Finite Group Databasebeta

← #7710084

Subgroups — #7710084

Order 512.

6712 conjugacy classes of subgroups.

The subgroup lattice has 1147 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3563C211yesmaximal, characteristic, complemented
2C23×#125C211yesmaximal, characteristic, complemented
3#59154C214yesmaximal, complemented
4#59140C214yesmaximal, complemented
5C22⋊#564C214yesmaximal, complemented
6#45979C214yesmaximal, complemented
7#39122C212yesmaximal, complemented
8#38919C212yesmaximal, complemented
9#38045C214yesmaximal, complemented
10#37719C218yesmaximal, complemented
11#37705C214yesmaximal, complemented
12#37687C214yesmaximal, complemented
13#37549C211yesmaximal, characteristic, complemented
14#37540C211yesmaximal, characteristic, complemented
15#36968C212yesmaximal, complemented
16#36959C212yesmaximal, complemented
17#36625C211yesmaximal, characteristic, complemented
18#36621C211yesmaximal, characteristic
19#36546C212yesmaximal, complemented
20#36163C212yesmaximal, complemented
21#36163C214yesmaximal, complemented
22#35224C212yesmaximal, complemented
23#34989C212yesmaximal
24#34378C211yesmaximal, characteristic, complemented
25#3563—216no—
26C2×#564C2212yescomplemented
27C2×#563C2212yescomplemented
28C2×#557C2212yescomplemented
29C2×#554C2212yes—
30C2×#552C2212yes—
31C2×#552C2214yes—
32C2×#552C2212yescomplemented
33C2×#544C2212yes—
34C2×#544C2212yescomplemented
35C2×#541C2212yescomplemented
36C2×#541C2214yescomplemented
37C2×#539C2212yes—
38C2×#533C2211yescharacteristic
39C2×#529C2211yescharacteristic
40C22×#125—216no—
41C22×#125C2214yes—
42C22×#125C2211yescharacteristic
43C22×#125C2214yes—
44C22×#125C2214yes—
45C22×#125C2214yes—
46C22×#125C2212yes—
47C22×#125C2212yes—
48C22×#125C2211yescharacteristic
49C22×#125C2211yescharacteristic
50C22×#125C2211yescharacteristic
51C23×C4⋊C4C2211yescharacteristic
52C23×C4⋊C4C2212yes—
53C23×C4⋊C4C2212yes—
54C23×C4⋊C4C2211yescharacteristic
55C23×C42C2211yescharacteristic
56#2857C2212yes—
57#2857C2212yes—
58#2855C2212yes—
59#2855C2211yescharacteristic
60#2855C2212yes—
61#2854C2211yescharacteristic
62#2853C2212yes—
63#2852C2214yes—
64#2851C2212yes—
65#2851C2214yes—
66#2850C2212yes—
67#2849C2212yes—
68#2849C2214yes—
69#2848C2211yescharacteristic
70#2848C2212yes—
71#2848C2212yes—
72#2848C2214yes—
73#2847C2211yescharacteristic
74#2822C2212yescomplemented
75#2822C2214yescomplemented
76#2820C2212yescomplemented
77#2726C2218yescomplemented
78#2726C2218yescomplemented
79#2725C2218yescomplemented
80#2725C2218yescomplemented
81#2721C2218yescomplemented
82#2720C2218yescomplemented
83#2719C2218yescomplemented
84#2719C2218yescomplemented
85#2719C2218yescomplemented
86#2719C2218yescomplemented
87#2719C2218yescomplemented
88#2713C2218yescomplemented
89#2713C2218yescomplemented
90#2707C2218yescomplemented
91#2704C2218yescomplemented
92#2690C2218yescomplemented
93#2664C2214yescomplemented
94#2660C2212yescomplemented
95#2642C2212yescomplemented
96#2634C2214yescomplemented
97#2629C2214yescomplemented
98#2627C2212yes—
99#2627C2212yes—
100#2627C2212yes—
101#2627C2214yes—
102#2623C2214yes—
103#2618C2212yes—
104#2584C2212yescomplemented
105#2583C2214yes—
