Finite Group Databasebeta

← #7650065

Subgroups — #7650065

Order 512.

5400 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42624C214yesmaximal, complemented
2#42561C214yesmaximal, complemented
3#42472C214yesmaximal, complemented
4#42457C214yesmaximal, complemented
5#40699C218yesmaximal, complemented
6#40203C214yesmaximal, complemented
7#39903C214yesmaximal, complemented
8#39406C214yesmaximal, complemented
9#39351C214yesmaximal, complemented
10#37723C218yesmaximal, complemented
11#35592C211yesmaximal, characteristic, complemented
12#35576C211yesmaximal, characteristic, complemented
13#35558C211yesmaximal, characteristic, complemented
14#35556C211yesmaximal, characteristic, complemented
15#35532C211yesmaximal, characteristic, complemented
16#35530C211yesmaximal, characteristic, complemented
17#35264C211yesmaximal, characteristic, complemented
18#35256C211yesmaximal, characteristic
19#35152C211yesmaximal, characteristic, complemented
20C2×#2542C211yesmaximal, characteristic, complemented
21#34816C211yesmaximal, characteristic, complemented
22#34745C211yesmaximal, characteristic, complemented
23#34265C211yesmaximal, characteristic, complemented
24#34214C211yesmaximal, characteristic, complemented
25#34188C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#542C2218yescomplemented
28C2×#537C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C2×#533C2211yescharacteristic
32C22×C4⋊Q8C2211yescharacteristic
33C22×C22⋊Q8C2214yes—
34C2×#520C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C22×C4×D4C2211yescharacteristic
37#2861C2212yes—
38#2858C2212yes—
39#2856C2212yes—
40#2850C2212yes—
41#2849C2214yes—
42#2838C2218yescomplemented
43#2829C2218yescomplemented
44#2801C2218yescomplemented
45#2796C2218yescomplemented
46#2777C2218yescomplemented
47#2754C2218yescomplemented
48#2741C2218yescomplemented
49#2730C2218yescomplemented
50#2729C2218yescomplemented
51#2723C2218yescomplemented
52#2723C2218yescomplemented
53#2710C2218yescomplemented
54#2700C2218yescomplemented
55#2698C2218yescomplemented
56#2692C2218yescomplemented
57#2674C2218yescomplemented
58#2672C2218yescomplemented
59#2672C2218yescomplemented
60#2663C2218yescomplemented
61#2654C2218yescomplemented
62#2651C2218yescomplemented
63#2641C2212yes—
64#2640C2212yes—
65#2638C2218yescomplemented
66#2632C2218yescomplemented
67#2624C2218yescomplemented
68#2622C2214yes—
69#2620C2212yes—
70#2619C2212yes—
71#2592C2214yes—
72#2591C2214yes—
73#2583C2214yes—
74#2567C2212yescomplemented
75#2566C2212yescomplemented
76#2565C2212yescomplemented
77#2551C2214yescomplemented
78#2551C2214yescomplemented
79#2550C2214yescomplemented
80#2550C2214yescomplemented
81#2548C2214yes—
82#2542C2214yes—
83#2542C2214yes—
84#2542C2214yes—
85#2542C2214yes—
86#2542C2212yescomplemented
87#2514C2212yescomplemented
88#2513C2214yes—
89#2513C2214yes—
90#2513C2212yescomplemented
91#2512C2214yes—
92#2512C2214yes—
93#2512C2212yescomplemented
94#2511C2212yescomplemented
95#2510C2214yes—
96#2502C2212yescomplemented
97#2501C2212yescomplemented
98#2500C2212yescomplemented
99#2499C2212yescomplemented
100#2492C2214yescomplemented
101#2492C2214yescomplemented
102#2491C2214yes—
103#2491C2214yes—
104#2491C2214yescomplemented
105#2491C2214yescomplemented
106#2490C2214yes—
107#2490C2214yes—
108#2481C2214yes—
109#2480C2218yes—
110#2479C2218yescomplemented
