Finite Group Databasebeta

← #7682450

Subgroups — #7682450

Order 512.

5834 conjugacy classes of subgroups.

The subgroup lattice has 1401 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60007C214yesmaximal, complemented
2#59947C212yesmaximal, complemented
3#59923C211yesmaximal, characteristic, complemented
4#59885C211yesmaximal, characteristic, complemented
5#59810C214yesmaximal, complemented
6#59779C214yesmaximal, complemented
7#59633C214yesmaximal, complemented
8#59160C212yesmaximal, complemented
9#59124C212yesmaximal, complemented
10#44707C212yesmaximal, complemented
11#44670C212yesmaximal, complemented
12#44605C214yesmaximal, complemented
13#44326C212yesmaximal, complemented
14#44242C212yesmaximal, complemented
15#44200C214yesmaximal, complemented
16#43083C214yesmaximal, complemented
17#43006C214yesmaximal, complemented
18#35466C212yesmaximal, complemented
19#35392C214yesmaximal, complemented
20#34957C212yesmaximal, complemented
21C2×#2544C211yesmaximal, characteristic, complemented
22#34302C214yesmaximal, complemented
23#34278C212yesmaximal, complemented
24C2×#555C2212yescomplemented
25C2×#550C2212yes—
26C2×#546C2214yes—
27C2×#539C2212yes—
28C2×#538C2212yes—
29C22×#127C2211yescharacteristic
30C22×#124C2211yescharacteristic
31C22×#124C2211yescharacteristic
32C2×#525C2212yes—
33C22×C4×D4C2211yescharacteristic
34#2811C2211yescharacteristic, complemented
35#2809C2211yescharacteristic, complemented
36#2808C2214yescomplemented
37#2808C2214yescomplemented
38#2808C2212yescomplemented
39#2806C2212yescomplemented
40#2803C2214yescomplemented
41#2803C2214yescomplemented
42#2803C2214yescomplemented
43#2784C2212yescomplemented
44#2737C2214yescomplemented
45#2737C2214yescomplemented
46#2734C2211yescharacteristic, complemented
47#2733C2212yescomplemented
48#2733C2211yescharacteristic, complemented
49#2731C2212yescomplemented
50#2730C2214yescomplemented
51#2730C2214yescomplemented
52#2714C2214yescomplemented
53#2714C2214yescomplemented
54#2699C2212yescomplemented
55#2694C2214yescomplemented
56#2694C2214yescomplemented
57#2686C2214yescomplemented
58#2686C2214yescomplemented
59#2686C2214yescomplemented
60#2673C2214yes—
61#2673C2214yes—
62#2673C2214yescomplemented
63#2673C2214yescomplemented
64#2610C2214yescomplemented
65#2610C2214yescomplemented
66#2610C2214yescomplemented
67#2603C2214yescomplemented
68#2602C2214yescomplemented
69#2602C2214yescomplemented
70#2602C2214yescomplemented
71#2601C2214yescomplemented
72#2593C2212yescomplemented
73#2591C2212yes—
74#2586C2212yescomplemented
75#2586C2214yescomplemented
76#2583C2212yes—
77#2572C2212yescomplemented
78#2564C2212yescomplemented
79#2564C2212yescomplemented
80#2561C2212yes—
81#2561C2212yes—
82#2560C2214yescomplemented
83#2557C2214yescomplemented
84#2557C2214yescomplemented
85#2557C2214yescomplemented
86#2555C2214yescomplemented
87#2555C2212yescomplemented
88#2555C2214yescomplemented
89#2555C2214yescomplemented
90#2555C2214yescomplemented
91#2554C2214yescomplemented
92#2549C2214yes—
93#2548C2212yes—
94#2544C2212yes—
95#2544C2214yes—