106#2579C2214yes—
107#2565C2214yescomplemented
108#2562C2212yescomplemented
109#2552C2214yescomplemented
110#2550C2214yescomplemented
111#2519C2218yescomplemented
112#2506C2218yescomplemented
113#2503C2214yes—
114#2503C2212yes—
115#2502C2212yes—
116#2489C2214yescomplemented
117#2489C2214yescomplemented
118#2487C2212yes—
119#2486C2214yes—
120#2486C2212yes—
121#2484C2214yes—
122#2484C2214yes—
123#2484C2214yes—
124#2481C2218yes—
125#2481C2218yes—
126#2481C2218yes—
127#2481C2218yes—
128#2475C2218yescomplemented
129#2473C2218yes—
130#2473C2218yes—
131#2473C2218yes—
132#2473C2218yes—
133#2473C2218yes—
134#2462C2218yescomplemented
135#2453C2214yescomplemented
136#2453C2214yescomplemented
137#2449C2218yes—
138#2449C2218yes—
139#2443C2218yes—
140#2442C2218yes—
141#2442C2214yes—
142#2442C2218yes—
143#2442C2218yes—
144#2442C2214yescomplemented
145#2441C2214yescomplemented
146#2440C2214yes—
147#2440C2218yes—
148#2440C2218yes—
149#2417C2214yes—
150#2417C2214yes—
151#2417C2218yes—
152#2413C2214yes—
153#2413C2214yes—
154#2413C2214yes—
155#2382C2214yescomplemented
156#2370C2214yescomplemented
157#2360C2214yes—
158#2360C2218yes—
159#2360C2214yes—
160#2352C2214yes—
161#2352C2218yes—
162D4×C4⋊C4C2214yes—
163#2345C2212yes—
164#2344C2212yes—
165#2344C2214yes—
166#2336C2214yescomplemented
167#2330C2214yescomplemented
168#2322C2214yes—
169#2317C2214yes—
170#2316C2212yes—
171#2313C2212yes—
172C4×C22⋊Q8C2214yes—
173C4×C22⋊Q8C2212yes—
174C4×C22⋊Q8C2214yes—
175C4×#123C2212yes—
176C4×#121C2212yes—
177C4×#120C2212yes—
178C4×#120C2214yes—
179#2296C2212yes—
180#2290C2214yes—
181#2285C2211yescharacteristic
182#2283C2211yescharacteristic
183#2280C2212yes—
184#2280C2214yes—
185C24×C4C2311yescharacteristic
186C24×C4C2311yescharacteristic
187C24×C4C2312yes—
188C24×C4C2311yescharacteristic
189C24×C4C2312yes—
190#564—216no—
191#563—216no—
192#557—216no—
193#554—216no—
194#552—216no—
195#552—232no—
196#552—216no—
197#544—216no—
198#544—216no—
199#541—232no—
200#541—216no—
201#539—216no—
202#533—28no—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2314yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2312yes—
208#529—28no—
209C2×#126C2312yes—
210C2×#126C2314yes—
211C2×#126C2314yes—
212C2×#126C2314yes—
213C2×#126C2314yes—
214C2×#125—232no—
215C2×#125—232no—
216C2×#125—232no—
217C2×#125—232no—
218C2×#125—216no—
219C2×#125—28no—
220C2×#125—216no—
221C2×#125—28no—
222C2×#125—28no—
223C2×#125D4116yescomplemented
224C2×#125C2312yes—
225C2×#125C2312yes—
226C2×#125C2311yescharacteristic
227C2×#125C2312yes—
228C2×#125C2312yes—
229C2×#125C2312yes—
230C2×#125C2314yes—
231C2×#125C2314yes—
232C2×#125C2314yes—
233C2×#125C2318yes—
234C2×#125C2318yes—
235C2×#125C2318yes—
236C2×#125C2314yes—
237C2×#125C2318yes—
238C2×#125C2314yes—
239C2×#125C2314yes—
240C2×#125C2314yes—
241C2×#125C2314yes—
242C2×#125C2314yes—
243C2×#125C2314yes—
244C2×#125C2314yes—
245C2×#125C2312yes—
246C2×#125C2314yes—
247C2×#125C2312yes—
248C2×#125C2312yes—
249C2×#125C2312yes—
250C2×#125C2312yes—
251C2×#124C2311yescharacteristic
252C2×#123C2312yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2312yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2318yes—