111#2477C2218yescomplemented
112#2472C2218yes—
113#2472C2218yes—
114#2465C2218yescomplemented
115#2461C2218yescomplemented
116#2454C2212yescomplemented
117#2453C2212yescomplemented
118#2452C2218yescomplemented
119#2452C2212yescomplemented
120#2451C2212yescomplemented
121#2450C2214yes—
122#2449C2214yes—
123#2449C2218yes—
124#2448C2218yescomplemented
125#2447C2214yes—
126#2445C2214yes—
127#2443C2218yes—
128#2441C2214yescomplemented
129#2440C2214yescomplemented
130#2436C2214yes—
131#2434C2214yes—
132#2428C2214yes—
133#2426C2214yes—
134#2424C2218yes—
135#2423C2214yescomplemented
136#2422C2214yes—
137#2422C2214yescomplemented
138#2420C2214yes—
139#2401C2214yescomplemented
140#2396C2214yescomplemented
141C2×#399C2214yes—
142#2367C2214yes—
143#2366C2214yes—
144#2363C2214yes—
145#2361C2214yes—
146#2360C2218yes—
147#2355C2214yescomplemented
148#2355C2214yescomplemented
149#2354C2214yescomplemented
150#2352C2218yes—
151Q8×C4⋊C4C2214yescomplemented
152#2332C2218yescomplemented
153#2330C2214yescomplemented
154#2321C2214yes—
155#2317C2211yescharacteristic
156#2317C2211yescharacteristic
157#2317C2211yescharacteristic
158#2314C2214yescomplemented
159#2311C2211yescharacteristic
160#2311C2211yescharacteristic
161#2311C2211yescharacteristic
162#2309C2211yescharacteristic
163#2309C2211yescharacteristic
164C4×C4⋊Q8C2214yescomplemented
165C4×#126C2214yescomplemented
166C4×C22⋊Q8C2214yescomplemented
167C4×#120C2214yes—
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2297C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176C2×#390C2211yescharacteristic
177C2×#390C2211yescharacteristic
178#2285C2211yescharacteristic
179#2285C2214yescomplemented
180C2×#384C2211yescharacteristic
181C2×#384C2211yescharacteristic
182#2274C2211yescharacteristic
183#2274C2211yescharacteristic
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2312yes—
190C23×D4C2311yescharacteristic
191C24×C4C2312yes—
192#544—44no—
193#542—432no—
194#537—44no—
195#535—28no—
196#535—44no—
197#533—28no—
198C2×C4⋊Q8—44no—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2314yes—
203C2×C4⋊Q8C2314yes—
204C2×C4⋊Q8C2318yes—
205C2×#127C2312yes—
206C2×#127C2312yes—
207C2×#126C2314yes—
208C2×#126C2318yes—
209C2×#125C2312yes—
210C2×#125C2312yes—
211C2×#125C2312yes—
212C2×#124C2312yes—
213C2×#124C2318yes—
214C2×#124C2312yes—
215C2×#124C2318yes—
216C2×#124C2318yes—
217C2×#123C2318yes—
218C2×#123C2318yes—
219C2×C22⋊Q8—416no—
220C2×C22⋊Q8C2318yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2318yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2318yes—
228C2×C22⋊Q8C2318yes—
229C2×C22⋊Q8C2312yes—
230C2×#121C2314yes—
231C2×#121C2314yes—
232C2×#121C2312yes—
233C2×#121C2312yes—
234C2×#121C2312yes—
235C2×#121C2318yes—
236C2×#121C2312yes—
237C2×#120C2314yes—
238C2×#120C2314yes—
239#520—44no—
240C4×#41—28no—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2318yes—
244C2×C4×Q8C2312yes—
245C2×C4×D4—44no—
246C2×C4×D4C2314yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2318yes—
252C2×C4×D4C2314yes—
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2312yes—
258C2×#117C2311yescharacteristic
259C2×#117C2318yes—
260C2×#117C2312yes—
261C2×#117C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2314yes—
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2312yes—
270C22×C22⋊C4C2312yes—
271C22×C22⋊C4C2314yes—
