Finite Group Databasebeta

← #8094732

Subgroups — #8094732

Order 512.

4780 conjugacy classes of subgroups.

The subgroup lattice has 1309 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52905C214yesmaximal, complemented
2#52891C214yesmaximal, complemented
3#52885C214yesmaximal, complemented
4#52877C214yesmaximal, complemented
5#52374C214yesmaximal, complemented
6#52347C214yesmaximal, complemented
7#46334C212yesmaximal, complemented
8#46325C212yesmaximal, complemented
9#46323C212yesmaximal, complemented
10#46312C212yesmaximal, complemented
11#46269C212yesmaximal, complemented
12#46237C212yesmaximal, complemented
13#46136C211yesmaximal, characteristic, complemented
14#46098C212yesmaximal, complemented
15#45977C211yesmaximal, characteristic
16#45930C214yesmaximal, complemented
17#45908C214yesmaximal, complemented
18#35451C212yesmaximal, complemented
19#35449C214yesmaximal, complemented
20#35100C214yesmaximal, complemented
21#35098C212yesmaximal, complemented
22#34972C212yesmaximal, complemented
23C2×#2545C211yesmaximal, characteristic, complemented
24C2×#563C2211yescharacteristic, complemented
25C2×#563C2212yescomplemented
26C2×H(3,𝔽4)C2211yescharacteristic
27C22×C4⋊Q8C2211yescharacteristic, complemented
28C2×#529C2212yes—
29C22×#124C2211yescharacteristic
30C22×#124C2211yescharacteristic
31C2×#518C2212yescomplemented
32C22×C4×Q8C2211yescharacteristic, complemented
33#2866C2214yescomplemented
34#2865C2214yescomplemented
35#2861C2214yescomplemented
36#2860C2214yescomplemented
37#2852C2214yescomplemented
38#2851C2212yescomplemented
39#2850C2212yes—
40#2842C2214yescomplemented
41#2841C2214yescomplemented
42#2837C2214yescomplemented
43#2837C2214yescomplemented
44#2837C2214yescomplemented
45#2836C2214yescomplemented
46#2836C2214yescomplemented
47#2831C2214yescomplemented
48#2831C2214yescomplemented
49#2829C2214yes—
50#2829C2214yescomplemented
51#2829C2214yescomplemented
52#2827C2214yescomplemented
53#2827C2214yescomplemented
54#2827C2214yescomplemented
55#2826C2214yescomplemented
56#2823C2214yescomplemented
57#2821C2214yescomplemented
58#2820C2212yes—
59#2820C2214yescomplemented
60#2819C2212yes—
61#2808C2212yescomplemented
62#2806C2212yescomplemented
63#2806C2212yescomplemented
64#2803C2214yes—
65#2795C2214yescomplemented
66#2790C2214yescomplemented
67#2790C2214yescomplemented
68#2788C2214yescomplemented
69#2780C2214yescomplemented
70#2772C2214yescomplemented
71#2761C2214yescomplemented
72#2757C2214yes—
73#2756C2214yescomplemented
74#2755C2214yescomplemented
75#2754C2214yescomplemented
76#2748C2212yescomplemented
77#2744C2214yescomplemented
78#2743C2214yescomplemented
79#2735C2214yescomplemented
80#2734C2212yescomplemented
81#2733C2212yes—
82#2732C2212yescomplemented
83#2732C2214yescomplemented
84#2731C2212yes—
85#2731C2212yescomplemented
86#2729C2214yescomplemented
87#2717C2212yescomplemented
88#2716C2214yescomplemented
89#2715C2214yescomplemented
90#2713C2214yescomplemented
91#2712C2214yes—
92#2705C2214yescomplemented
93#2705C2214yescomplemented
94#2704C2214yescomplemented
95#2704C2214yescomplemented
96#2700C2214yescomplemented
97#2700C2214yescomplemented