270C2×#121C2311yescharacteristic
271C2×#121C2312yes—
272C2×#120C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×D4C2311yescharacteristic
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2318yes—
284C2×#117C2314yes—
285C2×#117C2314yes—
286C2×#117C2312yes—
287C2×#117C2312yes—
288C2×#117C2312yes—
289C2×#117C2314yes—
290C2×#117C2312yes—
291C22×C4⋊C4—216no—
292C22×C4⋊C4—28no—
293C22×C4⋊C4—216no—
294C22×C4⋊C4—28no—
295C22×C4⋊C4C2312yes—
296C22×C4⋊C4C2312yes—
297C22×C4⋊C4C2312yes—
298C22×C4⋊C4C2312yes—
299C22×C4⋊C4C2314yes—
300C22×C4⋊C4C2314yes—
301C22×C4⋊C4C2318yes—
302C22×C4⋊C4C2312yes—
303C22×C4⋊C4C2312yes—
304C22×C4⋊C4C2312yes—
305C22×C4⋊C4C2312yes—
306C22×C4⋊C4C2318yes—
307C22×C4⋊C4C2318yes—
308C22×C4⋊C4C2318yes—
309C22×C4⋊C4C2314yes—
310C22×C4⋊C4C2314yes—
311C22×C4⋊C4C2311yescharacteristic
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2311yescharacteristic
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2311yescharacteristic
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2311yescharacteristic
318C22×C42—28no—
319C22×C42C2312yes—
320C22×C42C2312yes—
321C22×C42C2311yescharacteristic
322C22×C42C2311yescharacteristic
323C22×C42C2311yescharacteristic
324C22×C42C2312yes—
325C22×C42C2312yes—
326C22×C42C2311yescharacteristic
327#400C2314yes—
328#400C2318yes—
329#400C2318yes—
330#400C2314yes—
331#400C2318yes—
332#400C2314yes—
333#400C2314yes—
334#400C2318yes—
335#400C2318yes—
336#400C2318yes—
337#400C2318yes—
338#400C2318yes—
339#399C2314yes—
340#399C2318yes—
341#398C2318yes—
342#398C2318yes—
343#398C2314yes—
344#398C2318yes—
345#398C2318yes—
346#398C2318yes—
347#398C2314yes—
348#398C2318yes—
349#398C2318yes—
350#398C2318yes—
351#398C2318yes—
352#398C2318yes—
353#398C2318yes—
354#398C2318yes—
355#398C2318yes—
356#398C2318yes—
357#398C2318yes—
358#398C2318yes—
359#397C2314yes—
360#397C2318yes—
361#397C2318yes—
362#396C2318yes—
363#396C2318yes—
364#396C2318yes—
365#396C2318yes—
366#396C2318yes—
367#395C2314yes—
368#395C2318yes—
369#395C2314yes—
370#395C2314yes—
371#395C2318yes—
372#394C2314yes—
373#391C2314yes—
374#391C2314yes—
375#391C2312yes—
376#391C2314yes—
377#391C2314yes—
378#391C2318yes—
379#390C2312yes—
380#389C2318yes—
381#389C2318yes—
382#389C2318yes—
383#389C2318yes—
384#389C2318yes—
385#389C2318yes—
386#389C2318yes—
387#389C2314yes—
388#389C2314yes—
389#389C2318yes—
390#389C2314yes—
391#389C2318yes—
392#389C2314yes—
393#389C2312yes—
394#389C2312yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2318yes—
400#389C2318yes—
401#389C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2318yes—
409#388C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2314yes—
421#387C2314yes—
422#387C2318yes—
423#387C2318yes—
424#387C2314yes—
425#387C2314yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#386C2312yes—
431#386C2312yes—
432#386C2314yes—
433#386C2314yes—
434#386C2314yes—
435#386C2314yes—
436#386C2318yes—
437#386C2318yes—
438#386C2314yes—
439#386C2318yes—
440#385C2312yes—
441#385C2314yes—
442#385C2314yes—
443#385C2314yes—
444#385C2318yes—
445#385C2314yes—
446#385C2318yes—
447#385C2312yes—
448#385C2314yes—
449#385C2318yes—