272C22×C22⋊C4C2314yes—
273C22×C42C2312yes—
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277#401C2314yes—
278#400C2314yes—
279#400C2318yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#399C2318yes—
284#399C2318yes—
285#399C2318yes—
286#399C2318yes—
287#399C2318yes—
288#399C2318yes—
289#399C2314yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2314yes—
294#398C2314yes—
295#397C2314yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2314yes—
302#397C2318yes—
303#397C2314yes—
304#397C2318yes—
305#397C2318yes—
306#396C2318yes—
307#396C2314yes—
308#396C2318yes—
309#396C2314yes—
310#396C2318yes—
311#396C2314yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#395C2314yes—
316#395C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#393C2318yes—
328#393C2318yes—
329#393C2314yes—
330#393C2318yes—
331#393C2318yes—
332#392C2318yes—
333#391C2318yes—
334#391C2311yescharacteristic
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#391C2311yescharacteristic
339#391C2318yes—
340#391C2318yes—
341#391C2312yes—
342#391C2311yescharacteristic
343#391C2312yes—
344#391C2311yescharacteristic
345#391C2312yes—
346#391C2314yes—
347#390C2314yes—
348#390C2312yes—
349#390C2312yes—
350#390C2314yes—
351#390C2314yes—
352#390C2311yescharacteristic
353#390C2312yes—
354#390C2312yes—
355#390C2312yes—
356#390C2318yes—
357#390C2314yes—
358#390C2312yes—
359#390C2311yescharacteristic
360#390C2318yes—
361#390C2311yescharacteristic
362#390C2312yes—
363#390C2318yes—
364#390C2312yes—
365#390C2312yes—
366#390C2318yes—
367#390C2312yes—
368#390C2311yescharacteristic
369#390C2312yes—
370#390C2314yes—
371#390C2312yes—
372#389C2314yes—
373#389C2314yes—
374#389C2318yes—
375#389C2318yes—
376#389C2314yes—
377#389C2318yes—
378#389C2318yes—
379#389C2318yes—
380#389C2318yes—
381#389C2312yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#389C2312yes—
386#389C2312yes—
387#389C2314yes—
388#388C2314yes—
389#388C2314yes—
390#388C2314yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2314yes—
415#387C2318yes—
416#387C2314yes—
417#386C2314yes—
418#386C2314yes—
419#386C2314yes—
420#386C2312yes—
421#386C2318yes—
422#386C2312yes—
423#386C2312yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2314yes—
428#386C2312yes—
429#386C2314yes—
430#386C2314yes—
431#385C2318yes—
432#385C2314yes—
433#385C2314yes—
434#385C2314yes—
435#385C2312yes—
436#385C2312yes—
437#385C2312yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2314yes—
442#385C2314yes—
443#385C2312yes—
444#385C2314yes—
445#384C2312yes—
446#384C2312yes—
447#384C2312yes—
448#384C2312yes—
449#384C2312yes—
450#384C2312yes—
451#384C2312yes—
452#384C2314yes—
453#384C2314yes—
454#384C2312yes—
455#383C2314yes—
456#382C2312yes—
457#382C2312yes—
458#382C2312yes—
459#382C2312yes—
460#382C2318yes—
461#381C2318yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2318yes—
467#380C2314yes—
468#379C2314yes—
469#379C2314yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2318yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2318yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2318yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2312yes—
500#376C2312yes—
501C2×#95C2312yes—
502C43C2312yes—
503C25C2412yes—
504C2×#41—24no—
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C2×#41—24no—
509C2×#41—24no—
510C22×Q8—44no—
511C22×Q8—48no—
