C22×Q8C2411yescharacteristic
812C22×Q8C2411yescharacteristic
813C22×Q8C2411yescharacteristic
814C22×Q8C2412yes—
815C22×Q8C2412yes—
816C22×Q8C2414yes—
817C22×D4C2411yescharacteristic
818C23×C4C2412yes—
819C23×C4C2414yes—
820C4⋊Q8—24no—
821C4⋊Q8—24no—
822C4⋊Q8—24no—
823C4⋊Q8—44no—
824C4⋊Q8—44no—
825C4⋊Q8—44no—
826C4⋊Q8—82no—
827#126—48no—
828#126—44no—
829#126—84no—
830#125—44no—
831#125—44no—
832#125—48no—
833#125—42no—
834#125—44no—
835#125—42no—
836#125—84no—
837#125—84no—
838#125—84no—
839#124—24no—
840#124—42no—
841C22⋊Q8—44no—
842C22⋊Q8—84no—
843C4×Q8—24no—
844C4×Q8—28no—
845C4×Q8—24no—
846C4×Q8—24no—
847C4×Q8—24no—
848C4×Q8—24no—
849C4×Q8—24no—
850C4×Q8—44no—
851C4×Q8—42no—
852C4×Q8—44no—
853C4×Q8—44no—
854C4×Q8—42no—
855C4×Q8—42no—
856C4×Q8—44no—
857C4×Q8—42no—
858C4×Q8—82no—
859C4×Q8—82no—
860C4×D4—24no—
861C4×D4—44no—
862#117—28no—
863#117—44no—
864#117—84no—
865C2×C4⋊C4—44no—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2411yescharacteristic
913C2×C4⋊C4C2411yescharacteristic
914C2×C4⋊C4C2411yescharacteristic
915C2×C4⋊C4C2411yescharacteristic
916C2×C4⋊C4C2411yescharacteristic
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2414yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2414yes—
928C2×C4⋊C4C2414yes—
929C2×C4⋊C4C2412yes—
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2412yes—
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2414yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2414yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2414yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2414yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2414yes—
957C2×C4⋊C4C2414yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2414yes—
961C2×C22⋊C4C2412yes—
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2412yes—
978C2×C22⋊C4C2412yes—
979C2×C22⋊C4C2414yes—
980C2×C22⋊C4C2414yes—
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2411yescharacteristic
984C2×C42C2411yescharacteristic
985C2×C42C2411yescharacteristic
986C2×C42C2412yes—
987C2×C42C2411yescharacteristic
988C2×C42C2414yes—
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991C2×C42C2412yes—
992C2×C42C2412yes—
993C2×C42C2411yescharacteristic
994C2×C42C2411yescharacteristic
995C2×C42C2412yes—
996C2×C42C2412yes—
997C2×C42C2412yes—
998C2×C42C2414yes—
999C2×C42C2412yes—
1000C2×C42C2411yescharacteristic
1001C2×C42C2411yescharacteristic
1002C2×C42C2411yescharacteristic
1003C2×C42C2411yescharacteristic
1004C2×C42C2414yes—
1005C2×C42C2414yes—
1006C2×C42C2414yes—
1007C2×C42C2411yescharacteristic
1008C2×C42C2411yescharacteristic
1009C2×C42C2414yes—
1010C2×C42C2412yes—
1011C2×C42C2411yescharacteristic
1012C2×C42C2411yescharacteristic
1013C2×C42C2412yes—
1014C2×C42C2414yes—
1015C2×C42C2414yes—
1016C2×C42C2412yes—
1017C2×C42C2412yes—
1018C2×C42C2412yes—
1019C2×C42C2411yescharacteristic
1020C2×C42C2412yes—
1021C2×C42C2411yescharacteristic
