Finite Group Databasebeta

← #7671752

Subgroups — #7671752

Order 512.

5046 conjugacy classes of subgroups.

The subgroup lattice has 1265 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59678C212yesmaximal, complemented
2#59456C212yesmaximal, complemented
3#59431C214yesmaximal, complemented
4#59306C214yesmaximal, complemented
5#59079C212yesmaximal, complemented
6#59065C212yesmaximal, complemented
7#40004C214yesmaximal, complemented
8#40000C214yesmaximal, complemented
9#39561C214yesmaximal, complemented
10#39478C212yesmaximal, complemented
11#39468C212yesmaximal
12#36645C211yesmaximal, characteristic, complemented
13#36534C212yesmaximal, complemented
14#36449C212yesmaximal, complemented
15#36315C212yesmaximal, complemented
16#36286C212yesmaximal, complemented
17#36209C212yesmaximal, complemented
18#36194C211yesmaximal, characteristic, complemented
19#36189C212yesmaximal, complemented
20#36188C211yesmaximal, characteristic, complemented
21#36188C211yesmaximal, characteristic, complemented
22#36180C211yesmaximal, characteristic, complemented
23#35596C214yesmaximal, complemented
24#35297C212yesmaximal, complemented
25#35184C212yesmaximal, complemented
26#34322C212yesmaximal, complemented
27#34188C212yesmaximal, complemented
28C4×#533C211yesmaximal, characteristic, complemented
29C4×#532C211yesmaximal, characteristic
30C2×#556C2212yes—
31C2×#556C2212yes—
32C2×#554C2212yes—
33C2×#533C2211yescharacteristic
34C2×#533C2212yes—
35C2×#532C2211yescharacteristic
36C2×C4×#41C2212yes—
37#2868C2211yescharacteristic
38#2868C2211yescharacteristic
39#2863C2214yes—
40#2862C2212yes—
41#2861C2214yes—
42#2859C2212yes—
43#2859C2212yes—
44#2857C2212yes—
45#2857C2212yes—
46#2857C2212yes—
47#2857C2212yes—
48#2857C2212yes—
49#2857C2212yes—
50#2857C2212yes—
51#2857C2212yes—
52#2796C2218yes—
53#2767C2218yes—
54#2755C2218yes—
55#2747C2218yes—
56#2728C2218yes—
57#2723C2218yes—
58#2715C2218yes—
59#2691C2218yes—
60#2654C2218yes—
61#2625C2214yes—
62#2616C2214yes—
63#2605C2218yes—
64#2597C2218yes—
65#2588C2218yes—
66#2585C2218yes—
67#2584C2214yes—
68#2581C2214yes—
69#2578C2218yes—
70#2571C2212yes—
71#2570C2214yes—
72#2568C2212yes—
73#2568C2212yes—
74#2567C2212yes—
75#2565C2214yes—
76#2563C2212yes—
77#2562C2214yes—
78#2560C2218yes—
79#2560C2218yes—
80#2552C2212yes—
81#2552C2212yes—
82#2547C2212yes—
83#2547C2212yes—
84#2547C2212yes—
85#2547C2212yes—
86#2544C2214yes—
87#2538C2212yes—
88#2536C2214yes—
89#2536C2214yes—
90#2531C2218yes—
91#2530C2218yes—
92#2529C2218yes—
93#2525C2218yes—
94#2511C2214yes—
95#2511C2214yes—
96#2508C2214yes—
97#2508C2214yes—
98#2507C2214yes—
99#2502C2214yes—
100#2499C2214yes—
101#2499C2214yes—
102#2497C2214yes—
103#2497C2214yes—
104#2496C2214yes—
105#2496C2214yes—
106#2496C2214yes—
107#2496C2214yes—
108#2495C2214yes—
109#2495C2214yes—
110#2492C2214yes—
111#2489C2214yes—
112#2489C2214yes—
113#2489C2214yes—
114#2487C2214yes—