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2414yes—
515C22×Q8C2418yes—
516C22×Q8C2414yes—
517C22×D4—24no—
518C22×D4—24no—
519C22×D4—24no—
520C22×D4C2412yes—
521C22×D4C2412yes—
522C22×D4C2412yes—
523C22×D4C2412yes—
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2418yes—
527C22×D4C2414yes—
528C22×D4C2414yes—
529C22×D4C2414yes—
530C23×C4—48no—
531C23×C4—44no—
532C23×C4C2411yescharacteristic
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2414yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2411yescharacteristic
541C23×C4C2412yes—
542C23×C4C2418yes—
543C23×C4C2414yes—
544C23×C4C2411yescharacteristic
545C4⋊Q8—28no—
546C4⋊Q8—48no—
547C4⋊Q8—48no—
548C4⋊Q8—44no—
549C4⋊Q8—44no—
550C4⋊Q8—416no—
551#127—28no—
552#127—44no—
553#126—216no—
554#126—416no—
555#125—28no—
556#125—44no—
557#125—44no—
558#124—28no—
559#124—416no—
560#124—44no—
561#124—416no—
562#124—416no—
563#123—416no—
564#123—416no—
565C22⋊Q8—232no—
566C22⋊Q8—216no—
567C22⋊Q8—216no—
568C22⋊Q8—48no—
569C22⋊Q8—416no—
570C22⋊Q8—416no—
571C22⋊Q8—416no—
572C22⋊Q8—416no—
573C22⋊Q8—44no—
574C22⋊Q8—44no—
575#121—216no—
576#121—416no—
577#121—44no—
578#121—44no—
579#121—44no—
580#121—44no—
581#121—48no—
582#120—216no—
583#120—48no—
584C4×Q8—28no—
585C4×Q8—216no—
586C4×Q8—44no—
587C4×Q8—416no—
588C4×D4—28no—
589C4×D4—216no—
590C4×D4—48no—
591C4×D4—48no—
592C4×D4—44no—
593C4×D4—416no—
594C4×D4—48no—
595#117—24no—
596#117—24no—
597#117—24no—
598#117—24no—
599#117—24no—
600#117—28no—
601#117—44no—
602#117—416no—
603#117#4118yes—
604C2×C4⋊C4—24no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—24no—
607C2×C4⋊C4—28no—
608C2×C4⋊C4—44no—
609C2×C4⋊C4—48no—
610C2×C4⋊C4—48no—
611C2×C4⋊C4—44no—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C22⋊C4—48no—
656C2×C22⋊C4—48no—
657C2×C22⋊C4—44no—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
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⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2412yes—
693C2×C42—24no—
694C2×C42—24no—
695C2×C42—24no—
696C2×C42—28no—
697C2×C42C2411yescharacteristic
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2414yes—
707C2×C42C2414yes—
708C2×C42C2412yes—
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2418yes—
713C2×C42C2414yes—
714C2×C42C2418yes—
715C2×C42C2418yes—
716C2×C42C2414yes—
717C2×C42C2412yes—
718#95C2412yes—
719#95C2412yes—
720#95C2412yes—
721#95C2412yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2418yes—
739#95C2414yes—
740#95C2418yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2418yes—
745#95C2418yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750#95C2418yes—
751C24—24no—
752C24—24no—
753C24—24no—
754C24—44no—
755C24—44no—
756C24C2514yes—
757C24C2512yes—
758C24C2512yes—
759C24C2511yescharacteristic
760#41—416no—
761#41—416no—
762C2×Q8—22no—
763C2×Q8—28no—
764C2×Q8—22no—
765C2×Q8—28no—
766C2×Q8—22no—
767C2×Q8—22no—
768C2×Q8—216no—
769C2×Q8—22no—
770C2×Q8—22no—
771C2×Q8—44no—
772C2×Q8—48no—
773C2×Q8—48no—
774C2×Q8—48no—
775C2×Q8—44no—
776C2×Q8—816no—
777C2×D4—24no—
778C2×D4—24no—
779C2×D4—24no—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—22no—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—22no—
787C2×D4—216no—
788C2×D4—24no—
789C2×D4—22no—
790C2×D4—24no—
791C2×D4—22no—
792C2×D4—24no—
793C2×D4—24no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—48no—
