Finite Group Databasebeta

← #8757419

Subgroups — #8757419

Order 512.

4816 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58951C214yesmaximal, complemented
2#57406C214yesmaximal, complemented
3#57235C214yesmaximal, complemented
4#56590C214yesmaximal, complemented
5#54166C214yesmaximal, complemented
6#53632C214yesmaximal, complemented
7#51326C212yesmaximal, complemented
8#50888C214yesmaximal, complemented
9#50165C212yesmaximal, complemented
10#49070C214yesmaximal, complemented
11#47692C214yesmaximal, complemented
12#47312C214yesmaximal, complemented
13#46426C212yesmaximal, complemented
14#46359C212yesmaximal, complemented
15#46228C211yesmaximal, characteristic, complemented
16#46228C211yesmaximal, characteristic, complemented
17#46136C212yesmaximal, complemented
18#46018C212yesmaximal, complemented
19#46018C212yesmaximal, complemented
20#45998C212yesmaximal, complemented
21#45998C212yesmaximal, complemented
22#35329C211yesmaximal, characteristic
23#35142C212yesmaximal, complemented
24C2×#563C2212yes—
25C2×#563C2212yes—
26C2×#563C2211yescharacteristic, complemented
27C2×#563C2211yescharacteristic, complemented
28C2×#551C2212yes—
29C2×#544C2212yescomplemented
30C2×#539C2212yes—
31C2×#536C2211yescharacteristic
32C2×#536C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#535C2211yescharacteristic
35C2×#532C2211yescharacteristic
36C22×#124C2211yescharacteristic
37#2864C2212yescomplemented
38#2859C2212yescomplemented
39#2858C2212yes—
40#2858C2212yes—
41#2851C2212yes—
42#2851C2212yes—
43#2838C2214yescomplemented
44#2838C2214yescomplemented
45#2829C2214yescomplemented
46#2826C2214yescomplemented
47#2824C2214yescomplemented
48#2821C2214yescomplemented
49#2820C2212yes—
50#2820C2212yes—
51#2820C2212yescomplemented
52#2820C2212yescomplemented
53#2817C2212yescomplemented
54#2816C2212yes—
55#2807C2214yescomplemented
56#2803C2214yescomplemented
57#2800C2214yescomplemented
58#2800C2214yescomplemented
59#2796C2214yescomplemented
60#2796C2214yescomplemented
61#2780C2214yescomplemented
62#2780C2214yescomplemented
63#2778C2214yescomplemented
64#2778C2214yescomplemented
65#2777C2214yescomplemented
66#2773C2214yescomplemented
67#2756C2214yescomplemented
68#2753C2214yescomplemented
69#2742C2214yescomplemented
70#2734C2212yescomplemented
71#2734C2212yescomplemented
72#2731C2214yes—
73#2729C2214yescomplemented
74#2727C2214yescomplemented
75#2727C2214yescomplemented
76#2724C2212yes—
77#2723C2214yescomplemented
78#2723C2214yescomplemented
79#2723C2214yescomplemented
80#2723C2214yescomplemented
81#2721C2214yescomplemented
82#2720C2214yescomplemented
83#2720C2214yescomplemented
84#2720C2214yescomplemented
85#2718C2214yes—
86#2717C2214yes—
87#2717C2212yes—
88#2715C2214yes—
89#2715C2214yes—
90#2713C2214yescomplemented
91#2713C2214yescomplemented
92#2711C2214yes—
93#2709C2214yes—
94#2709C2214yes—
95#2709C2212yescomplemented
96#2709C2212yescomplemented
97#2708C2214yes—
98#2705C2214yescomplemented
99#2701C2214yes—
100#2697C2214yes—
101#2697C2212yes—
102#2696C2214yescomplemented
103#2696C2214yescomplemented
104#2694C2214yescomplemented
105#2694C2214yescomplemented
106#2691C2214yes—
107#2691C2214yes—
108#2689C2214yescomplemented
109#2685C2214yes—
110#2685C2214yes—
111#2684C2212yes—