450#385C2318yes—
451#385C2314yes—
452#385C2318yes—
453#385C2318yes—
454#385C2314yes—
455#385C2314yes—
456#385C2318yes—
457#385C2318yes—
458#385C2314yes—
459#385C2318yes—
460#384C2314yes—
461#384C2318yes—
462#384C2312yes—
463#383C2312yes—
464#382C2312yes—
465#382C2314yes—
466#382C2312yes—
467#382C2318yes—
468#382C2318yes—
469#381C2314yes—
470#381C2314yes—
471#381C2312yes—
472#381C2312yes—
473#381C2314yes—
474#381C2314yes—
475#381C2314yes—
476#380C2314yes—
477#380C2314yes—
478#380C2311yescharacteristic
479#380C2312yes—
480#380C2311yescharacteristic
481#380C2314yes—
482#380C2312yes—
483#380C2312yes—
484#380C2312yes—
485#380C2314yes—
486#380C2314yes—
487#380C2318yes—
488#380C2314yes—
489#380C2314yes—
490#380C2318yes—
491#380C2318yes—
492#380C2318yes—
493#379C2314yes—
494#379C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2318yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2318yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2314yes—
511#376C2312yes—
512C25C2411yescharacteristic
513C22×Q8C2412yes—
514C22×Q8C2414yes—
515C22×Q8C2412yes—
516C22×Q8C2411yescharacteristic
517C22×D4C2412yes—
518C22×D4C2414yes—
519C22×D4C2411yescharacteristic
520C23×C4—24no—
521C23×C4—28no—
522C23×C4—24no—
523C23×C4—28no—
524C23×C4—28no—
525C23×C4—28no—
526C23×C4—24no—
527C23×C4—24no—
528C23×C4—42no—
529C23×C4—44no—
530C23×C4—48no—
531C23×C4—44no—
532C23×C4C2412yes—
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2418yes—
538C23×C4C2418yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2411yescharacteristic
549C23×C4C2414yes—
550C23×C4C2412yes—
551C23×C4C2411yescharacteristic
552C4⋊Q8—216no—
553C4⋊Q8—28no—
554C4⋊Q8—216no—
555C4⋊Q8—24no—
556C4⋊Q8—24no—
557#126—216no—
558#126—216no—
559#126—216no—
560#126—216no—
561#126—28no—
562#125—216no—
563#125—216no—
564#125—232no—
565#125—216no—
566#125—232no—
567#125—232no—
568#125—232no—
569#125—216no—
570#125—216no—
571#125—216no—
572#125—216no—
573#125—216no—
574#125—216no—
575#125—216no—
576#125—28no—
577#125—216no—
578#125—216no—
579#125—28no—
580#125—28no—
581#125—28no—
582#125—28no—
583#125—24no—
584#125—28no—
585#125C2×D4116yes—
586#125C2×D4116yes—
587#125C2×D4116yes—
588#125C2×D4116yes—
589#124—24no—
590#123—28no—
591#123—216no—
592#123—216no—
593#123—48no—
594#123—44no—
595C22⋊Q8—24no—
596C22⋊Q8—28no—
597C22⋊Q8—28no—
598C22⋊Q8—216no—
599C22⋊Q8—216no—
600C22⋊Q8—216no—
601C22⋊Q8—28no—
602C22⋊Q8—28no—
603C22⋊Q8—216no—
604C22⋊Q8—216no—
605C22⋊Q8—48no—
606C22⋊Q8—416no—
607C22⋊Q8—44no—
608#121—24no—
609#121—44no—
610#120—28no—
611C4×Q8—216no—
612C4×Q8—28no—
613C4×Q8—28no—
614C4×Q8—24no—
615C4×Q8—28no—
616C4×Q8—28no—
617C4×D4—28no—
618C4×D4—216no—
619C4×D4—216no—
620C4×D4—24no—
621C4×D4—416no—
622#117—28no—
623#117—216no—
624#117—216no—
625#117—28no—
626#117—28no—
627#117—48no—
628#117—44no—
629C2×C4⋊C4—28no—
630C2×C4⋊C4—28no—
631C2×C4⋊C4—28no—
632C2×C4⋊C4—28no—
633C2×C4⋊C4—28no—
634C2×C4⋊C4—28no—
635C2×C4⋊C4—28no—
636C2×C4⋊C4—24no—
637C2×C4⋊C4—24no—
638C2×C4⋊C4—28no—
639C2×C4⋊C4—216no—
640C2×C4⋊C4—216no—
641C2×C4⋊C4—232no—
642C2×C4⋊C4—216no—
643C2×C4⋊C4—232no—
644C2×C4⋊C4—232no—
645C2×C4⋊C4—232no—
646C2×C4⋊C4—216no—
647C2×C4⋊C4—28no—
