Finite Group Databasebeta

← #7671757

Subgroups — #7671757

Order 512.

5526 conjugacy classes of subgroups.

The subgroup lattice has 1285 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59479C214yesmaximal, complemented
2#59450C212yesmaximal, complemented
3#59421C212yesmaximal, complemented
4#59275C214yesmaximal, complemented
5#59042C212yesmaximal, complemented
6#59040C212yesmaximal, complemented
7#40076C214yesmaximal, complemented
8#40072C214yesmaximal, complemented
9#39124C212yesmaximal, complemented
10#38930C212yesmaximal, complemented
11#38272C214yesmaximal, complemented
12#36645C211yesmaximal, characteristic, complemented
13#36598C211yesmaximal, characteristic, complemented
14Q8×#127C211yesmaximal, characteristic, complemented
15#36504C212yesmaximal, complemented
16#36454C212yesmaximal, complemented
17#36303C212yesmaximal, complemented
18#36274C212yesmaximal, complemented
19#36194C212yesmaximal, complemented
20#36188C211yesmaximal, characteristic, complemented
21#36149C212yesmaximal, complemented
22#36127C211yesmaximal, characteristic, complemented
23#35553C214yesmaximal, complemented
24#35283C212yesmaximal, complemented
25#35196C212yesmaximal, complemented
26#34334C212yesmaximal, complemented
27#34226C212yesmaximal, complemented
28C4×#532C211yesmaximal, characteristic, complemented
29C4×#529C211yesmaximal, characteristic, complemented
30C2×#556C2212yes—
31C2×D4×Q8C2212yes—
32C2×D4×Q8C2212yes—
33C2×D4×Q8C2212yes—
34C2×#547C2212yes—
35C2×#533C2212yes—
36C2×#532C2212yes—
37C2×#532C2211yescharacteristic
38C2×#529C2211yescharacteristic
39C2×C4×#41C2212yes—
40#2868C2211yescharacteristic
41#2868C2211yescharacteristic
42#2868C2212yes—
43#2862C2212yes—
44#2862C2212yes—
45#2859C2212yes—
46#2859C2212yes—
47#2857C2212yes—
48#2857C2212yes—
49#2857C2212yes—
50#2857C2212yes—
51#2857C2212yes—
52#2857C2212yes—
53#2855C2214yes—
54#2850C2214yes—
55#2771C2218yes—
56#2743C2218yes—
57#2738C2218yes—
58#2723C2218yes—
59#2702C2218yes—
60#2696C2218yes—
61#2694C2218yes—
62#2690C2218yes—
63#2649C2218yes—
64#2647C2214yes—
65#2628C2214yes—
66#2582C2212yes—
67#2575C2218yes—
68#2575C2218yes—
69#2571C2212yes—
70#2571C2214yes—
71#2570C2214yes—
72#2568C2212yes—
73#2568C2212yes—
74#2563C2214yes—
75#2560C2218yes—
76#2547C2212yes—
77#2547C2212yes—
78#2547C2212yes—
79#2542C2212yes—
80#2542C2212yes—
81#2542C2214yes—
82#2542C2212yes—
83#2542C2214yes—
84#2542C2214yes—
85#2540C2214yes—
86#2538C2214yes—
87#2537C2212yes—
88#2537C2212yes—
89#2536C2214yes—
90#2535C2214yes—
91#2517C2218yes—
92#2516C2218yes—
93#2511C2214yes—
94#2511C2214yes—
95#2511C2214yes—
96#2503C2214yes—
97#2499C2214yes—
98#2497C2214yes—
99#2497C2214yes—
100#2496C2214yes—
101#2496C2214yes—
102#2492C2214yes—
103#2492C2214yes—
104#2492C2214yes—
105#2492C2214yes—
106#2489C2214yes—
107#2488C2218yes—
108#2488C2218yes—
109#2479C2218yes—
110#2477C2218yes—
111#2471C2218yes—
112#2467C2218yes—
113#2451C2214yes—
114#2451C2214yes—
115#2450C2218yes—
116#2447C2214yes—