115#2485C2214yes—
116#2485C2214yes—
117#2485C2214yes—
118#2485C2214yes—
119#2469C2218yes—
120#2453C2214yes—
121#2451C2214yes—
122#2448C2214yes—
123#2442C2214yes—
124#2441C2214yes—
125#2440C2214yes—
126#2440C2214yes—
127#2439C2214yes—
128#2427C2214yes—
129#2426C2214yes—
130#2423C2214yes—
131#2421C2218yes—
132#2421C2214yes—
133#2417C2214yes—
134#2415C2214yes—
135#2415C2214yes—
136#2373C2218yes—
137#2369C2212yes—
138#2367C2214yes—
139#2365C2212yes—
140#2365C2212yes—
141#2365C2212yes—
142#2365C2212yes—
143#2360C2214yes—
144#2356C2214yes—
145#2355C2212yes—
146#2355C2214yes—
147#2355C2214yes—
148#2354C2212yes—
149#2354C2214yes—
150#2354C2214yes—
151#2352C2214yes—
152#2352C2214yes—
153#2352C2214yes—
154#2352C2214yes—
155#2352C2214yes—
156#2351C2214yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2212yes—
159#2346C2214yes—
160#2346C2214yes—
161#2345C2214yes—
162#2334C2218yes—
163#2323C2214yes—
164#2323C2214yes—
165#2314C2214yes—
166#2314C2214yes—
167#2311C2214yes—
168C4×C4⋊Q8C2212yes—
169C4×C4⋊Q8C2212yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2211yescharacteristic
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2211yescharacteristic
178C4×#127C2211yescharacteristic
179C4×#127C2211yescharacteristic
180C4×#125C2212yes—
181C4×#125C2212yes—
182C4×#124C2214yes—
183C4×#124C2212yes—
184C4×#124C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189C4×#121C2212yes—
190C4×#121C2211yescharacteristic
191C4×#121C2212yes—
192C4×#121C2211yescharacteristic
193C4×#121C2211yescharacteristic
194C4×#121C2211yescharacteristic
195#2297C2212yes—
196#2296C2212yes—
197#2295C2212yes—
198#2295C2214yes—
199#2295C2212yes—
200#2293C2212yes—
201#2293C2211yescharacteristic
202#2293C2211yescharacteristic
203#2285C2212yes—
204#2285C2212yes—
205#2285C2211yescharacteristic
206#2285C2212yes—
207#2285C2212yes—
208#2285C2212yes—
209#2285C2211yescharacteristic
210C2×#384C2212yes—
211#2274C2214yes—
212C42×Q8C2212yes—
213C42×Q8C2212yes—
214C42×D4C2211yescharacteristic
215C42×D4C2211yescharacteristic
216C42×D4C2212yes—
217C4×#117C2212yes—
218C2×C43C2211yescharacteristic
219C22×#41C2312yes—
220#556—216no—
221#556—48no—
222#554—48no—
223#533—28no—
224#533—48no—
225#532—28no—
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235C2×#127C2311yescharacteristic
236C2×#126C2318yes—
237C2×#126C2318yes—
238C2×#125C2312yes—
239C2×#125C2314yes—
240C2×#125C2314yes—
241C2×#124C2314yes—
242C2×#124C2312yes—
243C2×#124C2314yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2312yes—
247C2×C22⋊Q8C2318yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2314yes—
253C2×#121C2311yescharacteristic
254C2×#121C2311yescharacteristic
255C2×#121C2312yes—
256C4×#41—216no—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2314yes—
265C2×C4×Q8C2314yes—
266C2×C4×Q8C2314yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2314yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2311yescharacteristic
