Finite Group Databasebeta

← #8093532

Subgroups — #8093532

Order 512.

4810 conjugacy classes of subgroups.

The subgroup lattice has 1135 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53130C214yesmaximal, complemented
2#53110C214yesmaximal, complemented
3#53068C214yesmaximal, complemented
4#53056C214yesmaximal, complemented
5#53029C214yesmaximal, complemented
6#53025C214yesmaximal, complemented
7#52964C214yesmaximal, complemented
8#52959C214yesmaximal, complemented
9#52374C218yesmaximal, complemented
10#52373C218yesmaximal, complemented
11#35679C211yesmaximal, characteristic, complemented
12#35662C211yesmaximal, characteristic, complemented
13#35661C211yesmaximal, characteristic, complemented
14#35644C211yesmaximal, characteristic, complemented
15#35619C211yesmaximal, characteristic, complemented
16#35617C211yesmaximal, characteristic, complemented
17#35563C211yesmaximal, characteristic
18#35556C211yesmaximal, characteristic, complemented
19#35555C211yesmaximal, characteristic, complemented
20#35540C211yesmaximal, characteristic, complemented
21#35532C211yesmaximal, characteristic, complemented
22#35529C211yesmaximal, characteristic, complemented
23#34635C211yesmaximal, characteristic, complemented
24#34634C211yesmaximal, characteristic, complemented
25C2×#2620C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#533C2211yescharacteristic
30C22×#124C2211yescharacteristic
31C2×#525C2211yescharacteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×#121C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×#519C2211yescharacteristic
36C2×#518C2211yescharacteristic
37C22×#117C2211yescharacteristic
38#2841C2218yescomplemented
39#2837C2218yescomplemented
40#2837C2218yescomplemented
41#2836C2218yescomplemented
42#2836C2218yescomplemented
43#2832C2218yescomplemented
44#2831C2218yescomplemented
45#2830C2218yescomplemented
46#2829C2218yescomplemented
47#2829C2218yescomplemented
48#2827C2218yescomplemented
49#2827C2218yescomplemented
50#2826C2218yescomplemented
51#2820C2218yescomplemented
52#2816C2218yescomplemented
53#2814C2218yescomplemented
54#2800C2218yescomplemented
55#2788C2218yescomplemented
56#2786C2218yescomplemented
57#2772C2218yescomplemented
58#2761C2218yescomplemented
59#2744C2218yescomplemented
60#2743C2218yescomplemented
61#2741C2218yescomplemented
62#2732C2218yescomplemented
63#2711C2218yescomplemented
64#2710C2218yescomplemented
65#2704C2218yescomplemented
66#2700C2218yescomplemented
67#2694C2218yescomplemented
68#2686C2218yescomplemented
69#2681C2218yescomplemented
70#2629C2212yescomplemented
71#2629C2212yescomplemented
72#2628C2212yescomplemented
73#2628C2212yescomplemented
74#2627C2214yes—
75#2626C2214yes—
76#2625C2212yescomplemented
77#2625C2212yescomplemented
78#2624C2212yescomplemented
79#2624C2212yescomplemented
80#2623C2214yes—
81#2622C2214yes—
82#2620C2214yes—
83#2620C2214yes—
84#2620C2214yes—
85#2620C2214yes—
86#2592C2214yescomplemented
87#2582C2214yescomplemented
88#2581C2214yescomplemented
89#2570C2214yescomplemented
90#2567C2212yescomplemented
91#2566C2212yescomplemented
92#2566C2212yescomplemented
93#2566C2212yescomplemented
94#2565C2212yescomplemented
95#2563C2212yescomplemented
96#2561C2214yes—
97#2552C2214yescomplemented
98#2548C2214yescomplemented
99#2547C2212yescomplemented
100#2547C2212yescomplemented
