Finite Group Databasebeta

← #7652673

Subgroups — #7652673

Order 512.

4940 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42729C214yesmaximal, complemented
2#42694C214yesmaximal, complemented
3#42624C214yesmaximal, complemented
4#42515C214yesmaximal, complemented
5#40722C218yesmaximal, complemented
6#40179C214yesmaximal, complemented
7#40002C214yesmaximal, complemented
8#39789C214yesmaximal, complemented
9#39194C214yesmaximal, complemented
10#38571C218yesmaximal, complemented
11#35629C211yesmaximal, characteristic, complemented
12#35584C211yesmaximal, characteristic, complemented
13#35532C211yesmaximal, characteristic, complemented
14#35531C211yesmaximal, characteristic, complemented
15#35515C211yesmaximal, characteristic, complemented
16#35514C211yesmaximal, characteristic
17#35330C211yesmaximal, characteristic, complemented
18#35264C211yesmaximal, characteristic, complemented
19#35151C211yesmaximal, characteristic, complemented
20#34814C211yesmaximal, characteristic, complemented
21#34813C211yesmaximal, characteristic, complemented
22C2×#2500C211yesmaximal, characteristic, complemented
23#34255C211yesmaximal, characteristic, complemented
24#34214C211yesmaximal, characteristic, complemented
25#34201C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#544C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#533C2211yescharacteristic
30C2×#525C2211yescharacteristic
31C22×#121C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C22×#117C2211yescharacteristic
35#2862C2212yescomplemented
36#2861C2212yescomplemented
37#2859C2212yescomplemented
38#2858C2212yescomplemented
39#2855C2214yes—
40#2837C2218yescomplemented
41#2829C2218yescomplemented
42#2801C2218yescomplemented
43#2801C2218yescomplemented
44#2800C2218yescomplemented
45#2800C2218yescomplemented
46#2759C2218yescomplemented
47#2754C2218yescomplemented
48#2742C2218yescomplemented
49#2741C2218yescomplemented
50#2738C2218yescomplemented
51#2737C2218yescomplemented
52#2730C2218yescomplemented
53#2712C2218yescomplemented
54#2702C2218yescomplemented
55#2701C2218yescomplemented
56#2700C2218yescomplemented
57#2672C2218yescomplemented
58#2663C2218yescomplemented
59#2662C2218yescomplemented
60#2660C2212yescomplemented
61#2660C2212yescomplemented
62#2653C2218yescomplemented
63#2650C2218yescomplemented
64#2641C2212yescomplemented
65#2640C2212yescomplemented
66#2632C2218yescomplemented
67#2626C2214yes—
68#2624C2218yescomplemented
69#2580C2214yescomplemented
70#2567C2212yescomplemented
71#2566C2212yescomplemented
72#2565C2212yescomplemented
73#2561C2214yes—
74#2550C2214yescomplemented
75#2550C2214yescomplemented
76#2549C2218yes—
77#2542C2212yescomplemented
78#2538C2214yescomplemented
79#2537C2214yes—
80#2535C2214yes—
81#2525C2218yescomplemented
82#2514C2214yescomplemented
83#2513C2214yescomplemented
84#2510C2218yes—
85#2504C2212yescomplemented
86#2501C2212yescomplemented
87#2500C2214yes—
88#2500C2214yes—
89#2500C2214yes—
90#2500C2214yes—
91#2500C2212yescomplemented
92#2500C2212yescomplemented
93#2497C2212yescomplemented
94#2496C2212yescomplemented
95#2495C2214yescomplemented
96#2495C2212yescomplemented
97#2494C2212yescomplemented
98#2494C2214yescomplemented
99#2494C2218yescomplemented
100#2493C2214yes—
101#2492C2212yescomplemented
102#2491C2214yes—
103#2491C2214yes—
104#2491C2214yescomplemented
105#2491C2212yescomplemented
106#2490C2214yes—
107#2490C2214yes—
108#2490C2214yescomplemented
