Finite Group Databasebeta

← #8461537

Subgroups — #8461537

Order 512.

3963 conjugacy classes of subgroups.

The subgroup lattice has 1521 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59445C211yesmaximal, characteristic, complemented
2#59436C211yesmaximal, characteristic
3#59429C211yesmaximal, characteristic
4#58141C214yesmaximal, complemented
5#56520C214yesmaximal, complemented
6#54641C214yesmaximal, complemented
7#53143C212yesmaximal, complemented
8#53042C212yesmaximal, complemented
9#48620C214yesmaximal, complemented
10#46175C212yesmaximal, complemented
11#45719C212yesmaximal, complemented
12#45381C212yesmaximal
13#45174C212yesmaximal, complemented
14#42765C212yesmaximal, complemented
15#42753C212yesmaximal, complemented
16#42636C212yesmaximal, complemented
17#42494C212yesmaximal
18#40080C212yesmaximal
19#39751C212yesmaximal, complemented
20#39626C211yesmaximal, characteristic, complemented
21#39182C211yesmaximal, characteristic, complemented
22#38977C211yesmaximal, characteristic
23#38977C212yesmaximal
24#38976C211yesmaximal, characteristic, complemented
25#38069C212yesmaximal, complemented
26#37638C211yesmaximal, characteristic, complemented
27#37404C212yesmaximal, complemented
28#37291C212yesmaximal, complemented
29#36574C211yesmaximal, characteristic, complemented
30#36555C211yesmaximal, characteristic
31#36290C211yesmaximal, characteristic
32#35208C211yesmaximal, characteristic, complemented
33#35177C211yesmaximal, characteristic
34#34945C211yesmaximal, characteristic
35#34920C211yesmaximal, characteristic, complemented
36#2864C2212yes—
37#2863C2212yes—
38#2859C2211yescharacteristic
39#2859C2211yescharacteristic
40#2859C2212yes—
41#2859C2211yescharacteristic
42#2857C2212yes—
43#2855C2212yes—
44#2851C2212yes—
45#2841C2214yes—
46#2839C2214yes—
47#2839C2214yes—
48#2839C2214yes—
49#2833C2214yes—
50#2833C2214yes—
51#2833C2214yes—
52#2833C2214yes—
53#2806C2214yes—
54#2805C2214yes—
55#2805C2214yes—
56#2794C2214yes—
57#2794C2214yes—
58#2792C2214yes—
59#2789C2214yes—
60#2788C2214yes—
61#2788C2214yes—
62#2776C2214yes—
63#2774C2214yes—
64#2774C2214yes—
65#2771C2214yes—
66#2770C2214yes—
67#2767C2214yes—
68#2767C2214yes—
69#2766C2214yes—
70#2766C2214yes—
71#2766C2214yes—
72#2766C2214yes—
73#2765C2214yes—
74#2765C2214yes—
75#2765C2214yes—
76#2762C2214yes—
77#2762C2214yes—
78#2758C2214yes—
79#2758C2214yes—
80#2758C2214yes—
81#2755C2214yes—
82#2755C2214yes—
83#2755C2214yes—
84#2747C2214yes—
85#2745C2214yes—
86#2745C2214yes—
87#2744C2214yes—
88#2744C2214yes—
89#2739C2214yes—
90#2739C2214yes—
91#2739C2214yes—
92#2738C2214yes—
93#2726C2214yes—
94#2720C2214yes—
95#2719C2214yes—
96#2719C2214yes—
97#2719C2214yes—
98#2719C2214yes—
99#2704C2214yes—
100#2704C2214yes—
101#2690C2214yes—
102#2666C2214yes—
103#2665C2214yes—
104#2660C2212yes—
105#2659C2214yes—
106#2655C2214yes—
107#2655C2214yes—
108#2652C2214yes—
109#2647C2212yes—
110#2647C2212yes—
111#2647C2212yes—
112#2645C2212yes—
113#2645C2212yes—
114#2645C2212yes—
115#2645C2212yes—
116#2634C2214yes—
117#2629C2214yes—
118#2599C2214yes—
119#2590C2212yes—
120#2588C2212yes—
121#2587C2214yes—
122#2584C2211yescharacteristic
123#2584C2212yes—
124#2584C2212yes—
125#2582C2211yescharacteristic
