Finite Group Databasebeta

← #7683822

Subgroups — #7683822

Order 512.

5026 conjugacy classes of subgroups.

The subgroup lattice has 1123 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59645C214yesmaximal, complemented
2#59643C214yesmaximal, complemented
3#59639C214yesmaximal, complemented
4#59626C218yesmaximal, complemented
5#59451C214yesmaximal, complemented
6#45222C214yesmaximal, complemented
7#45201C214yesmaximal, complemented
8#45167C214yesmaximal, complemented
9#44986C214yesmaximal, complemented
10#44105C218yesmaximal, complemented
11#35672C211yesmaximal, characteristic, complemented
12#35634C211yesmaximal, characteristic
13#35628C211yesmaximal, characteristic, complemented
14#35628C211yesmaximal, characteristic, complemented
15#35618C211yesmaximal, characteristic, complemented
16#35530C211yesmaximal, characteristic, complemented
17#34813C211yesmaximal, characteristic, complemented
18#34813C211yesmaximal, characteristic, complemented
19C2×#2499C211yesmaximal, characteristic, complemented
20#34276C211yesmaximal, characteristic, complemented
21#34276C211yesmaximal, characteristic, complemented
22#34215C211yesmaximal, characteristic, complemented
23#34214C211yesmaximal, characteristic, complemented
24#34201C211yesmaximal, characteristic, complemented
25#34201C211yesmaximal, characteristic, complemented
26C2×#537C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#533C2211yescharacteristic
30C2×#533C2211yescharacteristic
31C2×#525C2211yescharacteristic
32C2×#525C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C22×#117C2211yescharacteristic
38#2808C2218yescomplemented
39#2803C2218yes—
40#2798C2218yes—
41#2798C2218yescomplemented
42#2797C2218yes—
43#2796C2218yes—
44#2794C2218yescomplemented
45#2773C2218yes—
46#2773C2218yescomplemented
47#2754C2218yes—
48#2751C2218yes—
49#2710C2218yes—
50#2607C2218yescomplemented
51#2597C2218yescomplemented
52#2596C2218yes—
53#2596C2218yescomplemented
54#2596C2218yescomplemented
55#2595C2218yes—
56#2592C2218yes—
57#2592C2214yescomplemented
58#2592C2214yescomplemented
59#2589C2218yescomplemented
60#2575C2218yescomplemented
61#2570C2218yescomplemented
62#2568C2214yescomplemented
63#2568C2214yescomplemented
64#2557C2218yes—
65#2542C2214yes—
66#2542C2214yes—
67#2540C2214yes—
68#2540C2214yes—
69#2539C2214yes—
70#2517C2218yescomplemented
71#2516C2218yes—
72#2513C2218yes—
73#2513C2218yes—
74#2511C2218yescomplemented
75#2504C2212yescomplemented
76#2503C2212yescomplemented
77#2502C2212yescomplemented
78#2501C2214yes—
79#2501C2212yescomplemented
80#2500C2212yescomplemented
81#2500C2212yescomplemented
82#2499C2214yes—
83#2499C2214yes—
84#2499C2214yes—
85#2499C2214yes—
86#2499C2212yescomplemented
87#2499C2212yescomplemented
88#2492C2212yes—
89#2492C2212yes—
90#2492C2214yescomplemented
91#2492C2214yescomplemented
92#2491C2212yes—
93#2491C2212yes—
94#2490C2212yes—
95#2490C2212yes—
96#2489C2212yes—
97#2489C2212yes—
98#2489C2214yescomplemented
99#2489C2214yescomplemented
100#2488C2218yes—
101#2488C2218yes—
102#2488C2214yes—
103#2488C2214yes—
104#2484C2214yes—
105#2482C2214yes—
106#2472C2214yes—
107#2472C2214yes—
108#2458C2218yescomplemented
109#2448C2218yes—
110#2444C2218yes—
111#2443C2218yes—
112#2423C2214yes—
113#2423C2214yes—
114#2423C2214yescomplemented
115#2422C2214yescomplemented
116#2421C2214yes—
117#2421C2214yes—
118#2421C2214yescomplemented
119#2420C2214yescomplemented
120#2398C2214yes—
121#2398C2214yes—
122C2×#397C2214yes—
123#2374C2218yescomplemented
124#2368C2218yes—
125#2363C2214yes—
126#2363C2214yes—
127#2362C2214yes—
128#2362C2214yes—
129#2362C2214yescomplemented
130#2362C2214yescomplemented
131#2360C2218yes—
132#2360C2214yescomplemented
133#2360C2214yescomplemented
