Finite Group Databasebeta

← #7710066

Subgroups — #7710066

Order 512.

6390 conjugacy classes of subgroups.

The subgroup lattice has 1113 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3563C212yesmaximal, complemented
2#59667C212yesmaximal, complemented
3#59656C214yesmaximal, complemented
4#59444C212yesmaximal, complemented
5#46150C214yesmaximal, complemented
6C4⋊#564C212yesmaximal, complemented
7#45998C212yesmaximal, complemented
8#39614C212yesmaximal, complemented
9#39487C212yesmaximal, complemented
10#39447C214yesmaximal, complemented
11#39427C214yesmaximal, complemented
12#39399C214yesmaximal, complemented
13#39385C212yesmaximal, complemented
14#39369C212yesmaximal, complemented
15#37867C214yesmaximal, complemented
16#37555C212yesmaximal, complemented
17#36742C214yesmaximal, complemented
18#36645C211yesmaximal, characteristic, complemented
19#36631C211yesmaximal, characteristic
20#36561C212yesmaximal, complemented
21#36186C214yesmaximal, complemented
22#36186C212yesmaximal, complemented
23#35167C212yesmaximal, complemented
24#35006C212yesmaximal
25C2×C4×#125C211yesmaximal, characteristic, complemented
26#3563—232no—
27C2×#564C2214yes—
28C2×#563C2214yes—
29C2×#557C2214yes—
30C2×#554C2214yes—
31C2×#552C2214yes—
32C2×#552C2214yes—
33C2×#552C2218yes—
34C2×#544C2214yes—
35C2×#544C2214yes—
36C2×#541C2214yes—
37C2×#541C2218yes—
38C2×#539C2214yes—
39C2×#533C2212yes—
40C2×#529C2212yes—
41C22×#125C2211yescharacteristic
42#2868C2211yescharacteristic
43#2868C2211yescharacteristic
44#2862C2212yes—
45#2861C2212yes—
46#2860C2212yes—
47#2860C2212yes—
48#2859C2211yescharacteristic
49#2859C2212yes—
50#2859C2212yes—
51#2858C2211yescharacteristic
52#2857C2211yescharacteristic
53#2857C2212yes—
54#2857C2212yes—
55#2857C2212yes—
56#2857C2212yes—
57#2857C2214yes—
58#2856C2211yescharacteristic
59#2854C2212yes—
60#2854C2212yes—
61#2854C2214yes—
62#2850C2212yes—
63#2822C2214yes—
64#2820C2214yes—
65#2727C2214yes—
66#2726C2214yes—
67#2726C2214yes—
68#2725C2218yes—
69#2723C2218yes—
70#2721C2218yes—
71#2721C2218yes—
72#2720C2218yes—
73#2719C2218yes—
74#2719C2218yes—
75#2716C2218yes—
76#2713C2218yes—
77#2704C2218yes—
78#2694C2218yes—
79#2690C2218yes—
80#2683C2214yes—
81#2677C2218yes—
82#2674C2218yes—
83#2659C2214yes—
84#2659C2214yes—
85#2639C2214yes—
86#2637C2218yes—
87#2628C2214yes—
88#2621C2214yes—
89#2618C2214yes—
90#2581C2214yes—
91#2564C2218yes—
92#2560C2218yes—
93#2558C2218yes—
94#2556C2218yes—
95#2552C2212yes—
96#2552C2214yes—
97#2552C2214yes—
98#2552C2214yes—
99#2551C2214yes—
100#2551C2212yes—
101#2551C2214yes—
102#2550C2218yes—
103#2550C2218yes—
104#2542C2212yes—
105#2542C2212yes—
106#2542C2214yes—
107#2536C2214yes—
108#2519C2218yes—
109#2519C2218yes—
110#2519C2218yes—
111#2512C2214yes—
112#2512C2214yes—
113#2512C2214yes—
114#2512C2214yes—
115#2506C2214yes—
116#2506C2214yes—
117#2506C2214yes—
118#2506C2214yes—
119#2506C2214yes—
120#2498C2218yes—
121#2498C2218yes—
122#2498C2218yes—
123#2492C2214yes—
124#2489C2214yes—
125#2489C2218yes—