96#2544C2214yes—
97#2544C2212yes—
98#2544C2212yes—
99#2544C2212yes—
100#2544C2214yescomplemented
101#2543C2214yes—
102#2543C2212yescomplemented
103#2543C2214yescomplemented
104#2543C2212yescomplemented
105#2541C2214yes—
106#2541C2212yes—
107#2539C2212yes—
108#2539C2212yes—
109#2532C2214yescomplemented
110#2531C2214yescomplemented
111#2531C2214yescomplemented
112#2526C2214yescomplemented
113#2521C2214yescomplemented
114#2521C2214yescomplemented
115#2491C2214yescomplemented
116#2491C2214yescomplemented
117#2491C2214yescomplemented
118#2490C2214yescomplemented
119#2490C2214yescomplemented
120#2485C2214yescomplemented
121#2485C2214yescomplemented
122#2476C2214yescomplemented
123#2476C2214yescomplemented
124#2476C2214yescomplemented
125#2474C2214yescomplemented
126#2472C2214yes—
127#2472C2214yes—
128#2467C2214yescomplemented
129#2467C2214yescomplemented
130#2464C2214yescomplemented
131#2461C2214yescomplemented
132#2459C2214yescomplemented
133#2459C2214yescomplemented
134#2459C2214yescomplemented
135#2459C2214yescomplemented
136#2451C2214yescomplemented
137#2445C2214yes—
138#2445C2214yescomplemented
139#2445C2214yescomplemented
140#2445C2214yescomplemented
141#2436C2212yes—
142#2434C2212yes—
143#2433C2214yes—
144#2431C2214yes—
145#2431C2214yescomplemented
146#2430C2214yescomplemented
147#2428C2214yes—
148#2428C2214yescomplemented
149#2424C2214yes—
150#2424C2214yes—
151#2414C2214yescomplemented
152#2412C2214yes—
153#2412C2214yes—
154#2410C2214yes—
155#2410C2214yes—
156#2408C2214yes—
157#2407C2214yescomplemented
158#2407C2214yescomplemented
159#2395C2212yescomplemented
160#2395C2212yescomplemented
161#2388C2212yescomplemented
162#2388C2212yescomplemented
163C2×#394C2214yes—
164#2374C2214yescomplemented
165#2374C2214yescomplemented
166#2373C2214yescomplemented
167#2373C2214yescomplemented
168#2372C2212yescomplemented
169#2372C2214yescomplemented
170#2372C2212yescomplemented
171#2371C2214yescomplemented
172#2370C2214yescomplemented
173#2369C2212yescomplemented
174#2368C2214yes—
175#2368C2214yescomplemented
176#2366C2212yes—
177#2364C2214yescomplemented
178#2364C2214yescomplemented
179#2363C2214yescomplemented
180#2363C2214yescomplemented
181#2362C2214yescomplemented
182#2359C2214yescomplemented
183#2359C2214yescomplemented
184#2358C2214yes—
185#2358C2214yes—
186#2353C2214yes—
187#2353C2214yescomplemented
188#2342C2214yes—
189#2342C2214yes—
190#2339C2214yescomplemented
191D4×C22⋊C4C2214yes—
192#2337C2214yescomplemented
193#2335C2214yescomplemented
194#2333C2214yescomplemented
195#2333C2214yescomplemented
196#2329C2212yes—
197#2325C2212yes—
198#2322C2214yes—
199#2321C2214yes—
200#2313C2212yes—
201C4×C22⋊Q8C2212yes—
202C4×#123C2214yes—
203C4×#123C2214yescomplemented
204C4×#121C2212yes—
205C4×#121C2214yescomplemented
206C4×#121C2214yescomplemented
207C4×#121C2214yescomplemented
208C4×#120C2214yes—
209#2297C2214yescomplemented
210C2×#391C2211yescharacteristic
211C2×#390C2211yescharacteristic
212#2290C2214yes—
213#2290C2214yescomplemented
214C2×#386C2214yes—
215#2275C2214yes—
216#2273C2212yes—
