Finite Group Databasebeta

← #7674395

Subgroups — #7674395

Order 512.

5188 conjugacy classes of subgroups.

The subgroup lattice has 1161 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45160C214yesmaximal, complemented
2#45158C214yesmaximal, complemented
3#44974C214yesmaximal, complemented
4#44972C214yesmaximal, complemented
5#39814C218yesmaximal, complemented
6#39812C218yesmaximal, complemented
7#39555C214yesmaximal, complemented
8#39554C214yesmaximal, complemented
9#37947C214yesmaximal, complemented
10#37946C214yesmaximal, complemented
11#35629C211yesmaximal, characteristic, complemented
12#35618C211yesmaximal, characteristic, complemented
13#35557C211yesmaximal, characteristic, complemented
14#35530C211yesmaximal, characteristic, complemented
15#35286C211yesmaximal, characteristic, complemented
16#35273C211yesmaximal, characteristic, complemented
17#35223C211yesmaximal, characteristic, complemented
18#35150C211yesmaximal, characteristic, complemented
19#34633C211yesmaximal, characteristic, complemented
20#34208C211yesmaximal, characteristic, complemented
21#34201C211yesmaximal, characteristic, complemented
22#34200C211yesmaximal, characteristic, complemented
23#34189C211yesmaximal, characteristic, complemented
24#34065C211yesmaximal, characteristic, complemented
25C2×#2317C211yesmaximal, characteristic, complemented
26C2×#537C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#532C2211yescharacteristic
29C2×#525C2211yescharacteristic
30C2×#525C2211yescharacteristic
31C2×#525C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C22×#117C2211yescharacteristic
37C23×C4⋊C4C2211yescharacteristic
38#2859C2214yescomplemented
39#2857C2212yescomplemented
40#2856C2212yescomplemented
41#2854C2214yes—
42#2847C2214yes—
43#2801C2218yescomplemented
44#2800C2218yescomplemented
45#2779C2218yes—
46#2776C2218yescomplemented
47#2772C2218yescomplemented
48#2770C2218yes—
49#2757C2218yes—
50#2757C2218yescomplemented
51#2753C2218yes—
52#2749C2218yes—
53#2746C2218yes—
54#2739C2218yescomplemented
55#2725C2218yescomplemented
56#2711C2218yes—
57#2701C2218yescomplemented
58#2688C2218yes—
59#2647C2214yescomplemented
60#2621C2212yes—
61#2620C2212yes—
62#2620C2212yes—
63#2620C2212yescomplemented
64#2620C2212yescomplemented
65#2619C2212yes—
66#2618C2214yes—
67#2618C2214yes—
68#2617C2214yes—
69#2617C2214yes—
70#2608C2218yescomplemented
71#2606C2218yescomplemented
72#2603C2218yes—
73#2602C2218yes—
74#2587C2218yescomplemented
75#2578C2218yes—
76#2576C2218yes—
77#2571C2214yescomplemented
78#2559C2218yes—
79#2559C2218yescomplemented
80#2558C2218yescomplemented
81#2552C2214yescomplemented
82#2538C2214yescomplemented
83#2537C2214yescomplemented
84#2530C2218yes—
85#2526C2218yescomplemented
86#2522C2218yescomplemented
87#2518C2218yescomplemented
88#2514C2214yescomplemented
89#2513C2214yescomplemented
90#2512C2214yescomplemented
91#2511C2214yescomplemented
92#2510C2218yes—
93#2504C2212yescomplemented
94#2503C2212yescomplemented
95#2502C2212yescomplemented
96#2501C2212yescomplemented
97#2500C2212yescomplemented
98#2500C2212yescomplemented
99#2499C2212yescomplemented
100#2499C2212yescomplemented
101#2497C2214yescomplemented
102#2496C2214yescomplemented
103#2495C2214yescomplemented
104#2494C2214yescomplemented
105#2481C2218yes—
106#2464C2218yes—
107#2460C2218yes—
