Finite Group Databasebeta

← #7680723

Subgroups — #7680723

Order 512.

5020 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59440C214yesmaximal, complemented
2#59259C212yesmaximal, complemented
3#59258C212yesmaximal, complemented
4#59249C212yesmaximal, complemented
5#59235C212yesmaximal, complemented
6#59140C214yesmaximal, complemented
7#45346C214yesmaximal, complemented
8#45050C214yesmaximal, complemented
9#43152C218yesmaximal, complemented
10#39479C212yesmaximal, complemented
11#39478C212yesmaximal, complemented
12#37983C214yesmaximal, complemented
13#37982C214yesmaximal, complemented
14#36193C212yesmaximal, complemented
15#36186C212yesmaximal, complemented
16#35585C212yesmaximal, complemented
17#35557C212yesmaximal, complemented
18#35280C211yesmaximal, characteristic, complemented
19#35255C212yesmaximal
20#34947C211yesmaximal, characteristic, complemented
21C2×#2552C211yesmaximal, characteristic, complemented
22#34213C211yesmaximal, characteristic, complemented
23#34188C212yesmaximal, complemented
24#34188C211yesmaximal, characteristic, complemented
25C4⋊C4×#41C211yesmaximal, characteristic, complemented
26C4×#537C211yesmaximal, characteristic
27C2×#552C2214yes—
28C2×#537C2211yescharacteristic
29C2×#533C2211yescharacteristic
30C22×#125C2212yes—
31C2×C4×#41C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33C2×C4×#41C2212yes—
34#2857C2212yes—
35#2857C2212yes—
36#2855C2214yes—
37#2854C2214yes—
38#2772C2218yes—
39#2768C2218yes—
40#2767C2218yes—
41#2767C2218yes—
42#2754C2218yes—
43#2747C2218yes—
44#2744C2218yes—
45#2739C2218yes—
46#2719C2218yes—
47#2707C2218yes—
48#2702C2218yes—
49#2695C2218yes—
50#2629C2214yes—
51#2625C2214yes—
52#2624C2214yes—
53#2609C2218yes—
54#2601C2218yes—
55#2590C2218yes—
56#2585C2218yes—
57#2582C2212yes—
58#2582C2212yes—
59#2569C2218yes—
60#2568C2211yescharacteristic
61#2567C2211yescharacteristic
62#2566C2212yes—
63#2565C2214yes—
64#2565C2212yes—
65#2564C2214yes—
66#2563C2211yescharacteristic
67#2562C2214yes—
68#2552C2214yes—
69#2552C2212yes—
70#2552C2212yes—
71#2552C2214yes—
72#2552C2212yes—
73#2552C2212yes—
74#2542C2211yescharacteristic
75#2538C2212yes—
76#2538C2212yes—
77#2520C2218yes—
78#2519C2218yes—
79#2519C2218yes—
80#2512C2214yes—
81#2512C2214yes—
82#2511C2214yes—
83#2511C2214yes—
84#2511C2214yes—
85#2509C2214yes—
86#2509C2214yes—
87#2508C2214yes—
88#2508C2214yes—
89#2508C2214yes—
90#2507C2214yes—
91#2507C2214yes—
92#2506C2214yes—
93#2506C2214yes—
94#2498C2218yes—
95#2497C2214yes—
96#2497C2214yes—
97#2496C2214yes—
98#2496C2214yes—
99#2496C2214yes—
100#2489C2214yes—
101#2489C2214yes—
102#2485C2214yes—
103#2481C2218yes—
104#2481C2218yes—
105#2478C2218yes—
106#2475C2218yes—
107#2475C2218yes—
108#2444C2218yes—
109#2443C2218yes—
110#2442C2218yes—
111#2442C2214yes—
112#2441C2214yes—
113#2438C2218yes—
114#2423C2214yes—
115#2422C2214yes—
116#2421C2214yes—
117#2421C2214yes—
118#2420C2214yes—
119#2417C2212yes—
120#2417C2214yes—
121#2417C2212yes—
122#2417C2214yes—
123#2417C2214yes—
124#2396C2214yes—
125C2×#398C2214yes—
126#2370C2214yes—
127#2370C2214yes—
128#2369C2212yes—
129#2365C2212yes—
130#2362C2214yes—
131#2355C2214yes—
132#2355C2214yes—
133#2355C2214yes—
134#2355C2212yes—
135#2355C2212yes—
136#2355C2212yes—
137#2354C2212yes—
138#2354C2212yes—
139#2354C2214yes—
140#2354C2214yes—
141#2352C2214yes—
142#2352C2218yes—
143#2352C2218yes—
144#2352C2214yes—
145#2351C2212yes—
146Q8×C4⋊C4C2211yescharacteristic
147Q8×C4⋊C4C2211yescharacteristic
148Q8×C4⋊C4C2212yes—
149#2349C2214yes—
150#2349C2212yes—
151D4×C4⋊C4C2212yes—