126#2582C2211yescharacteristic
127#2582C2212yes—
128#2581C2212yes—
129#2581C2211yescharacteristic
130#2581C2212yes—
131#2577C2214yes—
132#2573C2212yes—
133#2573C2212yes—
134#2571C2212yes—
135#2571C2211yescharacteristic
136#2571C2211yescharacteristic
137#2570C2212yes—
138#2570C2212yes—
139#2570C2212yes—
140#2568C2212yes—
141#2568C2211yescharacteristic
142#2567C2211yescharacteristic
143#2567C2211yescharacteristic
144#2567C2212yes—
145#2567C2211yescharacteristic
146#2565C2211yescharacteristic
147#2563C2211yescharacteristic
148#2552C2212yes—
149#2552C2211yescharacteristic
150#2552C2212yes—
151#2551C2211yescharacteristic
152#2550C2211yescharacteristic
153#2550C2212yes—
154#2550C2212yes—
155#2550C2212yes—
156#2547C2211yescharacteristic
157#2538C2212yes—
158#2538C2211yescharacteristic
159#2538C2211yescharacteristic
160#2523C2214yes—
161#2522C2214yes—
162#2520C2212yes—
163#2514C2212yes—
164#2514C2212yes—
165#2514C2211yescharacteristic
166#2514C2212yes—
167#2514C2214yes—
168#2514C2211yescharacteristic
169#2514C2212yes—
170#2511C2212yes—
171#2511C2212yes—
172#2511C2212yes—
173#2509C2212yes—
174#2509C2212yes—
175#2509C2212yes—
176#2509C2212yes—
177#2508C2212yes—
178#2508C2212yes—
179#2508C2212yes—
180#2508C2212yes—
181#2508C2212yes—
182#2508C2212yes—
183#2508C2211yescharacteristic
184#2507C2212yes—
185#2507C2212yes—
186#2507C2212yes—
187#2506C2212yes—
188#2506C2212yes—
189#2506C2212yes—
190#2506C2212yes—
191#2506C2212yes—
192#2506C2212yes—
193#2506C2211yescharacteristic
194#2505C2214yes—
195#2503C2214yes—
196#2503C2212yes—
197#2497C2212yes—
198#2497C2212yes—
199#2497C2212yes—
200#2497C2212yes—
201#2495C2212yes—
202#2494C2212yes—
203#2494C2212yes—
204#2494C2214yes—
205#2494C2212yes—
206#2493C2214yes—
207#2492C2212yes—
208#2489C2214yes—
209#2489C2212yes—
210#2484C2214yes—
211#2475C2214yes—
212#2473C2214yes—
213#2465C2214yes—
214#2465C2214yes—
215#2462C2214yes—
216#2462C2212yes—
217#2462C2214yes—
218#2454C2212yes—
219#2453C2212yes—
220#2453C2212yes—
221#2453C2212yes—
222#2453C2212yes—
223#2453C2211yescharacteristic
224#2453C2212yes—
225#2452C2212yes—
226#2451C2212yes—
227#2451C2211yescharacteristic
228#2447C2212yes—
229#2447C2211yescharacteristic
230#2447C2212yes—
231#2447C2211yescharacteristic
232#2446C2212yes—
233#2446C2212yes—
234#2442C2212yes—
235#2442C2214yes—
236#2442C2212yes—
237#2442C2212yes—
238#2442C2214yes—
239#2442C2212yes—
240#2440C2212yes—
241#2438C2214yes—
242#2423C2212yes—
243#2421C2212yes—
244#2402C2212yes—
245#2401C2212yes—
246#2401C2212yes—
247#2399C2212yes—
248#2382C2214yes—
249#2370C2212yes—
250#2370C2212yes—
251#2370C2212yes—
252#2367C2212yes—
253#2360C2212yes—
254#2355C2212yes—
255#2355C2211yescharacteristic
256#2355C2211yescharacteristic
257#2354C2212yes—
258#2351C2212yes—
259Q8×C4⋊C4C2211yescharacteristic
260Q8×C4⋊C4C2211yescharacteristic
261#2349C2212yes—
262D4×C4⋊C4C2211yescharacteristic
263D4×C4⋊C4C2211yescharacteristic
264D4×C4⋊C4C2212yes—
265#2345C2212yes—
266#2345C2212yes—
267#2344C2212yes—
268#2331C2212yes—
269#2331C2212yes—
270#2331C2212yes—
271#2330C2212yes—
272#2329C2214yes—
273#2320C2212yes—
274#2320C2212yes—
275#2319C2212yes—
276#2319C2212yes—
277C4×C4⋊Q8C2211yescharacteristic