112#2683C2214yescomplemented
113#2683C2214yescomplemented
114#2681C2214yes—
115#2680C2214yes—
116#2677C2214yescomplemented
117#2677C2214yescomplemented
118#2674C2214yes—
119#2674C2214yes—
120#2674C2214yes—
121#2674C2214yes—
122#2674C2214yes—
123#2674C2214yescomplemented
124#2674C2214yescomplemented
125#2672C2214yes—
126#2672C2214yes—
127#2663C2214yes—
128#2658C2212yes—
129#2657C2212yes—
130#2655C2214yescomplemented
131#2654C2214yescomplemented
132#2652C2214yes—
133#2648C2214yescomplemented
134#2636C2214yescomplemented
135#2628C2214yescomplemented
136#2622C2214yes—
137#2601C2214yescomplemented
138#2601C2214yescomplemented
139#2598C2214yescomplemented
140#2597C2214yescomplemented
141#2597C2214yescomplemented
142#2596C2214yescomplemented
143#2591C2212yes—
144#2583C2212yescomplemented
145#2558C2214yes—
146#2558C2214yescomplemented
147#2558C2214yescomplemented
148#2556C2214yescomplemented
149#2551C2214yescomplemented
150#2551C2214yescomplemented
151#2542C2214yescomplemented
152#2542C2214yescomplemented
153#2540C2214yes—
154#2540C2214yes—
155#2539C2214yes—
156#2539C2214yes—
157#2533C2214yescomplemented
158#2528C2214yescomplemented
159#2522C2214yescomplemented
160#2521C2214yes—
161#2521C2214yescomplemented
162#2512C2214yescomplemented
163#2512C2214yescomplemented
164#2512C2214yescomplemented
165#2512C2214yescomplemented
166#2509C2212yescomplemented
167#2508C2212yescomplemented
168#2507C2212yescomplemented
169#2506C2212yescomplemented
170#2497C2212yes—
171#2496C2212yes—
172#2495C2212yes—
173#2494C2212yes—
174#2480C2214yes—
175#2480C2214yes—
176#2479C2214yescomplemented
177#2479C2214yescomplemented
178#2478C2214yes—
179#2476C2214yes—
180#2475C2214yes—
181#2474C2214yes—
182#2474C2214yescomplemented
183#2472C2214yes—
184#2471C2214yescomplemented
185#2470C2214yes—
186#2466C2214yescomplemented
187#2466C2214yescomplemented
188#2463C2214yescomplemented
189#2452C2214yescomplemented
190#2452C2214yescomplemented
191#2449C2214yescomplemented
192#2449C2214yescomplemented
193#2445C2214yes—
194#2445C2214yes—
195#2443C2214yes—
196#2441C2214yescomplemented
197#2440C2214yescomplemented
198#2437C2214yes—
199#2437C2214yes—
200#2434C2214yes—
201#2432C2212yes—
202#2432C2212yes—
203#2418C2214yes—
204#2406C2212yes—
205#2406C2212yes—
206#2405C2214yes—
207#2379C2212yes—
208#2379C2211yescharacteristic, complemented
209#2379C2211yescharacteristic, complemented
210#2375C2212yes—
211#2374C2212yes—
212#2336C2214yescomplemented
213#2334C2214yes—
214#2333C2212yes—
215#2332C2212yescomplemented
216C4×#125C2212yescomplemented
217C4×#125C2212yescomplemented
218C4×#117C2211yescharacteristic
219C22×#41C2311yescharacteristic
220C22×#41C2311yescharacteristic
221C23×Q8C2311yescharacteristic
222C23×D4C2311yescharacteristic
223#563—48no—
224#563—48no—
225#563—44no—
226#563—44no—
227#551—48no—
228#544—48no—
229#539—48no—
230#536—44no—
231#536—44no—
232#535—44no—
233#535—44no—
234#532—44no—
235C2×C4⋊Q8C2314yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2314yes—
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2314yes—
244C2×#127C2312yes—
245C2×#127C2312yes—
246C2×#127C2311yescharacteristic
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#125C2314yes—
257C2×#125C2314yes—
258C2×#125C2314yes—
259C2×#124—44no—
260C2×#124C2312yes—
