Finite Group Databasebeta

← #7650677

Subgroups — #7650677

Order 512.

4964 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42737C214yesmaximal, complemented
2#42661C214yesmaximal, complemented
3#42611C214yesmaximal, complemented
4#42467C214yesmaximal, complemented
5#41449C218yesmaximal, complemented
6#40121C214yesmaximal, complemented
7#39905C214yesmaximal, complemented
8#39010C214yesmaximal, complemented
9#38941C214yesmaximal, complemented
10#37910C218yesmaximal, complemented
11#35620C211yesmaximal, characteristic, complemented
12#35618C211yesmaximal, characteristic, complemented
13#35592C211yesmaximal, characteristic, complemented
14#35576C211yesmaximal, characteristic, complemented
15#35558C211yesmaximal, characteristic, complemented
16#35556C211yesmaximal, characteristic, complemented
17#35264C211yesmaximal, characteristic, complemented
18#35256C211yesmaximal, characteristic
19#35152C211yesmaximal, characteristic, complemented
20C2×#2563C211yesmaximal, characteristic, complemented
21#34816C211yesmaximal, characteristic, complemented
22#34745C211yesmaximal, characteristic, complemented
23#34265C211yesmaximal, characteristic, complemented
24#34215C211yesmaximal, characteristic, complemented
25#34189C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#533C2211yescharacteristic
31C22×C4⋊Q8C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35#2861C2212yes—
36#2858C2212yes—
37#2856C2212yes—
38#2850C2212yes—
39#2849C2214yes—
40#2832C2218yescomplemented
41#2830C2218yescomplemented
42#2779C2218yescomplemented
43#2770C2218yescomplemented
44#2759C2218yescomplemented
45#2751C2218yescomplemented
46#2739C2218yescomplemented
47#2737C2218yescomplemented
48#2737C2218yescomplemented
49#2737C2218yescomplemented
50#2731C2218yescomplemented
51#2716C2218yescomplemented
52#2715C2218yescomplemented
53#2712C2218yescomplemented
54#2705C2218yescomplemented
55#2687C2218yescomplemented
56#2686C2218yescomplemented
57#2686C2218yescomplemented
58#2665C2218yescomplemented
59#2662C2218yescomplemented
60#2653C2218yescomplemented
61#2650C2218yescomplemented
62#2641C2212yes—
63#2640C2212yes—
64#2640C2218yescomplemented
65#2630C2218yescomplemented
66#2622C2214yes—
67#2620C2212yes—
68#2619C2212yes—
69#2592C2214yes—
70#2591C2214yes—
71#2583C2214yes—
72#2568C2212yescomplemented
73#2566C2212yescomplemented
74#2565C2212yescomplemented
75#2563C2214yes—
76#2563C2214yes—
77#2563C2214yes—
78#2563C2214yes—
79#2563C2212yescomplemented
80#2551C2214yescomplemented
81#2551C2214yescomplemented
82#2550C2214yescomplemented
83#2550C2214yescomplemented
84#2548C2214yes—
85#2532C2218yescomplemented
86#2530C2218yescomplemented
87#2521C2218yescomplemented
88#2514C2212yescomplemented
89#2513C2214yes—
90#2513C2214yes—
91#2513C2212yescomplemented
92#2512C2214yes—
93#2512C2214yes—
94#2512C2212yescomplemented
95#2511C2212yescomplemented
96#2510C2214yes—
97#2504C2212yescomplemented
98#2503C2212yescomplemented
99#2500C2212yescomplemented
100#2499C2212yescomplemented
101#2492C2214yescomplemented
102#2492C2214yescomplemented
103#2491C2214yes—
104#2491C2214yes—
105#2491C2214yescomplemented
106#2491C2214yescomplemented
107#2491C2218yescomplemented
108#2490C2214yes—
109#2490C2214yes—
