Finite Group Databasebeta

← #8107458

Subgroups — #8107458

Order 512.

5174 conjugacy classes of subgroups.

The subgroup lattice has 1408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53112C212yesmaximal, complemented
2#53099C212yesmaximal, complemented
3#52642C214yesmaximal, complemented
4#52427C214yesmaximal, complemented
5#44982C211yesmaximal, characteristic, complemented
6#44965C211yesmaximal, characteristic, complemented
7#44948C211yesmaximal, characteristic, complemented
8#44931C211yesmaximal, characteristic, complemented
9#43423C214yesmaximal, complemented
10#43097C214yesmaximal, complemented
11#42524C212yesmaximal, complemented
12#42509C212yesmaximal, complemented
13#42494C212yesmaximal, complemented
14#42479C212yesmaximal, complemented
15#41252C214yesmaximal, complemented
16#41053C214yesmaximal, complemented
17#40518C214yesmaximal, complemented
18#40493C214yesmaximal, complemented
19#36596C212yesmaximal, complemented
20#36576C212yesmaximal, complemented
21#36570C212yesmaximal, complemented
22#36544C212yesmaximal, complemented
23#35271C211yesmaximal, characteristic, complemented
24#35271C211yesmaximal, characteristic, complemented
25#35082C212yesmaximal, complemented
26#35006C212yesmaximal, complemented
27C2×#2399C211yesmaximal, characteristic, complemented
28C2×#554C2212yes—
29C2×#553C2214yes—
30C2×#550C2212yes—
31C2×#548C2214yes—
32C2×#539C2214yes—
33C22×C4×Q8C2212yes—
34#2857C2212yes—
35#2856C2212yes—
36#2856C2212yes—
37#2856C2211yescharacteristic
38#2856C2211yescharacteristic
39#2854C2212yes—
40#2854C2212yes—
41#2851C2212yes—
42#2851C2211yescharacteristic
43#2851C2211yescharacteristic
44#2841C2214yes—
45#2837C2214yes—
46#2836C2214yes—
47#2830C2214yes—
48#2829C2214yes—
49#2827C2214yes—
50#2823C2214yes—
51#2820C2214yes—
52#2816C2214yes—
53#2814C2214yes—
54#2814C2214yes—
55#2814C2214yes—
56#2802C2214yes—
57#2788C2214yes—
58#2786C2214yes—
59#2739C2214yes—
60#2726C2214yes—
61#2723C2214yes—
62#2722C2214yes—
63#2720C2214yes—
64#2717C2214yes—
65#2715C2214yes—
66#2715C2214yes—
67#2715C2214yes—
68#2707C2214yes—
69#2704C2214yes—
70#2704C2214yes—
71#2704C2214yes—
72#2701C2214yes—
73#2698C2214yes—
74#2695C2214yes—
75#2692C2214yes—
76#2691C2214yes—
77#2686C2214yes—
78#2683C2214yes—
79#2683C2214yes—
80#2681C2214yes—
81#2681C2214yes—
82#2680C2214yes—
83#2672C2214yes—
84#2672C2214yes—
85#2672C2214yes—
86#2671C2214yes—
87#2671C2214yes—
88#2664C2214yes—
89#2662C2214yes—
90#2659C2214yes—
91#2651C2214yes—
92#2651C2214yes—
93#2647C2211yescharacteristic
94#2647C2211yescharacteristic
95#2644C2212yes—
96#2644C2212yes—
97#2641C2211yescharacteristic
98#2641C2211yescharacteristic
99#2639C2214yes—
100#2637C2214yes—
101#2630C2214yes—
102#2629C2214yes—
103#2618C2214yes—
104#2618C2214yes—
105#2616C2214yes—
106#2601C2214yes—
107#2587C2214yes—
108#2584C2214yes—
109#2584C2212yes—
110#2584C2212yes—
111#2580C2212yes—
112#2580C2212yes—
113#2579C2214yes—
114#2574C2214yes—
115#2567C2212yes—
116#2566C2212yes—
117#2560C2214yes—
118#2560C2214yes—
119#2558C2214yes—
