Finite Group Databasebeta

← #8429365

Subgroups — #8429365

Order 512.

4421 conjugacy classes of subgroups.

The subgroup lattice has 1451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59946C211yesmaximal, characteristic, complemented
2#59537C212yesmaximal, complemented
3#59475C212yesmaximal, complemented
4#59374C212yesmaximal, complemented
5#57459C214yesmaximal, complemented
6#55616C212yesmaximal, complemented
7#53979C212yesmaximal, complemented
8#53110C212yesmaximal, complemented
9#53017C211yesmaximal, characteristic, complemented
10#53005C211yesmaximal, characteristic, complemented
11#52848C214yesmaximal, complemented
12#52806C214yesmaximal, complemented
13#42985C211yesmaximal, characteristic
14#42913C211yesmaximal, characteristic, complemented
15#42793C212yesmaximal, complemented
16#41565C214yesmaximal, complemented
17#41541C214yesmaximal, complemented
18#39827C214yesmaximal, complemented
19#39437C212yesmaximal, complemented
20#39417C212yesmaximal, complemented
21#39238C212yesmaximal, complemented
22#39224C212yesmaximal, complemented
23#37612C212yesmaximal, complemented
24#37573C212yesmaximal, complemented
25#37516C212yesmaximal, complemented
26#36457C211yesmaximal, characteristic, complemented
27#36373C212yesmaximal, complemented
28#34975C212yesmaximal, complemented
29#34871C211yesmaximal, characteristic, complemented
30C2×Q82C2211yescharacteristic
31C2×#550C2211yescharacteristic
32C2×#541C2212yes—
33C2×#537C2211yescharacteristic
34C2×#536C2211yescharacteristic
35#2861C2212yes—
36#2858C2211yescharacteristic
37#2858C2212yes—
38#2850C2212yes—
39#2844C2212yes—
40#2841C2212yes—
41#2838C2214yes—
42#2832C2214yes—
43#2831C2214yes—
44#2829C2214yes—
45#2829C2214yes—
46#2827C2214yes—
47#2826C2214yes—
48#2826C2214yes—
49#2824C2212yes—
50#2824C2214yes—
51#2822C2212yes—
52#2821C2214yes—
53#2820C2214yes—
54#2816C2212yes—
55#2815C2212yes—
56#2804C2214yes—
57#2789C2212yes—
58#2785C2212yes—
59#2779C2214yes—
60#2778C2214yes—
61#2769C2212yes—
62#2764C2212yes—
63#2763C2212yes—
64#2761C2214yes—
65#2759C2214yes—
66#2757C2214yes—
67#2754C2214yes—
68#2753C2214yes—
69#2750C2214yes—
70#2749C2214yes—
71#2746C2214yes—
72#2746C2214yes—
73#2745C2214yes—
74#2743C2214yes—
75#2739C2214yes—
76#2717C2212yes—
77#2716C2214yes—
78#2716C2214yes—
79#2713C2214yes—
80#2713C2214yes—
81#2711C2214yes—
82#2711C2214yes—
83#2709C2214yes—
84#2708C2214yes—
85#2707C2214yes—
86#2707C2214yes—
87#2705C2214yes—
88#2704C2214yes—
89#2702C2214yes—
90#2691C2214yes—
91#2691C2214yes—
92#2690C2214yes—
93#2688C2214yes—
94#2686C2214yes—
95#2673C2214yes—
96#2665C2214yes—
97#2662C2214yes—
98#2662C2214yes—
99#2654C2214yes—
100#2654C2214yes—
101#2653C2214yes—
102#2650C2214yes—
103#2650C2214yes—
104#2649C2214yes—
105#2648C2214yes—
106#2642C2214yes—
107#2639C2212yes—
108#2639C2212yes—
109#2638C2212yes—
110#2638C2212yes—
111#2634C2214yes—
112#2629C2212yes—
113#2628C2212yes—
114#2624C2212yes—
115#2624C2211yescharacteristic
116#2620C2212yes—
117#2616C2212yes—
118#2615C2211yescharacteristic
119#2612C2211yescharacteristic
120#2610C2214yes—
121#2610C2212yes—
122#2609C2211yescharacteristic
123#2604C2214yes—
124#2602C2214yes—
125#2601C2214yes—
126#2595C2214yes—
127#2593C2214yes—
128#2586C2212yes—
129#2586C2211yescharacteristic
130#2581C2212yes—
131#2573C2214yes—
132#2573C2214yes—
133#2572C2211yescharacteristic
134#2572C2214yes—
135#2568C2212yes—
136#2566C2212yes—
137#2564C2212yes—
