Finite Group Databasebeta

← #7644211

Subgroups — #7644211

Order 512.

5560 conjugacy classes of subgroups.

The subgroup lattice has 1185 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42895C214yesmaximal, complemented
2#42893C214yesmaximal, complemented
3#42872C214yesmaximal, complemented
4#42869C214yesmaximal, complemented
5#42842C214yesmaximal, complemented
6#42838C214yesmaximal, complemented
7#42834C214yesmaximal, complemented
8#42829C214yesmaximal, complemented
9#37496C218yesmaximal, complemented
10#36791C218yesmaximal, complemented
11#35677C211yesmaximal, characteristic, complemented
12#35676C211yesmaximal, characteristic, complemented
13#35662C211yesmaximal, characteristic, complemented
14#35660C211yesmaximal, characteristic, complemented
15#35557C211yesmaximal, characteristic, complemented
16#35556C211yesmaximal, characteristic, complemented
17#35533C211yesmaximal, characteristic, complemented
18#35530C211yesmaximal, characteristic, complemented
19#35168C211yesmaximal, characteristic, complemented
20#35152C211yesmaximal, characteristic, complemented
21#34639C211yesmaximal, characteristic, complemented
22#34637C211yesmaximal, characteristic, complemented
23#34266C211yesmaximal, characteristic, complemented
24#34257C211yesmaximal, characteristic, complemented
25C2×#2326C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C2×#535C2211yescharacteristic
32C2×#533C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C22×#124C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38C22×C4×D4C2211yescharacteristic
39#2849C2214yes—
40#2847C2214yes—
41#2832C2218yescomplemented
42#2831C2218yescomplemented
43#2829C2218yescomplemented
44#2828C2218yescomplemented
45#2804C2218yescomplemented
46#2797C2218yescomplemented
47#2788C2218yescomplemented
48#2784C2218yescomplemented
49#2780C2218yescomplemented
50#2778C2218yescomplemented
51#2751C2218yescomplemented
52#2750C2218yescomplemented
53#2745C2218yescomplemented
54#2714C2218yescomplemented
55#2710C2218yescomplemented
56#2708C2218yescomplemented
57#2708C2218yescomplemented
58#2695C2218yescomplemented
59#2686C2218yescomplemented
60#2682C2218yescomplemented
61#2662C2218yescomplemented
62#2661C2218yescomplemented
63#2653C2218yescomplemented
64#2653C2218yescomplemented
65#2650C2218yescomplemented
66#2649C2218yescomplemented
67#2648C2218yescomplemented
68#2648C2218yescomplemented
69#2645C2212yescomplemented
70#2645C2212yescomplemented
71#2644C2212yescomplemented
72#2644C2212yescomplemented
73#2643C2214yes—
74#2643C2214yes—
75#2642C2212yescomplemented
76#2641C2212yescomplemented
77#2640C2212yescomplemented
78#2640C2212yescomplemented
79#2639C2214yes—
80#2639C2214yes—
81#2622C2214yes—
82#2617C2214yes—
83#2597C2218yescomplemented
84#2595C2218yescomplemented
85#2592C2214yes—
86#2582C2214yescomplemented
87#2581C2214yescomplemented
88#2559C2218yescomplemented
89#2557C2218yescomplemented
90#2548C2214yes—
91#2548C2212yes—
92#2548C2214yes—
93#2545C2212yes—
94#2545C2214yes—
95#2544C2212yes—
96#2541C2212yes—
97#2512C2214yescomplemented
98#2511C2214yescomplemented
99#2502C2212yescomplemented
100#2501C2212yescomplemented
101#2500C2212yescomplemented
102#2499C2212yescomplemented
103#2497C2214yescomplemented
104#2496C2214yescomplemented
105#2491C2214yes—
106#2490C2214yes—
107#2481C2218yes—
108#2472C2218yes—
109#2453C2214yescomplemented
110#2451C2214yescomplemented
111#2447C2214yes—
112#2445C2214yes—
113#2443C2218yes—
114#2438C2218yes—
115#2436C2212yes—
116#2436C2214yes—