126#2479C2218yes—
127#2475C2218yes—
128#2469C2218yes—
129#2462C2218yes—
130#2453C2214yes—
131#2452C2214yes—
132#2452C2214yes—
133#2451C2214yes—
134#2445C2214yes—
135#2441C2214yes—
136#2440C2214yes—
137#2429C2214yes—
138#2429C2214yes—
139#2417C2214yes—
140#2417C2214yes—
141#2417C2218yes—
142#2417C2214yes—
143#2415C2214yes—
144#2365C2212yes—
145#2365C2214yes—
146#2365C2212yes—
147#2362C2214yes—
148#2362C2218yes—
149#2360C2214yes—
150#2354C2212yes—
151#2354C2214yes—
152D4×C4⋊C4C2212yes—
153#2325C2214yes—
154#2316C2214yes—
155C4×C4⋊Q8C2212yes—
156C4×C4⋊Q8C2211yescharacteristic
157C4×C4⋊Q8C2212yes—
158C4×C4⋊Q8C2212yes—
159C4×C4⋊Q8C2212yes—
160C4×#127C2211yescharacteristic
161C4×#125C2212yes—
162C4×#125C2212yes—
163C4×#125C2212yes—
164C4×#125C2212yes—
165C4×#125C2212yes—
166C4×#125C2212yes—
167C4×#125C2212yes—
168C4×#125C2212yes—
169C4×#124C2212yes—
170C4×#121C2212yes—
171C4×#121C2212yes—
172C4×#121C2214yes—
173#2293C2212yes—
174#2293C2212yes—
175C2×#389C2211yescharacteristic
176C2×#389C2211yescharacteristic
177C2×#387C2212yes—
178C2×#387C2212yes—
179#2285C2212yes—
180#2285C2212yes—
181#2285C2214yes—
182C2×#382C2211yescharacteristic
183C2×C4×C4⋊C4C2211yescharacteristic
184C2×C4×C4⋊C4C2212yes—
185C2×C4×C4⋊C4C2212yes—
186C2×C4×C4⋊C4C2211yescharacteristic
187C2×C43C2211yescharacteristic
188#564—232no—
189#563—232no—
190#557—232no—
191#554—232no—
192#552—232no—
193#552—264no—
194#552—232no—
195#544—232no—
196#544—232no—
197#541—264no—
198#541—232no—
199#539—232no—
200#533—216no—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2318yes—
205C2×C4⋊Q8C2318yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×#127C2311yescharacteristic
213#529—216no—
214C2×#126C2318yes—
215C2×#126C2314yes—
216C2×#126C2318yes—
217C2×#126C2318yes—
218C2×#126C2318yes—
219C2×#125D4116yescomplemented
220C2×#125C2314yes—
221C2×#125C2312yes—
222C2×#125C2318yes—
223C2×#125C2318yes—
224C2×#125C2318yes—
225C2×#125C2318yes—
226C2×#125C2318yes—
227C2×#125C2318yes—
228C2×#125C2318yes—
229C2×#125C2314yes—
230C2×#125C2318yes—
231C2×#125C2312yes—
232C2×#125C2312yes—
233C2×#125C2312yes—
234C2×#125C2312yes—
235C2×#124C2312yes—
236C2×#124C2312yes—
237C2×#123C2314yes—
238C2×#123C2318yes—
239C2×#123C2318yes—
240C2×C22⋊Q8C2318yes—
241C2×C22⋊Q8C2318yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2318yes—
248C2×C22⋊Q8C2318yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2318yes—
252C2×#121C2312yes—
253C2×#121C2312yes—
254C2×#121C2312yes—
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2314yes—
259C2×C4×Q8C2314yes—
260C2×C4×Q8C2318yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2318yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2314yes—
267C2×#117C2318yes—
268C2×#117C2314yes—
269C2×#117C2318yes—
270C2×#117C2314yes—
271C2×#117C2314yes—
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2314yes—
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2312yes—
277C22×C4⋊C4C2312yes—
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C42C2311yescharacteristic