217C2×C4×C4⋊C4C2211yescharacteristic
218C2×C4×C22⋊C4C2212yes—
219C22×#41C2314yes—
220C22×#41C2312yes—
221C23×Q8C2311yescharacteristic
222C23×D4C2311yescharacteristic
223C23×D4C2314yes—
224C23×D4C2311yescharacteristic
225C24×C4C2312yes—
226#555—48no—
227#550—48no—
228#546—232no—
229#539—216no—
230#538—48no—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×#127—44no—
234C2×#127C2312yes—
235C2×#127C2312yes—
236C2×#127C2312yes—
237C2×#127C2312yes—
238C2×#127C2314yes—
239C2×#127C2314yes—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#125C2314yes—
243C2×#124—44no—
244C2×#124—44no—
245C2×#124C2314yes—
246C2×#124C2312yes—
247C2×#124C2312yes—
248C2×#124C2314yes—
249C2×#124C2312yes—
250C2×#124C2312yes—
251C2×#124C2312yes—
252C2×#124C2312yes—
253C2×#124C2314yes—
254C2×#124C2312yes—
255C2×#124C2314yes—
256C2×#124C2312yes—
257C2×#124C2314yes—
258#525—48no—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×#121C2312yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2312yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#121C2312yes—
282C2×#121C2312yes—
283C2×#121C2314yes—
284C2×#121C2314yes—
285C2×#121C2314yes—
286C2×#120C2314yes—
287C2×#120C2314yes—
288C2×#120C2314yes—
289C2×#120C2314yes—
290C2×C4×Q8C2312yes—
291C2×C4×D4—44no—
292C2×C4×D4C2314yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2314yes—
308C2×#117C2314yes—
309C2×#117C2312yes—
310C2×#117C2314yes—
311C2×#117C2314yes—
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2311yescharacteristic
314C22×C22⋊C4C2312yes—
315C22×C22⋊C4C2314yes—
316C22×C22⋊C4C2314yes—
317C22×C22⋊C4C2312yes—
318C22×C22⋊C4C2312yes—
319C22×C22⋊C4C2314yes—
320C22×C22⋊C4C2314yes—
321C22×C42C2311yescharacteristic
322C22×C42C2311yescharacteristic
323C22×C42C2311yescharacteristic
324C22×C42C2314yes—
325#400C2312yes—
326#400C2312yes—
327#399C2312yes—
328#399C2312yes—
329#399C2314yes—
330#398C2314yes—
331#398C2312yes—
332#398C2312yes—
333#398C2314yes—
334#398C2314yes—
335#397C2314yes—
336#397C2312yes—
337#397C2312yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#396C2314yes—
346#396C2314yes—
347#395C2312yes—
348#395C2312yes—
349#395C2314yes—
350#395C2314yes—
351#395C2314yes—
352#395C2314yes—
353#394C2314yes—
354#394C2312yes—
355#394C2312yes—
356#394C2314yes—
357#394C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#393C2314yes—
383#393C2312yes—
384#393C2312yes—
385#393C2314yes—
386#393C2314yes—
387#393C2314yes—
388#393C2314yes—
389#392C2314yes—
390#392C2314yes—
391#392C2314yes—
392#392C2314yes—
393#392C2314yes—
394#392C2314yes—
395#392C2312yes—
396#392C2312yes—
397#392C2314yes—
398#392C2314yes—
399#392C2314yes—
400#392C2314yes—
401#392C2314yes—
402#392C2314yes—
403#392C2314yes—
404#392C2314yes—
405#391C2314yes—
406#391C2311yescharacteristic
407#391C2314yes—
408#391C2312yes—
409#391C2311yescharacteristic
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2312yes—
414#391C2311yescharacteristic
415#391C2312yes—
416#391C2314yes—
417#391C2311yescharacteristic
418#391C2312yes—
419#391C2312yes—
420#390C2314yes—
421#390C2314yes—
