Finite Group Databasebeta

← #7645036

Subgroups — #7645036

Order 512.

6974 conjugacy classes of subgroups.

The subgroup lattice has 1141 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3492C211yesmaximal, characteristic, complemented
2C22×#554C211yesmaximal, characteristic, complemented
3#41417C218yesmaximal, complemented
4#40599C218yesmaximal, complemented
5#39610C218yesmaximal, complemented
6#39160C218yesmaximal, complemented
7#37447C212yesmaximal, complemented
8#37442C212yesmaximal, complemented
9#37233C212yesmaximal, complemented
10#37118C212yesmaximal, complemented
11#36959C211yesmaximal, characteristic, complemented
12#36958C211yesmaximal, characteristic, complemented
13#36708C211yesmaximal, characteristic, complemented
14#36707C211yesmaximal, characteristic, complemented
15#35453C212yesmaximal, complemented
16#35357C212yesmaximal, complemented
17#35092C212yesmaximal, complemented
18#35085C212yesmaximal, complemented
19#35077C212yesmaximal, complemented
20#35063C212yesmaximal, complemented
21#34989C212yesmaximal, complemented
22#34957C212yesmaximal, complemented
23C2×#2313C211yesmaximal, characteristic, complemented
24#3492—216no—
25C2×#554—216no—
26C2×#554C2218yes—
27C2×#554C2218yes—
28C2×#554C2214yescomplemented
29C2×#553C2214yescomplemented
30C2×#552C2214yescomplemented
31C2×#547C2214yescomplemented
32C2×#544C2211yescharacteristic
33C2×#539C2212yes—
34C2×#539C2212yes—
35C2×#537C2211yescharacteristic
36C22×C4⋊Q8C2211yescharacteristic
37C22×#125C2211yescharacteristic
38C22×#125C2211yescharacteristic
39C2×#525C2212yes—
40C2×#525C2212yes—
41C2×#525C2212yes—
42C22×C22⋊Q8C2211yescharacteristic
43C22×C22⋊Q8C2211yescharacteristic
44C22×C22⋊Q8C2211yescharacteristic
45C22×C22⋊Q8C2211yescharacteristic
46C22×C22⋊Q8C2211yescharacteristic
47C22×C22⋊Q8C2211yescharacteristic
48C2×#520C2212yes—
49C22×C4×Q8C2211yescharacteristic
50C22×C4×D4C2211yescharacteristic
51C22×C4×D4C2211yescharacteristic
52C22×C4×D4C2211yescharacteristic
53C23×C4⋊C4C2211yescharacteristic
54C23×C4⋊C4C2211yescharacteristic
55#2857C2214yescomplemented
56#2855C2212yes—
57#2854C2212yes—
58#2853C2214yes—
59#2850C2214yescomplemented
60#2849C2214yes—
61#2848C2212yes—
62#2847C2212yes—
63#2817C2214yescomplemented
64#2816C2214yescomplemented
65#2814C2218yescomplemented
66#2723C2218yescomplemented
67#2720C2218yescomplemented
68#2720C2218yescomplemented
69#2719C2218yescomplemented
70#2716C2218yescomplemented
71#2713C2218yescomplemented
72#2713C2218yescomplemented
73#2711C2218yescomplemented
74#2696C2218yescomplemented
75#2692C2218yescomplemented
76#2692C2218yescomplemented
77#2690C2218yescomplemented
78#2677C2218yescomplemented
79#2677C2218yescomplemented
80#2676C2218yescomplemented
81#2674C2218yescomplemented
82#2663C2218yescomplemented
83#2659C2214yescomplemented
84#2659C2214yescomplemented
85#2639C2214yescomplemented
86#2639C2214yescomplemented
87#2638C2214yes—
88#2638C2218yescomplemented
89#2635C2214yes—
90#2630C2218yes—
91#2627C2212yes—
92#2627C2212yes—