282C22×C42C2311yescharacteristic
283C22×C42C2312yes—
284C22×C42C2311yescharacteristic
285C22×C42C2311yescharacteristic
286C22×C42C2311yescharacteristic
287C22×C42C2311yescharacteristic
288C22×C42C2312yes—
289C22×C42C2311yescharacteristic
290#400C2318yes—
291#400C2318yes—
292#400C2318yes—
293#400C2318yes—
294#400C2318yes—
295#399C2318yes—
296#399C2318yes—
297#399C2318yes—
298#399C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#398C2318yes—
307#398C2318yes—
308#398C2318yes—
309#398C2318yes—
310#398C2318yes—
311#397C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2318yes—
315#396C2318yes—
316#396C2318yes—
317#396C2318yes—
318#396C2318yes—
319#396C2318yes—
320#396C2318yes—
321#395C2318yes—
322#395C2318yes—
323#395C2318yes—
324#395C2318yes—
325#395C2318yes—
326#394C2318yes—
327#394C2318yes—
328#393C2318yes—
329#393C2318yes—
330#391C2314yes—
331#391C2312yes—
332#391C2314yes—
333#391C2314yes—
334#391C2314yes—
335#391C2314yes—
336#391C2314yes—
337#391C2312yes—
338#391C2318yes—
339#391C2318yes—
340#390C2312yes—
341#390C2312yes—
342#390C2312yes—
343#390C2312yes—
344#390C2312yes—
345#390C2312yes—
346#390C2314yes—
347#390C2314yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2312yes—
352#390C2314yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2318yes—
372#389C2318yes—
373#389C2318yes—
374#389C2318yes—
375#389C2314yes—
376#389C2314yes—
377#389C2312yes—
378#389C2312yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2312yes—
383#389C2312yes—
384#389C2318yes—
385#389C2314yes—
386#389C2312yes—
387#389C2312yes—
388#389C2318yes—
389#389C2314yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2314yes—
395#388C2314yes—
396#388C2314yes—
397#388C2314yes—
398#388C2314yes—
399#388C2314yes—
400#388C2314yes—
401#388C2314yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#387C2318yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#386C2318yes—
426#386C2314yes—
427#386C2318yes—
428#386C2318yes—
429#386C2314yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#384C2312yes—
436#384C2312yes—
437#384C2312yes—
438#384C2312yes—
439#384C2314yes—
440#384C2312yes—
441#384C2312yes—
442#384C2312yes—
443#384C2312yes—
444#384C2314yes—
445#384C2314yes—
446#382C2312yes—
447#382C2312yes—
448#382C2312yes—
449#382C2312yes—
450#382C2312yes—
451#382C2314yes—
452#382C2314yes—
453#382C2318yes—
454#380C2314yes—
455#380C2318yes—
456#380C2312yes—
457#380C2314yes—
458#380C2314yes—
459#380C2312yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2318yes—
464#380C2318yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2318yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C22⋊C4C2318yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C2×#95C2312yes—
495C2×#95C2312yes—
496C2×#95C2312yes—
497C2×#95C2312yes—
498C2×#95C2312yes—
499C2×#95C2312yes—
500C43C2311yescharacteristic
501C43C2311yescharacteristic
502C43C2311yescharacteristic
503C43C2311yescharacteristic
504C43C2311yescharacteristic
505C43C2311yescharacteristic
506C43C2311yescharacteristic
507C43C2311yescharacteristic
