Finite Group Databasebeta

← #7711148

Subgroups — #7711148

Order 512.

4660 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic, complemented
2#59863C211yesmaximal, characteristic, complemented
3#59828C211yesmaximal, characteristic, complemented
4#59827C211yesmaximal, characteristic, complemented
5#59429C212yesmaximal, complemented
6#59427C212yesmaximal, complemented
7#45802C214yesmaximal, complemented
8#45512C214yesmaximal, complemented
9#40023C214yesmaximal, complemented
10#40005C214yesmaximal, complemented
11#39731C214yesmaximal, complemented
12#39726C212yesmaximal
13#39724C212yesmaximal, complemented
14#39547C214yesmaximal, complemented
15#39513C212yesmaximal, complemented
16#39497C212yesmaximal, complemented
17#37633C212yesmaximal, complemented
18#37143C214yesmaximal, complemented
19#36645C211yesmaximal, characteristic, complemented
20#36631C211yesmaximal, characteristic
21#36538C212yesmaximal, complemented
22#36449C212yesmaximal, complemented
23#36315C212yesmaximal, complemented
24#36285C212yesmaximal, complemented
25#35117C214yesmaximal, complemented
26#34383C212yesmaximal, complemented
27C4×#533C211yesmaximal, characteristic, complemented
28C2×#559C2212yes—
29C2×#557C2212yes—
30C2×#533C2211yescharacteristic
31C2×#533C2212yes—
32C2×#529C2212yes—
33#2868C2211yescharacteristic
34#2868C2211yescharacteristic
35#2863C2214yes—
36#2862C2212yes—
37#2861C2212yes—
38#2861C2214yes—
39#2860C2212yes—
40#2860C2212yes—
41#2859C2211yescharacteristic
42#2859C2212yes—
43#2859C2212yes—
44#2858C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2212yes—
47#2857C2211yescharacteristic
48#2857C2212yes—
49#2857C2211yescharacteristic
50#2857C2212yes—
51#2856C2211yescharacteristic
52#2854C2212yes—
53#2854C2212yes—
54#2850C2212yes—
55#2814C2218yes—
56#2808C2214yes—
57#2805C2214yes—
58#2793C2218yes—
59#2793C2218yes—
60#2790C2218yes—
61#2788C2218yes—
62#2786C2218yes—
63#2783C2218yes—
64#2772C2218yes—
65#2750C2218yes—
66#2739C2218yes—
67#2729C2218yes—
68#2726C2214yes—
69#2724C2214yes—
70#2719C2218yes—
71#2707C2218yes—
72#2690C2218yes—
73#2681C2218yes—
74#2650C2218yes—
75#2637C2218yes—
76#2629C2214yes—
77#2629C2214yes—
78#2621C2214yes—
79#2620C2214yes—
80#2606C2218yes—
81#2592C2214yes—
82#2592C2214yes—
83#2590C2218yes—
84#2582C2212yes—
85#2582C2212yes—
86#2581C2214yes—
87#2581C2214yes—
88#2578C2218yes—
89#2571C2212yes—
90#2570C2214yes—
91#2568C2214yes—
92#2568C2212yes—
93#2567C2212yes—
94#2566C2214yes—
95#2565C2214yes—
96#2563C2212yes—
97#2558C2218yes—
98#2558C2218yes—
99#2552C2212yes—
100#2550C2214yes—
101#2548C2212yes—
102#2547C2212yes—
103#2547C2212yes—
104#2547C2212yes—
105#2546C2212yes—
106#2545C2214yes—
107#2545C2214yes—
108#2545C2214yes—
109#2545C2214yes—
110#2538C2214yes—
111#2532C2218yes—
112#2531C2218yes—
113#2530C2218yes—
114#2529C2218yes—
115#2529C2218yes—
116#2515C2218yes—
117#2513C2214yes—
118#2511C2214yes—
119#2509C2214yes—
120#2507C2214yes—
121#2506C2214yes—
122#2497C2214yes—
123#2497C2214yes—
124#2497C2214yes—
125#2495C2214yes—
126#2489C2214yes—
127#2486C2214yes—
128#2485C2214yes—
129#2485C2214yes—
130#2485C2214yes—
131#2465C2218yes—
132#2453C2214yes—
133#2452C2214yes—
134#2447C2214yes—
135#2447C2214yes—
136#2446C2214yes—
137#2446C2214yes—
138#2446C2214yes—
139#2440C2214yes—
140#2439C2214yes—
141#2427C2214yes—
142#2426C2214yes—
143#2421C2214yes—
144#2376C2218yes—
145#2370C2214yes—
146#2367C2214yes—
147#2367C2214yes—
148#2365C2212yes—
149#2365C2212yes—
150#2356C2214yes—
151#2355C2212yes—
152#2355C2212yes—
153#2354C2212yes—
154#2354C2214yes—
155#2354C2212yes—
156#2352C2214yes—
157Q8×C4⋊C4C2212yes—
158Q8×C4⋊C4C2212yes—
159D4×C4⋊C4C2212yes—
160D4×C4⋊C4C2212yes—
161#2346C2214yes—
162#2345C2214yes—
163#2334C2218yes—
164#2332C2218yes—
165#2324C2214yes—
166#2323C2214yes—
167#2317C2214yes—
168#2314C2214yes—
169C4×C4⋊Q8C2211yescharacteristic
170C4×C4⋊Q8C2211yescharacteristic