117#2436C2212yes—
118#2436C2212yescomplemented
119#2434C2212yescomplemented
120#2432C2212yescomplemented
121#2431C2212yes—
122#2431C2214yes—
123#2431C2212yes—
124#2431C2212yescomplemented
125#2430C2218yes—
126#2428C2214yes—
127#2428C2214yes—
128#2427C2214yes—
129#2427C2214yes—
130#2426C2214yes—
131#2426C2214yes—
132#2424C2218yes—
133#2423C2214yescomplemented
134#2422C2214yes—
135#2422C2214yescomplemented
136#2420C2214yes—
137#2416C2214yes—
138#2414C2214yes—
139#2411C2218yes—
140#2409C2214yescomplemented
141#2407C2214yescomplemented
142#2404C2218yes—
143#2401C2214yescomplemented
144#2401C2214yescomplemented
145#2398C2214yescomplemented
146#2398C2214yescomplemented
147#2367C2214yescomplemented
148#2365C2214yescomplemented
149#2362C2214yescomplemented
150#2360C2214yescomplemented
151#2341C2214yescomplemented
152#2341C2214yescomplemented
153Q8×C22⋊C4C2214yescomplemented
154Q8×C22⋊C4C2214yescomplemented
155#2326C2214yes—
156#2326C2214yes—
157#2326C2214yes—
158#2326C2214yes—
159#2322C2214yes—
160#2317C2211yescharacteristic
161#2316C2211yescharacteristic
162#2311C2211yescharacteristic
163#2311C2214yes—
164#2311C2211yescharacteristic
165#2311C2211yescharacteristic
166#2310C2211yescharacteristic
167#2309C2211yescharacteristic
168C4×#123C2214yes—
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2297C2214yes—
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179#2296C2211yescharacteristic
180C2×#391C2211yescharacteristic
181C2×#390C2211yescharacteristic
182C2×#388C2214yes—
183C2×#385C2214yes—
184C2×#384C2211yescharacteristic
185#2274C2211yescharacteristic
186C2×#376C2211yescharacteristic
187C2×2−1+4—28no—
188C2×2−1+4—44no—
189C2×2−1+4—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2311yescharacteristic
193C22×#41C2314yes—
194C22×#41C2312yes—
195C22×#41C2312yes—
196C23×Q8C2311yescharacteristic
197C23×Q8C2312yes—
198C23×Q8C2312yes—
199C23×D4C2311yescharacteristic
200C24×C4C2312yes—
201#537—44no—
202#536—28no—
203#535—44no—
204#535—44no—
205#535—44no—
206#533—44no—
207#532—44no—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#127C2312yes—
213C2×#127C2312yes—
214C2×#127C2312yes—
215C2×#126C2318yes—
216C2×#125C2312yes—
217C2×#124—28no—
218C2×#124C2312yes—
219C2×#124C2312yes—
220C2×#124C2314yes—
221C2×#124C2312yes—
222C2×#124C2312yes—
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2312yes—
226C2×#124C2312yes—
227C2×#124C2318yes—
228C2×#123C2314yes—
229C2×#123C2318yes—
230C2×#123C2318yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×#121C2314yes—
236C2×#121C2314yes—
237C2×#121C2312yes—
238C2×#121C2312yes—
239C2×#121C2314yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2314yes—
243C2×#121C2318yes—
244C2×#121C2318yes—
245C2×#120C2314yes—
246C2×#120C2314yes—
247C2×#120C2314yes—
248#520—44no—
249#519—44no—
250C2×C4×Q8—44no—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2312yes—
257C2×C4×D4—44no—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2314yes—
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C2×#117C2311yescharacteristic
268C2×#117C2314yes—
269C2×#117C2312yes—
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2314yes—
275C22×C22⋊C4C2314yes—
276C22×C22⋊C4C2312yes—
277C22×C22⋊C4C2314yes—
278C22×C42C2311yescharacteristic
279C22×C42C2311yescharacteristic
280C22×C42C2311yescharacteristic
281C22×C42C2312yes—
282#401C2314yes—
283#401C2314yes—
284#400C2318yes—
285#400C2314yes—
286#400C2314yes—
287#400C2318yes—
288#400C2314yes—