261C2×#124C2311yescharacteristic
262C2×#124C2311yescharacteristic
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2312yes—
266C2×#124C2312yes—
267C2×#124C2312yes—
268C2×#124C2314yes—
269C2×#124C2312yes—
270C2×#124C2312yes—
271C2×#123C2312yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2312yes—
275C2×#123C2312yes—
276C2×#123C2312yes—
277C2×#123C2312yes—
278C2×#123C2312yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×#120C2312yes—
301C2×#120C2312yes—
302C2×#120C2314yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2314yes—
306C2×#117C2311yescharacteristic
307C2×#117C2311yescharacteristic
308C2×#117C2314yes—
309C2×#117C2314yes—
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2312yes—
312C22×C22⋊C4C2314yes—
313C22×C22⋊C4C2314yes—
314C22×C42C2311yescharacteristic
315#401C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2314yes—
337#399C2314yes—
338#399C2314yes—
339#399C2314yes—
340#399C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#393C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2312yes—
438#391C2312yes—
439#390C2314yes—
440#390C2314yes—
441#390C2314yes—
442#390C2314yes—
443#390C2314yes—
444#390C2314yes—
445#390C2314yes—
446#390C2314yes—
447#390C2314yes—
448#390C2312yes—
449#390C2314yes—
450#390C2312yes—
451#390C2314yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2312yes—
552#386C2312yes—
553#386C2314yes—
554#386C2312yes—
555#386C2312yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#384C2312yes—
584#384C2312yes—
585#384C2314yes—
586#384C2314yes—
587#383C2314yes—
588#382C2312yes—
589#382C2312yes—
590#382C2314yes—
591#382C2312yes—
592#382C2312yes—
593#381C2312yes—
594#381C2312yes—
595#380C2312yes—
596#380C2312yes—
597#380C2312yes—
598#380C2312yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#379C2314yes—
604#379C2314yes—
605#379C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2312yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2312yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2312yes—
618C4×C22⋊C4C2312yes—
619C4×C22⋊C4C2312yes—
620C4×C22⋊C4C2314yes—
621C4×C22⋊C4C2312yes—
622C4×C22⋊C4C2314yes—
623C4×C22⋊C4C2314yes—
624C4×C22⋊C4C2312yes—
625#376C2312yes—
626C43C2312yes—
627C25C2412yes—
628C2×#41—42no—
629C2×#41—42no—
630C2×#41—42no—
631C2×#41—42no—
632C2×#41—42no—
633C2×#41—42no—
634C22×Q8—42no—
635C22×Q8—42no—
636C22×Q8—42no—
637C22×Q8C2412yes—
638C22×Q8C2412yes—
639C22×Q8C2411yescharacteristic
640C22×Q8C2411yescharacteristic
641C22×Q8C2412yes—
642C22×Q8C2412yes—
643C22×Q8C2414yes—
644C22×D4—42no—
645C22×D4—42no—
646C22×D4—42no—
647C22×D4C2414yes—
648C22×D4C2414yes—
649C22×D4C2412yes—
650C22×D4C2412yes—
651C22×D4C2412yes—
652C22×D4C2412yes—
653C22×D4C2411yescharacteristic
654C22×D4C2411yescharacteristic
655C22×D4C2414yes—
656C22×D4C2414yes—
657C22×D4C2414yes—
658C23×C4C2411yescharacteristic
659C23×C4C2412yes—
660C23×C4C2412yes—
661C23×C4C2412yes—
662C23×C4C2412yes—
663C23×C4C2414yes—
664C23×C4C2414yes—
665C23×C4C2412yes—
666C23×C4C2412yes—
667C23×C4C2412yes—
668C23×C4C2412yes—
669C4⋊Q8—44no—
670C4⋊Q8—44no—
671C4⋊Q8—48no—
672C4⋊Q8—48no—
673C4⋊Q8—42no—
674C4⋊Q8—48no—
675C4⋊Q8—48no—
676C4⋊Q8—44no—
677C4⋊Q8—44no—
678#127—42no—
679#127—44no—
680#127—44no—
681#126—216no—
682#126—48no—
683#126—48no—