108#2444C2218yes—
109#2443C2218yes—
110#2442C2218yes—
111#2423C2214yescomplemented
112#2422C2214yescomplemented
113#2421C2214yescomplemented
114#2420C2214yescomplemented
115#2417C2214yes—
116#2417C2214yes—
117#2416C2214yes—
118#2416C2214yes—
119#2416C2218yes—
120#2415C2214yes—
121#2415C2214yes—
122#2414C2214yes—
123#2414C2214yes—
124#2392C2214yes—
125#2392C2214yes—
126#2364C2218yes—
127#2363C2214yes—
128#2362C2214yes—
129#2361C2214yes—
130#2360C2214yes—
131#2357C2214yescomplemented
132#2356C2214yescomplemented
133#2354C2214yes—
134#2353C2218yes—
135#2352C2214yes—
136#2352C2214yes—
137#2352C2214yescomplemented
138#2352C2214yescomplemented
139D4×C4⋊C4C2214yes—
140#2328C2212yescomplemented
141#2327C2212yescomplemented
142#2324C2212yes—
143#2324C2212yes—
144#2323C2212yes—
145#2323C2212yes—
146#2322C2214yes—
147#2322C2214yes—
148#2321C2214yes—
149#2321C2214yes—
150#2317C2214yes—
151#2317C2214yes—
152#2317C2214yes—
153#2317C2214yes—
154#2317C2211yescharacteristic
155#2317C2211yescharacteristic
156#2316C2211yescharacteristic
157#2316C2211yescharacteristic
158#2314C2214yescomplemented
159#2311C2211yescharacteristic
160#2311C2211yescharacteristic
161#2311C2211yescharacteristic
162#2311C2211yescharacteristic
163#2311C2211yescharacteristic
164#2311C2211yescharacteristic
165C4×#124C2212yescomplemented
166C4×#124C2212yescomplemented
167C4×#123C2214yes—
168C4×#120C2214yes—
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2296C2211yescharacteristic
173#2293C2214yes—
174C2×#389C2214yes—
175#2290C2214yes—
176C2×#385C2214yes—
177#2285C2211yescharacteristic
178C2×#384C2211yescharacteristic
179C2×#384C2211yescharacteristic
180#2283C2214yescomplemented
181C2×#382C2211yescharacteristic
182C2×#382C2211yescharacteristic
183#2280C2211yescharacteristic
184#2274C2211yescharacteristic
185#2274C2211yescharacteristic
186C4×#117C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C22×#41C2311yescharacteristic
190C24×C4C2311yescharacteristic
191C24×C4C2312yes—
192#537—44no—
193#537—44no—
194#532—28no—
195C2×C4⋊Q8C2311yescharacteristic
196C2×#127C2311yescharacteristic
197C2×#126C2318yes—
198C2×#125C2318yes—
199C2×#124C2311yescharacteristic
200C2×#124C2311yescharacteristic
201#525—28no—
202#525—28no—
203#525—28no—
204C2×#123C2312yes—
205C2×#123C2312yes—
206C2×#123C2312yes—
207C2×#123C2318yes—
208C2×C22⋊Q8C2312yes—
209C2×C22⋊Q8C2312yes—
210C2×C22⋊Q8C2312yes—
211C2×C22⋊Q8C2312yes—
212C2×C22⋊Q8C2312yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2312yes—
215C2×#121C2312yes—
216C2×#121C2312yes—
217C2×#121C2314yes—
218C2×#121C2312yes—
219C2×#121C2314yes—
220C2×#121C2314yes—
221C2×#121C2312yes—
222C2×#121C2312yes—
223C2×#121C2312yes—
224C2×#121C2312yes—
225C2×#121C2318yes—
226C2×#121C2318yes—
227C2×#120C2312yes—
228C2×#120C2312yes—
229C2×#120C2312yes—
230#520—44no—
231#520—44no—
232C4×#41—28no—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2318yes—
247C2×#117—28no—
248C2×#117—44no—
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2312yes—
254C2×#117C2312yes—
255C2×#117C2312yes—
256C2×#117C2312yes—
257C2×#117C2312yes—
258C2×#117C2311yescharacteristic
259C2×#117C2314yes—
260C2×#117C2314yes—
261C2×#117C2312yes—
262C2×#117C2312yes—
263C22×C4⋊C4—44no—
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2314yes—