93#2625C2214yescomplemented
94#2623C2214yes—
95#2618C2212yes—
96#2618C2212yes—
97#2616C2214yescomplemented
98#2614C2214yes—
99#2602C2218yes—
100#2600C2218yes—
101#2591C2212yes—
102#2583C2212yes—
103#2579C2214yes—
104#2564C2214yes—
105#2564C2214yes—
106#2564C2218yescomplemented
107#2564C2218yescomplemented
108#2561C2212yes—
109#2543C2214yes—
110#2543C2214yes—
111#2539C2212yes—
112#2534C2214yes—
113#2503C2212yes—
114#2501C2212yes—
115#2499C2214yescomplemented
116#2486C2214yes—
117#2485C2214yes—
118#2484C2212yes—
119#2484C2212yes—
120#2484C2212yes—
121#2482C2212yes—
122#2481C2218yescomplemented
123#2477C2218yescomplemented
124#2475C2218yescomplemented
125#2473C2218yescomplemented
126#2473C2218yescomplemented
127#2469C2218yescomplemented
128#2465C2218yescomplemented
129#2465C2218yescomplemented
130#2463C2218yescomplemented
131#2462C2218yescomplemented
132#2462C2218yescomplemented
133#2460C2218yescomplemented
134#2458C2218yescomplemented
135#2449C2218yescomplemented
136#2449C2218yescomplemented
137#2443C2218yescomplemented
138#2436C2212yes—
139#2434C2212yes—
140#2432C2214yescomplemented
141#2417C2214yes—
142#2417C2218yescomplemented
143#2416C2214yes—
144#2412C2214yes—
145#2412C2214yes—
146#2412C2214yes—
147#2410C2214yes—
148#2409C2214yes—
149#2407C2214yes—
150#2406C2212yes—
151#2406C2212yes—
152#2406C2212yes—
153#2404C2212yes—
154#2395C2214yes—
155#2388C2214yes—
156#2325C2218yes—
157#2325C2218yes—
158#2322C2214yes—
159#2322C2214yes—
160#2313C2212yes—
161#2313C2212yes—
162#2313C2211yescharacteristic
163#2313C2211yescharacteristic
164#2313C2212yes—
165#2313C2218yescomplemented
166C4×#123C2214yes—
167C4×#121C2218yes—
168C4×#120C2214yes—
169C2×#387C2218yescomplemented
170C2×#381C2212yes—
171C2×#380C2212yes—
172C2×C4×C22⋊C4C2212yes—
173C22×#41C2312yes—
174C22×#41C2312yes—
175C22×#41C2312yes—
176C23×Q8C2311yescharacteristic
177C23×Q8C2311yescharacteristic
178C23×Q8C2311yescharacteristic
179C23×D4C2311yescharacteristic
180C24×C4C2311yescharacteristic
181C24×C4C2311yescharacteristic
182C24×C4C2311yescharacteristic
183C24×C4C2311yescharacteristic
184C24×C4C2311yescharacteristic
185C24×C4C2311yescharacteristic
186#554—264no—
187#554—264no—
188#554—232no—
189#553—232no—
190#552—232no—
191#547—232no—
192#544—28no—
193#539—216no—
194#539—216no—
195#537—28no—
196C2×C4⋊Q8—28no—
197C2×C4⋊Q8C2318yes—
198C2×C4⋊Q8C2314yes—
199C2×C4⋊Q8C2314yes—
200C2×#126C2314yes—
201C2×#126C2314yes—
202C2×#125—28no—
203C2×#125—28no—
204C2×#125C2318yes—
205C2×#125C2318yes—
206C2×#125C2314yes—
207C2×#125C2314yes—
208C2×#125C2314yes—
209C2×#124C2314yes—
210#525—216no—
211#525—216no—
212#525—216no—
213C2×#123C2314yes—
214C2×#123C2314yes—
215C2×#123C2314yes—
216C2×#123C2314yes—
217C2×#123C2314yes—
218C2×#123C2314yes—
219C2×#123C2314yes—
220C2×#123C2314yes—
221C2×C22⋊Q8—28no—
222C2×C22⋊Q8—28no—
223C2×C22⋊Q8—28no—
224C2×C22⋊Q8—28no—
225C2×C22⋊Q8—28no—
226C2×C22⋊Q8—28no—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2318yes—
240C2×C22⋊Q8C2318yes—
241C2×C22⋊Q8C2318yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2318yes—
