Finite Group Databasebeta

← #7710065

Subgroups — #7710065

Order 512.

6856 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3563C211yesmaximal, characteristic, complemented
2C22×#529C211yesmaximal, characteristic, complemented
3#59085C214yesmaximal, complemented
4#59059C214yesmaximal, complemented
5#46135C214yesmaximal, complemented
6#45975C214yesmaximal, complemented
7#39594C212yesmaximal, complemented
8#39467C212yesmaximal, complemented
9#37843C214yesmaximal, complemented
10#37774C214yesmaximal, complemented
11#37759C214yesmaximal, complemented
12#37731C218yesmaximal, complemented
13#37546C211yesmaximal, characteristic, complemented
14#37537C211yesmaximal, characteristic, complemented
15#36971C212yesmaximal, complemented
16#36962C212yesmaximal, complemented
17#36625C211yesmaximal, characteristic, complemented
18#36621C211yesmaximal, characteristic, complemented
19#36528C212yesmaximal, complemented
20#36427C214yesmaximal, complemented
21#36423C212yesmaximal, complemented
22#35174C212yesmaximal, complemented
23#34987C212yesmaximal, complemented
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×#541C2214yescomplemented
36C2×#541C2212yescomplemented
37C2×#539C2212yes—
38C2×#533C2211yescharacteristic
39C2×#529—216no—
40C2×#529C2211yescharacteristic
41C2×#529C2214yes—
42C2×#529C2214yes—
43C2×#529C2214yes—
44C2×#529C2214yes—
45C22×#126C2212yes—
46C22×#125C2211yescharacteristic
47C22×#124C2211yescharacteristic
48C22×#123C2212yes—
49C22×C22⋊Q8C2211yescharacteristic
50C22×#121C2211yescharacteristic
51C22×C4×Q8C2211yescharacteristic
52C22×C4×D4C2212yes—
53C22×C4×D4C2211yescharacteristic
54C22×#117C2212yes—
55C23×C42C2211yescharacteristic
56#2857C2212yescomplemented
57#2857C2212yescomplemented
58#2855C2211yescharacteristic
59#2855C2212yes—
60#2855C2212yes—
61#2854C2211yescharacteristic
62#2853C2212yes—
63#2853C2214yes—
64#2852C2214yescomplemented
65#2851C2212yescomplemented
66#2851C2214yescomplemented
67#2850C2212yescomplemented
68#2849C2212yes—
69#2848C2211yescharacteristic
70#2848C2212yes—
71#2848C2212yes—
72#2848C2214yes—
73#2847C2211yescharacteristic
74#2820C2212yescomplemented
75#2820C2214yescomplemented
76#2819C2212yescomplemented
77#2727C2218yescomplemented
78#2725C2218yescomplemented
79#2721C2218yescomplemented
80#2721C2218yescomplemented
81#2720C2218yescomplemented
82#2716C2218yescomplemented
83#2716C2218yescomplemented
84#2714C2218yes—
85#2711C2218yes—
86#2707C2218yescomplemented
87#2705C2218yescomplemented
88#2705C2218yescomplemented
89#2702C2218yescomplemented
90#2696C2218yescomplemented
91#2694C2218yescomplemented
92#2692C2218yescomplemented
93#2662C2214yescomplemented
94#2658C2212yescomplemented
95#2640C2212yescomplemented
96#2632C2214yescomplemented
97#2626C2212yes—
98#2626C2212yes—
99#2626C2212yes—
100#2626C2214yes—
101#2620C2214yescomplemented
102#2617C2212yes—
103#2613C2214yes—
104#2592C2212yescomplemented
105#2561C2214yes—
106#2558C2218yescomplemented
107#2554C2218yescomplemented
108#2545C2214yescomplemented
