Finite Group Databasebeta

← #7671758

Subgroups — #7671758

Order 512.

5548 conjugacy classes of subgroups.

The subgroup lattice has 1281 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59660C212yesmaximal, complemented
2#59503C214yesmaximal, complemented
3#59436C212yesmaximal, complemented
4#59278C214yesmaximal, complemented
5#59235C212yesmaximal, complemented
6#59220C212yesmaximal, complemented
7#40052C214yesmaximal, complemented
8#40048C214yesmaximal, complemented
9#39146C212yesmaximal, complemented
10#38908C212yesmaximal, complemented
11#38248C214yesmaximal, complemented
12#36645C211yesmaximal, characteristic, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36559C211yesmaximal, characteristic, complemented
15#36492C212yesmaximal, complemented
16#36453C212yesmaximal, complemented
17#36290C212yesmaximal, complemented
18#36275C212yesmaximal, complemented
19#36189C212yesmaximal, complemented
20#36180C211yesmaximal, characteristic, complemented
21#36149C212yesmaximal, complemented
22#36127C211yesmaximal, characteristic, complemented
23#35526C214yesmaximal, complemented
24#35291C212yesmaximal, complemented
25#35206C212yesmaximal, complemented
26#34308C212yesmaximal, complemented
27#34207C212yesmaximal, complemented
28C4×#532C211yesmaximal, characteristic, complemented
29C4×#529C211yesmaximal, characteristic, complemented
30C2×#554C2212yes—
31C2×#554C2212yes—
32C2×#547C2212yes—
33C2×#533C2212yes—
34C2×#532C2212yes—
35C2×#532C2211yescharacteristic
36C2×#529C2211yescharacteristic
37C2×#520C2214yes—
38C2×C4×#41C2212yes—
39#2868C2211yescharacteristic
40#2868C2211yescharacteristic
41#2862C2212yes—
42#2862C2212yes—
43#2859C2212yes—
44#2859C2212yes—
45#2859C2212yes—
46#2857C2212yes—
47#2857C2212yes—
48#2857C2212yes—
49#2857C2212yes—
50#2857C2212yes—
51#2857C2212yes—
52#2855C2214yes—
53#2851C2214yes—
54#2782C2218yes—
55#2770C2218yes—
56#2746C2218yes—
57#2745C2218yes—
58#2744C2218yes—
59#2728C2218yes—
60#2695C2218yes—
61#2693C2218yes—
62#2652C2218yes—
63#2645C2214yes—
64#2625C2214yes—
65#2609C2218yes—
66#2599C2218yes—
67#2598C2218yes—
68#2582C2212yes—
69#2576C2218yes—
70#2571C2212yes—
71#2570C2214yes—
72#2570C2214yes—
73#2568C2212yes—
74#2567C2212yes—
75#2566C2214yes—
76#2563C2212yes—
77#2562C2214yes—
78#2552C2212yes—
79#2552C2212yes—
80#2547C2212yes—
81#2538C2212yes—
82#2538C2212yes—
83#2537C2212yes—
84#2537C2212yes—
85#2536C2218yes—
86#2535C2214yes—
87#2535C2214yes—
88#2515C2218yes—
89#2514C2214yes—
90#2511C2214yes—
91#2511C2214yes—
92#2509C2214yes—
93#2508C2214yes—
94#2507C2214yes—
95#2505C2218yes—
96#2502C2214yes—
97#2497C2214yes—
98#2495C2214yes—
99#2495C2214yes—
100#2494C2214yes—
101#2494C2214yes—
102#2489C2214yes—
103#2489C2214yes—
104#2487C2214yes—
105#2487C2214yes—
106#2477C2218yes—
107#2473C2218yes—
108#2463C2218yes—
109#2460C2218yes—
110#2453C2214yes—
111#2452C2214yes—
112#2452C2214yes—
113#2449C2218yes—
114#2447C2214yes—
115#2447C2214yes—
116#2446C2214yes—
117#2442C2214yes—
118#2442C2214yes—
119#2442C2214yes—
120#2441C2214yes—