247C2×#121C2312yes—
248C2×#121C2318yes—
249C2×#121C2312yes—
250C2×#121C2312yes—
251C2×#121C2312yes—
252C2×#121C2312yes—
253C2×#121C2312yes—
254C2×#121C2314yes—
255C2×#121C2314yes—
256C2×#120C2314yes—
257C2×#120C2314yes—
258#520—216no—
259C2×C4×Q8—28no—
260C2×C4×Q8C2318yes—
261C2×C4×Q8C2314yes—
262C2×C4×D4—28no—
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×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2318yes—
279C2×#117C2312yes—
280C2×#117C2312yes—
281C2×#117C2312yes—
282C2×#117C2314yes—
283C22×C4⋊C4—28no—
284C22×C4⋊C4D4116yescomplemented
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2311yescharacteristic
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2318yes—
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2314yes—
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2311yescharacteristic
299C22×C4⋊C4C2314yes—
300C22×C4⋊C4C2311yescharacteristic
301C22×C4⋊C4C2311yescharacteristic
302C22×C4⋊C4C2311yescharacteristic
303C22×C4⋊C4C2311yescharacteristic
304C22×C4⋊C4C2314yes—
305C22×C4⋊C4C2314yes—
306C22×C22⋊C4C2311yescharacteristic
307C22×C22⋊C4C2311yescharacteristic
308C22×C22⋊C4C2311yescharacteristic
309C22×C22⋊C4C2311yescharacteristic
310C22×C22⋊C4C2311yescharacteristic
311C22×C22⋊C4C2311yescharacteristic
312C22×C22⋊C4C2314yes—
313C22×C42C2311yescharacteristic
314C22×C42C2311yescharacteristic
315C22×C42C2311yescharacteristic
316C22×C42C2314yes—
317#400C2318yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2318yes—
323#400C2314yes—
324#400C2314yes—
325#399C2318yes—
326#399C2314yes—
327#399C2314yes—
328#399C2318yes—
329#398C2314yes—
330#398C2314yes—
331#398C2318yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2318yes—
336#398C2318yes—
337#398C2318yes—
338#398C2314yes—
339#398C2318yes—
340#397C2314yes—
341#397C2318yes—
342#397C2318yes—
343#397C2318yes—
344#397C2318yes—
345#397C2314yes—
346#397C2318yes—
347#396C2318yes—
348#396C2318yes—
349#396C2318yes—
350#396C2318yes—
351#395C2318yes—
352#395C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2314yes—
356#395C2318yes—
357#395C2318yes—
358#395C2314yes—
359#395C2314yes—
360#395C2318yes—
361#394C2318yes—
362#394C2318yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2318yes—
367#394C2318yes—
368#394C2314yes—
369#394C2314yes—
370#394C2318yes—
371#394C2314yes—
372#393C2318yes—
373#393C2314yes—
374#393C2314yes—
375#393C2318yes—
376#393C2318yes—
377#393C2318yes—
378#392C2318yes—
379#392C2314yes—
380#392C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2314yes—
384#391C2314yes—
385#391C2318yes—
386#390C2314yes—
387#390C2314yes—
388#390C2318yes—
389#389C2318yes—
390#389C2318yes—
391#389C2318yes—
392#389C2314yes—
393#389C2314yes—
394#389C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#386C2318yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2314yes—
428#386C2314yes—
429#386C2314yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2314yes—
435#386C2318yes—
436#386C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2314yes—
