Finite Group Databasebeta

← #7672501

Subgroups — #7672501

Order 512.

5282 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59645C214yesmaximal, complemented
2#59644C214yesmaximal, complemented
3#59643C214yesmaximal, complemented
4#59584C214yesmaximal, complemented
5#39811C214yesmaximal, complemented
6#39810C214yesmaximal, complemented
7#39195C218yesmaximal, complemented
8#36639C211yesmaximal, characteristic, complemented
9#36602C214yesmaximal, complemented
10#36591C214yesmaximal, complemented
11#36521C218yesmaximal, complemented
12#35628C211yesmaximal, characteristic, complemented
13#35619C211yesmaximal, characteristic, complemented
14#35556C211yesmaximal, characteristic, complemented
15#35531C211yesmaximal, characteristic, complemented
16#35338C211yesmaximal, characteristic, complemented
17#35329C211yesmaximal, characteristic
18#35182C211yesmaximal, characteristic, complemented
19#35152C211yesmaximal, characteristic, complemented
20#34266C211yesmaximal, characteristic, complemented
21#34265C211yesmaximal, characteristic, complemented
22#34215C211yesmaximal, characteristic, complemented
23#34208C211yesmaximal, characteristic, complemented
24C4×#533C211yesmaximal, characteristic, complemented
25C2×C4×#124C211yesmaximal, characteristic, complemented
26C2×#536C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#533C2211yescharacteristic
31C2×#533C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C22×#124C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37C22×C4×D4C2211yescharacteristic
38#2862C2212yescomplemented
39#2861C2214yes—
40#2861C2212yescomplemented
41#2861C2212yescomplemented
42#2858C2212yes—
43#2858C2212yes—
44#2858C2212yescomplemented
45#2853C2214yes—
46#2850C2214yes—
47#2850C2214yes—
48#2849C2214yes—
49#2798C2218yescomplemented
50#2797C2218yescomplemented
51#2773C2218yescomplemented
52#2754C2218yescomplemented
53#2754C2218yescomplemented
54#2752C2218yescomplemented
55#2712C2218yescomplemented
56#2710C2218yescomplemented
57#2658C2212yes—
58#2657C2212yes—
59#2640C2214yes—
60#2623C2214yes—
61#2622C2214yes—
62#2607C2218yescomplemented
63#2602C2218yescomplemented
64#2597C2218yescomplemented
65#2597C2218yescomplemented
66#2595C2218yescomplemented
67#2595C2218yescomplemented
68#2593C2218yescomplemented
69#2593C2218yescomplemented
70#2592C2214yes—
71#2592C2214yes—
72#2592C2214yes—
73#2592C2214yescomplemented
74#2589C2218yescomplemented
75#2575C2218yescomplemented
76#2568C2214yescomplemented
77#2561C2218yes—
78#2557C2218yescomplemented
79#2557C2218yescomplemented
80#2548C2214yes—
81#2540C2214yes—
82#2540C2214yes—
83#2539C2218yes—
84#2517C2218yescomplemented
85#2516C2218yescomplemented
86#2516C2218yescomplemented
87#2513C2218yescomplemented
88#2504C2212yes—
89#2503C2212yescomplemented
90#2502C2212yescomplemented
91#2501C2212yes—
92#2500C2212yes—
93#2500C2212yes—
94#2499C2212yescomplemented
95#2499C2212yescomplemented
96#2492C2214yescomplemented
97#2491C2214yes—
98#2490C2214yes—
99#2489C2214yescomplemented
100#2488C2218yes—
101#2472C2218yes—
102#2459C2218yescomplemented
103#2458C2218yescomplemented
104#2458C2218yescomplemented
105#2448C2214yes—
106#2448C2218yescomplemented
107#2448C2214yescomplemented
108#2447C2214yes—
109#2447C2214yescomplemented