121#2440C2214yes—
122#2440C2214yes—
123#2438C2218yes—
124#2432C2214yes—
125#2427C2214yes—
126#2427C2214yes—
127#2427C2214yes—
128#2423C2214yes—
129#2422C2214yes—
130#2422C2214yes—
131#2421C2214yes—
132#2420C2214yes—
133#2420C2214yes—
134#2417C2214yes—
135#2417C2214yes—
136#2407C2214yes—
137#2407C2214yes—
138#2365C2212yes—
139#2361C2214yes—
140#2361C2214yes—
141#2361C2214yes—
142#2361C2214yes—
143#2361C2214yes—
144#2360C2214yes—
145#2359C2218yes—
146#2355C2212yes—
147#2355C2212yes—
148#2354C2214yes—
149#2354C2214yes—
150#2352C2214yes—
151#2349C2214yes—
152D4×C4⋊C4C2212yes—
153D4×C4⋊C4C2212yes—
154D4×C4⋊C4C2212yes—
155D4×C4⋊C4C2212yes—
156D4×C4⋊C4C2212yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2214yes—
159D4×C4⋊C4C2214yes—
160#2345C2214yes—
161#2344C2214yes—
162#2339C2214yes—
163#2339C2214yes—
164#2326C2214yes—
165#2326C2214yes—
166#2323C2214yes—
167#2322C2218yes—
168#2320C2214yes—
169#2311C2214yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2211yescharacteristic
177C4×#127C2211yescharacteristic
178C4×#127C2212yes—
179C4×#127C2211yescharacteristic
180C4×#125C2211yescharacteristic
181C4×#125C2211yescharacteristic
182C4×#126C2212yes—
183C4×#126C2212yes—
184C4×#124C2211yescharacteristic
185C4×#124C2212yes—
186C4×#124C2211yescharacteristic
187C4×#124C2212yes—
188C4×C22⋊Q8C2211yescharacteristic
189C4×C22⋊Q8C2211yescharacteristic
190C4×#123C2212yes—
191C4×#123C2212yes—
192C4×#121C2214yes—
193C4×#121C2211yescharacteristic
194C4×#121C2212yes—
195C4×#121C2212yes—
196C4×#121C2211yescharacteristic
197C4×#121C2212yes—
198C4×#121C2212yes—
199#2298C2212yes—
200#2297C2212yes—
201#2295C2211yescharacteristic
202#2293C2211yescharacteristic
203#2293C2212yes—
204#2293C2212yes—
205C2×#389C2214yes—
206#2290C2212yes—
207#2285C2212yes—
208#2285C2212yes—
209#2285C2211yescharacteristic
210C2×#384C2212yes—
211#2283C2211yescharacteristic
212C42×Q8C2211yescharacteristic
213C42×D4C2212yes—
214C42×D4C2211yescharacteristic
215C42×D4C2212yes—
216C42×D4C2212yes—
217C4×#117C2212yes—
218C2×C43C2211yescharacteristic
219C22×#41C2314yes—
220C22×#41C2312yes—
221#554—48no—
222#554—48no—
223#547—216no—
224#533—48no—
225#532—216no—
226#532—28no—
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×#127C2311yescharacteristic
235#529—28no—
236C2×#126C2312yes—
237C2×#125C2311yescharacteristic
238C2×#125C2314yes—
239C2×#125C2314yes—
240C2×#125C2314yes—
241C2×#124C2314yes—
242C2×#124C2311yescharacteristic
243C2×#124C2312yes—
244C2×#123C2318yes—
245C2×#123C2312yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2311yescharacteristic
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2318yes—
253C2×C22⋊Q8C2318yes—
254C2×#121C2314yes—
255C2×#121C2314yes—
256C2×#121C2314yes—
257C2×#121C2312yes—
258C2×#121C2311yescharacteristic
259C2×#121C2312yes—
260#520—416no—
261C4×#41—48no—
262C2×C4×Q8C2314yes—
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2314yes—
268C2×C4×Q8C2314yes—
269C2×C4×Q8C2312yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2311yescharacteristic