117#2447C2214yes—
118#2446C2214yes—
119#2439C2214yes—
120#2439C2214yes—
121#2438C2218yes—
122#2436C2214yes—
123#2432C2214yes—
124#2427C2214yes—
125#2427C2214yes—
126#2426C2214yes—
127#2423C2214yes—
128#2423C2214yes—
129#2422C2214yes—
130#2422C2214yes—
131#2421C2214yes—
132#2421C2214yes—
133#2420C2214yes—
134#2420C2214yes—
135#2417C2214yes—
136#2409C2214yes—
137#2407C2214yes—
138#2407C2214yes—
139#2369C2214yes—
140#2368C2218yes—
141#2367C2214yes—
142#2367C2214yes—
143#2365C2212yes—
144#2365C2212yes—
145#2365C2212yes—
146#2363C2214yes—
147#2363C2214yes—
148#2360C2214yes—
149#2357C2214yes—
150#2355C2212yes—
151#2355C2212yes—
152#2355C2214yes—
153#2354C2214yes—
154#2349C2214yes—
155#2349C2214yes—
156D4×C4⋊C4C2212yes—
157D4×C4⋊C4C2212yes—
158#2341C2214yes—
159Q8×C22⋊C4C2214yes—
160#2339C2214yes—
161#2339C2214yes—
162#2339C2214yes—
163#2331C2214yes—
164#2329C2218yes—
165#2324C2214yes—
166#2324C2214yes—
167#2319C2214yes—
168#2314C2214yes—
169C4×C4⋊Q8C2212yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2211yescharacteristic
176C4×#127C2211yescharacteristic
177C4×#127C2212yes—
178C4×#127C2211yescharacteristic
179C4×#125C2211yescharacteristic
180C4×#125C2211yescharacteristic
181C4×#126C2212yes—
182C4×#126C2212yes—
183C4×#124C2211yescharacteristic
184C4×#124C2212yes—
185C4×#124C2212yes—
186C4×#124C2211yescharacteristic
187C4×C22⋊Q8C2214yes—
188C4×C22⋊Q8C2211yescharacteristic
189C4×C22⋊Q8C2211yescharacteristic
190C4×#123C2212yes—
191C4×#123C2212yes—
192C4×#121C2212yes—
193C4×#121C2212yes—
194C4×#121C2211yescharacteristic
195C4×#121C2211yescharacteristic
196C4×#121C2212yes—
197C4×#121C2212yes—
198#2298C2212yes—
199#2297C2212yes—
200#2295C2211yescharacteristic
201C2×#391C2214yes—
202#2293C2212yes—
203#2293C2211yescharacteristic
204#2293C2212yes—
205#2290C2212yes—
206#2285C2212yes—
207#2285C2212yes—
208#2285C2212yes—
209#2285C2211yescharacteristic
210#2283C2211yescharacteristic
211#2275C2214yes—
212C42×Q8C2211yescharacteristic
213C42×D4C2212yes—
214C42×D4C2211yescharacteristic
215C42×D4C2212yes—
216C42×D4C2212yes—
217C4×#117C2212yes—
218C2×C43C2211yescharacteristic
219C22×#41C2312yes—
220C22×#41C2314yes—
221C23×Q8C2314yes—
222#556—48no—
223D4×Q8—216no—
224D4×Q8—48no—
225D4×Q8—48no—
226#547—48no—
227#533—48no—
228#532—28no—
229#532—216no—
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2314yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2314yes—
240C2×#127C2311yescharacteristic
241#529—28no—
242C2×#126C2312yes—
243C2×#126C2318yes—
244C2×#125C2311yescharacteristic
245C2×#125C2314yes—
246C2×#124C2314yes—
247C2×#124C2311yescharacteristic
248C2×#124C2312yes—
249C2×#124C2314yes—
250C2×#123C2312yes—
251C2×#123C2318yes—
252C2×C22⋊Q8C2318yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2311yescharacteristic
255C2×C22⋊Q8C2318yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2318yes—
263C2×#121C2314yes—
264C2×#121C2314yes—
265C2×#121C2312yes—
266C2×#121C2311yescharacteristic