120#2558C2214yes—
121#2554C2214yes—
122#2554C2214yes—
123#2552C2212yes—
124#2550C2212yes—
125#2548C2212yes—
126#2548C2212yes—
127#2548C2212yes—
128#2543C2214yes—
129#2543C2214yes—
130#2541C2212yes—
131#2538C2212yes—
132#2538C2212yes—
133#2538C2212yes—
134#2538C2212yes—
135#2531C2214yes—
136#2531C2214yes—
137#2526C2214yes—
138#2526C2214yes—
139#2522C2214yes—
140#2513C2212yes—
141#2513C2212yes—
142#2512C2212yes—
143#2512C2212yes—
144#2512C2212yes—
145#2512C2212yes—
146#2508C2212yes—
147#2507C2212yes—
148#2507C2212yes—
149#2507C2212yes—
150#2506C2212yes—
151#2506C2212yes—
152#2490C2214yes—
153#2474C2214yes—
154#2469C2214yes—
155#2465C2214yes—
156#2465C2214yes—
157#2462C2214yes—
158#2461C2214yes—
159#2454C2212yes—
160#2454C2212yes—
161#2454C2212yes—
162#2452C2212yes—
163#2452C2212yes—
164#2452C2212yes—
165#2450C2214yes—
166#2449C2214yes—
167#2449C2214yes—
168#2449C2214yes—
169#2449C2214yes—
170#2445C2212yes—
171#2445C2212yes—
172#2445C2212yes—
173#2445C2212yes—
174#2445C2212yes—
175#2445C2212yes—
176#2444C2214yes—
177#2444C2214yes—
178#2443C2214yes—
179#2443C2214yes—
180#2438C2214yes—
181#2430C2214yes—
182#2430C2214yes—
183#2426C2214yes—
184#2426C2214yes—
185#2426C2214yes—
186#2425C2214yes—
187#2425C2214yes—
188#2425C2214yes—
189#2425C2214yes—
190#2423C2214yes—
191#2417C2214yes—
192#2416C2214yes—
193#2416C2214yes—
194#2416C2214yes—
195#2416C2214yes—
196#2409C2214yes—
197#2406C2214yes—
198#2399C2212yes—
199#2399C2212yes—
200#2399C2212yes—
201#2399C2212yes—
202#2399C2211yescharacteristic
203#2399C2211yescharacteristic
204#2399C2211yescharacteristic
205#2399C2211yescharacteristic
206#2399C2212yes—
207#2399C2212yes—
208C2×#398C2212yes—
209C2×#398C2212yes—
210C2×#395C2212yes—
211C2×#395C2212yes—
212#2370C2212yes—
213#2368C2214yes—
214#2366C2212yes—
215#2363C2214yes—
216#2360C2214yes—
217#2355C2212yes—
218#2354C2212yes—
219Q8×C4⋊C4C2212yes—
220#2349C2214yes—
221#2349C2212yes—
222D4×C4⋊C4C2214yes—
223#2341C2214yes—
224#2335C2214yes—
225#2335C2214yes—
226#2330C2211yescharacteristic
227#2330C2211yescharacteristic
228#2328C2211yescharacteristic
229#2328C2211yescharacteristic
230#2325C2214yes—
231#2319C2212yes—
232#2319C2212yes—
233C4×#121C2212yes—
234C4×#121C2212yes—
235C4×#121C2212yes—
236C4×#121C2212yes—
237C4×#121C2212yes—
238C4×#121C2212yes—
239C2×C4×C4⋊C4C2211yescharacteristic
240C2×C4×C4⋊C4C2211yescharacteristic
241C2×C4×C4⋊C4C2212yes—
242C2×#376C2211yescharacteristic
243C22×#41C2314yes—
244C23×Q8C2312yes—
245#554—48no—
246#553—416no—
247#550—48no—
248#548—416no—
249#539—416no—
250C2×C4⋊Q8C2312yes—
251C2×#127C2311yescharacteristic
252C2×#127C2311yescharacteristic
253C2×#127C2312yes—
254C2×#127C2312yes—
255C2×#126C2314yes—
256C2×#126C2314yes—
257C2×#126C2314yes—
258C2×#126C2314yes—
259C2×#125C2311yescharacteristic
260C2×#125C2311yescharacteristic
261C2×#125C2314yes—
262C2×#125C2312yes—
263C2×#125C2314yes—
264C2×#125C2314yes—
265C2×#124C2314yes—
266C2×#124C2314yes—
267C2×#124C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×#121C2314yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2314yes—
