Finite Group Databasebeta

← #7681455

Subgroups — #7681455

Order 512.

6894 conjugacy classes of subgroups.

The subgroup lattice has 1143 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3495C212yesmaximal, complemented
2#59317C214yesmaximal, complemented
3#59316C214yesmaximal, complemented
4#59310C218yesmaximal, complemented
5#45261C214yesmaximal, complemented
6#44921C214yesmaximal, complemented
7#44461C214yesmaximal, complemented
8#43959C214yesmaximal, complemented
9#39374C212yesmaximal, complemented
10#39373C212yesmaximal, complemented
11#37766C214yesmaximal, complemented
12#37765C214yesmaximal, complemented
13#36151C212yesmaximal, complemented
14#36135C212yesmaximal, complemented
15#35672C212yesmaximal, complemented
16#35516C212yesmaximal, complemented
17#35330C211yesmaximal, characteristic, complemented
18#35253C212yesmaximal, complemented
19#34935C211yesmaximal, characteristic
20C2×#2536C211yesmaximal, characteristic, complemented
21#34184C211yesmaximal, characteristic, complemented
22#34182C211yesmaximal, characteristic, complemented
23D4×#117C211yesmaximal, characteristic, complemented
24C4×#536C211yesmaximal, characteristic, complemented
25#3495—232no—
26C2×#556C2214yescomplemented
27C2×#554C2214yescomplemented
28C2×#552C2218yes—
29C2×#552C2214yescomplemented
30C2×#552C2214yescomplemented
31C2×#551C2218yes—
32C2×#544C2212yes—
33C2×#542C2214yescomplemented
34C2×#541C2214yescomplemented
35C2×#536C2211yescharacteristic
36C2×#533C2214yescomplemented
37C2×#529C2214yescomplemented
38C2×#525C2212yes—
39C22×C22⋊Q8C2212yes—
40C2×#520C2212yes—
41C2×#519C2212yes—
42C2×C4×#41C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44C22×C4×D4C2211yescharacteristic
45C22×#117C2212yes—
46#2862C2212yescomplemented
47#2859C2212yescomplemented
48#2857C2214yescomplemented
49#2851C2214yescomplemented
50#2727C2218yes—
51#2726C2218yescomplemented
52#2723C2218yes—
53#2722C2218yescomplemented
54#2721C2218yescomplemented
55#2720C2218yescomplemented
56#2719C2218yescomplemented
57#2718C2218yescomplemented
58#2710C2218yes—
59#2689C2218yescomplemented
60#2680C2218yescomplemented
61#2672C2218yes—
62#2660C2214yescomplemented
63#2629C2214yescomplemented
64#2628C2214yescomplemented
65#2553C2218yescomplemented
66#2550C2214yescomplemented
67#2550C2214yescomplemented
68#2549C2214yes—
69#2549C2214yes—
70#2538C2212yes—
71#2537C2212yes—
72#2536C2212yes—
73#2536C2211yescharacteristic
74#2536C2212yes—
75#2536C2214yes—
76#2536C2214yes—
77#2536C2212yes—
78#2536C2212yes—
79#2536C2211yescharacteristic
80#2535C2211yescharacteristic
81#2535C2211yescharacteristic
82#2534C2214yes—
83#2521C2218yescomplemented
84#2519C2218yescomplemented
85#2519C2218yescomplemented
86#2489C2218yescomplemented
87#2488C2218yescomplemented
88#2487C2214yescomplemented
89#2486C2212yes—
90#2486C2214yescomplemented
91#2485C2214yescomplemented
92#2485C2214yescomplemented
93#2484C2218yes—
94#2482C2218yes—
95#2479C2218yes—
96#2478C2218yescomplemented
97#2475C2218yescomplemented
98#2474C2218yescomplemented
99#2469C2218yescomplemented
100#2468C2218yescomplemented
101#2462C2218yescomplemented
102#2455C2218yes—
103#2453C2218yescomplemented
104#2442C2214yescomplemented
105#2441C2214yescomplemented
106#2440C2214yescomplemented
107#2439C2214yescomplemented
108#2438C2218yes—
109#2438C2218yescomplemented
110#2437C2218yes—
111#2425C2218yes—
112#2423C2214yescomplemented
113#2423C2214yescomplemented
114#2423C2214yescomplemented
115#2423C2214yescomplemented
116#2423C2214yescomplemented
117#2422C2214yescomplemented
118#2421C2214yescomplemented
119#2421C2214yescomplemented