422#390C2314yes—
423#390C2314yes—
424#390C2314yes—
425#390C2314yes—
426#390C2312yes—
427#390C2314yes—
428#390C2314yes—
429#390C2314yes—
430#390C2314yes—
431#390C2314yes—
432#390C2314yes—
433#390C2314yes—
434#390C2314yes—
435#390C2314yes—
436#390C2314yes—
437#390C2312yes—
438#390C2314yes—
439#390C2312yes—
440#390C2314yes—
441#390C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2312yes—
450#389C2312yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
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#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
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#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#383C2314yes—
560#381C2314yes—
561#381C2314yes—
562#381C2314yes—
563#381C2314yes—
564#380C2314yes—
565#380C2314yes—
566#380C2312yes—
567#380C2312yes—
568#380C2314yes—
569#380C2314yes—
570#380C2314yes—
571#380C2314yes—
572#379C2314yes—
573#379C2314yes—
574C4×C4⋊C4C2314yes—
575C4×C4⋊C4C2312yes—
576C4×C4⋊C4C2314yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2314yes—
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2314yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2312yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2312yes—
586C4×C4⋊C4C2312yes—
587C4×C4⋊C4C2314yes—
588C4×C22⋊C4C2314yes—
589C4×C22⋊C4C2312yes—
590C4×C22⋊C4C2312yes—
591C4×C22⋊C4C2314yes—
592C4×C22⋊C4C2314yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2312yes—
596C4×C22⋊C4C2312yes—
597C4×C22⋊C4C2312yes—
598C4×C22⋊C4C2314yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2312yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616#376C2314yes—
617#376C2314yes—
618#376C2314yes—
619C2×#95C2312yes—
620C2×#95C2312yes—
621C2×#95C2312yes—
622C2×#95C2314yes—
623C2×#95C2314yes—
624C25C2412yes—
625C25C2412yes—
626C2×#41—216no—
627C2×#41—44no—
628C2×#41—48no—
629C2×#41—84no—
630C2×#41—84no—
631C22×Q8—42no—
632C22×Q8—42no—
633C22×Q8—42no—
634C22×Q8C2411yescharacteristic
635C22×Q8C2412yes—
636C22×Q8C2411yescharacteristic
637C22×Q8C2412yes—
638C22×Q8C2412yes—
639C22×Q8C2412yes—
640C22×D4—24no—
641C22×D4—216no—
642C22×D4—42no—
643C22×D4—42no—
644C22×D4—42no—
645C22×D4—42no—
646C22×D4—42no—
647C22×D4—48no—
648C22×D4—84no—
649C22×D4C2414yes—
650C22×D4C2414yes—
651C22×D4C2412yes—
652C22×D4C2414yes—
653C22×D4C2414yes—
654C22×D4C2411yescharacteristic
655C22×D4C2414yes—
656C22×D4C2414yes—
657C22×D4C2414yes—
658C22×D4C2412yes—
659C22×D4C2414yes—
660C22×D4C2412yes—
661C22×D4C2412yes—
662C22×D4C2414yes—
663C22×D4C2414yes—
664C22×D4C2414yes—
665C22×D4C2414yes—
666C22×D4C2414yes—
667C22×D4C2412yes—
668C22×D4C2412yes—
669C22×D4C2411yescharacteristic
670C23×C4—28no—
671C23×C4—84no—
672C23×C4C2411yescharacteristic
673C23×C4C2411yescharacteristic
674C23×C4C2414yes—
675C23×C4C2412yes—
676C23×C4C2412yes—
677C23×C4C2412yes—
678C23×C4C2414yes—
679C23×C4C2414yes—
680C23×C4C2414yes—
681C23×C4C2414yes—
682C23×C4C2412yes—
683C23×C4C2412yes—
684C23×C4C2414yes—
685C23×C4C2412yes—
686C23×C4C2412yes—
687C23×C4C2414yes—
688C23×C4C2412yes—
689C23×C4C2411yescharacteristic