289#400C2318yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#399C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#397C2314yes—
302#397C2318yes—
303#397C2314yes—
304#397C2314yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2314yes—
311#397C2314yes—
312#397C2314yes—
313#397C2314yes—
314#397C2314yes—
315#397C2314yes—
316#397C2314yes—
317#396C2318yes—
318#396C2318yes—
319#396C2318yes—
320#396C2318yes—
321#396C2314yes—
322#396C2314yes—
323#395C2318yes—
324#395C2318yes—
325#394C2314yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2318yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#394C2318yes—
338#394C2314yes—
339#394C2314yes—
340#394C2314yes—
341#393C2318yes—
342#393C2314yes—
343#393C2318yes—
344#393C2318yes—
345#393C2318yes—
346#393C2314yes—
347#393C2314yes—
348#393C2314yes—
349#392C2318yes—
350#392C2318yes—
351#392C2318yes—
352#392C2318yes—
353#392C2318yes—
354#391C2312yes—
355#391C2312yes—
356#391C2314yes—
357#391C2312yes—
358#391C2318yes—
359#391C2312yes—
360#391C2312yes—
361#391C2318yes—
362#391C2314yes—
363#391C2312yes—
364#391C2312yes—
365#391C2318yes—
366#391C2312yes—
367#391C2312yes—
368#391C2312yes—
369#391C2312yes—
370#391C2312yes—
371#391C2312yes—
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#390C2314yes—
375#390C2314yes—
376#390C2318yes—
377#390C2312yes—
378#390C2312yes—
379#390C2312yes—
380#390C2318yes—
381#390C2314yes—
382#390C2312yes—
383#390C2312yes—
384#390C2318yes—
385#390C2312yes—
386#390C2312yes—
387#390C2318yes—
388#390C2312yes—
389#390C2312yes—
390#390C2312yes—
391#390C2312yes—
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2318yes—
395#390C2318yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2318yes—
400#389C2312yes—
401#389C2312yes—
402#389C2318yes—
403#389C2312yes—
404#389C2312yes—
405#389C2312yes—
406#389C2312yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#386C2312yes—
428#386C2312yes—
429#386C2314yes—
430#386C2314yes—
431#386C2314yes—
432#386C2312yes—
433#386C2318yes—
434#386C2318yes—
435#386C2318yes—
436#386C2318yes—
437#386C2318yes—
438#386C2312yes—
439#386C2312yes—
440#386C2312yes—
441#386C2314yes—
442#386C2314yes—
443#386C2314yes—
444#386C2314yes—
445#386C2318yes—
446#386C2318yes—
447#386C2318yes—
448#386C2318yes—
449#386C2318yes—
450#385C2314yes—
451#385C2312yes—
452#385C2318yes—
453#385C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2318yes—
458#385C2318yes—
459#385C2318yes—
460#385C2312yes—
461#385C2314yes—
462#385C2314yes—
463#385C2318yes—
464#384C2312yes—
465#384C2314yes—
466#384C2312yes—
467#384C2312yes—
468#382C2312yes—
469#381C2314yes—
470#381C2318yes—
471#380C2314yes—
472#380C2314yes—
473#380C2318yes—
474#380C2318yes—
475#380C2314yes—
476#380C2314yes—
477#380C2318yes—
478#379C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2318yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2318yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2318yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2312yes—
499C4×C22⋊C4C2312yes—
500#376C2312yes—
501#376C2312yes—
502#376C2312yes—
503#376C2312yes—
504C2×#95C2312yes—
505C2×#95C2312yes—
506C2×#95C2314yes—
507C25C2412yes—
5082−1+4—464no—
509C2×#41—28no—
510C2×#41—28no—
511C2×#41—24no—
512C2×#41—216no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—24no—
520C2×#41—24no—
521C2×#41—48no—
522C2×#41—48no—
523C2×#41—44no—
524C2×#41—44no—
525C2×#41—44no—
526C2×#41—44no—
527C22×Q8—28no—
528C22×Q8—28no—
529C22×Q8—24no—
530C22×Q8—24no—
531C22×Q8—44no—
532C22×Q8—44no—
533C22×Q8—44no—
534C22×Q8—44no—