109#2542C2214yescomplemented
110#2540C2214yes—
111#2540C2212yescomplemented
112#2534C2214yes—
113#2502C2214yes—
114#2492C2214yescomplemented
115#2490C2214yes—
116#2487C2214yes—
117#2484C2214yes—
118#2482C2214yes—
119#2482C2214yes—
120#2479C2218yescomplemented
121#2479C2218yescomplemented
122#2475C2218yescomplemented
123#2475C2218yescomplemented
124#2471C2218yescomplemented
125#2469C2218yescomplemented
126#2467C2218yescomplemented
127#2463C2218yescomplemented
128#2463C2218yescomplemented
129#2462C2218yescomplemented
130#2460C2218yescomplemented
131#2460C2218yescomplemented
132#2458C2218yescomplemented
133#2456C2218yescomplemented
134#2454C2218yescomplemented
135#2454C2218yescomplemented
136#2453C2214yescomplemented
137#2452C2218yescomplemented
138#2452C2218yescomplemented
139#2452C2214yescomplemented
140#2441C2218yescomplemented
141#2435C2212yes—
142#2434C2212yes—
143#2429C2214yescomplemented
144#2429C2214yescomplemented
145#2427C2214yescomplemented
146#2426C2214yes—
147#2417C2214yescomplemented
148#2415C2218yescomplemented
149#2414C2214yes—
150#2413C2214yes—
151#2411C2214yes—
152#2411C2214yes—
153#2409C2212yes—
154#2408C2212yes—
155#2382C2214yescomplemented
156#2370C2214yescomplemented
157#2367C2214yescomplemented
158#2365C2214yescomplemented
159#2362C2214yescomplemented
160#2362C2218yescomplemented
161#2361C2214yescomplemented
162#2354C2218yescomplemented
163#2345C2212yes—
164#2344C2212yes—
165#2344C2214yes—
166#2336C2214yescomplemented
167#2330C2214yescomplemented
168#2321C2214yes—
169#2316C2212yes—
170#2313C2212yes—
171#2309C2214yes—
172C4×C22⋊Q8C2212yescomplemented
173C4×C22⋊Q8C2214yescomplemented
174C4×C22⋊Q8C2214yescomplemented
175C4×#123C2212yes—
176C4×#121C2212yescomplemented
177C4×#120C2212yes—
178C4×#120C2214yes—
179#2296C2212yes—
180#2296C2214yes—
181#2290C2214yescomplemented
182#2285C2211yescharacteristic
183#2283C2211yescharacteristic
184#2280C2212yes—
185C23×Q8C2311yescharacteristic
186C23×D4C2312yes—
187C23×D4C2311yescharacteristic
188C24×C4C2311yescharacteristic
189C24×C4C2311yescharacteristic
190C24×C4C2311yescharacteristic
191C24×C4C2312yes—
192#564—216no—
193#563—216no—
194#557—216no—
195#554—216no—
196#552—216no—
197#552—232no—
198#552—216no—
199#544—216no—
200#544—216no—
201#541—232no—
202#541—216no—
203#539—216no—
204#533—28no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211#529—232no—
212#529—232no—
213#529—232no—
214#529—232no—
215#529—28no—
216C2×#126—216no—
217C2×#126C2312yes—
218C2×#126C2318yes—
219C2×#126C2318yes—
220C2×#126C2314yes—
221C2×#126C2314yes—
222C2×#126C2314yes—
223C2×#126C2314yes—
224C2×#125D4116yescomplemented
225C2×#125C2311yescharacteristic
226C2×#125C2312yes—
227C2×#125C2314yes—
228C2×#125C2314yes—
229C2×#125C2314yes—
230C2×#125C2314yes—
231C2×#125C2314yes—
232C2×#125C2314yes—
233C2×#125C2314yes—
234C2×#125C2314yes—
235C2×#125C2312yes—
236C2×#125C2312yes—
237C2×#125C2312yes—
238C2×#125C2312yes—
239C2×#125C2312yes—
240C2×#124—28no—
241C2×#124C2311yescharacteristic