278C2×C4×D4C2312yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2311yescharacteristic
282C2×C4×D4C2314yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2318yes—
289C2×C4×D4C2318yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2311yescharacteristic
294C2×#117C2312yes—
295C2×#117C2312yes—
296C2×#117C2314yes—
297C2×#117C2318yes—
298C2×#117C2312yes—
299C2×#117C2314yes—
300C22×C4⋊C4C2314yes—
301C22×C4⋊C4C2314yes—
302C22×C4⋊C4C2318yes—
303C22×C4⋊C4C2314yes—
304C22×C4⋊C4C2314yes—
305C22×C4⋊C4C2314yes—
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309C22×C42C2312yes—
310C22×C42C2311yescharacteristic
311C22×C42C2311yescharacteristic
312C22×C42C2311yescharacteristic
313C22×C42C2314yes—
314C22×C42C2311yescharacteristic
315#401C2318yes—
316#400C2318yes—
317#400C2318yes—
318#400C2318yes—
319#400C2318yes—
320#400C2318yes—
321#400C2318yes—
322#400C2318yes—
323#400C2318yes—
324#399C2318yes—
325#398C2318yes—
326#398C2318yes—
327#398C2318yes—
328#398C2318yes—
329#398C2318yes—
330#398C2318yes—
331#397C2318yes—
332#397C2318yes—
333#397C2318yes—
334#397C2318yes—
335#397C2318yes—
336#397C2318yes—
337#396C2318yes—
338#396C2318yes—
339#396C2318yes—
340#395C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#393C2318yes—
346#392C2318yes—
347#391C2314yes—
348#391C2314yes—
349#391C2314yes—
350#391C2314yes—
351#391C2314yes—
352#391C2312yes—
353#391C2312yes—
354#391C2314yes—
355#391C2314yes—
356#391C2314yes—
357#391C2314yes—
358#391C2314yes—
359#391C2314yes—
360#391C2311yescharacteristic
361#391C2314yes—
362#391C2311yescharacteristic
363#390C2314yes—
364#390C2312yes—
365#390C2312yes—
366#390C2314yes—
367#390C2312yes—
368#390C2312yes—
369#390C2314yes—
370#390C2312yes—
371#390C2312yes—
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2312yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2318yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2318yes—
405#388C2312yes—
406#388C2312yes—
407#388C2312yes—
408#388C2312yes—
409#388C2312yes—
410#388C2312yes—
411#388C2318yes—
412#388C2318yes—
413#388C2312yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2314yes—
420#388C2314yes—
421#388C2312yes—
422#388C2314yes—
423#388C2314yes—
424#387C2312yes—
425#387C2312yes—
426#387C2312yes—
427#387C2312yes—
428#387C2312yes—
429#387C2312yes—
430#387C2312yes—
431#387C2312yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#386C2318yes—
443#386C2318yes—
444#386C2318yes—
445#386C2318yes—
446#386C2318yes—
447#386C2318yes—
448#386C2312yes—
449#386C2314yes—
450#386C2318yes—
451#386C2314yes—
452#386C2312yes—
453#385C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2318yes—
458#385C2318yes—
459#385C2318yes—
460#385C2318yes—
461#385C2318yes—
462#385C2318yes—
463#385C2318yes—
464#385C2318yes—
465#385C2318yes—
466#385C2312yes—
467#385C2312yes—
468#384C2311yescharacteristic
469#384C2311yescharacteristic
470#384C2312yes—
471#384C2312yes—
472#384C2312yes—
473#384C2312yes—
474#384C2312yes—
475#384C2314yes—
476#384C2312yes—
477#384C2314yes—
478#384C2312yes—
479#384C2312yes—
