Finite Group Databasebeta

← #7893288

Subgroups — #7893288

Order 512.

4673 conjugacy classes of subgroups.

The subgroup lattice has 1468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59822C211yesmaximal, characteristic
2#59118C212yesmaximal, complemented
3#52273C211yesmaximal, characteristic, complemented
4#50842C214yesmaximal, complemented
5#50451C214yesmaximal, complemented
6#50042C214yesmaximal, complemented
7#47600C214yesmaximal, complemented
8#45940C212yesmaximal, complemented
9#45270C212yesmaximal, complemented
10#45072C212yesmaximal, complemented
11#44989C212yesmaximal, complemented
12#44510C214yesmaximal, complemented
13#42873C214yesmaximal, complemented
14#42740C212yesmaximal, complemented
15#42515C212yesmaximal, complemented
16#40127C212yesmaximal, complemented
17#39830C212yesmaximal, complemented
18#39628C211yesmaximal, characteristic, complemented
19#39621C211yesmaximal, characteristic, complemented
20#38830C212yesmaximal, complemented
21#38104C212yesmaximal, complemented
22#37766C212yesmaximal, complemented
23#37267C212yesmaximal, complemented
24#36534C211yesmaximal, characteristic, complemented
25#36050C212yesmaximal, complemented
26#35572C212yesmaximal, complemented
27#35186C211yesmaximal, characteristic, complemented
28#34467C212yesmaximal, complemented
29#34337C211yesmaximal, characteristic, complemented
30C2×#557C2211yescharacteristic
31C2×#556C2211yescharacteristic
32C2×#555C2212yes—
33C2×#554C2211yescharacteristic
34C2×#542C2212yes—
35C2×#529C2212yes—
36#2862C2211yescharacteristic
37#2861C2212yes—
38#2861C2212yes—
39#2860C2212yes—
40#2857C2212yes—
41#2837C2214yes—
42#2837C2214yes—
43#2811C2212yes—
44#2808C2211yescharacteristic
45#2808C2211yescharacteristic
46#2806C2212yes—
47#2806C2212yes—
48#2804C2211yescharacteristic
49#2804C2212yes—
50#2804C2212yes—
51#2796C2214yes—
52#2796C2212yes—
53#2796C2212yes—
54#2794C2212yes—
55#2780C2214yes—
56#2775C2214yes—
57#2768C2214yes—
58#2761C2214yes—
59#2757C2214yes—
60#2752C2214yes—
61#2751C2212yes—
62#2751C2212yes—
63#2742C2214yes—
64#2738C2214yes—
65#2737C2214yes—
66#2734C2212yes—
67#2733C2212yes—
68#2733C2212yes—
69#2732C2212yes—
70#2732C2212yes—
71#2732C2214yes—
72#2731C2214yes—
73#2731C2214yes—
74#2731C2214yes—
75#2730C2214yes—
76#2724C2211yescharacteristic
77#2723C2214yes—
78#2722C2214yes—
79#2720C2214yes—
80#2720C2214yes—
81#2718C2214yes—
82#2718C2214yes—
83#2711C2214yes—
84#2711C2214yes—
85#2710C2214yes—
86#2710C2214yes—
87#2709C2214yes—
88#2709C2212yes—
89#2705C2214yes—
90#2701C2214yes—
91#2698C2214yes—
92#2680C2214yes—
93#2680C2214yes—
94#2674C2214yes—
95#2672C2214yes—
96#2672C2214yes—
97#2663C2214yes—
98#2663C2214yes—
99#2662C2214yes—
100#2660C2212yes—
101#2651C2214yes—
102#2651C2214yes—
103#2647C2212yes—
104#2644C2214yes—
105#2632C2214yes—
106#2629C2212yes—
107#2610C2214yes—
108#2603C2214yes—
109#2602C2214yes—
110#2601C2214yes—
111#2596C2214yes—
112#2593C2214yes—
113#2587C2214yes—
114#2586C2214yes—
115#2582C2211yescharacteristic
116#2580C2212yes—
117#2565C2212yes—
118#2563C2211yescharacteristic
119#2560C2214yes—
120#2560C2214yes—
121#2560C2214yes—
122#2557C2214yes—
123#2556C2214yes—
124#2554C2214yes—
125#2552C2211yescharacteristic
126#2551C2212yes—
127#2550C2212yes—
128#2550C2212yes—
129#2548C2211yescharacteristic
130#2548C2211yescharacteristic
131#2548C2214yes—
132#2547C2211yescharacteristic
133#2544C2214yes—
134#2544C2212yes—
135#2542C2214yes—
136#2541C2212yes—
137#2541C2212yes—