242C2×#124C2312yes—
243C2×#124C2312yes—
244C2×#124C2312yes—
245C2×#124C2312yes—
246C2×#124C2314yes—
247C2×#123—216no—
248C2×#123C2312yes—
249C2×#123C2314yes—
250C2×#123C2318yes—
251C2×#123C2318yes—
252C2×#123C2314yes—
253C2×#123C2312yes—
254C2×C22⋊Q8—28no—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2311yescharacteristic
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2318yes—
270C2×C22⋊Q8C2314yes—
271C2×#121—28no—
272C2×#121C2311yescharacteristic
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2312yes—
276C2×#121C2314yes—
277C2×#120C2312yes—
278C2×#120C2314yes—
279C2×C4×Q8—28no—
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2314yes—
282C2×C4×Q8C2314yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2314yes—
287C2×C4×Q8C2312yes—
288C2×C4×D4—216no—
289C2×C4×D4—28no—
290C2×C4×D4C2314yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2318yes—
293C2×C4×D4C2318yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2311yescharacteristic
297C2×C4×D4C2318yes—
298C2×C4×D4C2314yes—
299C2×#117—216no—
300C2×#117C2314yes—
301C2×#117C2314yes—
302C2×#117C2318yes—
303C2×#117C2312yes—
304C2×#117C2312yes—
305C2×#117C2318yes—
306C2×#117C2312yes—
307C2×#117C2314yes—
308C2×#117C2312yes—
309C22×C4⋊C4C2312yes—
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2311yescharacteristic
315C22×C4⋊C4C2311yescharacteristic
316C22×C22⋊C4C2312yes—
317C22×C22⋊C4C2312yes—
318C22×C22⋊C4C2312yes—
319C22×C22⋊C4C2312yes—
320C22×C22⋊C4C2312yes—
321C22×C42—28no—
322C22×C42C2312yes—
323C22×C42C2312yes—
324C22×C42C2311yescharacteristic
325C22×C42C2312yes—
326C22×C42C2311yescharacteristic
327C22×C42C2311yescharacteristic
328C22×C42C2312yes—
329C22×C42C2312yes—
330C22×C42C2311yescharacteristic
331#400C2318yes—
332#400C2318yes—
333#399C2314yes—
334#399C2318yes—
335#399C2314yes—
336#399C2314yes—
337#399C2318yes—
338#399C2318yes—
339#399C2318yes—
340#398C2318yes—
341#398C2318yes—
342#398C2318yes—
343#398C2318yes—
344#397C2318yes—
345#397C2314yes—
346#397C2318yes—
347#397C2318yes—
348#396C2318yes—
349#396C2318yes—
350#396C2318yes—
351#396C2318yes—
352#396C2318yes—
353#396C2318yes—
354#396C2318yes—
355#396C2318yes—
356#396C2318yes—
357#395C2318yes—
358#395C2314yes—
359#394C2318yes—
360#394C2318yes—
361#394C2314yes—
362#394C2318yes—
363#394C2318yes—
364#394C2318yes—
365#394C2318yes—
366#394C2318yes—
367#393C2318yes—
368#393C2314yes—
369#393C2314yes—
370#393C2314yes—
371#393C2314yes—
372#393C2318yes—
373#392C2314yes—
374#392C2314yes—
375#392C2318yes—
376#392C2318yes—
377#391C2314yes—
378#391C2312yes—
379#391C2314yes—
380#391C2314yes—
381#391C2314yes—
382#391C2318yes—
383#390C2318yes—
384#390C2318yes—
385#390C2318yes—
386#390C2318yes—
387#390C2318yes—
388#390C2314yes—
389#390C2312yes—
390#390C2318yes—
391#390C2318yes—
392#390C2314yes—
393#389C2318yes—
394#389C2318yes—
395#389C2314yes—
396#389C2318yes—
397#389C2314yes—
398#389C2312yes—
399#389C2312yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2318yes—
405#389C2318yes—