110#2446C2214yescomplemented
111#2446C2214yescomplemented
112#2445C2214yes—
113#2445C2214yes—
114#2423C2214yescomplemented
115#2422C2214yes—
116#2421C2214yescomplemented
117#2420C2214yes—
118#2419C2218yes—
119#2418C2218yes—
120#2374C2218yescomplemented
121#2374C2218yescomplemented
122#2368C2218yes—
123#2367C2214yes—
124#2367C2214yescomplemented
125#2367C2218yescomplemented
126#2366C2214yes—
127#2365C2214yescomplemented
128#2364C2218yes—
129#2363C2214yes—
130#2362C2214yescomplemented
131#2361C2214yes—
132#2360C2214yescomplemented
133#2357C2218yescomplemented
134#2355C2214yescomplemented
135#2355C2214yescomplemented
136#2352C2214yescomplemented
137#2352C2214yescomplemented
138#2331C2214yescomplemented
139#2328C2212yescomplemented
140#2327C2212yescomplemented
141#2322C2214yes—
142#2321C2214yes—
143#2317C2211yescharacteristic
144#2317C2211yescharacteristic
145#2311C2211yescharacteristic
146#2311C2211yescharacteristic
147#2310C2211yescharacteristic
148#2310C2211yescharacteristic
149#2309C2211yescharacteristic
150#2309C2211yescharacteristic
151C4×C4⋊Q8C2212yescomplemented
152C4×C4⋊Q8C2212yescomplemented
153C4×#125C2214yescomplemented
154C4×#125C2212yescomplemented
155C4×#125C2212yescomplemented
156C4×#124C2214yes—
157C4×#124C2214yes—
158C4×#124C2214yes—
159C4×#124C2214yes—
160C4×#124C2214yescomplemented
161C4×#124C2214yescomplemented
162C4×#124C2212yescomplemented
163C4×#124C2212yescomplemented
164C4×C22⋊Q8C2214yes—
165C4×C22⋊Q8C2214yes—
166C4×#123C2214yes—
167C4×#120C2214yes—
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2295C2214yescomplemented
175C2×#391C2211yescharacteristic
176C2×#390C2211yescharacteristic
177C2×#388C2214yes—
178#2285C2211yescharacteristic
179C2×#382C2211yescharacteristic
180#2274C2211yescharacteristic
181#2274C2211yescharacteristic
182C42×Q8C2214yescomplemented
183C4×#117C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C2×C4×C22⋊C4C2214yes—
186C2×C43C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C23×D4C2311yescharacteristic
191C24×C4C2312yes—
192#536—28no—
193#536—44no—
194#535—28no—
195#535—44no—
196#533—28no—
197#533—28no—
198#532—28no—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2311yescharacteristic
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×#127C2311yescharacteristic
205C2×#127C2312yes—
206C2×#127C2312yes—
207C2×#125C2312yes—
208C2×#125C2312yes—
209C2×#124—28no—
210C2×#124C2312yes—
211C2×#124C2314yes—
212C2×#124C2312yes—
213C2×#124C2312yes—
214C2×#124C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#124C2312yes—
217C2×#124C2314yes—
218C2×#124C2314yes—
219C2×#124C2312yes—
220C2×#124C2312yes—
221C2×#124C2318yes—
222C2×#123C2314yes—
223C2×#123C2318yes—
224C2×#123C2314yes—
225C2×#123C2318yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×#121C2314yes—
232C2×#121C2314yes—
233C2×#121C2312yes—
234C2×#121C2312yes—
235C2×#120C2314yes—
236C2×#120C2314yes—
237#520—44no—
238#520—44no—
239C2×C4×Q8—44no—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×D4—44no—
249C2×C4×D4C2314yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2318yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2312yes—
263C2×#117C2312yes—
264C2×#117C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2312yes—
270C22×C22⋊C4C2314yes—