134#2359C2218yes—
135#2359C2218yes—
136#2355C2218yescomplemented
137#2355C2214yescomplemented
138#2355C2214yescomplemented
139#2355C2214yescomplemented
140#2354C2214yes—
141#2354C2214yes—
142#2352C2214yes—
143#2352C2214yes—
144Q8×C4⋊C4C2214yescomplemented
145#2331C2214yescomplemented
146#2330C2214yescomplemented
147#2327C2212yescomplemented
148#2327C2212yescomplemented
149#2326C2212yescomplemented
150#2326C2212yescomplemented
151#2321C2214yes—
152#2321C2214yes—
153#2317C2211yescharacteristic
154#2317C2211yescharacteristic
155#2317C2211yescharacteristic
156#2317C2211yescharacteristic
157#2311C2211yescharacteristic
158#2311C2211yescharacteristic
159#2310C2211yescharacteristic
160C4×C4⋊Q8C2212yescomplemented
161C4×C4⋊Q8C2214yescomplemented
162C4×C4⋊Q8C2212yescomplemented
163C4×#125C2214yescomplemented
164C4×#124C2214yes—
165C4×#124C2214yes—
166C4×#124C2212yescomplemented
167C4×#124C2212yescomplemented
168C4×#123C2214yes—
169C4×#123C2214yes—
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174C2×#391C2211yescharacteristic
175C2×#391C2211yescharacteristic
176C2×#387C2214yes—
177C2×#384C2211yescharacteristic
178C2×#382C2211yescharacteristic
179#2280C2211yescharacteristic
180#2280C2211yescharacteristic
181#2274C2211yescharacteristic
182#2274C2211yescharacteristic
183#2274C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C24×C4C2311yescharacteristic
191#537—44no—
192#536—28no—
193#536—28no—
194#533—28no—
195#533—28no—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×#125C2312yes—
201C2×#125C2312yes—
202C2×#124C2312yes—
203C2×#124C2312yes—
204C2×#124C2314yes—
205C2×#124C2314yes—
206#525—28no—
207#525—28no—
208C2×#123C2314yes—
209C2×#123C2314yes—
210C2×#123C2312yes—
211C2×#123C2312yes—
212C2×#123C2318yes—
213C2×C22⋊Q8—44no—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×#121C2312yes—
225C2×#121C2312yes—
226C2×#121C2312yes—
227C2×#121C2312yes—
228C2×#121C2314yes—
229C2×#120C2312yes—
230C2×#120C2312yes—
231#520—44no—
232#520—44no—
233#519—44no—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2318yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2312yes—
249C2×#117—44no—
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2314yes—
255C2×#117C2314yes—
256C2×#117C2312yes—
257C2×#117C2312yes—
258C2×#117C2314yes—
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2314yes—
267C22×C4⋊C4C2312yes—
268C22×C22⋊C4C2312yes—
269C22×C22⋊C4C2312yes—
270C22×C22⋊C4C2312yes—
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2312yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2314yes—
279#400C2314yes—
280#400C2318yes—
281#400C2314yes—
282#400C2314yes—
283#400C2318yes—
284#399C2318yes—
285#399C2318yes—
286#399C2318yes—
287#399C2318yes—
288#399C2318yes—
289#398C2318yes—
290#398C2318yes—
291#397C2314yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2314yes—
301#397C2318yes—
302#397C2314yes—
303#397C2314yes—
304#397C2318yes—
305#394C2314yes—
306#394C2318yes—
307#394C2314yes—
308#394C2314yes—
309#394C2314yes—
310#394C2318yes—
311#393C2314yes—
312#393C2314yes—
313#393C2318yes—
314#393C2318yes—
315#393C2314yes—
316#393C2314yes—
317#392C2318yes—
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#391C2318yes—
321#391C2312yes—
322#391C2312yes—
323#391C2314yes—
324#391C2314yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#391C2318yes—
330#391C2314yes—
331#391C2314yes—
332#391C2318yes—
333#391C2312yes—
334#391C2312yes—
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2318yes—
338#391C2318yes—
339#391C2314yes—
340#391C2314yes—
341#390C2312yes—
342#390C2312yes—
343#390C2318yes—
344#390C2318yes—
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2318yes—
348#390C2312yes—
349#390C2312yes—
350#390C2318yes—