109#2490C2212yescomplemented
110#2489C2212yescomplemented
111#2488C2214yes—
112#2480C2214yes—
113#2477C2218yescomplemented
114#2474C2218yescomplemented
115#2472C2214yes—
116#2472C2218yes—
117#2458C2218yescomplemented
118#2454C2214yescomplemented
119#2452C2214yescomplemented
120#2449C2218yes—
121#2448C2214yescomplemented
122#2445C2214yescomplemented
123#2441C2214yescomplemented
124#2441C2214yescomplemented
125#2441C2214yescomplemented
126#2440C2214yescomplemented
127#2439C2214yescomplemented
128#2439C2214yescomplemented
129#2437C2218yes—
130#2435C2214yes—
131#2428C2214yes—
132#2427C2214yes—
133#2426C2218yescomplemented
134#2418C2218yes—
135#2412C2214yes—
136#2410C2214yes—
137#2401C2214yescomplemented
138#2398C2214yescomplemented
139C2×#394C2214yes—
140#2363C2214yescomplemented
141#2362C2214yescomplemented
142#2360C2218yes—
143#2357C2214yescomplemented
144#2355C2214yescomplemented
145#2354C2214yescomplemented
146#2354C2214yescomplemented
147#2352C2214yescomplemented
148Q8×C4⋊C4C2214yescomplemented
149#2342C2218yes—
150#2337C2218yescomplemented
151#2330C2214yescomplemented
152#2323C2218yescomplemented
153#2321C2214yes—
154#2319C2214yescomplemented
155#2317C2211yescharacteristic
156#2317C2211yescharacteristic
157#2317C2211yescharacteristic
158#2317C2211yescharacteristic
159#2316C2211yescharacteristic
160#2311C2211yescharacteristic
161#2311C2211yescharacteristic
162#2309C2211yescharacteristic
163#2309C2211yescharacteristic
164C4×C4⋊Q8C2214yescomplemented
165C4×#126C2214yescomplemented
166C4×#124C2214yescomplemented
167C4×#123C2214yes—
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172#2293C2214yescomplemented
173C2×#390C2211yescharacteristic
174C2×#390C2211yescharacteristic
175C2×#388C2214yes—
176#2285C2211yescharacteristic
177C2×#384C2211yescharacteristic
178C2×#382C2211yescharacteristic
179#2280C2211yescharacteristic
180#2280C2211yescharacteristic
181#2280C2211yescharacteristic
182#2274C2211yescharacteristic
183#2274C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×D4C2311yescharacteristic
189C23×D4C2312yes—
190C24×C4C2311yescharacteristic
191#544—44no—
192#544—44no—
193#535—44no—
194#533—28no—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×#127C2312yes—
201C2×#126C2314yes—
202C2×#125C2312yes—
203C2×#125C2312yes—
204C2×#125C2312yes—
205C2×#125C2312yes—
206C2×#125C2312yes—
207C2×#124C2318yes—
208C2×#124C2312yes—
209C2×#124C2314yes—
210C2×#124C2318yes—
211#525—28no—
212C2×#123C2312yes—
213C2×#123C2318yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2318yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2318yes—
220C2×#121—44no—
221C2×#121C2312yes—
222C2×#121C2314yes—
223C2×#121C2314yes—
224C2×#121C2312yes—
225C2×#121C2312yes—
226C2×#121C2318yes—
227C2×#120C2312yes—
228C2×#120C2314yes—
229#520—44no—
230#518—28no—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2318yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2314yes—
239C2×#117—44no—
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2314yes—
247C2×#117C2312yes—
248C2×#117C2314yes—
249C2×#117C2318yes—
250C2×#117C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2314yes—
256C22×C22⋊C4C2314yes—
257C22×C22⋊C4C2312yes—
258C22×C22⋊C4C2312yes—
259C22×C22⋊C4C2312yes—
260C22×C22⋊C4C2314yes—
261C22×C22⋊C4C2314yes—
262C22×C42C2311yescharacteristic
263C22×C42C2311yescharacteristic
264C22×C42C2312yes—
265#401C2318yes—
266#401C2314yes—