480#384C2314yes—
481#383C2312yes—
482#383C2318yes—
483#382C2311yescharacteristic
484#382C2311yescharacteristic
485#382C2314yes—
486#382C2314yes—
487#382C2312yes—
488#382C2314yes—
489#382C2314yes—
490#382C2318yes—
491#382C2314yes—
492#382C2314yes—
493#381C2318yes—
494#381C2318yes—
495#381C2312yes—
496#380C2311yescharacteristic
497#380C2314yes—
498#380C2314yes—
499#380C2314yes—
500#380C2314yes—
501#380C2318yes—
502#380C2318yes—
503#380C2314yes—
504#380C2314yes—
505#380C2314yes—
506#380C2314yes—
507#380C2318yes—
508#380C2314yes—
509#380C2314yes—
510#380C2314yes—
511#380C2314yes—
512#380C2318yes—
513#380C2312yes—
514#380C2311yescharacteristic
515#380C2312yes—
516C4×C4⋊C4C2312yes—
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2312yes—
519C4×C4⋊C4C2312yes—
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2312yes—
522C4×C4⋊C4C2311yescharacteristic
523C4×C4⋊C4C2311yescharacteristic
524C4×C4⋊C4C2311yescharacteristic
525C4×C4⋊C4C2312yes—
526C4×C4⋊C4C2311yescharacteristic
527C4×C4⋊C4C2312yes—
528C4×C4⋊C4C2314yes—
529C4×C4⋊C4C2314yes—
530C4×C4⋊C4C2314yes—
531C4×C4⋊C4C2314yes—
532C4×C4⋊C4C2314yes—
533C4×C4⋊C4C2312yes—
534C4×C4⋊C4C2314yes—
535C4×C4⋊C4C2314yes—
536C4×C4⋊C4C2312yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2312yes—
540C4×C4⋊C4C2311yescharacteristic
541C4×C4⋊C4C2312yes—
542C4×C4⋊C4C2312yes—
543C4×C4⋊C4C2312yes—
544C4×C4⋊C4C2311yescharacteristic
545C4×C22⋊C4C2312yes—
546C4×C22⋊C4C2312yes—
547C4×C22⋊C4C2312yes—
548C4×C22⋊C4C2312yes—
549C4×C22⋊C4C2312yes—
550C4×C22⋊C4C2312yes—
551C4×C22⋊C4C2314yes—
552C4×C22⋊C4C2318yes—
553C4×C22⋊C4C2314yes—
554C4×C22⋊C4C2312yes—
555C4×C22⋊C4C2312yes—
556C4×C22⋊C4C2314yes—
557C4×C22⋊C4C2314yes—
558C4×C22⋊C4C2312yes—
559C4×C22⋊C4C2312yes—
560C4×C22⋊C4C2312yes—
561C4×C22⋊C4C2312yes—
562C4×C22⋊C4C2314yes—
563C4×C22⋊C4C2312yes—
564C4×C22⋊C4C2314yes—
565#376C2312yes—
566#376C2312yes—
567C2×#95C2318yes—
568C43C2311yescharacteristic
569C43C2311yescharacteristic
570C43C2311yescharacteristic
571C43C2311yescharacteristic
572C43C2311yescharacteristic
573C43C2312yes—
574C43C2311yescharacteristic
575C43C2311yescharacteristic
576C43C2311yescharacteristic
577C2×#41—28no—
578C2×#41—216no—
579C2×#41—216no—
580C2×#41—28no—
581C2×#41—44no—
582C2×#41—48no—
583C22×Q8C2411yescharacteristic
584C22×Q8C2414yes—
585C22×Q8C2412yes—
586C22×Q8C2414yes—
587C22×D4C2412yes—
588C22×D4C2418yes—
589C22×D4C2414yes—
590C22×D4C2411yescharacteristic
591C22×D4C2412yes—
592C22×D4C2412yes—
593C22×D4C2412yes—
594C23×C4C2414yes—
595C23×C4C2412yes—
596C23×C4C2412yes—
597C23×C4C2411yescharacteristic
598C23×C4C2411yescharacteristic
599C23×C4C2411yescharacteristic
600C23×C4C2411yescharacteristic
601C23×C4C2418yes—
602C23×C4C2414yes—
603C23×C4C2411yescharacteristic
604C23×C4C2411yescharacteristic
605C23×C4C2412yes—
606C23×C4C2411yescharacteristic
607C23×C4C2414yes—
608C23×C4C2418yes—
609C23×C4C2418yes—
610C4⋊Q8—24no—
611C4⋊Q8—28no—
612C4⋊Q8—28no—
613C4⋊Q8—28no—
614C4⋊Q8—44no—
615C4⋊Q8—44no—
616C4⋊Q8—44no—
617#127#4118yes—
618#126—28no—