120#2421C2214yescomplemented
121#2421C2214yescomplemented
122#2421C2214yescomplemented
123#2420C2214yescomplemented
124#2419C2218yes—
125#2418C2218yes—
126#2415C2218yes—
127#2408C2212yes—
128#2392C2212yes—
129#2392C2212yes—
130C2×#398C2212yes—
131C2×#394C2212yes—
132#2362C2218yescomplemented
133#2359C2218yescomplemented
134#2354C2212yes—
135#2352C2212yes—
136#2352C2212yes—
137#2351C2212yescomplemented
138#2351C2212yescomplemented
139#2351C2212yescomplemented
140#2351C2212yescomplemented
141#2351C2212yescomplemented
142#2351C2212yescomplemented
143Q8×C4⋊C4C2214yescomplemented
144Q8×C4⋊C4C2214yescomplemented
145#2349C2214yes—
146#2349C2214yes—
147#2349C2212yescomplemented
148#2349C2212yescomplemented
149D4×C4⋊C4C2212yes—
150#2344C2212yes—
151#2342C2214yes—
152D4×C22⋊C4C2212yes—
153#2327C2212yescomplemented
154#2326C2212yescomplemented
155#2323C2214yescomplemented
156#2322C2214yes—
157#2317C2212yes—
158#2317C2211yescharacteristic
159#2317C2212yes—
160#2317C2214yescomplemented
161#2316C2214yes—
162#2316C2212yes—
163#2311C2211yescharacteristic
164#2310C2211yescharacteristic
165C4×C4⋊Q8C2212yescomplemented
166C4×#124C2212yescomplemented
167C4×C22⋊Q8C2214yescomplemented
168C4×#123C2214yes—
169C4×#121C2214yes—
170#2293C2212yes—
171#2290C2214yes—
172C2×#388C2214yes—
173#2285C2211yescharacteristic
174#2285C2211yescharacteristic
175#2285C2214yes—
176#2285C2212yescomplemented
177C2×#382C2211yescharacteristic
178C2×#382C2212yescomplemented
179#2280C2212yes—
180#2280C2212yes—
181C2×#380C2212yes—
182C42×D4C2212yes—
183C4×#117C2211yescharacteristic
184C22×#41C2311yescharacteristic
185C23×Q8C2311yescharacteristic
186C23×D4C2311yescharacteristic
187C24×C4C2312yes—
188#556—232no—
189#554—232no—
190#552—264no—
191#552—232no—
192#552—232no—
193#551—264no—
194#544—216no—
195#542—232no—
196#541—232no—
197#536D4116yescomplemented
198#533—232no—
199C2×C4⋊Q8C2314yes—
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2312yes—
202#529—232no—
203C2×#126C2318yes—
204C2×#126C2318yes—
205C2×#126C2318yes—
206C2×#126C2318yes—
207C2×#125C2314yes—
208C2×#125C2318yes—
209C2×#125C2318yes—
210C2×#125C2318yes—
211C2×#125C2314yes—
212C2×#124C2318yes—
213C2×#124C2312yes—
214#525—216no—
215C2×#123C2314yes—
216C2×#123C2318yes—
217C2×#123C2318yes—
218C2×#123C2318yes—
219C2×#123C2314yes—
220C2×C22⋊Q8—216no—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2318yes—
228C2×C22⋊Q8C2318yes—
229C2×C22⋊Q8C2318yes—
230C2×C22⋊Q8C2318yes—
231C2×C22⋊Q8C2314yes—
232C2×#121C2312yes—
233C2×#121C2312yes—
234C2×#121C2314yes—
235C2×#120C2314yes—
236#520—216no—
237#519—216no—
238C4×#41—28no—
239C2×C4×Q8—28no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2318yes—
252C2×C4×D4—28no—
253C2×C4×D4C2312yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2312yes—
257C2×C4×D4C2318yes—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2314yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2318yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2312yes—
268C2×C4×D4C2314yes—
269C2×#117—216no—
270C2×#117C2311yescharacteristic
271C2×#117C2311yescharacteristic
272C2×#117C2312yes—
273C2×#117C2312yes—
274C2×#117C2318yes—
275C2×#117C2312yes—
276C2×#117C2314yes—
277C2×#117C2314yes—
278C2×#117C2312yes—
279C2×#117C2312yes—
280C2×#117C2318yes—
281C2×#117C2318yes—
282C2×#117C2314yes—
283C2×#117C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2314yes—
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2314yes—
292C22×C22⋊C4C2314yes—
293C22×C22⋊C4C2312yes—
294C22×C22⋊C4C2314yes—
295C22×C22⋊C4C2314yes—
296C22×C42C2314yes—
