Finite Group Databasebeta

← #7711953

Subgroups — #7711953

Order 512.

4692 conjugacy classes of subgroups.

The subgroup lattice has 1149 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59642C212yesmaximal, complemented
2#59639C212yesmaximal, complemented
3#59428C212yesmaximal, complemented
4#59427C212yesmaximal, complemented
5#46163C214yesmaximal, complemented
6#46025C214yesmaximal, complemented
7#39771C212yesmaximal, complemented
8#39761C212yesmaximal, complemented
9#39731C214yesmaximal, complemented
10#39719C214yesmaximal, complemented
11#39643C212yesmaximal, complemented
12#39633C212yesmaximal, complemented
13#39563C214yesmaximal, complemented
14#39561C214yesmaximal, complemented
15#37641C211yesmaximal, characteristic, complemented
16#37640C211yesmaximal, characteristic
17#37326C214yesmaximal, complemented
18#36645C211yesmaximal, characteristic, complemented
19#36639C211yesmaximal, characteristic
20#36312C212yesmaximal, complemented
21#36299C212yesmaximal, complemented
22#36286C212yesmaximal, complemented
23#36271C212yesmaximal, complemented
24#35299C214yesmaximal, complemented
25#34374C211yesmaximal, characteristic, complemented
26#34368C211yesmaximal, characteristic
27C4×#533C211yesmaximal, characteristic, complemented
28C2×#556C2214yes—
29C2×#533C2211yescharacteristic
30C2×#533C2211yescharacteristic
31C2×#533C2212yes—
32C2×#532C2211yescharacteristic
33#2868C2211yescharacteristic
34#2868C2211yescharacteristic
35#2863C2214yes—
36#2862C2211yescharacteristic
37#2862C2211yescharacteristic
38#2862C2212yes—
39#2861C2212yes—
40#2861C2212yes—
41#2860C2214yes—
42#2859C2212yes—
43#2859C2211yescharacteristic
44#2859C2211yescharacteristic
45#2858C2211yescharacteristic
46#2858C2211yescharacteristic
47#2857C2212yes—
48#2857C2212yes—
49#2857C2212yes—
50#2857C2212yes—
51#2850C2212yes—
52#2850C2212yes—
53#2850C2212yes—
54#2850C2212yes—
55#2822C2214yes—
56#2820C2214yes—
57#2807C2218yes—
58#2799C2218yes—
59#2798C2218yes—
60#2796C2218yes—
61#2793C2218yes—
62#2790C2218yes—
63#2786C2218yes—
64#2783C2218yes—
65#2755C2218yes—
66#2751C2218yes—
67#2750C2218yes—
68#2729C2218yes—
69#2728C2218yes—
70#2723C2218yes—
71#2716C2218yes—
72#2689C2218yes—
73#2647C2214yes—
74#2640C2214yes—
75#2625C2214yes—
76#2625C2214yes—
77#2624C2214yes—
78#2621C2214yes—
79#2620C2214yes—
80#2616C2214yes—
81#2605C2218yes—
82#2601C2218yes—
83#2596C2218yes—
84#2592C2214yes—
85#2592C2214yes—
86#2589C2218yes—
87#2588C2218yes—
88#2582C2212yes—
89#2582C2212yes—
90#2582C2214yes—
91#2581C2214yes—
92#2580C2214yes—
93#2578C2218yes—
94#2570C2214yes—
95#2568C2212yes—
96#2568C2212yes—
97#2568C2214yes—
98#2567C2212yes—
99#2560C2218yes—
100#2560C2218yes—
101#2548C2212yes—
102#2547C2212yes—
103#2546C2212yes—
104#2546C2212yes—
105#2545C2214yes—
106#2542C2212yes—
107#2538C2212yes—
108#2538C2212yes—
109#2532C2218yes—
110#2531C2218yes—
111#2529C2218yes—
112#2519C2218yes—
113#2515C2218yes—
114#2513C2214yes—
115#2512C2214yes—
116#2511C2214yes—
117#2511C2214yes—
118#2509C2214yes—
119#2508C2214yes—
120#2502C2214yes—
121#2499C2214yes—
122#2497C2214yes—
123#2496C2214yes—
124#2496C2214yes—
125#2495C2214yes—
126#2492C2214yes—
127#2492C2214yes—
128#2478C2218yes—
129#2477C2218yes—
130#2475C2218yes—
131#2452C2214yes—
132#2451C2214yes—
133#2448C2214yes—