619#125—24no—
620#125—48no—
621#125—48no—
622#125—48no—
623#124—24no—
624#124—28no—
625#124—216no—
626#123—28no—
627#123—232no—
628C22⋊Q8—216no—
629C22⋊Q8—24no—
630C22⋊Q8—416no—
631C22⋊Q8—416no—
632C22⋊Q8—48no—
633C22⋊Q8—48no—
634C22⋊Q8—48no—
635C22⋊Q8—48no—
636#121—24no—
637#121—216no—
638#121—28no—
639#121—216no—
640#121—28no—
641#121—216no—
642C4×Q8—24no—
643C4×Q8—28no—
644C4×Q8—216no—
645C4×Q8—24no—
646C4×Q8—24no—
647C4×Q8—48no—
648C4×Q8—44no—
649C4×Q8—48no—
650C4×D4—216no—
651C4×D4—28no—
652C4×D4—216no—
653C4×D4—28no—
654C4×D4—28no—
655C4×D4—28no—
656C4×D4—28no—
657C4×D4—28no—
658C4×D4—28no—
659C4×D4—24no—
660C4×D4—28no—
661C4×D4—24no—
662C4×D4—416no—
663C4×D4—44no—
664C4×D4—48no—
665C4×D4—44no—
666C4×D4—48no—
667C4×D4—48no—
668C4×D4—48no—
669C4×D4—44no—
670C4×D4—48no—
671C4×D4—48no—
672C4×D4—416no—
673C4×D4#4118yescomplemented
674#117—28no—
675#117—28no—
676#117—48no—
677#117—48no—
678#117—416no—
679#117—44no—
680C2×C4⋊C4—216no—
681C2×C4⋊C4—48no—
682C2×C4⋊C4—416no—
683C2×C4⋊C4—48no—
684C2×C4⋊C4—48no—
685C2×C4⋊C4—48no—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2412yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2418yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2418yes—
720C2×C4⋊C4C2418yes—
721C2×C4⋊C4C2418yes—
722C2×C4⋊C4C2418yes—
723C2×C4⋊C4C2418yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2418yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2418yes—
731C2×C4⋊C4C2418yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2412yes—
736C2×C22⋊C4C2412yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2412yes—
739C2×C22⋊C4C2412yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2418yes—
743C2×C22⋊C4C2418yes—
744C2×C22⋊C4C2412yes—
745C2×C22⋊C4C2412yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2412yes—
748C2×C22⋊C4C2412yes—
749C2×C22⋊C4C2412yes—
750C2×C22⋊C4C2412yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2418yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2418yes—
756C2×C22⋊C4C2418yes—
757C2×C22⋊C4C2418yes—
758C2×C22⋊C4C2418yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2412yes—
761C2×C22⋊C4C2412yes—
762C2×C22⋊C4C2418yes—
763C2×C22⋊C4C2412yes—
764C2×C42—24no—
765C2×C42—24no—
766C2×C42—24no—
767C2×C42—28no—
768C2×C42—24no—
769C2×C42—24no—
770C2×C42—24no—
771C2×C42—48no—
772C2×C42—42no—
773C2×C42C2411yescharacteristic
774C2×C42C2418yes—
775C2×C42C2411yescharacteristic
776C2×C42C2412yes—
777C2×C42C2412yes—
778C2×C42C2412yes—
779C2×C42C2411yescharacteristic
780C2×C42C2412yes—
781C2×C42C2414yes—
782C2×C42C2411yescharacteristic
783C2×C42C2411yescharacteristic
784C2×C42C2411yescharacteristic
785C2×C42C2412yes—
786C2×C42C2412yes—
787C2×C42C2412yes—
788C2×C42C2411yescharacteristic
789C2×C42C2412yes—
790C2×C42C2411yescharacteristic
791C2×C42C2412yes—
792C2×C42C2411yescharacteristic
793C2×C42C2411yescharacteristic
794C2×C42C2411yescharacteristic
795C2×C42C2411yescharacteristic
796C2×C42C2411yescharacteristic
797C2×C42C2411yescharacteristic
798C2×C42C2411yescharacteristic