267C2×#121C2312yes—
268C2×#121C2314yes—
269C4×#41—48no—
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2314yes—
274C2×C4×Q8C2314yes—
275C2×C4×Q8C2314yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2314yes—
278C2×C4×Q8C2311yescharacteristic
279C2×C4×D4C2312yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2311yescharacteristic
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2312yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2312yes—
300C2×#117C2312yes—
301C2×#117C2312yes—
302C2×#117C2312yes—
303C2×#117C2314yes—
304C2×#117C2314yes—
305C2×#117C2314yes—
306C22×C4⋊C4C2314yes—
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309C22×C42C2311yescharacteristic
310C22×C42C2312yes—
311C22×C42C2311yescharacteristic
312C22×C42C2311yescharacteristic
313C22×C42C2311yescharacteristic
314C22×C42C2314yes—
315C22×C42C2311yescharacteristic
316#400C2318yes—
317#400C2318yes—
318#400C2318yes—
319#400C2318yes—
320#400C2318yes—
321#400C2318yes—
322#400C2318yes—
323#400C2318yes—
324#399C2318yes—
325#399C2318yes—
326#399C2318yes—
327#399C2318yes—
328#398C2318yes—
329#398C2318yes—
330#398C2318yes—
331#397C2318yes—
332#397C2318yes—
333#397C2318yes—
334#397C2318yes—
335#397C2318yes—
336#397C2318yes—
337#396C2318yes—
338#396C2318yes—
339#395C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#393C2318yes—
345#393C2318yes—
346#393C2318yes—
347#392C2318yes—
348#391C2318yes—
349#391C2314yes—
350#391C2314yes—
351#391C2314yes—
352#391C2314yes—
353#391C2314yes—
354#391C2312yes—
355#391C2312yes—
356#391C2314yes—
357#391C2314yes—
358#391C2314yes—
359#391C2314yes—
360#391C2314yes—
361#391C2314yes—
362#391C2318yes—
363#391C2318yes—
364#391C2311yescharacteristic
365#391C2314yes—
366#391C2314yes—
367#391C2314yes—
368#391C2318yes—
369#391C2311yescharacteristic
370#390C2318yes—
371#390C2312yes—
372#390C2314yes—
373#390C2312yes—
374#390C2314yes—
375#390C2312yes—
376#390C2314yes—
377#390C2312yes—
378#390C2312yes—
379#390C2312yes—
380#390C2318yes—
381#390C2318yes—
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2312yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2312yes—
400#389C2312yes—
401#389C2312yes—
402#389C2314yes—
403#389C2318yes—
404#389C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#388C2312yes—
409#388C2312yes—
410#388C2312yes—
411#388C2312yes—
412#388C2312yes—
413#388C2312yes—
414#388C2314yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2314yes—
424#388C2312yes—
425#388C2314yes—
426#388C2314yes—
427#388C2312yes—
428#387C2312yes—
429#387C2312yes—
430#387C2312yes—
431#387C2312yes—
432#387C2312yes—
433#387C2312yes—
434#387C2318yes—
435#387C2312yes—
436#387C2312yes—
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#386C2318yes—
451#386C2318yes—
452#386C2318yes—
453#386C2314yes—
454#386C2312yes—
455#386C2312yes—
456#386C2314yes—
457#385C2318yes—
458#385C2318yes—
459#385C2318yes—
460#385C2318yes—
461#385C2318yes—
462#385C2318yes—
463#385C2312yes—
464#385C2312yes—
