Finite Group Databasebeta

← #7782134

Subgroups — #7782134

Order 512.

4574 conjugacy classes of subgroups.

The subgroup lattice has 1063 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59946C212yesmaximal, complemented
2#59379C212yesmaximal, complemented
3#59256C212yesmaximal, complemented
4#59144C212yesmaximal, complemented
5#51708C214yesmaximal, complemented
6#49032C214yesmaximal, complemented
7#47544C214yesmaximal, complemented
8#47183C214yesmaximal, complemented
9#46190C212yesmaximal, complemented
10#45684C212yesmaximal, complemented
11#45390C214yesmaximal, complemented
12#42941C212yesmaximal, complemented
13#42695C212yesmaximal, complemented
14#40219C214yesmaximal, complemented
15#39975C214yesmaximal, complemented
16#39819C214yesmaximal, complemented
17#39734C212yesmaximal, complemented
18#37386C212yesmaximal
19#36577C212yesmaximal, complemented
20#36545C212yesmaximal, complemented
21#36314C212yesmaximal, complemented
22#35316C211yesmaximal, characteristic
23#34952C211yesmaximal, characteristic
24#34412C212yesmaximal
25C4×#536C211yesmaximal, characteristic
26C2×#557C2212yes—
27C2×#536C2211yescharacteristic
28C2×#536C2212yes—
29C22×C4⋊Q8C2211yescharacteristic
30C2×C4×#41C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33#2864C2214yes—
34#2857C2214yes—
35#2857C2212yes—
36#2857C2212yes—
37#2851C2214yes—
38#2834C2214yes—
39#2833C2214yes—
40#2802C2218yes—
41#2791C2218yes—
42#2789C2214yes—
43#2787C2218yes—
44#2776C2218yes—
45#2771C2214yes—
46#2770C2218yes—
47#2770C2218yes—
48#2769C2214yes—
49#2766C2218yes—
50#2765C2218yes—
51#2764C2214yes—
52#2762C2218yes—
53#2755C2218yes—
54#2747C2218yes—
55#2744C2218yes—
56#2738C2218yes—
57#2734C2218yes—
58#2724C2218yes—
59#2717C2214yes—
60#2717C2214yes—
61#2717C2214yes—
62#2717C2214yes—
63#2713C2218yes—
64#2666C2218yes—
65#2652C2218yes—
66#2621C2214yes—
67#2621C2212yes—
68#2621C2212yes—
69#2612C2218yes—
70#2606C2218yes—
71#2605C2218yes—
72#2590C2218yes—
73#2586C2214yes—
74#2584C2214yes—
75#2582C2212yes—
76#2582C2214yes—
77#2582C2212yes—
78#2581C2214yes—
79#2581C2212yes—
80#2580C2212yes—
81#2579C2212yes—
82#2579C2212yes—
83#2577C2218yes—
84#2573C2218yes—
85#2571C2212yes—
86#2570C2214yes—
87#2570C2214yes—
88#2568C2212yes—
89#2568C2214yes—
90#2550C2214yes—
91#2547C2212yes—
92#2547C2212yes—
93#2546C2212yes—
94#2546C2214yes—
95#2546C2212yes—
96#2546C2212yes—
97#2538C2212yes—
98#2533C2218yes—
99#2530C2218yes—
100#2530C2218yes—
101#2528C2218yes—
102#2527C2218yes—
103#2523C2214yes—
104#2514C2214yes—
105#2514C2214yes—
106#2511C2214yes—
107#2508C2214yes—
108#2507C2214yes—
109#2499C2214yes—
110#2499C2214yes—
111#2495C2214yes—
112#2495C2214yes—
113#2494C2214yes—
114#2494C2214yes—
115#2487C2211yescharacteristic
116#2487C2211yescharacteristic
117#2486C2212yes—
118#2486C2212yes—
119#2486C2212yes—
120#2486C2212yes—
121#2473C2218yes—
122#2473C2218yes—
123#2462C2218yes—
124#2453C2214yes—
125#2453C2218yes—
126#2451C2214yes—
127#2446C2214yes—
128#2446C2214yes—
129#2446C2214yes—
130#2442C2214yes—
131#2442C2214yes—
132#2442C2218yes—
133#2434C2214yes—
134#2434C2214yes—
135#2421C2214yes—
136#2421C2214yes—
137#2409C2211yescharacteristic
138#2409C2211yescharacteristic
139#2396C2212yes—
140#2396C2212yes—
141#2379C2214yes—
142#2376C2214yes—
143#2374C2214yes—
144#2372C2214yes—
145#2365C2212yes—
146#2365C2214yes—
147#2362C2214yes—