648C2×C4⋊C4C2×D4116yes—
649C2×C4⋊C4C2×D418yes—
650C2×C4⋊C4C2×D4116yes—
651C2×C4⋊C4C2×D418yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2418yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2418yes—
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2418yes—
698C2×C4⋊C4C2418yes—
699C2×C4⋊C4C2418yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2418yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2412yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2412yes—
712C2×C22⋊C4C2412yes—
713C2×C22⋊C4C2412yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2412yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2412yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2412yes—
721C2×C22⋊C4C2418yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2412yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2418yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2418yes—
732C2×C42—24no—
733C2×C42—24no—
734C2×C42—24no—
735C2×C42—28no—
736C2×C42—28no—
737C2×C42—28no—
738C2×C42—28no—
739C2×C42C2×D418yes—
740C2×C42C2414yes—
741C2×C42C2414yes—
742C2×C42C2412yes—
743C2×C42C2414yes—
744C2×C42C2414yes—
745C2×C42C2414yes—
746C2×C42C2412yes—
747C2×C42C2412yes—
748C2×C42C2412yes—
749C2×C42C2412yes—
750C2×C42C2412yes—
751C2×C42C2412yes—
752C2×C42C2414yes—
753C2×C42C2418yes—
754C2×C42C2418yes—
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759#95C2412yes—
760#95C2412yes—
761#95C2414yes—
762#95C2418yes—
763#95C2418yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2418yes—
772#95C2414yes—
773#95C2414yes—
774#95C2418yes—
775#95C2418yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2418yes—
780#95C2418yes—
781#95C2418yes—
782#95C2414yes—
783#95C2418yes—
784#95C2418yes—
785#95C2414yes—
786#95C2418yes—
787#95C2418yes—
788#95C2418yes—
789#95C2418yes—
790C24—22no—
791C24—24no—
792C24—24no—
793C24—22no—
794C242−1+414yes—
795C24C2512yes—
796C24C2511yescharacteristic
797C24C2512yes—
798C2×Q8—24no—
799C2×Q8—28no—
800C2×Q8—24no—
801C2×Q8—22no—
802C2×Q8—28no—
803C2×Q8—48no—
804C2×Q8—42no—
805C2×Q8—44no—
806C2×D4—24no—
807C2×D4—28no—
808C2×D4—24no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—24no—
812C2×D4—22no—
813C2×D4—42no—
814C22×C4—232no—
815C22×C4—22no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—216no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—22no—
836C22×C4—216no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—22no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—216no—
846C22×C4—216no—
847C22×C4—24no—
848C22×C4—28no—
849C22×C4—28no—
850C22×C4—42no—
851C22×C4—48no—
852C22×C4—44no—
853C22×C4—48no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—44no—
860C22×C4—48no—
861C22×C4—432no—
862C22×C4—416no—
863C22×C4—432no—
864C22×C4—416no—
865C22×C4C22×D414yes—
866C22×C4C22×D414yes—
867C22×C4C22×D418yes—
868C22×C4C22×D414yes—
869C22×C4C22×D418yes—
870C22×C42−1+418yes—
871C22×C4C2514yes—
872C22×C4C2514yes—
873C22×C4C2518yes—
874C22×C4C2512yes—
875C22×C4C2514yes—
876C22×C4C2512yes—
877C22×C4C2514yes—
878C22×C4C2512yes—
879C22×C4C2512yes—
880C22×C4C2512yes—
881C22×C4C2514yes—
882C22×C4C2514yes—
883C22×C4C2511yescharacteristic