291C2×#121C2314yes—
292C2×#121C2314yes—
293C2×#121C2314yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2314yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×C4×Q8—48no—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2314yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2312yes—
323C2×#117C2314yes—
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2312yes—
326C22×C4⋊C4C2312yes—
327C22×C4⋊C4C2314yes—
328C22×C4⋊C4C2312yes—
329C22×C4⋊C4C2312yes—
330C22×C4⋊C4C2312yes—
331C22×C4⋊C4C2312yes—
332C22×C42C2311yescharacteristic
333C22×C42C2311yescharacteristic
334C22×C42C2311yescharacteristic
335C22×C42C2312yes—
336C22×C42C2312yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2312yes—
350#398C2314yes—
351#398C2312yes—
352#398C2314yes—
353#398C2314yes—
354#398C2312yes—
355#398C2314yes—
356#398C2312yes—
357#398C2312yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2312yes—
365#398C2312yes—
366#398C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2312yes—
376#398C2312yes—
377#398C2312yes—
378#398C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#395C2312yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2312yes—
422#395C2312yes—
423#395C2312yes—
424#395C2312yes—
425#395C2312yes—
426#395C2312yes—
427#395C2312yes—
428#395C2312yes—
429#395C2312yes—
430#395C2312yes—
431#395C2312yes—
432#395C2312yes—
433#395C2312yes—
434#395C2312yes—
435#395C2312yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#393C2314yes—
459#393C2314yes—
460#393C2314yes—
461#393C2314yes—
462#393C2314yes—
463#392C2314yes—
464#392C2314yes—
465#391C2314yes—
466#391C2314yes—
467#391C2314yes—
468#391C2314yes—
469#390C2314yes—
470#390C2312yes—
471#390C2312yes—
472#390C2314yes—
473#390C2314yes—
474#390C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2312yes—
481#390C2312yes—
482#390C2312yes—
483#390C2314yes—
484#390C2314yes—
485#390C2314yes—
486#390C2314yes—
487#390C2314yes—
488#390C2312yes—
489#390C2312yes—
490#390C2314yes—
491#390C2314yes—
492#390C2312yes—
493#390C2312yes—
494#390C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2312yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2312yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#388C2314yes—
528#388C2314yes—
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#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#384C2312yes—
606#384C2314yes—
607#384C2311yescharacteristic
608#384C2311yescharacteristic
609#384C2312yes—
610#384C2312yes—
611#382C2314yes—
612#382C2312yes—
613#382C2311yescharacteristic
614#382C2311yescharacteristic
615#381C2314yes—
616#381C2314yes—
617#380C2314yes—
618#380C2314yes—
619#380C2314yes—
620#380C2314yes—
621#380C2314yes—
622#380C2314yes—
623#380C2314yes—
624#380C2314yes—
625#380C2312yes—
626#380C2312yes—
627#380C2314yes—
628#380C2314yes—
629#380C2314yes—
630#380C2314yes—
631C4×C4⋊C4C2311yescharacteristic
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2311yescharacteristic
