Finite Group Databasebeta

← #7643492

Subgroups — #7643492

Order 512.

5446 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40217C214yesmaximal, complemented
2#40170C214yesmaximal, complemented
3#39212C214yesmaximal, complemented
4#39023C214yesmaximal, complemented
5#38534C218yesmaximal, complemented
6#38176C218yesmaximal, complemented
7#37409C214yesmaximal, complemented
8#37372C214yesmaximal, complemented
9#36626C211yesmaximal, characteristic, complemented
10C2×#2850C211yesmaximal, characteristic, complemented
11#35677C211yesmaximal, characteristic, complemented
12#35672C211yesmaximal, characteristic, complemented
13#35634C211yesmaximal, characteristic, complemented
14#35627C211yesmaximal, characteristic, complemented
15#35618C211yesmaximal, characteristic, complemented
16#35617C211yesmaximal, characteristic, complemented
17#35563C211yesmaximal, characteristic, complemented
18#35514C211yesmaximal, characteristic, complemented
19#35307C211yesmaximal, characteristic, complemented
20#35256C211yesmaximal, characteristic, complemented
21#35196C214yesmaximal, complemented
22#35109C214yesmaximal, complemented
23#34276C211yesmaximal, characteristic, complemented
24#34255C211yesmaximal, characteristic, complemented
25C4×#525C211yesmaximal, characteristic, complemented
26C2×#537C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C22×#124C2211yescharacteristic
32C2×#525C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C22×#121C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×#518C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C23×C42C2211yescharacteristic
41#2856C2212yescomplemented
42#2855C2212yescomplemented
43#2855C2212yescomplemented
44#2855C2214yescomplemented
45#2854C2212yescomplemented
46#2854C2212yescomplemented
47#2853C2214yes—
48#2850C2214yes—
49#2850C2214yes—
50#2850C2214yes—
51#2850C2214yes—
52#2850C2212yescomplemented
53#2849C2214yes—
54#2803C2218yescomplemented
55#2797C2218yescomplemented
56#2793C2218yescomplemented
57#2793C2218yescomplemented
58#2753C2218yescomplemented
59#2753C2218yescomplemented
60#2752C2218yescomplemented
61#2748C2218yescomplemented
62#2743C2218yescomplemented
63#2743C2218yescomplemented
64#2741C2218yescomplemented
65#2741C2218yescomplemented
66#2740C2218yescomplemented
67#2703C2218yescomplemented
68#2701C2218yescomplemented
69#2688C2218yescomplemented
70#2651C2218yescomplemented
71#2649C2218yescomplemented
72#2649C2218yescomplemented
73#2635C2218yescomplemented
74#2625C2214yescomplemented
75#2620C2212yescomplemented
76#2619C2212yescomplemented
77#2571C2214yescomplemented
78#2570C2214yescomplemented
79#2548C2212yescomplemented
80#2548C2212yescomplemented
81#2547C2214yescomplemented
82#2545C2212yescomplemented
83#2545C2212yescomplemented
84#2544C2214yescomplemented
85#2542C2214yescomplemented
86#2542C2214yescomplemented
87#2540C2214yescomplemented
88#2540C2214yescomplemented
89#2539C2214yes—
90#2537C2214yes—
91#2535C2214yes—
92#2534C2214yes—
93#2516C2218yescomplemented
94#2516C2218yescomplemented
95#2516C2218yescomplemented
96#2509C2214yescomplemented
97#2508C2214yescomplemented