884C22×C4C2511yescharacteristic
885C22×C4C2514yes—
886C22×C4C2511yescharacteristic
887C22×C4C2511yescharacteristic
888C22×C4C2511yescharacteristic
889C22×C4C2514yes—
890C22×C4C2512yes—
891C22×C4C2511yescharacteristic
892C4⋊C4—216no—
893C4⋊C4—216no—
894C4⋊C4—216no—
895C4⋊C4—216no—
896C4⋊C4—216no—
897C4⋊C4—216no—
898C4⋊C4—28no—
899C4⋊C4—28no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—28no—
903C4⋊C4—28no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—24no—
910C4⋊C4—28no—
911C4⋊C4—24no—
912C4⋊C4—28no—
913C4⋊C4—24no—
914C4⋊C4—24no—
915C4⋊C4—22no—
916C4⋊C4—28no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—22no—
920C4⋊C4—28no—
921C4⋊C4—28no—
922C4⋊C4—28no—
923C4⋊C4—28no—
924C4⋊C4—24no—
925C4⋊C4—28no—
926C4⋊C4—28no—
927C4⋊C4—28no—
928C4⋊C4—216no—
929C4⋊C4—48no—
930C4⋊C4—44no—
931C4⋊C4—48no—
932C4⋊C4—42no—
933C4⋊C4—48no—
934C4⋊C4—42no—
935C4⋊C4—44no—
936C4⋊C4—48no—
937C4⋊C4—48no—
938C4⋊C4—48no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—48no—
942C4⋊C4C22×D418yes—
943C4⋊C4C22×D418yes—
944C4⋊C4C22×D4116yes—
945C4⋊C4C22×D418yes—
946C4⋊C4C22×D4116yes—
947C4⋊C4C22×D4116yes—
948C4⋊C4C22×D4116yes—
949C4⋊C4C22×D418yes—
950C22⋊C4—28no—
951C22⋊C4—24no—
952C22⋊C4—28no—
953C22⋊C4—24no—
954C22⋊C4—28no—
955C22⋊C4—216no—
956C22⋊C4—24no—
957C22⋊C4—28no—
958C22⋊C4—216no—
959C22⋊C4—28no—
960C22⋊C4—24no—
961C22⋊C4—24no—
962C22⋊C4—28no—
963C22⋊C4—24no—
964C22⋊C4—28no—
965C22⋊C4—28no—
966C22⋊C4—24no—
967C22⋊C4—28no—
968C22⋊C4—48no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—48no—
972C42—24no—
973C42—24no—
974C42—24no—
975C42—24no—
976C42—24no—
977C42—24no—
978C42—28no—
979C42—28no—
980C42—24no—
981C42—28no—
982C42—28no—
983C42—28no—
984C42—44no—
985C42—48no—
986C42—48no—
987C42C22×D414yes—
988C42C22×D414yes—
989C42C22×D414yes—
990C42C22×D414yes—
991C23—28no—
992C23—28no—
993C23—216no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—28no—
1001C23—216no—
1002C23—22no—
1003C23—24no—
1004C23—22no—
1005C23—22no—
1006C23—24no—
1007C23C23×D412yes—
1008C23C2×2−1+412yes—
1009C23C2×2−1+414yes—
1010C23C2×2−1+414yes—
1011C23#58512yes—
1012C23#58514yes—
1013C23C2611yescharacteristic
1014Q8—48no—
1015Q8—88no—
1016Q8—82no—
1017Q8—84no—
1018D4—48no—
1019D4—416no—
1020D4—82no—
1021C2×C4—216no—
1022C2×C4—28no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—21no—
1027C2×C4—24no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—24no—
1031C2×C4—28no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—28no—
1036C2×C4—216no—
1037C2×C4—28no—
1038C2×C4—216no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—28no—
1053C2×C4—24no—
1054C2×C4—28no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—28no—
1059C2×C4—24no—
1060C2×C4—28no—
1061C2×C4—24no—
1062C2×C4—28no—
1063C2×C4—24no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—28no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—48no—
1071C2×C4—44no—
1072C2×C4—48no—
1073C2×C4—48no—
1074C2×C4—432no—
1075C2×C4—432no—
1076C2×C4—48no—
1077C2×C4—48no—
1078C2×C4—44no—
1079C2×C4—48no—
1080C2×C4—44no—
1081C2×C4—48no—
1082C2×C4—48no—
1083C2×C4—88no—
1084C2×C4C23×D412yes—
1085C2×C4C23×D412yes—
1086C2×C4C23×D412yes—
1087C2×C4C23×D412yes—