134#2447C2214yes—
135#2447C2214yes—
136#2446C2214yes—
137#2440C2214yes—
138#2439C2214yes—
139#2423C2214yes—
140#2421C2214yes—
141#2382C2214yes—
142#2379C2214yes—
143#2369C2212yes—
144#2367C2214yes—
145#2366C2212yes—
146#2365C2212yes—
147#2365C2212yes—
148#2362C2214yes—
149#2360C2214yes—
150#2356C2214yes—
151#2355C2212yes—
152#2355C2214yes—
153#2355C2212yes—
154#2354C2212yes—
155#2354C2212yes—
156Q8×C4⋊C4C2212yes—
157Q8×C4⋊C4C2212yes—
158D4×C4⋊C4C2212yes—
159D4×C4⋊C4C2212yes—
160#2346C2214yes—
161#2344C2214yes—
162#2331C2214yes—
163#2326C2214yes—
164#2324C2214yes—
165#2324C2214yes—
166#2323C2214yes—
167#2323C2214yes—
168#2314C2214yes—
169#2311C2214yes—
170C4×C4⋊Q8C2211yescharacteristic
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2211yescharacteristic
178C4×#125C2212yes—
179C4×#125C2212yes—
180C4×#124C2212yes—
181C4×#124C2212yes—
182C4×#124C2212yes—
183C4×#124C2212yes—
184C4×C22⋊Q8C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2212yes—
188#2297C2212yes—
189#2297C2212yes—
190#2296C2212yes—
191#2295C2212yes—
192#2295C2212yes—
193#2295C2214yes—
194#2293C2214yes—
195#2285C2211yescharacteristic
196#2285C2211yescharacteristic
197#2285C2212yes—
198#2285C2211yescharacteristic
199C42×Q8C2212yes—
200C42×Q8C2212yes—
201C4×#117C2212yes—
202C2×C43C2211yescharacteristic
203C22×#41C2312yes—
204#556—416no—
205#533—28no—
206#533—28no—
207#533—48no—
208#532—28no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2314yes—
219C2×C4⋊Q8C2312yes—
220C2×C4⋊Q8C2312yes—
221C2×#127C2311yescharacteristic
222C2×#126C2318yes—
223C2×#126C2318yes—
224C2×#125C2312yes—
225C2×#125C2312yes—
226C2×#125C2312yes—
227C2×#125C2312yes—
228C2×#124C2312yes—
229C2×#124C2312yes—
230C2×#124C2312yes—
231C2×#124C2312yes—
232C2×#124C2314yes—
233C2×#124C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2318yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×#121C2312yes—
244C2×#121C2312yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2314yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×#117C2312yes—
262C2×#117C2312yes—
263C2×#117C2314yes—
264C2×#117C2312yes—
265C2×#117C2312yes—
266C2×#117C2312yes—
267C2×#117C2318yes—
268C22×C4⋊C4C2314yes—
269C22×C42C2311yescharacteristic
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#399C2318yes—
286#399C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#395C2318yes—
309#395C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#393C2318yes—
314#393C2318yes—
315#393C2318yes—
316#391C2314yes—
317#391C2318yes—
318#391C2312yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2312yes—
323#391C2312yes—
324#391C2312yes—
325#391C2318yes—
326#391C2314yes—
327#391C2312yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2314yes—
335#391C2314yes—
336#391C2318yes—
337#391C2312yes—
338#391C2312yes—
339#391C2312yes—
340#391C2312yes—
341#391C2312yes—
342#391C2318yes—
343#391C2312yes—
344#391C2312yes—
345#390C2312yes—
346#390C2318yes—
347#390C2314yes—
348#390C2314yes—
349#390C2312yes—
350#390C2314yes—
351#390C2314yes—
352#390C2312yes—
353#390C2312yes—
354#390C2312yes—
355#390C2312yes—
356#390C2312yes—
357#390C2312yes—
358#390C2314yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2314yes—
365#389C2314yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2314yes—