444#385C2314yes—
445#385C2318yes—
446#385C2314yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2314yes—
451#384C2314yes—
452#382C2314yes—
453#381C2314yes—
454#381C2314yes—
455#381C2314yes—
456#381C2312yes—
457#381C2312yes—
458#381C2314yes—
459#381C2314yes—
460#381C2314yes—
461#380C2318yes—
462#380C2318yes—
463#380C2318yes—
464#380C2314yes—
465#380C2312yes—
466#380C2312yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2318yes—
472#379C2314yes—
473C4×C4⋊C4C2318yes—
474C4×C22⋊C4C2312yes—
475C4×C22⋊C4C2314yes—
476C4×C22⋊C4C2312yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2318yes—
480C4×C22⋊C4C2318yes—
481C2×#95C2314yes—
482C2×#95C2314yes—
483C2×#95C2314yes—
484C2×#95C2314yes—
485C25C2411yescharacteristic
486C25C2411yescharacteristic
487C2×#41—28no—
488C2×#41—28no—
489C2×#41—28no—
490C2×#41—48no—
491C2×#41—84no—
492C2×#41—84no—
493C22×Q8—24no—
494C22×Q8—24no—
495C22×Q8—24no—
496C22×Q8—44no—
497C22×Q8—82no—
498C22×Q8—82no—
499C22×Q8C2414yes—
500C22×Q8C2412yes—
501C22×Q8C2414yes—
502C22×Q8C2412yes—
503C22×Q8C2414yes—
504C22×Q8C2412yes—
505C22×D4—24no—
506C22×D4—28no—
507C22×D4C2412yes—
508C22×D4C2414yes—
509C22×D4C2414yes—
510C22×D4C2412yes—
511C22×D4C2412yes—
512C22×D4C2418yes—
513C22×D4C2414yes—
514C22×D4C2412yes—
515C22×D4C2412yes—
516C23×C4—24no—
517C23×C4—24no—
518C23×C4—24no—
519C23×C4—44no—
520C23×C4—44no—
521C23×C4—82no—
522C23×C4—82no—
523C23×C4—82no—
524C23×C4—82no—
525C23×C4C2×D418yes—
526C23×C4C2×D418yes—
527C23×C4C2×D418yes—
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2418yes—
538C23×C4C2414yes—
539C23×C4C2414yes—
540C23×C4C2414yes—
541C23×C4C2414yes—
542C23×C4C2414yes—
543C23×C4C2414yes—
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C23×C4C2412yes—
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2412yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C4⋊Q8—232no—
555C4⋊Q8—216no—
556C4⋊Q8—84no—
557#126—216no—
558#126—216no—
559#125—232no—
560#125—232no—
561#125—216no—
562#125—216no—
563#125—216no—
564#124—84no—
565#123—216no—
566#123—216no—
567#123—216no—
568#123—216no—
569#123—216no—
570#123—48no—
571#123—48no—
572#123—48no—
573C22⋊Q8—216no—
574C22⋊Q8—216no—
575C22⋊Q8—216no—
576C22⋊Q8—216no—
577C22⋊Q8—216no—
578C22⋊Q8—216no—
579C22⋊Q8—28no—
580C22⋊Q8—28no—
581C22⋊Q8—28no—
582C22⋊Q8—28no—
583C22⋊Q8—28no—
584C22⋊Q8—28no—
585C22⋊Q8—232no—
586C22⋊Q8—232no—
587C22⋊Q8—232no—
588C22⋊Q8—216no—
589C22⋊Q8—216no—
590C22⋊Q8—216no—
591C22⋊Q8—84no—
592C22⋊Q8—88no—
593#121—232no—
594#121—28no—
595#121—28no—
596#121—28no—
597#121—28no—
598#121—28no—
599#121—28no—
600#121—216no—
601#121—84no—
602#120—216no—
603#120—48no—
604C4×Q8—232no—
605C4×Q8—216no—
606C4×D4—216no—
607C4×D4—216no—
608C4×D4—216no—
609C4×D4—216no—
610C4×D4—216no—
611C4×D4—216no—
612C4×D4—216no—
613C4×D4—216no—
614C4×D4—216no—
615C4×D4—216no—
616C4×D4—216no—
617C4×D4—216no—
618C4×D4—216no—
619C4×D4—88no—
620#117—28no—
621#117—28no—
622#117—28no—
623#117—216no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—24no—