278C4×C4⋊Q8C2211yescharacteristic
279C4×C4⋊Q8C2211yescharacteristic
280C4×C4⋊Q8C2211yescharacteristic
281C4×C4⋊Q8C2211yescharacteristic
282C4×#125C2211yescharacteristic
283C4×#125C2211yescharacteristic
284C4×#125C2212yes—
285C4×#124C2211yescharacteristic
286C4×#124C2211yescharacteristic
287C4×#124C2212yes—
288C4×C22⋊Q8C2212yes—
289#2295C2211yescharacteristic
290#2295C2211yescharacteristic
291#2295C2211yescharacteristic
292#2295C2212yes—
293#2295C2211yescharacteristic
294C2×#389C2212yes—
295#2283C2212yes—
296C42×Q8C2211yescharacteristic
297C42×Q8C2211yescharacteristic
298C42×D4C2211yescharacteristic
299C2×C4⋊Q8C2311yescharacteristic
300C2×C4⋊Q8C2311yescharacteristic
301C2×C4⋊Q8C2311yescharacteristic
302C2×C4⋊Q8C2312yes—
303C2×C4⋊Q8C2312yes—
304C2×#125C2311yescharacteristic
305C2×#125C2311yescharacteristic
306C2×#125C2312yes—
307C2×#125C2312yes—
308C2×#125C2312yes—
309C2×#125C2312yes—
310C2×#125C2314yes—
311C2×#125C2314yes—
312C2×#125C2312yes—
313C2×#125C2314yes—
314C2×#125C2314yes—
315C2×#124C2311yescharacteristic
316C2×#124C2311yescharacteristic
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2312yes—
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2314yes—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2311yescharacteristic
330C2×C4×Q8C2311yescharacteristic
331C2×C4×Q8C2311yescharacteristic
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2312yes—
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2311yescharacteristic
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2311yescharacteristic
340C2×#117C2314yes—
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2312yes—
343C22×C4⋊C4C2314yes—
344C22×C42C2312yes—
345#401C2314yes—
346#401C2314yes—
347#401C2314yes—
348#401C2314yes—
349#401C2314yes—
350#401C2312yes—
351#401C2312yes—
352#400C2314yes—
353#400C2312yes—
354#400C2312yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2312yes—
360#400C2312yes—
361#400C2314yes—
362#400C2314yes—
363#400C2312yes—
364#400C2312yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2312yes—
380#400C2314yes—
381#400C2314yes—
382#400C2314yes—
383#400C2314yes—
384#400C2314yes—
385#400C2314yes—
386#400C2314yes—
387#400C2314yes—
388#400C2314yes—
389#400C2312yes—
390#400C2312yes—
391#400C2314yes—
392#400C2314yes—
393#400C2314yes—
394#400C2314yes—
395#400C2314yes—
396#400C2312yes—
397#400C2314yes—
398#400C2314yes—
399#400C2314yes—
400#399C2314yes—
401#398C2312yes—
402#398C2312yes—
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#398C2312yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2312yes—
425#398C2314yes—
426#398C2312yes—
427#398C2312yes—
428#398C2312yes—
429#398C2314yes—
430#398C2314yes—
431#398C2312yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#397C2312yes—
439#397C2312yes—
440#397C2312yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2312yes—
445#397C2312yes—
446#397C2312yes—
447#397C2314yes—
448#396C2312yes—
449#396C2312yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#395C2314yes—
456#395C2314yes—
457#395C2314yes—
458#395C2314yes—
459#395C2314yes—
460#395C2312yes—
461#395C2312yes—
462#395C2314yes—
463#395C2314yes—
464#395C2314yes—
465#395C2314yes—
466#395C2312yes—
467#395C2312yes—