267#400C2318yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#399C2318yes—
274#399C2318yes—
275#399C2318yes—
276#399C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#397C2318yes—
281#397C2314yes—
282#397C2318yes—
283#397C2314yes—
284#397C2318yes—
285#397C2314yes—
286#397C2318yes—
287#397C2318yes—
288#397C2314yes—
289#397C2318yes—
290#397C2314yes—
291#396C2318yes—
292#396C2318yes—
293#396C2318yes—
294#396C2314yes—
295#396C2318yes—
296#396C2318yes—
297#395C2318yes—
298#395C2318yes—
299#395C2318yes—
300#394C2314yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2314yes—
313#394C2318yes—
314#393C2318yes—
315#393C2318yes—
316#393C2318yes—
317#393C2314yes—
318#393C2318yes—
319#393C2314yes—
320#392C2318yes—
321#391C2318yes—
322#391C2311yescharacteristic
323#391C2312yes—
324#391C2312yes—
325#391C2311yescharacteristic
326#391C2314yes—
327#391C2318yes—
328#391C2318yes—
329#391C2318yes—
330#391C2312yes—
331#390C2314yes—
332#390C2312yes—
333#390C2312yes—
334#390C2312yes—
335#390C2314yes—
336#390C2312yes—
337#390C2311yescharacteristic
338#390C2312yes—
339#390C2312yes—
340#390C2318yes—
341#390C2312yes—
342#390C2314yes—
343#390C2312yes—
344#390C2318yes—
345#390C2314yes—
346#390C2314yes—
347#390C2312yes—
348#390C2311yescharacteristic
349#390C2318yes—
350#390C2312yes—
351#390C2312yes—
352#389C2314yes—
353#389C2314yes—
354#389C2318yes—
355#389C2318yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2312yes—
361#389C2318yes—
362#389C2318yes—
363#389C2312yes—
364#389C2318yes—
365#389C2318yes—
366#389C2318yes—
367#389C2312yes—
368#389C2312yes—
369#388C2314yes—
370#388C2314yes—
371#388C2314yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2314yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2314yes—
390#388C2318yes—
391#388C2318yes—
392#388C2314yes—
393#388C2314yes—
394#388C2318yes—
395#387C2314yes—
396#387C2314yes—
397#387C2314yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#386C2314yes—
406#386C2314yes—
407#386C2318yes—
408#386C2318yes—
409#386C2318yes—
410#386C2318yes—
411#386C2314yes—
412#386C2314yes—
413#385C2318yes—
414#385C2314yes—
415#385C2314yes—
416#385C2314yes—
417#385C2314yes—
418#385C2318yes—
419#385C2318yes—
420#385C2314yes—
421#385C2314yes—
422#384C2312yes—
423#384C2312yes—
424#384C2312yes—
425#384C2312yes—
426#384C2312yes—
427#384C2312yes—
428#384C2314yes—
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#383C2314yes—
432#383C2318yes—
433#382C2312yes—
434#382C2312yes—
435#382C2312yes—
436#382C2312yes—
437#382C2311yescharacteristic
438#382C2312yes—
439#382C2311yescharacteristic
440#382C2312yes—
441#382C2314yes—
442#382C2314yes—
443#381C2312yes—
444#381C2312yes—
445#381C2318yes—
446#381C2312yes—
447#380C2314yes—
448#380C2314yes—
449#380C2314yes—
450#380C2318yes—
451#380C2318yes—
452#380C2312yes—
453#380C2312yes—
454#380C2318yes—
455#380C2314yes—
456#380C2312yes—
457#380C2312yes—
458#380C2312yes—
459#380C2312yes—
460#379C2314yes—
461#379C2314yes—
462#379C2312yes—
463#379C2312yes—
464#379C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2318yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C22⋊C4C2312yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2318yes—
485C4×C22⋊C4C2318yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495#376C2312yes—
496#376C2312yes—
497C2×#95C2314yes—
498C2×#95C2312yes—
499C43C2312yes—
500C43C2312yes—
501C25C2412yes—
502C25C2411yescharacteristic
503C2×#41—24no—
504C2×#41—24no—
505C2×#41—24no—