1022C2×C42C2411yescharacteristic
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2414yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2414yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2411yescharacteristic
1055#95C2412yes—
1056#95C2411yescharacteristic
1057#95C2412yes—
1058#95C2411yescharacteristic
1059#95C2411yescharacteristic
1060#95C2412yes—
1061#95C2412yes—
1062#95C2411yescharacteristic
1063#95C2412yes—
1064#95C2412yes—
1065#95C2411yescharacteristic
1066#95C2412yes—
1067#95C2412yes—
1068#95C2414yes—
1069#95C2414yes—
1070#95C2414yes—
1071#95C2412yes—
1072#95C2414yes—
1073#95C2414yes—
1074#95C2412yes—
1075#95C2414yes—
1076#95C2414yes—
1077#95C2414yes—
1078#95C2412yes—
1079#95C2414yes—
1080#95C2414yes—
1081#95C2414yes—
1082#95C2412yes—
1083#95C2414yes—
1084#95C2412yes—
1085#95C2412yes—
1086#95C2414yes—
1087#95C2412yes—
1088#95C2412yes—
1089#95C2412yes—
1090#95C2414yes—
1091#95C2414yes—
1092#95C2412yes—
1093#95C2412yes—
1094#95C2412yes—
1095#95C2412yes—
1096#95C2412yes—
1097#95C2414yes—
1098#95C2412yes—
1099#95C2414yes—
1100#95C2414yes—
1101#95C2414yes—
1102#95C2412yes—
1103#95C2414yes—
1104#95C2414yes—
1105#95C2414yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110#95C2414yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2414yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119C24C2512yes—
1120C2×Q8—22no—
1121C2×Q8—22no—
1122C2×Q8—22no—
1123C2×Q8—22no—
1124C2×Q8—22no—
1125C2×Q8—24no—
1126C2×Q8—22no—
1127C2×Q8—24no—
1128C2×Q8—22no—
1129C2×Q8—22no—
1130C2×Q8—22no—
1131C2×Q8—22no—
1132C2×Q8—42no—
1133C2×Q8—41no—
1134C2×Q8—42no—
1135C2×Q8—42no—
1136C2×Q8—42no—
1137C2×Q8—44no—
1138C2×Q8—44no—
1139C2×Q8—44no—
1140C2×Q82−1+414yes—
1141C2×D4—22no—
1142C2×D4—22no—
1143C2×D4—22no—
1144C22×C4—24no—
1145C22×C4—24no—
1146C22×C4—24no—
1147C22×C4—44no—
1148C22×C4—44no—
1149C22×C4—44no—
1150C22×C4C2512yes—
1151C22×C4C2512yes—
1152C22×C4C2512yes—
1153C22×C4C2512yes—
1154C22×C4C2511yescharacteristic
1155C22×C4C2511yescharacteristic
1156C22×C4C2512yes—
1157C22×C4C2511yescharacteristic
1158C22×C4C2512yes—
1159C22×C4C2512yes—
1160C22×C4C2511yescharacteristic
1161C22×C4C2511yescharacteristic
1162C22×C4C2511yescharacteristic
1163C22×C4C2512yes—
1164C22×C4C2514yes—
1165C22×C4C2511yescharacteristic
1166C22×C4C2512yes—
1167C22×C4C2514yes—
1168C22×C4C2512yes—
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2514yes—
1172C22×C4C2512yes—
1173C22×C4C2514yes—
1174C22×C4C2511yescharacteristic
1175C22×C4C2511yescharacteristic
1176C22×C4C2512yes—
1177C22×C4C2512yes—
1178C22×C4C2511yescharacteristic
1179C22×C4C2511yescharacteristic
1180C22×C4C2511yescharacteristic
1181C22×C4C2511yescharacteristic
1182C22×C4C2511yescharacteristic
1183C22×C4C2511yescharacteristic
1184C4⋊C4—24no—
1185C4⋊C4—24no—
1186C4⋊C4—22no—
1187C4⋊C4—22no—
1188C4⋊C4—24no—
1189C4⋊C4—24no—
1190C4⋊C4—28no—
1191C4⋊C4—22no—
1192C4⋊C4—22no—
1193C4⋊C4—22no—
1194C4⋊C4—22no—