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2211yescharacteristic
178C4×C4⋊Q8C2211yescharacteristic
179C4×#127C2211yescharacteristic
180C4×#125C2212yes—
181C4×#125C2212yes—
182C4×#124C2212yes—
183C4×#124C2214yes—
184C4×C22⋊Q8C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×#121C2212yes—
189C4×#121C2212yes—
190#2296C2212yes—
191#2295C2212yes—
192#2295C2214yes—
193#2295C2212yes—
194#2293C2212yes—
195#2293C2212yes—
196#2285C2212yes—
197#2285C2212yes—
198#2285C2211yescharacteristic
199C42×Q8C2212yes—
200C42×Q8C2212yes—
201C4×#117C2212yes—
202C2×C43C2211yescharacteristic
203#559—48no—
204#557—48no—
205#533—28no—
206#533—48no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2312yes—
218C2×#127C2311yescharacteristic
219#529—216no—
220C2×#126C2314yes—
221C2×#125C2312yes—
222C2×#125C2312yes—
223C2×#125C2314yes—
224C2×#125C2314yes—
225C2×#125C2318yes—
226C2×#124C2312yes—
227C2×#124C2312yes—
228C2×#124C2314yes—
229C2×#124C2314yes—
230C2×#124C2314yes—
231C2×#123C2314yes—
232C2×#123C2318yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2318yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2312yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2314yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×#117C2314yes—
263C2×#117C2312yes—
264C2×#117C2314yes—
265C2×#117C2314yes—
266C2×#117C2312yes—
267C22×C4⋊C4C2314yes—
268C22×C42C2311yescharacteristic
269C22×C42C2311yescharacteristic
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#396C2318yes—
301#396C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#395C2318yes—
309#395C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#393C2318yes—
314#393C2318yes—
315#391C2312yes—
316#391C2312yes—
317#391C2314yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2312yes—
322#391C2314yes—
323#391C2312yes—
324#391C2312yes—
325#391C2312yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2312yes—
331#391C2314yes—
332#391C2318yes—
333#391C2314yes—
334#391C2314yes—
335#391C2314yes—
336#390C2312yes—
337#390C2312yes—
338#390C2312yes—
339#390C2314yes—
340#390C2312yes—
341#390C2314yes—
342#390C2314yes—
343#390C2318yes—
344#390C2312yes—
345#390C2312yes—
346#390C2312yes—
347#390C2312yes—
348#390C2312yes—
349#390C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2314yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2314yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2312yes—
365#389C2312yes—
366#389C2314yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2318yes—
378#389C2318yes—
379#389C2314yes—
380#389C2314yes—
381#389C2318yes—
382#389C2312yes—
383#389C2318yes—
384#389C2312yes—
385#389C2312yes—
386#389C2312yes—
387#389C2312yes—
388#389C2314yes—
389#389C2312yes—
390#389C2314yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2314yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2318yes—
410#388C2314yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#386C2314yes—
437#386C2318yes—
438#386C2314yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2314yes—
445#385C2314yes—
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#384C2312yes—
450#384C2311yescharacteristic
451#384C2311yescharacteristic
452#384C2311yescharacteristic
453#384C2312yes—
454#384C2312yes—
455#384C2314yes—
456#384C2312yes—
457#384C2312yes—
458#384C2314yes—
459#384C2312yes—
460#384C2312yes—
461#383C2318yes—
462#382C2312yes—
463#382C2314yes—
464#382C2314yes—
465#382C2318yes—
466#382C2312yes—
467#382C2314yes—
468#382C2314yes—
469#382C2314yes—
470#381C2318yes—
471#380C2314yes—
472#380C2314yes—
473#380C2314yes—
474#380C2314yes—
475#380C2312yes—
476#380C2312yes—
477#380C2312yes—
478#380C2312yes—
479#380C2318yes—
480#380C2312yes—
481#380C2312yes—
482#380C2314yes—
483#380C2314yes—
484#380C2312yes—
485#380C2314yes—
486#380C2314yes—
487#380C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2314yes—
513C4×C4⋊C4C2318yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2314yes—
