Finite Group Databasebeta

← #7645466

Subgroups — #7645466

Order 512.

7252 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3493C211yesmaximal, characteristic, complemented
2C22×#551C211yesmaximal, characteristic, complemented
3#41994C218yesmaximal, complemented
4#41993C218yesmaximal, complemented
5#39947C218yesmaximal, complemented
6#39944C218yesmaximal, complemented
7#37546C212yesmaximal, complemented
8#37443C212yesmaximal, complemented
9#36962C211yesmaximal, characteristic, complemented
10#36961C211yesmaximal, characteristic, complemented
11#36716C212yesmaximal, complemented
12#36711C211yesmaximal, characteristic, complemented
13#36710C211yesmaximal, characteristic, complemented
14#36703C212yesmaximal, complemented
15#35357C212yesmaximal, complemented
16#35356C212yesmaximal, complemented
17#35302C212yesmaximal, complemented
18#35145C212yesmaximal, complemented
19#35050C212yesmaximal, complemented
20#34988C212yesmaximal, complemented
21#34986C212yesmaximal, complemented
22#34965C212yesmaximal, complemented
23#34048C211yesmaximal, characteristic, complemented
24#3493—216no—
25C2×#556C2214yescomplemented
26C2×#555C2214yescomplemented
27C2×#553C2214yescomplemented
28C2×#552C2214yescomplemented
29C2×#551—216no—
30C2×#551C2218yes—
31C2×#551C2218yes—
32C2×#544C2211yescharacteristic, complemented
33C2×#538C2212yes—
34C2×#538C2212yes—
35C2×#537C2211yescharacteristic, complemented
36C2×#529C2212yescomplemented
37C2×#529C2212yescomplemented
38C22×#126C2211yescharacteristic
39C22×#126C2211yescharacteristic
40C22×#124C2211yescharacteristic
41C2×#525C2212yes—
42C22×#123C2211yescharacteristic
43C22×#123C2211yescharacteristic
44C22×#123C2211yescharacteristic
45C22×C22⋊Q8C2211yescharacteristic
46C22×C22⋊Q8C2211yescharacteristic
47C22×#120C2211yescharacteristic
48C2×#520C2212yescomplemented
49C22×C4×D4C2211yescharacteristic
50C22×C4×D4C2211yescharacteristic
51C22×#117C2211yescharacteristic
52C22×#117C2211yescharacteristic
53C23×C22⋊C4C2211yescharacteristic
54C23×C22⋊C4C2211yescharacteristic
55#2860C2218yescomplemented
56#2855C2212yescomplemented
57#2854C2212yescomplemented
58#2849C2214yes—
59#2848C2212yes—
60#2847C2212yes—
61#2846C2214yes—
62#2820C2214yescomplemented
63#2819C2214yescomplemented
64#2814C2214yescomplemented
65#2813C2214yescomplemented
66#2723C2218yescomplemented
67#2721C2218yescomplemented
68#2716C2218yescomplemented
69#2714C2218yescomplemented
70#2700C2218yescomplemented
71#2698C2218yescomplemented
72#2696C2218yescomplemented
73#2694C2218yescomplemented
74#2685C2218yes—
75#2681C2218yescomplemented
76#2680C2218yescomplemented
77#2678C2218yes—
78#2674C2218yescomplemented
79#2673C2218yescomplemented
80#2670C2218yes—
81#2669C2218yes—
82#2664C2214yescomplemented
83#2663C2214yescomplemented
84#2662C2218yescomplemented
85#2662C2214yescomplemented
86#2661C2214yescomplemented
87#2630C2218yescomplemented
88#2629C2214yescomplemented
89#2626C2212yes—
90#2626C2214yescomplemented
91#2626C2212yescomplemented
92#2622C2214yes—
93#2620C2214yescomplemented
94#2620C2218yescomplemented
95#2617C2212yes—
96#2617C2214yescomplemented
97#2617C2212yescomplemented
98#2613C2214yes—
99#2609C2218yescomplemented
100#2604C2214yescomplemented
101#2603C2218yescomplemented
102#2603C2214yescomplemented
103#2602C2218yescomplemented
104#2601C2218yescomplemented
105#2601C2218yescomplemented
106#2592C2214yescomplemented
107#2591C2212yescomplemented