468#395C2314yes—
469#393C2314yes—
470#393C2314yes—
471#391C2311yescharacteristic
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2311yescharacteristic
476#391C2312yes—
477#391C2311yescharacteristic
478#391C2311yescharacteristic
479#391C2312yes—
480#391C2312yes—
481#391C2314yes—
482#391C2312yes—
483#391C2311yescharacteristic
484#391C2312yes—
485#391C2311yescharacteristic
486#391C2311yescharacteristic
487#391C2314yes—
488#391C2314yes—
489#391C2312yes—
490#391C2311yescharacteristic
491#391C2311yescharacteristic
492#391C2312yes—
493#391C2312yes—
494#391C2314yes—
495#391C2314yes—
496#391C2311yescharacteristic
497#391C2311yescharacteristic
498#391C2312yes—
499#391C2312yes—
500#391C2312yes—
501#391C2314yes—
502#391C2314yes—
503#391C2314yes—
504#391C2312yes—
505#391C2311yescharacteristic
506#391C2312yes—
507#390C2312yes—
508#390C2312yes—
509#390C2311yescharacteristic
510#390C2311yescharacteristic
511#389C2311yescharacteristic
512#389C2312yes—
513#389C2311yescharacteristic
514#389C2311yescharacteristic
515#389C2312yes—
516#389C2311yescharacteristic
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2311yescharacteristic
521#389C2312yes—
522#389C2311yescharacteristic
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2311yescharacteristic
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2311yescharacteristic
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2314yes—
548#389C2311yescharacteristic
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2312yes—
556#389C2312yes—
557#389C2312yes—
558#389C2314yes—
559#389C2314yes—
560#389C2314yes—
561#389C2314yes—
562#389C2314yes—
563#389C2312yes—
564#389C2312yes—
565#389C2311yescharacteristic
566#389C2312yes—
567#389C2314yes—
568#389C2314yes—
569#389C2311yescharacteristic
570#389C2314yes—
571#389C2314yes—
572#389C2312yes—
573#389C2312yes—
574#389C2312yes—
575#389C2314yes—
576#389C2314yes—
577#389C2314yes—
578#389C2312yes—
579#389C2312yes—
580#389C2312yes—
581#389C2314yes—
582#389C2314yes—
583#389C2314yes—
584#389C2311yescharacteristic
585#389C2312yes—
586#389C2314yes—
587#389C2314yes—
588#389C2311yescharacteristic
589#389C2311yescharacteristic
590#388C2312yes—
591#388C2312yes—
592#388C2312yes—
593#388C2312yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#387C2312yes—
605#387C2312yes—
606#387C2312yes—
607#387C2312yes—
608#387C2312yes—
609#387C2312yes—
610#387C2312yes—
611#387C2312yes—
612#387C2312yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2312yes—
620#387C2312yes—
621#387C2312yes—
622#387C2312yes—
623#387C2312yes—
624#387C2312yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2312yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2312yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
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#387C2312yes—
658#387C2312yes—
659#387C2312yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2312yes—
672#387C2312yes—
673#385C2312yes—
674#385C2312yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2314yes—
683#385C2314yes—
684#385C2314yes—
685#385C2314yes—
686#384C2311yescharacteristic
687#384C2311yescharacteristic
688#384C2311yescharacteristic
689#384C2311yescharacteristic
690#384C2311yescharacteristic