508C22×Q8C2414yes—
509C22×Q8C2418yes—
510C22×Q8C2414yes—
511C22×Q8C2412yes—
512C22×D4C2414yes—
513C22×D4C2412yes—
514C22×D4C2412yes—
515C22×D4C2412yes—
516C23×C4C2414yes—
517C23×C4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C23×C4C2412yes—
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C23×C4C2412yes—
524C23×C4C2412yes—
525C23×C4C2418yes—
526C23×C4C2412yes—
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C4⋊Q8—232no—
530C4⋊Q8—216no—
531C4⋊Q8—232no—
532C4⋊Q8—28no—
533C4⋊Q8—28no—
534C4⋊Q8—28no—
535C4⋊Q8—48no—
536C4⋊Q8—42no—
537C4⋊Q8—44no—
538C4⋊Q8—44no—
539C4⋊Q8—44no—
540#127—42no—
541#126—232no—
542#126—232no—
543#126—232no—
544#126—232no—
545#126—216no—
546#125—232no—
547#125—232no—
548#125—232no—
549#125—232no—
550#125—232no—
551#125—232no—
552#125—216no—
553#125—232no—
554#125—232no—
555#125—28no—
556#125—216no—
557#125C2×D4116yes—
558#125C2×D4116yes—
559#125C2×D4116yes—
560#125C2×D4116yes—
561#124—28no—
562#124—44no—
563#123—216no—
564#123—232no—
565#123—232no—
566C22⋊Q8—28no—
567C22⋊Q8—216no—
568C22⋊Q8—216no—
569C22⋊Q8—232no—
570C22⋊Q8—232no—
571C22⋊Q8—216no—
572C22⋊Q8—216no—
573C22⋊Q8—232no—
574C22⋊Q8—232no—
575C22⋊Q8—416no—
576C22⋊Q8—48no—
577C22⋊Q8—48no—
578#121—28no—
579#121—28no—
580#121—28no—
581C4×Q8—232no—
582C4×Q8—216no—
583C4×Q8—216no—
584C4×Q8—28no—
585C4×Q8—216no—
586C4×Q8—216no—
587C4×D4—216no—
588C4×D4—232no—
589C4×D4—28no—
590C4×D4—28no—
591C4×D4—48no—
592C4×D4—44no—
593#117—216no—
594#117—232no—
595#117—232no—
596#117—216no—
597#117—216no—
598C2×C4⋊C4—28no—
599C2×C4⋊C4—216no—
600C2×C4⋊C4—42no—
601C2×C4⋊C4—42no—
602C2×C4⋊C4—44no—
603C2×C4⋊C4C2×D4116yes—
604C2×C4⋊C4C2×D418yes—
605C2×C4⋊C4C2×D4116yes—
606C2×C4⋊C4C2×D418yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C42—24no—
681C2×C42—24no—
682C2×C42—28no—
683C2×C42—24no—
684C2×C42—42no—
685C2×C42—44no—
686C2×C42—42no—
687C2×C42—42no—
688C2×C42C2×D418yes—
689C2×C42C2418yes—
690C2×C42C2418yes—
691C2×C42C2414yes—
692C2×C42C2418yes—
693C2×C42C2411yescharacteristic
694C2×C42C2418yes—
695C2×C42C2414yes—
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2414yes—
713C2×C42C2414yes—
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2414yes—
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2418yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2414yes—
750#95C2418yes—
751#95C2414yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756C24C2514yes—
757C24C2511yescharacteristic
758C2×Q8—28no—
759C2×Q8—216no—
760C2×Q8—28no—
761C2×Q8—24no—
762C2×Q8—28no—
763C2×Q8—28no—
764C2×Q8—48no—
765C2×Q8—42no—
766C2×Q8—48no—
767C2×Q8—42no—
768C2×Q8—44no—
769C2×Q8—44no—
770C2×D4—28no—
771C2×D4—28no—
772C2×D4—28no—
773C2×D4—24no—
774C2×D4—24no—
775C2×D4—24no—
776C2×D4—24no—
777C2×D4—24no—
778C2×D4—42no—
779C2×D4—42no—
780C2×D4—42no—
781C2×D4—42no—
782C22×C4—24no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—24no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—28no—
795C22×C4—22no—
796C22×C4—28no—
797C22×C4—22no—
798C22×C4—28no—