506C22×Q8C2411yescharacteristic
507C22×Q8C2414yes—
508C22×Q8C2414yes—
509C22×Q8C2414yes—
510C22×D4—24no—
511C22×D4—24no—
512C22×D4—24no—
513C22×D4—44no—
514C22×D4—84no—
515C22×D4C2412yes—
516C22×D4C2412yes—
517C22×D4C2412yes—
518C22×D4C2411yescharacteristic
519C22×D4C2414yes—
520C22×D4C2414yes—
521C22×D4C2414yes—
522C22×D4C2418yes—
523C23×C4—24no—
524C23×C4—24no—
525C23×C4—24no—
526C23×C4C2411yescharacteristic
527C23×C4C2412yes—
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2418yes—
536C23×C4C2414yes—
537C23×C4C2411yescharacteristic
538C4⋊Q8—28no—
539C4⋊Q8—44no—
540C4⋊Q8—44no—
541C4⋊Q8—44no—
542C4⋊Q8—44no—
543#127—44no—
544#126—48no—
545#125—28no—
546#125—44no—
547#125—44no—
548#125—44no—
549#125—44no—
550#124—416no—
551#124—44no—
552#124—48no—
553#124—88no—
554#123—28no—
555#123—88no—
556C22⋊Q8—28no—
557C22⋊Q8—216no—
558C22⋊Q8—48no—
559C22⋊Q8—48no—
560C22⋊Q8—416no—
561C22⋊Q8—88no—
562#121—28no—
563#121—48no—
564#121—48no—
565#121—44no—
566#121—44no—
567#121—88no—
568#120—28no—
569#120—48no—
570C4×Q8—216no—
571C4×Q8—44no—
572C4×Q8—88no—
573C4×D4—216no—
574C4×D4—216no—
575C4×D4—216no—
576C4×D4—44no—
577C4×D4—48no—
578#117—24no—
579#117—24no—
580#117—24no—
581#117—24no—
582#117—24no—
583#117—24no—
584#117—48no—
585#117—48no—
586#117—44no—
587#117—88no—
588#117#4118yes—
589C2×C4⋊C4—24no—
590C2×C4⋊C4—24no—
591C2×C4⋊C4—24no—
592C2×C4⋊C4—44no—
593C2×C4⋊C4—84no—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2412yes—
634C2×C22⋊C4—216no—
635C2×C22⋊C4—48no—
636C2×C22⋊C4—44no—
637C2×C22⋊C4—44no—
638C2×C22⋊C4—44no—
639C2×C22⋊C4—84no—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2412yes—
679C2×C42—24no—
680C2×C42—24no—
681C2×C42—44no—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2414yes—
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2412yes—
695C2×C42C2414yes—
696C2×C42C2418yes—
697C2×C42C2414yes—
698C2×C42C2418yes—
699C2×C42C2414yes—
700C2×C42C2418yes—
701C2×C42C2414yes—
702C2×C42C2412yes—
703#95C2412yes—
704#95C2412yes—
705#95C2412yes—
706#95C2412yes—
707#95C2418yes—
708#95C2418yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2418yes—
716#95C2414yes—
717#95C2418yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2418yes—
723#95C2418yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2418yes—
732#95C2414yes—
733#95C2418yes—
734#95C2418yes—
735#95C2414yes—
736#95C2418yes—
737#95C2418yes—
738C24—22no—
739C24—24no—
740C24—22no—
741C24—24no—
742C24—22no—
743C24—24no—
744C24—42no—
745C24—42no—
746C24—44no—
747C24—44no—
748C24C2512yes—
749C24C2514yes—
750C24C2512yes—
751C24C2511yescharacteristic
752#41—416no—
753C2×Q8—28no—
754C2×Q8—22no—
755C2×Q8—22no—
756C2×Q8—22no—
757C2×Q8—28no—
758C2×Q8—44no—
759C2×Q8—44no—
760C2×Q8—44no—
761C2×Q8—48no—
762C2×Q8—48no—
763C2×D4—24no—
764C2×D4—24no—
765C2×D4—24no—
766C2×D4—24no—
767C2×D4—24no—
768C2×D4—22no—
769C2×D4—28no—
770C2×D4—22no—
771C2×D4—24no—
772C2×D4—24no—
773C2×D4—24no—
774C2×D4—24no—
775C2×D4—22no—
776C2×D4—48no—
777C2×D4—44no—
778C2×D4—48no—
779C2×D4—44no—
780C2×D4—48no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—416no—
786C2×D4—816no—
787C22×C4—24no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—216no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—44no—
809C22×C4—42no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—48no—
813C22×C4—48no—
814C22×C4—44no—
815C22×C4—48no—
816C22×C4—416no—
817C22×C4C2×#4114yes—
818C22×C4H(5,𝔽2)14yes—
819C22×C42−1+414yes—