138#2563C2211yescharacteristic
139#2563C2212yes—
140#2562C2212yes—
141#2560C2214yes—
142#2559C2214yes—
143#2559C2214yes—
144#2558C2214yes—
145#2557C2214yes—
146#2556C2214yes—
147#2556C2214yes—
148#2554C2212yes—
149#2554C2214yes—
150#2550C2212yes—
151#2550C2212yes—
152#2548C2212yes—
153#2548C2211yescharacteristic
154#2544C2212yes—
155#2543C2212yes—
156#2535C2212yes—
157#2533C2214yes—
158#2532C2212yes—
159#2531C2214yes—
160#2530C2214yes—
161#2528C2214yes—
162#2527C2214yes—
163#2526C2214yes—
164#2526C2212yes—
165#2526C2214yes—
166#2521C2214yes—
167#2516C2214yes—
168#2514C2212yes—
169#2506C2212yes—
170#2505C2214yes—
171#2504C2211yescharacteristic
172#2497C2212yes—
173#2496C2212yes—
174#2495C2212yes—
175#2495C2214yes—
176#2494C2212yes—
177#2493C2214yes—
178#2492C2212yes—
179#2492C2212yes—
180#2491C2212yes—
181#2491C2214yes—
182#2491C2212yes—
183#2491C2214yes—
184#2490C2212yes—
185#2490C2214yes—
186#2489C2212yes—
187#2489C2212yes—
188#2486C2211yescharacteristic
189#2479C2212yes—
190#2479C2214yes—
191#2478C2214yes—
192#2476C2214yes—
193#2475C2214yes—
194#2474C2214yes—
195#2474C2214yes—
196#2471C2212yes—
197#2467C2214yes—
198#2459C2214yes—
199#2459C2214yes—
200#2454C2212yes—
201#2453C2212yes—
202#2448C2212yes—
203#2447C2212yes—
204#2446C2212yes—
205#2446C2212yes—
206#2442C2212yes—
207#2436C2211yescharacteristic
208#2432C2212yes—
209#2429C2212yes—
210#2428C2212yes—
211#2427C2212yes—
212#2426C2212yes—
213#2426C2212yes—
214#2421C2212yes—
215#2421C2212yes—
216#2421C2212yes—
217#2420C2212yes—
218#2409C2211yescharacteristic
219#2409C2212yes—
220#2407C2212yes—
221#2402C2214yes—
222#2401C2214yes—
223#2396C2212yes—
224#2395C2211yescharacteristic
225#2388C2211yescharacteristic
226#2374C2212yes—
227#2372C2214yes—
228#2367C2212yes—
229#2363C2214yes—
230#2360C2212yes—
231#2357C2212yes—
232#2356C2212yes—
233#2353C2214yes—
234#2343C2214yes—
235#2341C2212yes—
236#2341C2212yes—
237Q8×C22⋊C4C2212yes—
238#2339C2211yescharacteristic
239#2339C2211yescharacteristic
240#2337C2214yes—
241#2337C2214yes—
242C4×C4⋊Q8C2212yes—
243C4×#125C2212yes—
244C4×#125C2214yes—
245C4×#126C2212yes—
246C4×#126C2214yes—
247C4×#124C2211yescharacteristic
248C4×#124C2212yes—
249C4×C22⋊Q8C2212yes—
250C4×C22⋊Q8C2212yes—
251C4×#123C2212yes—
252C4×#121C2212yes—
253#2297C2212yes—
254#2295C2212yes—
255#2293C2212yes—
256#2293C2212yes—
257C42×Q8C2211yescharacteristic
258C4×#117C2212yes—
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C22×#41C2311yescharacteristic
262C23×Q8C2311yescharacteristic
263Q82—44no—
264#550—44no—
265#541—48no—
266#537—44no—
267#536—44no—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2312yes—
273C2×#127C2312yes—
274C2×#127C2311yescharacteristic
275C2×#126C2312yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#125C2312yes—
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#124C2312yes—
285C2×#124C2314yes—
286C2×#124C2314yes—
287C2×#124C2312yes—
288C2×#124C2314yes—
289C2×#124C2312yes—
290C2×#124C2311yescharacteristic
291C2×#123C2312yes—
292C2×#123C2312yes—
293C2×#123C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2311yescharacteristic
305C2×#121C2314yes—
306C2×#121C2311yescharacteristic
307C2×#121C2312yes—
308C2×#121C2314yes—
309C2×#121C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×#117C2314yes—
324C2×#117C2312yes—
325C2×#117C2312yes—
326C2×#117C2312yes—
327C2×#117C2311yescharacteristic
328C22×C4⋊C4C2311yescharacteristic