108#2583C2212yescomplemented
109#2579C2214yescomplemented
110#2566C2214yescomplemented
111#2561C2212yes—
112#2561C2214yescomplemented
113#2544C2214yescomplemented
114#2540C2214yescomplemented
115#2539C2212yes—
116#2539C2214yescomplemented
117#2534C2214yes—
118#2534C2218yescomplemented
119#2504C2212yescomplemented
120#2502C2212yescomplemented
121#2484C2212yescomplemented
122#2482C2212yes—
123#2482C2212yes—
124#2482C2212yescomplemented
125#2480C2218yescomplemented
126#2477C2218yescomplemented
127#2472C2218yescomplemented
128#2471C2218yescomplemented
129#2466C2218yescomplemented
130#2465C2218yescomplemented
131#2463C2218yescomplemented
132#2459C2218yescomplemented
133#2458C2218yescomplemented
134#2456C2218yescomplemented
135#2456C2218yescomplemented
136#2455C2218yescomplemented
137#2449C2218yescomplemented
138#2443C2218yescomplemented
139#2435C2212yes—
140#2433C2212yes—
141#2424C2218yescomplemented
142#2418C2218yescomplemented
143#2413C2214yescomplemented
144#2411C2214yes—
145#2411C2214yes—
146#2411C2214yescomplemented
147#2409C2214yescomplemented
148#2408C2214yes—
149#2406C2212yescomplemented
150#2404C2212yes—
151#2404C2212yes—
152#2404C2212yescomplemented
153#2392C2218yescomplemented
154#2324C2214yescomplemented
155#2323C2214yescomplemented
156#2322C2214yescomplemented
157#2321C2214yes—
158#2321C2218yescomplemented
159#2314C2218yescomplemented
160#2313C2212yescomplemented
161#2313C2211yescharacteristic, complemented
162#2313C2211yescharacteristic, complemented
163#2312C2212yes—
164#2312C2212yes—
165C4×#127C2214yescomplemented
166C4×#124C2214yescomplemented
167C4×#120C2214yes—
168C4×#120C2214yescomplemented
169#2298C2218yescomplemented
170#2285C2212yescomplemented
171#2280C2212yes—
172C4×#117C2212yescomplemented
173C26C2311yescharacteristic
174C22×#41C2312yes—
175C23×Q8C2311yescharacteristic
176C23×D4C2311yescharacteristic
177C23×D4C2311yescharacteristic
178C23×D4C2311yescharacteristic
179C24×C4C2311yescharacteristic
180C24×C4C2311yescharacteristic
181C24×C4C2311yescharacteristic
182C24×C4C2311yescharacteristic
183C24×C4C2311yescharacteristic
184#556—232no—
185#555—232no—
186#553—232no—
187#552—232no—
188#551—264no—
189#551—264no—
190#544—28no—
191#538—216no—
192#538—216no—
193#537—28no—
194C2×C4⋊Q8C2314yescomplemented
195C2×#127C2314yes—
196#529—216no—
197#529—216no—
198C2×#126—28no—
199C2×#126—28no—
200C2×#126C2314yes—
201C2×#126C2314yes—
202C2×#126C2318yes—
203C2×#126C2314yes—
204C2×#126C2314yes—
205C2×#126C2314yescomplemented
206C2×#126C2314yescomplemented
207C2×#125C2312yescomplemented
208C2×#125C2312yescomplemented
209C2×#125C2314yescomplemented
210C2×#124—28no—
211C2×#124C2314yes—
212C2×#124C2314yes—
213C2×#124C2314yes—
214C2×#124C2314yes—
215C2×#124C2314yes—
216C2×#124C2312yescomplemented
217C2×#124C2312yescomplemented
218#525—216no—
219C2×#123—28no—
220C2×#123—28no—
221C2×#123—28no—
222C2×#123C2314yes—
223C2×#123C2314yes—
224C2×#123C2318yes—
225C2×#123C2318yes—
226C2×#123C2314yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×#123C2314yes—
230C2×#123C2318yes—
231C2×C22⋊Q8—28no—
232C2×C22⋊Q8—28no—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2318yes—
238C2×C22⋊Q8C2318yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2314yescomplemented
241C2×C22⋊Q8C2318yescomplemented
242C2×#121C2312yes—
243C2×#121C2312yes—
244C2×#121C2312yes—
245C2×#121C2312yes—
246C2×#121C2314yes—