820C22×C4C2512yes—
821C22×C4C2512yes—
822C22×C4C2512yes—
823C22×C4C2512yes—
824C22×C4C2512yes—
825C22×C4C2514yes—
826C22×C4C2514yes—
827C22×C4C2514yes—
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2514yes—
831C22×C4C2514yes—
832C22×C4C2512yes—
833C22×C4C2514yes—
834C22×C4C2512yes—
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2512yes—
839C22×C4C2511yescharacteristic
840C22×C4C2511yescharacteristic
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—28no—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—22no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—24no—
860C4⋊C4—28no—
861C4⋊C4—44no—
862C4⋊C4—48no—
863C4⋊C4—48no—
864C4⋊C4—44no—
865C4⋊C4—48no—
866C4⋊C4—48no—
867C4⋊C4—48no—
868C4⋊C4—48no—
869C4⋊C4—48no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4C2×#4118yes—
881C22⋊C4—24no—
882C22⋊C4—24no—
883C22⋊C4—24no—
884C22⋊C4—24no—
885C22⋊C4—24no—
886C22⋊C4—24no—
887C22⋊C4—216no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—216no—
891C22⋊C4—24no—
892C22⋊C4—24no—
893C22⋊C4—28no—
894C22⋊C4—42no—
895C22⋊C4—48no—
896C22⋊C4—42no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—44no—
902C22⋊C4—48no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4C2×#4118yes—
920C42—24no—
921C42—22no—
922C42—22no—
923C42—24no—
924C42—24no—
925C42—24no—
926C42—24no—
927C42—24no—
928C42—24no—
929C42—22no—
930C42—22no—
931C42—24no—
932C42—28no—
933C42—48no—
934C42—44no—
935C42—44no—
936C42—48no—
937C42—44no—
938C42—48no—
939C42—44no—
940C42C2×#4118yes—
941C23—22no—
942C23—22no—
943C23—24no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—24no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—24no—
952C23—22no—
953C23—28no—
954C23—24no—
955C23—22no—
956C23—24no—
957C23—28no—
958C23—22no—
959C23—22no—
960C23—44no—
961C23—44no—
962C23—44no—
963C23—48no—
964C23—84no—
965C23—84no—
966C23—84no—
967C23—88no—
968C23—84no—
969C23—88no—
970C23C22×#4112yes—
971C23C2×H(5,𝔽2)12yes—
972C23C2×2−1+412yes—
973C23C2611yescharacteristic
974Q8—416no—
975Q8—44no—
976Q8—164no—
977Q8—164no—
978D4—48no—
979D4—48no—
980D4—48no—
981D4—44no—
982D4—88no—
983D4—816no—
984D4—164no—
985D4—164no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—28no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—28no—
1026C2×C4—24no—
1027C2×C4—28no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—22no—
1032C2×C4—48no—
1033C2×C4—44no—
1034C2×C4—48no—
1035C2×C4—48no—
1036C2×C4—48no—
1037C2×C4—816no—
1038C2×C4—84no—
1039C2×C4—84no—
1040C2×C4—84no—
1041C2×C4—84no—
1042C2×C4—164no—
1043C2×C4#542116yes—
1044C2×C4C22×#4118yes—
1045C2×C4C22×#4112yes—
1046C2×C4C22×#4112yes—
1047C2×C4C2×H(5,𝔽2)12yes—
1048C2×C4C2×H(5,𝔽2)12yes—
1049C2×C4C2×2−1+412yes—
1050C2×C4C2×2−1+412yes—
1051C2×C4#58514yes—
1052C22—24no—
1053C22—22no—
1054C22—22no—
1055C22—24no—
1056C22—48no—
1057C22—42no—
1058C22—44no—
1059C22—42no—
1060C22—42no—
1061C22—44no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—44no—
1066C22—44no—
1067C22—42no—
1068C22—42no—
1069C22—48no—
1070C22—42no—
1071C22—42no—
1072C22—44no—
1073C22—88no—
1074C22—168no—
1075C22C2×#54214yes—
1076C22C23×#4111yescharacteristic
1077C22C22×H(5,𝔽2)11yescharacteristic
1078C22C22×2−1+411yescharacteristic
1079C22C2×#58512yes—
1080C22H(7,𝔽2)12yes—
1081C4—24no—
1082C4—28no—
1083C4—42no—
1084C4—44no—
1085C4—44no—
1086C4—42no—
1087C4—44no—
1088C4—42no—
1089C4—42no—
1090C4—44no—
1091C4—44no—
1092C4—42no—
1093C4—42no—
1094C4—42no—