275C2×C4×D4C2311yescharacteristic
276C2×C4×D4C2312yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2311yescharacteristic
282C2×C4×D4C2312yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2311yescharacteristic
285C2×#117C2314yes—
286C2×#117C2312yes—
287C2×#117C2312yes—
288C2×#117C2312yes—
289C2×#117C2312yes—
290C2×#117C2314yes—
291C2×#117C2312yes—
292C2×#117C2314yes—
293C2×#117C2314yes—
294C22×C4⋊C4C2314yes—
295C22×C4⋊C4C2314yes—
296C22×C4⋊C4C2314yes—
297C22×C42C2312yes—
298C22×C42C2312yes—
299C22×C42C2311yescharacteristic
300C22×C42C2311yescharacteristic
301C22×C42C2311yescharacteristic
302C22×C42C2311yescharacteristic
303C22×C42C2311yescharacteristic
304C22×C42C2311yescharacteristic
305C22×C42C2311yescharacteristic
306#400C2318yes—
307#400C2318yes—
308#400C2318yes—
309#400C2318yes—
310#400C2318yes—
311#400C2318yes—
312#400C2318yes—
313#400C2318yes—
314#399C2318yes—
315#398C2318yes—
316#398C2318yes—
317#398C2318yes—
318#398C2318yes—
319#398C2318yes—
320#398C2318yes—
321#397C2318yes—
322#397C2318yes—
323#397C2318yes—
324#397C2318yes—
325#397C2318yes—
326#397C2318yes—
327#397C2318yes—
328#397C2318yes—
329#396C2318yes—
330#396C2318yes—
331#395C2318yes—
332#395C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#393C2318yes—
338#391C2314yes—
339#391C2314yes—
340#391C2314yes—
341#391C2314yes—
342#391C2312yes—
343#391C2312yes—
344#391C2312yes—
345#391C2312yes—
346#391C2312yes—
347#391C2312yes—
348#391C2314yes—
349#391C2318yes—
350#391C2314yes—
351#391C2314yes—
352#391C2314yes—
353#391C2314yes—
354#391C2314yes—
355#391C2314yes—
356#391C2314yes—
357#391C2318yes—
358#390C2312yes—
359#390C2312yes—
360#390C2312yes—
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2312yes—
365#390C2311yescharacteristic
366#390C2314yes—
367#390C2318yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2312yes—
385#389C2312yes—
386#389C2311yescharacteristic
387#389C2312yes—
388#389C2312yes—
389#389C2311yescharacteristic
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2318yes—
397#389C2318yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2312yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2312yes—
420#388C2312yes—
421#388C2312yes—
422#388C2312yes—
423#388C2312yes—
424#388C2312yes—
425#388C2312yes—
426#387C2318yes—
427#387C2318yes—
428#387C2314yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#387C2318yes—
444#387C2318yes—
445#387C2318yes—
446#387C2318yes—
447#386C2318yes—
448#386C2318yes—
449#386C2318yes—
450#386C2312yes—
451#386C2312yes—
452#386C2312yes—
453#386C2312yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2314yes—
458#385C2314yes—
459#384C2311yescharacteristic
460#384C2311yescharacteristic
461#384C2311yescharacteristic
462#384C2311yescharacteristic
463#384C2312yes—
464#384C2312yes—
465#384C2312yes—
466#384C2312yes—
467#384C2314yes—
468#384C2314yes—
469#384C2312yes—
470#384C2312yes—