247C2×#121C2314yes—
248C2×#121C2314yes—
249C2×#121C2318yes—
250C2×#121C2314yescomplemented
251C2×#120—28no—
252C2×#120C2314yes—
253C2×#120C2318yes—
254C2×#120C2314yes—
255C2×#120C2318yes—
256C2×#120C2314yes—
257C2×#120C2314yes—
258C2×#120C2318yes—
259#520—216no—
260C2×C4×Q8C2312yescomplemented
261C2×C4×Q8C2312yescomplemented
262C2×C4×Q8C2314yescomplemented
263C2×C4×D4—28no—
264C2×C4×D4—28no—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2318yes—
272C2×C4×D4C2318yes—
273C2×C4×D4C2312yescomplemented
274C2×C4×D4C2312yescomplemented
275C2×C4×D4C2314yescomplemented
276C2×C4×D4C2318yescomplemented
277C2×#117—28no—
278C2×#117D4116yescomplemented
279C2×#117C2314yes—
280C2×#117C2314yes—
281C2×#117C2312yes—
282C2×#117C2314yes—
283C2×#117C2314yes—
284C2×#117C2314yes—
285C2×#117C2314yescomplemented
286C2×#117C2314yescomplemented
287C2×#117C2314yescomplemented
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2311yescharacteristic
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2314yescomplemented
297C22×C22⋊C4—28no—
298C22×C22⋊C4—28no—
299C22×C22⋊C4C2311yescharacteristic
300C22×C22⋊C4C2314yes—
301C22×C22⋊C4C2311yescharacteristic
302C22×C22⋊C4C2311yescharacteristic
303C22×C22⋊C4C2311yescharacteristic
304C22×C22⋊C4C2314yes—
305C22×C22⋊C4C2311yescharacteristic
306C22×C22⋊C4C2311yescharacteristic
307C22×C22⋊C4C2311yescharacteristic
308C22×C22⋊C4C2311yescharacteristic
309C22×C22⋊C4C2311yescharacteristic
310C22×C22⋊C4C2318yes—
311C22×C22⋊C4C2311yescharacteristic
312C22×C22⋊C4C2311yescharacteristic
313C22×C22⋊C4C2311yescharacteristic
314C22×C22⋊C4C2311yescharacteristic
315C22×C22⋊C4C2311yescharacteristic
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319#400C2314yescomplemented
320#400C2314yescomplemented
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yescomplemented
326#399C2314yescomplemented
327#398C2318yescomplemented
328#398C2314yescomplemented
329#398C2318yescomplemented
330#398C2318yescomplemented
331#398C2314yescomplemented
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2318yes—
337#397C2318yes—
338#397C2314yescomplemented
339#397C2318yescomplemented
340#397C2314yescomplemented
341#396C2318yes—
342#396C2318yes—
343#396C2318yes—
344#396C2318yes—
345#396C2318yescomplemented
346#396C2318yescomplemented
347#396C2318yescomplemented
348#396C2318yescomplemented
349#395C2318yescomplemented
350#395C2314yescomplemented
351#395C2314yescomplemented
352#394C2318yes—
353#394C2318yes—
354#394C2318yes—
355#394C2318yes—
356#394C2318yes—
357#394C2318yes—
358#394C2318yes—
359#394C2318yes—
360#394C2318yes—
361#394C2318yes—
362#394C2318yescomplemented
363#394C2314yescomplemented
364#394C2318yescomplemented
365#394C2314yescomplemented
366#393C2314yes—
367#393C2314yes—
368#393C2314yes—
369#393C2314yes—
370#393C2314yescomplemented
371#393C2318yescomplemented
372#393C2314yescomplemented
373#392C2314yes—
374#392C2318yes—
375#392C2318yes—
376#392C2318yes—
377#392C2314yes—
378#392C2318yes—
379#392C2314yes—
380#392C2314yes—
381#392C2314yescomplemented
382#392C2314yescomplemented
383#391C2314yescomplemented
384#391C2318yescomplemented
385#391C2314yescomplemented
386#390C2314yes—
387#390C2318yes—
388#390C2314yes—
389#390C2318yes—
390#390C2318yes—
391#390C2318yes—
392#390C2318yes—
393#390C2318yescomplemented
394#390C2314yescomplemented
395#390C2314yescomplemented
396#389C2318yescomplemented
397#389C2314yescomplemented