1195C4⋊C4—24no—
1196C4⋊C4—22no—
1197C4⋊C4—22no—
1198C4⋊C4—24no—
1199C4⋊C4—22no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—24no—
1205C4⋊C4—22no—
1206C4⋊C4—22no—
1207C4⋊C4—24no—
1208C4⋊C4—24no—
1209C4⋊C4—22no—
1210C4⋊C4—24no—
1211C4⋊C4—22no—
1212C4⋊C4—24no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—22no—
1216C4⋊C4—22no—
1217C4⋊C4—22no—
1218C4⋊C4—24no—
1219C4⋊C4—24no—
1220C4⋊C4—24no—
1221C4⋊C4—24no—
1222C4⋊C4—44no—
1223C4⋊C4—42no—
1224C4⋊C4—44no—
1225C4⋊C4—42no—
1226C4⋊C4—41no—
1227C4⋊C4—41no—
1228C4⋊C4—42no—
1229C4⋊C4—42no—
1230C4⋊C4—44no—
1231C4⋊C4—41no—
1232C4⋊C4—42no—
1233C4⋊C4—42no—
1234C4⋊C4—41no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—41no—
1238C4⋊C4—42no—
1239C4⋊C4—44no—
1240C4⋊C4—44no—
1241C4⋊C4—42no—
1242C4⋊C4—42no—
1243C4⋊C4—44no—
1244C4⋊C4—42no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—44no—
1252C4⋊C4—44no—
1253C4⋊C4—42no—
1254C4⋊C4—44no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—44no—
1258C4⋊C4—42no—
1259C4⋊C4—42no—
1260C4⋊C4—42no—
1261C4⋊C4—42no—
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⋊C4—44no—
1273C4⋊C4—44no—
1274C4⋊C4—42no—
1275C4⋊C4—44no—
1276C4⋊C4—44no—
1277C4⋊C4—42no—
1278C4⋊C4—42no—
1279C22⋊C4—24no—
1280C22⋊C4—24no—
1281C22⋊C4—24no—
1282C22⋊C4—24no—
1283C22⋊C4—24no—
1284C22⋊C4—24no—
1285C22⋊C4—44no—
1286C22⋊C4—42no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—42no—
1291C22⋊C4—44no—
1292C22⋊C4—42no—
1293C22⋊C4—42no—
1294C22⋊C4—44no—
1295C22⋊C4—44no—
1296C22⋊C4—42no—
1297C22⋊C4—42no—
1298C22⋊C4—42no—
1299C42—24no—
1300C42—24no—
1301C42—22no—
1302C42—24no—
1303C42—28no—
1304C42—22no—
1305C42—24no—
1306C42—24no—
1307C42—22no—
1308C42—24no—
1309C42—24no—
1310C42—22no—
1311C42—22no—
1312C42—24no—
1313C42—22no—
1314C42—22no—
1315C42—22no—
1316C42—24no—
1317C42—22no—
1318C42—28no—
1319C42—22no—
1320C42—22no—
1321C42—22no—
1322C42—44no—
1323C42—44no—
1324C42—44no—
1325C42—41no—
1326C42—41no—
1327C42—42no—
1328C42—44no—
1329C42—42no—
1330C42—44no—
1331C42—41no—
1332C42—41no—
1333C42—44no—
1334C42—42no—
1335C42—42no—
1336C42—42no—
1337C42—42no—
1338C42—41no—
1339C422−1+414yes—
1340C422−1+414yes—
1341C23—22no—
1342C23—22no—
1343C23—22no—
1344C23—22no—
1345C23—22no—
1346C23—22no—
1347C23—22no—
1348C23C2611yescharacteristic
1349Q8—28no—
1350Q8—44no—
1351Q8—48no—
1352Q8—44no—
1353Q8—44no—
1354Q8—84no—
1355Q8—164no—
1356D4—44no—
1357C2×C4—21no—
1358C2×C4—22no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—22no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—22no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—24no—
1374C2×C4—22no—
1375C2×C4—21no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—21no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—21no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—21no—
1395C2×C4—22no—
1396C2×C4—21no—
1397C2×C4—22no—
1398C2×C4—21no—
1399C2×C4—24no—
1400C2×C4—24no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—22no—