98#2697C2214yescomplemented
99#2697C2212yescomplemented
100#2685C2214yes—
101#2685C2214yescomplemented
102#2684C2212yes—
103#2677C2214yescomplemented
104#2674C2214yescomplemented
105#2674C2214yescomplemented
106#2670C2214yes—
107#2654C2214yescomplemented
108#2651C2214yescomplemented
109#2651C2214yescomplemented
110#2650C2214yescomplemented
111#2627C2212yescomplemented
112#2623C2214yescomplemented
113#2618C2212yes—
114#2609C2214yescomplemented
115#2604C2214yescomplemented
116#2604C2214yescomplemented
117#2600C2214yescomplemented
118#2599C2214yescomplemented
119#2598C2214yescomplemented
120#2565C2212yescomplemented
121#2565C2212yescomplemented
122#2545C2212yes—
123#2545C2212yes—
124#2545C2214yescomplemented
125#2545C2212yescomplemented
126#2545C2214yescomplemented
127#2545C2212yescomplemented
128#2545C2212yescomplemented
129#2545C2212yescomplemented
130#2536C2214yescomplemented
131#2534C2214yes—
132#2534C2214yescomplemented
133#2532C2214yescomplemented
134#2531C2214yescomplemented
135#2529C2214yescomplemented
136#2526C2214yescomplemented
137#2525C2214yescomplemented
138#2525C2214yescomplemented
139#2524C2214yescomplemented
140#2522C2214yescomplemented
141#2521C2214yescomplemented
142#2521C2214yescomplemented
143#2520C2214yescomplemented
144#2519C2214yescomplemented
145#2519C2214yescomplemented
146#2516C2214yescomplemented
147#2516C2214yescomplemented
148#2515C2214yescomplemented
149#2503C2212yescomplemented
150#2501C2212yes—
151#2498C2214yescomplemented
152#2485C2214yescomplemented
153#2483C2212yescomplemented
154#2482C2214yescomplemented
155#2482C2214yescomplemented
156#2481C2214yescomplemented
157#2480C2214yescomplemented
158#2480C2214yescomplemented
159#2479C2214yescomplemented
160#2475C2214yescomplemented
161#2474C2214yes—
162#2474C2214yescomplemented
163#2473C2214yescomplemented
164#2472C2214yes—
165#2472C2214yes—
166#2472C2214yescomplemented
167#2472C2214yescomplemented
168#2468C2214yescomplemented
169#2467C2214yescomplemented
170#2461C2214yes—
171#2461C2214yescomplemented
172#2461C2214yescomplemented
173#2460C2214yescomplemented
174#2459C2214yes—
175#2459C2214yescomplemented
176#2449C2214yescomplemented
177#2443C2214yes—
178#2438C2214yescomplemented
179#2437C2214yescomplemented
180#2436C2212yes—
181#2434C2212yescomplemented
182#2425C2214yes—
183#2419C2214yescomplemented
184#2413C2214yescomplemented
185#2413C2214yescomplemented
186#2412C2214yes—
187#2411C2214yes—
188#2410C2214yes—
189#2409C2214yescomplemented
190#2405C2212yes—
191#2405C2214yescomplemented
192#2405C2212yescomplemented
193#2403C2212yes—
194#2396C2214yescomplemented
195#2396C2214yescomplemented
196C2×#396C2214yescomplemented
197#2381C2212yescomplemented
198#2379C2211yescharacteristic
199#2379C2211yescharacteristic, complemented
200#2378C2214yescomplemented
201#2376C2212yescomplemented
202#2375C2212yescomplemented
203#2329C2212yescomplemented
204#2325C2212yes—
205#2321C2214yes—
206#2318C2214yescomplemented
207#2312C2212yescomplemented
208C4×C4⋊Q8C2212yescomplemented
209C4×C4⋊Q8C2212yescomplemented
210C4×#124C2212yescomplemented
211C4×#124C2212yescomplemented
212C4×#123C2214yescomplemented