691#384C2312yes—
692#384C2312yes—
693#384C2312yes—
694#384C2314yes—
695#384C2312yes—
696#384C2312yes—
697#384C2312yes—
698#383C2312yes—
699#383C2312yes—
700#383C2314yes—
701#383C2314yes—
702#383C2314yes—
703#383C2314yes—
704#382C2311yescharacteristic
705#382C2311yescharacteristic
706#382C2312yes—
707#382C2312yes—
708#382C2312yes—
709#382C2312yes—
710#382C2312yes—
711#382C2311yescharacteristic
712#382C2311yescharacteristic
713#382C2312yes—
714#382C2312yes—
715#382C2314yes—
716#382C2312yes—
717#382C2314yes—
718#382C2314yes—
719#382C2312yes—
720#382C2312yes—
721#382C2314yes—
722#382C2312yes—
723#382C2314yes—
724#382C2314yes—
725#381C2312yes—
726#381C2312yes—
727#381C2314yes—
728#381C2314yes—
729#381C2314yes—
730#381C2314yes—
731#380C2312yes—
732#380C2312yes—
733#380C2314yes—
734#380C2314yes—
735#380C2314yes—
736#380C2312yes—
737#380C2314yes—
738#380C2314yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2314yes—
743#380C2314yes—
744#380C2312yes—
745#380C2312yes—
746C4×C4⋊C4C2311yescharacteristic
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2311yescharacteristic
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2311yescharacteristic
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2314yes—
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2314yes—
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2311yescharacteristic
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801#376C2312yes—
802#376C2312yes—
803#376C2312yes—
804#376C2312yes—
805C2×#95C2314yes—
806C43C2311yescharacteristic
807C43C2311yescharacteristic
808C43C2312yes—
809C43C2311yescharacteristic
810C22×Q8C2411yescharacteristic
811C22×Q8C2411yescharacteristic
812C22×Q8C2411yescharacteristic
813C22×Q8C2411yescharacteristic
814C22×Q8C2412yes—
815C22×Q8C2412yes—
816C22×Q8C2414yes—
817C22×D4C2411yescharacteristic
818C23×C4C2412yes—
819C23×C4C2414yes—
820C23×C4C2414yes—
821C23×C4C2412yes—
822C23×C4C2412yes—
823C4⋊Q8—24no—
824C4⋊Q8—24no—
825C4⋊Q8—44no—
826C4⋊Q8—44no—
827C4⋊Q8—42no—
828#125—24no—
829#125—44no—
830#125—42no—
831#125—44no—
832#125—44no—
833#125—48no—
834#125—44no—
835#125—84no—
836#125—84no—
837#125—82no—
838#125—84no—
839#124—24no—
840#124—24no—
841C22⋊Q8—48no—
842C22⋊Q8—44no—
843C22⋊Q8—44no—
844C22⋊Q8—84no—
845C4×Q8—24no—
846C4×Q8—24no—
847C4×Q8—24no—
848C4×Q8—24no—
849C4×Q8—42no—
850C4×Q8—44no—
851C4×Q8—42no—
852C4×Q8—44no—
853C4×Q8—44no—
854C4×Q8—42no—
855C4×Q8—42no—
856C4×Q8—44no—
857C4×Q8—82no—
858C4×Q8—82no—
859C4×D4—24no—
860C4×D4—28no—
861C4×D4—24no—
862C4×D4—44no—
863C4×D4—42no—
864#117—84no—
865C2×C4⋊C4—28no—
866C2×C4⋊C4—44no—
867C2×C4⋊C4—84no—
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2411yescharacteristic
893C2×C4⋊C4C2411yescharacteristic
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2411yescharacteristic
912C2×C4⋊C4C2411yescharacteristic
913C2×C4⋊C4C2411yescharacteristic
914C2×C4⋊C4C2411yescharacteristic
915C2×C4⋊C4C2411yescharacteristic
916C2×C4⋊C4C2411yescharacteristic
917C2×C4⋊C4C2411yescharacteristic
918C2×C4⋊C4C2411yescharacteristic
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2412yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2414yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2412yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2412yes—