138#2537C2212yes—
139#2536C2212yes—
140#2536C2212yes—
141#2532C2214yes—
142#2532C2214yes—
143#2532C2214yes—
144#2529C2214yes—
145#2524C2214yes—
146#2520C2214yes—
147#2519C2214yes—
148#2516C2214yes—
149#2512C2214yes—
150#2512C2212yes—
151#2507C2214yes—
152#2501C2212yes—
153#2500C2212yes—
154#2497C2212yes—
155#2495C2212yes—
156#2491C2212yes—
157#2490C2212yes—
158#2490C2212yes—
159#2490C2212yes—
160#2479C2214yes—
161#2475C2214yes—
162#2475C2214yes—
163#2474C2214yes—
164#2469C2214yes—
165#2468C2214yes—
166#2468C2214yes—
167#2466C2214yes—
168#2461C2214yes—
169#2461C2214yes—
170#2461C2214yes—
171#2461C2214yes—
172#2458C2214yes—
173#2455C2214yes—
174#2454C2212yes—
175#2452C2214yes—
176#2452C2212yes—
177#2452C2212yes—
178#2451C2214yes—
179#2450C2214yes—
180#2450C2214yes—
181#2448C2212yes—
182#2448C2214yes—
183#2448C2214yes—
184#2447C2212yes—
185#2445C2214yes—
186#2445C2214yes—
187#2441C2212yes—
188#2441C2212yes—
189#2441C2212yes—
190#2440C2212yes—
191#2438C2214yes—
192#2426C2212yes—
193#2426C2212yes—
194#2425C2214yes—
195#2423C2212yes—
196#2422C2212yes—
197#2421C2212yes—
198#2420C2212yes—
199#2414C2214yes—
200#2414C2212yes—
201#2414C2212yes—
202#2402C2214yes—
203#2398C2212yes—
204#2398C2212yes—
205#2395C2212yes—
206#2379C2214yes—
207#2377C2214yes—
208#2370C2214yes—
209#2370C2212yes—
210#2367C2214yes—
211#2365C2212yes—
212#2365C2211yescharacteristic
213#2363C2212yes—
214#2362C2214yes—
215#2362C2212yes—
216#2362C2212yes—
217#2361C2212yes—
218#2355C2212yes—
219#2354C2212yes—
220#2354C2212yes—
221#2352C2212yes—
222#2352C2212yes—
223Q8×C4⋊C4C2211yescharacteristic
224Q8×C4⋊C4C2212yes—
225Q8×C4⋊C4C2211yescharacteristic
226Q8×C4⋊C4C2212yes—
227#2349C2212yes—
228#2347C2212yes—
229#2346C2212yes—
230#2343C2214yes—
231#2337C2214yes—
232#2334C2214yes—
233#2331C2212yes—
234#2330C2212yes—
235#2330C2214yes—
236#2328C2212yes—
237#2326C2212yes—
238#2326C2214yes—
239#2325C2214yes—
240#2324C2212yes—
241#2319C2212yes—
242#2317C2212yes—
243#2314C2214yes—
244C4×C4⋊Q8C2212yes—
245C4×C4⋊Q8C2211yescharacteristic
246C4×#127C2211yescharacteristic
247C4×#127C2211yescharacteristic
248C4×#124C2212yes—
249C4×#123C2212yes—
250C4×#121C2212yes—
251#2296C2212yes—
252#2295C2211yescharacteristic
253#2295C2212yes—
254#2295C2211yescharacteristic
255#2290C2212yes—
256#2290C2212yes—
257#2276C2212yes—
258C42×Q8C2211yescharacteristic
259#557—28no—
260#556—44no—
261#555—216no—
262#554—44no—
263#542—48no—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×#127C2311yescharacteristic
271C2×#127C2311yescharacteristic
272C2×#127C2314yes—
273#529—48no—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#124C2314yes—
284C2×#124C2312yes—
285C2×#124C2314yes—
286C2×#124C2312yes—
287C2×#124C2314yes—
288C2×#124C2312yes—
289C2×#124C2312yes—
290C2×#124C2314yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×#123C2312yes—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×#121C2312yes—
306C2×#121C2314yes—
307C2×#121C2312yes—
308C2×#121C2312yes—
309C2×#121C2312yes—
310C2×#121C2314yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2312yes—
328C2×C4×D4C2311yescharacteristic
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2314yes—
336C2×#117C2314yes—
337C2×#117C2312yes—
338C2×#117C2312yes—
339C2×#117C2312yes—
340C2×#117C2314yes—
341C2×#117C2312yes—
342C22×C4⋊C4C2312yes—
343C22×C42C2312yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2312yes—
350#400C2312yes—
351#400C2312yes—
352#400C2312yes—
353#400C2314yes—