517C4×C4⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2318yes—
520C4×C22⋊C4C2318yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2314yes—
524#376C2318yes—
525#376C2314yes—
526C43C2311yescharacteristic
527C43C2311yescharacteristic
528C43C2311yescharacteristic
529C43C2311yescharacteristic
530C43C2311yescharacteristic
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2311yescharacteristic
534C43C2314yes—
535C22×Q8C2412yes—
536C22×Q8C2412yes—
537C22×Q8C2412yes—
538C22×Q8C2412yes—
539C22×Q8C2412yes—
540C22×Q8C2414yes—
541C22×D4C2412yes—
542C22×D4C2412yes—
543C22×D4C2414yes—
544C22×D4C2412yes—
545C23×C4C2414yes—
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2418yes—
553C23×C4C2411yescharacteristic
554C4⋊Q8—24no—
555C4⋊Q8—24no—
556C4⋊Q8—24no—
557C4⋊Q8—24no—
558C4⋊Q8—24no—
559C4⋊Q8—44no—
560C4⋊Q8—44no—
561C4⋊Q8—44no—
562C4⋊Q8—44no—
563C4⋊Q8—44no—
564C4⋊Q8—48no—
565#127—24no—
566#126—216no—
567#125—28no—
568#125—28no—
569#125—48no—
570#125—48no—
571#125—416no—
572#124—28no—
573#124—28no—
574#124—48no—
575#124—48no—
576#124—48no—
577#123—216no—
578#123—416no—
579C22⋊Q8—28no—
580C22⋊Q8—28no—
581C22⋊Q8—28no—
582C22⋊Q8—416no—
583C22⋊Q8—48no—
584C22⋊Q8—44no—
585C22⋊Q8—44no—
586#121—28no—
587#121—44no—
588#121—44no—
589C4×Q8—28no—
590C4×Q8—28no—
591C4×Q8—28no—
592C4×Q8—28no—
593C4×Q8—28no—
594C4×Q8—28no—
595C4×Q8—28no—
596C4×Q8—44no—
597C4×Q8—48no—
598C4×Q8—44no—
599C4×Q8—48no—
600C4×Q8—48no—
601C4×Q8—48no—
602C4×D4—216no—
603C4×D4—28no—
604C4×D4—28no—
605C4×D4—48no—
606C4×D4—48no—
607C4×D4—44no—
608#117—28no—
609#117—216no—
610#117—48no—
611#117—44no—
612#117—48no—
613C2×C4⋊C4—48no—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2412yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2418yes—
692C2×C42—24no—
693C2×C42—24no—
694C2×C42—24no—
695C2×C42—42no—
696C2×C42—42no—
697C2×C42—42no—
698C2×C42#4118yes—
699C2×C42C2414yes—
700C2×C42C2414yes—
701C2×C42C2414yes—
702C2×C42C2414yes—
703C2×C42C2411yescharacteristic
704C2×C42C2414yes—
705C2×C42C2411yescharacteristic
706C2×C42C2414yes—
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2414yes—
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2414yes—
722C2×C42C2418yes—
723C2×C42C2418yes—
724C2×C42C2414yes—
725C2×C42C2418yes—
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2418yes—
763#95C2414yes—
764#95C2418yes—
765#95C2414yes—
766#95C2414yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2414yes—
772#95C2414yes—
773#95C2418yes—
774#95C2418yes—
775#95C2418yes—
776#95C2418yes—
777C24C2514yes—
778C24C2511yescharacteristic
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—24no—
783C2×Q8—24no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—28no—
793C2×Q8—42no—
794C2×Q8—42no—
795C2×Q8—44no—
796C2×Q8—44no—
797C2×D4—28no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—28no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—28no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—28no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4C2×#4114yes—
834C22×C4C2×#4114yes—
835C22×C4C2×#4114yes—
836C22×C4C2511yescharacteristic
837C22×C4C2514yes—
838C22×C4C2514yes—
839C22×C4C2511yescharacteristic
840C22×C4C2514yes—
841C22×C4C2514yes—
842C22×C4C2514yes—
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2514yes—
847C22×C4C2514yes—
848C22×C4C2514yes—
849C22×C4C2511yescharacteristic
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C22×C4C2511yescharacteristic
853C22×C4C2511yescharacteristic
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—28no—
867C4⋊C4—24no—
868C4⋊C4—28no—
869C4⋊C4—28no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—28no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—28no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—28no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—28no—
894C4⋊C4—48no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—44no—