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2414yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2414yes—
958C2×C4⋊C4C2414yes—
959C2×C4⋊C4C2411yescharacteristic
960C2×C22⋊C4C2412yes—
961C2×C22⋊C4C2412yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2414yes—
977C2×C42—44no—
978C2×C42C2412yes—
979C2×C42C2411yescharacteristic
980C2×C42C2411yescharacteristic
981C2×C42C2412yes—
982C2×C42C2411yescharacteristic
983C2×C42C2411yescharacteristic
984C2×C42C2411yescharacteristic
985C2×C42C2412yes—
986C2×C42C2411yescharacteristic
987C2×C42C2411yescharacteristic
988C2×C42C2411yescharacteristic
989C2×C42C2412yes—
990C2×C42C2412yes—
991C2×C42C2411yescharacteristic
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2411yescharacteristic
995C2×C42C2411yescharacteristic
996C2×C42C2412yes—
997C2×C42C2411yescharacteristic
998C2×C42C2411yescharacteristic
999C2×C42C2414yes—
1000C2×C42C2414yes—
1001C2×C42C2411yescharacteristic
1002C2×C42C2411yescharacteristic
1003C2×C42C2414yes—
1004C2×C42C2411yescharacteristic
1005C2×C42C2412yes—
1006C2×C42C2411yescharacteristic
1007C2×C42C2414yes—
1008C2×C42C2414yes—
1009C2×C42C2414yes—
1010C2×C42C2412yes—
1011C2×C42C2411yescharacteristic
1012C2×C42C2412yes—
1013C2×C42C2414yes—
1014C2×C42C2412yes—
1015C2×C42C2412yes—
1016C2×C42C2411yescharacteristic
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2414yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2411yescharacteristic
1055#95C2412yes—
1056#95C2411yescharacteristic
1057#95C2411yescharacteristic
1058#95C2411yescharacteristic
1059#95C2411yescharacteristic
1060#95C2412yes—
1061#95C2412yes—
1062#95C2411yescharacteristic
1063#95C2412yes—
1064#95C2412yes—
1065#95C2414yes—
1066#95C2414yes—
1067#95C2414yes—
1068#95C2414yes—
1069#95C2412yes—
1070#95C2414yes—
1071#95C2412yes—
1072#95C2414yes—
1073#95C2414yes—
1074#95C2414yes—
1075#95C2412yes—
1076#95C2412yes—
1077#95C2412yes—
1078#95C2412yes—
1079#95C2414yes—
1080#95C2414yes—
1081#95C2412yes—
1082#95C2412yes—
1083#95C2412yes—
1084#95C2412yes—
1085#95C2412yes—
1086#95C2412yes—
1087#95C2412yes—
1088#95C2414yes—
1089#95C2412yes—
1090#95C2412yes—
1091#95C2412yes—
1092#95C2414yes—
1093#95C2412yes—
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—
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—22no—
1126C2×Q8—24no—
1127C2×Q8—24no—
1128C2×Q8—22no—
1129C2×Q8—22no—
1130C2×Q8—22no—
1131C2×Q8—22no—
1132C2×Q8—42no—
1133C2×Q8—41no—
1134C2×Q8—41no—
1135C2×Q8—42no—
1136C2×Q8—42no—
1137C2×Q8—42no—
1138C2×Q8—44no—
1139C2×Q8—44no—
1140C2×Q8—44no—
1141C2×D4—22no—
1142C2×D4—22no—
1143C2×D42−1+414yes—
1144C22×C4—28no—
1145C22×C4—24no—
1146C22×C4—24no—
1147C22×C4—24no—
1148C22×C4—24no—
1149C22×C4—28no—
1150C22×C4—24no—
1151C22×C4—42no—
1152C22×C4—42no—
1153C22×C4—44no—
1154C22×C4—42no—
1155C22×C4—44no—
1156C22×C4—44no—
1157C22×C4—44no—
1158C22×C4—42no—
1159C22×C4C2512yes—
1160C22×C4C2512yes—
1161C22×C4C2512yes—
1162C22×C4C2512yes—
1163C22×C4C2511yescharacteristic
1164C22×C4C2511yescharacteristic
1165C22×C4C2511yescharacteristic
1166C22×C4C2512yes—
1167C22×C4C2511yescharacteristic
1168C22×C4C2511yescharacteristic