271C22×C22⋊C4C2312yes—
272C22×C22⋊C4C2314yes—
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2312yes—
276C22×C42C2312yes—
277C22×C42C2312yes—
278C22×C42C2311yescharacteristic
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#399C2318yes—
284#399C2318yes—
285#399C2318yes—
286#399C2318yes—
287#398C2318yes—
288#398C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#393C2318yes—
306#393C2318yes—
307#393C2318yes—
308#393C2318yes—
309#392C2318yes—
310#392C2318yes—
311#391C2314yes—
312#391C2314yes—
313#391C2314yes—
314#391C2312yes—
315#391C2312yes—
316#391C2314yes—
317#391C2314yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2314yes—
322#391C2318yes—
323#391C2318yes—
324#391C2318yes—
325#391C2314yes—
326#391C2312yes—
327#391C2314yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2312yes—
332#390C2312yes—
333#390C2312yes—
334#390C2314yes—
335#390C2314yes—
336#390C2314yes—
337#390C2312yes—
338#390C2312yes—
339#390C2318yes—
340#390C2314yes—
341#390C2312yes—
342#390C2318yes—
343#390C2318yes—
344#390C2314yes—
345#390C2314yes—
346#390C2318yes—
347#390C2318yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2318yes—
352#390C2312yes—
353#390C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2314yes—
377#388C2314yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2314yes—
382#388C2314yes—
383#388C2314yes—
384#388C2314yes—
385#388C2314yes—
386#388C2314yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#387C2314yes—
394#387C2318yes—
395#387C2318yes—
396#387C2314yes—
397#387C2314yes—
398#387C2314yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#386C2314yes—
410#386C2314yes—
411#386C2312yes—
412#386C2318yes—
413#386C2312yes—
414#386C2318yes—
415#386C2318yes—
416#386C2312yes—
417#386C2318yes—
418#386C2312yes—
419#386C2314yes—
420#386C2314yes—
421#386C2318yes—
422#386C2318yes—
423#385C2314yes—
424#385C2314yes—
425#385C2318yes—
426#385C2312yes—
427#385C2318yes—
428#385C2318yes—
429#385C2312yes—
430#385C2318yes—
431#385C2312yes—
432#385C2312yes—
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#384C2312yes—
436#384C2312yes—
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#382C2312yes—
440#382C2318yes—
441#382C2312yes—
442#382C2312yes—
443#382C2314yes—
444#382C2312yes—
445#382C2314yes—
446#382C2314yes—
447#381C2314yes—
448#381C2314yes—
449#381C2318yes—
450#381C2318yes—
451#380C2314yes—
452#380C2314yes—
453#380C2314yes—
454#379C2314yes—
455#379C2314yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2318yes—
464C4×C4⋊C4C2318yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C22⋊C4C2314yes—
477C4×C22⋊C4C2318yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2314yes—
480C4×C22⋊C4C2318yes—
481C4×C22⋊C4C2318yes—
482C4×C22⋊C4C2318yes—
483C4×C22⋊C4C2318yes—
484C4×C22⋊C4C2318yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2318yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2312yes—
494#376C2312yes—
495#376C2312yes—
496C2×#95C2314yes—
497C2×#95C2314yes—
498C43C2312yes—
499C43C2312yes—
500C43C2312yes—
501C43C2312yes—
502C43C2312yes—
503C43C2312yes—
504C25C2412yes—
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C2×#41—24no—
509C2×#41—24no—
510C2×#41—24no—
511C22×Q8—24no—
512C22×Q8—24no—
513C22×Q8—24no—
514C22×Q8C2412yes—