329C22×C42C2312yes—
330#401C2314yes—
331#401C2314yes—
332#400C2314yes—
333#400C2311yescharacteristic
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#399C2311yescharacteristic
356#399C2312yes—
357#399C2314yes—
358#399C2314yes—
359#399C2312yes—
360#399C2314yes—
361#399C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2311yescharacteristic
366#398C2314yes—
367#398C2312yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2312yes—
389#397C2312yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2312yes—
395#397C2312yes—
396#397C2311yescharacteristic
397#397C2312yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2312yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2312yes—
410#396C2314yes—
411#395C2312yes—
412#395C2312yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2311yescharacteristic
419#395C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2311yescharacteristic
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2312yes—
442#394C2314yes—
443#394C2314yes—
444#394C2312yes—
445#394C2314yes—
446#393C2314yes—
447#393C2312yes—
448#393C2312yes—
449#393C2312yes—
450#393C2314yes—
451#393C2312yes—
452#393C2314yes—
453#393C2312yes—
454#393C2314yes—
455#393C2314yes—
456#393C2314yes—
457#393C2312yes—
458#393C2312yes—
459#393C2311yescharacteristic
460#392C2312yes—
461#392C2311yescharacteristic
462#392C2314yes—
463#392C2314yes—
464#392C2314yes—
465#392C2314yes—
466#392C2312yes—
467#391C2314yes—
468#391C2312yes—
469#391C2312yes—
470#391C2314yes—
471#391C2314yes—
472#391C2312yes—
473#391C2312yes—
474#391C2311yescharacteristic
475#391C2314yes—
476#391C2314yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2314yes—
481#391C2314yes—
482#391C2312yes—
483#391C2312yes—
484#391C2314yes—
485#391C2312yes—
486#390C2314yes—
487#390C2312yes—
488#390C2312yes—
489#390C2312yes—
490#390C2312yes—
491#390C2312yes—
492#390C2312yes—
493#390C2314yes—
494#390C2312yes—
495#390C2312yes—
496#390C2314yes—
497#390C2314yes—
498#390C2312yes—
499#390C2312yes—
500#390C2314yes—
501#390C2314yes—
502#390C2311yescharacteristic
503#390C2312yes—
504#390C2314yes—
505#390C2312yes—
506#390C2312yes—
507#390C2312yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2312yes—
519#389C2314yes—
520#389C2314yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#388C2314yes—
526#388C2312yes—
527#388C2314yes—
528#388C2312yes—
529#388C2312yes—
530#388C2314yes—
531#388C2312yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2312yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2312yes—
561#388C2312yes—
562#388C2312yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2312yes—
567#388C2312yes—
568#388C2312yes—
569#387C2314yes—
570#387C2312yes—
571#387C2314yes—
572#387C2312yes—
573#387C2312yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2312yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2312yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2312yes—
601#386C2314yes—
602#386C2314yes—
603#386C2312yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2312yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2312yes—
618#386C2312yes—
619#386C2312yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2312yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2312yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#384C2312yes—
636#383C2314yes—
637#383C2312yes—
638#383C2314yes—
639#383C2314yes—
640#382C2314yes—
641#382C2312yes—
642#382C2312yes—