297C22×C42C2312yes—
298C22×C42C2312yes—
299C22×C42C2311yescharacteristic
300#400C2318yes—
301#400C2318yes—
302#400C2318yes—
303#400C2318yes—
304#399C2318yes—
305#399C2318yes—
306#399C2318yes—
307#399C2318yes—
308#398C2318yes—
309#398C2318yes—
310#398C2314yes—
311#398C2318yes—
312#398C2314yes—
313#398C2312yes—
314#398C2312yes—
315#398C2318yes—
316#398C2318yes—
317#398C2318yes—
318#398C2318yes—
319#398C2318yes—
320#397C2312yes—
321#397C2312yes—
322#397C2318yes—
323#397C2318yes—
324#397C2318yes—
325#397C2318yes—
326#397C2318yes—
327#396C2318yes—
328#396C2318yes—
329#396C2314yes—
330#396C2314yes—
331#395C2318yes—
332#395C2318yes—
333#395C2318yes—
334#394C2314yes—
335#394C2318yes—
336#394C2314yes—
337#394C2312yes—
338#394C2312yes—
339#394C2314yes—
340#394C2314yes—
341#394C2318yes—
342#394C2318yes—
343#393C2318yes—
344#392C2312yes—
345#392C2312yes—
346#391C2312yes—
347#391C2312yes—
348#391C2314yes—
349#391C2312yes—
350#391C2318yes—
351#391C2318yes—
352#391C2318yes—
353#390C2312yes—
354#390C2314yes—
355#390C2314yes—
356#389C2318yes—
357#389C2314yes—
358#389C2314yes—
359#389C2318yes—
360#389C2318yes—
361#389C2318yes—
362#389C2314yes—
363#389C2314yes—
364#389C2318yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2318yes—
371#389C2318yes—
372#389C2314yes—
373#389C2318yes—
374#389C2318yes—
375#389C2318yes—
376#389C2314yes—
377#388C2318yes—
378#388C2318yes—
379#388C2314yes—
380#388C2314yes—
381#388C2314yes—
382#388C2314yes—
383#388C2318yes—
384#388C2318yes—
385#388C2314yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2314yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2314yes—
400#387C2314yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#386C2314yes—
408#386C2314yes—
409#386C2314yes—
410#386C2314yes—
411#386C2318yes—
412#386C2314yes—
413#385C2314yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2314yes—
422#385C2314yes—
423#385C2318yes—
424#384C2312yes—
425#384C2314yes—
426#384C2314yes—
427#384C2312yes—
428#384C2312yes—
429#384C2318yes—
430#382C2314yes—
431#382C2312yes—
432#382C2314yes—
433#382C2312yes—
434#382C2311yescharacteristic
435#382C2312yes—
436#382C2314yes—
437#382C2314yes—
438#382C2312yes—
439#382C2311yescharacteristic
440#382C2311yescharacteristic
441#382C2311yescharacteristic
442#382C2314yes—
443#382C2314yes—
444#382C2312yes—
445#381C2314yes—
446#381C2314yes—
447#381C2318yes—
448#381C2314yes—
449#380C2314yes—
450#380C2312yes—
451#380C2312yes—
452#380C2318yes—
453#380C2312yes—
454#380C2314yes—
455#380C2312yes—
456#380C2312yes—
457#380C2318yes—
458#380C2312yes—
459#380C2312yes—
460#380C2314yes—
461#380C2314yes—
462#380C2312yes—
463#380C2312yes—
464#380C2312yes—
465#380C2314yes—
466#380C2312yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2312yes—
471#379C2314yes—
472#379C2314yes—
473C4×C4⋊C4C2318yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2318yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495#376C2312yes—
496C2×#95C2312yes—
497C2×#95C2312yes—
498C2×#95C2314yes—
499C2×#95C2314yes—
500C2×#95C2314yes—
501C43C2312yes—
502C25C2412yes—
503C2×#41—24no—
504C2×#41—24no—
505C2×#41C2×D418yes—
506C22×Q8—24no—
507C22×Q8—24no—
508C22×Q8C2×D418yes—
509C22×Q8C2412yes—
510C22×Q8C2412yes—
511C22×Q8C2411yescharacteristic
512C22×Q8C2418yes—
513C22×D4—24no—
514C22×D4—44no—
515C22×D4C2411yescharacteristic
516C22×D4C2414yes—
517C22×D4C2412yes—
518C22×D4C2412yes—
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2414yes—
522C23×C4—28no—
523C23×C4—28no—
524C23×C4—28no—
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2412yes—