213C4×#123C2214yescomplemented
214C2×#391C2211yescharacteristic, complemented
215C2×#390C2211yescharacteristic
216C2×#388C2214yescomplemented
217C4×#117C2212yescomplemented
218C2×C4×C4⋊C4C2211yescharacteristic, complemented
219C23×Q8C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×D4C2312yes—
222C23×D4C2311yescharacteristic
223#563—44no—
224#563—48no—
225H(3,𝔽4)—44no—
226C2×C4⋊Q8—44no—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2314yes—
232#529—48no—
233C2×#126C2314yes—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#126C2314yes—
237C2×#125C2312yes—
238C2×#125C2314yes—
239C2×#125C2312yes—
240C2×#124—44no—
241C2×#124—44no—
242C2×#124C2311yescharacteristic
243C2×#124C2311yescharacteristic
244C2×#124C2312yes—
245C2×#124C2311yescharacteristic
246C2×#124C2312yes—
247C2×#124C2311yescharacteristic
248C2×#124C2314yes—
249C2×#124C2314yes—
250C2×#124C2314yes—
251C2×#124C2312yes—
252C2×#124C2312yes—
253C2×#124C2312yes—
254C2×#124C2312yes—
255C2×#123C2314yes—
256C2×#123C2312yes—
257C2×#123C2312yes—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×#121C2312yes—
268C2×#121C2312yes—
269C2×#120C2314yes—
270C2×#120C2312yes—
271C2×#120C2312yes—
272C2×#120C2314yes—
273#518—48no—
274C2×C4×Q8—44no—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×#117C2314yes—
286C2×#117C2314yes—
287C2×#117C2314yes—
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2314yes—
291C22×C4⋊C4C2311yescharacteristic
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2312yes—
294C22×C22⋊C4C2314yes—
295C22×C22⋊C4C2314yes—
296C22×C22⋊C4C2312yes—
297C22×C22⋊C4C2314yes—
298C22×C42C2311yescharacteristic
299C22×C42C2312yes—
300C22×C42C2311yescharacteristic
301C22×C42C2311yescharacteristic
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#399C2314yes—
314#399C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
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#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
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#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2314yes—
430#391C2312yes—
431#391C2314yes—
432#391C2312yes—
433#391C2314yes—
434#391C2314yes—
435#391C2312yes—
436#391C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2314yes—
440#390C2314yes—
441#390C2314yes—
442#390C2312yes—
443#390C2314yes—
444#390C2314yes—
445#390C2312yes—
446#390C2312yes—
447#390C2312yes—
448#390C2312yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
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#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
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#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2312yes—
551#386C2312yes—
552#386C2312yes—
553#386C2312yes—
554#386C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#384C2312yes—
573#384C2312yes—
574#383C2314yes—
575#383C2314yes—
576#382C2312yes—
577#382C2312yes—
578#382C2312yes—
579#382C2312yes—
580#382C2314yes—
581#381C2314yes—
582#381C2314yes—
583#381C2314yes—
584#381C2314yes—
585#381C2314yes—
586#380C2314yes—
587#380C2314yes—
588#380C2312yes—
589#380C2312yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#379C2312yes—