690C4⋊Q8—44no—
691C4⋊Q8—44no—
692#127—28no—
693#127—44no—
694#127—44no—
695#127—44no—
696#127—48no—
697#127—84no—
698#126—216no—
699#126—48no—
700#125—216no—
701#124—216no—
702#124—28no—
703#124—44no—
704#124—48no—
705#124—44no—
706#124—48no—
707#124—44no—
708#124—44no—
709#124—44no—
710#124—48no—
711#124—44no—
712#124—44no—
713#124—84no—
714#123—216no—
715#123—216no—
716#123—216no—
717#123—216no—
718#123—48no—
719#123—48no—
720C22⋊Q8—216no—
721C22⋊Q8—44no—
722C22⋊Q8—44no—
723C22⋊Q8—44no—
724C22⋊Q8#41116yescomplemented
725#121—216no—
726#121—28no—
727#121—216no—
728#121—216no—
729#121—216no—
730#121—44no—
731#121—48no—
732#121—48no—
733#121—48no—
734#121—48no—
735#121—48no—
736#121—48no—
737#121—44no—
738#121—44no—
739#121—84no—
740#121—84no—
741#120—216no—
742#120—216no—
743#120—48no—
744#120—48no—
745C4×Q8—44no—
746C4×D4—216no—
747C4×D4—216no—
748C4×D4—216no—
749C4×D4—216no—
750C4×D4—44no—
751C4×D4—44no—
752C4×D4—44no—
753C4×D4—44no—
754C4×D4—44no—
755C4×D4—48no—
756C4×D4—48no—
757C4×D4—48no—
758C4×D4—84no—
759C4×D4—84no—
760C4×D4—84no—
761C4×D4—84no—
762#117—44no—
763#117—48no—
764#117—48no—
765#117—84no—
766C2×C4⋊C4—28no—
767C2×C4⋊C4—42no—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C22⋊C4—28no—
800C2×C22⋊C4—216no—
801C2×C22⋊C4—216no—
802C2×C22⋊C4—48no—
803C2×C22⋊C4—44no—
804C2×C22⋊C4—44no—
805C2×C22⋊C4—84no—
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⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C42—24no—
862C2×C42—42no—
863C2×C42—42no—
864C2×C42—84no—
865C2×C42C2412yes—
866C2×C42C2414yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2414yes—
870C2×C42C2412yes—
871C2×C42C2414yes—
872C2×C42C2412yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2412yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2411yescharacteristic
885C2×C42C2411yescharacteristic
886C2×C42C2412yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2412yes—
893#95C2412yes—
894#95C2412yes—
895#95C2412yes—
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—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927C24—24no—
928C24—28no—
929C24—24no—
930C24—28no—
931C24—24no—
932C24—44no—
933C24—42no—
934C24—44no—
935C24—42no—
936C24—42no—
937C24C2512yes—
938C24C2514yes—
939C24C2514yes—
940C24C2512yes—
941C24C2511yescharacteristic
942#41—832no—
943#41—816no—
944C2×Q8—24no—
945C2×Q8—22no—
946C2×Q8—22no—
947C2×Q8—42no—
948C2×Q8—42no—
949C2×Q8—42no—
950C2×Q8—41no—
951C2×Q8—42no—
952C2×Q8—41no—
953C2×Q8—41no—
954C2×Q8—41no—
955C2×Q8—44no—
956C2×Q8—42no—
957C2×Q8—42no—
958C2×Q8—42no—
959C2×Q8—42no—
960C2×Q8—88no—
961C2×Q8C2×#4118yes—
962C2×D4—28no—
963C2×D4—28no—
964C2×D4—28no—
965C2×D4—28no—
966C2×D4—28no—
967C2×D4—28no—
968C2×D4—24no—
969C2×D4—28no—
970C2×D4—28no—
971C2×D4—28no—
972C2×D4—28no—
973C2×D4—28no—
974C2×D4—28no—
975C2×D4—28no—
976C2×D4—24no—
977C2×D4—28no—
978C2×D4—28no—
979C2×D4—22no—
980C2×D4—24no—
981C2×D4—24no—
982C2×D4—24no—
983C2×D4—41no—
984C2×D4—42no—
985C2×D4—41no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—41no—
989C2×D4—41no—
990C2×D4—44no—