98#2505C2218yes—
99#2504C2212yescomplemented
100#2503C2212yescomplemented
101#2501C2214yes—
102#2500C2212yescomplemented
103#2499C2212yescomplemented
104#2497C2218yescomplemented
105#2484C2214yes—
106#2482C2214yes—
107#2476C2218yescomplemented
108#2471C2218yescomplemented
109#2464C2218yescomplemented
110#2447C2214yescomplemented
111#2446C2214yescomplemented
112#2444C2218yes—
113#2428C2214yes—
114#2428C2214yes—
115#2428C2214yescomplemented
116#2427C2214yes—
117#2427C2214yescomplemented
118#2427C2214yescomplemented
119#2426C2214yes—
120#2426C2214yescomplemented
121#2426C2214yescomplemented
122#2426C2214yescomplemented
123#2424C2218yes—
124#2423C2214yescomplemented
125#2423C2214yescomplemented
126#2421C2214yescomplemented
127#2421C2214yescomplemented
128#2421C2214yescomplemented
129#2420C2214yescomplemented
130#2420C2218yescomplemented
131#2419C2218yes—
132#2416C2214yes—
133#2414C2214yes—
134#2412C2214yes—
135#2412C2218yes—
136#2411C2218yes—
137#2410C2214yes—
138#2408C2214yes—
139#2362C2214yescomplemented
140#2360C2214yescomplemented
141#2359C2218yes—
142#2357C2214yescomplemented
143#2354C2214yescomplemented
144#2342C2218yes—
145#2333C2218yescomplemented
146#2333C2218yescomplemented
147#2327C2212yescomplemented
148#2326C2212yescomplemented
149#2324C2218yescomplemented
150#2319C2214yescomplemented
151#2317C2211yescharacteristic
152#2317C2211yescharacteristic
153#2317C2211yescharacteristic
154#2316C2211yescharacteristic
155#2314C2218yescomplemented
156#2311C2211yescharacteristic
157#2310C2211yescharacteristic
158#2309C2211yescharacteristic
159C4×C4⋊Q8C2212yescomplemented
160C4×#124C2212yescomplemented
161C4×C22⋊Q8C2212yescomplemented
162C4×C22⋊Q8C2212yescomplemented
163C4×#123C2214yes—
164C4×#123C2214yescomplemented
165C4×#123C2214yescomplemented
166C4×#121C2212yescomplemented
167C4×#121C2212yescomplemented
168C4×#120C2214yes—
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175C2×#391C2211yescharacteristic
176#2293C2214yescomplemented
177C2×#390C2211yescharacteristic
178#2290C2214yescomplemented
179C2×#388C2214yes—
180C2×#386C2214yes—
181C2×#382C2211yescharacteristic
182#2280C2211yescharacteristic
183#2280C2211yescharacteristic
184#2274C2211yescharacteristic
185C42×D4C2214yescomplemented
186C4×#117C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C23×D4C2311yescharacteristic
191C23×D4C2312yes—
192C24×C4C2311yescharacteristic
193C24×C4C2312yes—
194#537—44no—
195#536—28no—
196#536—44no—
197#535—44no—
198#535—44no—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×#127C2312yes—
202C2×#127C2312yes—
203C2×#124—44no—
204C2×#124C2312yes—
205C2×#124C2314yes—
206C2×#124C2312yes—
207C2×#124C2312yes—
208C2×#124C2312yes—
209C2×#124C2312yes—
210C2×#124C2312yes—
211#525—28no—
212#525—44no—
213C2×#123C2314yes—
214C2×#123C2312yes—
215C2×#123C2314yes—
216C2×#123C2314yes—
217C2×#123C2312yes—
218C2×#123C2314yes—
219C2×C22⋊Q8—44no—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2312yes—
228C2×#121—44no—
229C2×#121C2312yes—
230C2×#121C2318yes—
231C2×#121C2318yes—
232C2×#121C2318yes—
233C2×#121C2314yes—
234C2×#121C2314yes—