471#384C2312yes—
472#384C2312yes—
473#384C2314yes—
474#383C2318yes—
475#382C2312yes—
476#382C2314yes—
477#382C2314yes—
478#382C2314yes—
479#382C2314yes—
480#382C2314yes—
481#382C2314yes—
482#382C2318yes—
483#382C2318yes—
484#382C2312yes—
485#380C2314yes—
486#380C2314yes—
487#380C2314yes—
488#380C2314yes—
489#380C2314yes—
490#380C2314yes—
491#380C2312yes—
492#380C2314yes—
493#380C2314yes—
494#380C2314yes—
495#380C2314yes—
496#380C2314yes—
497#380C2314yes—
498#380C2318yes—
499#380C2314yes—
500#380C2314yes—
501#380C2314yes—
502#380C2312yes—
503#380C2314yes—
504#380C2314yes—
505#380C2314yes—
506#380C2311yescharacteristic
507#380C2311yescharacteristic
508#380C2312yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2314yes—
517C4×C4⋊C4C2314yes—
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2314yes—
520C4×C4⋊C4C2314yes—
521C4×C4⋊C4C2314yes—
522C4×C4⋊C4C2312yes—
523C4×C4⋊C4C2311yescharacteristic
524C4×C4⋊C4C2311yescharacteristic
525C4×C4⋊C4C2312yes—
526C4×C4⋊C4C2312yes—
527C4×C4⋊C4C2311yescharacteristic
528C4×C4⋊C4C2312yes—
529C4×C4⋊C4C2312yes—
530C4×C4⋊C4C2311yescharacteristic
531C4×C4⋊C4C2312yes—
532C4×C4⋊C4C2311yescharacteristic
533C4×C4⋊C4C2312yes—
534C4×C4⋊C4C2314yes—
535C4×C4⋊C4C2314yes—
536C4×C4⋊C4C2318yes—
537C4×C4⋊C4C2318yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2312yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2314yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2311yescharacteristic
546C4×C4⋊C4C2312yes—
547C4×C22⋊C4C2318yes—
548C4×C22⋊C4C2318yes—
549C4×C22⋊C4C2314yes—
550C4×C22⋊C4C2318yes—
551C4×C22⋊C4C2312yes—
552C4×C22⋊C4C2312yes—
553C4×C22⋊C4C2312yes—
554C4×C22⋊C4C2314yes—
555C4×C22⋊C4C2312yes—
556C4×C22⋊C4C2312yes—
557C4×C22⋊C4C2312yes—
558C4×C22⋊C4C2312yes—
559C4×C22⋊C4C2312yes—
560C4×C22⋊C4C2312yes—
561C4×C22⋊C4C2312yes—
562C4×C22⋊C4C2312yes—
563C4×C22⋊C4C2312yes—
564#376C2318yes—
565#376C2314yes—
566C43C2311yescharacteristic
567C43C2311yescharacteristic
568C43C2311yescharacteristic
569C43C2311yescharacteristic
570C43C2311yescharacteristic
571C43C2311yescharacteristic
572C43C2311yescharacteristic
573C43C2311yescharacteristic
574C43C2314yes—
575C2×#41—28no—
576C2×#41—28no—
577C2×#41—44no—
578C22×Q8C2412yes—
579C22×Q8C2412yes—
580C22×Q8C2414yes—
581C22×Q8C2412yes—
582C22×Q8C2414yes—
583C22×D4C2411yescharacteristic
584C22×D4C2412yes—
585C22×D4C2412yes—
586C22×D4C2412yes—
587C22×D4C2412yes—
588C22×D4C2411yescharacteristic
589C23×C4C2412yes—
590C23×C4C2412yes—
591C23×C4C2412yes—
592C23×C4C2412yes—
593C23×C4C2412yes—
594C23×C4C2411yescharacteristic
595C23×C4C2411yescharacteristic
596C23×C4C2411yescharacteristic
597C23×C4C2412yes—
598C23×C4C2411yescharacteristic
599C23×C4C2411yescharacteristic
600C23×C4C2411yescharacteristic
601C23×C4C2411yescharacteristic
602C23×C4C2418yes—
603C4⋊Q8—24no—
604C4⋊Q8—24no—
605C4⋊Q8—24no—
606C4⋊Q8—28no—
607C4⋊Q8—28no—
608C4⋊Q8—28no—
609C4⋊Q8—28no—