148#2360C2214yes—
149#2360C2214yes—
150#2356C2214yes—
151#2356C2214yes—
152#2355C2212yes—
153#2351C2214yes—
154Q8×C4⋊C4C2212yes—
155#2346C2214yes—
156Q8×C22⋊C4C2214yes—
157Q8×C22⋊C4C2214yes—
158#2335C2218yes—
159#2331C2218yes—
160#2327C2212yes—
161#2326C2212yes—
162#2323C2212yes—
163#2323C2212yes—
164#2323C2214yes—
165#2322C2212yes—
166#2322C2212yes—
167#2317C2211yescharacteristic
168#2311C2211yescharacteristic
169#2310C2211yescharacteristic
170#2310C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×#124C2212yes—
173C4×C22⋊Q8C2212yes—
174C4×C22⋊Q8C2212yes—
175C4×C22⋊Q8C2214yes—
176C4×C22⋊Q8C2212yes—
177C4×C22⋊Q8C2214yes—
178C4×C22⋊Q8C2212yes—
179C4×#123C2212yes—
180C4×#123C2212yes—
181#2297C2212yes—
182#2296C2212yes—
183#2295C2214yes—
184#2285C2211yescharacteristic
185#2285C2211yescharacteristic
186C4×#117C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×Q8C2312yes—
190C23×Q8C2311yescharacteristic
191#557—48no—
192#536—28no—
193#536—216no—
194C2×C4⋊Q8—44no—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2314yes—
198C2×C4⋊Q8C2314yes—
199C2×C4⋊Q8C2314yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2312yes—
203C2×#125C2314yes—
204C2×#125C2318yes—
205C2×#124C2312yes—
206C2×#124C2314yes—
207C2×#123C2312yes—
208C2×#123C2312yes—
209C2×#123C2314yes—
210C2×#123C2314yes—
211C2×C22⋊Q8C2312yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2312yes—
217C4×#41—44no—
218C2×C4×Q8—44no—
219C2×C4×Q8—44no—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2312yes—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117C2312yes—
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2312yes—
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2312yes—
253C22×C42C2311yescharacteristic
254C22×C42C2311yescharacteristic
255C22×C42C2311yescharacteristic
256C22×C42C2312yes—
257C22×C42C2312yes—
258#401C2318yes—
259#401C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2312yes—
268#400C2318yes—
269#400C2318yes—
270#400C2312yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#399C2312yes—
275#399C2312yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2314yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2314yes—
284#398C2314yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2314yes—
290#398C2318yes—
291#398C2314yes—
292#398C2318yes—
293#398C2318yes—
294#397C2318yes—
295#397C2314yes—
296#397C2318yes—
297#397C2314yes—
298#397C2318yes—
299#397C2314yes—
300#397C2318yes—
301#397C2314yes—
302#397C2318yes—
303#397C2318yes—
304#396C2314yes—
305#396C2314yes—
306#395C2318yes—
307#395C2312yes—
308#395C2318yes—
309#395C2312yes—
310#395C2318yes—
311#395C2318yes—
312#393C2312yes—
313#393C2312yes—
314#391C2312yes—
315#391C2312yes—
316#391C2312yes—
317#391C2314yes—
318#391C2312yes—
319#391C2312yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2318yes—
327#391C2314yes—
328#391C2314yes—
329#391C2312yes—
330#391C2314yes—
331#391C2314yes—
332#391C2318yes—
333#391C2312yes—
334#391C2318yes—
335#391C2318yes—
336#391C2314yes—
337#391C2314yes—
338#390C2312yes—
339#390C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2312yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2312yes—
349#389C2318yes—
350#389C2318yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2312yes—
356#389C2314yes—
357#389C2312yes—
358#389C2318yes—
359#389C2318yes—
360#389C2318yes—
361#389C2318yes—