515C22×Q8C2412yes—
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×Q8C2414yes—
519C22×Q8C2414yes—
520C22×D4—24no—
521C22×D4—24no—
522C22×D4—24no—
523C22×D4C2412yes—
524C22×D4C2412yes—
525C22×D4C2412yes—
526C22×D4C2412yes—
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2418yes—
530C22×D4C2414yes—
531C22×D4C2414yes—
532C22×D4C2414yes—
533C23×C4—48no—
534C23×C4—44no—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2411yescharacteristic
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2411yescharacteristic
542C23×C4C2412yes—
543C23×C4C2418yes—
544C23×C4C2414yes—
545C23×C4C2414yes—
546C23×C4C2412yes—
547C23×C4C2411yescharacteristic
548C4⋊Q8—28no—
549C4⋊Q8—24no—
550C4⋊Q8—28no—
551C4⋊Q8—28no—
552C4⋊Q8—44no—
553#127—24no—
554#127—28no—
555#127—44no—
556#125—28no—
557#125—28no—
558#124—216no—
559#124—28no—
560#124—28no—
561#124—24no—
562#124—24no—
563#124—28no—
564#124—28no—
565#124—48no—
566#124—48no—
567#124—44no—
568#124—44no—
569#124—416no—
570#123—216no—
571#123—416no—
572#123—416no—
573#123—48no—
574C22⋊Q8—216no—
575C22⋊Q8—216no—
576C22⋊Q8—216no—
577C22⋊Q8—44no—
578C22⋊Q8—44no—
579#121—216no—
580#121—216no—
581#121—44no—
582#121—44no—
583#120—216no—
584#120—48no—
585C4×Q8—216no—
586C4×Q8—216no—
587C4×Q8—48no—
588C4×Q8—48no—
589C4×Q8—48no—
590C4×Q8—48no—
591C4×Q8—44no—
592C4×Q8—44no—
593C4×D4—216no—
594C4×D4—48no—
595C4×D4—48no—
596C4×D4—44no—
597C4×D4—44no—
598C4×D4—416no—
599C4×D4—48no—
600C4×D4—48no—
601#117—24no—
602#117—24no—
603#117—24no—
604#117—24no—
605#117—24no—
606#117—44no—
607#117—44no—
608#117#4118yes—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—44no—
612C2×C4⋊C4—44no—
613C2×C4⋊C4—44no—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2412yes—
647C2×C22⋊C4—216no—
648C2×C22⋊C4—48no—
649C2×C22⋊C4—44no—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2412yes—
685C2×C42—24no—
686C2×C42—24no—
687C2×C42—44no—
688C2×C42—44no—
689C2×C42—44no—
690C2×C42#4118yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2414yes—
706C2×C42C2414yes—
707C2×C42C2418yes—
708C2×C42C2418yes—
709C2×C42C2414yes—
710C2×C42C2414yes—
711C2×C42C2414yes—
712C2×C42C2414yes—
713C2×C42C2418yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2418yes—
754C24—24no—
755C24—24no—
756C24—24no—
757C24—44no—
758C24—44no—
759C24C2514yes—
760C24C2512yes—
761C24C2512yes—
762C24C2511yescharacteristic
763#41—416no—
764#41—416no—
765C2×Q8—28no—
766C2×Q8—24no—
767C2×Q8—24no—
768C2×Q8—24no—
769C2×Q8—22no—
770C2×Q8—24no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—22no—
774C2×Q8—28no—
775C2×Q8—24no—
776C2×Q8—22no—
777C2×Q8—24no—
778C2×Q8—22no—
779C2×Q8—28no—
780C2×Q8—44no—
781C2×Q8—44no—
782C2×Q8—44no—
783C2×Q8—416no—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—24no—
793C2×D4—22no—
794C2×D4—24no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—28no—
799C2×D4—216no—
800C2×D4—24no—
801C2×D4—22no—
802C2×D4—24no—
803C2×D4—22no—
804C2×D4—48no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—48no—
808C2×D4—44no—
809C2×D4—44no—
810C2×D4—48no—
811C2×D4—48no—
812C2×D4—416no—
813C22×C4—22no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—22no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—216no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—44no—