643#382C2311yescharacteristic
644#382C2312yes—
645#382C2312yes—
646#382C2314yes—
647#381C2312yes—
648#381C2312yes—
649#381C2314yes—
650#381C2312yes—
651#381C2312yes—
652#381C2314yes—
653#381C2314yes—
654#380C2311yescharacteristic
655#380C2312yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2314yes—
660#380C2314yes—
661#380C2314yes—
662#380C2314yes—
663#380C2311yescharacteristic
664#380C2312yes—
665#380C2314yes—
666#380C2314yes—
667#380C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2311yescharacteristic
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2311yescharacteristic
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708#376C2314yes—
709#376C2312yes—
710#376C2314yes—
711#376C2312yes—
712C2×#95C2312yes—
713C2×#95C2312yes—
714C43C2312yes—
715C43C2312yes—
716C43C2311yescharacteristic
717C2×#41—24no—
718C2×#41—24no—
719C2×#41—42no—
720C2×#41—44no—
721C2×#41—44no—
722C2×#41—44no—
723C22×Q8—42no—
724C22×Q8—44no—
725C22×Q8C2412yes—
726C22×Q8C2411yescharacteristic
727C22×Q8C2411yescharacteristic
728C22×Q8C2412yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2414yes—
731C22×Q8C2412yes—
732C22×D4C2411yescharacteristic
733C22×D4C2411yescharacteristic
734C22×D4C2412yes—
735C22×D4C2411yescharacteristic
736C22×D4C2412yes—
737C22×D4C2412yes—
738C22×D4C2414yes—
739C22×D4C2412yes—
740C22×D4C2414yes—
741C22×D4C2412yes—
742C22×D4C2412yes—
743C22×D4C2412yes—
744C22×D4C2411yescharacteristic
745C22×D4C2412yes—
746C23×C4C2411yescharacteristic
747C23×C4C2411yescharacteristic
748C23×C4C2412yes—
749C23×C4C2412yes—
750C23×C4C2412yes—
751C23×C4C2412yes—
752C23×C4C2412yes—
753C23×C4C2412yes—
754C23×C4C2414yes—
755C23×C4C2414yes—
756C23×C4C2412yes—
757C4⋊Q8—28no—
758C4⋊Q8—44no—
759C4⋊Q8—42no—
760C4⋊Q8—44no—
761C4⋊Q8—48no—
762#127—42no—
763#127—44no—
764#126—44no—
765#126—48no—
766#126—48no—
767#126—48no—
768#125—44no—
769#125—48no—
770#125—44no—
771#125—48no—
772#125—48no—
773#124—48no—
774#124—48no—
775#124—48no—
776#124—44no—
777#124—42no—
778#124—44no—
779#124—44no—
780#123—44no—
781#123—44no—
782#123—48no—
783C22⋊Q8—28no—
784C22⋊Q8—44no—
785C22⋊Q8—44no—
786C22⋊Q8—44no—
787C22⋊Q8—44no—
788C22⋊Q8—44no—
789C22⋊Q8—44no—
790#121—44no—
791#121—48no—
792#121—48no—
793#121—44no—
794#121—44no—
795#121—42no—
796#121—42no—
797#121—44no—
798#121—44no—
799C4×Q8—28no—
800C4×Q8—24no—
801C4×Q8—42no—
802C4×Q8—44no—
803C4×Q8—44no—
804C4×Q8—44no—
805C4×Q8—44no—
806C4×D4—44no—
807C4×D4—44no—
808C4×D4—44no—
809C4×D4—42no—
810C4×D4—44no—
811C4×D4—48no—
812#117—42no—
813#117—44no—
814#117—44no—
815#117—48no—
816#117—44no—
817C2×C4⋊C4—42no—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2411yescharacteristic
883C2×C22⋊C4C2411yescharacteristic
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C42—44no—
924C2×C42C2412yes—
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2411yescharacteristic
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2414yes—
934C2×C42C2412yes—
935C2×C42C2414yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2411yescharacteristic
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2414yes—
948C2×C42C2412yes—
949#95C2411yescharacteristic
950#95C2411yescharacteristic
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2411yescharacteristic
982#95C2412yes—
983#95C2411yescharacteristic
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016C24C2512yes—
1017C24C2512yes—
1018C24C2511yescharacteristic
1019C24C2512yes—