991C2×D4—416no—
992C2×D4—44no—
993C2×D4—42no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—42no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—42no—
1007C2×D4—42no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—42no—
1011C2×D4—42no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—42no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—42no—
1018C2×D4—42no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—42no—
1024C2×D4—88no—
1025C2×D4—832no—
1026C2×D4H(5,𝔽2)14yes—
1027C22×C4—22no—
1028C22×C4—22no—
1029C22×C4—22no—
1030C22×C4—24no—
1031C22×C4—22no—
1032C22×C4—28no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—28no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—28no—
1040C22×C4—28no—
1041C22×C4—28no—
1042C22×C4—28no—
1043C22×C4—28no—
1044C22×C4—28no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—42no—
1048C22×C4—44no—
1049C22×C4—44no—
1050C22×C4—42no—
1051C22×C4—44no—
1052C22×C4—42no—
1053C22×C4—42no—
1054C22×C4—44no—
1055C22×C4—42no—
1056C22×C4—42no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—42no—
1072C22×C4—816no—
1073C22×C4C2×#4118yes—
1074C22×C4H(5,𝔽2)14yes—
1075C22×C4C2514yes—
1076C22×C4C2512yes—
1077C22×C4C2514yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2514yes—
1081C22×C4C2514yes—
1082C22×C4C2512yes—
1083C22×C4C2514yes—
1084C22×C4C2514yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2514yes—
1089C22×C4C2514yes—
1090C22×C4C2512yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2511yescharacteristic
1093C4⋊C4—28no—
1094C4⋊C4—28no—
1095C4⋊C4—28no—
1096C4⋊C4—28no—
1097C4⋊C4—24no—
1098C4⋊C4—28no—
1099C4⋊C4—28no—
1100C4⋊C4—28no—
1101C4⋊C4—28no—
1102C4⋊C4—28no—
1103C4⋊C4—41no—
1104C4⋊C4—42no—
1105C4⋊C4—41no—
1106C4⋊C4—44no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—42no—
1115C4⋊C4—44no—
1116C4⋊C4—42no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—44no—
1122C4⋊C4C2×#4118yes—
1123C4⋊C4C2×#41116yes—
1124C22⋊C4—28no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—28no—
1133C22⋊C4—28no—
1134C22⋊C4—28no—
1135C22⋊C4—28no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—28no—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—28no—
1143C22⋊C4—28no—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
1146C22⋊C4—28no—
1147C22⋊C4—42no—
1148C22⋊C4—42no—
1149C22⋊C4—42no—
1150C22⋊C4—42no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4C2×#41116yes—
1179C42—28no—
1180C42—28no—
1181C42—24no—
1182C42—24no—
1183C42—24no—
1184C42—24no—
1185C42—28no—
1186C42—42no—
1187C42—41no—
1188C42—41no—
1189C42—44no—
1190C42—44no—
1191C42—44no—
1192C42—44no—
1193C42—44no—
1194C42—42no—
1195C42—44no—
1196C42—42no—
1197C42—44no—
1198C42—44no—
1199C42—42no—
1200C42—42no—
1201C23—21no—
1202C23—21no—
1203C23—22no—
1204C23—24no—
1205C23—22no—
1206C23—22no—
1207C23—24no—
1208C23—24no—
1209C23—24no—
1210C23—24no—
1211C23—24no—
1212C23—24no—
1213C23—24no—
1214C23—24no—
1215C23—24no—
1216C23—22no—
1217C23—22no—
1218C23—24no—
1219C23—24no—
1220C23—22no—
1221C23—24no—
1222C23—24no—
1223C23—24no—
1224C23—24no—