406#389C2318yes—
407#389C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#387C2314yes—
433#387C2314yes—
434#387C2318yes—
435#387C2318yes—
436#387C2314yes—
437#387C2314yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#386C2314yes—
443#386C2318yes—
444#386C2314yes—
445#386C2312yes—
446#386C2314yes—
447#386C2314yes—
448#386C2314yes—
449#386C2312yes—
450#386C2318yes—
451#386C2318yes—
452#385C2314yes—
453#385C2312yes—
454#385C2314yes—
455#385C2318yes—
456#385C2318yes—
457#385C2314yes—
458#385C2314yes—
459#385C2318yes—
460#385C2318yes—
461#385C2314yes—
462#385C2314yes—
463#385C2314yes—
464#385C2312yes—
465#385C2314yes—
466#385C2314yes—
467#385C2318yes—
468#384C2312yes—
469#384C2318yes—
470#383C2312yes—
471#382C2312yes—
472#382C2312yes—
473#381C2312yes—
474#381C2314yes—
475#381C2314yes—
476#381C2312yes—
477#380C2311yescharacteristic
478#380C2312yes—
479#380C2311yescharacteristic
480#380C2314yes—
481#380C2312yes—
482#380C2312yes—
483#380C2312yes—
484#380C2314yes—
485#380C2314yes—
486#380C2318yes—
487#380C2314yes—
488#380C2314yes—
489#380C2318yes—
490#379C2314yes—
491#379C2314yes—
492#379C2312yes—
493#379C2314yes—
494#379C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2318yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2318yes—
501C4×C4⋊C4C2318yes—
502C4×C4⋊C4C2318yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2312yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2318yes—
511#376C2312yes—
512C25C2412yes—
513C25C2411yescharacteristic
514C22×Q8—24no—
515C22×Q8—44no—
516C22×Q8C2412yes—
517C22×Q8C2412yes—
518C22×Q8C2412yes—
519C22×Q8C2414yes—
520C22×Q8C2412yes—
521C22×Q8C2411yescharacteristic
522C22×D4—28no—
523C22×D4—28no—
524C22×D4—24no—
525C22×D4—44no—
526C22×D4—44no—
527C22×D4C2412yes—
528C22×D4C2412yes—
529C22×D4C2418yes—
530C22×D4C2412yes—
531C22×D4C2414yes—
532C22×D4C2411yescharacteristic
533C22×D4C2418yes—
534C23×C4—24no—
535C23×C4—28no—
536C23×C4—24no—
537C23×C4—24no—
538C23×C4—24no—
539C23×C4—48no—
540C23×C4—44no—
541C23×C4—44no—
542C23×C4—42no—
543C23×C4C2411yescharacteristic
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2411yescharacteristic
547C23×C4C2418yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2412yes—
552C23×C4C2411yescharacteristic
553C23×C4C2412yes—
554C23×C4C2411yescharacteristic
555C23×C4C2412yes—
556C23×C4C2411yescharacteristic
557C23×C4C2414yes—
558C23×C4C2412yes—
559C23×C4C2412yes—
560C23×C4C2411yescharacteristic
561C4⋊Q8—216no—
562C4⋊Q8—28no—
563C4⋊Q8—216no—
564C4⋊Q8—24no—
565C4⋊Q8—24no—
566C4⋊Q8—48no—
567#126—232no—
568#126—232no—
569#126—216no—
570#126—216no—
571#126—216no—
572#126—216no—
573#126—28no—
574#125—216no—
575#125—216no—
576#125—216no—
577#125—216no—
578#125—216no—
579#125—216no—
580#125—28no—
581#125—216no—
582#125—216no—
583#125—24no—
584#125—28no—
585#125C2×D4116yes—
586#125C2×D4116yes—
587#125C2×D4116yes—
588#125C2×D4116yes—
589#124—28no—
590#124—28no—
591#124—28no—
592#124—28no—
593#124—24no—
594#124—48no—
595#123—28no—
596#123—216no—
597#123—232no—