835C22×C4—48no—
836C22×C4—48no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—816no—
843C22×C4C2×#4118yes—
844C22×C4C2×#4114yes—
845C22×C4C2×#4114yes—
846C22×C4H(5,𝔽2)14yes—
847C22×C4C2514yes—
848C22×C4C2512yes—
849C22×C4C2514yes—
850C22×C4C2514yes—
851C22×C4C2514yes—
852C22×C4C2514yes—
853C22×C4C2512yes—
854C22×C4C2512yes—
855C22×C4C2512yes—
856C22×C4C2512yes—
857C22×C4C2514yes—
858C22×C4C2512yes—
859C22×C4C2512yes—
860C22×C4C2512yes—
861C22×C4C2512yes—
862C22×C4C2514yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2512yes—
866C22×C4C2511yescharacteristic
867C22×C4C2511yescharacteristic
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—28no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—28no—
878C4⋊C4—216no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—28no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—48no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—48no—
899C4⋊C4—48no—
900C4⋊C4C2×#4118yes—
901C22⋊C4—24no—
902C22⋊C4—24no—
903C22⋊C4—24no—
904C22⋊C4—24no—
905C22⋊C4—24no—
906C22⋊C4—216no—
907C22⋊C4—216no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—216no—
911C22⋊C4—216no—
912C22⋊C4—216no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—48no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4C2×#4118yes—
936C42—24no—
937C42—22no—
938C42—22no—
939C42—24no—
940C42—24no—
941C42—24no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—24no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—42no—
951C42—42no—
952C42—42no—
953C42—42no—
954C42—48no—
955C42—44no—
956C42—44no—
957C42—48no—
958C42—44no—
959C42—44no—
960C42—44no—
961C42—44no—
962C42—48no—
963C42C2×#4118yes—
964C42C2×#4114yes—
965C42C2×#4114yes—
966C42C2×#4118yes—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—24no—
971C23—22no—
972C23—22no—
973C23—24no—
974C23—22no—
975C23—22no—
976C23—24no—
977C23—22no—
978C23—24no—
979C23—24no—
980C23—28no—
981C23—24no—
982C23—24no—
983C23—28no—
984C23—416no—
985C23—48no—
986C23—84no—
987C23—88no—
988C23—84no—
989C23C22×#4112yes—
990C23C22×#4112yes—
991C23C2×H(5,𝔽2)12yes—
992C23C2611yescharacteristic
993Q8—416no—
994Q8—48no—
995Q8—48no—
996Q8—44no—
997Q8—44no—
998Q8—88no—
999D4—48no—
1000D4—48no—
1001D4—48no—
1002D4—48no—
1003D4—44no—
1004D4—44no—
1005D4—816no—
1006D4—88no—
1007D4—164no—
1008D4—164no—
1009C2×C4—28no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—28no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—28no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—48no—
1057C2×C4—48no—
1058C2×C4—44no—
1059C2×C4—48no—
1060C2×C4—48no—
1061C2×C4—48no—
1062C2×C4—816no—
1063C2×C4—84no—
1064C2×C4—84no—
1065C2×C4—164no—
1066C2×C4—164no—
1067C2×C4#559116yes—
1068C2×C4C22×#4114yes—
1069C2×C4C22×#4114yes—
1070C2×C4C22×#4118yes—
1071C2×C4C22×#4112yes—
1072C2×C4C22×#4112yes—
1073C2×C4C22×#4112yes—
1074C2×C4C22×#4112yes—
1075C2×C4C2×H(5,𝔽2)12yes—
1076C2×C4C2×H(5,𝔽2)12yes—
1077C2×C4#58514yes—
1078C2×C4#58514yes—
1079C22—24no—
1080C22—24no—
1081C22—22no—
1082C22—22no—
1083C22—44no—
1084C22—48no—
1085C22—44no—
1086C22—44no—
1087C22—44no—
1088C22—48no—
1089C22—44no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—44no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—44no—
1098C22—816no—
1099C22C2×#55914yes—