465#384C2311yescharacteristic
466#384C2311yescharacteristic
467#384C2312yes—
468#384C2312yes—
469#384C2312yes—
470#384C2312yes—
471#384C2314yes—
472#384C2312yes—
473#384C2314yes—
474#384C2312yes—
475#384C2312yes—
476#384C2312yes—
477#384C2314yes—
478#383C2312yes—
479#382C2311yescharacteristic
480#382C2311yescharacteristic
481#382C2318yes—
482#382C2314yes—
483#382C2314yes—
484#382C2314yes—
485#382C2314yes—
486#382C2312yes—
487#382C2314yes—
488#382C2314yes—
489#381C2318yes—
490#381C2318yes—
491#381C2318yes—
492#381C2312yes—
493#380C2312yes—
494#380C2314yes—
495#380C2314yes—
496#380C2314yes—
497#380C2314yes—
498#380C2318yes—
499#380C2318yes—
500#380C2314yes—
501#380C2314yes—
502#380C2314yes—
503#380C2314yes—
504#380C2314yes—
505#380C2314yes—
506#380C2314yes—
507#380C2314yes—
508#380C2311yescharacteristic
509#380C2312yes—
510#380C2311yescharacteristic
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2312yes—
516C4×C4⋊C4C2312yes—
517C4×C4⋊C4C2314yes—
518C4×C4⋊C4C2311yescharacteristic
519C4×C4⋊C4C2311yescharacteristic
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2311yescharacteristic
522C4×C4⋊C4C2311yescharacteristic
523C4×C4⋊C4C2312yes—
524C4×C4⋊C4C2314yes—
525C4×C4⋊C4C2314yes—
526C4×C4⋊C4C2314yes—
527C4×C4⋊C4C2314yes—
528C4×C4⋊C4C2312yes—
529C4×C4⋊C4C2312yes—
530C4×C4⋊C4C2314yes—
531C4×C4⋊C4C2312yes—
532C4×C4⋊C4C2312yes—
533C4×C4⋊C4C2312yes—
534C4×C4⋊C4C2311yescharacteristic
535C4×C4⋊C4C2314yes—
536C4×C4⋊C4C2318yes—
537C4×C4⋊C4C2311yescharacteristic
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2312yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2312yes—
543C4×C22⋊C4C2312yes—
544C4×C22⋊C4C2312yes—
545C4×C22⋊C4C2312yes—
546C4×C22⋊C4C2312yes—
547C4×C22⋊C4C2312yes—
548C4×C22⋊C4C2312yes—
549C4×C22⋊C4C2318yes—
550C4×C22⋊C4C2314yes—
551C4×C22⋊C4C2318yes—
552C4×C22⋊C4C2314yes—
553C4×C22⋊C4C2318yes—
554C4×C22⋊C4C2312yes—
555C4×C22⋊C4C2312yes—
556C4×C22⋊C4C2314yes—
557C4×C22⋊C4C2312yes—
558C4×C22⋊C4C2314yes—
559C4×C22⋊C4C2312yes—
560C4×C22⋊C4C2312yes—
561C4×C22⋊C4C2314yes—
562C4×C22⋊C4C2312yes—
563C4×C22⋊C4C2312yes—
564C4×C22⋊C4C2314yes—
565#376C2312yes—
566#376C2312yes—
567C2×#95C2318yes—
568C2×#95C2318yes—
569C43C2311yescharacteristic
570C43C2311yescharacteristic
571C43C2311yescharacteristic
572C43C2311yescharacteristic
573C43C2311yescharacteristic
574C43C2312yes—
575C43C2311yescharacteristic
576C43C2311yescharacteristic
577C43C2311yescharacteristic
578C2×#41—28no—
579C2×#41—216no—
580C2×#41—28no—
581C2×#41—44no—
582C2×#41—48no—
583C2×#41—48no—
584C22×Q8—216no—
585C22×Q8—48no—
586C22×Q8—48no—
587C22×Q8C2414yes—
588C22×Q8C2414yes—
589C22×Q8C2412yes—
590C22×Q8C2411yescharacteristic
591C22×Q8C2418yes—
592C22×D4C2411yescharacteristic
593C22×D4C2412yes—
594C22×D4C2414yes—
595C22×D4C2412yes—
596C22×D4C2412yes—
597C22×D4C2412yes—
598C22×D4C2418yes—
599C23×C4C2414yes—
600C23×C4C2411yescharacteristic
601C23×C4C2412yes—
602C23×C4C2412yes—
603C23×C4C2411yescharacteristic
604C23×C4C2411yescharacteristic