626C2×C4⋊C4—24no—
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—24no—
634C2×C4⋊C4—24no—
635C2×C4⋊C4—24no—
636C2×C4⋊C4—232no—
637C2×C4⋊C4—216no—
638C2×C4⋊C4—84no—
639C2×C4⋊C4C2×D418yes—
640C2×C4⋊C4C2×D418yes—
641C2×C4⋊C4C2×D418yes—
642C2×C4⋊C4C2×D418yes—
643C2×C4⋊C4C2×D4132yes—
644C2×C4⋊C4C2×D4132yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2418yes—
677C2×C4⋊C4C2418yes—
678C2×C4⋊C4C2418yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C22⋊C4—24no—
684C2×C22⋊C4—24no—
685C2×C22⋊C4—24no—
686C2×C22⋊C4—24no—
687C2×C22⋊C4—24no—
688C2×C22⋊C4—24no—
689C2×C22⋊C4—48no—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2412yes—
692C2×C22⋊C4C2412yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2412yes—
697C2×C22⋊C4C2412yes—
698C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
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×C42—24no—
722C2×C42—24no—
723C2×C42—24no—
724C2×C42—84no—
725C2×C42C2414yes—
726C2×C42C2414yes—
727C2×C42C2414yes—
728C2×C42C2414yes—
729C2×C42C2414yes—
730C2×C42C2414yes—
731C2×C42C2418yes—
732C2×C42C2414yes—
733C2×C42C2414yes—
734#95C2418yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2418yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745#95C2414yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760C24—22no—
761C24—24no—
762C24—24no—
763C24—24no—
764C24—24no—
765C24—42no—
766C24—42no—
767C24C22×D414yes—
768C24C2514yes—
769C24C2511yescharacteristic
770C24C2512yes—
771C24C2511yescharacteristic
772C24C2511yescharacteristic
773#41—432no—
774#41—816no—
775#41—816no—
776C2×Q8—28no—
777C2×Q8—24no—
778C2×Q8—28no—
779C2×Q8—28no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—48no—
783C2×Q8—44no—
784C2×Q8—48no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—416no—
790C2×Q8—88no—
791C2×Q8—88no—
792C2×D4—232no—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—216no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—216no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—44no—
809C2×D4—48no—
810C2×D4—48no—
811C2×D4—48no—
812C2×D4—44no—
813C2×D4—44no—
814C2×D42−1+418yes—
815C22×C4—22no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—216no—
829C22×C4—28no—
830C22×C4—28no—
831C22×C4—28no—
832C22×C4—28no—
833C22×C4—28no—
834C22×C4—28no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—416no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—48no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—42no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—48no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—48no—
859C22×C4—416no—
860C22×C4—88no—
861C22×C4—88no—
862C22×C4—88no—
863C22×C4—88no—
864C22×C4C22×D414yes—
865C22×C4C22×D414yes—
866C22×C4C22×D414yes—
867C22×C4C22×D414yes—
868C22×C4C22×D414yes—
869C22×C4C22×D414yes—
870C22×C4C22×D418yes—
871C22×C4C22×D418yes—
872C22×C4C22×D418yes—
873C22×C4C22×D418yes—
874C22×C4C22×D418yes—
875C22×C4C22×D418yes—
876C22×C4C2518yes—
877C22×C4C2518yes—
878C22×C4C2514yes—
879C22×C4C2512yes—
880C22×C4C2512yes—