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2512yes—
1172C22×C4C2514yes—
1173C22×C4C2512yes—
1174C22×C4C2512yes—
1175C22×C4C2514yes—
1176C22×C4C2514yes—
1177C22×C4C2511yescharacteristic
1178C22×C4C2511yescharacteristic
1179C22×C4C2511yescharacteristic
1180C22×C4C2511yescharacteristic
1181C22×C4C2512yes—
1182C22×C4C2512yes—
1183C22×C4C2512yes—
1184C22×C4C2511yescharacteristic
1185C22×C4C2511yescharacteristic
1186C22×C4C2514yes—
1187C22×C4C2512yes—
1188C22×C4C2512yes—
1189C22×C4C2511yescharacteristic
1190C22×C4C2511yescharacteristic
1191C22×C4C2511yescharacteristic
1192C22×C4C2511yescharacteristic
1193C4⋊C4—28no—
1194C4⋊C4—24no—
1195C4⋊C4—22no—
1196C4⋊C4—24no—
1197C4⋊C4—22no—
1198C4⋊C4—22no—
1199C4⋊C4—22no—
1200C4⋊C4—22no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—22no—
1208C4⋊C4—24no—
1209C4⋊C4—24no—
1210C4⋊C4—22no—
1211C4⋊C4—24no—
1212C4⋊C4—22no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—22no—
1216C4⋊C4—28no—
1217C4⋊C4—22no—
1218C4⋊C4—22no—
1219C4⋊C4—24no—
1220C4⋊C4—24no—
1221C4⋊C4—24no—
1222C4⋊C4—24no—
1223C4⋊C4—24no—
1224C4⋊C4—22no—
1225C4⋊C4—44no—
1226C4⋊C4—42no—
1227C4⋊C4—44no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C4⋊C4—42no—
1231C4⋊C4—44no—
1232C4⋊C4—42no—
1233C4⋊C4—41no—
1234C4⋊C4—42no—
1235C4⋊C4—41no—
1236C4⋊C4—41no—
1237C4⋊C4—41no—
1238C4⋊C4—41no—
1239C4⋊C4—41no—
1240C4⋊C4—42no—
1241C4⋊C4—41no—
1242C4⋊C4—42no—
1243C4⋊C4—41no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4—42no—
1247C4⋊C4—44no—
1248C4⋊C4—42no—
1249C4⋊C4—42no—
1250C4⋊C4—44no—
1251C4⋊C4—42no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—42no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—42no—
1258C4⋊C4—44no—
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—42no—
1269C4⋊C4—44no—
1270C4⋊C4—42no—
1271C4⋊C4—42no—
1272C4⋊C4—42no—
1273C4⋊C4—42no—
1274C4⋊C4—42no—
1275C4⋊C4—44no—
1276C4⋊C4—42no—
1277C4⋊C4—44no—
1278C4⋊C4—44no—
1279C4⋊C4—44no—
1280C4⋊C4—42no—
1281C4⋊C4—44no—
1282C4⋊C4—42no—
1283C4⋊C4—44no—
1284C4⋊C42−1+414yes—
1285C22⋊C4—24no—
1286C22⋊C4—28no—
1287C22⋊C4—24no—
1288C22⋊C4—24no—
1289C22⋊C4—24no—
1290C22⋊C4—24no—
1291C22⋊C4—24no—
1292C22⋊C4—42no—
1293C22⋊C4—44no—
1294C22⋊C4—44no—
1295C22⋊C4—42no—
1296C22⋊C4—42no—
1297C22⋊C4—44no—
1298C22⋊C4—42no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—42no—
1302C42—22no—
1303C42—24no—
1304C42—22no—
1305C42—24no—
1306C42—24no—
1307C42—24no—
1308C42—24no—
1309C42—22no—
1310C42—22no—
1311C42—22no—
1312C42—22no—
1313C42—22no—
1314C42—24no—
1315C42—24no—
1316C42—22no—
1317C42—22no—
1318C42—22no—
1319C42—22no—
1320C42—24no—
1321C42—22no—
1322C42—22no—
1323C42—42no—
1324C42—42no—
1325C42—44no—
1326C42—44no—
1327C42—41no—
1328C42—41no—
1329C42—44no—
1330C42—44no—
1331C42—42no—
1332C42—44no—
1333C42—41no—
1334C42—41no—
1335C42—44no—
1336C42—42no—
1337C42—44no—
1338C42—41no—
1339C42—42no—
1340C422−1+414yes—
1341C23—22no—
1342C23—22no—
1343C23—22no—
1344C23—22no—
1345C23—22no—
1346C23—22no—
1347C23C2×2−1+414yes—
1348C23C2611yescharacteristic
1349Q8—44no—
1350Q8—48no—
1351Q8—44no—
1352Q8—44no—
1353Q8—44no—
1354Q8—84no—
1355Q8—164no—
1356D4—28no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—22no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—22no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—22no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—21no—