101#2544C2212yescomplemented
102#2544C2212yescomplemented
103#2542C2212yescomplemented
104#2542C2212yescomplemented
105#2538C2214yescomplemented
106#2536C2214yescomplemented
107#2534C2214yes—
108#2507C2214yescomplemented
109#2506C2214yescomplemented
110#2503C2214yes—
111#2503C2212yescomplemented
112#2502C2212yescomplemented
113#2499C2212yescomplemented
114#2499C2212yescomplemented
115#2492C2214yescomplemented
116#2492C2214yescomplemented
117#2491C2214yescomplemented
118#2490C2214yescomplemented
119#2489C2214yescomplemented
120#2489C2214yescomplemented
121#2483C2214yes—
122#2482C2218yes—
123#2473C2218yes—
124#2472C2218yes—
125#2454C2214yescomplemented
126#2453C2214yescomplemented
127#2452C2214yescomplemented
128#2451C2214yescomplemented
129#2449C2218yes—
130#2448C2214yescomplemented
131#2448C2214yescomplemented
132#2448C2214yescomplemented
133#2448C2214yescomplemented
134#2447C2214yescomplemented
135#2446C2214yescomplemented
136#2441C2214yescomplemented
137#2440C2214yescomplemented
138#2438C2218yes—
139#2437C2218yes—
140#2429C2214yescomplemented
141#2428C2214yes—
142#2427C2214yescomplemented
143#2427C2214yescomplemented
144#2426C2214yes—
145#2426C2214yescomplemented
146#2422C2214yes—
147#2422C2214yes—
148#2420C2214yes—
149#2420C2214yes—
150#2419C2218yes—
151#2416C2214yes—
152#2414C2214yes—
153#2413C2214yes—
154#2412C2218yes—
155#2411C2214yes—
156#2408C2214yes—
157#2405C2214yes—
158#2396C2214yescomplemented
159#2396C2214yescomplemented
160#2395C2214yescomplemented
161#2395C2214yescomplemented
162C2×#396C2214yes—
163C2×#394C2214yes—
164#2317C2211yescharacteristic
165#2317C2211yescharacteristic
166#2317C2211yescharacteristic
167#2316C2211yescharacteristic
168#2311C2211yescharacteristic
169#2310C2211yescharacteristic
170#2310C2211yescharacteristic
171#2309C2211yescharacteristic
172#2309C2211yescharacteristic
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2296C2211yescharacteristic
176#2296C2211yescharacteristic
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179C2×#391C2211yescharacteristic
180C2×#390C2211yescharacteristic
181#2285C2211yescharacteristic
182C2×#384C2211yescharacteristic
183#2280C2211yescharacteristic
184#2280C2211yescharacteristic
185#2280C2211yescharacteristic
186#2274C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×D4C2311yescharacteristic
190C23×D4C2312yes—
191C24×C4C2311yescharacteristic
192#544—44no—
193#536—44no—
194#535—44no—
195#533—44no—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×#127C2312yes—
201C2×#125C2312yes—
202C2×#125C2312yes—
203C2×#125C2312yes—
204C2×#125C2318yes—
205C2×#124—44no—
206C2×#124C2312yes—
207C2×#124C2314yes—
208C2×#124C2312yes—
209C2×#124C2312yes—
210C2×#124C2312yes—
211C2×#124C2318yes—
212#525—44no—
213C2×#123C2312yes—
214C2×#123C2314yes—
215C2×#123C2318yes—
216C2×C22⋊Q8—44no—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2318yes—
226C2×#121—44no—
227C2×#121C2314yes—
228C2×#121C2314yes—
229C2×#121C2312yes—
230C2×#121C2314yes—
231C2×#121C2318yes—
232C2×#120C2312yes—
233C2×#120C2314yes—
234#520—44no—
235#519—44no—
236#518—44no—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2314yes—
248C2×#117—44no—
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2312yes—
257C2×#117C2312yes—
258C2×#117C2312yes—
259C2×#117C2312yes—
260C2×#117C2314yes—
261C2×#117C2312yes—