684#126—48no—
685#126—48no—
686#126—48no—
687#126—48no—
688#125—216no—
689#125—28no—
690#125—28no—
691#125—48no—
692#125—48no—
693#124—28no—
694#124—24no—
695#124—24no—
696#124—48no—
697#124—44no—
698#124—44no—
699#124—44no—
700#124—44no—
701#124—44no—
702#124—44no—
703#124—44no—
704#123—28no—
705#123—48no—
706#123—44no—
707#123—44no—
708#123—44no—
709#123—48no—
710#123—48no—
711#123—48no—
712#123—48no—
713#123—44no—
714#123—44no—
715C22⋊Q8—28no—
716C22⋊Q8—48no—
717C22⋊Q8—48no—
718C22⋊Q8—48no—
719C22⋊Q8—48no—
720C22⋊Q8—48no—
721C22⋊Q8—48no—
722C22⋊Q8—48no—
723C22⋊Q8—48no—
724C22⋊Q8—48no—
725C22⋊Q8—48no—
726C22⋊Q8—44no—
727C22⋊Q8—44no—
728C22⋊Q8—44no—
729#121—28no—
730#121—48no—
731#121—48no—
732#121—44no—
733#120—28no—
734#120—48no—
735#120—44no—
736C4×D4—48no—
737C4×D4—48no—
738C4×D4—48no—
739#117—24no—
740#117—24no—
741#117—48no—
742#117—48no—
743C2×C4⋊C4—44no—
744C2×C4⋊C4—44no—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2411yescharacteristic
796C2×C22⋊C4—48no—
797C2×C22⋊C4—48no—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2411yescharacteristic
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2411yescharacteristic
849C2×C42—24no—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2412yes—
855C2×C42C2411yescharacteristic
856C2×C42C2412yes—
857C2×C42C2414yes—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2414yes—
862C2×C42C2412yes—
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2412yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2411yescharacteristic
869#95C2412yes—
870#95C2412yes—
871#95C2412yes—
872#95C2412yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913C24—24no—
914C24—42no—
915C24—44no—
916C24—44no—
917C24—42no—
918C24C2514yes—
919C24C2512yes—
920C24C2512yes—
921C24C2511yescharacteristic
922#41—88no—
923#41—88no—
924C2×Q8—24no—
925C2×Q8—24no—
926C2×Q8—22no—
927C2×Q8—22no—
928C2×Q8—42no—
929C2×Q8—42no—
930C2×Q8—41no—
931C2×Q8—41no—
932C2×Q8—42no—
933C2×Q8—42no—
934C2×Q8—41no—
935C2×Q8—41no—
936C2×Q8—42no—
937C2×Q8—42no—
938C2×Q8—44no—
939C2×Q8—44no—
940C2×Q8—42no—
941C2×Q8—42no—
942C2×Q8—42no—
943C2×Q8—44no—
944C2×Q8—42no—
945C2×Q8—88no—
946C2×D4—24no—
947C2×D4—24no—
948C2×D4—28no—
949C2×D4—28no—
950C2×D4—24no—
951C2×D4—24no—
952C2×D4—22no—
953C2×D4—22no—
954C2×D4—44no—
955C2×D4—42no—
956C2×D4—42no—
957C2×D4—42no—
958C2×D4—42no—
959C2×D4—42no—
960C2×D4—42no—
961C2×D4—41no—
962C2×D4—41no—
963C2×D4—42no—
964C2×D4—42no—
965C2×D4—41no—
966C2×D4—41no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—44no—
979C2×D4—88no—
980C22×C4—22no—
981C22×C4—22no—
982C22×C4—22no—
983C22×C4—24no—
984C22×C4—24no—
985C22×C4—24no—
986C22×C4—24no—
987C22×C4—42no—
988C22×C4—44no—
989C22×C4—42no—
990C22×C4—44no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—42no—
998C22×C4—42no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—44no—
1007C22×C4—42no—
1008C22×C4—44no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2514yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C22×C4C2514yes—
1018C22×C4C2514yes—
1019C22×C4C2514yes—
1020C22×C4C2514yes—
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2514yes—
1024C22×C4C2514yes—
1025C22×C4C2511yescharacteristic
1026C22×C4C2511yescharacteristic
1027C22×C4C2512yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—24no—