398#389C2318yescomplemented
399#389C2314yescomplemented
400#389C2318yescomplemented
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yescomplemented
414#388C2318yescomplemented
415#388C2318yescomplemented
416#388C2318yescomplemented
417#388C2318yescomplemented
418#388C2318yescomplemented
419#387C2318yescomplemented
420#387C2318yescomplemented
421#387C2318yescomplemented
422#387C2318yescomplemented
423#387C2318yescomplemented
424#387C2318yescomplemented
425#387C2318yescomplemented
426#387C2318yescomplemented
427#386C2314yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2314yes—
433#386C2314yes—
434#386C2318yes—
435#386C2318yes—
436#386C2318yes—
437#386C2314yes—
438#386C2318yescomplemented
439#386C2318yescomplemented
440#385C2318yes—
441#385C2314yes—
442#385C2318yes—
443#385C2314yes—
444#385C2314yes—
445#385C2318yes—
446#385C2314yes—
447#385C2318yescomplemented
448#385C2318yescomplemented
449#385C2318yescomplemented
450#385C2318yescomplemented
451#384C2314yescomplemented
452#384C2314yescomplemented
453#382C2314yescomplemented
454#382C2314yescomplemented
455#381C2314yes—
456#381C2318yes—
457#381C2312yes—
458#381C2312yes—
459#380C2314yes—
460#380C2312yes—
461#380C2312yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#379C2314yes—
467#379C2318yes—
468#379C2314yes—
469#379C2318yes—
470#379C2314yes—
471#379C2314yes—
472C4×C4⋊C4C2314yescomplemented
473C4×C4⋊C4C2314yescomplemented
474C4×C4⋊C4C2314yescomplemented
475C4×C4⋊C4C2314yescomplemented
476C4×C22⋊C4C2312yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2312yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2318yes—
482C4×C22⋊C4C2318yescomplemented
483#376C2314yescomplemented
484C43C2314yescomplemented
485C25—24no—
486C25—44no—
487C25—44no—
488C25—82no—
489C25C2411yescharacteristic
490C25C2411yescharacteristic
491C25C2411yescharacteristic
492C25C2414yes—
493C25C2411yescharacteristic
494C2×#41—28no—
495C2×#41—48no—
496C22×Q8—24no—
497C22×Q8—82no—
498C22×Q8C2412yes—
499C22×Q8C2412yes—
500C22×Q8C2412yes—
501C22×Q8C2414yes—
502C22×D4—24no—
503C22×D4—24no—
504C22×D4—24no—
505C22×D4—44no—
506C22×D4—44no—
507C22×D4—82no—
508C22×D4C2414yes—
509C22×D4C2414yes—
510C22×D4C2414yes—
511C22×D4C2414yes—
512C22×D4C2414yes—
513C22×D4C2418yes—
514C22×D4C2412yes—
515C22×D4C2412yes—
516C22×D4C2412yes—
517C22×D4C2414yes—
518C22×D4C2418yes—
519C22×D4C2418yes—
520C23×C4—24no—
521C23×C4—24no—
522C23×C4—24no—
523C23×C4—24no—
524C23×C4—44no—
525C23×C4—44no—
526C23×C4—82no—
527C23×C4—82no—
528C23×C4—82no—
529C23×C4C2×D418yes—
530C23×C4C2411yescharacteristic
531C23×C4C2414yes—
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C23×C4C2414yes—
539C23×C4C2414yes—
540C23×C4C2414yes—
541C23×C4C2414yes—
542C23×C4C2414yes—
543C23×C4C2414yes—
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C23×C4C2412yes—
549C23×C4C2412yes—
550C4⋊Q8—216no—
551#127—48no—
552#126—232no—
553#126—216no—
554#126—216no—
555#126—216no—
556#126—216no—
557#126—216no—
558#126—216no—
559#125—216no—
560#125—28no—
561#125—28no—
562#124—216no—
563#124—216no—
564#124—216no—
565#124—216no—
566#124—28no—
567#124—28no—
568#124—48no—
569#123—216no—
570#123—216no—
571#123—216no—
572#123—232no—
573#123—232no—
574#123—216no—
575#123—216no—
576#123—48no—
577#123—88no—
578C22⋊Q8—28no—
579C22⋊Q8—28no—
580C22⋊Q8—28no—
581C22⋊Q8—28no—
582C22⋊Q8—232no—
583C22⋊Q8—216no—
584C22⋊Q8—232no—
585C22⋊Q8—48no—