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2314yes—
268C22×C22⋊C4C2312yes—
269C22×C22⋊C4C2312yes—
270C22×C22⋊C4C2314yes—
271C22×C22⋊C4C2312yes—
272C22×C22⋊C4C2314yes—
273C22×C22⋊C4C2314yes—
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276#400C2318yes—
277#400C2318yes—
278#400C2314yes—
279#400C2318yes—
280#400C2318yes—
281#400C2314yes—
282#400C2314yes—
283#400C2318yes—
284#400C2314yes—
285#399C2314yes—
286#399C2318yes—
287#399C2314yes—
288#399C2318yes—
289#399C2318yes—
290#399C2318yes—
291#399C2314yes—
292#399C2314yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2314yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2318yes—
305#398C2314yes—
306#398C2314yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2318yes—
311#397C2314yes—
312#397C2314yes—
313#397C2318yes—
314#397C2318yes—
315#397C2314yes—
316#397C2318yes—
317#397C2318yes—
318#397C2318yes—
319#397C2314yes—
320#397C2318yes—
321#397C2314yes—
322#397C2314yes—
323#396C2318yes—
324#396C2318yes—
325#396C2318yes—
326#396C2318yes—
327#396C2318yes—
328#396C2314yes—
329#396C2318yes—
330#396C2318yes—
331#396C2314yes—
332#396C2318yes—
333#396C2318yes—
334#396C2318yes—
335#396C2314yes—
336#396C2314yes—
337#395C2314yes—
338#395C2318yes—
339#395C2318yes—
340#395C2314yes—
341#394C2314yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#394C2318yes—
346#394C2318yes—
347#394C2318yes—
348#394C2318yes—
349#394C2314yes—
350#394C2318yes—
351#394C2318yes—
352#394C2314yes—
353#394C2314yes—
354#394C2318yes—
355#394C2318yes—
356#394C2318yes—
357#394C2318yes—
358#393C2318yes—
359#393C2318yes—
360#393C2314yes—
361#393C2318yes—
362#393C2314yes—
363#392C2318yes—
364#391C2311yescharacteristic
365#391C2312yes—
366#391C2312yes—
367#391C2312yes—
368#391C2314yes—
369#391C2314yes—
370#391C2312yes—
371#391C2312yes—
372#391C2311yescharacteristic
373#391C2318yes—
374#391C2318yes—
375#391C2314yes—
376#391C2312yes—
377#391C2312yes—
378#391C2312yes—
379#390C2312yes—
380#390C2312yes—
381#390C2312yes—
382#390C2314yes—
383#390C2314yes—
384#390C2314yes—
385#390C2311yescharacteristic
386#390C2312yes—
387#390C2312yes—
388#390C2318yes—
389#390C2318yes—
390#390C2318yes—
391#390C2314yes—
392#390C2312yes—
393#390C2311yescharacteristic
394#389C2318yes—
395#389C2312yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2318yes—
402#389C2312yes—
403#389C2318yes—
404#389C2318yes—
405#389C2312yes—
406#389C2312yes—
407#389C2312yes—
408#389C2312yes—
409#389C2312yes—
410#389C2312yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#386C2314yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2314yes—
435#386C2314yes—
436#385C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2314yes—
442#385C2314yes—
443#385C2314yes—
444#385C2314yes—
445#385C2314yes—
446#385C2314yes—
447#385C2314yes—
448#384C2312yes—
449#384C2311yescharacteristic
450#384C2312yes—
451#384C2312yes—
452#384C2312yes—
453#384C2314yes—
454#384C2312yes—
455#384C2311yescharacteristic
456#382C2311yescharacteristic
457#382C2312yes—
458#382C2318yes—
459#382C2312yes—
460#382C2311yescharacteristic
461#382C2312yes—
462#381C2318yes—
463#381C2314yes—
464#381C2314yes—
465#381C2318yes—
466#381C2312yes—
467#381C2312yes—
468#381C2312yes—
469#380C2318yes—
470#380C2314yes—
471#380C2314yes—
472#380C2318yes—
473#380C2312yes—
474#380C2312yes—
475#380C2314yes—
476#380C2312yes—