881C22×C4C2512yes—
882C22×C4C2514yes—
883C22×C4C2514yes—
884C22×C4C2512yes—
885C22×C4C2512yes—
886C22×C4C2512yes—
887C22×C4C2512yes—
888C22×C4C2512yes—
889C22×C4C2512yes—
890C22×C4C2512yes—
891C22×C4C2512yes—
892C22×C4C2512yes—
893C22×C4C2512yes—
894C4⋊C4—28no—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—24no—
898C4⋊C4—28no—
899C4⋊C4—28no—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—28no—
904C4⋊C4—28no—
905C4⋊C4—28no—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—24no—
910C4⋊C4—24no—
911C4⋊C4—24no—
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—28no—
915C4⋊C4—28no—
916C4⋊C4—28no—
917C4⋊C4—28no—
918C4⋊C4—216no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—48no—
922C4⋊C4—48no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—48no—
926C4⋊C4—48no—
927C4⋊C4—48no—
928C4⋊C4C22×D4116yes—
929C4⋊C4C22×D4116yes—
930C4⋊C4C22×D4116yes—
931C4⋊C4C22×D4116yes—
932C22⋊C4—24no—
933C22⋊C4—24no—
934C22⋊C4—24no—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—24no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—216no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—28no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—28no—
953C22⋊C4—216no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—48no—
960C22⋊C4—48no—
961C22⋊C4—48no—
962C22⋊C4—48no—
963C42—28no—
964C42—28no—
965C42—28no—
966C42—28no—
967C42—28no—
968C42—28no—
969C42—48no—
970C42—44no—
971C42—44no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—28no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—24no—
982C23—24no—
983C23—22no—
984C23—28no—
985C23—28no—
986C23—24no—
987C23—28no—
988C23—24no—
989C23—24no—
990C23—28no—
991C23—44no—
992C23—416no—
993C23—416no—
994C23—44no—
995C23—44no—
996C23C23×D412yes—
997C23C23×D412yes—
998C23C23×D412yes—
999C23C2×2−1+414yes—
1000C23C2×2−1+414yes—
1001C23#58514yes—
1002C23C2611yescharacteristic
1003Q8—416no—
1004Q8—48no—
1005Q8—88no—
1006Q8—88no—
1007Q8—84no—
1008Q8—84no—
1009D4—216no—
1010D4—216no—
1011D4—48no—
1012D4—416no—
1013D4—416no—
1014D4—416no—
1015D4—84no—
1016D4—84no—
1017D4—816no—
1018C2×C4—28no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—28no—
1028C2×C4—28no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—28no—
1039C2×C4—28no—
1040C2×C4—28no—
1041C2×C4—28no—
1042C2×C4—28no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—28no—
1049C2×C4—28no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—28no—
1054C2×C4—22no—
1055C2×C4—48no—
1056C2×C4—48no—
1057C2×C4—44no—
1058C2×C4—44no—
1059C2×C4—48no—
1060C2×C4—48no—
1061C2×C4—44no—
1062C2×C4—44no—
1063C2×C4—48no—
1064C2×C4—48no—
1065C2×C4—416no—
1066C2×C4—416no—
1067C2×C4—44no—
1068C2×C4—44no—
1069C2×C4—44no—
1070C2×C4—44no—
1071C2×C4—44no—
1072C2×C4—44no—
1073C2×C4—88no—
1074C2×C4—88no—
1075C2×C4—88no—
1076C2×C4—88no—
1077C2×C4—816no—
1078C2×C4C23×D414yes—
1079C2×C4C23×D414yes—
1080C2×C4C23×D414yes—
1081C2×C4C23×D414yes—
1082C2×C4C23×D414yes—
1083C2×C4C23×D414yes—
1084C2×C4C2×2−1+414yes—
1085C22—22no—
1086C22—22no—