605C23×C4C2411yescharacteristic
606C23×C4C2412yes—
607C23×C4C2414yes—
608C23×C4C2411yescharacteristic
609C23×C4C2411yescharacteristic
610C23×C4C2411yescharacteristic
611C23×C4C2418yes—
612C23×C4C2414yes—
613C23×C4C2418yes—
614C4⋊Q8—24no—
615C4⋊Q8—28no—
616C4⋊Q8—28no—
617C4⋊Q8—216no—
618C4⋊Q8—28no—
619C4⋊Q8—28no—
620C4⋊Q8—28no—
621C4⋊Q8—48no—
622C4⋊Q8—48no—
623C4⋊Q8—44no—
624#127#4118yes—
625#126—28no—
626#126—416no—
627#125—24no—
628#125—48no—
629#124—24no—
630#124—28no—
631#124—216no—
632#124—48no—
633#123—28no—
634#123—416no—
635C22⋊Q8—24no—
636C22⋊Q8—216no—
637C22⋊Q8—232no—
638C22⋊Q8—416no—
639C22⋊Q8—416no—
640C22⋊Q8—48no—
641C22⋊Q8—48no—
642C22⋊Q8—48no—
643C22⋊Q8—48no—
644C22⋊Q8—48no—
645C22⋊Q8—48no—
646#121—28no—
647#121—28no—
648#121—216no—
649#121—216no—
650#121—24no—
651#121—48no—
652C4×Q8—28no—
653C4×Q8—24no—
654C4×Q8—24no—
655C4×Q8—48no—
656C4×Q8—44no—
657C4×Q8—48no—
658C4×Q8—48no—
659C4×Q8—48no—
660C4×Q8#4118yescomplemented
661C4×D4—28no—
662C4×D4—28no—
663C4×D4—216no—
664C4×D4—216no—
665C4×D4—28no—
666C4×D4—24no—
667C4×D4—28no—
668C4×D4—28no—
669C4×D4—216no—
670C4×D4—28no—
671C4×D4—24no—
672C4×D4—28no—
673C4×D4—24no—
674C4×D4—28no—
675C4×D4—44no—
676C4×D4—44no—
677C4×D4—48no—
678C4×D4—48no—
679C4×D4—44no—
680C4×D4—48no—
681C4×D4—48no—
682#117—28no—
683#117—28no—
684#117—48no—
685#117—44no—
686#117—48no—
687#117—48no—
688C2×C4⋊C4—48no—
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2412yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2418yes—
722C2×C4⋊C4C2418yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2418yes—
726C2×C4⋊C4C2418yes—
727C2×C4⋊C4C2418yes—
728C2×C4⋊C4C2418yes—
729C2×C4⋊C4C2418yes—
730C2×C4⋊C4C2418yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2412yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2412yes—
737C2×C22⋊C4C2412yes—
738C2×C22⋊C4C2412yes—
739C2×C22⋊C4C2412yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2418yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2418yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2418yes—
747C2×C22⋊C4C2412yes—
748C2×C22⋊C4C2412yes—
749C2×C22⋊C4C2412yes—
750C2×C22⋊C4C2412yes—
751C2×C22⋊C4C2412yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2412yes—
754C2×C22⋊C4C2412yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2418yes—
758C2×C22⋊C4C2418yes—
759C2×C22⋊C4C2418yes—
760C2×C22⋊C4C2418yes—
761C2×C22⋊C4C2412yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2412yes—
764C2×C22⋊C4C2418yes—
765C2×C22⋊C4C2418yes—
766C2×C42—24no—
767C2×C42—24no—
768C2×C42—24no—
769C2×C42—28no—
770C2×C42—24no—
771C2×C42—24no—
772C2×C42—24no—
773C2×C42—48no—
774C2×C42—42no—
775C2×C42C2411yescharacteristic
776C2×C42C2411yescharacteristic
777C2×C42C2412yes—
778C2×C42C2411yescharacteristic
779C2×C42C2412yes—
780C2×C42C2412yes—
781C2×C42C2411yescharacteristic
782C2×C42C2411yescharacteristic
783C2×C42C2411yescharacteristic
784C2×C42C2412yes—
785C2×C42C2412yes—
786C2×C42C2414yes—
787C2×C42C2412yes—