1225C23—24no—
1226C23—24no—
1227C23—48no—
1228C23—416no—
1229C23—48no—
1230C23—48no—
1231C23—84no—
1232C23—88no—
1233C23—88no—
1234C23—84no—
1235C23—88no—
1236C23—84no—
1237C23C22×#4114yes—
1238C23C2×H(5,𝔽2)14yes—
1239C23C2×H(5,𝔽2)12yes—
1240C23C2611yescharacteristic
1241Q8—48no—
1242Q8—84no—
1243Q8—82no—
1244Q8—82no—
1245Q8—84no—
1246Q8—162no—
1247D4—44no—
1248D4—48no—
1249D4—416no—
1250D4—416no—
1251D4—416no—
1252D4—44no—
1253D4—416no—
1254D4—84no—
1255D4—88no—
1256D4—88no—
1257D4—88no—
1258D4—88no—
1259D4—84no—
1260D4—84no—
1261D4—88no—
1262D4—88no—
1263D4—84no—
1264D4—88no—
1265D4—162no—
1266D4—164no—
1267D4—164no—
1268C2×C4—28no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—21no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—21no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—44no—
1313C2×C4—48no—
1314C2×C4—416no—
1315C2×C4—48no—
1316C2×C4—48no—
1317C2×C4—44no—
1318C2×C4—88no—
1319C2×C4—88no—
1320C2×C4—88no—
1321C2×C4—84no—
1322C2×C4—84no—
1323C2×C4—88no—
1324C2×C4—88no—
1325C2×C4—88no—
1326C2×C4—84no—
1327C2×C4—84no—
1328C2×C4—84no—
1329C2×C4C22×#4114yes—
1330C2×C4C22×#4118yes—
1331C2×C4C22×#4118yes—
1332C2×C4C22×#4114yes—
1333C2×C4C2×H(5,𝔽2)14yes—
1334C2×C4C2×H(5,𝔽2)12yes—
1335C2×C4#58512yes—
1336C22—24no—
1337C22—24no—
1338C22—22no—
1339C22—22no—
1340C22—28no—
1341C22—24no—
1342C22—44no—
1343C22—42no—
1344C22—42no—
1345C22—44no—
1346C22—44no—
1347C22—44no—
1348C22—44no—
1349C22—44no—
1350C22—44no—
1351C22—44no—
1352C22—44no—
1353C22—44no—
1354C22—44no—
1355C22—42no—
1356C22—44no—
1357C22—44no—
1358C22—42no—
1359C22—44no—
1360C22—44no—
1361C22—44no—
1362C22—42no—
1363C22—44no—
1364C22—816no—
1365C22—168no—
1366C22#348314yes—
1367C22C23×#4112yes—
1368C22C22×H(5,𝔽2)11yescharacteristic
1369C22C22×H(5,𝔽2)11yescharacteristic
1370C22C2×#58511yescharacteristic
1371C22H(7,𝔽2)12yes—
1372C4—24no—
1373C4—28no—
1374C4—24no—
1375C4—28no—
1376C4—22no—
1377C4—22no—
1378C4—24no—
1379C4—44no—
1380C4—44no—
1381C4—44no—
1382C4—42no—
1383C4—42no—
1384C4—44no—
1385C4—42no—
1386C4—42no—
1387C4—44no—
1388C4—42no—
1389C4—44no—
1390C2—24no—
1391C2—44no—
1392C2—84no—
1393C2—82no—
1394C2—84no—
1395C2C2×#348311yescharacteristic
1396C2#6281811yescharacteristic
1397C2#6286211yescharacteristic
1398C2#6298312yes—
1399C2#6301012yes—
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. #60007C2semidirect
2. #59947C2semidirect
3. #59923C2semidirect
4. #59885C2semidirect
5. #59810C2semidirect
6. #59779C2semidirect
7. #59633C2semidirect
8. #59160C2semidirect
9. #59124C2semidirect
10. #44707C2semidirect
11. #44670C2semidirect
12. #44605C2semidirect
13. #44326C2semidirect
14. #44242C2semidirect
15. #44200C2semidirect
16. #43083C2semidirect
17. #43006C2semidirect
18. #35466C2semidirect
19. #35392C2semidirect
20. #34957C2semidirect
21. C2×#2544C2semidirect
22. #34302C2semidirect
23. #34278C2semidirect
24. C2×#555C22semidirect
34. #2811C22semidirect
35. #2809C22semidirect
36. #2808C22semidirect
37. #2808C22semidirect
38. #2808C22semidirect
39. #2806C22semidirect
40. #2803C22semidirect