270C22×C4⋊C4C2314yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2314yes—
275C22×C4⋊C4C2314yes—
276C22×C22⋊C4C2312yes—
277C22×C22⋊C4C2312yes—
278C22×C42C2312yes—
279C22×C42C2311yescharacteristic
280C22×C42C2312yes—
281C22×C42C2311yescharacteristic
282#401C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#399C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2314yes—
293#398C2318yes—
294#398C2314yes—
295#398C2318yes—
296#397C2318yes—
297#397C2314yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2314yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#396C2318yes—
306#396C2314yes—
307#396C2318yes—
308#396C2314yes—
309#396C2318yes—
310#396C2318yes—
311#396C2314yes—
312#396C2314yes—
313#396C2318yes—
314#394C2314yes—
315#394C2318yes—
316#394C2314yes—
317#394C2318yes—
318#394C2318yes—
319#394C2314yes—
320#394C2314yes—
321#394C2314yes—
322#394C2314yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#392C2318yes—
328#392C2314yes—
329#392C2314yes—
330#391C2312yes—
331#391C2312yes—
332#391C2312yes—
333#391C2312yes—
334#391C2312yes—
335#391C2312yes—
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2312yes—
339#391C2312yes—
340#390C2312yes—
341#390C2312yes—
342#390C2312yes—
343#390C2312yes—
344#390C2312yes—
345#390C2312yes—
346#390C2314yes—
347#390C2314yes—
348#390C2318yes—
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2318yes—
352#390C2318yes—
353#390C2312yes—
354#390C2312yes—
355#389C2314yes—
356#389C2314yes—
357#389C2318yes—
358#389C2314yes—
359#389C2314yes—
360#389C2318yes—
361#389C2318yes—
362#389C2318yes—
363#389C2318yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2318yes—
369#389C2312yes—
370#389C2312yes—
371#389C2318yes—
372#389C2318yes—
373#389C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2314yes—
377#388C2318yes—
378#388C2318yes—
379#388C2314yes—
380#388C2314yes—
381#388C2314yes—
382#388C2318yes—
383#388C2314yes—
384#388C2314yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2314yes—
399#387C2314yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#386C2314yes—
409#386C2314yes—
410#386C2314yes—
411#386C2314yes—
412#386C2314yes—
413#386C2314yes—
414#386C2318yes—
415#386C2318yes—
416#386C2314yes—
417#386C2314yes—
418#386C2314yes—
419#386C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2318yes—
423#386C2314yes—
424#386C2314yes—
425#386C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2314yes—
431#385C2314yes—
432#385C2314yes—
433#385C2314yes—
434#385C2314yes—
435#385C2318yes—
436#385C2318yes—
437#385C2318yes—
438#384C2312yes—
439#384C2314yes—
440#384C2312yes—
441#384C2312yes—
442#384C2314yes—
443#384C2312yes—
444#384C2312yes—
445#384C2312yes—
446#384C2312yes—
447#383C2318yes—
448#383C2318yes—
449#382C2312yes—
450#382C2312yes—
451#382C2312yes—
452#382C2318yes—
453#382C2312yes—
454#382C2314yes—
455#382C2314yes—
456#382C2312yes—
457#382C2312yes—
458#382C2312yes—
459#381C2318yes—
460#381C2312yes—
461#381C2318yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2318yes—
471#380C2312yes—
472#380C2312yes—
473#380C2318yes—
474#380C2314yes—
475#379C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2318yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C22⋊C4C2318yes—
486C4×C22⋊C4C2318yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2318yes—
492C4×C22⋊C4C2318yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2314yes—