598#123—232no—
599#123—216no—
600#123—44no—
601C22⋊Q8—24no—
602C22⋊Q8—28no—
603C22⋊Q8—28no—
604C22⋊Q8—216no—
605C22⋊Q8—216no—
606C22⋊Q8—216no—
607C22⋊Q8—216no—
608C22⋊Q8—28no—
609C22⋊Q8—28no—
610C22⋊Q8—216no—
611C22⋊Q8—216no—
612C22⋊Q8—48no—
613C22⋊Q8—416no—
614C22⋊Q8—44no—
615C22⋊Q8—48no—
616C22⋊Q8—48no—
617#121—24no—
618#121—216no—
619#121—216no—
620#121—44no—
621#121—48no—
622#120—28no—
623#120—48no—
624C4×Q8—216no—
625C4×Q8—216no—
626C4×Q8—216no—
627C4×Q8—28no—
628C4×Q8—28no—
629C4×Q8—24no—
630C4×Q8—28no—
631C4×Q8—28no—
632C4×D4—28no—
633C4×D4—216no—
634C4×D4—216no—
635C4×D4—216no—
636C4×D4—232no—
637C4×D4—232no—
638C4×D4—24no—
639C4×D4—48no—
640C4×D4—416no—
641#117—28no—
642#117—216no—
643#117—232no—
644#117—232no—
645#117—216no—
646#117—28no—
647#117—28no—
648#117—44no—
649#117—48no—
650C2×C4⋊C4—28no—
651C2×C4⋊C4—28no—
652C2×C4⋊C4—28no—
653C2×C4⋊C4C2×D4116yes—
654C2×C4⋊C4C2×D418yes—
655C2×C4⋊C4C2×D4116yes—
656C2×C4⋊C4C2×D418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2418yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2418yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2418yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2418yes—
693C2×C4⋊C4C2418yes—
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2412yes—
702C2×C22⋊C4—28no—
703C2×C22⋊C4—28no—
704C2×C22⋊C4—28no—
705C2×C22⋊C4—28no—
706C2×C22⋊C4—28no—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2412yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2412yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2412yes—
719C2×C22⋊C4C2412yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2412yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2412yes—
726C2×C22⋊C4C2412yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2418yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2418yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2418yes—
734C2×C22⋊C4C2418yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2418yes—
737C2×C22⋊C4C2418yes—
738C2×C22⋊C4C2418yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2418yes—
741C2×C22⋊C4C2418yes—
742C2×C42—24no—
743C2×C42—28no—
744C2×C42—24no—
745C2×C42—24no—
746C2×C42—28no—
747C2×C42—28no—
748C2×C42—28no—
749C2×C42—28no—
750C2×C42C2×D418yes—
751C2×C42C2412yes—
752C2×C42C2412yes—
753C2×C42C2414yes—
754C2×C42C2418yes—
755C2×C42C2414yes—
756C2×C42C2412yes—
757C2×C42C2414yes—
758C2×C42C2412yes—
759C2×C42C2412yes—
760C2×C42C2414yes—
761C2×C42C2414yes—
762C2×C42C2412yes—
763C2×C42C2412yes—
764C2×C42C2414yes—
765C2×C42C2418yes—
766C2×C42C2418yes—
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769C2×C42C2411yescharacteristic
770C2×C42C2411yescharacteristic
771#95C2412yes—
772#95C2412yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2418yes—
777#95C2418yes—
778#95C2418yes—
779#95C2414yes—
780#95C2414yes—
781#95C2418yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2418yes—
786#95C2414yes—
787#95C2414yes—
788#95C2418yes—
789#95C2418yes—
790#95C2414yes—
791#95C2418yes—