152D4×C4⋊C4C2212yes—
153D4×C4⋊C4C2211yescharacteristic
154D4×C4⋊C4C2211yescharacteristic
155#2344C2214yes—
156#2329C2214yes—
157#2325C2214yes—
158#2324C2212yes—
159#2324C2212yes—
160#2323C2212yes—
161#2323C2212yes—
162#2317C2212yes—
163#2316C2211yescharacteristic
164#2316C2212yes—
165#2314C2214yes—
166#2314C2214yes—
167#2314C2214yes—
168#2311C2211yescharacteristic
169#2311C2211yescharacteristic
170#2311C2212yes—
171#2311C2212yes—
172C4×C22⋊Q8C2214yes—
173C4×C22⋊Q8C2212yes—
174C4×C22⋊Q8C2212yes—
175C4×C22⋊Q8C2212yes—
176C4×C22⋊Q8C2212yes—
177C4×#121C2214yes—
178C4×#121C2212yes—
179C4×#121C2212yes—
180#2297C2212yes—
181#2296C2212yes—
182#2296C2214yes—
183C2×#389C2212yes—
184C2×#389C2212yes—
185#2285C2212yes—
186#2285C2212yes—
187#2285C2211yescharacteristic
188#2285C2214yes—
189#2285C2214yes—
190#2285C2212yes—
191#2285C2212yes—
192C2×#384C2211yescharacteristic
193C2×#384C2212yes—
194#2274C2212yes—
195#2274C2212yes—
196C2×C4×C4⋊C4C2211yescharacteristic
197C2×C4×C4⋊C4C2212yes—
198C2×C4×C4⋊C4C2211yescharacteristic
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201#552—416no—
202#537—28no—
203#533—28no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×#126C2318yes—
207C2×#126C2318yes—
208C2×#125—48no—
209C2×#125C2312yes—
210C2×#125C2314yes—
211C2×#125C2314yes—
212C2×#125C2318yes—
213C2×#125C2318yes—
214C2×#123C2318yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×#121C2312yes—
224C2×#121C2312yes—
225C2×#121C2314yes—
226C4×#41—216no—
227C4×#41—28no—
228C4×#41—28no—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2312yes—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2312yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2314yes—
251C2×#117C2311yescharacteristic
252C2×#117C2312yes—
253C2×#117C2311yescharacteristic
254C2×#117C2312yes—
255C2×#117C2312yes—
256C2×#117C2314yes—
257C2×#117C2312yes—
258C2×#117C2314yes—
259C2×#117C2318yes—
260C2×#117C2318yes—
261C2×#117C2314yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2314yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2314yes—
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2314yes—
274C22×C42C2314yes—
275C22×C42C2312yes—
276C22×C42C2312yes—
277C22×C42C2312yes—
278C22×C42C2312yes—
279C22×C42C2311yescharacteristic
280#400C2318yes—
281#400C2314yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#399C2314yes—
291#399C2318yes—
292#398C2318yes—
293#398C2314yes—
294#398C2314yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#396C2314yes—
311#396C2314yes—
312#396C2318yes—
313#396C2318yes—
314#396C2318yes—
315#396C2318yes—
316#395C2314yes—
317#394C2318yes—
318#394C2318yes—
319#393C2314yes—
320#391C2312yes—
321#391C2312yes—
322#391C2312yes—
323#391C2314yes—
324#391C2312yes—
325#391C2312yes—
326#391C2314yes—
327#391C2314yes—
328#391C2312yes—
329#391C2314yes—
330#391C2318yes—
331#391C2314yes—
332#390C2312yes—
333#390C2312yes—
334#390C2312yes—
335#390C2312yes—
336#390C2314yes—
337#390C2314yes—
338#390C2314yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2318yes—
355#389C2314yes—
356#389C2318yes—
357#389C2314yes—
358#389C2318yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2312yes—
363#389C2312yes—
364#389C2314yes—
365#389C2312yes—
366#389C2312yes—
367#389C2314yes—
368#389C2314yes—
369#389C2318yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2314yes—
381#388C2314yes—
382#388C2314yes—
383#388C2314yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#387C2314yes—
388#387C2314yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2314yes—