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2414yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2414yes—
534C23×C4C2412yes—
535C23×C4C2414yes—
536C23×C4C2418yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C4⋊Q8—216no—
543C4⋊Q8—216no—
544C4⋊Q8C2×D4116yescomplemented
545#126—232no—
546#126—232no—
547#126—232no—
548#126—232no—
549#125—232no—
550#125—232no—
551#125—232no—
552#125—216no—
553#125—216no—
554#124—232no—
555#124C2×D4116yescomplemented
556#123—216no—
557#123—232no—
558#123—232no—
559#123—416no—
560#123C2×D4132yes—
561C22⋊Q8—216no—
562C22⋊Q8—216no—
563C22⋊Q8—216no—
564C22⋊Q8—216no—
565C22⋊Q8—28no—
566C22⋊Q8—28no—
567C22⋊Q8—232no—
568C22⋊Q8—232no—
569C22⋊Q8—232no—
570C22⋊Q8—416no—
571C22⋊Q8C2×D4132yescomplemented
572#121—28no—
573#121—28no—
574#121—48no—
575#120—216no—
576C4×Q8—216no—
577C4×Q8—216no—
578C4×Q8—216no—
579C4×Q8—216no—
580C4×Q8—216no—
581C4×Q8—232no—
582C4×Q8—28no—
583C4×Q8—28no—
584C4×Q8—28no—
585C4×Q8—28no—
586C4×Q8—24no—
587C4×Q8—24no—
588C4×D4—216no—
589C4×D4—232no—
590C4×D4—216no—
591C4×D4—216no—
592C4×D4—28no—
593C4×D4—28no—
594C4×D4—232no—
595C4×D4—28no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—24no—
600C4×D4—28no—
601C4×D4—24no—
602C4×D4—24no—
603C4×D4—48no—
604#117—28no—
605#117—28no—
606#117—232no—
607#117—216no—
608#117—24no—
609#117—24no—
610#117—28no—
611#117—28no—
612#117—232no—
613#117—216no—
614#117—232no—
615#117—216no—
616#117—28no—
617#117C2×D418yes—
618C2×C4⋊C4—28no—
619C2×C4⋊C4—216no—
620C2×C4⋊C4—216no—
621C2×C4⋊C4—24no—
622C2×C4⋊C4—28no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—28no—
625C2×C4⋊C4—28no—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2418yes—
669C2×C22⋊C4—216no—
670C2×C22⋊C4—28no—
671C2×C22⋊C4—216no—
672C2×C22⋊C4—48no—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2412yes—
704C2×C22⋊C4C2418yes—
705C2×C42—28no—
706C2×C42—216no—
707C2×C42—28no—
708C2×C42#4118yes—
709C2×C42C2414yes—
710C2×C42C2414yes—
711C2×C42C2418yes—
712C2×C42C2418yes—
713C2×C42C2418yes—
714C2×C42C2414yes—
715C2×C42C2412yes—
716C2×C42C2414yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2414yes—
721C2×C42C2414yes—
722C2×C42C2414yes—
723C2×C42C2414yes—
724C2×C42C2412yes—
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#95C2412yes—
730#95C2412yes—
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2412yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2418yes—
751#95C2418yes—
752#95C2412yes—
753#95C2412yes—
754#95C2412yes—
755#95C2418yes—
756#95C2418yes—
757#95C2412yes—
758#95C2412yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762#95C2418yes—
763C24—24no—
764C24—24no—
765C24—24no—
766C24—24no—
767C24—42no—
768C24—42no—
769C24—42no—
770C24C2512yes—
771C24C2512yes—
772C24C2512yes—
773C24C2511yescharacteristic
774#41—232no—
775C2×Q8—232no—
776C2×Q8—216no—
777C2×Q8—24no—
778C2×Q8—24no—
779C2×Q8—22no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—22no—
783C2×Q8—48no—
784C2×Q8—48no—
785C2×Q8C22×D418yes—
786C2×Q8C22×D418yes—
787C2×Q8C22×D414yes—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—28no—
792C2×D4—24no—
793C2×D4—28no—
794C2×D4—28no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—24no—
798C2×D4—22no—
799C2×D4—22no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—44no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—416no—
806C2×D4C22×D418yes—
807C2×D4C22×D414yes—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—28no—
816C22×C4—28no—
817C22×C4—216no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—28no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—28no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—42no—