1382C2×C4—22no—
1383C2×C4—21no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—24no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—24no—
1392C2×C4—24no—
1393C2×C4—22no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—22no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—22no—
1412C2×C4—24no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—24no—
1422C2×C4—24no—
1423C2×C4—21no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—24no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—24no—
1430C2×C4—22no—
1431C2×C4—24no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—22no—
1439C2×C4—22no—
1440C2×C4—24no—
1441C2×C4—24no—
1442C2×C4—21no—
1443C2×C4—22no—
1444C2×C4—21no—
1445C2×C4—24no—
1446C2×C4—21no—
1447C2×C4—22no—
1448C2×C4—22no—
1449C2×C4—22no—
1450C2×C4—48no—
1451C2×C4—84no—
1452C2×C4—88no—
1453C2×C4—84no—
1454C2×C4—88no—
1455C2×C4C2×2−1+414yes—
1456C2×C4C2×2−1+412yes—
1457C2×C4C2×2−1+412yes—
1458C2×C4C2×2−1+412yes—
1459C2×C4C2×2−1+412yes—
1460C2×C4C2×2−1+412yes—
1461C2×C4#58512yes—
1462C2×C4#58512yes—
1463C2×C4#58512yes—
1464C22—24no—
1465C22—24no—
1466C22—24no—
1467C22—42no—
1468C22—42no—
1469C22—42no—
1470C22—42no—
1471C22C22×2−1+411yescharacteristic
1472C22C22×2−1+411yescharacteristic
1473C22C22×2−1+411yescharacteristic
1474C22C2×#58511yescharacteristic
1475C22C2×#58511yescharacteristic
1476C22C2×#58511yescharacteristic
1477C22H(7,𝔽2)11yescharacteristic
1478C4—22no—
1479C4—22no—
1480C4—24no—
1481C4—42no—
1482C4—42no—
1483C4—42no—
1484C4—42no—
1485C4—41no—
1486C4—41no—
1487C4—41no—
1488C4—42no—
1489C4—42no—
1490C4—42no—
1491C4—41no—
1492C4—41no—
1493C4—44no—
1494C4—42no—
1495C4—42no—
1496C4—42no—
1497C4—42no—
1498C4—44no—
1499C4—41no—
1500C4—41no—
1501C4—41no—
1502C4—41no—
1503C4—44no—
1504C4—42no—
1505C4—44no—
1506C4—41no—
1507C4—42no—
1508C4—42no—
1509C4—41no—
1510C4#355514yes—
1511C4#356314yes—
1512C2—44no—
1513C2C2×#356311yescharacteristic
1514C2C2×#355511yescharacteristic
1515C2#6282711yescharacteristic
1516C2#6292611yescharacteristic
1517C2#6295111yescharacteristic
1518C2#6295111yescharacteristic
1519C2#6303211yescharacteristic
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. #59445C2semidirect
4. #58141C2semidirect
5. #56520C2semidirect
6. #54641C2semidirect
7. #53143C2semidirect
8. #53042C2semidirect
9. #48620C2semidirect
10. #46175C2semidirect
11. #45719C2semidirect
13. #45174C2semidirect
14. #42765C2semidirect
15. #42753C2semidirect
16. #42636C2semidirect
19. #39751C2semidirect
20. #39626C2semidirect
21. #39182C2semidirect
24. #38976C2semidirect
25. #38069C2semidirect
26. #37638C2semidirect
27. #37404C2semidirect
28. #37291C2semidirect
29. #36574C2semidirect
32. #35208C2semidirect
35. #34920C2semidirect

Maximal subgroups

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

subgroupindex
#594452
#594362
#594292
#581412
#565202
#546412
#531432
#530422
#486202
#461752
#457192
#453812
#451742
#427652
#427532
#426362
#424942
#400802
#397512
#396262
#391822
#389772
#389762
#380692
#376382
#374042
#372912
#365742
#365552
#362902
#352082
#351772
#349452
#349202