110#2481C2214yes—
111#2480C2218yes—
112#2472C2218yes—
113#2472C2218yes—
114#2468C2218yescomplemented
115#2454C2212yescomplemented
116#2453C2212yescomplemented
117#2452C2212yescomplemented
118#2451C2212yescomplemented
119#2450C2218yes—
120#2450C2214yes—
121#2449C2214yes—
122#2447C2214yes—
123#2445C2214yes—
124#2444C2218yes—
125#2442C2214yescomplemented
126#2439C2214yescomplemented
127#2436C2214yes—
128#2434C2214yes—
129#2428C2214yes—
130#2427C2218yescomplemented
131#2426C2214yes—
132#2424C2218yes—
133#2422C2214yes—
134#2421C2214yescomplemented
135#2420C2214yes—
136#2420C2214yescomplemented
137#2401C2214yescomplemented
138#2396C2214yescomplemented
139C2×#393C2214yes—
140#2368C2218yes—
141#2367C2214yes—
142#2366C2214yes—
143#2363C2214yes—
144#2361C2214yes—
145#2357C2214yescomplemented
146#2356C2214yescomplemented
147#2355C2214yescomplemented
148#2355C2214yescomplemented
149#2353C2218yes—
150#2335C2218yescomplemented
151#2331C2214yescomplemented
152#2321C2214yes—
153#2319C2218yescomplemented
154#2317C2211yescharacteristic
155#2317C2211yescharacteristic
156#2317C2211yescharacteristic
157#2314C2214yescomplemented
158#2311C2211yescharacteristic
159#2311C2211yescharacteristic
160#2311C2211yescharacteristic
161#2309C2211yescharacteristic
162#2309C2211yescharacteristic
163C4×#125C2214yescomplemented
164C4×#126C2214yescomplemented
165C4×C22⋊Q8C2214yescomplemented
166C4×#120C2214yes—
167#2297C2211yescharacteristic
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175C2×#390C2211yescharacteristic
176C2×#390C2211yescharacteristic
177#2285C2211yescharacteristic
178#2283C2214yescomplemented
179C2×#382C2211yescharacteristic
180C2×#382C2211yescharacteristic
181C2×#380C2214yes—
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#537—44no—
194#535—28no—
195#535—44no—
196#533—28no—
197C2×C4⋊Q8—44no—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2314yes—
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2318yes—
204C2×#127C2312yes—
205C2×#127C2312yes—
206C2×#126C2314yes—
207C2×#126C2318yes—
208C2×#125C2312yes—
209C2×#125C2312yes—
210C2×#125C2312yes—
211C2×#124C2312yes—
212C2×#124C2312yes—
213C2×#124C2318yes—
214C2×#124C2318yes—
215C2×#124C2318yes—
216C2×#123C2318yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×#121C2314yes—
223C2×#121C2314yes—
224C2×#121C2312yes—
225C2×#121C2312yes—
226C2×#121C2312yes—
227C2×#121C2312yes—
228C2×#121C2318yes—
229C2×#120C2314yes—
230C2×#120C2314yes—
231#520—44no—
232C4×#41—28no—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×D4—44no—
237C2×C4×D4C2314yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2318yes—
243C2×C4×D4C2314yes—
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2312yes—
249C2×#117C2311yescharacteristic
250C2×#117C2312yes—
251C2×#117C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C22⋊C4C2312yes—
259C22×C22⋊C4C2314yes—
260C22×C22⋊C4C2314yes—
261C22×C42C2312yes—
262C22×C42C2311yescharacteristic
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265#401C2314yes—
266#400C2318yes—
267#400C2314yes—
268#400C2318yes—
269#400C2314yes—
270#400C2318yes—
271#400C2314yes—
272#400C2314yes—
273#399C2314yes—
274#398C2318yes—
275#398C2314yes—
276#398C2318yes—
277#398C2314yes—