836C22×C4—44no—
837C22×C4—42no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—48no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—48no—
846C22×C4—44no—
847C22×C4—432no—
848C22×C4C22×D418yes—
849C22×C4C22×D418yes—
850C22×C4C22×D414yes—
851C22×C4C2×#4114yes—
852C22×C4C2×#4114yes—
853C22×C4C2×#4114yes—
854C22×C42−1+414yes—
855C22×C4C2514yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2514yes—
860C22×C4C2512yes—
861C22×C4C2514yes—
862C22×C4C2514yes—
863C22×C4C2518yes—
864C22×C4C2514yes—
865C22×C4C2514yes—
866C22×C4C2514yes—
867C22×C4C2512yes—
868C22×C4C2514yes—
869C22×C4C2511yescharacteristic
870C22×C4C2511yescharacteristic
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C4⋊C4—24no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—216no—
881C4⋊C4—28no—
882C4⋊C4—216no—
883C4⋊C4—216no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—216no—
887C4⋊C4—216no—
888C4⋊C4—216no—
889C4⋊C4—216no—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—216no—
893C4⋊C4—24no—
894C4⋊C4—22no—
895C4⋊C4—22no—
896C4⋊C4—28no—
897C4⋊C4—28no—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—22no—
903C4⋊C4—22no—
904C4⋊C4—24no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—48no—
914C4⋊C4—48no—
915C4⋊C4—48no—
916C4⋊C4C22×D418yes—
917C4⋊C4C22×D4132yes—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—216no—
922C22⋊C4—28no—
923C22⋊C4—24no—
924C22⋊C4—24no—
925C22⋊C4—216no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—216no—
931C22⋊C4—216no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—24no—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—24no—
940C22⋊C4—48no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4C22×D418yes—
949C22⋊C4C22×D4132yes—
950C42—28no—
951C42—28no—
952C42—28no—
953C42—216no—
954C42—216no—
955C42—216no—
956C42—28no—
957C42—24no—
958C42—24no—
959C42—24no—
960C42—28no—
961C42—28no—
962C42—24no—
963C42—44no—
964C42—44no—
965C42C22×D418yes—
966C42C2×#4114yes—
967C42C2×#4114yes—
968C42C2×#4114yes—
969C42C2×#4114yes—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—24no—
978C23—22no—
979C23—22no—
980C23—24no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—48no—
990C23—48no—
991C23—48no—
992C23—48no—
993C23—84no—
994C23—84no—
995C23—84no—
996C23C23×D414yes—
997C23C23×D412yes—
998C23C22×#4112yes—
999C23C2×2−1+412yes—
1000C23#58514yes—
1001C23C2611yescharacteristic
1002Q8—216no—
1003Q8—216no—
1004Q8—28no—
1005Q8—816no—
1006D4—28no—
1007D4—216no—
1008D4—28no—
1009D4—48no—
1010D4—44no—
1011D4—416no—
1012D4—88no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—216no—
1024C2×C4—216no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—28no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—28no—
1042C2×C4—24no—
1043C2×C4—28no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—28no—
1055C2×C4—44no—
1056C2×C4—44no—
1057C2×C4—416no—
1058C2×C4—48no—
1059C2×C4—48no—
1060C2×C4—48no—
1061C2×C4—48no—
1062C2×C4—48no—
1063C2×C4—88no—
1064C2×C4—84no—
1065C2×C4—84no—
1066C2×C4—816no—
1067C2×C4—88no—
1068C2×C4—84no—
1069C2×C4#547116yes—
1070C2×C4C23×D418yes—
1071C2×C4C23×D414yes—
1072C2×C4C23×D418yes—
1073C2×C4C23×D412yes—
1074C2×C4C23×D412yes—
1075C2×C4C22×#4112yes—
1076C2×C4C22×#4112yes—
1077C2×C4C22×#4112yes—
1078C2×C4C22×#4112yes—
1079C2×C4C22×#4112yes—
1080C2×C4C22×#4112yes—
1081C2×C4C2×2−1+412yes—
1082C2×C4C2×2−1+412yes—
1083C22—24no—
1084C22—22no—
1085C22—22no—
1086C22—24no—
1087C22—24no—
1088C22—28no—
1089C22—24no—
1090C22—24no—
1091C22—24no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—44no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—816no—