586C22⋊Q8—88no—
587#121—28no—
588#121—28no—
589#121—28no—
590#121—28no—
591#121—216no—
592#121—216no—
593#121—216no—
594#121—48no—
595#121—88no—
596#120—216no—
597#120—232no—
598#120—48no—
599#120—48no—
600#120—48no—
601#120—416no—
602#120—88no—
603C4×Q8—216no—
604C4×Q8—28no—
605C4×Q8—28no—
606C4×D4—216no—
607C4×D4—216no—
608C4×D4—216no—
609C4×D4—216no—
610C4×D4—216no—
611C4×D4—232no—
612C4×D4—216no—
613C4×D4—216no—
614C4×D4—28no—
615C4×D4—28no—
616C4×D4—88no—
617C4×D4—88no—
618#117—28no—
619#117—216no—
620#117—216no—
621#117—216no—
622#117—216no—
623#117—216no—
624#117—48no—
625#117C2×D4132yes—
626#117C2×D4132yes—
627C2×C4⋊C4—24no—
628C2×C4⋊C4—24no—
629C2×C4⋊C4—24no—
630C2×C4⋊C4—24no—
631C2×C4⋊C4—24no—
632C2×C4⋊C4—24no—
633C2×C4⋊C4—216no—
634C2×C4⋊C4C2×D418yes—
635C2×C4⋊C4C2×D418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C22⋊C4—24no—
667C2×C22⋊C4—24no—
668C2×C22⋊C4—24no—
669C2×C22⋊C4—24no—
670C2×C22⋊C4—24no—
671C2×C22⋊C4—24no—
672C2×C22⋊C4—24no—
673C2×C22⋊C4—216no—
674C2×C22⋊C4—216no—
675C2×C22⋊C4—24no—
676C2×C22⋊C4—24no—
677C2×C22⋊C4—24no—
678C2×C22⋊C4—24no—
679C2×C22⋊C4—24no—
680C2×C22⋊C4—232no—
681C2×C22⋊C4C2×D418yes—
682C2×C22⋊C4C2×D418yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2412yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2412yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2418yes—
715C2×C22⋊C4C2418yes—
716C2×C22⋊C4C2418yes—
717C2×C22⋊C4C2418yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2418yes—
721C2×C22⋊C4C2418yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2418yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C42—24no—
728C2×C42C2×D418yes—
729C2×C42C2×D418yes—
730C2×C42C2414yes—
731C2×C42C2414yes—
732C2×C42C2414yes—
733C2×C42C2414yes—
734C2×C42C2418yes—
735C2×C42C2418yes—
736C2×C42C2414yes—
737C2×C42C2414yes—
738C2×C42C2412yes—
739C2×C42C2412yes—
740C2×C42C2412yes—
741C2×C42C2412yes—
742#95C2418yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2414yes—
754#95C2418yes—
755#95C2414yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762C24—22no—
763C24—24no—
764C24—24no—
765C24—22no—
766C24—22no—
767C24—24no—
768C24—28no—
769C24—24no—
770C24—28no—
771C24—24no—
772C24—42no—
773C24—42no—
774C24—42no—
775C24—42no—
776C24—42no—
777C24—42no—
778C24—42no—
779C24—44no—
780C24—48no—
781C24—48no—
782C24—416no—
783C24—416no—
784C24—88no—
785C24—832no—
786C24C22×D414yes—
787C24C2512yes—
788C24C2512yes—
789C24C2514yes—
790C24C2512yes—
791C24C2512yes—
792C24C2511yescharacteristic
793#41—432no—
794C2×Q8—24no—
795C2×Q8—24no—
796C2×Q8—24no—
797C2×Q8—28no—
798C2×Q8—44no—
799C2×Q8—44no—
800C2×Q8—48no—
801C2×Q8—44no—
802C2×Q8—88no—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—28no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—28no—
810C2×D4—216no—
811C2×D4—28no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—28no—
816C2×D4—44no—
817C2×D4—48no—
818C2×D4—44no—
819C2×D4—48no—
820C2×D4—48no—
821C2×D4—48no—
822C2×D4—48no—
823C2×D4—48no—
824C2×D4—48no—
825C2×D4—44no—
826C2×D4—48no—
827C2×D4—44no—
828C2×D4—48no—
829C2×D4—48no—
830C2×D4—48no—
831C2×D4—48no—
832C2×D4—416no—
833C2×D4—416no—
834C2×D4—88no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—28no—
843C22×C4—24no—
844C22×C4—28no—
845C22×C4—28no—
846C22×C4—28no—
847C22×C4—28no—
848C22×C4—28no—
849C22×C4—28no—
850C22×C4—28no—
851C22×C4—416no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—42no—