41. #2803C22semidirect
42. #2803C22semidirect
43. #2784C22semidirect
44. #2737C22semidirect
45. #2737C22semidirect
46. #2734C22semidirect
47. #2733C22semidirect
48. #2733C22semidirect
49. #2731C22semidirect
50. #2730C22semidirect
51. #2730C22semidirect
52. #2714C22semidirect
53. #2714C22semidirect
54. #2699C22semidirect
55. #2694C22semidirect
56. #2694C22semidirect
57. #2686C22semidirect
58. #2686C22semidirect
59. #2686C22semidirect
62. #2673C22semidirect
63. #2673C22semidirect
64. #2610C22semidirect
65. #2610C22semidirect
66. #2610C22semidirect
67. #2603C22semidirect
68. #2602C22semidirect
69. #2602C22semidirect
70. #2602C22semidirect
71. #2601C22semidirect
72. #2593C22semidirect
74. #2586C22semidirect
75. #2586C22semidirect
77. #2572C22semidirect
78. #2564C22semidirect
79. #2564C22semidirect
82. #2560C22semidirect
83. #2557C22semidirect
84. #2557C22semidirect
85. #2557C22semidirect
86. #2555C22semidirect
87. #2555C22semidirect
88. #2555C22semidirect
89. #2555C22semidirect
90. #2555C22semidirect
91. #2554C22semidirect
100. #2544C22semidirect
102. #2543C22semidirect
103. #2543C22semidirect
104. #2543C22semidirect
109. #2532C22semidirect
110. #2531C22semidirect
111. #2531C22semidirect
112. #2526C22semidirect
113. #2521C22semidirect
114. #2521C22semidirect
115. #2491C22semidirect
116. #2491C22semidirect
117. #2491C22semidirect
118. #2490C22semidirect
119. #2490C22semidirect
120. #2485C22semidirect
121. #2485C22semidirect
122. #2476C22semidirect
123. #2476C22semidirect
124. #2476C22semidirect
125. #2474C22semidirect
128. #2467C22semidirect
129. #2467C22semidirect
130. #2464C22semidirect
131. #2461C22semidirect
132. #2459C22semidirect
133. #2459C22semidirect
134. #2459C22semidirect
135. #2459C22semidirect
136. #2451C22semidirect
138. #2445C22semidirect
139. #2445C22semidirect
140. #2445C22semidirect
145. #2431C22semidirect
146. #2430C22semidirect
148. #2428C22semidirect
151. #2414C22semidirect
157. #2407C22semidirect
158. #2407C22semidirect
159. #2395C22semidirect
160. #2395C22semidirect
161. #2388C22semidirect
162. #2388C22semidirect
164. #2374C22semidirect
165. #2374C22semidirect
166. #2373C22semidirect
167. #2373C22semidirect
168. #2372C22semidirect
169. #2372C22semidirect
170. #2372C22semidirect
171. #2371C22semidirect
172. #2370C22semidirect
173. #2369C22semidirect
175. #2368C22semidirect
177. #2364C22semidirect
178. #2364C22semidirect
179. #2363C22semidirect
180. #2363C22semidirect
181. #2362C22semidirect
182. #2359C22semidirect
183. #2359C22semidirect
187. #2353C22semidirect
190. #2339C22semidirect
192. #2337C22semidirect
193. #2335C22semidirect
194. #2333C22semidirect
195. #2333C22semidirect
203. C4×#123C22semidirect
205. C4×#121C22semidirect
206. C4×#121C22semidirect
207. C4×#121C22semidirect
209. #2297C22semidirect
213. #2290C22semidirect
724. C22⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#600072
#599472
#599232
#598852
#598102
#597792
#596332
#591602
#591242
#447072
#446702
#446052
#443262
#442422
#442002
#430832
#430062
#354662
#353922
#349572
C2×#25442
#343022
#342782