235C2×#121C2312yes—
236C2×#121C2312yes—
237C2×#121C2312yes—
238C2×#121C2312yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C2×#121C2312yes—
242C2×#120C2312yes—
243C2×#120C2312yes—
244C2×#120C2314yes—
245C2×#120C2314yes—
246#520—44no—
247#519—44no—
248#518—28no—
249C4×#41—44no—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2312yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×#117C2311yescharacteristic
267C2×#117C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C2×#117C2311yescharacteristic
270C2×#117C2311yescharacteristic
271C2×#117C2318yes—
272C2×#117C2314yes—
273C2×#117C2312yes—
274C2×#117C2312yes—
275C2×#117C2311yescharacteristic
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2311yescharacteristic
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2312yes—
280C22×C22⋊C4C2314yes—
281C22×C22⋊C4C2314yes—
282C22×C22⋊C4C2312yes—
283C22×C22⋊C4C2312yes—
284C22×C22⋊C4C2314yes—
285C22×C42—44no—
286C22×C42C2311yescharacteristic
287C22×C42C2311yescharacteristic
288C22×C42C2312yes—
289C22×C42C2312yes—
290C22×C42C2312yes—
291C22×C42C2312yes—
292C22×C42C2312yes—
293C22×C42C2312yes—
294#400C2318yes—
295#400C2318yes—
296#400C2318yes—
297#400C2318yes—
298#400C2318yes—
299#400C2318yes—
300#399C2318yes—
301#399C2318yes—
302#399C2318yes—
303#399C2318yes—
304#398C2318yes—
305#398C2318yes—
306#398C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2318yes—
311#397C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2318yes—
315#396C2318yes—
316#396C2318yes—
317#396C2318yes—
318#396C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2318yes—
330#392C2318yes—
331#392C2318yes—
332#392C2318yes—
333#392C2318yes—
334#391C2311yescharacteristic
335#391C2312yes—
336#391C2314yes—
337#391C2314yes—
338#391C2312yes—
339#391C2312yes—
340#391C2311yescharacteristic
341#391C2314yes—
342#391C2312yes—
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#390C2314yes—
346#390C2312yes—
347#390C2312yes—
348#390C2312yes—
349#390C2312yes—
350#390C2318yes—
351#390C2318yes—
352#390C2318yes—
353#390C2311yescharacteristic
354#390C2318yes—
355#390C2318yes—
356#390C2318yes—
357#390C2318yes—
358#390C2312yes—
359#390C2314yes—
360#390C2311yescharacteristic
361#390C2312yes—
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#389C2318yes—
365#389C2312yes—
366#389C2314yes—
367#389C2312yes—
368#389C2318yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#389C2312yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2314yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2314yes—
393#388C2314yes—
394#388C2314yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2314yes—
399#388C2314yes—
400#387C2314yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#386C2314yes—
416#386C2318yes—
417#386C2318yes—
418#386C2314yes—
419#386C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2318yes—
423#386C2318yes—
424#386C2318yes—
425#386C2314yes—
426#386C2314yes—
427#386C2314yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2314yes—
432#386C2314yes—
433#386C2314yes—
434#385C2314yes—
435#385C2314yes—
436#385C2314yes—
437#385C2314yes—
438#385C2318yes—