855C22×C4—44no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4—42no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—48no—
866C22×C4—48no—
867C22×C4—48no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—416no—
871C22×C4—88no—
872C22×C4—88no—
873C22×C4—88no—
874C22×C4C22×D414yes—
875C22×C4C22×D414yes—
876C22×C4C22×D414yes—
877C22×C4C22×D414yes—
878C22×C4C22×D414yes—
879C22×C4C22×D414yes—
880C22×C4C22×D418yes—
881C22×C4C22×D418yes—
882C22×C4C2518yes—
883C22×C4C2518yes—
884C22×C4C2514yes—
885C22×C4C2514yes—
886C22×C4C2512yes—
887C22×C4C2512yes—
888C22×C4C2512yes—
889C22×C4C2512yes—
890C22×C4C2512yes—
891C22×C4C2514yes—
892C22×C4C2512yes—
893C22×C4C2512yes—
894C22×C4C2512yes—
895C22×C4C2512yes—
896C22×C4C2512yes—
897C22×C4C2511yescharacteristic
898C22×C4C2511yescharacteristic
899C4⋊C4—24no—
900C4⋊C4—28no—
901C4⋊C4—24no—
902C4⋊C4—24no—
903C4⋊C4—28no—
904C4⋊C4—28no—
905C4⋊C4—28no—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—24no—
910C4⋊C4—28no—
911C4⋊C4—28no—
912C4⋊C4—28no—
913C4⋊C4—28no—
914C4⋊C4—24no—
915C4⋊C4—24no—
916C4⋊C4—24no—
917C4⋊C4—24no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—44no—
922C4⋊C4—48no—
923C4⋊C4—44no—
924C4⋊C4—48no—
925C4⋊C4—48no—
926C4⋊C4—48no—
927C4⋊C4C22×D4116yes—
928C4⋊C4C22×D4116yes—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—216no—
936C22⋊C4—24no—
937C22⋊C4—24no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—24no—
947C22⋊C4—24no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—28no—
953C22⋊C4—28no—
954C22⋊C4—28no—
955C22⋊C4—28no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—48no—
960C22⋊C4—48no—
961C22⋊C4—48no—
962C22⋊C4—48no—
963C22⋊C4—48no—
964C22⋊C4—48no—
965C22⋊C4—48no—
966C22⋊C4—48no—
967C22⋊C4—48no—
968C22⋊C4—48no—
969C22⋊C4—48no—
970C22⋊C4—48no—
971C22⋊C4C22×D4116yes—
972C22⋊C4C22×D4116yes—
973C42—28no—
974C42—28no—
975C42—28no—
976C42—28no—
977C42—48no—
978C42—48no—
979C42—44no—
980C42—44no—
981C42C22×D418yes—
982C42C22×D418yes—
983C42C22×D418yes—
984C42C22×D418yes—
985C23—22no—
986C23—22no—
987C23—28no—
988C23—22no—
989C23—24no—
990C23—24no—
991C23—22no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—28no—
996C23—22no—
997C23—24no—
998C23—22no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—28no—
1005C23—24no—
1006C23—28no—
1007C23—24no—
1008C23—24no—
1009C23—44no—
1010C23—44no—
1011C23—416no—
1012C23—416no—
1013C23—44no—
1014C23—416no—
1015C23—44no—
1016C23—44no—
1017C23—44no—
1018C23—44no—
1019C23—416no—
1020C23—44no—
1021C23—44no—
1022C23—44no—
1023C23—88no—
1024C23—88no—
1025C23—88no—
1026C23—816no—
1027C23—816no—
1028C23—864no—
1029C23C23×D414yes—
1030C23C23×D412yes—
1031C23#58514yes—
1032C23#58514yes—
1033C23C2611yescharacteristic
1034Q8—48no—
1035Q8—84no—
1036Q8—84no—
1037Q8—88no—
1038D4—416no—
1039D4—48no—
1040D4—416no—
1041D4—416no—
1042D4—84no—
1043D4—84no—
1044D4—88no—
1045D4—88no—
1046D4—88no—
1047D4—816no—
1048D4—816no—
1049D4—168no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—28no—
1058C2×C4—28no—
1059C2×C4—24no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—28no—
1068C2×C4—28no—
1069C2×C4—28no—
1070C2×C4—28no—
1071C2×C4—28no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—28no—
1077C2×C4—28no—
1078C2×C4—28no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—44no—
1083C2×C4—48no—
1084C2×C4—48no—
1085C2×C4—44no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—416no—