788C2×C42C2412yes—
789C2×C42C2411yescharacteristic
790C2×C42C2411yescharacteristic
791C2×C42C2411yescharacteristic
792C2×C42C2412yes—
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×C42C2418yes—
808C2×C42C2414yes—
809C2×C42C2418yes—
810C2×C42C2411yescharacteristic
811C2×C42C2411yescharacteristic
812C2×C42C2412yes—
813C2×C42C2411yescharacteristic
814C2×C42C2411yescharacteristic
815C2×C42C2411yescharacteristic
816C2×C42C2411yescharacteristic
817C2×C42C2411yescharacteristic
818#95C2412yes—
819#95C2412yes—
820#95C2418yes—
821#95C2418yes—
822#95C2418yes—
823#95C2418yes—
824#95C2418yes—
825#95C2418yes—
826#95C2412yes—
827#95C2412yes—
828#95C2412yes—
829#95C2412yes—
830#95C2412yes—
831#95C2412yes—
832#95C2412yes—
833#95C2412yes—
834#95C2414yes—
835#95C2414yes—
836#95C2412yes—
837#95C2412yes—
838#95C2412yes—
839#95C2412yes—
840#95C2412yes—
841#95C2412yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2412yes—
847#95C2412yes—
848#95C2412yes—
849#95C2412yes—
850#95C2418yes—
851#95C2418yes—
852#95C2418yes—
853#95C2418yes—
854#95C2418yes—
855#95C2418yes—
856#95C2418yes—
857#95C2418yes—
858#95C2418yes—
859#95C2418yes—
860C24C2512yes—
861C24C2514yes—
862C24C2511yescharacteristic
863#41—432no—
864#41—832no—
865C2×Q8—28no—
866C2×Q8—28no—
867C2×Q8—24no—
868C2×Q8—216no—
869C2×Q8—22no—
870C2×Q8—22no—
871C2×Q8—24no—
872C2×Q8—28no—
873C2×Q8—28no—
874C2×Q8—28no—
875C2×Q8—24no—
876C2×Q8—28no—
877C2×Q8—48no—
878C2×Q8—48no—
879C2×Q8—832no—
880C2×Q8C2×#4114yes—
881C2×D4—28no—
882C2×D4—24no—
883C2×D4—28no—
884C2×D4—216no—
885C2×D4—24no—
886C2×D4—24no—
887C2×D4—22no—
888C2×D4—24no—
889C2×D4—24no—
890C2×D4—22no—
891C2×D4—22no—
892C2×D4—24no—
893C2×D4—24no—
894C2×D4—24no—
895C2×D4—44no—
896C2×D4—42no—
897C2×D4—48no—
898C2×D4—48no—
899C2×D4C2×#4118yes—
900C2×D4C2×#4118yes—
901C2×D4C2×#4118yes—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—28no—
908C22×C4—22no—
909C22×C4—216no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—24no—
913C22×C4—22no—
914C22×C4—24no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—28no—
920C22×C4—22no—
921C22×C4—22no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—28no—
925C22×C4—28no—
926C22×C4—24no—
927C22×C4—24no—
928C22×C4—22no—
929C22×C4—22no—
930C22×C4—24no—
931C22×C4—24no—
932C22×C4—28no—
933C22×C4—22no—
934C22×C4—24no—
935C22×C4—216no—
936C22×C4—28no—
937C22×C4—44no—
938C22×C4—41no—
939C22×C4—41no—
940C22×C4—44no—
941C22×C4—48no—
942C22×C4—48no—
943C22×C4—48no—
944C22×C4—44no—
945C22×C4—48no—
946C22×C42−1+414yes—
947C22×C4C2511yescharacteristic
948C22×C4C2511yescharacteristic
949C22×C4C2512yes—
950C22×C4C2514yes—
951C22×C4C2512yes—
952C22×C4C2512yes—
953C22×C4C2512yes—
954C22×C4C2514yes—
955C22×C4C2518yes—
956C22×C4C2512yes—
957C22×C4C2511yescharacteristic
958C22×C4C2514yes—
959C22×C4C2518yes—
960C22×C4C2511yescharacteristic
961C22×C4C2512yes—
962C22×C4C2512yes—
963C22×C4C2511yescharacteristic
964C22×C4C2511yescharacteristic
965C22×C4C2511yescharacteristic