799C22×C4—216no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4—41no—
804C22×C4—42no—
805C22×C4—41no—
806C22×C4—41no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—48no—
813C22×C4—48no—
814C22×C4C22×D414yes—
815C22×C4C22×D414yes—
816C22×C4C22×D418yes—
817C22×C4C22×D414yes—
818C22×C4C22×D418yes—
819C22×C42−1+414yes—
820C22×C42−1+414yes—
821C22×C4C2511yescharacteristic
822C22×C4C2511yescharacteristic
823C22×C4C2514yes—
824C22×C4C2514yes—
825C22×C4C2514yes—
826C22×C4C2518yes—
827C22×C4C2514yes—
828C22×C4C2514yes—
829C22×C4C2518yes—
830C22×C4C2511yescharacteristic
831C22×C4C2511yescharacteristic
832C22×C4C2514yes—
833C22×C4C2511yescharacteristic
834C22×C4C2511yescharacteristic
835C22×C4C2514yes—
836C22×C4C2511yescharacteristic
837C22×C4C2511yescharacteristic
838C22×C4C2511yescharacteristic
839C22×C4C2511yescharacteristic
840C22×C4C2511yescharacteristic
841C22×C4C2511yescharacteristic
842C22×C4C2511yescharacteristic
843C22×C4C2511yescharacteristic
844C4⋊C4—28no—
845C4⋊C4—216no—
846C4⋊C4—216no—
847C4⋊C4—28no—
848C4⋊C4—216no—
849C4⋊C4—28no—
850C4⋊C4—216no—
851C4⋊C4—28no—
852C4⋊C4—28no—
853C4⋊C4—24no—
854C4⋊C4—216no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—24no—
858C4⋊C4—216no—
859C4⋊C4—216no—
860C4⋊C4—216no—
861C4⋊C4—216no—
862C4⋊C4—28no—
863C4⋊C4—216no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—28no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—24no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—44no—
880C4⋊C4—42no—
881C4⋊C4—48no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—42no—
889C4⋊C4—48no—
890C4⋊C4C22×D418yes—
891C4⋊C4C22×D418yes—
892C4⋊C4C22×D4116yes—
893C4⋊C4C22×D418yes—
894C4⋊C4C22×D4116yes—
895C4⋊C4C22×D4116yes—
896C4⋊C4C22×D4116yes—
897C4⋊C4C22×D418yes—
898C22⋊C4—216no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—216no—
903C22⋊C4—28no—
904C22⋊C4—216no—
905C22⋊C4—216no—
906C22⋊C4—28no—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—44no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—44no—
917C42—216no—
918C42—216no—
919C42—28no—
920C42—216no—
921C42—216no—
922C42—22no—
923C42—22no—
924C42—22no—
925C42—22no—
926C42—22no—
927C42—22no—
928C42—28no—
929C42—22no—
930C42—22no—
931C42—22no—
932C42—22no—
933C42—28no—
934C42—22no—
935C42—22no—
936C42—28no—
937C42—22no—
938C42—22no—
939C42—22no—
940C42—22no—
941C42—22no—
942C42—41no—
943C42—41no—
944C42—41no—
945C42—41no—
946C42—41no—
947C42—44no—
948C42—41no—
949C42C22×D414yes—
950C42C22×D414yes—
951C42C22×D414yes—
952C42C22×D414yes—
953C422−1+414yes—
954C23—21no—
955C23—21no—
956C23—21no—
957C23—21no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23C23×D412yes—
966C23C2×2−1+412yes—
967C23C2×2−1+412yes—
968C23C2611yescharacteristic
969Q8—416no—
970Q8—816no—
971Q8—84no—
972Q8—88no—
973D4—416no—
974D4—48no—
975D4—84no—
976D4—84no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—24no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—24no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—24no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—24no—