595#379C2312yes—
596#379C2314yes—
597#379C2314yes—
598#379C2314yes—
599#379C2314yes—
600#379C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2312yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2312yes—
617C4×C22⋊C4C2312yes—
618#376C2314yes—
619C2×#95C2312yes—
620C2×#95C2314yes—
621C43C2312yes—
622C43C2312yes—
623C25C2412yes—
624C25C2412yes—
625C22×Q8—24no—
626C22×Q8—42no—
627C22×Q8—42no—
628C22×Q8—42no—
629C22×Q8—42no—
630C22×Q8—42no—
631C22×Q8C2412yes—
632C22×Q8C2411yescharacteristic
633C22×Q8C2412yes—
634C22×Q8C2412yes—
635C22×Q8C2412yes—
636C22×Q8C2412yes—
637C22×Q8C2411yescharacteristic
638C22×D4—42no—
639C22×D4—42no—
640C22×D4—42no—
641C22×D4—44no—
642C22×D4—48no—
643C22×D4C2414yes—
644C22×D4C2412yes—
645C22×D4C2411yescharacteristic
646C22×D4C2412yes—
647C22×D4C2411yescharacteristic
648C22×D4C2414yes—
649C22×D4C2414yes—
650C22×D4C2412yes—
651C22×D4C2414yes—
652C23×C4C2411yescharacteristic
653C23×C4C2412yes—
654C23×C4C2411yescharacteristic
655C23×C4C2412yes—
656C23×C4C2412yes—
657C23×C4C2412yes—
658C23×C4C2412yes—
659C23×C4C2414yes—
660C23×C4C2414yes—
661C23×C4C2412yes—
662C23×C4C2412yes—
663C23×C4C2412yes—
664C23×C4C2411yescharacteristic
665C4⋊Q8—28no—
666C4⋊Q8—28no—
667C4⋊Q8—44no—
668C4⋊Q8—48no—
669C4⋊Q8—44no—
670#126—48no—
671#126—48no—
672#126—48no—
673#126—48no—
674#125—44no—
675#125—44no—
676#125—48no—
677#124—24no—
678#124—24no—
679#124—28no—
680#124—44no—
681#124—48no—
682#124—44no—
683#124—44no—
684#124—44no—
685#124—48no—
686#124—42no—
687#124—42no—
688#124—48no—
689#124—44no—
690#123—48no—
691#123—48no—
692#123—48no—
693#123—44no—
694#123—48no—
695#123—44no—
696C22⋊Q8—44no—
697C22⋊Q8—44no—
698C22⋊Q8—48no—
699C22⋊Q8—48no—
700C22⋊Q8—48no—
701C22⋊Q8—48no—
702#121—44no—
703#121—44no—
704#120—44no—
705#120—48no—
706#120—44no—
707#120—48no—
708C4×Q8—44no—
709C4×Q8—44no—
710C4×Q8—44no—
711C4×Q8—44no—
712C4×Q8—44no—
713C4×D4—216no—
714C4×D4—48no—
715C4×D4—44no—
716C4×D4—48no—
717C4×D4—48no—
718#117—48no—
719#117—48no—
720#117—48no—
721C2×C4⋊C4—48no—
722C2×C4⋊C4—44no—
723C2×C4⋊C4—42no—
724C2×C4⋊C4—44no—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C22⋊C4—28no—
773C2×C22⋊C4—48no—
774C2×C22⋊C4—48no—
775C2×C22⋊C4—44no—
776C2×C22⋊C4—48no—
777C2×C22⋊C4—44no—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2412yes—
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×C42—24no—
829C2×C42—28no—
830C2×C42—42no—
831C2×C42—42no—
832C2×C42C2414yes—
833C2×C42C2412yes—
834C2×C42C2412yes—
835C2×C42C2412yes—
836C2×C42C2412yes—
837C2×C42C2412yes—
838C2×C42C2412yes—
839C2×C42C2411yescharacteristic
840C2×C42C2412yes—
841C2×C42C2411yescharacteristic
842C2×C42C2412yes—
843C2×C42C2412yes—
844C2×C42C2414yes—
845C2×C42C2414yes—
846C2×C42C2414yes—
847C2×C42C2412yes—
848C2×C42C2412yes—
849C2×C42C2412yes—
850C2×C42C2412yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
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—
899C24—24no—
900C24—28no—
901C24—42no—
902C24—44no—
903C24—42no—
904C24—42no—
905C24—44no—
906C24—42no—
907C24—42no—
908C24—44no—
909C24C2512yes—
910C24C2512yes—
911C24C2514yes—
912C24C2511yescharacteristic