966C22×C4C2511yescharacteristic
967C22×C4C2511yescharacteristic
968C22×C4C2511yescharacteristic
969C22×C4C2511yescharacteristic
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2511yescharacteristic
973C4⋊C4—24no—
974C4⋊C4—24no—
975C4⋊C4—24no—
976C4⋊C4—28no—
977C4⋊C4—24no—
978C4⋊C4—28no—
979C4⋊C4—22no—
980C4⋊C4—24no—
981C4⋊C4—24no—
982C4⋊C4—28no—
983C4⋊C4—28no—
984C4⋊C4—216no—
985C4⋊C4—22no—
986C4⋊C4—28no—
987C4⋊C4—24no—
988C4⋊C4—24no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—22no—
994C4⋊C4—24no—
995C4⋊C4—28no—
996C4⋊C4—24no—
997C4⋊C4—24no—
998C4⋊C4—22no—
999C4⋊C4—22no—
1000C4⋊C4—28no—
1001C4⋊C4—24no—
1002C4⋊C4—24no—
1003C4⋊C4—24no—
1004C4⋊C4—24no—
1005C4⋊C4—24no—
1006C4⋊C4—48no—
1007C4⋊C4—44no—
1008C4⋊C4—42no—
1009C4⋊C4—48no—
1010C4⋊C4—48no—
1011C4⋊C4—48no—
1012C4⋊C4—48no—
1013C4⋊C4—48no—
1014C4⋊C4—48no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4C2×#4114yes—
1018C4⋊C4C2×#4118yes—
1019C22⋊C4—216no—
1020C22⋊C4—28no—
1021C22⋊C4—28no—
1022C22⋊C4—216no—
1023C22⋊C4—24no—
1024C22⋊C4—24no—
1025C22⋊C4—24no—
1026C22⋊C4—28no—
1027C22⋊C4—216no—
1028C22⋊C4—24no—
1029C22⋊C4—24no—
1030C22⋊C4—24no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—24no—
1034C22⋊C4—24no—
1035C22⋊C4—24no—
1036C22⋊C4—24no—
1037C22⋊C4—24no—
1038C22⋊C4—28no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C22⋊C4—48no—
1042C22⋊C4—48no—
1043C22⋊C4—44no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—48no—
1047C22⋊C4—48no—
1048C22⋊C4—48no—
1049C22⋊C4—48no—
1050C42—22no—
1051C42—22no—
1052C42—22no—
1053C42—24no—
1054C42—24no—
1055C42—24no—
1056C42—22no—
1057C42—22no—
1058C42—22no—
1059C42—22no—
1060C42—22no—
1061C42—22no—
1062C42—22no—
1063C42—22no—
1064C42—22no—
1065C42—28no—
1066C42—24no—
1067C42—24no—
1068C42—22no—
1069C42—22no—
1070C42—22no—
1071C42—22no—
1072C42—22no—
1073C42—22no—
1074C42—22no—
1075C42—24no—
1076C42—24no—
1077C42—22no—
1078C42—22no—
1079C42—24no—
1080C42—41no—
1081C42—41no—
1082C42—44no—
1083C42—44no—
1084C42—48no—
1085C42—48no—
1086C42—48no—
1087C42C2×#4114yes—
1088C42C2×#4114yes—
1089C42C2×#4118yes—
1090C42H(5,𝔽2)14yes—
1091C42H(5,𝔽2)14yes—
1092C422−1+414yes—
1093C23—24no—
1094C23—21no—
1095C23—21no—
1096C23—24no—
1097C23—24no—
1098C23—21no—
1099C23—21no—
1100C23—24no—
1101C23—21no—
1102C23—24no—
1103C23—21no—
1104C23—24no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—22no—
1111C23—22no—
1112C23C22×#4118yes—
1113C23C2×2−1+412yes—
1114C23C2611yescharacteristic
1115Q8—28no—
1116Q8—416no—
1117Q8—416no—
1118Q8—48no—
1119Q8—816no—
1120D4—216no—
1121D4—216no—
1122D4—216no—
1123D4—48no—
1124D4—416no—
1125D4—44no—
1126D4—816no—
1127C2×C4—28no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—28no—
1145C2×C4—22no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—22no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—28no—
1156C2×C4—24no—
1157C2×C4—28no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—28no—
1168C2×C4—28no—