401#387C2314yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#386C2314yes—
411#386C2314yes—
412#386C2314yes—
413#386C2314yes—
414#386C2318yes—
415#386C2318yes—
416#386C2314yes—
417#386C2314yes—
418#386C2318yes—
419#385C2314yes—
420#385C2314yes—
421#385C2314yes—
422#385C2318yes—
423#385C2314yes—
424#385C2314yes—
425#385C2318yes—
426#385C2314yes—
427#385C2314yes—
428#385C2314yes—
429#385C2314yes—
430#385C2314yes—
431#384C2312yes—
432#384C2312yes—
433#384C2312yes—
434#384C2312yes—
435#384C2314yes—
436#384C2314yes—
437#384C2312yes—
438#384C2312yes—
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2312yes—
442#384C2312yes—
443#384C2314yes—
444#384C2314yes—
445#384C2314yes—
446#382C2312yes—
447#382C2314yes—
448#382C2312yes—
449#382C2312yes—
450#382C2314yes—
451#382C2314yes—
452#382C2318yes—
453#382C2314yes—
454#382C2318yes—
455#382C2318yes—
456#381C2318yes—
457#380C2312yes—
458#380C2312yes—
459#380C2314yes—
460#380C2314yes—
461#380C2312yes—
462#380C2314yes—
463#380C2314yes—
464#380C2312yes—
465#380C2312yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2312yes—
471#380C2312yes—
472#380C2314yes—
473#380C2318yes—
474#380C2312yes—
475#380C2314yes—
476#380C2312yes—
477#380C2312yes—
478#380C2314yes—
479#380C2318yes—
480#380C2318yes—
481#380C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2318yes—
497C4×C4⋊C4C2318yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2318yes—
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2314yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2314yes—
515C4×C4⋊C4C2314yes—
516C4×C22⋊C4C2318yes—
517C4×C22⋊C4C2318yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522C2×#95C2312yes—
523C2×#95C2314yes—
524C2×#95C2312yes—
525C2×#95C2314yes—
526C2×#41—24no—
527C2×#41—24no—
528C2×#41—24no—
529C2×#41—24no—
530C2×#41—24no—
531C2×#41#4118yes—
532C22×Q8C2412yes—
533C22×Q8C2411yescharacteristic
534C22×Q8C2411yescharacteristic
535C22×Q8C2412yes—
536C22×D4C2412yes—
537C22×D4C2411yescharacteristic
538C22×D4C2412yes—
539C22×D4C2411yescharacteristic
540C22×D4C2414yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2414yes—
547C23×C4C2414yes—
548C23×C4C2411yescharacteristic
549C23×C4C2412yes—
550C23×C4C2414yes—
551C23×C4C2412yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2411yescharacteristic
556C23×C4C2411yescharacteristic
557C4⋊Q8—24no—
558C4⋊Q8—24no—
559#126—416no—
560#126—88no—
561#125—216no—
562#125—28no—
563#125—48no—
564#125—416no—
565#125—416no—
566#123—416no—
567C22⋊Q8—28no—
568C22⋊Q8—28no—
569C22⋊Q8—28no—
570C22⋊Q8—28no—
571C22⋊Q8—28no—
572C22⋊Q8—28no—
573C22⋊Q8—48no—
574C22⋊Q8—84no—
575#121—28no—
576#121—216no—
577#121—28no—
578C4×Q8—28no—
579C4×Q8—28no—
580C4×Q8—24no—
581C4×Q8—24no—
582C4×Q8—24no—
583C4×Q8—24no—
584C4×Q8—28no—
585C4×Q8—28no—
586C4×Q8—48no—
587C4×D4—216no—
588C4×D4—216no—
589C4×D4—28no—
590C4×D4—28no—
591C4×D4—28no—
592C4×D4—28no—
593C4×D4—28no—
594C4×D4—28no—
595C4×D4—24no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—48no—
600#117—216no—
601#117—28no—
602#117—24no—
603#117—24no—
604#117—28no—
605#117—28no—
606#117—28no—
607#117—48no—
608#117—416no—
609#117—84no—
610#117—88no—
611C2×C4⋊C4—24no—
612C2×C4⋊C4—28no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—28no—
616C2×C4⋊C4—24no—
617C2×C4⋊C4—28no—
618C2×C4⋊C4—44no—
619C2×C4⋊C4—48no—
620C2×C4⋊C4—48no—
621C2×C4⋊C4—82no—
622C2×C4⋊C4—84no—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2418yes—
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C42—216no—
707C2×C42—28no—
708C2×C42—28no—
709C2×C42—28no—
710C2×C42—44no—