610C4⋊Q8—44no—
611C4⋊Q8—44no—
612#127—24no—
613#126—232no—
614#126—416no—
615#125—28no—
616#125—48no—
617#125—48no—
618#124—216no—
619#124—28no—
620#124—48no—
621C22⋊Q8—28no—
622C22⋊Q8—28no—
623C22⋊Q8—216no—
624C22⋊Q8—416no—
625C22⋊Q8—48no—
626C22⋊Q8—48no—
627C22⋊Q8—48no—
628C22⋊Q8—48no—
629C22⋊Q8—48no—
630#121—24no—
631#121—24no—
632#121—28no—
633C4×Q8—216no—
634C4×Q8—28no—
635C4×Q8—28no—
636C4×Q8—28no—
637C4×Q8—28no—
638C4×Q8—28no—
639C4×Q8—28no—
640C4×Q8—28no—
641C4×Q8—44no—
642C4×Q8—48no—
643C4×Q8—48no—
644C4×Q8—48no—
645C4×D4—28no—
646C4×D4—28no—
647C4×D4—28no—
648C4×D4—28no—
649C4×D4—28no—
650C4×D4—28no—
651C4×D4—28no—
652C4×D4—24no—
653C4×D4—24no—
654C4×D4—24no—
655C4×D4—28no—
656C4×D4—24no—
657C4×D4—24no—
658C4×D4—48no—
659C4×D4—44no—
660C4×D4#4118yes—
661#117—28no—
662#117—28no—
663#117—216no—
664#117—28no—
665#117—28no—
666#117—44no—
667#117—48no—
668#117—48no—
669#117—48no—
670C2×C4⋊C4—48no—
671C2×C4⋊C4—48no—
672C2×C4⋊C4—48no—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2412yes—
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2418yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2418yes—
713C2×C4⋊C4C2418yes—
714C2×C4⋊C4C2418yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2418yes—
717C2×C4⋊C4C2418yes—
718C2×C4⋊C4C2418yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2418yes—
721C2×C4⋊C4C2418yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C22⋊C4C2412yes—
726C2×C22⋊C4C2412yes—
727C2×C22⋊C4C2412yes—
728C2×C22⋊C4C2412yes—
729C2×C22⋊C4C2412yes—
730C2×C22⋊C4C2412yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2412yes—
734C2×C22⋊C4C2412yes—
735C2×C22⋊C4C2412yes—
736C2×C22⋊C4C2412yes—
737C2×C22⋊C4C2412yes—
738C2×C22⋊C4C2412yes—
739C2×C22⋊C4C2412yes—
740C2×C22⋊C4C2412yes—
741C2×C22⋊C4C2412yes—
742C2×C22⋊C4C2418yes—
743C2×C22⋊C4C2418yes—
744C2×C22⋊C4C2418yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2418yes—
747C2×C22⋊C4C2418yes—
748C2×C22⋊C4C2412yes—
749C2×C22⋊C4C2412yes—
750C2×C22⋊C4C2418yes—
751C2×C22⋊C4C2418yes—
752C2×C22⋊C4C2412yes—
753C2×C42—28no—
754C2×C42—28no—
755C2×C42—24no—
756C2×C42—24no—
757C2×C42—24no—
758C2×C42—24no—
759C2×C42—42no—
760C2×C42—42no—
761C2×C42#4118yes—
762C2×C42C2412yes—
763C2×C42C2412yes—
764C2×C42C2414yes—
765C2×C42C2418yes—
766C2×C42C2411yescharacteristic
767C2×C42C2411yescharacteristic
768C2×C42C2414yes—
769C2×C42C2412yes—
770C2×C42C2412yes—
771C2×C42C2412yes—
772C2×C42C2412yes—
773C2×C42C2411yescharacteristic
774C2×C42C2411yescharacteristic
775C2×C42C2414yes—
776C2×C42C2411yescharacteristic
777C2×C42C2414yes—
778C2×C42C2411yescharacteristic
779C2×C42C2411yescharacteristic
780C2×C42C2411yescharacteristic
781C2×C42C2411yescharacteristic
782C2×C42C2411yescharacteristic
783C2×C42C2411yescharacteristic
784C2×C42C2411yescharacteristic
785C2×C42C2411yescharacteristic
786C2×C42C2411yescharacteristic
787C2×C42C2411yescharacteristic
788C2×C42C2411yescharacteristic