797C2×D4—48no—
798C2×D4—44no—
799C2×D4—44no—
800C2×D4—44no—
801C2×D4—48no—
802C2×D4—48no—
803C2×D4—48no—
804C2×D4—416no—
805C22×C4—22no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—22no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—28no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—28no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—216no—
824C22×C4—42no—
825C22×C4—44no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—44no—
834C22×C4—48no—
835C22×C4—816no—
836C22×C4C2×#4114yes—
837C22×C4H(5,𝔽2)14yes—
838C22×C42−1+414yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2512yes—
842C22×C4C2514yes—
843C22×C4C2514yes—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2514yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2514yes—
850C22×C4C2512yes—
851C22×C4C2514yes—
852C22×C4C2514yes—
853C22×C4C2512yes—
854C22×C4C2514yes—
855C22×C4C2512yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C4⋊C4—28no—
861C4⋊C4—24no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—22no—
875C4⋊C4—216no—
876C4⋊C4—216no—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—44no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—48no—
901C4⋊C4C2×#4118yes—
902C4⋊C4H(5,𝔽2)18yes—
903C22⋊C4—24no—
904C22⋊C4—24no—
905C22⋊C4—24no—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—28no—
909C22⋊C4—216no—
910C22⋊C4—216no—
911C22⋊C4—216no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—44no—
921C22⋊C4—48no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—48no—
927C22⋊C4—44no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4C2×#4118yes—
938C42—22no—
939C42—22no—
940C42—24no—
941C42—28no—
942C42—24no—
943C42—22no—
944C42—22no—
945C42—24no—
946C42—24no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—28no—
951C42—24no—
952C42—24no—
953C42—44no—
954C42—48no—
955C42—44no—
956C42—48no—
957C42—48no—
958C42C2×#4118yes—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—24no—
963C23—22no—
964C23—24no—
965C23—28no—
966C23—24no—
967C23—22no—
968C23—24no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—28no—
976C23—416no—
977C23—48no—
978C23—84no—
979C23—88no—
980C23—84no—
981C23C22×#4112yes—
982C23C2×H(5,𝔽2)12yes—
983C23C2×2−1+412yes—
984C23C2611yescharacteristic
985Q8—416no—
986Q8—44no—
987Q8—44no—
988Q8—816no—
989Q8—164no—
990D4—48no—
991D4—48no—
992D4—48no—
993D4—48no—
994D4—44no—
995D4—44no—
996D4—816no—
997D4—164no—
998D4—164no—
999D4—164no—
1000C2×C4—28no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—28no—
1025C2×C4—28no—
1026C2×C4—24no—
1027C2×C4—28no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—416no—
1048C2×C4—48no—
1049C2×C4—48no—
1050C2×C4—44no—
1051C2×C4—48no—
1052C2×C4—48no—
1053C2×C4—816no—
1054C2×C4—84no—
1055C2×C4—84no—
1056C2×C4—84no—
1057C2×C4—164no—
1058C2×C4#542116yescomplemented
1059C2×C4C22×#4118yes—
1060C2×C4C22×#4112yes—
1061C2×C4C22×#4112yes—
1062C2×C4C2×H(5,𝔽2)14yes—
1063C2×C4C2×H(5,𝔽2)14yes—
1064C2×C4C2×H(5,𝔽2)14yes—
1065C2×C4C2×H(5,𝔽2)12yes—
1066C2×C4C2×H(5,𝔽2)12yes—
1067C2×C4C2×2−1+412yes—
1068C2×C4C2×2−1+412yes—
1069C22—24no—
1070C22—22no—
1071C22—22no—
1072C22—24no—
1073C22—44no—
1074C22—44no—
1075C22—48no—
1076C22—44no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—44no—
1081C22—42no—
1082C22—44no—
1083C22—44no—
1084C22—48no—
1085C22—42no—
1086C22—42no—
1087C22—44no—
1088C22—816no—