278#397C2314yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2314yes—
287#397C2318yes—
288#397C2318yes—
289#397C2314yes—
290#396C2318yes—
291#396C2318yes—
292#396C2318yes—
293#396C2314yes—
294#396C2314yes—
295#396C2314yes—
296#395C2318yes—
297#395C2318yes—
298#395C2318yes—
299#395C2314yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#393C2318yes—
311#393C2318yes—
312#393C2318yes—
313#393C2318yes—
314#393C2318yes—
315#393C2318yes—
316#393C2314yes—
317#393C2318yes—
318#393C2318yes—
319#393C2318yes—
320#392C2318yes—
321#391C2311yescharacteristic
322#391C2312yes—
323#391C2312yes—
324#391C2312yes—
325#391C2311yescharacteristic
326#391C2318yes—
327#391C2318yes—
328#391C2318yes—
329#391C2312yes—
330#391C2311yescharacteristic
331#391C2312yes—
332#391C2311yescharacteristic
333#391C2314yes—
334#391C2318yes—
335#391C2318yes—
336#391C2312yes—
337#390C2314yes—
338#390C2312yes—
339#390C2312yes—
340#390C2312yes—
341#390C2312yes—
342#390C2314yes—
343#390C2311yescharacteristic
344#390C2312yes—
345#390C2314yes—
346#390C2312yes—
347#390C2312yes—
348#390C2314yes—
349#390C2314yes—
350#390C2311yescharacteristic
351#390C2312yes—
352#390C2312yes—
353#390C2318yes—
354#390C2318yes—
355#390C2318yes—
356#390C2318yes—
357#390C2311yescharacteristic
358#390C2312yes—
359#390C2311yescharacteristic
360#390C2312yes—
361#390C2312yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2318yes—
367#389C2318yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#388C2314yes—
375#388C2314yes—
376#388C2314yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#387C2314yes—
393#387C2314yes—
394#387C2314yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2314yes—
404#387C2314yes—
405#386C2314yes—
406#386C2314yes—
407#386C2314yes—
408#386C2312yes—
409#386C2318yes—
410#386C2318yes—
411#386C2312yes—
412#386C2312yes—
413#386C2318yes—
414#386C2318yes—
415#386C2312yes—
416#386C2318yes—
417#386C2314yes—
418#386C2314yes—
419#386C2314yes—
420#385C2318yes—
421#385C2314yes—
422#385C2314yes—
423#385C2314yes—
424#385C2312yes—
425#385C2312yes—
426#385C2312yes—
427#385C2314yes—
428#385C2318yes—
429#385C2318yes—
430#385C2312yes—
431#385C2314yes—
432#385C2314yes—
433#384C2312yes—
434#384C2312yes—
435#384C2312yes—
436#384C2312yes—
437#383C2314yes—
438#383C2318yes—
439#382C2312yes—
440#382C2312yes—
441#382C2312yes—
442#382C2312yes—
443#382C2314yes—
444#382C2314yes—
445#382C2312yes—
446#382C2312yes—
447#382C2312yes—
448#382C2312yes—
449#381C2318yes—
450#381C2318yes—
451#381C2318yes—
452#380C2318yes—
453#380C2318yes—
454#380C2318yes—
455#380C2318yes—
456#380C2318yes—
457#380C2314yes—
458#380C2314yes—
459#380C2314yes—
460#380C2314yes—
461#380C2314yes—
462#379C2314yes—
463#379C2314yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2318yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2312yes—
495#376C2318yes—
496#376C2312yes—
497C2×#95C2314yes—
498C2×#95C2314yes—
499C2×#95C2312yes—
500C43C2312yes—
501C25C2412yes—
502C2×#41—24no—
503C2×#41—24no—
504C2×#41—24no—
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C22×Q8—44no—
509C22×Q8—84no—
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×Q8C2414yes—
513C22×Q8C2414yes—
514C22×Q8C2418yes—
515C22×D4—24no—
516C22×D4—24no—