354#399C2314yes—
355#399C2312yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2312yes—
381#397C2314yes—
382#397C2312yes—
383#397C2312yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2312yes—
388#397C2312yes—
389#397C2314yes—
390#397C2314yes—
391#397C2312yes—
392#397C2312yes—
393#397C2314yes—
394#397C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2312yes—
423#394C2314yes—
424#394C2314yes—
425#394C2312yes—
426#394C2312yes—
427#394C2312yes—
428#394C2314yes—
429#394C2312yes—
430#394C2312yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2312yes—
441#393C2312yes—
442#393C2312yes—
443#393C2312yes—
444#393C2314yes—
445#393C2314yes—
446#392C2314yes—
447#392C2314yes—
448#392C2314yes—
449#392C2314yes—
450#391C2312yes—
451#391C2312yes—
452#391C2314yes—
453#391C2312yes—
454#391C2311yescharacteristic
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2314yes—
459#391C2312yes—
460#391C2314yes—
461#391C2314yes—
462#391C2312yes—
463#391C2314yes—
464#391C2311yescharacteristic
465#391C2312yes—
466#391C2314yes—
467#391C2311yescharacteristic
468#391C2311yescharacteristic
469#390C2312yes—
470#390C2312yes—
471#390C2314yes—
472#390C2312yes—
473#390C2311yescharacteristic
474#390C2312yes—
475#390C2312yes—
476#390C2311yescharacteristic
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2314yes—
481#390C2312yes—
482#390C2312yes—
483#390C2314yes—
484#390C2312yes—
485#390C2314yes—
486#390C2312yes—
487#390C2312yes—
488#390C2314yes—
489#390C2312yes—
490#390C2314yes—
491#390C2314yes—
492#390C2314yes—
493#390C2314yes—
494#390C2314yes—
495#390C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2314yes—
510#389C2312yes—
511#389C2312yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2312yes—
519#389C2314yes—
520#389C2312yes—
521#389C2311yescharacteristic
522#389C2311yescharacteristic
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2311yescharacteristic
528#389C2311yescharacteristic
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
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#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2312yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2312yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2312yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2312yes—
573#388C2312yes—
574#388C2314yes—
575#388C2312yes—
576#387C2312yes—
577#387C2314yes—
578#387C2314yes—
579#387C2312yes—
580#387C2314yes—
581#387C2314yes—
582#387C2312yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2312yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2312yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2312yes—
596#387C2312yes—
597#387C2312yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2312yes—
602#387C2312yes—
603#387C2314yes—
604#387C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2312yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2312yes—
617#386C2314yes—
618#386C2312yes—
619#386C2312yes—
620#386C2312yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2312yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2312yes—
637#385C2314yes—
638#385C2312yes—
639#385C2314yes—
640#385C2312yes—
641#385C2312yes—
642#384C2311yescharacteristic
643#384C2311yescharacteristic
644#384C2311yescharacteristic
645#384C2312yes—
646#384C2314yes—
647#384C2312yes—
648#384C2314yes—
649#384C2312yes—
650#384C2312yes—
651#383C2314yes—
652#383C2314yes—
653#382C2312yes—
654#382C2314yes—
655#382C2314yes—
656#382C2312yes—