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2311yescharacteristic
649C4×C4⋊C4C2311yescharacteristic
650C4×C4⋊C4C2311yescharacteristic
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2311yescharacteristic
656C4×C4⋊C4C2311yescharacteristic
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2311yescharacteristic
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2314yes—
665#376C2311yescharacteristic
666#376C2311yescharacteristic
667#376C2311yescharacteristic
668#376C2311yescharacteristic
669#376C2312yes—
670#376C2312yes—
671C2×#95C2311yescharacteristic
672C2×#95C2314yes—
673C2×#95C2312yes—
674C2×#95C2311yescharacteristic
675C2×#95C2311yescharacteristic
676C2×#95C2312yes—
677C2×#95C2312yes—
678C2×#95C2311yescharacteristic
679C2×#95C2312yes—
680C2×#41—48no—
681C2×#41—48no—
682C2×#41—48no—
683C22×Q8—28no—
684C22×Q8—44no—
685C22×Q8—44no—
686C22×Q8C2412yes—
687C22×Q8C2412yes—
688C22×Q8C2412yes—
689C22×Q8C2412yes—
690C22×Q8C2414yes—
691C22×D4C2414yes—
692C22×D4C2414yes—
693C22×D4C2412yes—
694C22×D4C2412yes—
695C22×D4C2414yes—
696C22×D4C2414yes—
697C22×D4C2414yes—
698C22×D4C2414yes—
699C22×D4C2414yes—
700C22×D4C2414yes—
701C23×C4C2411yescharacteristic
702C23×C4C2412yes—
703C23×C4C2412yes—
704C23×C4C2412yes—
705C23×C4C2411yescharacteristic
706C23×C4C2412yes—
707C23×C4C2412yes—
708C23×C4C2411yescharacteristic
709C23×C4C2414yes—
710C23×C4C2414yes—
711C23×C4C2414yes—
712C23×C4C2414yes—
713C23×C4C2414yes—
714C23×C4C2414yes—
715C23×C4C2412yes—
716C4⋊Q8—44no—
717#127—24no—
718#127—24no—
719#127—44no—
720#127—44no—
721#126—48no—
722#126—48no—
723#126—48no—
724#126—48no—
725#125—24no—
726#125—24no—
727#125—48no—
728#125—48no—
729#125—44no—
730#125—48no—
731#124—48no—
732#124—48no—
733#124—48no—
734#123—48no—
735#123—48no—
736#123—48no—
737#123—48no—
738#123—48no—
739#123—48no—
740#123—48no—
741#123—48no—
742C22⋊Q8—48no—
743C22⋊Q8—48no—
744C22⋊Q8—48no—
745C22⋊Q8—48no—
746C22⋊Q8—48no—
747C22⋊Q8—48no—
748C22⋊Q8—48no—
749C22⋊Q8—48no—
750C22⋊Q8—48no—
751C22⋊Q8—48no—
752C22⋊Q8—48no—
753#121—216no—
754#121—28no—
755#121—28no—
756#121—48no—
757#121—48no—
758#121—48no—
759#121—48no—
760#121—48no—
761#121—48no—
762#121—48no—
763#121—48no—
764#121—48no—
765#121—48no—
766C4×Q8—28no—
767C4×Q8—28no—
768C4×Q8—44no—
769C4×Q8—44no—
770C4×Q8—44no—
771C4×Q8—44no—
772C4×Q8—44no—
773C4×Q8—44no—
774C4×Q8—48no—
775C4×D4—216no—
776C4×D4—216no—
777C4×D4—28no—
778C4×D4—28no—
779C4×D4—44no—
780C4×D4—44no—
781C4×D4—44no—
782C4×D4—44no—
783C4×D4—48no—
784C4×D4—48no—
785C4×D4—48no—
786C4×D4—48no—
787C4×D4—48no—
788#117—48no—
789C2×C4⋊C4—28no—
790C2×C4⋊C4—28no—
791C2×C4⋊C4—44no—
792C2×C4⋊C4—44no—
793C2×C4⋊C4—44no—
794C2×C4⋊C4—44no—
795C2×C4⋊C4—44no—
796C2×C4⋊C4—48no—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C42—24no—
903C2×C42—24no—
904C2×C42—24no—
905C2×C42—44no—
906C2×C42—44no—
907C2×C42C2414yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2411yescharacteristic
915C2×C42C2412yes—
916C2×C42C2411yescharacteristic
917C2×C42C2411yescharacteristic
918C2×C42C2411yescharacteristic