375#389C2314yes—
376#389C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2318yes—
384#389C2314yes—
385#389C2318yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2318yes—
391#389C2314yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2314yes—
403#388C2318yes—
404#388C2318yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2318yes—
413#388C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
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#386C2314yes—
435#386C2318yes—
436#386C2318yes—
437#386C2314yes—
438#386C2314yes—
439#386C2314yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2318yes—
445#385C2318yes—
446#385C2314yes—
447#385C2314yes—
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#384C2312yes—
451#384C2312yes—
452#384C2312yes—
453#384C2312yes—
454#384C2314yes—
455#384C2314yes—
456#384C2311yescharacteristic
457#384C2311yescharacteristic
458#384C2311yescharacteristic
459#384C2311yescharacteristic
460#384C2312yes—
461#384C2312yes—
462#383C2318yes—
463#382C2312yes—
464#382C2312yes—
465#382C2312yes—
466#382C2314yes—
467#382C2318yes—
468#382C2314yes—
469#382C2312yes—
470#382C2312yes—
471#382C2312yes—
472#382C2312yes—
473#382C2312yes—
474#382C2312yes—
475#381C2318yes—
476#380C2312yes—
477#380C2312yes—
478#380C2314yes—
479#380C2314yes—
480#380C2312yes—
481#380C2314yes—
482#380C2312yes—
483#380C2312yes—
484#380C2312yes—
485#380C2314yes—
486#380C2314yes—
487#380C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2318yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2314yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2318yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2314yes—
524#376C2314yes—
525#376C2318yes—
526C43C2311yescharacteristic
527C43C2311yescharacteristic
528C43C2311yescharacteristic
529C43C2311yescharacteristic
530C43C2311yescharacteristic
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2314yes—
534C43C2311yescharacteristic
535C2×#41—28no—
536C2×#41—44no—
537C2×#41—44no—
538C22×Q8C2412yes—
539C22×Q8C2412yes—
540C22×Q8C2412yes—
541C22×Q8C2412yes—
542C22×Q8C2414yes—
543C22×Q8C2414yes—
544C22×Q8C2412yes—
545C22×D4C2412yes—
546C22×D4C2412yes—
547C22×D4C2414yes—
548C22×D4C2412yes—
549C23×C4C2414yes—
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2411yescharacteristic
553C23×C4C2411yescharacteristic
554C23×C4C2411yescharacteristic
555C23×C4C2411yescharacteristic
556C23×C4C2411yescharacteristic
557C23×C4C2418yes—
558C4⋊Q8—24no—
559C4⋊Q8—24no—
560C4⋊Q8—24no—
561C4⋊Q8—24no—
562C4⋊Q8—24no—
563C4⋊Q8—28no—
564C4⋊Q8—44no—
565C4⋊Q8—44no—
566C4⋊Q8—44no—
567C4⋊Q8—44no—
568C4⋊Q8—44no—
569C4⋊Q8—48no—
570#127—24no—
571#126—416no—
572#126—416no—
573#125—28no—
574#125—28no—
575#125—44no—
576#125—44no—
577#124—28no—
578#124—28no—
579#124—28no—
580#124—28no—
581#124—44no—
582#124—48no—
583C22⋊Q8—28no—
584C22⋊Q8—28no—
585C22⋊Q8—28no—
586C22⋊Q8—28no—
587C22⋊Q8—416no—
588C22⋊Q8—48no—
589C22⋊Q8—48no—
590C22⋊Q8—48no—
591C22⋊Q8—48no—
592#121—28no—
593#121—28no—
594C4×Q8—28no—
595C4×Q8—28no—
596C4×Q8—28no—
597C4×Q8—28no—
598C4×Q8—216no—
599C4×Q8—28no—
600C4×Q8—28no—
601C4×Q8—48no—
602C4×Q8—44no—
603C4×Q8—44no—
604C4×Q8—48no—
605C4×Q8—48no—
606C4×D4—28no—
607C4×D4—28no—
608C4×D4—48no—
609C4×D4—48no—
610#117—28no—
611#117—28no—
612#117—44no—