1087C22—22no—
1088C22—22no—
1089C22—28no—
1090C22—28no—
1091C22—22no—
1092C22—24no—
1093C22—22no—
1094C22—22no—
1095C22—28no—
1096C22—416no—
1097C22—416no—
1098C22—42no—
1099C22—42no—
1100C22—44no—
1101C22—44no—
1102C22—44no—
1103C22—44no—
1104C22—44no—
1105C22—48no—
1106C22—48no—
1107C22#344914yes—
1108C22#348614yes—
1109C22C24×D411yescharacteristic
1110C22C22×2−1+412yes—
1111C22C2×#58512yes—
1112C22H(7,𝔽2)12yes—
1113C4—24no—
1114C4—24no—
1115C4—24no—
1116C4—24no—
1117C4—24no—
1118C4—24no—
1119C4—24no—
1120C4—44no—
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—44no—
1125C4—42no—
1126C4—44no—
1127C4—42no—
1128C4—42no—
1129C4—48no—
1130C4—48no—
1131C2—24no—
1132C2—24no—
1133C2—42no—
1134C2—44no—
1135C2—84no—
1136C2C2×#344911yescharacteristic
1137C2C2×#348611yescharacteristic
1138C2#6284211yescharacteristic
1139C2#6294814yes—
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×#3492C2semidirect
2. C22×#554C2semidirect
3. #41417C2semidirect
4. #40599C2semidirect
5. #39610C2semidirect
6. #39160C2semidirect
7. #37447C2semidirect
8. #37442C2semidirect
9. #37233C2semidirect
10. #37118C2semidirect
11. #36959C2semidirect
12. #36958C2semidirect
13. #36708C2semidirect
14. #36707C2semidirect
15. #35453C2semidirect
16. #35357C2semidirect
17. #35092C2semidirect
18. #35085C2semidirect
19. #35077C2semidirect
20. #35063C2semidirect
21. #34989C2semidirect
22. #34957C2semidirect
23. C2×#2313C2semidirect
28. C2×#554C22semidirect
29. C2×#553C22semidirect
30. C2×#552C22semidirect
31. C2×#547C22semidirect
55. #2857C22semidirect
59. #2850C22semidirect
63. #2817C22semidirect
64. #2816C22semidirect
65. #2814C22semidirect
66. #2723C22semidirect
67. #2720C22semidirect
68. #2720C22semidirect
69. #2719C22semidirect
70. #2716C22semidirect
71. #2713C22semidirect
72. #2713C22semidirect
73. #2711C22semidirect
74. #2696C22semidirect
75. #2692C22semidirect
76. #2692C22semidirect
77. #2690C22semidirect
78. #2677C22semidirect
79. #2677C22semidirect
80. #2676C22semidirect
81. #2674C22semidirect
82. #2663C22semidirect
83. #2659C22semidirect
84. #2659C22semidirect
85. #2639C22semidirect
86. #2639C22semidirect
88. #2638C22semidirect
93. #2625C22semidirect
97. #2616C22semidirect
106. #2564C22semidirect
107. #2564C22semidirect
115. #2499C22semidirect
122. #2481C22semidirect
123. #2477C22semidirect
124. #2475C22semidirect
125. #2473C22semidirect
126. #2473C22semidirect
127. #2469C22semidirect
128. #2465C22semidirect
129. #2465C22semidirect
130. #2463C22semidirect
131. #2462C22semidirect
132. #2462C22semidirect
133. #2460C22semidirect
134. #2458C22semidirect
135. #2449C22semidirect
136. #2449C22semidirect
137. #2443C22semidirect
140. #2432C22semidirect
142. #2417C22semidirect
165. #2313C22semidirect
169. C2×#387C22semidirect
284. C22×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34922
C22×#5542
#414172
#405992
#396102
#391602
#374472
#374422
#372332
#371182
#369592
#369582
#367082
#367072
#354532
#353572
#350922
#350852
#350772
#350632
#349892
#349572
C2×#23132