913C2×Q8—24no—
914C2×Q8—22no—
915C2×Q8—24no—
916C2×Q8—24no—
917C2×Q8—24no—
918C2×Q8—24no—
919C2×Q8—41no—
920C2×Q8—42no—
921C2×Q8—41no—
922C2×Q8—41no—
923C2×Q8—41no—
924C2×Q8—42no—
925C2×Q8—42no—
926C2×Q8—42no—
927C2×Q8—42no—
928C2×Q8—42no—
929C2×Q8—42no—
930C2×Q8—42no—
931C2×Q8—42no—
932C2×Q8—42no—
933C2×Q8—416no—
934C2×Q8—88no—
935C2×Q8H(5,𝔽2)14yes—
936C2×D4—28no—
937C2×D4—28no—
938C2×D4—28no—
939C2×D4—24no—
940C2×D4—22no—
941C2×D4—22no—
942C2×D4—24no—
943C2×D4—44no—
944C2×D4—44no—
945C2×D4—44no—
946C2×D4—42no—
947C2×D4—41no—
948C2×D4—42no—
949C2×D4—41no—
950C2×D4—42no—
951C2×D4—42no—
952C2×D4—41no—
953C2×D4—41no—
954C2×D4—42no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—42no—
960C2×D4—44no—
961C2×D4—44no—
962C2×D4—42no—
963C2×D4—432no—
964C2×D4—88no—
965C22×C4—22no—
966C22×C4—22no—
967C22×C4—22no—
968C22×C4—22no—
969C22×C4—24no—
970C22×C4—24no—
971C22×C4—24no—
972C22×C4—28no—
973C22×C4—24no—
974C22×C4—24no—
975C22×C4—24no—
976C22×C4—24no—
977C22×C4—28no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—44no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—42no—
991C22×C4—44no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—42no—
997C22×C4—44no—
998C22×C4H(5,𝔽2)14yes—
999C22×C4C2514yes—
1000C22×C4C2512yes—
1001C22×C4C2514yes—
1002C22×C4C2514yes—
1003C22×C4C2514yes—
1004C22×C4C2514yes—
1005C22×C4C2512yes—
1006C22×C4C2514yes—
1007C22×C4C2514yes—
1008C22×C4C2512yes—
1009C22×C4C2514yes—
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2514yes—
1014C22×C4C2512yes—
1015C22×C4C2511yescharacteristic
1016C22×C4C2512yes—
1017C22×C4C2511yescharacteristic
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—41no—
1029C4⋊C4—42no—
1030C4⋊C4—41no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—42no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—42no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—44no—
1048C4⋊C4—42no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—42no—
1052C4⋊C4—44no—
1053C4⋊C4—42no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—42no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—28no—
1069C22⋊C4—28no—
1070C22⋊C4—28no—
1071C22⋊C4—28no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—42no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
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⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—42no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—42no—
1114C22⋊C4—44no—
1115C42—24no—
1116C42—24no—
1117C42—24no—
1118C42—24no—
1119C42—24no—
1120C42—24no—
1121C42—22no—
1122C42—22no—
1123C42—24no—
1124C42—28no—
1125C42—24no—
1126C42—24no—
1127C42—42no—
1128C42—42no—
1129C42—44no—
1130C42—44no—
1131C42—44no—
1132C42—44no—
1133C42—44no—
1134C42—42no—
1135C42—42no—
1136C23—21no—
1137C23—21no—
1138C23—22no—
1139C23—22no—
1140C23—24no—
1141C23—22no—
1142C23—22no—
1143C23—22no—
1144C23—24no—
1145C23—24no—
1146C23—24no—
1147C23—24no—
1148C23—22no—
1149C23—24no—
1150C23—24no—
1151C23—22no—
1152C23—24no—
1153C23—24no—
1154C23—24no—
1155C23—24no—
1156C23—48no—
1157C23—48no—
1158C23—84no—
1159C23—84no—
1160C23—88no—
1161C23—88no—
1162C23—162no—