1169C2×C4—28no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—21no—
1182C2×C4—22no—
1183C2×C4—21no—
1184C2×C4—24no—
1185C2×C4—28no—
1186C2×C4—22no—
1187C2×C4—44no—
1188C2×C4—44no—
1189C2×C4—416no—
1190C2×C4—44no—
1191C2×C4—48no—
1192C2×C4—44no—
1193C2×C4—416no—
1194C2×C4—44no—
1195C2×C4—48no—
1196C2×C4—48no—
1197C2×C4—88no—
1198C2×C4—816no—
1199C2×C4—816no—
1200C2×C4C22×#4112yes—
1201C2×C4C22×#4114yes—
1202C2×C4C22×#4114yes—
1203C2×C4C22×#4112yes—
1204C2×C4C22×#4112yes—
1205C2×C4C22×#4112yes—
1206C2×C4C22×#4112yes—
1207C2×C4C22×#4112yes—
1208C2×C4C2×H(5,𝔽2)12yes—
1209C2×C4C2×H(5,𝔽2)12yes—
1210C2×C4C2×H(5,𝔽2)12yes—
1211C2×C4C2×H(5,𝔽2)12yes—
1212C2×C4C2×H(5,𝔽2)12yes—
1213C2×C4C2×H(5,𝔽2)12yes—
1214C2×C4C2×2−1+412yes—
1215C2×C4C2×2−1+412yes—
1216C2×C4C2×2−1+412yes—
1217C2×C4C2×2−1+412yes—
1218C2×C4C2×2−1+412yes—
1219C2×C4#58512yes—
1220C22—22no—
1221C22—28no—
1222C22—28no—
1223C22—22no—
1224C22—22no—
1225C22—28no—
1226C22—41no—
1227C22—44no—
1228C22—41no—
1229C22—44no—
1230C22—44no—
1231C22—41no—
1232C22—44no—
1233C22—41no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22C23×#4111yescharacteristic
1242C22C23×#4111yescharacteristic
1243C22C22×H(5,𝔽2)11yescharacteristic
1244C22C22×H(5,𝔽2)11yescharacteristic
1245C22C22×2−1+411yescharacteristic
1246C22C22×2−1+411yescharacteristic
1247C22C2×#58511yescharacteristic
1248C4—22no—
1249C4—24no—
1250C4—22no—
1251C4—24no—
1252C4—22no—
1253C4—22no—
1254C4—22no—
1255C4—22no—
1256C4—42no—
1257C4—44no—
1258C4—41no—
1259C4—42no—
1260C4—48no—
1261C4—41no—
1262C4—44no—
1263C4—48no—
1264C4—41no—
1265C4—42no—
1266C4—42no—
1267C4—44no—
1268C4—41no—
1269C4—42no—
1270C4#348214yes—
1271C4#350814yes—
1272C4#351414yes—
1273C4#352014yes—
1274C2—42no—
1275C2—48no—
1276C2—82no—
1277C2C2×#348211yescharacteristic
1278C2C2×#352011yescharacteristic
1279C2C2×#351411yescharacteristic
1280C2C2×#350811yescharacteristic
1281C2#6280511yescharacteristic
1282C2#6283311yescharacteristic
1283C2#6283511yescharacteristic
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. #59479C2semidirect
2. #59450C2semidirect
3. #59421C2semidirect
4. #59275C2semidirect
5. #59042C2semidirect
6. #59040C2semidirect
7. #40076C2semidirect
8. #40072C2semidirect
9. #39124C2semidirect
10. #38930C2semidirect
11. #38272C2semidirect
12. #36645C2semidirect
13. #36598C2semidirect
14. Q8×#127C2semidirect
15. #36504C2semidirect
16. #36454C2semidirect
17. #36303C2semidirect
18. #36274C2semidirect
19. #36194C2semidirect
20. #36188C2semidirect
21. #36149C2semidirect
22. #36127C2semidirect
23. #35553C2semidirect
24. #35283C2semidirect
25. #35196C2semidirect
26. #34334C2semidirect
27. #34226C2semidirect
28. C4×#532C2semidirect
29. C4×#529C2semidirect
660. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#594792
#594502
#594212
#592752
#590422
#590402
#400762
#400722
#391242
#389302
#382722
#366452
#365982
Q8×#1272
#365042
#364542
#363032
#362742
#361942
#361882
#361492
#361272
#355532
#352832
#351962
#343342
#342262
C4×#5322
C4×#5292