362#389C2318yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2318yes—
367#389C2318yes—
368#389C2314yes—
369#388C2314yes—
370#388C2318yes—
371#388C2314yes—
372#388C2318yes—
373#388C2314yes—
374#388C2314yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#387C2314yes—
393#387C2314yes—
394#387C2314yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#386C2312yes—
412#386C2312yes—
413#386C2312yes—
414#386C2312yes—
415#386C2312yes—
416#386C2312yes—
417#385C2312yes—
418#385C2312yes—
419#385C2318yes—
420#385C2312yes—
421#385C2314yes—
422#385C2314yes—
423#385C2318yes—
424#385C2314yes—
425#385C2314yes—
426#385C2312yes—
427#385C2312yes—
428#385C2312yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#384C2312yes—
434#384C2312yes—
435#384C2314yes—
436#384C2312yes—
437#383C2318yes—
438#383C2318yes—
439#383C2318yes—
440#382C2314yes—
441#382C2318yes—
442#382C2312yes—
443#382C2314yes—
444#382C2314yes—
445#382C2314yes—
446#382C2312yes—
447#382C2312yes—
448#382C2318yes—
449#381C2314yes—
450#381C2312yes—
451#381C2312yes—
452#381C2314yes—
453#380C2312yes—
454#380C2312yes—
455#380C2318yes—
456#380C2312yes—
457#380C2318yes—
458#380C2312yes—
459#380C2314yes—
460#380C2314yes—
461#380C2318yes—
462#380C2314yes—
463#380C2314yes—
464#380C2311yescharacteristic
465#380C2311yescharacteristic
466#380C2312yes—
467#380C2312yes—
468#380C2312yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2318yes—
481C4×C4⋊C4C2318yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C22⋊C4C2318yes—
487C4×C22⋊C4C2318yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2312yes—
495#376C2312yes—
496#376C2318yes—
497#376C2318yes—
498C43C2312yes—
499C2×#41—42no—
500C2×#41—42no—
501C2×#41#4118yes—
502C22×Q8—28no—
503C22×Q8—24no—
504C22×Q8—28no—
505C22×Q8—42no—
506C22×Q8—42no—
507C22×Q8—42no—
508C22×Q8—44no—
509C22×Q8—44no—
510C22×Q8C2412yes—
511C22×Q8C2414yes—
512C22×Q8C2412yes—
513C22×Q8C2412yes—
514C22×Q8C2412yes—
515C22×Q8C2414yes—
516C22×Q8C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C23×C4C2412yes—
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2414yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C4⋊Q8—28no—
535C4⋊Q8—216no—
536C4⋊Q8—28no—
537C4⋊Q8—44no—
538C4⋊Q8—44no—
539C4⋊Q8—44no—
540C4⋊Q8—48no—
541C4⋊Q8—48no—
542#125—48no—
543#125—416no—
544#124—28no—
545#124—216no—
546#123—28no—
547#123—28no—
548#123—216no—
549#123—216no—
550C22⋊Q8—28no—
551C22⋊Q8—28no—
552C22⋊Q8—28no—
553C22⋊Q8—216no—
554C22⋊Q8—28no—
555C22⋊Q8—216no—
556C4×Q8—216no—
557C4×Q8—28no—
558C4×Q8—28no—
559C4×Q8—44no—
560C4×Q8—44no—
561C4×Q8—42no—
562C4×Q8—42no—
563C4×Q8—44no—
564C4×Q8—44no—
565C4×Q8—44no—
566C4×Q8—44no—
567C4×Q8—48no—
568C4×Q8—48no—
569C4×Q8—48no—
570C4×D4—42no—
571C4×D4—42no—
572C4×D4—42no—
573C4×D4—42no—
574C4×D4—42no—
575C4×D4—42no—
576#117—28no—
577#117—24no—
578#117—44no—
579#117—42no—
580#117—42no—
581#117—42no—
582#117—42no—
583C2×C4⋊C4—42no—
584C2×C4⋊C4—42no—
585C2×C4⋊C4—44no—
586C2×C4⋊C4—44no—
587C2×C4⋊C4—44no—
588C2×C4⋊C4—44no—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2418yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2411yescharacteristic
645C2×C22⋊C4C2411yescharacteristic
646C2×C22⋊C4C2411yescharacteristic
647C2×C22⋊C4C2411yescharacteristic
648C2×C22⋊C4C2411yescharacteristic
649C2×C22⋊C4C2411yescharacteristic