1163C23—162no—
1164C23—164no—
1165C23—164no—
1166C23C2×H(5,𝔽2)12yes—
1167C23#58514yes—
1168C23C2611yescharacteristic
1169Q8—44no—
1170Q8—48no—
1171Q8—44no—
1172Q8—84no—
1173Q8—84no—
1174Q8—84no—
1175Q8—162no—
1176D4—416no—
1177D4—416no—
1178D4—84no—
1179D4—82no—
1180D4—82no—
1181D4—84no—
1182D4—162no—
1183D4—164no—
1184D4—164no—
1185C2×C4—28no—
1186C2×C4—22no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
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—22no—
1235C2×C4—44no—
1236C2×C4—48no—
1237C2×C4—48no—
1238C2×C4—48no—
1239C2×C4—44no—
1240C2×C4—48no—
1241C2×C4—88no—
1242C2×C4—84no—
1243C2×C4—84no—
1244C2×C4—164no—
1245C2×C4—162no—
1246C2×C4—162no—
1247C2×C4C2×H(5,𝔽2)14yes—
1248C2×C4C2×H(5,𝔽2)12yes—
1249C2×C4C2×H(5,𝔽2)14yes—
1250C2×C4#58512yes—
1251C22—22no—
1252C22—22no—
1253C22—24no—
1254C22—24no—
1255C22—42no—
1256C22—44no—
1257C22—42no—
1258C22—44no—
1259C22—42no—
1260C22—42no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—42no—
1266C22—42no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—168no—
1273C22—168no—
1274C22#352914yes—
1275C22C22×H(5,𝔽2)11yescharacteristic
1276C22C22×H(5,𝔽2)11yescharacteristic
1277C22C2×#58511yescharacteristic
1278C22C2×#58512yes—
1279C222−1+612yes—
1280C4—22no—
1281C4—22no—
1282C4—24no—
1283C4—24no—
1284C4—42no—
1285C4—44no—
1286C4—44no—
1287C4—44no—
1288C4—44no—
1289C4—44no—
1290C4—42no—
1291C4—42no—
1292C4—44no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—44no—
1297C4—44no—
1298C4—44no—
1299C2—24no—
1300C2—82no—
1301C2—84no—
1302C2—82no—
1303C2C2×#352911yescharacteristic
1304C2#6281811yescharacteristic
1305C2#6287111yescharacteristic
1306C2#6291912yes—
1307C2#6296412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#45977C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52905C2semidirect
2. #52891C2semidirect
3. #52885C2semidirect
4. #52877C2semidirect
5. #52374C2semidirect
6. #52347C2semidirect
7. #46334C2semidirect
8. #46325C2semidirect
9. #46323C2semidirect
10. #46312C2semidirect
11. #46269C2semidirect
12. #46237C2semidirect
13. #46136C2semidirect
14. #46098C2semidirect
16. #45930C2semidirect
17. #45908C2semidirect
18. #35451C2semidirect
19. #35449C2semidirect
20. #35100C2semidirect
21. #35098C2semidirect
22. #34972C2semidirect
23. C2×#2545C2semidirect
24. C2×#563C22semidirect
25. C2×#563C22semidirect
27. C22×C4⋊Q8C22semidirect
31. C2×#518C22semidirect
32. C22×C4×Q8C22semidirect
33. #2866C22semidirect
34. #2865C22semidirect
35. #2861C22semidirect
36. #2860C22semidirect
37. #2852C22semidirect
38. #2851C22semidirect
40. #2842C22semidirect
41. #2841C22semidirect
42. #2837C22semidirect
43. #2837C22semidirect
44. #2837C22semidirect
45. #2836C22semidirect
46. #2836C22semidirect
47. #2831C22semidirect
48. #2831C22semidirect
50. #2829C22semidirect
51. #2829C22semidirect
52. #2827C22semidirect
53. #2827C22semidirect
54. #2827C22semidirect
55. #2826C22semidirect
56. #2823C22semidirect
57. #2821C22semidirect
59. #2820C22semidirect
61. #2808C22semidirect
62. #2806C22semidirect
63. #2806C22semidirect
65. #2795C22semidirect
66. #2790C22semidirect
67. #2790C22semidirect
68. #2788C22semidirect