789C2×C42C2418yes—
790C2×C42C2418yes—
791C2×C42C2414yes—
792C2×C42C2418yes—
793C2×C42C2414yes—
794C2×C42C2411yescharacteristic
795C2×C42C2411yescharacteristic
796C2×C42C2411yescharacteristic
797C2×C42C2411yescharacteristic
798C2×C42C2411yescharacteristic
799C2×C42C2411yescharacteristic
800C2×C42C2411yescharacteristic
801C2×C42C2411yescharacteristic
802C2×C42C2411yescharacteristic
803C2×C42C2411yescharacteristic
804C2×C42C2411yescharacteristic
805C2×C42C2411yescharacteristic
806#95C2412yes—
807#95C2414yes—
808#95C2418yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2418yes—
813#95C2418yes—
814#95C2414yes—
815#95C2412yes—
816#95C2412yes—
817#95C2412yes—
818#95C2412yes—
819#95C2412yes—
820#95C2412yes—
821#95C2412yes—
822#95C2412yes—
823#95C2412yes—
824#95C2412yes—
825#95C2412yes—
826#95C2418yes—
827#95C2418yes—
828#95C2418yes—
829#95C2418yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2418yes—
836#95C2418yes—
837#95C2418yes—
838#95C2418yes—
839#95C2418yes—
840#95C2418yes—
841#95C2418yes—
842#95C2418yes—
843#95C2418yes—
844#95C2418yes—
845#95C2418yes—
846C24C2512yes—
847C24C2512yes—
848C24C2511yescharacteristic
849#41—432no—
850C2×Q8—24no—
851C2×Q8—24no—
852C2×Q8—24no—
853C2×Q8—24no—
854C2×Q8—28no—
855C2×Q8—24no—
856C2×Q8—24no—
857C2×Q8—28no—
858C2×Q8—28no—
859C2×Q8—24no—
860C2×Q8—28no—
861C2×Q8—24no—
862C2×Q8—42no—
863C2×Q8—44no—
864C2×Q8—44no—
865C2×D4—24no—
866C2×D4—24no—
867C2×D4—24no—
868C2×D4—24no—
869C2×D4—24no—
870C2×D4—24no—
871C2×D4—22no—
872C2×D4—24no—
873C2×D4—22no—
874C2×D4—22no—
875C2×D4—22no—
876C2×D4—24no—
877C2×D4—22no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4C2×#4114yes—
883C22×C4—24no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—24no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—24no—
894C22×C4—24no—
895C22×C4—24no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—24no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—24no—
908C22×C4—24no—
909C22×C4—24no—
910C22×C4—24no—
911C22×C4—24no—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—41no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—48no—
919C22×C4—48no—
920C22×C4—48no—
921C22×C4C2×#4114yes—
922C22×C4C2×#4114yes—
923C22×C4C2×#4114yes—
924C22×C4C2×#4118yes—
925C22×C4C2512yes—
926C22×C4C2512yes—
927C22×C4C2512yes—
928C22×C4C2514yes—
929C22×C4C2511yescharacteristic
930C22×C4C2512yes—
931C22×C4C2514yes—
932C22×C4C2518yes—
933C22×C4C2514yes—
934C22×C4C2512yes—
935C22×C4C2514yes—
936C22×C4C2518yes—
937C22×C4C2511yescharacteristic
938C22×C4C2511yescharacteristic
939C22×C4C2511yescharacteristic
940C22×C4C2511yescharacteristic
941C22×C4C2512yes—
942C22×C4C2511yescharacteristic
943C22×C4C2511yescharacteristic
944C22×C4C2511yescharacteristic
945C22×C4C2511yescharacteristic
946C22×C4C2511yescharacteristic
947C22×C4C2511yescharacteristic
948C22×C4C2511yescharacteristic
949C22×C4C2511yescharacteristic