799C2×C42C2411yescharacteristic
800C2×C42C2411yescharacteristic
801C2×C42C2411yescharacteristic
802C2×C42C2411yescharacteristic
803C2×C42C2411yescharacteristic
804C2×C42C2411yescharacteristic
805C2×C42C2414yes—
806C2×C42C2418yes—
807C2×C42C2414yes—
808C2×C42C2411yescharacteristic
809C2×C42C2411yescharacteristic
810C2×C42C2411yescharacteristic
811C2×C42C2411yescharacteristic
812C2×C42C2411yescharacteristic
813C2×C42C2411yescharacteristic
814C2×C42C2411yescharacteristic
815#95C2412yes—
816#95C2418yes—
817#95C2418yes—
818#95C2418yes—
819#95C2412yes—
820#95C2412yes—
821#95C2412yes—
822#95C2412yes—
823#95C2412yes—
824#95C2412yes—
825#95C2412yes—
826#95C2412yes—
827#95C2412yes—
828#95C2414yes—
829#95C2414yes—
830#95C2412yes—
831#95C2412yes—
832#95C2412yes—
833#95C2414yes—
834#95C2412yes—
835#95C2412yes—
836#95C2412yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2412yes—
841#95C2418yes—
842#95C2412yes—
843#95C2412yes—
844#95C2412yes—
845#95C2418yes—
846#95C2418yes—
847#95C2418yes—
848#95C2418yes—
849#95C2418yes—
850#95C2418yes—
851#95C2418yes—
852#95C2418yes—
853#95C2418yes—
854#95C2418yes—
855#95C2418yes—
856#95C2418yes—
857C24C2514yes—
858C24C2512yes—
859C24C2511yescharacteristic
860#41—464no—
861#41—432no—
862C2×Q8—22no—
863C2×Q8—28no—
864C2×Q8—28no—
865C2×Q8—24no—
866C2×Q8—24no—
867C2×Q8—28no—
868C2×Q8—22no—
869C2×Q8—28no—
870C2×Q8—22no—
871C2×Q8—24no—
872C2×Q8—44no—
873C2×Q8—44no—
874C2×D4—24no—
875C2×D4—216no—
876C2×D4—28no—
877C2×D4—216no—
878C2×D4—24no—
879C2×D4—28no—
880C2×D4—24no—
881C2×D4—22no—
882C2×D4—24no—
883C2×D4—24no—
884C2×D4—22no—
885C2×D4—24no—
886C2×D4—24no—
887C2×D4—24no—
888C2×D4—44no—
889C2×D4—48no—
890C2×D4—42no—
891C2×D4C2×#4118yes—
892C2×D4C2×#4118yes—
893C2×D4C2×#4118yes—
894C2×D4C2×#4114yes—
895C22×C4—22no—
896C22×C4—24no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—24no—
901C22×C4—22no—
902C22×C4—216no—
903C22×C4—28no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—24no—
908C22×C4—22no—
909C22×C4—24no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—28no—
913C22×C4—216no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—28no—
919C22×C4—24no—
920C22×C4—22no—
921C22×C4—22no—
922C22×C4—28no—
923C22×C4—24no—
924C22×C4—24no—
925C22×C4—28no—
926C22×C4—22no—
927C22×C4—24no—
928C22×C4—28no—
929C22×C4—44no—
930C22×C4—41no—
931C22×C4—41no—
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×C4C2×#4118yes—
942C22×C42−1+414yes—
943C22×C4C2511yescharacteristic
944C22×C4C2511yescharacteristic
945C22×C4C2512yes—
946C22×C4C2512yes—
947C22×C4C2514yes—
948C22×C4C2512yes—
949C22×C4C2511yescharacteristic
950C22×C4C2512yes—
951C22×C4C2512yes—
952C22×C4C2514yes—
953C22×C4C2518yes—
954C22×C4C2512yes—
955C22×C4C2511yescharacteristic
956C22×C4C2514yes—
957C22×C4C2518yes—
958C22×C4C2511yescharacteristic
959C22×C4C2512yes—
960C22×C4C2511yescharacteristic
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C22×C4C2511yescharacteristic
964C22×C4C2511yescharacteristic
965C22×C4C2511yescharacteristic
966C22×C4C2511yescharacteristic