517C22×D4—24no—
518C22×D4C2412yes—
519C22×D4C2412yes—
520C22×D4C2412yes—
521C22×D4C2412yes—
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2418yes—
525C22×D4C2414yes—
526C22×D4C2414yes—
527C22×D4C2414yes—
528C23×C4—48no—
529C23×C4—44no—
530C23×C4C2411yescharacteristic
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2411yescharacteristic
538C23×C4C2412yes—
539C23×C4C2418yes—
540C23×C4C2414yes—
541C23×C4C2414yes—
542C23×C4C2411yescharacteristic
543C4⋊Q8—28no—
544C4⋊Q8—48no—
545C4⋊Q8—48no—
546C4⋊Q8—44no—
547C4⋊Q8—44no—
548C4⋊Q8—88no—
549#127—28no—
550#127—44no—
551#126—48no—
552#126—88no—
553#125—28no—
554#125—44no—
555#125—44no—
556#124—28no—
557#124—44no—
558#124—88no—
559#124—88no—
560#124—88no—
561#123—416no—
562C22⋊Q8—216no—
563C22⋊Q8—48no—
564C22⋊Q8—48no—
565C22⋊Q8—44no—
566C22⋊Q8—44no—
567#121—216no—
568#121—44no—
569#121—44no—
570#121—44no—
571#121—44no—
572#121—48no—
573#121—88no—
574#120—216no—
575#120—48no—
576C4×Q8—28no—
577C4×Q8—216no—
578C4×Q8—44no—
579C4×D4—28no—
580C4×D4—216no—
581C4×D4—48no—
582C4×D4—48no—
583C4×D4—44no—
584C4×D4—416no—
585C4×D4—48no—
586#117—24no—
587#117—24no—
588#117—24no—
589#117—24no—
590#117—24no—
591#117—28no—
592#117—44no—
593#117#4118yes—
594C2×C4⋊C4—24no—
595C2×C4⋊C4—24no—
596C2×C4⋊C4—24no—
597C2×C4⋊C4—44no—
598C2×C4⋊C4—44no—
599C2×C4⋊C4—44no—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C22⋊C4—44no—
640C2×C22⋊C4—84no—
641C2×C22⋊C4—84no—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2412yes—
677C2×C42—24no—
678C2×C42—24no—
679C2×C42—24no—
680C2×C42—28no—
681C2×C42C2411yescharacteristic
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2414yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2414yes—
696C2×C42C2418yes—
697C2×C42C2414yes—
698C2×C42C2418yes—
699C2×C42C2418yes—
700C2×C42C2414yes—
701C2×C42C2412yes—
702#95C2418yes—
703#95C2418yes—
704#95C2412yes—
705#95C2412yes—
706#95C2412yes—
707#95C2412yes—
708#95C2418yes—
709#95C2418yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2418yes—
714#95C2418yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2418yes—
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2418yes—
738#95C2418yes—
739C24—24no—
740C24—24no—
741C24—24no—
742C24—44no—
743C24—44no—
744C24C2514yes—
745C24C2512yes—
746C24C2512yes—
747C24C2511yescharacteristic
748#41—416no—
749#41—416no—
750C2×Q8—22no—
751C2×Q8—22no—
752C2×Q8—28no—
753C2×Q8—22no—
754C2×Q8—22no—
755C2×Q8—22no—
756C2×Q8—22no—
757C2×Q8—44no—
758C2×Q8—44no—
759C2×Q8—48no—
760C2×Q8—48no—
761C2×Q8—48no—
762C2×Q8—44no—
763C2×Q8—48no—
764C2×Q8—816no—
765C2×D4—24no—
766C2×D4—24no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—22no—
772C2×D4—24no—
773C2×D4—24no—
774C2×D4—22no—
775C2×D4—216no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—24no—
779C2×D4—22no—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—48no—
790C2×D4—48no—
791C2×D4—48no—
792C2×D4—416no—
793C22×C4—22no—
794C22×C4—24no—
795C22×C4—22no—
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—24no—
806C22×C4—24no—
807C22×C4—28no—
808C22×C4—216no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—48no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—48no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—48no—