950C22×C4C2511yescharacteristic
951C4⋊C4—24no—
952C4⋊C4—24no—
953C4⋊C4—24no—
954C4⋊C4—24no—
955C4⋊C4—24no—
956C4⋊C4—24no—
957C4⋊C4—24no—
958C4⋊C4—28no—
959C4⋊C4—24no—
960C4⋊C4—24no—
961C4⋊C4—24no—
962C4⋊C4—22no—
963C4⋊C4—28no—
964C4⋊C4—28no—
965C4⋊C4—216no—
966C4⋊C4—24no—
967C4⋊C4—24no—
968C4⋊C4—28no—
969C4⋊C4—28no—
970C4⋊C4—24no—
971C4⋊C4—28no—
972C4⋊C4—28no—
973C4⋊C4—22no—
974C4⋊C4—22no—
975C4⋊C4—28no—
976C4⋊C4—28no—
977C4⋊C4—28no—
978C4⋊C4—24no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—24no—
982C4⋊C4—28no—
983C4⋊C4—28no—
984C4⋊C4—28no—
985C4⋊C4—24no—
986C4⋊C4—24no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—24no—
990C4⋊C4—48no—
991C4⋊C4—48no—
992C4⋊C4—48no—
993C4⋊C4—42no—
994C4⋊C4—44no—
995C4⋊C4—48no—
996C4⋊C4—48no—
997C4⋊C4—48no—
998C4⋊C4—48no—
999C4⋊C4—48no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4C2×#4114yes—
1003C22⋊C4—24no—
1004C22⋊C4—24no—
1005C22⋊C4—28no—
1006C22⋊C4—216no—
1007C22⋊C4—24no—
1008C22⋊C4—216no—
1009C22⋊C4—24no—
1010C22⋊C4—24no—
1011C22⋊C4—24no—
1012C22⋊C4—24no—
1013C22⋊C4—24no—
1014C22⋊C4—24no—
1015C22⋊C4—24no—
1016C22⋊C4—24no—
1017C22⋊C4—24no—
1018C22⋊C4—24no—
1019C22⋊C4—24no—
1020C22⋊C4—24no—
1021C22⋊C4—44no—
1022C22⋊C4—48no—
1023C22⋊C4—48no—
1024C22⋊C4—48no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—48no—
1028C22⋊C4—48no—
1029C22⋊C4—48no—
1030C22⋊C4C2×#4118yes—
1031C42—24no—
1032C42—24no—
1033C42—22no—
1034C42—24no—
1035C42—24no—
1036C42—24no—
1037C42—24no—
1038C42—22no—
1039C42—22no—
1040C42—28no—
1041C42—216no—
1042C42—28no—
1043C42—22no—
1044C42—22no—
1045C42—22no—
1046C42—28no—
1047C42—22no—
1048C42—22no—
1049C42—22no—
1050C42—22no—
1051C42—22no—
1052C42—22no—
1053C42—28no—
1054C42—22no—
1055C42—22no—
1056C42—22no—
1057C42—22no—
1058C42—41no—
1059C42—41no—
1060C42—41no—
1061C42—41no—
1062C42—44no—
1063C42—48no—
1064C42—48no—
1065C42—48no—
1066C42—44no—
1067C42C2×#4114yes—
1068C42C2×#4114yes—
1069C42C2×#4114yes—
1070C42C2×#4114yes—
1071C42C2×#4114yes—
1072C42H(5,𝔽2)14yes—
1073C422−1+414yes—
1074C422−1+414yes—
1075C23—22no—
1076C23—21no—
1077C23—22no—
1078C23—21no—
1079C23—22no—
1080C23—22no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—22no—
1085C23—22no—
1086C23—21no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23C22×#4114yes—
1095C23C22×#4112yes—
1096C23C2611yescharacteristic
1097Q8—48no—
1098Q8—48no—
1099Q8—48no—
1100Q8—416no—
1101Q8—88no—
1102D4—28no—
1103D4—48no—
1104D4—48no—
1105D4—48no—
1106D4—48no—
1107D4—44no—
1108C2×C4—21no—
1109C2×C4—22no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—22no—
1126C2×C4—216no—
1127C2×C4—28no—
1128C2×C4—28no—
1129C2×C4—28no—
1130C2×C4—24no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—28no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—22no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—28no—
1148C2×C4—28no—
1149C2×C4—22no—