477#380C2312yes—
478#380C2312yes—
479#380C2312yes—
480#380C2318yes—
481#379C2312yes—
482#379C2312yes—
483#379C2314yes—
484#379C2314yes—
485#379C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2314yes—
503C2×#95C2314yes—
504C25C2412yes—
505C25C2411yescharacteristic
506C2×#41—24no—
507C2×#41—24no—
508C2×#41—24no—
509C22×Q8—24no—
510C22×Q8—24no—
511C22×Q8—24no—
512C22×Q8C2412yes—
513C22×Q8C2412yes—
514C22×Q8C2411yescharacteristic
515C22×Q8C2414yes—
516C22×Q8C2414yes—
517C22×D4—24no—
518C22×D4—24no—
519C22×D4—24no—
520C22×D4—44no—
521C22×D4—84no—
522C22×D4C2412yes—
523C22×D4C2412yes—
524C22×D4C2412yes—
525C22×D4C2411yescharacteristic
526C22×D4C2414yes—
527C22×D4C2418yes—
528C22×D4C2418yes—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—24no—
532C23×C4C2412yes—
533C23×C4C2411yescharacteristic
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2414yes—
542C23×C4C2414yes—
543C23×C4C2414yes—
544C23×C4C2411yescharacteristic
545C4⋊Q8—44no—
546C4⋊Q8—44no—
547C4⋊Q8—44no—
548C4⋊Q8—44no—
549#127—44no—
550#125—44no—
551#125—44no—
552#125—44no—
553#125—88no—
554#124—48no—
555#124—44no—
556#124—44no—
557#124—44no—
558#124—44no—
559#124—88no—
560#123—44no—
561#123—48no—
562#123—88no—
563C22⋊Q8—48no—
564C22⋊Q8—48no—
565C22⋊Q8—48no—
566C22⋊Q8—48no—
567C22⋊Q8—44no—
568C22⋊Q8—44no—
569C22⋊Q8—44no—
570C22⋊Q8—88no—
571C22⋊Q8—88no—
572#121—48no—
573#121—48no—
574#121—44no—
575#121—48no—
576#121—88no—
577#120—44no—
578#120—48no—
579C4×Q8—48no—
580C4×Q8—48no—
581C4×Q8—48no—
582C4×Q8—44no—
583C4×D4—44no—
584C4×D4—44no—
585C4×D4—44no—
586C4×D4—44no—
587C4×D4—44no—
588C4×D4—48no—
589C4×D4—48no—
590#117—24no—
591#117—24no—
592#117—24no—
593#117—24no—
594#117—24no—
595#117—24no—
596#117—24no—
597#117—44no—
598#117—44no—
599#117—44no—
600#117—44no—
601#117—48no—
602#117—44no—
603C2×C4⋊C4—24no—
604C2×C4⋊C4—24no—
605C2×C4⋊C4—44no—
606C2×C4⋊C4—44no—
607C2×C4⋊C4—44no—
608C2×C4⋊C4—84no—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C22⋊C4—48no—
656C2×C22⋊C4—44no—
657C2×C22⋊C4—44no—
658C2×C22⋊C4—44no—
659C2×C22⋊C4—48no—
660C2×C22⋊C4—84no—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C42—24no—
702C2×C42—24no—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2414yes—
717C2×C42C2418yes—
718C2×C42C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751C24—22no—
752C24—24no—
753C24—22no—
754C24—24no—
755C24—22no—
756C24—24no—
757C24—42no—
758C24—42no—
759C24—44no—
760C24—44no—
761C24C2512yes—
762C24C2514yes—
763C24C2512yes—
764C24C2511yescharacteristic
765#41—416no—
766C2×Q8—24no—
767C2×Q8—24no—
768C2×Q8—22no—
769C2×Q8—24no—
770C2×Q8—22no—
771C2×Q8—24no—
772C2×Q8—24no—
773C2×Q8—24no—
774C2×Q8—22no—
775C2×Q8—44no—
776C2×Q8—44no—
777C2×Q8—44no—
778C2×Q8—44no—
779C2×Q8—48no—
780C2×Q8—416no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—24no—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—22no—
787C2×D4—24no—
788C2×D4—22no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—22no—
793C2×D4—44no—
794C2×D4—48no—
795C2×D4—44no—
796C2×D4—48no—
797C2×D4—48no—
798C2×D4—44no—
799C2×D4—48no—
800C2×D4—48no—
801C2×D4—48no—
802C2×D4—416no—
803C2×D4—816no—
804C22×C4—24no—
805C22×C4—22no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—22no—
809C22×C4—22no—
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—24no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—42no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4—416no—