535C22×Q8#4118yes—
536C22×Q8C2411yescharacteristic
537C22×Q8C2411yescharacteristic
538C22×Q8C2411yescharacteristic
539C22×Q8C2412yes—
540C22×Q8C2412yes—
541C22×Q8C2414yes—
542C22×Q8C2414yes—
543C22×D4—24no—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4C2412yes—
547C22×D4C2412yes—
548C22×D4C2412yes—
549C22×D4C2411yescharacteristic
550C22×D4C2412yes—
551C22×D4C2412yes—
552C22×D4C2411yescharacteristic
553C22×D4C2411yescharacteristic
554C22×D4C2414yes—
555C22×D4C2414yes—
556C22×D4C2414yes—
557C22×D4C2418yes—
558C22×D4C2418yes—
559C22×D4C2414yes—
560C22×D4C2414yes—
561C23×C4—44no—
562C23×C4—84no—
563C23×C4C2412yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2412yes—
568C23×C4C2412yes—
569C23×C4C2412yes—
570C23×C4C2411yescharacteristic
571C23×C4C2412yes—
572C23×C4C2411yescharacteristic
573C23×C4C2414yes—
574C23×C4C2414yes—
575C23×C4C2414yes—
576C23×C4C2418yes—
577C23×C4C2411yescharacteristic
578C4⋊Q8—28no—
579C4⋊Q8—44no—
580C4⋊Q8—42no—
581#127—42no—
582#127—44no—
583#127—44no—
584#127—44no—
585#126—88no—
586#125—44no—
587#124—28no—
588#124—28no—
589#124—216no—
590#124—28no—
591#124—42no—
592#124—42no—
593#124—44no—
594#124—44no—
595#124—44no—
596#124—88no—
597#123—216no—
598#123—88no—
599#123—88no—
600C22⋊Q8—216no—
601C22⋊Q8—48no—
602C22⋊Q8—44no—
603C22⋊Q8—44no—
604#121—44no—
605#121—44no—
606#121—48no—
607#121—48no—
608#121—44no—
609#121—44no—
610#121—48no—
611#121—48no—
612#121—88no—
613#121—88no—
614#120—48no—
615#120—48no—
616#120—48no—
617C4×Q8—48no—
618C4×Q8—48no—
619C4×Q8—48no—
620C4×Q8—48no—
621C4×Q8—48no—
622C4×Q8—44no—
623C4×D4—48no—
624C4×D4—48no—
625C4×D4—44no—
626C4×D4—48no—
627C4×D4—48no—
628#117—24no—
629#117—24no—
630#117—24no—
631#117—24no—
632#117—24no—
633#117—48no—
634#117—44no—
635C2×C4⋊C4—24no—
636C2×C4⋊C4—24no—
637C2×C4⋊C4—44no—
638C2×C4⋊C4—44no—
639C2×C4⋊C4—84no—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C22⋊C4—216no—
670C2×C22⋊C4—44no—
671C2×C22⋊C4—84no—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2418yes—
711C2×C42—24no—
712C2×C42—24no—
713C2×C42—24no—
714C2×C42—44no—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2412yes—
727C2×C42C2411yescharacteristic
728C2×C42C2414yes—
729C2×C42C2418yes—
730C2×C42C2418yes—
731C2×C42C2418yes—
732#95C2412yes—
733#95C2412yes—
734#95C2412yes—
735#95C2412yes—
736#95C2412yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2418yes—
741#95C2418yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750#95C2414yes—
751#95C2418yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770C24—24no—
771C24—24no—
772C24—24no—
773C24—44no—
774C24—44no—
775C24C2514yes—
776C24C2512yes—
777C24C2512yes—
778C24C2512yes—
779C24C2511yescharacteristic
780#41—464no—
781#41—432no—
782#41—432no—
783#41—416no—
784#41—416no—
785#41—416no—
786C2×Q8—232no—
787C2×Q8—22no—
788C2×Q8—28no—
789C2×Q8—22no—
790C2×Q8—22no—
791C2×Q8—24no—
792C2×Q8—24no—
793C2×Q8—24no—
794C2×Q8—24no—
795C2×Q8—22no—
796C2×Q8—22no—
797C2×Q8—22no—
798C2×Q8—22no—
799C2×Q8—22no—
800C2×Q8—22no—
801C2×Q8—44no—
802C2×Q8—44no—
803C2×Q8—44no—
804C2×Q8—44no—
805C2×Q8—44no—
806C2×Q8—432no—
807C2×Q8—432no—
808C2×Q8C2×#4118yes—
809C2×Q8C2×#4118yes—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—22no—
822C2×D4—28no—
823C2×D4—22no—
824C2×D4—22no—
825C2×D4—24no—
826C2×D4—22no—
827C2×D4—24no—
828C2×D4—24no—
829C2×D4—24no—
830C2×D4—22no—
831C2×D4—22no—
832C2×D4—22no—
833C2×D4—22no—
834C2×D4—22no—
835C2×D4—44no—
836C2×D4—44no—
837C2×D4—44no—
838C2×D4—44no—
839C2×D4—44no—