1150C2×C4—21no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—28no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—28no—
1165C2×C4—24no—
1166C2×C4—28no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—44no—
1170C2×C4—44no—
1171C2×C4—44no—
1172C2×C4—48no—
1173C2×C4—48no—
1174C2×C4—48no—
1175C2×C4—48no—
1176C2×C4—48no—
1177C2×C4—44no—
1178C2×C4—168no—
1179C2×C4C22×#4112yes—
1180C2×C4C22×#4114yes—
1181C2×C4C22×#4112yes—
1182C2×C4C22×#4112yes—
1183C2×C4C22×#4112yes—
1184C2×C4C22×#4112yes—
1185C2×C4C22×#4112yes—
1186C2×C4C22×#4112yes—
1187C2×C4C22×#4112yes—
1188C2×C4C22×#4112yes—
1189C2×C4C2×H(5,𝔽2)12yes—
1190C2×C4C2×H(5,𝔽2)12yes—
1191C2×C4C2×H(5,𝔽2)12yes—
1192C2×C4C2×2−1+412yes—
1193C2×C4C2×2−1+412yes—
1194C2×C4C2×2−1+412yes—
1195C2×C4C2×2−1+412yes—
1196C2×C4C2×2−1+412yes—
1197C2×C4C2×2−1+412yes—
1198C2×C4#58512yes—
1199C2×C4#58512yes—
1200C22—22no—
1201C22—22no—
1202C22—24no—
1203C22—24no—
1204C22—22no—
1205C22—24no—
1206C22—42no—
1207C22—42no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—42no—
1212C22—41no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22C23×#4111yescharacteristic
1222C22C23×#4111yescharacteristic
1223C22C22×H(5,𝔽2)11yescharacteristic
1224C22C22×2−1+411yescharacteristic
1225C22C22×2−1+411yescharacteristic
1226C22C2×#58511yescharacteristic
1227C22C2×#58511yescharacteristic
1228C4—22no—
1229C4—22no—
1230C4—22no—
1231C4—22no—
1232C4—22no—
1233C4—22no—
1234C4—22no—
1235C4—22no—
1236C4—24no—
1237C4—42no—
1238C4—42no—
1239C4—42no—
1240C4—42no—
1241C4—41no—
1242C4—44no—
1243C4—48no—
1244C4—44no—
1245C4—41no—
1246C4—44no—
1247C4—48no—
1248C4—42no—
1249C4—44no—
1250C4#347514yes—
1251C4#350714yes—
1252C4#351114yes—
1253C4#351114yes—
1254C2—42no—
1255C2—44no—
1256C2—82no—
1257C2C2×#347511yescharacteristic
1258C2C2×#350711yescharacteristic
1259C2C2×#351111yescharacteristic
1260C2C2×#351111yescharacteristic
1261C2#6280511yescharacteristic
1262C2#6283611yescharacteristic
1263C2#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. #59678C2semidirect
2. #59456C2semidirect
3. #59431C2semidirect
4. #59306C2semidirect
5. #59079C2semidirect
6. #59065C2semidirect
7. #40004C2semidirect
8. #40000C2semidirect
9. #39561C2semidirect
10. #39478C2semidirect
12. #36645C2semidirect
13. #36534C2semidirect
14. #36449C2semidirect
15. #36315C2semidirect
16. #36286C2semidirect
17. #36209C2semidirect
18. #36194C2semidirect
19. #36189C2semidirect
20. #36188C2semidirect
21. #36188C2semidirect
22. #36180C2semidirect
23. #35596C2semidirect
24. #35297C2semidirect
25. #35184C2semidirect
26. #34322C2semidirect
27. #34188C2semidirect
28. C4×#533C2semidirect

Maximal subgroups

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

subgroupindex
#596782
#594562
#594312
#593062
#590792
#590652
#400042
#400002
#395612
#394782
#394682
#366452
#365342
#364492
#363152
#362862
#362092
#361942
#361892
#361882
#361802
#355962
#352972
#351842
#343222
#341882
C4×#5332
C4×#5322