1033C4⋊C4—22no—
1034C4⋊C4—28no—
1035C4⋊C4—28no—
1036C4⋊C4—28no—
1037C4⋊C4—28no—
1038C4⋊C4—28no—
1039C4⋊C4—24no—
1040C4⋊C4—24no—
1041C4⋊C4—28no—
1042C4⋊C4—28no—
1043C4⋊C4—28no—
1044C4⋊C4—28no—
1045C4⋊C4—28no—
1046C4⋊C4—28no—
1047C4⋊C4—28no—
1048C4⋊C4—24no—
1049C4⋊C4—24no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—42no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—42no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4H(5,𝔽2)14yes—
1081C22⋊C4—28no—
1082C22⋊C4—28no—
1083C22⋊C4—22no—
1084C22⋊C4—28no—
1085C22⋊C4—28no—
1086C22⋊C4—24no—
1087C22⋊C4—28no—
1088C22⋊C4—28no—
1089C22⋊C4—28no—
1090C22⋊C4—28no—
1091C22⋊C4—28no—
1092C22⋊C4—28no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—42no—
1126C22⋊C4—44no—
1127C22⋊C4—42no—
1128C22⋊C4—44no—
1129C22⋊C4—42no—
1130C22⋊C4—42no—
1131C22⋊C4H(5,𝔽2)14yes—
1132C42—24no—
1133C42—22no—
1134C42—24no—
1135C42—24no—
1136C42—28no—
1137C42—28no—
1138C42—42no—
1139C42—44no—
1140C42—44no—
1141C42—42no—
1142C42—42no—
1143C42—42no—
1144C42—42no—
1145C42—44no—
1146C42—42no—
1147C42—44no—
1148C42—42no—
1149C42—42no—
1150C42H(5,𝔽2)14yes—
1151C23—21no—
1152C23—21no—
1153C23—22no—
1154C23—22no—
1155C23—22no—
1156C23—24no—
1157C23—22no—
1158C23—22no—
1159C23—22no—
1160C23—24no—
1161C23—24no—
1162C23—22no—
1163C23—22no—
1164C23—24no—
1165C23—24no—
1166C23—24no—
1167C23—24no—
1168C23—24no—
1169C23—24no—
1170C23—24no—
1171C23—24no—
1172C23—84no—
1173C23—88no—
1174C23—88no—
1175C23—162no—
1176C23—162no—
1177C23C2×H(5,𝔽2)12yes—
1178C23C2611yescharacteristic
1179Q8—84no—
1180Q8—84no—
1181Q8—82no—
1182Q8—82no—
1183Q8—162no—
1184Q8—162no—
1185Q8—164no—
1186D4—88no—
1187D4—88no—
1188D4—84no—
1189D4—84no—
1190D4—82no—
1191D4—82no—
1192D4—84no—
1193D4—84no—
1194D4—88no—
1195D4—164no—
1196D4—164no—
1197C2×C4—28no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—48no—
1251C2×C4—84no—
1252C2×C4—84no—
1253C2×C4—84no—
1254C2×C4—84no—
1255C2×C4—84no—
1256C2×C4—88no—
1257C2×C4—162no—
1258C2×C4—162no—
1259C2×C4—164no—
1260C2×C4C2×H(5,𝔽2)14yes—
1261C2×C4C2×H(5,𝔽2)14yes—
1262C2×C4C2×H(5,𝔽2)14yes—
1263C2×C4C2×H(5,𝔽2)12yes—
1264C2×C4C2×H(5,𝔽2)12yes—
1265C22—24no—
1266C22—22no—
1267C22—41no—
1268C22—41no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—44no—
1273C22—42no—
1274C22—44no—
1275C22—44no—
1276C22—44no—
1277C22—44no—
1278C22—42no—
1279C22—44no—
1280C22—42no—
1281C22—42no—
1282C22—44no—
1283C22—44no—
1284C22—44no—
1285C22—44no—
1286C22—44no—
1287C22—168no—
1288C22C22×H(5,𝔽2)11yescharacteristic
1289C22C22×H(5,𝔽2)11yescharacteristic
1290C22C22×H(5,𝔽2)11yescharacteristic
1291C222−1+612yes—
1292C222−1+612yes—
1293C4—24no—
1294C4—24no—
1295C4—22no—
1296C4—22no—
1297C4—24no—
1298C4—44no—
1299C4—42no—
1300C4—44no—
1301C4—44no—
1302C4—44no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—44no—
1307C4—44no—
1308C4—44no—
1309C4—44no—
1310C4—44no—
1311C4—42no—
1312C2—42no—
1313C2—82no—
1314C2—82no—
1315C2—84no—
1316C2#6283211yescharacteristic
1317C2#6288812yes—
1318C2#6304811yescharacteristic
1319C2#6306311yescharacteristic
1320C2#6306312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35329C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58951C2semidirect
2. #57406C2semidirect
3. #57235C2semidirect