1020C24C2511yescharacteristic
1021#41—88no—
1022#41—88no—
1023#41—88no—
1024C2×Q8—24no—
1025C2×Q8—24no—
1026C2×Q8—24no—
1027C2×Q8—24no—
1028C2×Q8—22no—
1029C2×Q8—41no—
1030C2×Q8—41no—
1031C2×Q8—42no—
1032C2×Q8—41no—
1033C2×Q8—44no—
1034C2×Q8—42no—
1035C2×Q8—44no—
1036C2×Q8—44no—
1037C2×Q8—44no—
1038C2×Q8—44no—
1039C2×Q8—42no—
1040C2×Q8—88no—
1041C2×Q8H(5,𝔽2)14yes—
1042C2×D4—22no—
1043C2×D4—22no—
1044C2×D4—24no—
1045C2×D4—24no—
1046C2×D4—24no—
1047C2×D4—24no—
1048C2×D4—24no—
1049C2×D4—22no—
1050C2×D4—42no—
1051C2×D4—41no—
1052C2×D4—42no—
1053C2×D4—44no—
1054C2×D4—41no—
1055C2×D4—42no—
1056C2×D4—44no—
1057C2×D4—44no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—41no—
1061C2×D4—42no—
1062C2×D4—44no—
1063C2×D4—44no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D4—44no—
1068C2×D4—42no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C22×C4—22no—
1077C22×C4—22no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—24no—
1081C22×C4—24no—
1082C22×C4—24no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—42no—
1087C22×C4—42no—
1088C22×C4—42no—
1089C22×C4—42no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—42no—
1094C22×C4—42no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—42no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—42no—
1102C22×C4—44no—
1103C22×C4—42no—
1104C22×C4C2512yes—
1105C22×C4C2511yescharacteristic
1106C22×C4C2511yescharacteristic
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2511yescharacteristic
1110C22×C4C2512yes—
1111C22×C4C2514yes—
1112C22×C4C2514yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2514yes—
1116C22×C4C2514yes—
1117C22×C4C2512yes—
1118C22×C4C2514yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2514yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2511yescharacteristic
1126C22×C4C2512yes—
1127C22×C4C2511yescharacteristic
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—22no—
1131C4⋊C4—24no—
1132C4⋊C4—28no—
1133C4⋊C4—28no—
1134C4⋊C4—28no—
1135C4⋊C4—28no—
1136C4⋊C4—28no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—28no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—41no—
1150C4⋊C4—41no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—41no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—41no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—42no—
1175C4⋊C4—44no—
1176C4⋊C4—42no—
1177C4⋊C4—44no—
1178C22⋊C4—28no—
1179C22⋊C4—24no—
1180C22⋊C4—28no—
1181C22⋊C4—24no—
1182C22⋊C4—28no—
1183C22⋊C4—24no—
1184C22⋊C4—24no—
1185C22⋊C4—44no—
1186C22⋊C4—42no—
1187C22⋊C4—42no—
1188C22⋊C4—44no—
1189C22⋊C4—42no—
1190C22⋊C4—42no—
1191C22⋊C4—44no—
1192C22⋊C4—42no—
1193C22⋊C4—42no—
1194C22⋊C4—42no—
1195C22⋊C4—42no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—42no—
1199C22⋊C4—42no—
1200C22⋊C4—44no—
1201C22⋊C4—42no—
1202C22⋊C4—41no—
1203C22⋊C4—42no—
1204C22⋊C4—41no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—42no—
1214C22⋊C4—42no—
1215C22⋊C4—44no—
1216C22⋊C4—42no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—42no—
1221C22⋊C4—42no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—42no—
1230C22⋊C4—44no—
1231C22⋊C4—42no—
1232C22⋊C4—44no—
1233C42—24no—
1234C42—24no—
1235C42—24no—
1236C42—22no—
1237C42—28no—
1238C42—24no—
1239C42—24no—
1240C42—22no—
1241C42—24no—
1242C42—24no—
1243C42—24no—
1244C42—28no—
1245C42—24no—
1246C42—42no—
1247C42—42no—
1248C42—41no—
1249C42—42no—
1250C42—44no—
1251C42—44no—