351#390C2318yes—
352#390C2314yes—
353#390C2314yes—
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#389C2314yes—
357#389C2314yes—
358#389C2318yes—
359#389C2314yes—
360#389C2314yes—
361#389C2318yes—
362#389C2318yes—
363#389C2318yes—
364#389C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2314yes—
379#388C2318yes—
380#388C2314yes—
381#388C2314yes—
382#388C2314yes—
383#388C2314yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2314yes—
389#388C2314yes—
390#388C2314yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#386C2314yes—
412#386C2314yes—
413#386C2318yes—
414#386C2318yes—
415#386C2318yes—
416#386C2314yes—
417#386C2314yes—
418#386C2314yes—
419#386C2314yes—
420#385C2314yes—
421#385C2314yes—
422#385C2314yes—
423#385C2314yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#384C2312yes—
428#384C2312yes—
429#384C2312yes—
430#384C2318yes—
431#384C2312yes—
432#384C2312yes—
433#384C2312yes—
434#384C2314yes—
435#382C2312yes—
436#382C2318yes—
437#382C2318yes—
438#382C2314yes—
439#382C2312yes—
440#382C2312yes—
441#382C2312yes—
442#382C2312yes—
443#382C2312yes—
444#382C2314yes—
445#382C2314yes—
446#381C2314yes—
447#381C2318yes—
448#381C2312yes—
449#381C2312yes—
450#380C2314yes—
451#380C2314yes—
452#380C2312yes—
453#380C2312yes—
454#380C2312yes—
455#380C2312yes—
456#379C2312yes—
457#379C2312yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2318yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2318yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2318yes—
465C4×C4⋊C4C2318yes—
466C4×C4⋊C4C2318yes—
467C4×C4⋊C4C2318yes—
468C4×C4⋊C4C2318yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2312yes—
475C4×C22⋊C4C2318yes—
476C4×C22⋊C4C2314yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2318yes—
479C4×C22⋊C4C2318yes—
480C4×C22⋊C4C2318yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496#376C2312yes—
497#376C2312yes—
498C2×#95C2314yes—
499C2×#95C2314yes—
500C2×#95C2314yes—
501C2×#95C2312yes—
502C43C2312yes—
503C43C2312yes—
504C25C2411yescharacteristic
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×D4C2412yes—
521C22×D4C2412yes—
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2414yes—
525C22×D4C2414yes—
526C22×D4C2414yes—
527C23×C4—24no—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4C2412yes—
531C23×C4C2411yescharacteristic
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2414yes—
542C23×C4C2414yes—
543C23×C4C2411yescharacteristic
544C4⋊Q8—28no—
545C4⋊Q8—28no—
546C4⋊Q8—28no—
547C4⋊Q8—28no—
548#125—28no—
549#125—28no—
550#124—28no—
551#124—28no—
552#124—48no—
553#124—48no—
554#123—28no—
555#123—28no—
556#123—216no—
557#123—216no—
558#123—416no—
559C22⋊Q8—28no—
560C22⋊Q8—28no—
561C22⋊Q8—216no—
562C22⋊Q8—216no—
563C22⋊Q8—216no—
564C22⋊Q8—216no—
565C22⋊Q8—48no—
566C22⋊Q8—48no—
567C22⋊Q8—44no—
568C22⋊Q8—44no—
569#121—28no—
570#121—28no—
571#121—44no—
572#121—44no—
573#121—48no—
574#120—28no—
575#120—28no—
576C4×Q8—216no—
577C4×Q8—216no—
578C4×Q8—416no—
579C4×Q8—44no—
580C4×Q8—44no—
581C4×Q8—44no—
582C4×Q8—44no—
583C4×Q8—44no—
584C4×Q8—44no—
585C4×D4—216no—
586C4×D4—216no—
587C4×D4—44no—
588C4×D4—44no—
589C4×D4—48no—
590C4×D4—48no—
591#117—24no—
592#117—24no—
593#117—24no—
594#117—24no—
595#117—48no—
596#117—48no—
597#117—48no—
598#117—44no—
599#117—44no—
600#117#4118yes—
601#117#4118yes—
602C2×C4⋊C4—24no—
603C2×C4⋊C4—24no—
604C2×C4⋊C4—24no—
605C2×C4⋊C4—48no—
606C2×C4⋊C4—44no—
607C2×C4⋊C4—44no—
608C2×C4⋊C4—44no—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C22⋊C4—44no—
646C2×C22⋊C4—44no—
647C2×C22⋊C4—44no—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2412yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2412yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2412yes—