836C22×C4H(5,𝔽2)14yes—
837C22×C4H(5,𝔽2)14yes—
838C22×C42−1+414yes—
839C22×C4C2514yes—
840C22×C4C2512yes—
841C22×C4C2512yes—
842C22×C4C2514yes—
843C22×C4C2512yes—
844C22×C4C2514yes—
845C22×C4C2512yes—
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2514yes—
851C22×C4C2514yes—
852C22×C4C2514yes—
853C22×C4C2512yes—
854C22×C4C2512yes—
855C22×C4C2512yes—
856C22×C4C2514yes—
857C22×C4C2512yes—
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—22no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—44no—
879C4⋊C4—48no—
880C4⋊C4—48no—
881C4⋊C4—48no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—48no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—48no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—24no—
909C22⋊C4—24no—
910C22⋊C4—24no—
911C22⋊C4—24no—
912C22⋊C4—24no—
913C22⋊C4—42no—
914C22⋊C4—42no—
915C22⋊C4—42no—
916C22⋊C4—42no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—48no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—44no—
937C22⋊C4—48no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—48no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—48no—
945C22⋊C4—44no—
946C42—24no—
947C42—22no—
948C42—22no—
949C42—24no—
950C42—22no—
951C42—22no—
952C42—24no—
953C42—24no—
954C42—24no—
955C42—24no—
956C42—24no—
957C42—24no—
958C42—24no—
959C42—44no—
960C42—48no—
961C42—48no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—24no—
967C23—22no—
968C23—24no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—24no—
973C23—24no—
974C23—28no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—28no—
979C23—24no—
980C23—22no—
981C23—44no—
982C23—44no—
983C23—44no—
984C23—48no—
985C23—84no—
986C23—84no—
987C23—84no—
988C23—88no—
989C23—88no—
990C23—84no—
991C23C2×H(5,𝔽2)12yes—
992C23C2×H(5,𝔽2)12yes—
993C23C2×2−1+412yes—
994C23C2611yescharacteristic
995Q8—48no—
996Q8—48no—
997Q8—44no—
998Q8—88no—
999Q8—164no—
1000D4—48no—
1001D4—48no—
1002D4—48no—
1003D4—44no—
1004D4—88no—
1005D4—816no—
1006D4—168no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—28no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—28no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—48no—
1057C2×C4—44no—
1058C2×C4—48no—
1059C2×C4—48no—
1060C2×C4—48no—
1061C2×C4—48no—
1062C2×C4—84no—
1063C2×C4—84no—
1064C2×C4—84no—
1065C2×C4—164no—
1066C2×C4—164no—
1067C2×C4—164no—
1068C2×C4#562116yes—
1069C2×C4C2×H(5,𝔽2)12yes—
1070C2×C4C2×H(5,𝔽2)12yes—
1071C2×C4C2×H(5,𝔽2)12yes—
1072C2×C4C2×H(5,𝔽2)12yes—
1073C2×C4C2×2−1+412yes—
1074C2×C4C2×2−1+412yes—
1075C22—24no—
1076C22—22no—
1077C22—24no—
1078C22—22no—
1079C22—42no—
1080C22—44no—
1081C22—48no—
1082C22—42no—
1083C22—42no—
1084C22—44no—
1085C22—42no—
1086C22—44no—
1087C22—42no—
1088C22—42no—
1089C22—48no—
1090C22—44no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—44no—
1096C22—88no—
1097C22—168no—
1098C22C2×#56214yes—
1099C22C22×H(5,𝔽2)11yescharacteristic
1100C22C22×H(5,𝔽2)11yescharacteristic
1101C22C22×2−1+411yescharacteristic
1102C22H(7,𝔽2)12yes—
1103C222−1+612yes—
1104C4—42no—
1105C4—42no—
1106C4—42no—
1107C4—42no—
1108C4—44no—
1109C4—44no—
1110C4—44no—
1111C4—44no—
1112C4—44no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—44no—
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—44no—