711C2×C42#4118yes—
712C2×C42C2414yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2414yes—
717C2×C42C2414yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2414yes—
723C2×C42C2414yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2418yes—
728C2×C42C2418yes—
729C2×C42C2418yes—
730C2×C42C2418yes—
731C2×C42C2414yes—
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736#95C2412yes—
737#95C2414yes—
738#95C2412yes—
739#95C2412yes—
740#95C2412yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2414yes—
750#95C2418yes—
751#95C2418yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2418yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2418yes—
768#95C2414yes—
769#95C2418yes—
770#95C2418yes—
771#95C2414yes—
772#95C2418yes—
773#95C2418yes—
774#95C2418yes—
775#95C2418yes—
776C24C2512yes—
777C24C2512yes—
778C24C2511yescharacteristic
779#41—232no—
780#41—416no—
781C2×Q8—22no—
782C2×Q8—22no—
783C2×Q8—24no—
784C2×Q8—22no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—22no—
788C2×Q8—24no—
789C2×Q8—22no—
790C2×Q8—42no—
791C2×Q8—42no—
792C2×Q8C2×#4114yes—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—28no—
799C2×D4—22no—
800C2×D4—22no—
801C2×D4—22no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4C2×#4118yes—
807C2×D4C2×#4114yes—
808C22×C4—24no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—24no—
812C22×C4—28no—
813C22×C4—28no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—28no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—28no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—28no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—41no—
835C22×C4—42no—
836C22×C4—44no—
837C22×C4—42no—
838C22×C4—41no—
839C22×C4—42no—
840C22×C4—44no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—44no—
845C22×C4—42no—
846C22×C4—44no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4C2×#4118yes—
851C22×C4C2×#4114yes—
852C22×C4C2×#4114yes—
853C22×C4C2×#4114yes—
854C22×C4C2×#4114yes—
855C22×C42−1+414yes—
856C22×C4C2512yes—
857C22×C4C2514yes—
858C22×C4C2512yes—
859C22×C4C2512yes—
860C22×C4C2512yes—
861C22×C4C2514yes—
862C22×C4C2514yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2514yes—
866C22×C4C2514yes—
867C22×C4C2514yes—
868C22×C4C2512yes—
869C22×C4C2518yes—
870C22×C4C2512yes—
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C22×C4C2511yescharacteristic
874C22×C4C2512yes—
875C22×C4C2512yes—
876C22×C4C2511yescharacteristic
877C22×C4C2511yescharacteristic
878C22×C4C2511yescharacteristic
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—22no—
890C4⋊C4—22no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—24no—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—28no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—22no—
903C4⋊C4—28no—
904C4⋊C4—28no—
905C4⋊C4—216no—
906C4⋊C4—216no—
907C4⋊C4—28no—
908C4⋊C4—24no—
909C4⋊C4—28no—
910C4⋊C4—24no—
911C4⋊C4—24no—
912C4⋊C4—28no—
913C4⋊C4—28no—
914C4⋊C4—24no—
915C4⋊C4—22no—
916C4⋊C4—28no—
917C4⋊C4—44no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—48no—
924C4⋊C4—44no—
925C4⋊C4—42no—
926C4⋊C4—44no—
927C4⋊C4—48no—
928C4⋊C4—44no—
929C4⋊C4—42no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—48no—
933C4⋊C4—48no—
934C4⋊C4—48no—
935C4⋊C4—44no—
936C4⋊C4H(5,𝔽2)14yes—
937C4⋊C42−1+414yes—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—24no—
941C22⋊C4—24no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—28no—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—24no—
948C22⋊C4—24no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—44no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C42—24no—