967C22×C4C2511yescharacteristic
968C22×C4C2511yescharacteristic
969C4⋊C4—28no—
970C4⋊C4—216no—
971C4⋊C4—24no—
972C4⋊C4—24no—
973C4⋊C4—24no—
974C4⋊C4—24no—
975C4⋊C4—28no—
976C4⋊C4—28no—
977C4⋊C4—24no—
978C4⋊C4—24no—
979C4⋊C4—22no—
980C4⋊C4—24no—
981C4⋊C4—28no—
982C4⋊C4—24no—
983C4⋊C4—22no—
984C4⋊C4—24no—
985C4⋊C4—24no—
986C4⋊C4—216no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—24no—
991C4⋊C4—24no—
992C4⋊C4—28no—
993C4⋊C4—22no—
994C4⋊C4—24no—
995C4⋊C4—24no—
996C4⋊C4—22no—
997C4⋊C4—24no—
998C4⋊C4—22no—
999C4⋊C4—24no—
1000C4⋊C4—24no—
1001C4⋊C4—28no—
1002C4⋊C4—48no—
1003C4⋊C4—48no—
1004C4⋊C4—48no—
1005C4⋊C4—48no—
1006C4⋊C4—48no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—42no—
1011C4⋊C4—48no—
1012C4⋊C4—44no—
1013C4⋊C4—48no—
1014C4⋊C4—48no—
1015C4⋊C4—44no—
1016C4⋊C4C2×#4114yes—
1017C22⋊C4—24no—
1018C22⋊C4—24no—
1019C22⋊C4—28no—
1020C22⋊C4—28no—
1021C22⋊C4—216no—
1022C22⋊C4—216no—
1023C22⋊C4—24no—
1024C22⋊C4—216no—
1025C22⋊C4—24no—
1026C22⋊C4—24no—
1027C22⋊C4—28no—
1028C22⋊C4—24no—
1029C22⋊C4—24no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—24no—
1033C22⋊C4—24no—
1034C22⋊C4—24no—
1035C22⋊C4—28no—
1036C22⋊C4—44no—
1037C22⋊C4—48no—
1038C22⋊C4—44no—
1039C22⋊C4—48no—
1040C22⋊C4—44no—
1041C22⋊C4—48no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—48no—
1045C22⋊C4—48no—
1046C22⋊C4C2×#4118yes—
1047C42—22no—
1048C42—22no—
1049C42—22no—
1050C42—24no—
1051C42—24no—
1052C42—24no—
1053C42—22no—
1054C42—22no—
1055C42—22no—
1056C42—24no—
1057C42—22no—
1058C42—22no—
1059C42—22no—
1060C42—22no—
1061C42—22no—
1062C42—22no—
1063C42—28no—
1064C42—24no—
1065C42—216no—
1066C42—24no—
1067C42—22no—
1068C42—22no—
1069C42—22no—
1070C42—22no—
1071C42—22no—
1072C42—22no—
1073C42—22no—
1074C42—24no—
1075C42—24no—
1076C42—22no—
1077C42—22no—
1078C42—24no—
1079C42—41no—
1080C42—41no—
1081C42—44no—
1082C42—44no—
1083C42—48no—
1084C42C2×#4114yes—
1085C42C2×#4114yes—
1086C42H(5,𝔽2)14yes—
1087C42H(5,𝔽2)14yes—
1088C422−1+414yes—
1089C23—21no—
1090C23—24no—
1091C23—21no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—24no—
1096C23—24no—
1097C23—21no—
1098C23—21no—
1099C23—24no—
1100C23—22no—
1101C23—22no—
1102C23—21no—
1103C23—24no—
1104C23—24no—
1105C23—21no—
1106C23—22no—
1107C23C22×#4114yes—
1108C23C22×#4118yes—
1109C23C2×2−1+412yes—
1110C23C2611yescharacteristic
1111Q8—416no—
1112Q8—44no—
1113Q8—48no—
1114Q8—88no—
1115D4—216no—
1116D4—28no—
1117D4—216no—
1118D4—216no—
1119D4—48no—
1120D4—416no—
1121D4—432no—
1122C2×C4—28no—
1123C2×C4—21no—
1124C2×C4—22no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—22no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—216no—
1138C2×C4—28no—
1139C2×C4—22no—
1140C2×C4—21no—
1141C2×C4—22no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—28no—
1151C2×C4—28no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—28no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—28no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—22no—