657#382C2312yes—
658#382C2312yes—
659#381C2314yes—
660#381C2314yes—
661#381C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2314yes—
665#380C2314yes—
666#380C2312yes—
667#380C2312yes—
668#380C2314yes—
669#380C2312yes—
670#380C2312yes—
671#380C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2311yescharacteristic
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711#376C2312yes—
712#376C2314yes—
713#376C2312yes—
714#376C2314yes—
715C2×#95C2314yes—
716C43C2311yescharacteristic
717C43C2312yes—
718C22×Q8C2411yescharacteristic
719C22×Q8C2411yescharacteristic
720C22×Q8C2412yes—
721C22×Q8C2411yescharacteristic
722C22×Q8C2412yes—
723C22×Q8C2414yes—
724C22×Q8C2412yes—
725C22×D4C2412yes—
726C22×D4C2411yescharacteristic
727C22×D4C2412yes—
728C22×D4C2414yes—
729C22×D4C2414yes—
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2414yes—
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2414yes—
739C23×C4C2414yes—
740C23×C4C2414yes—
741C23×C4C2414yes—
742C23×C4C2412yes—
743C23×C4C2412yes—
744C4⋊Q8—28no—
745C4⋊Q8—44no—
746C4⋊Q8—42no—
747C4⋊Q8—42no—
748C4⋊Q8—84no—
749C4⋊Q8#4118yes—
750#127—24no—
751#127—42no—
752#127—84no—
753#126—48no—
754#126—48no—
755#126—48no—
756#126—48no—
757#125—216no—
758#125—28no—
759#125—44no—
760#125—44no—
761#125—82no—
762#124—216no—
763#124—216no—
764#124—28no—
765#124—48no—
766#124—44no—
767#124—44no—
768#124—84no—
769#124—82no—
770#123—48no—
771#123—48no—
772#123—44no—
773#123—84no—
774#123—84no—
775#123—84no—
776C22⋊Q8—28no—
777C22⋊Q8—28no—
778C22⋊Q8—48no—
779C22⋊Q8—48no—
780C22⋊Q8—48no—
781C22⋊Q8—84no—
782C22⋊Q8—84no—
783C22⋊Q8—84no—
784#121—28no—
785#121—28no—
786#121—216no—
787#121—44no—
788#121—44no—
789#121—84no—
790C4×Q8—28no—
791C4×Q8—28no—
792C4×Q8—24no—
793C4×Q8—28no—
794C4×Q8—24no—
795C4×Q8—24no—
796C4×Q8—24no—
797C4×Q8—24no—
798C4×Q8—44no—
799C4×Q8—82no—
800C4×Q8—82no—
801C4×Q8—82no—
802C4×D4—28no—
803C4×D4—28no—
804C4×D4—28no—
805C4×D4—44no—
806C4×D4—48no—
807C4×D4—44no—
808C4×D4—44no—
809C4×D4—44no—
810C4×D4—42no—
811C4×D4—42no—
812C4×D4—82no—
813C4×D4—84no—
814C4×D4—84no—
815#117—28no—
816#117—28no—
817#117—216no—
818#117—44no—
819#117—48no—
820#117—44no—
821C2×C4⋊C4—44no—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2414yes—
937C2×C42—44no—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2412yes—
941C2×C42C2414yes—
942C2×C42C2412yes—
943C2×C42C2411yescharacteristic
944C2×C42C2411yescharacteristic
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2414yes—
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2412yes—
953C2×C42C2414yes—
954C2×C42C2411yescharacteristic
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2412yes—
958C2×C42C2411yescharacteristic
959C2×C42C2414yes—
960C2×C42C2414yes—
961C2×C42C2412yes—
962C2×C42C2412yes—
963C2×C42C2411yescharacteristic
964C2×C42C2414yes—
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2412yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026C24C2514yes—
1027C24C2512yes—
1028C24C2512yes—
1029C2×Q8—22no—
1030C2×Q8—22no—
1031C2×Q8—22no—
1032C2×Q8—22no—
1033C2×Q8—24no—
1034C2×Q8—42no—
1035C2×Q8—41no—
1036C2×Q8—42no—
1037C2×Q8—41no—
1038C2×Q8—42no—
1039C2×Q8—41no—
1040C2×Q8—41no—
1041C2×Q8—42no—
1042C2×Q8—42no—
1043C2×Q8—44no—
1044C2×Q8—42no—
1045C2×Q8—44no—
1046C2×Q8—44no—
1047C2×Q8—42no—
1048C2×Q8C2×#4118yes—
1049C2×Q8H(5,𝔽2)14yes—
1050C2×D4—24no—
1051C2×D4—24no—
1052C2×D4—28no—
1053C2×D4—28no—
1054C2×D4—24no—
1055C2×D4—24no—
1056C2×D4—24no—