823C22×C4—816no—
824C22×C4C2×#4114yes—
825C22×C4H(5,𝔽2)14yes—
826C22×C42−1+414yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2514yes—
831C22×C4C2512yes—
832C22×C4C2514yes—
833C22×C4C2514yes—
834C22×C4C2512yes—
835C22×C4C2512yes—
836C22×C4C2514yes—
837C22×C4C2512yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2514yes—
841C22×C4C2514yes—
842C22×C4C2512yes—
843C22×C4C2512yes—
844C22×C4C2514yes—
845C22×C4C2512yes—
846C22×C4C2511yescharacteristic
847C22×C4C2511yescharacteristic
848C4⋊C4—28no—
849C4⋊C4—24no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—28no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—24no—
858C4⋊C4—24no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—44no—
872C4⋊C4—48no—
873C4⋊C4—44no—
874C4⋊C4—48no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—48no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—48no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4C2×#4118yes—
887C22⋊C4—24no—
888C22⋊C4—24no—
889C22⋊C4—24no—
890C22⋊C4—24no—
891C22⋊C4—24no—
892C22⋊C4—28no—
893C22⋊C4—216no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—48no—
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—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—48no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4C2×#4118yes—
922C42—22no—
923C42—22no—
924C42—24no—
925C42—28no—
926C42—24no—
927C42—22no—
928C42—22no—
929C42—24no—
930C42—24no—
931C42—24no—
932C42—24no—
933C42—24no—
934C42—24no—
935C42—24no—
936C42—44no—
937C42—48no—
938C42—44no—
939C42—48no—
940C42—48no—
941C42—44no—
942C42C2×#4118yes—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—24no—
947C23—22no—
948C23—22no—
949C23—24no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—28no—
957C23—28no—
958C23—24no—
959C23—24no—
960C23—416no—
961C23—48no—
962C23—84no—
963C23—88no—
964C23—84no—
965C23C22×#4112yes—
966C23C2×H(5,𝔽2)12yes—
967C23C2×2−1+412yes—
968C23C2611yescharacteristic
969Q8—44no—
970Q8—44no—
971Q8—88no—
972Q8—816no—
973Q8—164no—
974D4—48no—
975D4—48no—
976D4—48no—
977D4—48no—
978D4—44no—
979D4—44no—
980D4—816no—
981D4—164no—
982D4—164no—
983D4—164no—
984C2×C4—28no—
985C2×C4—22no—
986C2×C4—24no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—24no—
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—24no—
1007C2×C4—24no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—24no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—28no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—28no—
1025C2×C4—28no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—44no—
1034C2×C4—48no—
1035C2×C4—48no—
1036C2×C4—88no—
1037C2×C4—816no—
1038C2×C4—84no—
1039C2×C4—84no—
1040C2×C4—84no—
1041C2×C4—84no—
1042C2×C4—84no—
1043C2×C4—164no—
1044C2×C4#542116yes—
1045C2×C4C22×#4118yes—
1046C2×C4C22×#4112yes—
1047C2×C4C22×#4112yes—
1048C2×C4C2×H(5,𝔽2)12yes—
1049C2×C4C2×H(5,𝔽2)12yes—
1050C2×C4C2×2−1+412yes—
1051C2×C4C2×2−1+412yes—
1052C2×C4#58514yes—
1053C22—24no—
1054C22—22no—
1055C22—22no—
1056C22—24no—
1057C22—44no—
1058C22—44no—
1059C22—48no—
1060C22—44no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—44no—
1066C22—44no—
1067C22—44no—
1068C22—48no—
1069C22—42no—
1070C22—42no—
1071C22—44no—
1072C22—816no—