1165C2×C4—28no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—21no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—21no—
1181C2×C4—24no—
1182C2×C4—28no—
1183C2×C4—22no—
1184C2×C4—44no—
1185C2×C4—44no—
1186C2×C4—416no—
1187C2×C4—432no—
1188C2×C4—44no—
1189C2×C4—44no—
1190C2×C4—416no—
1191C2×C4—44no—
1192C2×C4—48no—
1193C2×C4—48no—
1194C2×C4—88no—
1195C2×C4—168no—
1196C2×C4—168no—
1197C2×C4C22×#4112yes—
1198C2×C4C22×#4114yes—
1199C2×C4C22×#4112yes—
1200C2×C4C22×#4112yes—
1201C2×C4C22×#4112yes—
1202C2×C4C22×#4112yes—
1203C2×C4C22×#4112yes—
1204C2×C4C2×H(5,𝔽2)12yes—
1205C2×C4C2×H(5,𝔽2)12yes—
1206C2×C4C2×H(5,𝔽2)12yes—
1207C2×C4C2×H(5,𝔽2)12yes—
1208C2×C4C2×H(5,𝔽2)12yes—
1209C2×C4C2×H(5,𝔽2)12yes—
1210C2×C4C2×2−1+412yes—
1211C2×C4C2×2−1+412yes—
1212C2×C4C2×2−1+412yes—
1213C2×C4C2×2−1+412yes—
1214C2×C4C2×2−1+412yes—
1215C2×C4#58512yes—
1216C22—22no—
1217C22—28no—
1218C22—28no—
1219C22—24no—
1220C22—22no—
1221C22—24no—
1222C22—22no—
1223C22—24no—
1224C22—28no—
1225C22—42no—
1226C22—42no—
1227C22—41no—
1228C22—41no—
1229C22—44no—
1230C22—44no—
1231C22—42no—
1232C22—44no—
1233C22—41no—
1234C22—44no—
1235C22—42no—
1236C22—41no—
1237C22C23×#4111yescharacteristic
1238C22C23×#4111yescharacteristic
1239C22C22×H(5,𝔽2)11yescharacteristic
1240C22C22×H(5,𝔽2)11yescharacteristic
1241C22C22×2−1+411yescharacteristic
1242C22C22×2−1+411yescharacteristic
1243C22C2×#58511yescharacteristic
1244C4—22no—
1245C4—22no—
1246C4—22no—
1247C4—22no—
1248C4—22no—
1249C4—22no—
1250C4—24no—
1251C4—42no—
1252C4—44no—
1253C4—41no—
1254C4—42no—
1255C4—41no—
1256C4—44no—
1257C4—42no—
1258C4—41no—
1259C4—42no—
1260C4—42no—
1261C4—44no—
1262C4—42no—
1263C4—48no—
1264C4—41no—
1265C4—48no—
1266C4#348114yes—
1267C4#351114yes—
1268C4#351514yes—
1269C4#352014yes—
1270C2—42no—
1271C2—48no—
1272C2—44no—
1273C2C2×#348111yescharacteristic
1274C2C2×#352011yescharacteristic
1275C2C2×#351511yescharacteristic
1276C2C2×#351111yescharacteristic
1277C2#6280511yescharacteristic
1278C2#6283311yescharacteristic
1279C2#6283411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59660C2semidirect
2. #59503C2semidirect
3. #59436C2semidirect
4. #59278C2semidirect
5. #59235C2semidirect
6. #59220C2semidirect
7. #40052C2semidirect
8. #40048C2semidirect
9. #39146C2semidirect
10. #38908C2semidirect
11. #38248C2semidirect
12. #36645C2semidirect
13. #36598C2semidirect
14. #36559C2semidirect
15. #36492C2semidirect
16. #36453C2semidirect
17. #36290C2semidirect
18. #36275C2semidirect
19. #36189C2semidirect
20. #36180C2semidirect
21. #36149C2semidirect
22. #36127C2semidirect
23. #35526C2semidirect
24. #35291C2semidirect
25. #35206C2semidirect
26. #34308C2semidirect
27. #34207C2semidirect
28. C4×#532C2semidirect
29. C4×#529C2semidirect
673. C4×D4#41semidirect

Maximal subgroups

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

subgroupindex
#596602
#595032
#594362
#592782
#592352
#592202
#400522
#400482
#391462
#389082
#382482
#366452
#365982
#365592
#364922
#364532
#362902
#362752
#361892
#361802
#361492
#361272
#355262
#352912
#352062
#343082
#342072
C4×#5322
C4×#5292