684C2×C42—24no—
685C2×C42—24no—
686C2×C42—44no—
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2414yes—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2418yes—
699C2×C42C2414yes—
700C2×C42C2414yes—
701C2×C42C2414yes—
702C2×C42C2414yes—
703C2×C42C2418yes—
704C2×C42C2418yes—
705C2×C42C2414yes—
706C2×C42C2414yes—
707C2×C42C2414yes—
708C2×C42C2418yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711#95C2412yes—
712#95C2412yes—
713#95C2412yes—
714#95C2412yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2418yes—
728#95C2418yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2418yes—
734#95C2414yes—
735#95C2418yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748C24—22no—
749C24—22no—
750C24—22no—
751C24—42no—
752C24—42no—
753C24C2512yes—
754C24C2512yes—
755C24C2512yes—
756C24C2511yescharacteristic
757#41—416no—
758#41—416no—
759C2×Q8—28no—
760C2×Q8—24no—
761C2×Q8—24no—
762C2×Q8—22no—
763C2×Q8—22no—
764C2×Q8—24no—
765C2×Q8—24no—
766C2×Q8—22no—
767C2×Q8—22no—
768C2×Q8—28no—
769C2×Q8—24no—
770C2×Q8—24no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—28no—
774C2×Q8—44no—
775C2×Q8—44no—
776C2×Q8—44no—
777C2×Q8—416no—
778C2×D4—24no—
779C2×D4—24no—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—24no—
784C2×D4—22no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4—28no—
789C2×D4—28no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4—48no—
798C22×C4—24no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—22no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—42no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—416no—
833C22×C4C2×#4114yes—
834C22×C4C2×#4114yes—
835C22×C4H(5,𝔽2)14yes—
836C22×C4C2512yes—
837C22×C4C2512yes—
838C22×C4C2512yes—
839C22×C4C2514yes—
840C22×C4C2514yes—
841C22×C4C2514yes—
842C22×C4C2512yes—
843C22×C4C2512yes—
844C22×C4C2514yes—
845C22×C4C2512yes—
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2514yes—
850C22×C4C2514yes—
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2512yes—
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C4⋊C4—24no—
858C4⋊C4—24no—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—28no—
867C4⋊C4—216no—
868C4⋊C4—216no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—216no—
880C4⋊C4—48no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—48no—
884C4⋊C4—48no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—44no—
890C4⋊C4—48no—
891C4⋊C4C2×#4118yes—
892C4⋊C4C2×#4118yes—
893C22⋊C4—24no—
894C22⋊C4—24no—
895C22⋊C4—24no—
896C22⋊C4—24no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—216no—
902C22⋊C4—216no—
903C22⋊C4—24no—
904C22⋊C4—24no—
905C22⋊C4—28no—
906C22⋊C4—28no—
907C22⋊C4—42no—
908C22⋊C4—42no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—48no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—48no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4C2×#4118yes—
928C22⋊C4C2×#4118yes—
929C42—24no—
930C42—24no—
931C42—22no—
932C42—22no—
933C42—22no—
934C42—22no—
935C42—24no—
936C42—24no—
937C42—24no—
938C42—24no—
939C42—28no—
940C42—48no—
941C42—44no—
942C42—48no—
943C42—44no—
944C42—44no—
945C42—44no—
946C42—44no—
947C42—44no—
948C42—48no—
949C42—48no—
950C42—44no—
951C42C2×#4118yes—
952C42C2×#4118yes—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—24no—
965C23—22no—
966C23—22no—
967C23—24no—
968C23—24no—
969C23—22no—
970C23—24no—
971C23—22no—
972C23—44no—
973C23—44no—
974C23—44no—
975C23—84no—
976C23—84no—
977C23C22×#4112yes—
978C23C22×#4112yes—
979C23C2×H(5,𝔽2)12yes—
980C23C2611yescharacteristic
981Q8—416no—
982Q8—48no—
983Q8—48no—
984Q8—44no—
985Q8—44no—
986Q8—88no—
987D4—48no—
988D4—48no—
989D4—44no—
990D4—44no—
991D4—88no—
992D4—88no—
993D4—164no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—28no—