1001C2×C4—28no—
1002C2×C4—216no—
1003C2×C4—28no—
1004C2×C4—28no—
1005C2×C4—28no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—28no—
1010C2×C4—21no—
1011C2×C4—24no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—28no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—24no—
1022C2×C4—21no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—28no—
1028C2×C4—28no—
1029C2×C4—28no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—48no—
1033C2×C4—44no—
1034C2×C4—44no—
1035C2×C4—44no—
1036C2×C4—44no—
1037C2×C4—416no—
1038C2×C4—816no—
1039C2×C4—84no—
1040C2×C4—84no—
1041C2×C4C23×D412yes—
1042C2×C4C23×D418yes—
1043C2×C4C23×D418yes—
1044C2×C4C23×D412yes—
1045C2×C4C23×D412yes—
1046C2×C4C23×D412yes—
1047C2×C4C23×D412yes—
1048C2×C4C23×D412yes—
1049C2×C4C2×2−1+412yes—
1050C2×C4C2×2−1+412yes—
1051C2×C4C2×2−1+412yes—
1052C2×C4C2×2−1+412yes—
1053C2×C4C2×2−1+412yes—
1054C2×C4C2×2−1+412yes—
1055C2×C4C2×2−1+412yes—
1056C2×C4#58512yes—
1057C2×C4#58512yes—
1058C2×C4#58512yes—
1059C22—22no—
1060C22—22no—
1061C22—22no—
1062C22—22no—
1063C22—22no—
1064C22—22no—
1065C22—44no—
1066C22—44no—
1067C22—44no—
1068C22—44no—
1069C22—44no—
1070C22—44no—
1071C22—44no—
1072C22#349914yes—
1073C22C24×D411yescharacteristic
1074C22C22×2−1+411yescharacteristic
1075C22C22×2−1+411yescharacteristic
1076C22C22×2−1+411yescharacteristic
1077C22C2×#58511yescharacteristic
1078C22C2×#58511yescharacteristic
1079C22C2×#58511yescharacteristic
1080C4—22no—
1081C4—22no—
1082C4—22no—
1083C4—22no—
1084C4—22no—
1085C4—28no—
1086C4—28no—
1087C4—22no—
1088C4—22no—
1089C4—22no—
1090C4—22no—
1091C4—22no—
1092C4—41no—
1093C4—44no—
1094C4—44no—
1095C4—48no—
1096C4—44no—
1097C4—48no—
1098C4—44no—
1099C4—44no—
1100C4—41no—
1101C4#349714yes—
1102C4#356314yescomplemented
1103C2—24no—
1104C2—84no—
1105C2C2×#356311yescharacteristic
1106C2#6275211yescharacteristic
1107C2C2×#349711yescharacteristic
1108C2C2×#349911yescharacteristic
1109C2#6281211yescharacteristic
1110C2#6282311yescharacteristic
1111C2#6283711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2856C22
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. #59667C2semidirect
3. #59656C2semidirect
4. #59444C2semidirect
5. #46150C2semidirect
6. C4⋊#564C2semidirect
7. #45998C2semidirect
8. #39614C2semidirect
9. #39487C2semidirect
10. #39447C2semidirect
11. #39427C2semidirect
12. #39399C2semidirect
13. #39385C2semidirect
14. #39369C2semidirect
15. #37867C2semidirect
16. #37555C2semidirect
17. #36742C2semidirect
18. #36645C2semidirect
20. #36561C2semidirect
21. #36186C2semidirect
22. #36186C2semidirect
23. #35167C2semidirect
25. C2×C4×#125C2semidirect
219. C2×#125D4semidirect
1102. C4#3563semidirect

Maximal subgroups

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

subgroupindex
C2×#35632
#596672
#596562
#594442
#461502
C4⋊#5642
#459982
#396142
#394872
#394472
#394272
#393992
#393852
#393692
#378672
#375552
#367422
#366452
#366312
#365612
#361862
#351672
#350062
C2×C4×#1252