1123C4C2×#56214yes—
1124C4C2×#56214yes—
1125C2—24no—
1126C2—82no—
1127C2—82no—
1128C2—84no—
1129C2C22×#56211yescharacteristic
1130C2#6287512yes—
1131C2#6287611yescharacteristic
1132C2#6287912yes—
1133C2#6288711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35563C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53130C2semidirect
2. #53110C2semidirect
3. #53068C2semidirect
4. #53056C2semidirect
5. #53029C2semidirect
6. #53025C2semidirect
7. #52964C2semidirect
8. #52959C2semidirect
9. #52374C2semidirect
10. #52373C2semidirect
11. #35679C2semidirect
12. #35662C2semidirect
13. #35661C2semidirect
14. #35644C2semidirect
15. #35619C2semidirect
16. #35617C2semidirect
18. #35556C2semidirect
19. #35555C2semidirect
20. #35540C2semidirect
21. #35532C2semidirect
22. #35529C2semidirect
23. #34635C2semidirect
24. #34634C2semidirect
25. C2×#2620C2semidirect
38. #2841C22semidirect
39. #2837C22semidirect
40. #2837C22semidirect
41. #2836C22semidirect
42. #2836C22semidirect
43. #2832C22semidirect
44. #2831C22semidirect
45. #2830C22semidirect
46. #2829C22semidirect
47. #2829C22semidirect
48. #2827C22semidirect
49. #2827C22semidirect
50. #2826C22semidirect
51. #2820C22semidirect
52. #2816C22semidirect
53. #2814C22semidirect
54. #2800C22semidirect
55. #2788C22semidirect
56. #2786C22semidirect
57. #2772C22semidirect
58. #2761C22semidirect
59. #2744C22semidirect
60. #2743C22semidirect
61. #2741C22semidirect
62. #2732C22semidirect
63. #2711C22semidirect
64. #2710C22semidirect
65. #2704C22semidirect
66. #2700C22semidirect
67. #2694C22semidirect
68. #2686C22semidirect
69. #2681C22semidirect
70. #2629C22semidirect
71. #2629C22semidirect
72. #2628C22semidirect
73. #2628C22semidirect
76. #2625C22semidirect
77. #2625C22semidirect
78. #2624C22semidirect
79. #2624C22semidirect
86. #2592C22semidirect
87. #2582C22semidirect
88. #2581C22semidirect
89. #2570C22semidirect
90. #2567C22semidirect
91. #2566C22semidirect
92. #2566C22semidirect
93. #2566C22semidirect
94. #2565C22semidirect
95. #2563C22semidirect
97. #2552C22semidirect
98. #2548C22semidirect
99. #2547C22semidirect
100. #2547C22semidirect
101. #2544C22semidirect
102. #2544C22semidirect
103. #2542C22semidirect
104. #2542C22semidirect
105. #2538C22semidirect
106. #2536C22semidirect
108. #2507C22semidirect
109. #2506C22semidirect
111. #2503C22semidirect
112. #2502C22semidirect
113. #2499C22semidirect
114. #2499C22semidirect
115. #2492C22semidirect
116. #2492C22semidirect
117. #2491C22semidirect
118. #2490C22semidirect
119. #2489C22semidirect
120. #2489C22semidirect
125. #2454C22semidirect
126. #2453C22semidirect
127. #2452C22semidirect
128. #2451C22semidirect
130. #2448C22semidirect
131. #2448C22semidirect
132. #2448C22semidirect
133. #2448C22semidirect
134. #2447C22semidirect
135. #2446C22semidirect
136. #2441C22semidirect
137. #2440C22semidirect
140. #2429C22semidirect
142. #2427C22semidirect
143. #2427C22semidirect
145. #2426C22semidirect
158. #2396C22semidirect
159. #2396C22semidirect
160. #2395C22semidirect
161. #2395C22semidirect

Maximal subgroups

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

subgroupindex
#531302
#531102
#530682
#530562
#530292
#530252
#529642
#529592
#523742
#523732
#356792
#356622
#356612
#356442
#356192
#356172
#355632
#355562
#355552
#355402
#355322
#355292
#346352
#346342
C2×#26202