Finite Group Databasebeta

← #8197118

Subgroups — #8197118

Order 512.

4326 conjugacy classes of subgroups.

The subgroup lattice has 1043 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59925C212yesmaximal, complemented
2#59869C212yesmaximal, complemented
3#59249C212yesmaximal, complemented
4#59144C212yesmaximal, complemented
5#58664C214yesmaximal, complemented
6#56834C214yesmaximal, complemented
7#53008C212yesmaximal, complemented
8#52961C212yesmaximal, complemented
9#51988C214yesmaximal
10#47419C214yesmaximal, complemented
11#46346C212yesmaximal, complemented
12#46331C212yesmaximal, complemented
13#45351C212yesmaximal, complemented
14#45226C212yesmaximal, complemented
15#42708C214yesmaximal, complemented
16#42707C214yesmaximal, complemented
17#40190C214yesmaximal, complemented
18#39724C212yesmaximal, complemented
19#39599C212yesmaximal, complemented
20#39216C214yesmaximal, complemented
21#36481C212yesmaximal, complemented
22#36450C212yesmaximal, complemented
23#35279C211yesmaximal, characteristic
24#34979C211yesmaximal, characteristic
25#34979C211yesmaximal, characteristic
26C2×#557C2212yes—
27C2×#533C2211yescharacteristic
28C2×#533C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C2×C4×#41C2211yescharacteristic
31#2863C2214yes—
32#2863C2214yes—
33#2857C2212yes—
34#2857C2212yes—
35#2843C2214yes—
36#2838C2218yes—
37#2836C2218yes—
38#2834C2214yes—
39#2833C2214yes—
40#2809C2214yes—
41#2809C2214yes—
42#2807C2214yes—
43#2800C2218yes—
44#2799C2214yes—
45#2794C2214yes—
46#2792C2214yes—
47#2791C2218yes—
48#2775C2218yes—
49#2774C2218yes—
50#2773C2218yes—
51#2773C2218yes—
52#2770C2218yes—
53#2767C2218yes—
54#2766C2218yes—
55#2758C2218yes—
56#2757C2218yes—
57#2754C2218yes—
58#2734C2214yes—
59#2726C2218yes—
60#2722C2214yes—
61#2719C2218yes—
62#2715C2218yes—
63#2713C2218yes—
64#2704C2218yes—
65#2690C2218yes—
66#2654C2218yes—
67#2651C2218yes—
68#2650C2218yes—
69#2629C2214yes—
70#2628C2212yes—
71#2628C2212yes—
72#2621C2214yes—
73#2611C2212yes—
74#2611C2212yes—
75#2611C2212yes—
76#2611C2212yes—
77#2606C2218yes—
78#2597C2218yes—
79#2586C2214yes—
80#2586C2218yes—
81#2584C2214yes—
82#2582C2212yes—
83#2582C2214yes—
84#2581C2214yes—
85#2577C2218yes—
86#2571C2214yes—
87#2568C2212yes—
88#2568C2212yes—
89#2568C2214yes—
90#2568C2211yescharacteristic
91#2568C2211yescharacteristic
92#2567C2212yes—
93#2563C2212yes—
94#2552C2212yes—
95#2550C2214yes—
96#2550C2214yes—
97#2547C2211yescharacteristic
98#2547C2211yescharacteristic
99#2546C2212yes—
100#2546C2214yes—
101#2546C2211yescharacteristic
102#2546C2214yes—
103#2546C2211yescharacteristic
104#2542C2211yescharacteristic
105#2542C2211yescharacteristic
106#2542C2212yes—
107#2528C2218yes—
108#2522C2218yes—
109#2521C2218yes—
110#2517C2214yes—
111#2514C2214yes—
112#2511C2214yes—
113#2509C2214yes—
114#2508C2218yes—
115#2508C2218yes—
116#2507C2218yes—
117#2507C2214yes—
118#2499C2212yes—
119#2499C2212yes—
120#2499C2214yes—
121#2496C2214yes—
122#2496C2214yes—
123#2494C2214yes—
124#2489C2214yes—
125#2489C2214yes—
126#2489C2214yes—
127#2487C2212yes—
128#2487C2212yes—
129#2478C2218yes—
130#2473C2218yes—
131#2451C2214yes—
132#2451C2214yes—
133#2446C2214yes—
134#2446C2214yes—
135#2442C2214yes—