499#376C2312yes—
500#376C2318yes—
501C2×#95C2314yes—
502C2×#95C2314yes—
503C43C2312yes—
504C25C2411yescharacteristic
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C2×#41—24no—
509C2×#41—24no—
510C2×#41—24no—
511C2×#41—24no—
512C2×#41—24no—
513C2×#41—24no—
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×Q8C2411yescharacteristic
517C22×D4C2412yes—
518C22×D4C2412yes—
519C22×D4C2412yes—
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2414yes—
524C22×D4C2414yes—
525C22×D4C2414yes—
526C22×D4C2414yes—
527C22×D4C2414yes—
528C22×D4C2414yes—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—44no—
532C23×C4—84no—
533C23×C4#4118yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2411yescharacteristic
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2414yes—
546C23×C4C2418yes—
547C23×C4C2414yes—
548C23×C4C2414yes—
549C23×C4C2412yes—
550C23×C4C2411yescharacteristic
551C4⋊Q8—24no—
552#127—24no—
553#126—88no—
554#125—88no—
555#124—24no—
556#124—24no—
557#123—28no—
558#123—28no—
559#123—28no—
560#123—88no—
561C22⋊Q8—28no—
562C22⋊Q8—28no—
563C22⋊Q8—28no—
564C22⋊Q8—44no—
565C22⋊Q8—44no—
566C22⋊Q8—44no—
567C22⋊Q8—44no—
568#121—28no—
569#121—28no—
570#121—28no—
571#121—216no—
572#121—44no—
573#121—44no—
574#121—44no—
575#121—44no—
576#121—48no—
577#121—48no—
578#121—88no—
579#121—88no—
580#120—28no—
581#120—28no—
582#120—28no—
583C4×Q8—28no—
584C4×Q8—44no—
585C4×Q8—44no—
586C4×D4—216no—
587C4×D4—216no—
588C4×D4—216no—
589C4×D4—216no—
590C4×D4—28no—
591C4×D4—216no—
592C4×D4—44no—
593C4×D4—44no—
594C4×D4—48no—
595C4×D4—48no—
596C4×D4—88no—
597#117—24no—
598#117—24no—
599#117—24no—
600#117—24no—
601#117—24no—
602#117—28no—
603#117—28no—
604#117—28no—
605#117—28no—
606#117—28no—
607#117—48no—
608#117—48no—
609#117—44no—
610#117—44no—
611C2×C4⋊C4—28no—
612C2×C4⋊C4—24no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—48no—
617C2×C4⋊C4—48no—
618C2×C4⋊C4—44no—
619C2×C4⋊C4—44no—
620C2×C4⋊C4—44no—
621C2×C4⋊C4—84no—
622C2×C4⋊C4—84no—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C22⋊C4—28no—
664C2×C22⋊C4—44no—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C42—24no—
705C2×C42—28no—
706C2×C42—44no—
707C2×C42#4118yes—
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2414yes—
717C2×C42C2418yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2418yes—
721C2×C42C2414yes—
722C2×C42C2414yes—
723C2×C42C2418yes—
724C2×C42C2411yescharacteristic
725C2×C42C2412yes—
726C2×C42C2411yescharacteristic
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2418yes—
735#95C2418yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2414yes—
745#95C2418yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2418yes—
757C24—22no—
758C24—22no—
759C24—42no—
760C24—42no—
761C24C2×#4114yes—
762C24C2512yes—
763C24C2512yes—
764C24C2512yes—
765C24C2512yes—
766C24C2511yescharacteristic
767#41—416no—
768#41—416no—
769#41—416no—
770C2×Q8—22no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—22no—
774C2×Q8—22no—
775C2×Q8—22no—
776C2×Q8—22no—
777C2×Q8—22no—
778C2×Q8—22no—
779C2×D4—24no—
780C2×D4—28no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—24no—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—28no—
790C2×D4—28no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—28no—
798C2×D4—22no—
799C2×D4—22no—
800C2×D4—22no—