1095C4—44no—
1096C4—42no—
1097C4—42no—
1098C4—42no—
1099C4—42no—
1100C4C2×#54214yes—
1101C4C2×#54214yes—
1102C2—24no—
1103C2—82no—
1104C2—82no—
1105C2—84no—
1106C2C22×#54211yescharacteristic
1107C2#6283611yescharacteristic
1108C2#6287611yescharacteristic
1109C2#6292912yes—
1110C2#6300812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35514C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42729C2semidirect
2. #42694C2semidirect
3. #42624C2semidirect
4. #42515C2semidirect
5. #40722C2semidirect
6. #40179C2semidirect
7. #40002C2semidirect
8. #39789C2semidirect
9. #39194C2semidirect
10. #38571C2semidirect
11. #35629C2semidirect
12. #35584C2semidirect
13. #35532C2semidirect
14. #35531C2semidirect
15. #35515C2semidirect
17. #35330C2semidirect
18. #35264C2semidirect
19. #35151C2semidirect
20. #34814C2semidirect
21. #34813C2semidirect
22. C2×#2500C2semidirect
23. #34255C2semidirect
24. #34214C2semidirect
25. #34201C2semidirect
35. #2862C22semidirect
36. #2861C22semidirect
37. #2859C22semidirect
38. #2858C22semidirect
40. #2837C22semidirect
41. #2829C22semidirect
42. #2801C22semidirect
43. #2801C22semidirect
44. #2800C22semidirect
45. #2800C22semidirect
46. #2759C22semidirect
47. #2754C22semidirect
48. #2742C22semidirect
49. #2741C22semidirect
50. #2738C22semidirect
51. #2737C22semidirect
52. #2730C22semidirect
53. #2712C22semidirect
54. #2702C22semidirect
55. #2701C22semidirect
56. #2700C22semidirect
57. #2672C22semidirect
58. #2663C22semidirect
59. #2662C22semidirect
60. #2660C22semidirect
61. #2660C22semidirect
62. #2653C22semidirect
63. #2650C22semidirect
64. #2641C22semidirect
65. #2640C22semidirect
66. #2632C22semidirect
68. #2624C22semidirect
69. #2580C22semidirect
70. #2567C22semidirect
71. #2566C22semidirect
72. #2565C22semidirect
74. #2550C22semidirect
75. #2550C22semidirect
77. #2542C22semidirect
78. #2538C22semidirect
81. #2525C22semidirect
82. #2514C22semidirect
83. #2513C22semidirect
85. #2504C22semidirect
86. #2501C22semidirect
91. #2500C22semidirect
92. #2500C22semidirect
93. #2497C22semidirect
94. #2496C22semidirect
95. #2495C22semidirect
96. #2495C22semidirect
97. #2494C22semidirect
98. #2494C22semidirect
99. #2494C22semidirect
101. #2492C22semidirect
104. #2491C22semidirect
105. #2491C22semidirect
108. #2490C22semidirect
109. #2490C22semidirect
110. #2489C22semidirect
113. #2477C22semidirect
114. #2474C22semidirect
117. #2458C22semidirect
118. #2454C22semidirect
119. #2452C22semidirect
121. #2448C22semidirect
122. #2445C22semidirect
123. #2441C22semidirect
124. #2441C22semidirect
125. #2441C22semidirect
126. #2440C22semidirect
127. #2439C22semidirect
128. #2439C22semidirect
133. #2426C22semidirect
137. #2401C22semidirect
138. #2398C22semidirect
140. #2363C22semidirect
141. #2362C22semidirect
143. #2357C22semidirect
144. #2355C22semidirect
145. #2354C22semidirect
146. #2354C22semidirect
147. #2352C22semidirect
148. Q8×C4⋊C4C22semidirect
150. #2337C22semidirect
151. #2330C22semidirect
152. #2323C22semidirect
154. #2319C22semidirect
164. C4×C4⋊Q8C22semidirect
165. C4×#126C22semidirect
166. C4×#124C22semidirect
172. #2293C22semidirect

Maximal subgroups

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

subgroupindex
#427292
#426942
#426242
#425152
#407222
#401792
#400022
#397892
#391942
#385712
#356292
#355842
#355322
#355312
#355152
#355142
#353302
#352642
#351512
#348142
#348132
C2×#25002
#342552
#342142
#342012