4. #56590C2semidirect
5. #54166C2semidirect
6. #53632C2semidirect
7. #51326C2semidirect
8. #50888C2semidirect
9. #50165C2semidirect
10. #49070C2semidirect
11. #47692C2semidirect
12. #47312C2semidirect
13. #46426C2semidirect
14. #46359C2semidirect
15. #46228C2semidirect
16. #46228C2semidirect
17. #46136C2semidirect
18. #46018C2semidirect
19. #46018C2semidirect
20. #45998C2semidirect
21. #45998C2semidirect
23. #35142C2semidirect
26. C2×#563C22semidirect
27. C2×#563C22semidirect
29. C2×#544C22semidirect
37. #2864C22semidirect
38. #2859C22semidirect
43. #2838C22semidirect
44. #2838C22semidirect
45. #2829C22semidirect
46. #2826C22semidirect
47. #2824C22semidirect
48. #2821C22semidirect
51. #2820C22semidirect
52. #2820C22semidirect
53. #2817C22semidirect
55. #2807C22semidirect
56. #2803C22semidirect
57. #2800C22semidirect
58. #2800C22semidirect
59. #2796C22semidirect
60. #2796C22semidirect
61. #2780C22semidirect
62. #2780C22semidirect
63. #2778C22semidirect
64. #2778C22semidirect
65. #2777C22semidirect
66. #2773C22semidirect
67. #2756C22semidirect
68. #2753C22semidirect
69. #2742C22semidirect
70. #2734C22semidirect
71. #2734C22semidirect
73. #2729C22semidirect
74. #2727C22semidirect
75. #2727C22semidirect
77. #2723C22semidirect
78. #2723C22semidirect
79. #2723C22semidirect
80. #2723C22semidirect
81. #2721C22semidirect
82. #2720C22semidirect
83. #2720C22semidirect
84. #2720C22semidirect
90. #2713C22semidirect
91. #2713C22semidirect
95. #2709C22semidirect
96. #2709C22semidirect
98. #2705C22semidirect
102. #2696C22semidirect
103. #2696C22semidirect
104. #2694C22semidirect
105. #2694C22semidirect
108. #2689C22semidirect
112. #2683C22semidirect
113. #2683C22semidirect
116. #2677C22semidirect
117. #2677C22semidirect
123. #2674C22semidirect
124. #2674C22semidirect
130. #2655C22semidirect
131. #2654C22semidirect
133. #2648C22semidirect
134. #2636C22semidirect
135. #2628C22semidirect
137. #2601C22semidirect
138. #2601C22semidirect
139. #2598C22semidirect
140. #2597C22semidirect
141. #2597C22semidirect
142. #2596C22semidirect
144. #2583C22semidirect
146. #2558C22semidirect
147. #2558C22semidirect
148. #2556C22semidirect
149. #2551C22semidirect
150. #2551C22semidirect
151. #2542C22semidirect
152. #2542C22semidirect
157. #2533C22semidirect
158. #2528C22semidirect
159. #2522C22semidirect
161. #2521C22semidirect
162. #2512C22semidirect
163. #2512C22semidirect
164. #2512C22semidirect
165. #2512C22semidirect
166. #2509C22semidirect
167. #2508C22semidirect
168. #2507C22semidirect
169. #2506C22semidirect
176. #2479C22semidirect
177. #2479C22semidirect
182. #2474C22semidirect
184. #2471C22semidirect
186. #2466C22semidirect
187. #2466C22semidirect
188. #2463C22semidirect
189. #2452C22semidirect
190. #2452C22semidirect
191. #2449C22semidirect
192. #2449C22semidirect
196. #2441C22semidirect
197. #2440C22semidirect
208. #2379C22semidirect
209. #2379C22semidirect
212. #2336C22semidirect
215. #2332C22semidirect
216. C4×#125C22semidirect
217. C4×#125C22semidirect

Maximal subgroups

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

subgroupindex
#589512
#574062
#572352
#565902
#541662
#536322
#513262
#508882
#501652
#490702
#476922
#473122
#464262
#463592
#462282
#461362
#460182
#459982
#353292
#351422