1107C22C2×#54714yes—
1108C22C24×D411yescharacteristic
1109C22C23×#4111yescharacteristic
1110C22C22×2−1+411yescharacteristic
1111C22C2×#58512yes—
1112C222−1+612yes—
1113C4—28no—
1114C4—22no—
1115C4—22no—
1116C4—22no—
1117C4—22no—
1118C4—24no—
1119C4—28no—
1120C4—44no—
1121C4—44no—
1122C4—48no—
1123C4—44no—
1124C4—44no—
1125C4—42no—
1126C4—44no—
1127C4—42no—
1128C4—44no—
1129C4—42no—
1130C4—42no—
1131C4C2×#54714yes—
1132C4C2×#54714yes—
1133C2—24no—
1134C2—44no—
1135C2—44no—
1136C2—82no—
1137C2C22×#54711yescharacteristic
1138C2#6281411yescharacteristic
1139C2#6286011yescharacteristic
1140C2#6292812yes—
1141C2#6300212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34935C2
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×#3495C2semidirect
2. #59317C2semidirect
3. #59316C2semidirect
4. #59310C2semidirect
5. #45261C2semidirect
6. #44921C2semidirect
7. #44461C2semidirect
8. #43959C2semidirect
9. #39374C2semidirect
10. #39373C2semidirect
11. #37766C2semidirect
12. #37765C2semidirect
13. #36151C2semidirect
14. #36135C2semidirect
15. #35672C2semidirect
16. #35516C2semidirect
17. #35330C2semidirect
18. #35253C2semidirect
20. C2×#2536C2semidirect
21. #34184C2semidirect
22. #34182C2semidirect
23. D4×#117C2semidirect
24. C4×#536C2semidirect
26. C2×#556C22semidirect
27. C2×#554C22semidirect
29. C2×#552C22semidirect
30. C2×#552C22semidirect
33. C2×#542C22semidirect
34. C2×#541C22semidirect
36. C2×#533C22semidirect
37. C2×#529C22semidirect
46. #2862C22semidirect
47. #2859C22semidirect
48. #2857C22semidirect
49. #2851C22semidirect
51. #2726C22semidirect
53. #2722C22semidirect
54. #2721C22semidirect
55. #2720C22semidirect
56. #2719C22semidirect
57. #2718C22semidirect
59. #2689C22semidirect
60. #2680C22semidirect
62. #2660C22semidirect
63. #2629C22semidirect
64. #2628C22semidirect
65. #2553C22semidirect
66. #2550C22semidirect
67. #2550C22semidirect
83. #2521C22semidirect
84. #2519C22semidirect
85. #2519C22semidirect
86. #2489C22semidirect
87. #2488C22semidirect
88. #2487C22semidirect
90. #2486C22semidirect
91. #2485C22semidirect
92. #2485C22semidirect
96. #2478C22semidirect
97. #2475C22semidirect
98. #2474C22semidirect
99. #2469C22semidirect
100. #2468C22semidirect
101. #2462C22semidirect
103. #2453C22semidirect
104. #2442C22semidirect
105. #2441C22semidirect
106. #2440C22semidirect
107. #2439C22semidirect
109. #2438C22semidirect
112. #2423C22semidirect
113. #2423C22semidirect
114. #2423C22semidirect
115. #2423C22semidirect
116. #2423C22semidirect
117. #2422C22semidirect
118. #2421C22semidirect
119. #2421C22semidirect
120. #2421C22semidirect
121. #2421C22semidirect
122. #2421C22semidirect
123. #2420C22semidirect
132. #2362C22semidirect
133. #2359C22semidirect
137. #2351C22semidirect
138. #2351C22semidirect
139. #2351C22semidirect
140. #2351C22semidirect
141. #2351C22semidirect
142. #2351C22semidirect
143. Q8×C4⋊C4C22semidirect
144. Q8×C4⋊C4C22semidirect
147. #2349C22semidirect
148. #2349C22semidirect
153. #2327C22semidirect
154. #2326C22semidirect
155. #2323C22semidirect
160. #2317C22semidirect
165. C4×C4⋊Q8C22semidirect
166. C4×#124C22semidirect
167. C4×C22⋊Q8C22semidirect
176. #2285C22semidirect
178. C2×#382C22semidirect
197. #536D4semidirect
544. C4⋊Q8C2×D4semidirect
555. #124C2×D4semidirect
571. C22⋊Q8C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34952
#593172
#593162
#593102
#452612
#449212
#444612
#439592
#393742
#393732
#377662
#377652
#361512
#361352
#356722
#355162
#353302
#352532
#349352
C2×#25362
#341842
#341822
D4×#1172
C4×#5362