840C2×D4—44no—
841C2×D4—48no—
842C2×D4—48no—
843C2×D4—44no—
844C2×D4—44no—
845C2×D4—48no—
846C2×D4—48no—
847C2×D4—48no—
848C2×D4—48no—
849C2×D4—48no—
850C2×D4—48no—
851C2×D4—48no—
852C2×D4—416no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—28no—
863C22×C4—28no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—42no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—48no—
884C22×C4—48no—
885C22×C4—48no—
886C22×C4—42no—
887C22×C4—44no—
888C22×C4—48no—
889C22×C4—816no—
890C22×C4C2×#4118yes—
891C22×C4C2×#4114yes—
892C22×C4H(5,𝔽2)14yes—
893C22×C4H(5,𝔽2)14yes—
894C22×C4C2512yes—
895C22×C4C2512yes—
896C22×C4C2512yes—
897C22×C4C2512yes—
898C22×C4C2514yes—
899C22×C4C2512yes—
900C22×C4C2512yes—
901C22×C4C2512yes—
902C22×C4C2512yes—
903C22×C4C2512yes—
904C22×C4C2514yes—
905C22×C4C2514yes—
906C22×C4C2512yes—
907C22×C4C2514yes—
908C22×C4C2514yes—
909C22×C4C2512yes—
910C22×C4C2514yes—
911C22×C4C2514yes—
912C22×C4C2511yescharacteristic
913C22×C4C2511yescharacteristic
914C4⋊C4—24no—
915C4⋊C4—216no—
916C4⋊C4—24no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—44no—
926C4⋊C4—48no—
927C4⋊C4—48no—
928C4⋊C4—48no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—48no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—48no—
940C4⋊C4—44no—
941C4⋊C4—48no—
942C4⋊C4—44no—
943C22⋊C4—24no—
944C22⋊C4—24no—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—24no—
948C22⋊C4—216no—
949C22⋊C4—216no—
950C22⋊C4—216no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—48no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—48no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—48no—
967C22⋊C4—48no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—48no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—48no—
978C22⋊C4—48no—
979C22⋊C4—48no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C42—24no—
983C42—22no—
984C42—22no—
985C42—24no—
986C42—24no—
987C42—24no—
988C42—24no—
989C42—22no—
990C42—22no—
991C42—24no—
992C42—24no—
993C42—24no—
994C42—24no—
995C42—48no—
996C42—44no—
997C42—48no—
998C42—48no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—24no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—24no—
1007C23—24no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—24no—
1014C23—24no—
1015C23—28no—
1016C23—24no—
1017C23—24no—
1018C23—24no—
1019C23—24no—
1020C23—28no—
1021C23—416no—
1022C23—48no—
1023C23—84no—
1024C23—88no—
1025C23—84no—
1026C23C22×#4112yes—
1027C23C2×H(5,𝔽2)12yes—
1028C23C2×H(5,𝔽2)12yes—
1029C23C2611yescharacteristic
1030Q8—216no—
1031Q8—216no—
1032Q8—416no—
1033Q8—44no—
1034Q8—44no—
1035Q8—44no—
1036Q8—88no—
1037D4—416no—
1038D4—48no—
1039D4—48no—
1040D4—48no—
1041D4—48no—
1042D4—48no—
1043D4—44no—
1044D4—44no—
1045D4—44no—
1046D4—88no—
1047D4—164no—
1048D4—164no—
1049D4—168no—
1050D4—168no—
1051D4—164no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—216no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—28no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—28no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—416no—
1103C2×C4—416no—
1104C2×C4—48no—
1105C2×C4—44no—
1106C2×C4—44no—
1107C2×C4—48no—
1108C2×C4—48no—
1109C2×C4—48no—
1110C2×C4—84no—
1111C2×C4—84no—
1112C2×C4—84no—
1113C2×C4—816no—
1114C2×C4—164no—
1115C2×C4#538116yes—
1116C2×C4C22×#4118yes—
1117C2×C4C22×#4112yes—
1118C2×C4C22×#4112yes—
1119C2×C4C2×H(5,𝔽2)12yes—
1120C2×C4C2×H(5,𝔽2)12yes—
1121C2×C4C2×H(5,𝔽2)12yes—
1122C2×C4C2×H(5,𝔽2)12yes—
1123C22—24no—
1124C22—22no—
1125C22—24no—