1252C42—42no—
1253C42—42no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C42—44no—
1258C23—22no—
1259C23—22no—
1260C23—21no—
1261C23—22no—
1262C23—21no—
1263C23—22no—
1264C23—22no—
1265C23—24no—
1266C23—22no—
1267C23—24no—
1268C23—22no—
1269C23—21no—
1270C23—21no—
1271C23—22no—
1272C23—22no—
1273C23—24no—
1274C23—22no—
1275C23—22no—
1276C23—24no—
1277C23—22no—
1278C23—22no—
1279C23—22no—
1280C23—21no—
1281C23—22no—
1282C23—22no—
1283C23—21no—
1284C23—22no—
1285C23C2611yescharacteristic
1286Q8—28no—
1287Q8—44no—
1288Q8—48no—
1289Q8—84no—
1290Q8—82no—
1291Q8—164no—
1292Q8—162no—
1293D4—44no—
1294D4—44no—
1295D4—82no—
1296D4—84no—
1297D4—84no—
1298D4—84no—
1299D4—88no—
1300D4—84no—
1301D4—82no—
1302D4—84no—
1303D4—162no—
1304D4—162no—
1305D4—162no—
1306D4—164no—
1307C2×C4—21no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—21no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—21no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—24no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—48no—
1369C2×C4—44no—
1370C2×C4—48no—
1371C2×C4—44no—
1372C2×C4—84no—
1373C2×C4—84no—
1374C2×C4—84no—
1375C2×C4—88no—
1376C2×C4—84no—
1377C2×C4—162no—
1378C2×C4—164no—
1379C2×C4C2×H(5,𝔽2)14yes—
1380C2×C4C2×H(5,𝔽2)12yes—
1381C2×C4#58514yes—
1382C2×C4#58512yes—
1383C2×C4#58514yes—
1384C22—41no—
1385C22—41no—
1386C22—42no—
1387C22—42no—
1388C22—42no—
1389C22—42no—
1390C22—44no—
1391C22—42no—
1392C22—44no—
1393C22—42no—
1394C22—42no—
1395C22—42no—
1396C22—41no—
1397C22—42no—
1398C22—41no—
1399C22—42no—
1400C22—41no—
1401C22—42no—
1402C22—42no—
1403C22—41no—
1404C22—42no—
1405C22—42no—
1406C22—44no—
1407C22—42no—
1408C22—42no—
1409C22—42no—
1410C22—44no—
1411C22C22×H(5,𝔽2)11yescharacteristic
1412C22C2×#58512yes—
1413C22C2×#58511yescharacteristic
1414C22C2×#58512yes—
1415C222−1+611yescharacteristic
1416C4—24no—
1417C4—22no—
1418C4—24no—
1419C4—41no—
1420C4—41no—
1421C4—42no—
1422C4—44no—
1423C4—44no—
1424C4—42no—
1425C4—42no—
1426C4—42no—
1427C4—44no—
1428C4—42no—
1429C4—41no—
1430C4—42no—
1431C4—42no—
1432C4—44no—
1433C4—42no—
1434C4—44no—
1435C4—42no—
1436C4—42no—
1437C4—44no—
1438C4—42no—
1439C4#354514yes—
1440C2—81no—
1441C2—81no—
1442C2—82no—
1443C2—82no—
1444C2—82no—
1445C2C2×#354511yescharacteristic
1446C2#6276212yes—
1447C2#6291911yescharacteristic
1448C2#6297112yes—
1449C2#6303511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#42985C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59946C2semidirect
2. #59537C2semidirect
3. #59475C2semidirect
4. #59374C2semidirect
5. #57459C2semidirect
6. #55616C2semidirect
7. #53979C2semidirect
8. #53110C2semidirect
9. #53017C2semidirect
10. #53005C2semidirect
11. #52848C2semidirect
12. #52806C2semidirect
14. #42913C2semidirect
15. #42793C2semidirect
16. #41565C2semidirect
17. #41541C2semidirect
18. #39827C2semidirect
19. #39437C2semidirect
20. #39417C2semidirect
21. #39238C2semidirect
22. #39224C2semidirect
23. #37612C2semidirect
24. #37573C2semidirect
25. #37516C2semidirect
26. #36457C2semidirect
27. #36373C2semidirect
28. #34975C2semidirect
29. #34871C2semidirect

Maximal subgroups

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

subgroupindex
#599462
#595372
#594752
#593742
#574592
#556162
#539792
#531102
#530172
#530052
#528482
#528062
#429852
#429132
#427932
#415652
#415412
#398272
#394372
#394172
#392382
#392242
#376122
#375732
#375162
#364572
#363732
#349752
#348712