801C2×D4—44no—
802C2×D4—44no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—44no—
810C2×D4—44no—
811C2×D4—48no—
812C2×D4—48no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—232no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—28no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—48no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—48no—
844C22×C4—44no—
845C22×C4—48no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—816no—
853C22×C4C2×#4118yes—
854C22×C4C2×#4118yes—
855C22×C4C2×#4114yes—
856C22×C4C2×#4118yes—
857C22×C4C2×#4114yes—
858C22×C4C2×#4114yes—
859C22×C4H(5,𝔽2)14yes—
860C22×C4C2512yes—
861C22×C4C2514yes—
862C22×C4C2514yes—
863C22×C4C2514yes—
864C22×C4C2514yes—
865C22×C4C2514yes—
866C22×C4C2512yes—
867C22×C4C2512yes—
868C22×C4C2512yes—
869C22×C4C2512yes—
870C22×C4C2512yes—
871C22×C4C2514yes—
872C22×C4C2514yes—
873C22×C4C2512yes—
874C22×C4C2514yes—
875C22×C4C2512yes—
876C22×C4C2512yes—
877C22×C4C2512yes—
878C22×C4C2511yescharacteristic
879C22×C4C2511yescharacteristic
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—28no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—24no—
894C4⋊C4—24no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—22no—
902C4⋊C4—22no—
903C4⋊C4—48no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—48no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—48no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—48no—
916C4⋊C4—48no—
917C4⋊C4—44no—
918C4⋊C4—48no—
919C4⋊C4—44no—
920C22⋊C4—24no—
921C22⋊C4—24no—
922C22⋊C4—24no—
923C22⋊C4—24no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—24no—
928C22⋊C4—24no—
929C22⋊C4—24no—
930C22⋊C4—24no—
931C22⋊C4—24no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—48no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—48no—
942C22⋊C4—44no—
943C22⋊C4—48no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—48no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—48no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C42—24no—
960C42—24no—
961C42—22no—
962C42—22no—
963C42—28no—
964C42—24no—
965C42—24no—
966C42—24no—
967C42—24no—
968C42—48no—
969C42—44no—
970C42—48no—
971C42—44no—
972C42—44no—
973C42—48no—
974C42—44no—
975C42C2×#4114yes—
976C42C2×#4114yes—
977C42C2×#4118yes—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—28no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—48no—
1003C23—44no—
1004C23—48no—
1005C23—44no—
1006C23C22×#4114yes—
1007C23C22×#4112yes—
1008C23C22×#4112yes—
1009C23C2×H(5,𝔽2)12yes—
1010C23C2611yescharacteristic
1011Q8—44no—
1012Q8—44no—
1013Q8—44no—
1014D4—416no—
1015D4—48no—
1016D4—48no—
1017D4—48no—
1018D4—44no—
1019D4—44no—
1020D4—44no—
1021D4—88no—
1022D4—88no—
1023D4—88no—
1024D4—164no—
1025D4—164no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—28no—
1033C2×C4—216no—
1034C2×C4—216no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—28no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—28no—
1065C2×C4—28no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—28no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—48no—
1075C2×C4—48no—
1076C2×C4—48no—
1077C2×C4—48no—
1078C2×C4—48no—
1079C2×C4—88no—
1080C2×C4—84no—
1081C2×C4—84no—
1082C2×C4—84no—
1083C2×C4—84no—
1084C2×C4—816no—
1085C2×C4—164no—
1086C2×C4—164no—
1087C2×C4#553116yes—
1088C2×C4C22×#4114yes—