1057C2×D4—24no—
1058C2×D4—24no—
1059C2×D4—22no—
1060C2×D4—22no—
1061C2×D4—41no—
1062C2×D4—41no—
1063C2×D4—44no—
1064C2×D4—41no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—42no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C2×D4—42no—
1073C2×D4—42no—
1074C2×D4—42no—
1075C2×D4—42no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—42no—
1079C2×D4—41no—
1080C2×D4—44no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—28no—
1090C22×C4—42no—
1091C22×C4—42no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—42no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—42no—
1098C22×C4—42no—
1099C22×C4—44no—
1100C22×C4—42no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2514yes—
1115C22×C4C2514yes—
1116C22×C4C2512yes—
1117C22×C4C2514yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2514yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2511yescharacteristic
1125C22×C4C2511yescharacteristic
1126C22×C4C2511yescharacteristic
1127C22×C4C2514yes—
1128C22×C4C2512yes—
1129C22×C4C2511yescharacteristic
1130C22×C4C2511yescharacteristic
1131C22×C4C2511yescharacteristic
1132C22×C4C2511yescharacteristic
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—22no—
1136C4⋊C4—24no—
1137C4⋊C4—28no—
1138C4⋊C4—24no—
1139C4⋊C4—22no—
1140C4⋊C4—28no—
1141C4⋊C4—28no—
1142C4⋊C4—22no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—28no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—28no—
1149C4⋊C4—28no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—22no—
1153C4⋊C4—22no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—41no—
1160C4⋊C4—41no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—41no—
1166C4⋊C4—41no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—44no—
1172C4⋊C4—41no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—42no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—42no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—41no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—42no—
1193C4⋊C4—42no—
1194C4⋊C4C2×#4118yes—
1195C4⋊C4C2×#4118yes—
1196C22⋊C4—28no—
1197C22⋊C4—28no—
1198C22⋊C4—28no—
1199C22⋊C4—28no—
1200C22⋊C4—24no—
1201C22⋊C4—24no—
1202C22⋊C4—28no—
1203C22⋊C4—28no—
1204C22⋊C4—28no—
1205C22⋊C4—28no—
1206C22⋊C4—28no—
1207C22⋊C4—24no—
1208C22⋊C4—24no—
1209C22⋊C4—28no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—42no—
1214C22⋊C4—44no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—44no—
1218C22⋊C4—42no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—42no—
1222C22⋊C4—42no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—42no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—42no—
1235C22⋊C4—42no—
1236C22⋊C4—42no—
1237C22⋊C4—42no—
1238C22⋊C4—42no—
1239C22⋊C4—42no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—42no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C42—28no—
1249C42—28no—
1250C42—28no—
1251C42—24no—
1252C42—24no—
1253C42—24no—
1254C42—24no—
1255C42—28no—
1256C42—22no—
1257C42—24no—
1258C42—24no—
1259C42—24no—
1260C42—22no—
1261C42—24no—
1262C42—42no—
1263C42—42no—
1264C42—41no—
1265C42—44no—
1266C42—44no—
1267C42—41no—
1268C42—44no—
1269C42—44no—
1270C42—41no—
1271C42—42no—
1272C42—44no—
1273C42—44no—
1274C42—42no—
1275C42C2×#4114yes—
1276C422−1+414yes—
1277C23—24no—
1278C23—22no—
1279C23—22no—
1280C23—24no—
1281C23—22no—
1282C23—22no—
1283C23—22no—
1284C23—22no—
1285C23—24no—
1286C23—24no—
1287C23—22no—
1288C23—22no—
1289C23—22no—
1290C23—24no—
1291C23—22no—