963C42—28no—
964C42—24no—
965C42—24no—
966C42—24no—
967C42—28no—
968C42—28no—
969C42—24no—
970C42—24no—
971C42—24no—
972C42—24no—
973C42—24no—
974C42—24no—
975C42—28no—
976C42—28no—
977C42—44no—
978C42—48no—
979C42—48no—
980C42—48no—
981C42—48no—
982C42C2×#4114yes—
983C42C2×#4114yes—
984C42C2×#4114yes—
985C42C2×#4114yes—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23C22×#4114yes—
1004C23C22×#4112yes—
1005C23C22×#4112yes—
1006C23C2×2−1+412yes—
1007C23C2611yescharacteristic
1008Q8—28no—
1009Q8—44no—
1010Q8—48no—
1011Q8—84no—
1012D4—216no—
1013D4—28no—
1014D4—48no—
1015D4—44no—
1016D4—88no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—216no—
1030C2×C4—28no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—28no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—28no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—28no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—24no—
1073C2×C4—44no—
1074C2×C4—48no—
1075C2×C4—416no—
1076C2×C4—48no—
1077C2×C4—416no—
1078C2×C4—48no—
1079C2×C4—48no—
1080C2×C4—48no—
1081C2×C4—48no—
1082C2×C4—84no—
1083C2×C4—84no—
1084C2×C4—84no—
1085C2×C4—88no—
1086C2×C4#552116yescomplemented
1087C2×C4C22×#4114yes—
1088C2×C4C22×#4112yes—
1089C2×C4C22×#4112yes—
1090C2×C4C22×#4112yes—
1091C2×C4C22×#4112yes—
1092C2×C4C22×#4112yes—
1093C2×C4C22×#4112yes—
1094C2×C4C22×#4112yes—
1095C2×C4C22×#4112yes—
1096C2×C4C2×H(5,𝔽2)14yes—
1097C2×C4C2×H(5,𝔽2)12yes—
1098C2×C4C2×2−1+414yes—
1099C2×C4C2×2−1+412yes—
1100C2×C4C2×2−1+412yes—
1101C2×C4C2×2−1+412yes—
1102C22—22no—
1103C22—22no—
1104C22—22no—
1105C22—22no—
1106C22—22no—
1107C22—22no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22C2×#55214yes—
1123C22C23×#4111yescharacteristic
1124C22C23×#4111yescharacteristic
1125C22C22×H(5,𝔽2)11yescharacteristic
1126C22C22×2−1+411yescharacteristic
1127C22C22×2−1+411yescharacteristic
1128C22H(7,𝔽2)11yescharacteristic
1129C222−1+611yescharacteristic
1130C4—24no—
1131C4—24no—
1132C4—22no—
1133C4—22no—
1134C4—22no—
1135C4—24no—
1136C4—44no—
1137C4—42no—
1138C4—44no—
1139C4—44no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—44no—
1144C4—42no—
1145C4—42no—
1146C4—44no—
1147C4—44no—
1148C4—48no—
1149C4—42no—
1150C4C2×#55214yes—
1151C4C2×#55214yes—
1152C4#351114yes—
1153C2—24no—
1154C2—44no—
1155C2—82no—
1156C2C22×#55211yescharacteristic
1157C2C2×#351111yescharacteristic
1158C2#6285611yescharacteristic
1159C2#6291711yescharacteristic
1160C2#6294711yescharacteristic
1161C2#6298511yescharacteristic
1162C2#6300011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#537C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59440C2semidirect
2. #59259C2semidirect
3. #59258C2semidirect
4. #59249C2semidirect
5. #59235C2semidirect
6. #59140C2semidirect
7. #45346C2semidirect
8. #45050C2semidirect
9. #43152C2semidirect
10. #39479C2semidirect
11. #39478C2semidirect
12. #37983C2semidirect
13. #37982C2semidirect
14. #36193C2semidirect
15. #36186C2semidirect
16. #35585C2semidirect
17. #35557C2semidirect
18. #35280C2semidirect
20. #34947C2semidirect
21. C2×#2552C2semidirect
22. #34213C2semidirect
23. #34188C2semidirect
24. #34188C2semidirect
25. C4⋊C4×#41C2semidirect
1086. C2×C4#552semidirect

Maximal subgroups

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

subgroupindex
#594402
#592592
#592582
#592492
#592352
#591402
#453462
#450502
#431522
#394792
#394782
#379832
#379822
#361932
#361862
#355852
#355572
#352802
#352552
#349472
C2×#25522
#342132
#341882
C4⋊C4×#412
C4×#5372