792#95C2418yes—
793#95C2418yes—
794#95C2418yes—
795#95C2418yes—
796C24—22no—
797C24—22no—
798C24—24no—
799C24—24no—
800C24—24no—
801C24—42no—
802C24—42no—
803C24—44no—
804C24—44no—
805C242−1+414yes—
806C24C2514yes—
807C24C2512yes—
808C24C2512yes—
809C24C2511yescharacteristic
810C2×Q8—24no—
811C2×Q8—24no—
812C2×Q8—24no—
813C2×Q8—28no—
814C2×Q8—24no—
815C2×Q8—22no—
816C2×Q8—28no—
817C2×Q8—28no—
818C2×Q8—44no—
819C2×Q8—48no—
820C2×Q8—42no—
821C2×Q8—44no—
822C2×Q8—416no—
823C2×D4—24no—
824C2×D4—24no—
825C2×D4—216no—
826C2×D4—24no—
827C2×D4—28no—
828C2×D4—216no—
829C2×D4—24no—
830C2×D4—24no—
831C2×D4—22no—
832C2×D4—28no—
833C2×D4—48no—
834C2×D4—44no—
835C2×D4—432no—
836C2×D4—416no—
837C2×D4—44no—
838C2×D4—48no—
839C2×D4—48no—
840C2×D4—42no—
841C2×D4—44no—
842C2×D4—48no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—24no—
846C22×C4—22no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—24no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—216no—
865C22×C4—24no—
866C22×C4—28no—
867C22×C4—216no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—24no—
871C22×C4—28no—
872C22×C4—42no—
873C22×C4—44no—
874C22×C4—48no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—44no—
883C22×C4—48no—
884C22×C4—416no—
885C22×C4—416no—
886C22×C4—432no—
887C22×C4—416no—
888C22×C4C22×D414yes—
889C22×C4C22×D414yes—
890C22×C4C22×D418yes—
891C22×C4C22×D414yes—
892C22×C4C22×D418yes—
893C22×C4C2514yes—
894C22×C4C2512yes—
895C22×C4C2518yes—
896C22×C4C2514yes—
897C22×C4C2512yes—
898C22×C4C2512yes—
899C22×C4C2512yes—
900C22×C4C2514yes—
901C22×C4C2514yes—
902C22×C4C2514yes—
903C22×C4C2512yes—
904C22×C4C2511yescharacteristic
905C22×C4C2511yescharacteristic
906C22×C4C2514yes—
907C22×C4C2511yescharacteristic
908C22×C4C2511yescharacteristic
909C22×C4C2511yescharacteristic
910C22×C4C2514yes—
911C22×C4C2512yes—
912C22×C4C2511yescharacteristic
913C4⋊C4—216no—
914C4⋊C4—24no—
915C4⋊C4—216no—
916C4⋊C4—28no—
917C4⋊C4—28no—
918C4⋊C4—24no—
919C4⋊C4—28no—
920C4⋊C4—24no—
921C4⋊C4—28no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—22no—
925C4⋊C4—28no—
926C4⋊C4—24no—
927C4⋊C4—24no—
928C4⋊C4—22no—
929C4⋊C4—28no—
930C4⋊C4—28no—
931C4⋊C4—28no—
932C4⋊C4—28no—
933C4⋊C4—24no—
934C4⋊C4—28no—
935C4⋊C4—216no—
936C4⋊C4—28no—
937C4⋊C4—28no—
938C4⋊C4—48no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—42no—
942C4⋊C4—48no—
943C4⋊C4—42no—
944C4⋊C4—44no—
945C4⋊C4—48no—
946C4⋊C4—48no—
947C4⋊C4—44no—
948C4⋊C4—48no—
949C4⋊C4—48no—
950C4⋊C4C22×D418yes—
951C4⋊C4C22×D4116yes—
952C4⋊C4C22×D4116yes—
953C4⋊C4C22×D418yes—
954C4⋊C4C22×D418yes—
955C4⋊C4C22×D4116yes—
956C4⋊C4C22×D4116yes—
957C4⋊C4C22×D418yes—
958C22⋊C4—28no—
959C22⋊C4—24no—
960C22⋊C4—28no—
961C22⋊C4—24no—
962C22⋊C4—28no—
963C22⋊C4—24no—
964C22⋊C4—216no—
965C22⋊C4—28no—
966C22⋊C4—28no—
967C22⋊C4—216no—
968C22⋊C4—216no—
969C22⋊C4—28no—
970C22⋊C4—28no—
971C22⋊C4—24no—
972C22⋊C4—24no—
973C22⋊C4—28no—
974C22⋊C4—24no—
975C22⋊C4—28no—
976C22⋊C4—28no—
977C22⋊C4—24no—
978C22⋊C4—28no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—48no—