1292C23—22no—
1293C23—24no—
1294C23—22no—
1295C23—22no—
1296C23—24no—
1297C23—22no—
1298C23C2611yescharacteristic
1299Q8—28no—
1300Q8—48no—
1301Q8—44no—
1302Q8—82no—
1303Q8—84no—
1304Q8—164no—
1305Q8—162no—
1306D4—44no—
1307D4—48no—
1308D4—84no—
1309D4—88no—
1310D4—88no—
1311D4—84no—
1312D4—82no—
1313D4—84no—
1314D4—84no—
1315D4—88no—
1316D4—164no—
1317C2×C4—22no—
1318C2×C4—21no—
1319C2×C4—22no—
1320C2×C4—21no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—24no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—24no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—21no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—21no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—21no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—24no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—24no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—48no—
1386C2×C4—48no—
1387C2×C4—88no—
1388C2×C4—84no—
1389C2×C4—84no—
1390C2×C4—88no—
1391C2×C4—164no—
1392C2×C4—164no—
1393C2×C4C22×#4118yes—
1394C2×C4C22×#4112yes—
1395C2×C4C22×#4112yes—
1396C2×C4C22×#4112yes—
1397C2×C4C2×H(5,𝔽2)14yes—
1398C2×C4C2×H(5,𝔽2)12yes—
1399C2×C4C2×2−1+412yes—
1400C2×C4C2×2−1+412yes—
1401C2×C4C2×2−1+412yes—
1402C2×C4#58512yes—
1403C22—44no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—42no—
1408C22—44no—
1409C22—42no—
1410C22—42no—
1411C22—44no—
1412C22—44no—
1413C22—42no—
1414C22—42no—
1415C22—44no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—44no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—44no—
1424C22C23×#4111yescharacteristic
1425C22C22×H(5,𝔽2)11yescharacteristic
1426C22C22×2−1+411yescharacteristic
1427C22C2×#58511yescharacteristic
1428C22H(7,𝔽2)11yescharacteristic
1429C22H(7,𝔽2)11yescharacteristic
1430C222−1+611yescharacteristic
1431C4—22no—
1432C4—24no—
1433C4—28no—
1434C4—22no—
1435C4—22no—
1436C4—22no—
1437C4—22no—
1438C4—42no—
1439C4—42no—
1440C4—44no—
1441C4—42no—
1442C4—42no—
1443C4—42no—
1444C4—42no—
1445C4—42no—
1446C4—44no—
1447C4—44no—
1448C4—41no—
1449C4—42no—
1450C4—42no—
1451C4—42no—
1452C4—42no—
1453C4—44no—
1454C4—42no—
1455C4—42no—
1456C4#352214yes—
1457C2—84no—
1458C2—82no—
1459C2—82no—
1460C2C2×#352211yescharacteristic
1461C2#6284711yescharacteristic
1462C2#6287911yescharacteristic
1463C2#6289711yescharacteristic
1464C2#6292911yescharacteristic
1465C2#6300611yescharacteristic
1466C2#6306611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#59822C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59118C2semidirect
3. #52273C2semidirect
4. #50842C2semidirect
5. #50451C2semidirect
6. #50042C2semidirect
7. #47600C2semidirect
8. #45940C2semidirect
9. #45270C2semidirect
10. #45072C2semidirect
11. #44989C2semidirect
12. #44510C2semidirect
13. #42873C2semidirect
14. #42740C2semidirect
15. #42515C2semidirect
16. #40127C2semidirect
17. #39830C2semidirect
18. #39628C2semidirect
19. #39621C2semidirect
20. #38830C2semidirect
21. #38104C2semidirect
22. #37766C2semidirect
23. #37267C2semidirect
24. #36534C2semidirect
25. #36050C2semidirect
26. #35572C2semidirect
27. #35186C2semidirect
28. #34467C2semidirect
29. #34337C2semidirect

Maximal subgroups

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

subgroupindex
#598222
#591182
#522732
#508422
#504512
#500422
#476002
#459402
#452702
#450722
#449892
#445102
#428732
#427402
#425152
#401272
#398302
#396282
#396212
#388302
#381042
#377662
#372672
#365342
#360502
#355722
#351862
#344672
#343372