901C4⋊C4—48no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—48no—
906C4⋊C4—48no—
907C4⋊C4—42no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—48no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—42no—
915C4⋊C4—44no—
916C4⋊C4—42no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—48no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C42—28no—
940C42—28no—
941C42—22no—
942C42—22no—
943C42—22no—
944C42—28no—
945C42—28no—
946C42—28no—
947C42—22no—
948C42—22no—
949C42—22no—
950C42—22no—
951C42—22no—
952C42—22no—
953C42—28no—
954C42—22no—
955C42—22no—
956C42—22no—
957C42—22no—
958C42—22no—
959C42—22no—
960C42—28no—
961C42—41no—
962C42—41no—
963C42—41no—
964C42—41no—
965C42—41no—
966C42—41no—
967C42—44no—
968C42—48no—
969C42—44no—
970C42—48no—
971C42—48no—
972C42C2×#4114yes—
973C42C2×#4114yes—
974C42C2×#4114yes—
975C42C2×#4114yes—
976C42H(5,𝔽2)14yes—
977C422−1+414yes—
978C422−1+414yes—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23C22×#4112yes—
993C23C2611yescharacteristic
994Q8—48no—
995Q8—48no—
996Q8—48no—
997Q8—48no—
998Q8—48no—
999Q8—88no—
1000D4—48no—
1001D4—48no—
1002D4—84no—
1003D4—88no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—28no—
1023C2×C4—28no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—21no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—21no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—44no—
1064C2×C4—44no—
1065C2×C4—44no—
1066C2×C4—44no—
1067C2×C4—416no—
1068C2×C4—44no—
1069C2×C4—168no—
1070C2×C4C22×#4112yes—
1071C2×C4C22×#4112yes—
1072C2×C4C22×#4112yes—
1073C2×C4C22×#4112yes—
1074C2×C4C22×#4112yes—
1075C2×C4C22×#4112yes—
1076C2×C4C2×H(5,𝔽2)12yes—
1077C2×C4C2×H(5,𝔽2)12yes—
1078C2×C4C2×H(5,𝔽2)12yes—
1079C2×C4C2×2−1+412yes—
1080C2×C4C2×2−1+412yes—
1081C2×C4C2×2−1+412yes—
1082C2×C4C2×2−1+412yes—
1083C2×C4C2×2−1+412yes—
1084C2×C4C2×2−1+412yes—
1085C2×C4#58512yes—
1086C2×C4#58512yes—
1087C2×C4#58512yes—
1088C22—22no—
1089C22—22no—
1090C22—22no—
1091C22—41no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—44no—
1096C22—44no—
1097C22—44no—
1098C22—44no—
1099C22—44no—
1100C22—44no—
1101C22—44no—
1102C22C23×#4111yescharacteristic
1103C22C22×H(5,𝔽2)11yescharacteristic
1104C22C22×2−1+411yescharacteristic
1105C22C22×2−1+411yescharacteristic
1106C22C2×#58511yescharacteristic
1107C22C2×#58511yescharacteristic
1108C22C2×#58511yescharacteristic
1109C4—22no—
1110C4—22no—
1111C4—22no—
1112C4—22no—
1113C4—22no—
1114C4—22no—
1115C4—22no—
1116C4—22no—
1117C4—22no—
1118C4—41no—
1119C4—44no—
1120C4—44no—
1121C4—44no—
1122C4—41no—
1123C4—44no—
1124C4—44no—
1125C4—44no—
1126C4—44no—
1127C4—44no—
1128C4—44no—
1129C4—44no—
1130C4—44no—
1131C4#350714yes—
1132C4#351114yes—
1133C4#354714yes—
1134C2—42no—
1135C2—84no—
1136C2C2×#354711yescharacteristic
1137C2#6276111yescharacteristic
1138C2C2×#350711yescharacteristic
1139C2C2×#351111yescharacteristic
1140C2#6281511yescharacteristic
1141C2#6283011yescharacteristic
1142C2#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. #59870C2semidirect
2. #59863C2semidirect
3. #59828C2semidirect
4. #59827C2semidirect
5. #59429C2semidirect
6. #59427C2semidirect
7. #45802C2semidirect
8. #45512C2semidirect
9. #40023C2semidirect
10. #40005C2semidirect
11. #39731C2semidirect
13. #39724C2semidirect
14. #39547C2semidirect
15. #39513C2semidirect
16. #39497C2semidirect
17. #37633C2semidirect
18. #37143C2semidirect
19. #36645C2semidirect
21. #36538C2semidirect
22. #36449C2semidirect
23. #36315C2semidirect
24. #36285C2semidirect
25. #35117C2semidirect
26. #34383C2semidirect
27. C4×#533C2semidirect

Maximal subgroups

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

subgroupindex
#598702
#598632
#598282
#598272
#594292
#594272
#458022
#455122
#400232
#400052
#397312
#397262
#397242
#395472
#395132
#394972
#376332
#371432
#366452
#366312
#365382
#364492
#363152
#362852
#351172
#343832
C4×#5332