69. #2780C22semidirect
70. #2772C22semidirect
71. #2761C22semidirect
73. #2756C22semidirect
74. #2755C22semidirect
75. #2754C22semidirect
76. #2748C22semidirect
77. #2744C22semidirect
78. #2743C22semidirect
79. #2735C22semidirect
80. #2734C22semidirect
82. #2732C22semidirect
83. #2732C22semidirect
85. #2731C22semidirect
86. #2729C22semidirect
87. #2717C22semidirect
88. #2716C22semidirect
89. #2715C22semidirect
90. #2713C22semidirect
92. #2705C22semidirect
93. #2705C22semidirect
94. #2704C22semidirect
95. #2704C22semidirect
96. #2700C22semidirect
97. #2700C22semidirect
98. #2697C22semidirect
99. #2697C22semidirect
101. #2685C22semidirect
103. #2677C22semidirect
104. #2674C22semidirect
105. #2674C22semidirect
107. #2654C22semidirect
108. #2651C22semidirect
109. #2651C22semidirect
110. #2650C22semidirect
111. #2627C22semidirect
112. #2623C22semidirect
114. #2609C22semidirect
115. #2604C22semidirect
116. #2604C22semidirect
117. #2600C22semidirect
118. #2599C22semidirect
119. #2598C22semidirect
120. #2565C22semidirect
121. #2565C22semidirect
124. #2545C22semidirect
125. #2545C22semidirect
126. #2545C22semidirect
127. #2545C22semidirect
128. #2545C22semidirect
129. #2545C22semidirect
130. #2536C22semidirect
132. #2534C22semidirect
133. #2532C22semidirect
134. #2531C22semidirect
135. #2529C22semidirect
136. #2526C22semidirect
137. #2525C22semidirect
138. #2525C22semidirect
139. #2524C22semidirect
140. #2522C22semidirect
141. #2521C22semidirect
142. #2521C22semidirect
143. #2520C22semidirect
144. #2519C22semidirect
145. #2519C22semidirect
146. #2516C22semidirect
147. #2516C22semidirect
148. #2515C22semidirect
149. #2503C22semidirect
151. #2498C22semidirect
152. #2485C22semidirect
153. #2483C22semidirect
154. #2482C22semidirect
155. #2482C22semidirect
156. #2481C22semidirect
157. #2480C22semidirect
158. #2480C22semidirect
159. #2479C22semidirect
160. #2475C22semidirect
162. #2474C22semidirect
163. #2473C22semidirect
166. #2472C22semidirect
167. #2472C22semidirect
168. #2468C22semidirect
169. #2467C22semidirect
171. #2461C22semidirect
172. #2461C22semidirect
173. #2460C22semidirect
175. #2459C22semidirect
176. #2449C22semidirect
178. #2438C22semidirect
179. #2437C22semidirect
181. #2434C22semidirect
183. #2419C22semidirect
184. #2413C22semidirect
185. #2413C22semidirect
189. #2409C22semidirect
191. #2405C22semidirect
192. #2405C22semidirect
194. #2396C22semidirect
195. #2396C22semidirect
196. C2×#396C22semidirect
197. #2381C22semidirect
199. #2379C22semidirect
200. #2378C22semidirect
201. #2376C22semidirect
202. #2375C22semidirect
203. #2329C22semidirect
206. #2318C22semidirect
207. #2312C22semidirect
208. C4×C4⋊Q8C22semidirect
209. C4×C4⋊Q8C22semidirect
210. C4×#124C22semidirect
211. C4×#124C22semidirect
212. C4×#123C22semidirect
213. C4×#123C22semidirect
214. C2×#391C22semidirect
216. C2×#388C22semidirect
217. C4×#117C22semidirect
218. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#529052
#528912
#528852
#528772
#523742
#523472
#463342
#463252
#463232
#463122
#462692
#462372
#461362
#460982
#459772
#459302
#459082
#354512
#354492
#351002
#350982
#349722
C2×#25452