1029C2×C4—28no—
1030C2×C4—24no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—28no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—48no—
1042C2×C4—44no—
1043C2×C4—48no—
1044C2×C4—48no—
1045C2×C4—48no—
1046C2×C4—48no—
1047C2×C4—48no—
1048C2×C4—84no—
1049C2×C4—84no—
1050C2×C4—84no—
1051C2×C4—84no—
1052C2×C4—164no—
1053C2×C4—164no—
1054C2×C4#559116yes—
1055C2×C4C22×#4118yes—
1056C2×C4C22×#4118yes—
1057C2×C4C22×#4112yes—
1058C2×C4C22×#4112yes—
1059C2×C4C22×#4112yes—
1060C2×C4C22×#4112yes—
1061C2×C4C2×H(5,𝔽2)12yes—
1062C2×C4C2×H(5,𝔽2)12yes—
1063C2×C4#58514yes—
1064C22—24no—
1065C22—24no—
1066C22—22no—
1067C22—22no—
1068C22—42no—
1069C22—44no—
1070C22—44no—
1071C22—42no—
1072C22—42no—
1073C22—44no—
1074C22—44no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—88no—
1086C22C2×#55914yes—
1087C22C23×#4111yescharacteristic
1088C22C23×#4111yescharacteristic
1089C22C22×H(5,𝔽2)11yescharacteristic
1090C22C2×#58512yes—
1091C222−1+612yes—
1092C4—24no—
1093C4—28no—
1094C4—28no—
1095C4—42no—
1096C4—44no—
1097C4—42no—
1098C4—42no—
1099C4—44no—
1100C4—42no—
1101C4—44no—
1102C4—44no—
1103C4—42no—
1104C4—42no—
1105C4—44no—
1106C4—42no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—44no—
1111C4C2×#55914yes—
1112C4C2×#55914yes—
1113C2—24no—
1114C2—82no—
1115C2—82no—
1116C2—82no—
1117C2C22×#55911yescharacteristic
1118C2#6283611yescharacteristic
1119C2#6288711yescharacteristic
1120C2#6299312yes—
1121C2#6300912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35634C2
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. #59643C2semidirect
3. #59639C2semidirect
4. #59626C2semidirect
5. #59451C2semidirect
6. #45222C2semidirect
7. #45201C2semidirect
8. #45167C2semidirect
9. #44986C2semidirect
10. #44105C2semidirect
11. #35672C2semidirect
13. #35628C2semidirect
14. #35628C2semidirect
15. #35618C2semidirect
16. #35530C2semidirect
17. #34813C2semidirect
18. #34813C2semidirect
19. C2×#2499C2semidirect
20. #34276C2semidirect
21. #34276C2semidirect
22. #34215C2semidirect
23. #34214C2semidirect
24. #34201C2semidirect
25. #34201C2semidirect
38. #2808C22semidirect
41. #2798C22semidirect
44. #2794C22semidirect
46. #2773C22semidirect
50. #2607C22semidirect
51. #2597C22semidirect
53. #2596C22semidirect
54. #2596C22semidirect
57. #2592C22semidirect
58. #2592C22semidirect
59. #2589C22semidirect
60. #2575C22semidirect
61. #2570C22semidirect
62. #2568C22semidirect
63. #2568C22semidirect
70. #2517C22semidirect
74. #2511C22semidirect
75. #2504C22semidirect
76. #2503C22semidirect
77. #2502C22semidirect
79. #2501C22semidirect
80. #2500C22semidirect
81. #2500C22semidirect
86. #2499C22semidirect
87. #2499C22semidirect
90. #2492C22semidirect
91. #2492C22semidirect
98. #2489C22semidirect
99. #2489C22semidirect
108. #2458C22semidirect
114. #2423C22semidirect
115. #2422C22semidirect
118. #2421C22semidirect
119. #2420C22semidirect
123. #2374C22semidirect
129. #2362C22semidirect
130. #2362C22semidirect
132. #2360C22semidirect
133. #2360C22semidirect
136. #2355C22semidirect
137. #2355C22semidirect
138. #2355C22semidirect
139. #2355C22semidirect
144. Q8×C4⋊C4C22semidirect
145. #2331C22semidirect
146. #2330C22semidirect
147. #2327C22semidirect
148. #2327C22semidirect
149. #2326C22semidirect
150. #2326C22semidirect
160. C4×C4⋊Q8C22semidirect
161. C4×C4⋊Q8C22semidirect
162. C4×C4⋊Q8C22semidirect
163. C4×#125C22semidirect
166. C4×#124C22semidirect
167. C4×#124C22semidirect

Maximal subgroups

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

subgroupindex
#596452
#596432
#596392
#596262
#594512
#452222
#452012
#451672
#449862
#441052
#356722
#356342
#356282
#356182
#355302
#348132
C2×#24992
#342762
#342152
#342142
#342012