1089C2×C4—416no—
1090C2×C4—44no—
1091C2×C4—44no—
1092C2×C4—44no—
1093C2×C4—44no—
1094C2×C4—44no—
1095C2×C4—88no—
1096C2×C4—88no—
1097C2×C4—88no—
1098C2×C4—88no—
1099C2×C4—88no—
1100C2×C4C23×D414yes—
1101C2×C4C23×D414yes—
1102C2×C4C23×D414yes—
1103C2×C4C23×D414yes—
1104C2×C4C23×D412yes—
1105C2×C4C23×D412yes—
1106C2×C4C23×D414yes—
1107C22—22no—
1108C22—22no—
1109C22—28no—
1110C22—24no—
1111C22—24no—
1112C22—24no—
1113C22—28no—
1114C22—24no—
1115C22—416no—
1116C22—416no—
1117C22—42no—
1118C22—44no—
1119C22—48no—
1120C22—42no—
1121C22—42no—
1122C22—44no—
1123C22—42no—
1124C22—42no—
1125C22—44no—
1126C22—42no—
1127C22—48no—
1128C22—48no—
1129C22—48no—
1130C22—48no—
1131C22—44no—
1132C22—42no—
1133C22—42no—
1134C22—88no—
1135C22—88no—
1136C22—832no—
1137C22#344914yes—
1138C22C24×D411yescharacteristic
1139C22C2×#58512yes—
1140C22C2×#58512yes—
1141C22H(7,𝔽2)12yes—
1142C4—24no—
1143C4—24no—
1144C4—24no—
1145C4—24no—
1146C4—24no—
1147C4—22no—
1148C4—22no—
1149C4—42no—
1150C4—44no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—44no—
1155C4—48no—
1156C4—48no—
1157C4—42no—
1158C4—44no—
1159C2—24no—
1160C2—44no—
1161C2—44no—
1162C2—84no—
1163C2—82no—
1164C2—82no—
1165C2C2×#344911yescharacteristic
1166C2#6281111yescharacteristic
1167C2#6285211yescharacteristic
1168C2#6293314yes—
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. C2×#3493C2semidirect
2. C22×#551C2semidirect
3. #41994C2semidirect
4. #41993C2semidirect
5. #39947C2semidirect
6. #39944C2semidirect
7. #37546C2semidirect
8. #37443C2semidirect
9. #36962C2semidirect
10. #36961C2semidirect
11. #36716C2semidirect
12. #36711C2semidirect
13. #36710C2semidirect
14. #36703C2semidirect
15. #35357C2semidirect
16. #35356C2semidirect
17. #35302C2semidirect
18. #35145C2semidirect
19. #35050C2semidirect
20. #34988C2semidirect
21. #34986C2semidirect
22. #34965C2semidirect
23. #34048C2semidirect
25. C2×#556C22semidirect
26. C2×#555C22semidirect
27. C2×#553C22semidirect
28. C2×#552C22semidirect
32. C2×#544C22semidirect
35. C2×#537C22semidirect
36. C2×#529C22semidirect
37. C2×#529C22semidirect
48. C2×#520C22semidirect
55. #2860C22semidirect
56. #2855C22semidirect
57. #2854C22semidirect
62. #2820C22semidirect
63. #2819C22semidirect
64. #2814C22semidirect
65. #2813C22semidirect
66. #2723C22semidirect
67. #2721C22semidirect
68. #2716C22semidirect
69. #2714C22semidirect
70. #2700C22semidirect
71. #2698C22semidirect
72. #2696C22semidirect
73. #2694C22semidirect
75. #2681C22semidirect
76. #2680C22semidirect
78. #2674C22semidirect
79. #2673C22semidirect
82. #2664C22semidirect
83. #2663C22semidirect
84. #2662C22semidirect
85. #2662C22semidirect
86. #2661C22semidirect
87. #2630C22semidirect
88. #2629C22semidirect
90. #2626C22semidirect
91. #2626C22semidirect
93. #2620C22semidirect
94. #2620C22semidirect
96. #2617C22semidirect
97. #2617C22semidirect
99. #2609C22semidirect
100. #2604C22semidirect
101. #2603C22semidirect
102. #2603C22semidirect
103. #2602C22semidirect
104. #2601C22semidirect
105. #2601C22semidirect
106. #2592C22semidirect
107. #2591C22semidirect
108. #2583C22semidirect
109. #2579C22semidirect
110. #2566C22semidirect
112. #2561C22semidirect
113. #2544C22semidirect
114. #2540C22semidirect
116. #2539C22semidirect
118. #2534C22semidirect
119. #2504C22semidirect
120. #2502C22semidirect
121. #2484C22semidirect
124. #2482C22semidirect
125. #2480C22semidirect