1100C22C23×#4111yescharacteristic
1101C22C23×#4111yescharacteristic
1102C22C22×H(5,𝔽2)11yescharacteristic
1103C22C2×#58512yes—
1104C22C2×#58512yes—
1105C4—24no—
1106C4—28no—
1107C4—24no—
1108C4—24no—
1109C4—24no—
1110C4—42no—
1111C4—44no—
1112C4—44no—
1113C4—44no—
1114C4—44no—
1115C4—42no—
1116C4—42no—
1117C4—42no—
1118C4—44no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—42no—
1123C4—44no—
1124C4C2×#55914yes—
1125C4C2×#55914yes—
1126C2—24no—
1127C2—82no—
1128C2—82no—
1129C2—84no—
1130C2C22×#55911yescharacteristic
1131C2#6281012yes—
1132C2#6281512yes—
1133C2#6282411yescharacteristic
1134C2#6283611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35329C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59645C2semidirect
2. #59644C2semidirect
3. #59643C2semidirect
4. #59584C2semidirect
5. #39811C2semidirect
6. #39810C2semidirect
7. #39195C2semidirect
8. #36639C2semidirect
9. #36602C2semidirect
10. #36591C2semidirect
11. #36521C2semidirect
12. #35628C2semidirect
13. #35619C2semidirect
14. #35556C2semidirect
15. #35531C2semidirect
16. #35338C2semidirect
18. #35182C2semidirect
19. #35152C2semidirect
20. #34266C2semidirect
21. #34265C2semidirect
22. #34215C2semidirect
23. #34208C2semidirect
24. C4×#533C2semidirect
25. C2×C4×#124C2semidirect
38. #2862C22semidirect
40. #2861C22semidirect
41. #2861C22semidirect
44. #2858C22semidirect
49. #2798C22semidirect
50. #2797C22semidirect
51. #2773C22semidirect
52. #2754C22semidirect
53. #2754C22semidirect
54. #2752C22semidirect
55. #2712C22semidirect
56. #2710C22semidirect
62. #2607C22semidirect
63. #2602C22semidirect
64. #2597C22semidirect
65. #2597C22semidirect
66. #2595C22semidirect
67. #2595C22semidirect
68. #2593C22semidirect
69. #2593C22semidirect
73. #2592C22semidirect
74. #2589C22semidirect
75. #2575C22semidirect
76. #2568C22semidirect
78. #2557C22semidirect
79. #2557C22semidirect
84. #2517C22semidirect
85. #2516C22semidirect
86. #2516C22semidirect
87. #2513C22semidirect
89. #2503C22semidirect
90. #2502C22semidirect
94. #2499C22semidirect
95. #2499C22semidirect
96. #2492C22semidirect
99. #2489C22semidirect
102. #2459C22semidirect
103. #2458C22semidirect
104. #2458C22semidirect
106. #2448C22semidirect
107. #2448C22semidirect
109. #2447C22semidirect
110. #2446C22semidirect
111. #2446C22semidirect
114. #2423C22semidirect
116. #2421C22semidirect
120. #2374C22semidirect
121. #2374C22semidirect
124. #2367C22semidirect
125. #2367C22semidirect
127. #2365C22semidirect
130. #2362C22semidirect
132. #2360C22semidirect
133. #2357C22semidirect
134. #2355C22semidirect
135. #2355C22semidirect
136. #2352C22semidirect
137. #2352C22semidirect
138. #2331C22semidirect
139. #2328C22semidirect
140. #2327C22semidirect
151. C4×C4⋊Q8C22semidirect
152. C4×C4⋊Q8C22semidirect
153. C4×#125C22semidirect
154. C4×#125C22semidirect
155. C4×#125C22semidirect
160. C4×#124C22semidirect
161. C4×#124C22semidirect
162. C4×#124C22semidirect
163. C4×#124C22semidirect
174. #2295C22semidirect
182. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#596452
#596442
#596432
#595842
#398112
#398102
#391952
#366392
#366022
#365912
#365212
#356282
#356192
#355562
#355312
#353382
#353292
#351822
#351522
#342662
#342652
#342152
#342082
C4×#5332
C2×C4×#1242