1407C2×C4—21no—
1408C2×C4—22no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—24no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—21no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—24no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—21no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—24no—
1429C2×C4—24no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—24no—
1433C2×C4—21no—
1434C2×C4—22no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—22no—
1438C2×C4—24no—
1439C2×C4—24no—
1440C2×C4—22no—
1441C2×C4—21no—
1442C2×C4—22no—
1443C2×C4—22no—
1444C2×C4—24no—
1445C2×C4—21no—
1446C2×C4—22no—
1447C2×C4—22no—
1448C2×C4—48no—
1449C2×C4—88no—
1450C2×C4C2×2−1+414yes—
1451C2×C4C2×2−1+412yes—
1452C2×C4C2×2−1+412yes—
1453C2×C4C2×2−1+412yes—
1454C2×C4C2×2−1+412yes—
1455C2×C4C2×2−1+412yes—
1456C2×C4C2×2−1+412yes—
1457C2×C4C2×2−1+412yes—
1458C2×C4#58512yes—
1459C2×C4#58512yes—
1460C2×C4#58512yes—
1461C22—42no—
1462C22—42no—
1463C22—42no—
1464C22—42no—
1465C22—42no—
1466C22—42no—
1467C22—42no—
1468C22C22×2−1+411yescharacteristic
1469C22C22×2−1+411yescharacteristic
1470C22C22×2−1+411yescharacteristic
1471C22C2×#58511yescharacteristic
1472C22C2×#58511yescharacteristic
1473C22C2×#58511yescharacteristic
1474C22H(7,𝔽2)11yescharacteristic
1475C4—24no—
1476C4—22no—
1477C4—22no—
1478C4—22no—
1479C4—22no—
1480C4—42no—
1481C4—42no—
1482C4—42no—
1483C4—41no—
1484C4—41no—
1485C4—44no—
1486C4—41no—
1487C4—42no—
1488C4—42no—
1489C4—41no—
1490C4—42no—
1491C4—42no—
1492C4—42no—
1493C4—42no—
1494C4—42no—
1495C4—44no—
1496C4—42no—
1497C4—41no—
1498C4—42no—
1499C4—41no—
1500C4—41no—
1501C4—41no—
1502C4—42no—
1503C4—42no—
1504C4—44no—
1505C4—44no—
1506C4—41no—
1507C4#355514yes—
1508C4#356314yes—
1509C2—82no—
1510C2C2×#356311yescharacteristic
1511C2C2×#355511yescharacteristic
1512C2#6283111yescharacteristic
1513C2#6292611yescharacteristic
1514C2#6294311yescharacteristic
1515C2#6296911yescharacteristic
1516C2#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. #59871C2semidirect
4. #58813C2semidirect
5. #57102C2semidirect
6. #56754C2semidirect
7. #53086C2semidirect
8. #52996C2semidirect
9. #52047C2semidirect
11. #46116C2semidirect
12. #45414C2semidirect
13. #44956C2semidirect
15. #42667C2semidirect
17. #42573C2semidirect
18. #40075C2semidirect
19. #39974C2semidirect
20. #39753C2semidirect
23. #39296C2semidirect
26. #37638C2semidirect
27. #37413C2semidirect
28. #37313C2semidirect
29. #36584C2semidirect
30. #36563C2semidirect
31. #36285C2semidirect
32. #35208C2semidirect
34. #34951C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#594362
#594352
#588132
#571022
#567542
#530862
#529962
#520472
#463432
#461162
#454142
#449562
#428302
#426672
#426262
#425732
#400752
#399742
#397532
#396332
#394982
#392962
#389782
#382252
#376382
#374132
#373132
#365842
#365632
#362852
#352082
#351852
#349512
#349022