613#117—44no—
614#117—44no—
615#117—416no—
616#117—48no—
617C2×C4⋊C4—48no—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊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⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C42—24no—
694C2×C42—24no—
695C2×C42—24no—
696C2×C42—42no—
697C2×C42—42no—
698C2×C42—42no—
699C2×C42#4118yes—
700C2×C42C2414yes—
701C2×C42C2414yes—
702C2×C42C2414yes—
703C2×C42C2414yes—
704C2×C42C2414yes—
705C2×C42C2414yes—
706C2×C42C2411yescharacteristic
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×C42C2411yescharacteristic
722C2×C42C2418yes—
723C2×C42C2418yes—
724C2×C42C2414yes—
725C2×C42C2414yes—
726C2×C42C2418yes—
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2418yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774#95C2418yes—
775#95C2418yes—
776#95C2418yes—
777#95C2418yes—
778#95C2418yes—
779#95C2418yes—
780C24C2514yes—
781C24C2511yescharacteristic
782#41—816no—
783C2×Q8—24no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—28no—
791C2×Q8—24no—
792C2×Q8—24no—
793C2×Q8—24no—
794C2×Q8—28no—
795C2×Q8—24no—
796C2×Q8—24no—
797C2×Q8—24no—
798C2×Q8—44no—
799C2×Q8—44no—
800C2×Q8—44no—
801C2×Q8—44no—
802C2×Q8—42no—
803C2×Q8—42no—
804C2×D4—28no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—42no—
813C2×D4—42no—
814C2×D4—44no—
815C2×D4—44no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—28no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—28no—
830C22×C4—28no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—41no—
836C22×C4—41no—
837C22×C4—48no—
838C22×C4—48no—
839C22×C4—48no—
840C22×C4C2×#4114yes—
841C22×C4C2×#4114yes—
842C22×C4C2×#4114yes—
843C22×C4C2511yescharacteristic
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2514yes—
847C22×C4C2514yes—
848C22×C4C2514yes—
849C22×C4C2514yes—
850C22×C4C2514yes—
851C22×C4C2514yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2511yescharacteristic
855C22×C4C2514yes—
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C22×C4C2511yescharacteristic
862C22×C4C2511yescharacteristic
863C22×C4C2511yescharacteristic
864C22×C4C2511yescharacteristic
865C22×C4C2511yescharacteristic
866C22×C4C2511yescharacteristic
867C22×C4C2511yescharacteristic
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—28no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—28no—
883C4⋊C4—24no—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—24no—
888C4⋊C4—28no—
889C4⋊C4—28no—
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—24no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—48no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—48no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—48no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—48no—
914C4⋊C4—44no—
915C4⋊C4—48no—
916C4⋊C4—48no—
917C4⋊C4—48no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C42—28no—
944C42—28no—
945C42—22no—
946C42—22no—
947C42—22no—
948C42—28no—
949C42—28no—
950C42—28no—
951C42—22no—
952C42—22no—
953C42—22no—
954C42—22no—
955C42—22no—
956C42—22no—
957C42—28no—
958C42—22no—
959C42—22no—
960C42—22no—
961C42—22no—
962C42—22no—
963C42—22no—
964C42—28no—
965C42—41no—
966C42—41no—
967C42—41no—
968C42—41no—
969C42—41no—
970C42—41no—
971C42—48no—
972C42—48no—
973C42—44no—
974C42—44no—