1089C22C2×#54214yes—
1090C22C23×#4111yescharacteristic
1091C22C22×H(5,𝔽2)12yes—
1092C22C22×H(5,𝔽2)11yescharacteristic
1093C22C22×2−1+411yescharacteristic
1094C222−1+612yes—
1095C4—24no—
1096C4—28no—
1097C4—24no—
1098C4—24no—
1099C4—42no—
1100C4—42no—
1101C4—44no—
1102C4—44no—
1103C4—44no—
1104C4—44no—
1105C4—42no—
1106C4—42no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—44no—
1111C4—44no—
1112C4—42no—
1113C4—42no—
1114C4C2×#54214yes—
1115C4C2×#54214yes—
1116C2—24no—
1117C2—82no—
1118C2—82no—
1119C2—84no—
1120C2C22×#54211yescharacteristic
1121C2#6283211yescharacteristic
1122C2#6288711yescharacteristic
1123C2#6291312yes—
1124C2#6298512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35256C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42624C2semidirect
2. #42561C2semidirect
3. #42472C2semidirect
4. #42457C2semidirect
5. #40699C2semidirect
6. #40203C2semidirect
7. #39903C2semidirect
8. #39406C2semidirect
9. #39351C2semidirect
10. #37723C2semidirect
11. #35592C2semidirect
12. #35576C2semidirect
13. #35558C2semidirect
14. #35556C2semidirect
15. #35532C2semidirect
16. #35530C2semidirect
17. #35264C2semidirect
19. #35152C2semidirect
20. C2×#2542C2semidirect
21. #34816C2semidirect
22. #34745C2semidirect
23. #34265C2semidirect
24. #34214C2semidirect
25. #34188C2semidirect
27. C2×#542C22semidirect
42. #2838C22semidirect
43. #2829C22semidirect
44. #2801C22semidirect
45. #2796C22semidirect
46. #2777C22semidirect
47. #2754C22semidirect
48. #2741C22semidirect
49. #2730C22semidirect
50. #2729C22semidirect
51. #2723C22semidirect
52. #2723C22semidirect
53. #2710C22semidirect
54. #2700C22semidirect
55. #2698C22semidirect
56. #2692C22semidirect
57. #2674C22semidirect
58. #2672C22semidirect
59. #2672C22semidirect
60. #2663C22semidirect
61. #2654C22semidirect
62. #2651C22semidirect
65. #2638C22semidirect
66. #2632C22semidirect
67. #2624C22semidirect
74. #2567C22semidirect
75. #2566C22semidirect
76. #2565C22semidirect
77. #2551C22semidirect
78. #2551C22semidirect
79. #2550C22semidirect
80. #2550C22semidirect
86. #2542C22semidirect
87. #2514C22semidirect
90. #2513C22semidirect
93. #2512C22semidirect
94. #2511C22semidirect
96. #2502C22semidirect
97. #2501C22semidirect
98. #2500C22semidirect
99. #2499C22semidirect
100. #2492C22semidirect
101. #2492C22semidirect
104. #2491C22semidirect
105. #2491C22semidirect
110. #2479C22semidirect
111. #2477C22semidirect
114. #2465C22semidirect
115. #2461C22semidirect
116. #2454C22semidirect
117. #2453C22semidirect
118. #2452C22semidirect
119. #2452C22semidirect
120. #2451C22semidirect
124. #2448C22semidirect
128. #2441C22semidirect
129. #2440C22semidirect
135. #2423C22semidirect
137. #2422C22semidirect
139. #2401C22semidirect
140. #2396C22semidirect
147. #2355C22semidirect
148. #2355C22semidirect
149. #2354C22semidirect
151. Q8×C4⋊C4C22semidirect
152. #2332C22semidirect
153. #2330C22semidirect
158. #2314C22semidirect
164. C4×C4⋊Q8C22semidirect
165. C4×#126C22semidirect
166. C4×C22⋊Q8C22semidirect
179. #2285C22semidirect
1058. C2×C4#542semidirect

Maximal subgroups

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

subgroupindex
#426242
#425612
#424722
#424572
#406992
#402032
#399032
#394062
#393512
#377232
#355922
#355762
#355582
#355562
#355322
#355302
#352642
#352562
#351522
C2×#25422
#348162
#347452
#342652
#342142
#341882