439#385C2318yes—
440#385C2314yes—
441#385C2314yes—
442#385C2314yes—
443#385C2314yes—
444#385C2314yes—
445#385C2314yes—
446#384C2312yes—
447#384C2318yes—
448#384C2312yes—
449#384C2312yes—
450#382C2318yes—
451#382C2312yes—
452#382C2314yes—
453#382C2312yes—
454#382C2312yes—
455#382C2312yes—
456#382C2312yes—
457#381C2314yes—
458#381C2318yes—
459#381C2318yes—
460#381C2318yes—
461#381C2314yes—
462#381C2314yes—
463#381C2312yes—
464#381C2312yes—
465#380C2314yes—
466#380C2318yes—
467#380C2318yes—
468#380C2314yes—
469#380C2318yes—
470#380C2318yes—
471#380C2312yes—
472#380C2312yes—
473#380C2312yes—
474#380C2312yes—
475#379C2314yes—
476#379C2312yes—
477#379C2312yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2314yes—
503#376C2312yes—
504C2×#95C2314yes—
505C2×#95C2314yes—
506C43C2312yes—
507C25C2411yescharacteristic
508C25C2412yes—
509C2×#41—24no—
510C2×#41—24no—
511C2×#41—24no—
512C2×#41—24no—
513C2×#41—24no—
514C2×#41—24no—
515C22×Q8—24no—
516C22×Q8—24no—
517C22×Q8—24no—
518C22×Q8C2412yes—
519C22×Q8C2412yes—
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×D4—24no—
523C22×D4—24no—
524C22×D4—24no—
525C22×D4—44no—
526C22×D4—48no—
527C22×D4C2412yes—
528C22×D4C2412yes—
529C22×D4C2412yes—
530C22×D4C2412yes—
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2414yes—
534C22×D4C2414yes—
535C22×D4C2418yes—
536C22×D4C2418yes—
537C22×D4C2414yes—
538C22×D4C2414yes—
539C22×D4C2414yes—
540C23×C4—24no—
541C23×C4—24no—
542C23×C4—24no—
543C23×C4—44no—
544C23×C4—44no—
545C23×C4—44no—
546C23×C4C2412yes—
547C23×C4C2411yescharacteristic
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2412yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2412yes—
556C23×C4C2412yes—
557C23×C4C2418yes—
558C23×C4C2414yes—
559C23×C4C2412yes—
560C23×C4C2412yes—
561C23×C4C2414yes—
562C23×C4C2412yes—
563C23×C4C2411yescharacteristic
564C4⋊Q8—28no—
565C4⋊Q8—44no—
566#127—44no—
567#127—44no—
568#124—28no—
569#124—44no—
570#124—44no—
571#124—48no—
572#124—44no—
573#124—44no—
574#124—44no—
575#123—28no—
576#123—216no—
577#123—48no—
578#123—48no—
579#123—44no—
580#123—48no—
581C22⋊Q8—28no—
582C22⋊Q8—216no—
583C22⋊Q8—48no—
584C22⋊Q8—48no—
585C22⋊Q8—44no—
586C22⋊Q8—48no—
587C22⋊Q8—44no—
588C22⋊Q8—44no—
589#121—28no—
590#121—416no—
591#121—416no—
592#121—416no—
593#121—48no—
594#121—48no—
595#121—44no—
596#121—48no—
597#121—44no—
598#121—44no—
599#121—44no—
600#121—44no—
601#121—48no—
602#120—28no—
603#120—44no—
604#120—48no—
605#120—48no—
606C4×Q8—44no—
607C4×Q8—44no—
608C4×Q8—44no—
609C4×Q8—44no—
610C4×Q8—44no—
611C4×Q8—44no—
612C4×D4—216no—
613C4×D4—216no—
614C4×D4—216no—
615C4×D4—44no—
616C4×D4—44no—
617C4×D4—48no—
618C4×D4—48no—
619C4×D4—48no—
620C4×D4—48no—
621C4×D4—48no—
622#117—24no—
623#117—24no—
624#117—24no—
625#117—24no—
626#117—24no—
627#117—44no—
628#117—416no—
629#117—48no—
630#117—44no—
631#117#4118yes—
632C2×C4⋊C4—24no—
633C2×C4⋊C4—24no—
634C2×C4⋊C4—44no—
635C2×C4⋊C4—44no—
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2412yes—
668C2×C22⋊C4—216no—
669C2×C22⋊C4—48no—
670C2×C22⋊C4—44no—
671C2×C22⋊C4—44no—