1089C2×C4C22×#4114yes—
1090C2×C4C22×#4114yes—
1091C2×C4C22×#4112yes—
1092C2×C4C22×#4112yes—
1093C2×C4C22×#4112yes—
1094C2×C4C22×#4112yes—
1095C2×C4C2×H(5,𝔽2)12yes—
1096C2×C4C2×H(5,𝔽2)12yes—
1097C22—24no—
1098C22—24no—
1099C22—22no—
1100C22—22no—
1101C22—24no—
1102C22—24no—
1103C22—24no—
1104C22—416no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—44no—
1110C22—44no—
1111C22—44no—
1112C22—44no—
1113C22—44no—
1114C22—44no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22C2×#55314yes—
1125C22C23×#4111yescharacteristic
1126C22C23×#4111yescharacteristic
1127C22C22×H(5,𝔽2)11yescharacteristic
1128C22H(7,𝔽2)12yes—
1129C222−1+612yes—
1130C4—24no—
1131C4—24no—
1132C4—24no—
1133C4—42no—
1134C4—42no—
1135C4—44no—
1136C4—44no—
1137C4—44no—
1138C4—44no—
1139C4—44no—
1140C4—44no—
1141C4—44no—
1142C4—42no—
1143C4—44no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4C2×#55314yes—
1149C4C2×#55314yes—
1150C2—24no—
1151C2—44no—
1152C2—82no—
1153C2—82no—
1154C2—82no—
1155C2C22×#55311yescharacteristic
1156C2#6285612yes—
1157C2#6285612yes—
1158C2#6287611yescharacteristic
1159C2#6288711yescharacteristic
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. #45160C2semidirect
2. #45158C2semidirect
3. #44974C2semidirect
4. #44972C2semidirect
5. #39814C2semidirect
6. #39812C2semidirect
7. #39555C2semidirect
8. #39554C2semidirect
9. #37947C2semidirect
10. #37946C2semidirect
11. #35629C2semidirect
12. #35618C2semidirect
13. #35557C2semidirect
14. #35530C2semidirect
15. #35286C2semidirect
16. #35273C2semidirect
17. #35223C2semidirect
18. #35150C2semidirect
19. #34633C2semidirect
20. #34208C2semidirect
21. #34201C2semidirect
22. #34200C2semidirect
23. #34189C2semidirect
24. #34065C2semidirect
25. C2×#2317C2semidirect
38. #2859C22semidirect
39. #2857C22semidirect
40. #2856C22semidirect
43. #2801C22semidirect
44. #2800C22semidirect
46. #2776C22semidirect
47. #2772C22semidirect
50. #2757C22semidirect
54. #2739C22semidirect
55. #2725C22semidirect
57. #2701C22semidirect
59. #2647C22semidirect
63. #2620C22semidirect
64. #2620C22semidirect
70. #2608C22semidirect
71. #2606C22semidirect
74. #2587C22semidirect
77. #2571C22semidirect
79. #2559C22semidirect
80. #2558C22semidirect
81. #2552C22semidirect
82. #2538C22semidirect
83. #2537C22semidirect
85. #2526C22semidirect
86. #2522C22semidirect
87. #2518C22semidirect
88. #2514C22semidirect
89. #2513C22semidirect
90. #2512C22semidirect
91. #2511C22semidirect
93. #2504C22semidirect
94. #2503C22semidirect
95. #2502C22semidirect
96. #2501C22semidirect
97. #2500C22semidirect
98. #2500C22semidirect
99. #2499C22semidirect
100. #2499C22semidirect
101. #2497C22semidirect
102. #2496C22semidirect
103. #2495C22semidirect
104. #2494C22semidirect
111. #2423C22semidirect
112. #2422C22semidirect
113. #2421C22semidirect
114. #2420C22semidirect
131. #2357C22semidirect
132. #2356C22semidirect
137. #2352C22semidirect
138. #2352C22semidirect
140. #2328C22semidirect
141. #2327C22semidirect
158. #2314C22semidirect
165. C4×#124C22semidirect
166. C4×#124C22semidirect
180. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#451602
#451582
#449742
#449722
#398142
#398122
#395552
#395542
#379472
#379462
#356292
#356182
#355572
#355302
#352862
#352732
#352232
#351502
#346332
#342082
#342012
#342002
#341892
#340652
C2×#23172