126. #2477C22semidirect
127. #2472C22semidirect
128. #2471C22semidirect
129. #2466C22semidirect
130. #2465C22semidirect
131. #2463C22semidirect
132. #2459C22semidirect
133. #2458C22semidirect
134. #2456C22semidirect
135. #2456C22semidirect
136. #2455C22semidirect
137. #2449C22semidirect
138. #2443C22semidirect
141. #2424C22semidirect
142. #2418C22semidirect
143. #2413C22semidirect
146. #2411C22semidirect
147. #2409C22semidirect
149. #2406C22semidirect
152. #2404C22semidirect
153. #2392C22semidirect
154. #2324C22semidirect
155. #2323C22semidirect
156. #2322C22semidirect
158. #2321C22semidirect
159. #2314C22semidirect
160. #2313C22semidirect
161. #2313C22semidirect
162. #2313C22semidirect
165. C4×#127C22semidirect
166. C4×#124C22semidirect
168. C4×#120C22semidirect
169. #2298C22semidirect
170. #2285C22semidirect
172. C4×#117C22semidirect
194. C2×C4⋊Q8C23semidirect
205. C2×#126C23semidirect
206. C2×#126C23semidirect
207. C2×#125C23semidirect
208. C2×#125C23semidirect
209. C2×#125C23semidirect
216. C2×#124C23semidirect
217. C2×#124C23semidirect
240. C2×C22⋊Q8C23semidirect
241. C2×C22⋊Q8C23semidirect
250. C2×#121C23semidirect
260. C2×C4×Q8C23semidirect
261. C2×C4×Q8C23semidirect
262. C2×C4×Q8C23semidirect
273. C2×C4×D4C23semidirect
274. C2×C4×D4C23semidirect
275. C2×C4×D4C23semidirect
276. C2×C4×D4C23semidirect
278. C2×#117D4semidirect
285. C2×#117C23semidirect
286. C2×#117C23semidirect
287. C2×#117C23semidirect
296. C22×C4⋊C4C23semidirect
319. #400C23semidirect
320. #400C23semidirect
325. #399C23semidirect
326. #399C23semidirect
327. #398C23semidirect
328. #398C23semidirect
329. #398C23semidirect
330. #398C23semidirect
331. #398C23semidirect
338. #397C23semidirect
339. #397C23semidirect
340. #397C23semidirect
345. #396C23semidirect
346. #396C23semidirect
347. #396C23semidirect
348. #396C23semidirect
349. #395C23semidirect
350. #395C23semidirect
351. #395C23semidirect
362. #394C23semidirect
363. #394C23semidirect
364. #394C23semidirect
365. #394C23semidirect
370. #393C23semidirect
371. #393C23semidirect
372. #393C23semidirect
381. #392C23semidirect
382. #392C23semidirect
383. #391C23semidirect
384. #391C23semidirect
385. #391C23semidirect
393. #390C23semidirect
394. #390C23semidirect
395. #390C23semidirect
396. #389C23semidirect
397. #389C23semidirect
398. #389C23semidirect
399. #389C23semidirect
400. #389C23semidirect
413. #388C23semidirect
414. #388C23semidirect
415. #388C23semidirect
416. #388C23semidirect
417. #388C23semidirect
418. #388C23semidirect
419. #387C23semidirect
420. #387C23semidirect
421. #387C23semidirect
422. #387C23semidirect
423. #387C23semidirect
424. #387C23semidirect
425. #387C23semidirect
426. #387C23semidirect
438. #386C23semidirect
439. #386C23semidirect
447. #385C23semidirect
448. #385C23semidirect
449. #385C23semidirect
450. #385C23semidirect
451. #384C23semidirect
452. #384C23semidirect
453. #382C23semidirect
454. #382C23semidirect
472. C4×C4⋊C4C23semidirect
473. C4×C4⋊C4C23semidirect
474. C4×C4⋊C4C23semidirect
475. C4×C4⋊C4C23semidirect
482. C4×C22⋊C4C23semidirect
483. #376C23semidirect
484. C43C23semidirect

Maximal subgroups

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

subgroupindex
C2×#34932
C22×#5512
#419942
#419932
#399472
#399442
#375462
#374432
#369622
#369612
#367162
#367112
#367102
#367032
#353572
#353562
#353022
#351452
#350502
#349882
#349862
#349652
#340482