919C2×C42C2411yescharacteristic
920C2×C42C2411yescharacteristic
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2411yescharacteristic
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2411yescharacteristic
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2411yescharacteristic
950#95C2411yescharacteristic
951#95C2412yes—
952#95C2412yes—
953#95C2411yescharacteristic
954#95C2412yes—
955#95C2412yes—
956#95C2411yescharacteristic
957#95C2411yescharacteristic
958#95C2411yescharacteristic
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987C24C2514yes—
988C24C2514yes—
989C24C2511yescharacteristic
990#41—832no—
991C2×Q8—24no—
992C2×Q8—24no—
993C2×Q8—24no—
994C2×Q8—24no—
995C2×Q8—24no—
996C2×Q8—24no—
997C2×Q8—24no—
998C2×Q8—24no—
999C2×Q8—42no—
1000C2×Q8—42no—
1001C2×Q8—42no—
1002C2×Q8—42no—
1003C2×Q8—44no—
1004C2×Q8—44no—
1005C2×Q8—44no—
1006C2×Q8—432no—
1007C2×D4—28no—
1008C2×D4—28no—
1009C2×D4—28no—
1010C2×D4—28no—
1011C2×D4—28no—
1012C2×D4—28no—
1013C2×D4—24no—
1014C2×D4—24no—
1015C2×D4—28no—
1016C2×D4—28no—
1017C2×D4—24no—
1018C2×D4—24no—
1019C2×D4—24no—
1020C2×D4—24no—
1021C2×D4—28no—
1022C2×D4—28no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C22×C4—22no—
1038C22×C4—22no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—22no—
1044C22×C4—22no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—28no—
1051C22×C4—28no—
1052C22×C4—28no—
1053C22×C4—28no—
1054C22×C4—28no—
1055C22×C4—42no—
1056C22×C4—42no—
1057C22×C4—42no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—44no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4H(5,𝔽2)18yes—
1079C22×C42−1+414yes—
1080C22×C4C2511yescharacteristic
1081C22×C4C2511yescharacteristic
1082C22×C4C2514yes—
1083C22×C4C2512yes—
1084C22×C4C2514yes—
1085C22×C4C2514yes—
1086C22×C4C2512yes—
1087C22×C4C2514yes—
1088C22×C4C2514yes—
1089C22×C4C2511yescharacteristic
1090C22×C4C2511yescharacteristic
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2514yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2511yescharacteristic
1102C22×C4C2512yes—
1103C22×C4C2511yescharacteristic
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—28no—
1119C4⋊C4—24no—
1120C4⋊C4—28no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—28no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—28no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—28no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C22⋊C4—28no—
1168C22⋊C4—28no—
1169C22⋊C4—28no—
1170C22⋊C4—28no—
1171C22⋊C4—28no—
1172C22⋊C4—28no—
1173C22⋊C4—28no—
1174C22⋊C4—28no—
1175C22⋊C4—28no—
1176C22⋊C4—28no—
1177C22⋊C4—28no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C42—24no—
1210C42—22no—
1211C42—24no—
1212C42—24no—
1213C42—24no—
1214C42—24no—
1215C42—28no—
1216C42—28no—
1217C42—24no—
1218C42—22no—
1219C42—22no—
1220C42—22no—
1221C42—22no—
1222C42—22no—
1223C42—42no—
1224C42—42no—
1225C42—42no—
1226C42—42no—
1227C42—44no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42H(5,𝔽2)14yes—
1232C422−1+414yes—
1233C23—21no—