672C2×C22⋊C4—48no—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2412yes—
712C2×C42—24no—
713C2×C42—24no—
714C2×C42—44no—
715C2×C42—44no—
716C2×C42—44no—
717C2×C42—44no—
718C2×C42—44no—
719C2×C42—44no—
720C2×C42C2414yes—
721C2×C42C2412yes—
722C2×C42C2411yescharacteristic
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2412yes—
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2414yes—
733C2×C42C2414yes—
734C2×C42C2414yes—
735C2×C42C2418yes—
736C2×C42C2414yes—
737C2×C42C2414yes—
738C2×C42C2412yes—
739C2×C42C2412yes—
740C2×C42C2412yes—
741C2×C42C2412yes—
742C2×C42C2412yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2418yes—
763#95C2414yes—
764#95C2418yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773C24—22no—
774C24—24no—
775C24—22no—
776C24—22no—
777C24—24no—
778C24—24no—
779C24—24no—
780C24—42no—
781C24—44no—
782C24—44no—
783C24C2514yes—
784C24C2512yes—
785C24C2512yes—
786C24C2512yes—
787C24C2511yescharacteristic
788#41—416no—
789#41—416no—
790C2×Q8—24no—
791C2×Q8—22no—
792C2×Q8—24no—
793C2×Q8—22no—
794C2×Q8—24no—
795C2×Q8—24no—
796C2×Q8—22no—
797C2×Q8—22no—
798C2×Q8—24no—
799C2×Q8—22no—
800C2×Q8—22no—
801C2×Q8—24no—
802C2×Q8—416no—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—216no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—28no—
815C2×D4—22no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—24no—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—24no—
825C2×D4—44no—
826C2×D4—44no—
827C2×D4—48no—
828C2×D4—44no—
829C2×D4—48no—
830C2×D4—44no—
831C2×D4—44no—
832C2×D4—48no—
833C2×D4—44no—
834C2×D4—48no—
835C2×D4—48no—
836C2×D4—48no—
837C2×D4—48no—
838C2×D4—48no—
839C2×D4—416no—
840C2×D4—816no—
841C22×C4—22no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—24no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—216no—
869C22×C4—28no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—48no—
884C22×C4—44no—
885C22×C4—48no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—48no—
889C22×C4—432no—
890C22×C4—416no—
891C22×C4C2×#4114yes—
892C22×C4H(5,𝔽2)14yes—
893C22×C4H(5,𝔽2)14yes—
894C22×C4C2514yes—
895C22×C4C2514yes—
896C22×C4C2512yes—
897C22×C4C2512yes—
898C22×C4C2512yes—
899C22×C4C2514yes—
900C22×C4C2512yes—
901C22×C4C2512yes—
902C22×C4C2512yes—
903C22×C4C2514yes—
904C22×C4C2512yes—
905C22×C4C2514yes—
906C22×C4C2514yes—
907C22×C4C2512yes—
908C22×C4C2512yes—
909C22×C4C2512yes—
910C22×C4C2514yes—
911C22×C4C2512yes—
912C22×C4C2511yescharacteristic
913C22×C4C2511yescharacteristic
914C4⋊C4—24no—
915C4⋊C4—28no—
916C4⋊C4—216no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—24no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—24no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—24no—
927C4⋊C4—28no—
928C4⋊C4—44no—
929C4⋊C4—48no—
930C4⋊C4—48no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—48no—
938C4⋊C4—48no—
939C4⋊C4—48no—
940C4⋊C4—44no—
941C4⋊C4—48no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4C2×#4118yes—
946C22⋊C4—24no—
947C22⋊C4—24no—
948C22⋊C4—24no—
949C22⋊C4—24no—
950C22⋊C4—24no—
951C22⋊C4—28no—
952C22⋊C4—28no—
953C22⋊C4—216no—
954C22⋊C4—28no—
955C22⋊C4—28no—