1073C22C2×#54214yes—
1074C22C23×#4111yescharacteristic
1075C22C22×H(5,𝔽2)11yescharacteristic
1076C22C22×2−1+411yescharacteristic
1077C22C2×#58512yes—
1078C22H(7,𝔽2)12yes—
1079C4—28no—
1080C4—24no—
1081C4—42no—
1082C4—42no—
1083C4—42no—
1084C4—42no—
1085C4—44no—
1086C4—44no—
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—44no—
1091C4—44no—
1092C4—42no—
1093C4—42no—
1094C4—44no—
1095C4—44no—
1096C4—42no—
1097C4—42no—
1098C4C2×#54214yes—
1099C4C2×#54214yes—
1100C2—24no—
1101C2—82no—
1102C2—82no—
1103C2—84no—
1104C2C22×#54211yescharacteristic
1105C2#6282411yescharacteristic
1106C2#6287611yescharacteristic
1107C2#6292612yes—
1108C2#6299412yes—
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. #42737C2semidirect
2. #42661C2semidirect
3. #42611C2semidirect
4. #42467C2semidirect
5. #41449C2semidirect
6. #40121C2semidirect
7. #39905C2semidirect
8. #39010C2semidirect
9. #38941C2semidirect
10. #37910C2semidirect
11. #35620C2semidirect
12. #35618C2semidirect
13. #35592C2semidirect
14. #35576C2semidirect
15. #35558C2semidirect
16. #35556C2semidirect
17. #35264C2semidirect
19. #35152C2semidirect
20. C2×#2563C2semidirect
21. #34816C2semidirect
22. #34745C2semidirect
23. #34265C2semidirect
24. #34215C2semidirect
25. #34189C2semidirect
40. #2832C22semidirect
41. #2830C22semidirect
42. #2779C22semidirect
43. #2770C22semidirect
44. #2759C22semidirect
45. #2751C22semidirect
46. #2739C22semidirect
47. #2737C22semidirect
48. #2737C22semidirect
49. #2737C22semidirect
50. #2731C22semidirect
51. #2716C22semidirect
52. #2715C22semidirect
53. #2712C22semidirect
54. #2705C22semidirect
55. #2687C22semidirect
56. #2686C22semidirect
57. #2686C22semidirect
58. #2665C22semidirect
59. #2662C22semidirect
60. #2653C22semidirect
61. #2650C22semidirect
64. #2640C22semidirect
65. #2630C22semidirect
72. #2568C22semidirect
73. #2566C22semidirect
74. #2565C22semidirect
79. #2563C22semidirect
80. #2551C22semidirect
81. #2551C22semidirect
82. #2550C22semidirect
83. #2550C22semidirect
85. #2532C22semidirect
86. #2530C22semidirect
87. #2521C22semidirect
88. #2514C22semidirect
91. #2513C22semidirect
94. #2512C22semidirect
95. #2511C22semidirect
97. #2504C22semidirect
98. #2503C22semidirect
99. #2500C22semidirect
100. #2499C22semidirect
101. #2492C22semidirect
102. #2492C22semidirect
105. #2491C22semidirect
106. #2491C22semidirect
107. #2491C22semidirect
114. #2468C22semidirect
115. #2454C22semidirect
116. #2453C22semidirect
117. #2452C22semidirect
118. #2451C22semidirect
125. #2442C22semidirect
126. #2439C22semidirect
130. #2427C22semidirect
134. #2421C22semidirect
136. #2420C22semidirect
137. #2401C22semidirect
138. #2396C22semidirect
145. #2357C22semidirect
146. #2356C22semidirect
147. #2355C22semidirect
148. #2355C22semidirect
150. #2335C22semidirect
151. #2331C22semidirect
153. #2319C22semidirect
157. #2314C22semidirect
163. C4×#125C22semidirect
164. C4×#126C22semidirect
165. C4×C22⋊Q8C22semidirect
178. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#427372
#426612
#426112
#424672
#414492
#401212
#399052
#390102
#389412
#379102
#356202
#356182
#355922
#355762
#355582
#355562
#352642
#352562
#351522
C2×#25632
#348162
#347452
#342652
#342152
#341892