650C2×C22⋊C4C2412yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2412yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C42—24no—
658C2×C42—24no—
659C2×C42—24no—
660C2×C42—44no—
661C2×C42—44no—
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2414yes—
666C2×C42C2412yes—
667C2×C42C2414yes—
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2414yes—
675C2×C42C2414yes—
676C2×C42C2414yes—
677C2×C42C2418yes—
678C2×C42C2412yes—
679C2×C42C2418yes—
680C2×C42C2414yes—
681C2×C42C2414yes—
682C2×C42C2418yes—
683C2×C42C2414yes—
684C2×C42C2418yes—
685C2×C42C2411yescharacteristic
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2418yes—
690#95C2414yes—
691#95C2414yes—
692#95C2418yes—
693#95C2418yes—
694#95C2418yes—
695#95C2418yes—
696#95C2418yes—
697#95C2414yes—
698#95C2418yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2418yes—
705#95C2414yes—
706#95C2414yes—
707#95C2418yes—
708#95C2418yes—
709#95C2412yes—
710#95C2414yes—
711#95C2414yes—
712#95C2412yes—
713#95C2414yes—
714#95C2414yes—
715#95C2418yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2418yes—
720#95C2418yes—
721#95C2414yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731C24C2511yescharacteristic
732C24C2511yescharacteristic
733C24C2511yescharacteristic
734#41—416no—
735C2×Q8—24no—
736C2×Q8—28no—
737C2×Q8—24no—
738C2×Q8—28no—
739C2×Q8—24no—
740C2×Q8—24no—
741C2×Q8—28no—
742C2×Q8—24no—
743C2×Q8—28no—
744C2×Q8—28no—
745C2×Q8—24no—
746C2×Q8—42no—
747C2×Q8—42no—
748C2×Q8—41no—
749C2×Q8—42no—
750C2×Q8—41no—
751C2×Q8—44no—
752C2×Q8—44no—
753C2×Q8—416no—
754C2×Q8—416no—
755C2×Q8—816no—
756C2×Q8C2×#4114yes—
757C2×Q82−1+418yes—
758C2×D4—41no—
759C2×D4—41no—
760C2×D4—41no—
761C2×D4—41no—
762C2×D4—41no—
763C2×D4—41no—
764C2×D4C2×#4114yes—
765C2×D4C2×#4114yes—
766C2×D4C2×#4114yes—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—24no—
774C22×C4—28no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—28no—
782C22×C4—24no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—44no—
792C22×C4—42no—
793C22×C4—42no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4C2×#4114yes—
798C22×C4C2×#4114yes—
799C22×C4C2×#4114yes—
800C22×C4C2511yescharacteristic
801C22×C4C2514yes—
802C22×C4C2511yescharacteristic
803C22×C4C2518yes—
804C22×C4C2514yes—
805C22×C4C2514yes—
806C22×C4C2514yes—
807C22×C4C2511yescharacteristic
808C22×C4C2511yescharacteristic
809C22×C4C2514yes—
810C22×C4C2511yescharacteristic
811C22×C4C2511yescharacteristic
812C22×C4C2514yes—
813C22×C4C2514yes—
814C22×C4C2518yes—
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C22×C4C2511yescharacteristic
818C22×C4C2511yescharacteristic
819C22×C4C2514yes—
820C22×C4C2511yescharacteristic
821C22×C4C2511yescharacteristic
822C4⋊C4—28no—
823C4⋊C4—24no—
824C4⋊C4—28no—
825C4⋊C4—216no—
826C4⋊C4—28no—
827C4⋊C4—216no—
828C4⋊C4—24no—
829C4⋊C4—28no—
830C4⋊C4—28no—
831C4⋊C4—24no—
832C4⋊C4—28no—
833C4⋊C4—28no—
834C4⋊C4—216no—
835C4⋊C4—28no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—24no—
841C4⋊C4—42no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—42no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—48no—
852C4⋊C4—48no—
853C4⋊C4—48no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—41no—
858C4⋊C4—41no—
859C4⋊C4—41no—
860C4⋊C4—41no—
861C4⋊C4—41no—
862C4⋊C4—41no—
863C4⋊C4—48no—
864C4⋊C4—48no—
865C4⋊C4—48no—
866C4⋊C4—48no—
867C4⋊C4—48no—
868C4⋊C4—48no—
869C22⋊C4—24no—
870C22⋊C4—28no—