982C22⋊C4—48no—
983C22⋊C4—48no—
984C22⋊C4—48no—
985C22⋊C4—48no—
986C22⋊C4—48no—
987C22⋊C4—44no—
988C22⋊C4—48no—
989C22⋊C4—48no—
990C22⋊C4—44no—
991C22⋊C4—48no—
992C22⋊C4—48no—
993C42—24no—
994C42—24no—
995C42—24no—
996C42—24no—
997C42—24no—
998C42—24no—
999C42—216no—
1000C42—28no—
1001C42—28no—
1002C42—24no—
1003C42—28no—
1004C42—28no—
1005C42—28no—
1006C42—44no—
1007C42—48no—
1008C42—48no—
1009C42C22×D414yes—
1010C42C22×D414yes—
1011C42C22×D414yes—
1012C42C22×D414yes—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—28no—
1022C23—22no—
1023C23—24no—
1024C23—22no—
1025C23—24no—
1026C23—24no—
1027C23—28no—
1028C23—24no—
1029C23—28no—
1030C23—22no—
1031C23—24no—
1032C23—48no—
1033C23—44no—
1034C23—44no—
1035C23—48no—
1036C23—48no—
1037C23—48no—
1038C23—48no—
1039C23—88no—
1040C23—88no—
1041C23C23×D412yes—
1042C23C2×2−1+414yes—
1043C23C2×2−1+412yes—
1044C23#58512yes—
1045C23C2611yescharacteristic
1046Q8—48no—
1047Q8—48no—
1048Q8—48no—
1049Q8—88no—
1050Q8—82no—
1051Q8—84no—
1052D4—432no—
1053D4—48no—
1054D4—48no—
1055D4—48no—
1056D4—82no—
1057D4—88no—
1058D4—816no—
1059C2×C4—28no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—24no—
1064C2×C4—21no—
1065C2×C4—24no—
1066C2×C4—28no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—28no—
1073C2×C4—216no—
1074C2×C4—28no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—24no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—22no—
1082C2×C4—24no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—28no—
1091C2×C4—28no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—28no—
1095C2×C4—28no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—28no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—28no—
1102C2×C4—22no—
1103C2×C4—48no—
1104C2×C4—44no—
1105C2×C4—432no—
1106C2×C4—48no—
1107C2×C4—48no—
1108C2×C4—48no—
1109C2×C4—48no—
1110C2×C4—48no—
1111C2×C4—44no—
1112C2×C4—48no—
1113C2×C4—44no—
1114C2×C4—48no—
1115C2×C4—48no—
1116C2×C4—88no—
1117C2×C4C23×D412yes—
1118C2×C4C23×D418yes—
1119C2×C4C23×D412yes—
1120C2×C4C23×D412yes—
1121C2×C4C23×D412yes—
1122C2×C4C23×D412yes—
1123C2×C4C23×D418yes—
1124C2×C4C23×D412yes—
1125C2×C4#58514yes—
1126C2×C4#58514yes—
1127C22—24no—
1128C22—22no—
1129C22—22no—
1130C22—24no—
1131C22—24no—
1132C22—24no—
1133C22—24no—
1134C22—416no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—44no—
1140C22—48no—
1141C22—42no—
1142C22—44no—
1143C22—44no—
1144C22—42no—
1145C22—44no—
1146C22—42no—
1147C22—44no—
1148C22—48no—
1149C22—816no—
1150C22#348914yes—
1151C22C24×D411yescharacteristic
1152C22C22×2−1+411yescharacteristic
1153C22C2×#58511yescharacteristic
1154C22C2×#58512yes—
1155C22C2×#58512yes—
1156C4—22no—
1157C4—22no—
1158C4—22no—
1159C4—28no—
1160C4—24no—
1161C4—28no—
1162C4—22no—
1163C4—22no—
1164C4—44no—
1165C4—48no—
1166C4—42no—
1167C4—42no—
1168C4—44no—
1169C4—44no—
1170C4—42no—
1171C4—42no—
1172C4—44no—
1173C4—42no—
1174C4—44no—
1175C4#348714yes—
1176C2—24no—
1177C2—44no—
1178C2—82no—
1179C2—84no—