956C22⋊C4—216no—
957C22⋊C4—216no—
958C22⋊C4—28no—
959C22⋊C4—48no—
960C22⋊C4—48no—
961C22⋊C4—48no—
962C22⋊C4—48no—
963C22⋊C4—48no—
964C22⋊C4—48no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—48no—
975C22⋊C4—48no—
976C22⋊C4—48no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—48no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4C2×#4118yes—
985C42—24no—
986C42—22no—
987C42—22no—
988C42—24no—
989C42—24no—
990C42—22no—
991C42—22no—
992C42—24no—
993C42—24no—
994C42—24no—
995C42—24no—
996C42—28no—
997C42—42no—
998C42—42no—
999C42—42no—
1000C42—42no—
1001C42—44no—
1002C42—48no—
1003C42—44no—
1004C42—44no—
1005C42—44no—
1006C42—44no—
1007C42C2×#4118yes—
1008C23—22no—
1009C23—22no—
1010C23—28no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—24no—
1019C23—22no—
1020C23—22no—
1021C23—24no—
1022C23—22no—
1023C23—24no—
1024C23—22no—
1025C23—22no—
1026C23—28no—
1027C23—24no—
1028C23—24no—
1029C23—24no—
1030C23—24no—
1031C23—28no—
1032C23—48no—
1033C23—48no—
1034C23—44no—
1035C23—44no—
1036C23—48no—
1037C23—84no—
1038C23—88no—
1039C23—88no—
1040C23—84no—
1041C23C22×#4112yes—
1042C23C2×H(5,𝔽2)12yes—
1043C23C2×H(5,𝔽2)12yes—
1044C23#58514yes—
1045C23C2611yescharacteristic
1046Q8—48no—
1047Q8—48no—
1048Q8—44no—
1049Q8—44no—
1050D4—416no—
1051D4—48no—
1052D4—48no—
1053D4—48no—
1054D4—48no—
1055D4—44no—
1056D4—44no—
1057D4—88no—
1058D4—816no—
1059D4—168no—
1060D4—164no—
1061D4—164no—
1062D4—164no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—22no—
1085C2×C4—24no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—28no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—28no—
1109C2×C4—48no—
1110C2×C4—48no—
1111C2×C4—48no—
1112C2×C4—48no—
1113C2×C4—48no—
1114C2×C4—48no—
1115C2×C4—44no—
1116C2×C4—48no—
1117C2×C4—48no—
1118C2×C4—48no—
1119C2×C4—48no—
1120C2×C4—48no—
1121C2×C4—816no—
1122C2×C4—88no—
1123C2×C4—84no—
1124C2×C4—84no—
1125C2×C4—164no—
1126C2×C4#540116yes—
1127C2×C4C22×#4118yes—
1128C2×C4C22×#4112yes—
1129C2×C4C22×#4112yes—
1130C2×C4C2×H(5,𝔽2)12yes—
1131C2×C4C2×H(5,𝔽2)12yes—
1132C2×C4C2×H(5,𝔽2)12yes—
1133C2×C4C2×H(5,𝔽2)12yes—
1134C2×C4#58514yes—
1135C22—24no—
1136C22—24no—
1137C22—22no—
1138C22—22no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—416no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—48no—
1148C22—44no—
1149C22—44no—
1150C22—44no—
1151C22—44no—
1152C22—48no—
1153C22—42no—
1154C22—44no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—44no—
1159C22—42no—
1160C22—42no—
1161C22—44no—
1162C22—168no—
1163C22C2×#54014yes—
1164C22C23×#4111yescharacteristic
1165C22C22×H(5,𝔽2)11yescharacteristic
1166C22C22×H(5,𝔽2)11yescharacteristic
1167C22C2×#58512yes—
1168C22C2×#58512yes—
1169C4—28no—
1170C4—24no—
1171C4—44no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—44no—
1176C4—44no—
1177C4—44no—
1178C4—42no—
1179C4—42no—
1180C4—42no—
1181C4—44no—
1182C4—42no—
1183C4—42no—
1184C4—42no—
1185C4—42no—
1186C4—44no—
1187C4C2×#54014yes—
1188C4C2×#54014yes—
1189C2—24no—
1190C2—44no—
1191C2—82no—
1192C2—82no—
1193C2—84no—
1194C2C22×#54011yescharacteristic
1195C2#6281012yes—
1196C2#6282112yes—