975C42—48no—
976C42C2×#4114yes—
977C42C2×#4114yes—
978C42C2×#4114yes—
979C42C2×#4114yes—
980C42H(5,𝔽2)14yes—
981C422−1+414yes—
982C422−1+414yes—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23C22×#4112yes—
997C23C2611yescharacteristic
998Q8—48no—
999Q8—48no—
1000Q8—48no—
1001Q8—48no—
1002Q8—88no—
1003Q8—88no—
1004Q8—84no—
1005D4—48no—
1006D4—48no—
1007D4—84no—
1008D4—88no—
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—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—28no—
1028C2×C4—28no—
1029C2×C4—28no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—21no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—21no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
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—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—44no—
1070C2×C4—44no—
1071C2×C4—44no—
1072C2×C4—44no—
1073C2×C4—416no—
1074C2×C4—816no—
1075C2×C4C22×#4112yes—
1076C2×C4C22×#4112yes—
1077C2×C4C22×#4112yes—
1078C2×C4C22×#4112yes—
1079C2×C4C22×#4112yes—
1080C2×C4C22×#4112yes—
1081C2×C4C2×H(5,𝔽2)12yes—
1082C2×C4C2×H(5,𝔽2)12yes—
1083C2×C4C2×H(5,𝔽2)12yes—
1084C2×C4C2×2−1+412yes—
1085C2×C4C2×2−1+412yes—
1086C2×C4C2×2−1+412yes—
1087C2×C4C2×2−1+412yes—
1088C2×C4C2×2−1+412yes—
1089C2×C4C2×2−1+412yes—
1090C2×C4#58512yes—
1091C2×C4#58512yes—
1092C2×C4#58512yes—
1093C22—22no—
1094C22—22no—
1095C22—22no—
1096C22—41no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22—44no—
1101C22—44no—
1102C22—44no—
1103C22—44no—
1104C22—44no—
1105C22—44no—
1106C22—44no—
1107C22C23×#4111yescharacteristic
1108C22C22×H(5,𝔽2)11yescharacteristic
1109C22C22×2−1+411yescharacteristic
1110C22C22×2−1+411yescharacteristic
1111C22C2×#58511yescharacteristic
1112C22C2×#58511yescharacteristic
1113C22C2×#58511yescharacteristic
1114C4—22no—
1115C4—22no—
1116C4—22no—
1117C4—22no—
1118C4—22no—
1119C4—22no—
1120C4—22no—
1121C4—22no—
1122C4—22no—
1123C4—41no—
1124C4—44no—
1125C4—44no—
1126C4—44no—
1127C4—44no—
1128C4—41no—
1129C4—44no—
1130C4—44no—
1131C4—44no—
1132C4—44no—
1133C4—44no—
1134C4—44no—
1135C4—44no—
1136C4#350714yes—
1137C4#351014yes—
1138C4#351114yes—
1139C2—42no—
1140C2—84no—
1141C2#6275911yescharacteristic
1142C2#6276111yescharacteristic
1143C2C2×#350711yescharacteristic
1144C2C2×#351111yescharacteristic
1145C2C2×#351011yescharacteristic
1146C2#6283511yescharacteristic
1147C2#6283711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59642C2semidirect
2. #59639C2semidirect
3. #59428C2semidirect
4. #59427C2semidirect
5. #46163C2semidirect
6. #46025C2semidirect
7. #39771C2semidirect
8. #39761C2semidirect
9. #39731C2semidirect
10. #39719C2semidirect
11. #39643C2semidirect
12. #39633C2semidirect
13. #39563C2semidirect
14. #39561C2semidirect
15. #37641C2semidirect
17. #37326C2semidirect
18. #36645C2semidirect
20. #36312C2semidirect
21. #36299C2semidirect
22. #36286C2semidirect
23. #36271C2semidirect
24. #35299C2semidirect
25. #34374C2semidirect
27. C4×#533C2semidirect

Maximal subgroups

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

subgroupindex
#596422
#596392
#594282
#594272
#461632
#460252
#397712
#397612
#397312
#397192
#396432
#396332
#395632
#395612
#376412
#376402
#373262
#366452
#366392
#363122
#362992
#362862
#362712
#352992
#343742
#343682
C4×#5332