1180C2#6274312yes—
1181C2C2×#348711yescharacteristic
1182C2C2×#348911yescharacteristic
1183C2#6281111yescharacteristic
1184C2#6282312yes—
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×#3563C2semidirect
2. C22×#529C2semidirect
3. #59085C2semidirect
4. #59059C2semidirect
5. #46135C2semidirect
6. #45975C2semidirect
7. #39594C2semidirect
8. #39467C2semidirect
9. #37843C2semidirect
10. #37774C2semidirect
11. #37759C2semidirect
12. #37731C2semidirect
13. #37546C2semidirect
14. #37537C2semidirect
15. #36971C2semidirect
16. #36962C2semidirect
17. #36625C2semidirect
18. #36621C2semidirect
19. #36528C2semidirect
20. #36427C2semidirect
21. #36423C2semidirect
22. #35174C2semidirect
23. #34987C2semidirect
24. #34378C2semidirect
26. C2×#564C22semidirect
27. C2×#563C22semidirect
28. C2×#557C22semidirect
32. C2×#552C22semidirect
34. C2×#544C22semidirect
35. C2×#541C22semidirect
36. C2×#541C22semidirect
56. #2857C22semidirect
57. #2857C22semidirect
64. #2852C22semidirect
65. #2851C22semidirect
66. #2851C22semidirect
67. #2850C22semidirect
74. #2820C22semidirect
75. #2820C22semidirect
76. #2819C22semidirect
77. #2727C22semidirect
78. #2725C22semidirect
79. #2721C22semidirect
80. #2721C22semidirect
81. #2720C22semidirect
82. #2716C22semidirect
83. #2716C22semidirect
86. #2707C22semidirect
87. #2705C22semidirect
88. #2705C22semidirect
89. #2702C22semidirect
90. #2696C22semidirect
91. #2694C22semidirect
92. #2692C22semidirect
93. #2662C22semidirect
94. #2658C22semidirect
95. #2640C22semidirect
96. #2632C22semidirect
101. #2620C22semidirect
104. #2592C22semidirect
106. #2558C22semidirect
107. #2554C22semidirect
108. #2545C22semidirect
109. #2542C22semidirect
111. #2540C22semidirect
114. #2492C22semidirect
120. #2479C22semidirect
121. #2479C22semidirect
122. #2475C22semidirect
123. #2475C22semidirect
124. #2471C22semidirect
125. #2469C22semidirect
126. #2467C22semidirect
127. #2463C22semidirect
128. #2463C22semidirect
129. #2462C22semidirect
130. #2460C22semidirect
131. #2460C22semidirect
132. #2458C22semidirect
133. #2456C22semidirect
134. #2454C22semidirect
135. #2454C22semidirect
136. #2453C22semidirect
137. #2452C22semidirect
138. #2452C22semidirect
139. #2452C22semidirect
140. #2441C22semidirect
143. #2429C22semidirect
144. #2429C22semidirect
145. #2427C22semidirect
147. #2417C22semidirect
148. #2415C22semidirect
155. #2382C22semidirect
156. #2370C22semidirect
157. #2367C22semidirect
158. #2365C22semidirect
159. #2362C22semidirect
160. #2362C22semidirect
161. #2361C22semidirect
162. #2354C22semidirect
166. #2336C22semidirect
167. #2330C22semidirect
172. C4×C22⋊Q8C22semidirect
173. C4×C22⋊Q8C22semidirect
174. C4×C22⋊Q8C22semidirect
176. C4×#121C22semidirect
181. #2290C22semidirect
224. C2×#125D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35632
C22×#5292
#590852
#590592
#461352
#459752
#395942
#394672
#378432
#377742
#377592
#377312
#375462
#375372
#369712
#369622
#366252
#366212
#365282
#364272
#364232
#351742
#349872
#343782