1197C2#6282411yescharacteristic
1198C2#6283611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40217C2semidirect
2. #40170C2semidirect
3. #39212C2semidirect
4. #39023C2semidirect
5. #38534C2semidirect
6. #38176C2semidirect
7. #37409C2semidirect
8. #37372C2semidirect
9. #36626C2semidirect
10. C2×#2850C2semidirect
11. #35677C2semidirect
12. #35672C2semidirect
13. #35634C2semidirect
14. #35627C2semidirect
15. #35618C2semidirect
16. #35617C2semidirect
17. #35563C2semidirect
18. #35514C2semidirect
19. #35307C2semidirect
20. #35256C2semidirect
21. #35196C2semidirect
22. #35109C2semidirect
23. #34276C2semidirect
24. #34255C2semidirect
25. C4×#525C2semidirect
41. #2856C22semidirect
42. #2855C22semidirect
43. #2855C22semidirect
44. #2855C22semidirect
45. #2854C22semidirect
46. #2854C22semidirect
52. #2850C22semidirect
54. #2803C22semidirect
55. #2797C22semidirect
56. #2793C22semidirect
57. #2793C22semidirect
58. #2753C22semidirect
59. #2753C22semidirect
60. #2752C22semidirect
61. #2748C22semidirect
62. #2743C22semidirect
63. #2743C22semidirect
64. #2741C22semidirect
65. #2741C22semidirect
66. #2740C22semidirect
67. #2703C22semidirect
68. #2701C22semidirect
69. #2688C22semidirect
70. #2651C22semidirect
71. #2649C22semidirect
72. #2649C22semidirect
73. #2635C22semidirect
74. #2625C22semidirect
75. #2620C22semidirect
76. #2619C22semidirect
77. #2571C22semidirect
78. #2570C22semidirect
79. #2548C22semidirect
80. #2548C22semidirect
81. #2547C22semidirect
82. #2545C22semidirect
83. #2545C22semidirect
84. #2544C22semidirect
85. #2542C22semidirect
86. #2542C22semidirect
87. #2540C22semidirect
88. #2540C22semidirect
93. #2516C22semidirect
94. #2516C22semidirect
95. #2516C22semidirect
96. #2509C22semidirect
97. #2508C22semidirect
99. #2504C22semidirect
100. #2503C22semidirect
102. #2500C22semidirect
103. #2499C22semidirect
104. #2497C22semidirect
107. #2476C22semidirect
108. #2471C22semidirect
109. #2464C22semidirect
110. #2447C22semidirect
111. #2446C22semidirect
115. #2428C22semidirect
117. #2427C22semidirect
118. #2427C22semidirect
120. #2426C22semidirect
121. #2426C22semidirect
122. #2426C22semidirect
124. #2423C22semidirect
125. #2423C22semidirect
126. #2421C22semidirect
127. #2421C22semidirect
128. #2421C22semidirect
129. #2420C22semidirect
130. #2420C22semidirect
139. #2362C22semidirect
140. #2360C22semidirect
142. #2357C22semidirect
143. #2354C22semidirect
145. #2333C22semidirect
146. #2333C22semidirect
147. #2327C22semidirect
148. #2326C22semidirect
149. #2324C22semidirect
150. #2319C22semidirect
155. #2314C22semidirect
159. C4×C4⋊Q8C22semidirect
160. C4×#124C22semidirect
161. C4×C22⋊Q8C22semidirect
162. C4×C22⋊Q8C22semidirect
164. C4×#123C22semidirect
165. C4×#123C22semidirect
166. C4×#121C22semidirect
167. C4×#121C22semidirect
176. #2293C22semidirect
178. #2290C22semidirect
185. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#402172
#401702
#392122
#390232
#385342
#381762
#374092
#373722
#366262
C2×#28502
#356772
#356722
#356342
#356272
#356182
#356172
#355632
#355142
#353072
#352562
#351962
#351092
#342762
#342552
C4×#5252