1088C2×C4C23×D412yes—
1089C2×C4C23×D418yes—
1090C2×C4C23×D418yes—
1091C2×C4C23×D412yes—
1092C2×C4C2×2−1+414yes—
1093C2×C4C2×2−1+414yes—
1094C22—232no—
1095C22—24no—
1096C22—24no—
1097C22—22no—
1098C22—24no—
1099C22—24no—
1100C22—22no—
1101C22—24no—
1102C22—24no—
1103C22—24no—
1104C22—24no—
1105C22—44no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—44no—
1110C22#348914yes—
1111C22#356318yescomplemented
1112C22C24×D411yescharacteristic
1113C22C22×2−1+411yescharacteristic
1114C22C22×2−1+412yes—
1115C22C2×#58512yes—
1116C22C2×#58511yescharacteristic
1117C4—22no—
1118C4—24no—
1119C4—22no—
1120C4—28no—
1121C4—22no—
1122C4—28no—
1123C4—22no—
1124C4—22no—
1125C4—44no—
1126C4—42no—
1127C4—44no—
1128C4—42no—
1129C4—44no—
1130C4—42no—
1131C4—42no—
1132C4—44no—
1133C4—44no—
1134C4—42no—
1135C4—44no—
1136C4—48no—
1137C4#348614yes—
1138C2—24no—
1139C2—28no—
1140C2—82no—
1141C2C2×#356312yes—
1142C2C2×#348611yescharacteristic
1143C2C2×#348911yescharacteristic
1144C2#6281111yescharacteristic
1145C2#6282512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2847C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3563C2semidirect
2. C23×#125C2semidirect
3. #59154C2semidirect
4. #59140C2semidirect
5. C22⋊#564C2semidirect
6. #45979C2semidirect
7. #39122C2semidirect
8. #38919C2semidirect
9. #38045C2semidirect
10. #37719C2semidirect
11. #37705C2semidirect
12. #37687C2semidirect
13. #37549C2semidirect
14. #37540C2semidirect
15. #36968C2semidirect
16. #36959C2semidirect
17. #36625C2semidirect
19. #36546C2semidirect
20. #36163C2semidirect
21. #36163C2semidirect
22. #35224C2semidirect
24. #34378C2semidirect
26. C2×#564C22semidirect
27. C2×#563C22semidirect
28. C2×#557C22semidirect
32. C2×#552C22semidirect
34. C2×#544C22semidirect
35. C2×#541C22semidirect
36. C2×#541C22semidirect
74. #2822C22semidirect
75. #2822C22semidirect
76. #2820C22semidirect
77. #2726C22semidirect
78. #2726C22semidirect
79. #2725C22semidirect
80. #2725C22semidirect
81. #2721C22semidirect
82. #2720C22semidirect
83. #2719C22semidirect
84. #2719C22semidirect
85. #2719C22semidirect
86. #2719C22semidirect
87. #2719C22semidirect
88. #2713C22semidirect
89. #2713C22semidirect
90. #2707C22semidirect
91. #2704C22semidirect
92. #2690C22semidirect
93. #2664C22semidirect
94. #2660C22semidirect
95. #2642C22semidirect
96. #2634C22semidirect
97. #2629C22semidirect
104. #2584C22semidirect
107. #2565C22semidirect
108. #2562C22semidirect
109. #2552C22semidirect
110. #2550C22semidirect
111. #2519C22semidirect
112. #2506C22semidirect
116. #2489C22semidirect
117. #2489C22semidirect
128. #2475C22semidirect
134. #2462C22semidirect
135. #2453C22semidirect
136. #2453C22semidirect
144. #2442C22semidirect
145. #2441C22semidirect
155. #2382C22semidirect
156. #2370C22semidirect
166. #2336C22semidirect
167. #2330C22semidirect
223. C2×#125D4semidirect
1111. C22#3563semidirect

Maximal subgroups

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

subgroupindex
C2×#35632
C23×#1252
#591542
#591402
C22⋊#5642
#459792
#391222
#389192
#380452
#377192
#377052
#376872
#375492
#375402
#369682
#369592
#366252
#366212
#365462
#361632
#352242
#349892
#343782