871C22⋊C4—28no—
872C22⋊C4—216no—
873C22⋊C4—216no—
874C22⋊C4—28no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—42no—
882C22⋊C4—42no—
883C22⋊C4—42no—
884C22⋊C4—41no—
885C22⋊C4—41no—
886C22⋊C4—41no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—41no—
890C42—28no—
891C42—24no—
892C42—22no—
893C42—22no—
894C42—22no—
895C42—22no—
896C42—22no—
897C42—22no—
898C42—22no—
899C42—22no—
900C42—22no—
901C42—28no—
902C42—28no—
903C42—216no—
904C42—28no—
905C42—28no—
906C42—44no—
907C42—44no—
908C42—48no—
909C42—44no—
910C42—42no—
911C42—48no—
912C42—48no—
913C42H(5,𝔽2)14yes—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—21no—
921C23—21no—
922C23—21no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23C22×#4112yes—
927C23C22×#4112yes—
928C23C22×#4112yes—
929C23C2611yescharacteristic
930Q8—216no—
931Q8—44no—
932Q8—48no—
933Q8—48no—
934Q8—48no—
935Q8—416no—
936Q8—88no—
937D4—44no—
938D4—44no—
939D4—44no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—22no—
949C2×C4—28no—
950C2×C4—28no—
951C2×C4—28no—
952C2×C4—28no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—28no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—28no—
966C2×C4—24no—
967C2×C4—28no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—28no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—28no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—48no—
992C2×C4—44no—
993C2×C4—48no—
994C2×C4—44no—
995C2×C4—44no—
996C2×C4—44no—
997C2×C4—82no—
998C2×C4—82no—
999C2×C4—88no—
1000C2×C4—84no—
1001C2×C4—84no—
1002C2×C4C22×#4112yes—
1003C2×C4C22×#4112yes—
1004C2×C4C22×#4112yes—
1005C2×C4C22×#4112yes—
1006C2×C4C2×H(5,𝔽2)12yes—
1007C2×C4C2×H(5,𝔽2)12yes—
1008C2×C4C2×H(5,𝔽2)12yes—
1009C2×C4C2×2−1+418yes—
1010C2×C4C2×2−1+414yes—
1011C2×C4#58512yes—
1012C22—24no—
1013C22—24no—
1014C22—24no—
1015C22—22no—
1016C22—22no—
1017C22—22no—
1018C22—41no—
1019C22—41no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22C23×#4111yescharacteristic
1028C22C22×H(5,𝔽2)11yescharacteristic
1029C22C22×2−1+412yes—
1030C22C2×#58511yescharacteristic
1031C222−1+612yes—
1032C4—28no—
1033C4—22no—
1034C4—22no—
1035C4—22no—
1036C4—22no—
1037C4—41no—
1038C4—41no—
1039C4—41no—
1040C4—48no—
1041C4—44no—
1042C4—44no—
1043C4—48no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—44no—
1048C4—44no—
1049C4—44no—
1050C4—44no—
1051C4—44no—
1052C4#350514yes—
1053C4#353814yes—
1054C2—42no—
1055C2—42no—
1056C2—42no—
1057C2C2×#353811yescharacteristic
1058C2C2×#350511yescharacteristic
1059C2#6288611yescharacteristic
1060C2#6295312yes—
1061C2#6300112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59946C2semidirect
2. #59379C2semidirect
3. #59256C2semidirect
4. #59144C2semidirect
5. #51708C2semidirect
6. #49032C2semidirect
7. #47544C2semidirect
8. #47183C2semidirect
9. #46190C2semidirect
10. #45684C2semidirect
11. #45390C2semidirect
12. #42941C2semidirect
13. #42695C2semidirect
14. #40219C2semidirect
15. #39975C2semidirect
16. #39819C2semidirect
17. #39734C2semidirect
19. #36577C2semidirect
20. #36545C2semidirect
21. #36314C2semidirect

Maximal subgroups

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

subgroupindex
#599462
#593792
#592562
#591442
#517082
#490322
#475442
#471832
#461902
#456842
#453902
#429412
#426952
#402192
#399752
#398192
#397342
#373862
#365772
#365452
#363142
#353162
#349522
#344122
C4×#5362