1126C22—22no—
1127C22—44no—
1128C22—44no—
1129C22—44no—
1130C22—48no—
1131C22—44no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—44no—
1136C22—44no—
1137C22—44no—
1138C22—48no—
1139C22—42no—
1140C22—44no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—44no—
1147C22—816no—
1148C22C2×#53814yes—
1149C22C23×#4111yescharacteristic
1150C22C22×H(5,𝔽2)11yescharacteristic
1151C22C22×H(5,𝔽2)11yescharacteristic
1152C22H(7,𝔽2)12yes—
1153C222−1+612yes—
1154C4—28no—
1155C4—44no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—44no—
1160C4—44no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—44no—
1165C4—44no—
1166C4—44no—
1167C4—42no—
1168C4—42no—
1169C4—42no—
1170C4—42no—
1171C4—42no—
1172C4C2×#53814yes—
1173C4C2×#53814yes—
1174C2—24no—
1175C2—82no—
1176C2—82no—
1177C2—82no—
1178C2—84no—
1179C2C22×#53811yescharacteristic
1180C2#6285112yes—
1181C2#6287611yescharacteristic
1182C2#6287812yes—
1183C2#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. #42895C2semidirect
2. #42893C2semidirect
3. #42872C2semidirect
4. #42869C2semidirect
5. #42842C2semidirect
6. #42838C2semidirect
7. #42834C2semidirect
8. #42829C2semidirect
9. #37496C2semidirect
10. #36791C2semidirect
11. #35677C2semidirect
12. #35676C2semidirect
13. #35662C2semidirect
14. #35660C2semidirect
15. #35557C2semidirect
16. #35556C2semidirect
17. #35533C2semidirect
18. #35530C2semidirect
19. #35168C2semidirect
20. #35152C2semidirect
21. #34639C2semidirect
22. #34637C2semidirect
23. #34266C2semidirect
24. #34257C2semidirect
25. C2×#2326C2semidirect
41. #2832C22semidirect
42. #2831C22semidirect
43. #2829C22semidirect
44. #2828C22semidirect
45. #2804C22semidirect
46. #2797C22semidirect
47. #2788C22semidirect
48. #2784C22semidirect
49. #2780C22semidirect
50. #2778C22semidirect
51. #2751C22semidirect
52. #2750C22semidirect
53. #2745C22semidirect
54. #2714C22semidirect
55. #2710C22semidirect
56. #2708C22semidirect
57. #2708C22semidirect
58. #2695C22semidirect
59. #2686C22semidirect
60. #2682C22semidirect
61. #2662C22semidirect
62. #2661C22semidirect
63. #2653C22semidirect
64. #2653C22semidirect
65. #2650C22semidirect
66. #2649C22semidirect
67. #2648C22semidirect
68. #2648C22semidirect
69. #2645C22semidirect
70. #2645C22semidirect
71. #2644C22semidirect
72. #2644C22semidirect
75. #2642C22semidirect
76. #2641C22semidirect
77. #2640C22semidirect
78. #2640C22semidirect
83. #2597C22semidirect
84. #2595C22semidirect
86. #2582C22semidirect
87. #2581C22semidirect
88. #2559C22semidirect
89. #2557C22semidirect
97. #2512C22semidirect
98. #2511C22semidirect
99. #2502C22semidirect
100. #2501C22semidirect
101. #2500C22semidirect
102. #2499C22semidirect
103. #2497C22semidirect
104. #2496C22semidirect
109. #2453C22semidirect
110. #2451C22semidirect
118. #2436C22semidirect
119. #2434C22semidirect
120. #2432C22semidirect
124. #2431C22semidirect
133. #2423C22semidirect
135. #2422C22semidirect
140. #2409C22semidirect
141. #2407C22semidirect
143. #2401C22semidirect
144. #2401C22semidirect
145. #2398C22semidirect
146. #2398C22semidirect
147. #2367C22semidirect
148. #2365C22semidirect
149. #2362C22semidirect
150. #2360C22semidirect
151. #2341C22semidirect
152. #2341C22semidirect
153. Q8×C22⋊C4C22semidirect
154. Q8×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#428952
#428932
#428722
#428692
#428422
#428382
#428342
#428292
#374962
#367912
#356772
#356762
#356622
#356602
#355572
#355562
#355332
#355302
#351682
#351522
#346392
#346372
#342662
#342572
C2×#23262