1234C23—21no—
1235C23—22no—
1236C23—24no—
1237C23—24no—
1238C23—24no—
1239C23—24no—
1240C23—24no—
1241C23—24no—
1242C23—24no—
1243C23—24no—
1244C23—24no—
1245C23—24no—
1246C23—24no—
1247C23—24no—
1248C23—24no—
1249C23—24no—
1250C23C2×H(5,𝔽2)14yes—
1251C23C2×2−1+412yes—
1252C23C2611yescharacteristic
1253Q8—216no—
1254Q8—48no—
1255Q8—48no—
1256Q8—48no—
1257Q8—164no—
1258D4—416no—
1259D4—416no—
1260D4—48no—
1261D4—48no—
1262D4—88no—
1263D4—88no—
1264D4—88no—
1265D4—88no—
1266D4—164no—
1267D4—164no—
1268C2×C4—21no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—21no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—28no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—48no—
1329C2×C4—48no—
1330C2×C4—48no—
1331C2×C4—48no—
1332C2×C4—44no—
1333C2×C4—44no—
1334C2×C4—88no—
1335C2×C4—88no—
1336C2×C4—88no—
1337C2×C4—88no—
1338C2×C4—88no—
1339C2×C4—84no—
1340C2×C4—84no—
1341C2×C4—164no—
1342C2×C4C2×H(5,𝔽2)14yes—
1343C2×C4C2×H(5,𝔽2)14yes—
1344C2×C4C2×H(5,𝔽2)14yes—
1345C2×C4C2×H(5,𝔽2)12yes—
1346C2×C4C2×2−1+412yes—
1347C2×C4C2×2−1+414yes—
1348C2×C4C2×2−1+412yes—
1349C2×C4C2×2−1+412yes—
1350C2×C4#58514yes—
1351C22—22no—
1352C22—22no—
1353C22—24no—
1354C22—24no—
1355C22—44no—
1356C22—44no—
1357C22—44no—
1358C22—44no—
1359C22—44no—
1360C22—44no—
1361C22—44no—
1362C22—44no—
1363C22—44no—
1364C22—44no—
1365C22—44no—
1366C22—44no—
1367C22—44no—
1368C22—44no—
1369C22#354814yes—
1370C22C22×H(5,𝔽2)11yescharacteristic
1371C22C22×H(5,𝔽2)12yes—
1372C22C22×2−1+411yescharacteristic
1373C22C22×2−1+411yescharacteristic
1374C22C2×#58512yes—
1375C4—22no—
1376C4—24no—
1377C4—24no—
1378C4—24no—
1379C4—24no—
1380C4—24no—
1381C4—41no—
1382C4—41no—
1383C4—44no—
1384C4—44no—
1385C4—41no—
1386C4—41no—
1387C4—42no—
1388C4—42no—
1389C4—44no—
1390C4—42no—
1391C4—44no—
1392C4—42no—
1393C4—42no—
1394C4—42no—
1395C4—44no—
1396C4—42no—
1397C4—44no—
1398C4#355214yes—
1399C2—24no—
1400C2—84no—
1401C2—84no—
1402C2C2×#355211yescharacteristic
1403C2C2×#354811yescharacteristic
1404C2#6276111yescharacteristic
1405C2#6281812yes—
1406C2#6283512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53112C2semidirect
2. #53099C2semidirect
3. #52642C2semidirect
4. #52427C2semidirect
5. #44982C2semidirect
6. #44965C2semidirect
7. #44948C2semidirect
8. #44931C2semidirect
9. #43423C2semidirect
10. #43097C2semidirect
11. #42524C2semidirect
12. #42509C2semidirect
13. #42494C2semidirect
14. #42479C2semidirect
15. #41252C2semidirect
16. #41053C2semidirect
17. #40518C2semidirect
18. #40493C2semidirect
19. #36596C2semidirect
20. #36576C2semidirect
21. #36570C2semidirect
22. #36544C2semidirect
23. #35271C2semidirect
24. #35271C2semidirect
25. #35082C2semidirect
26. #35006C2semidirect
27. C2×#2399C2semidirect

Maximal subgroups

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

subgroupindex
#531122
#530992
#526422
#524272
#449822
#449652
#449482
#449312
#434232
#430972
#425242
#425092
#424942
#424792
#412522
#410532
#405182
#404932
#365962
#365762
#365702
#365442
#352712
#350822
#350062
C2×#23992