136#2441C2214yes—
137#2434C2214yes—
138#2432C2212yes—
139#2432C2212yes—
140#2429C2214yes—
141#2429C2214yes—
142#2429C2214yes—
143#2423C2214yes—
144#2421C2214yes—
145#2421C2214yes—
146#2415C2212yes—
147#2415C2212yes—
148#2415C2212yes—
149#2415C2212yes—
150#2409C2212yes—
151#2409C2212yes—
152#2395C2212yes—
153#2395C2212yes—
154#2395C2212yes—
155#2395C2212yes—
156#2381C2214yes—
157#2370C2214yes—
158#2370C2214yes—
159#2369C2214yes—
160#2365C2212yes—
161#2362C2214yes—
162#2360C2214yes—
163#2355C2214yes—
164#2355C2212yes—
165#2355C2214yes—
166Q8×C4⋊C4C2212yes—
167#2347C2214yes—
168Q8×C22⋊C4C2214yes—
169#2334C2218yes—
170#2323C2214yes—
171#2323C2214yes—
172#2317C2212yes—
173#2311C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2214yes—
177C4×#125C2214yes—
178C4×#124C2212yes—
179C4×#124C2212yes—
180C4×C22⋊Q8C2212yes—
181C4×C22⋊Q8C2212yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2212yes—
184#2285C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C4×#117C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2312yes—
189#557—48no—
190#533—44no—
191#533—44no—
192C2×C4⋊Q8—44no—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2314yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2314yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2311yescharacteristic
201C2×C4⋊Q8C2311yescharacteristic
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×#126C2318yes—
206C2×#125C2314yes—
207C2×#125C2314yes—
208C2×#125C2312yes—
209C2×#125C2312yes—
210C2×#125C2318yes—
211C2×#124C2312yes—
212C2×#124C2312yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2312yes—
223C4×#41—44no—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2314yes—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117C2312yes—
241C2×#117C2312yes—
242C2×#117C2311yescharacteristic
243C2×#117C2312yes—
244C2×#117C2312yes—
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2312yes—
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2312yes—
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252C22×C42C2311yescharacteristic
253#401C2318yes—
254#400C2312yes—
255#400C2314yes—
256#400C2318yes—
257#400C2318yes—
258#400C2312yes—
259#400C2312yes—
260#400C2312yes—
261#400C2314yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#399C2312yes—
271#399C2314yes—
272#399C2312yes—
273#399C2312yes—
274#399C2312yes—
275#399C2314yes—
276#399C2318yes—
277#398C2318yes—
278#398C2312yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2312yes—
290#398C2318yes—
291#398C2318yes—
292#398C2312yes—
293#398C2312yes—
294#398C2318yes—
295#398C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2312yes—
299#397C2318yes—
300#397C2312yes—
301#397C2314yes—
302#397C2314yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2312yes—
307#397C2312yes—
308#397C2314yes—
309#397C2314yes—
310#396C2318yes—
311#396C2318yes—
312#396C2318yes—
313#395C2314yes—
314#395C2314yes—
315#395C2318yes—
316#395C2318yes—
317#395C2318yes—
318#395C2318yes—
319#394C2314yes—
320#394C2314yes—
321#394C2314yes—
322#394C2314yes—
323#393C2314yes—
324#393C2314yes—
325#391C2312yes—
326#391C2314yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2312yes—
335#391C2314yes—
336#391C2318yes—
337#391C2314yes—
338#391C2314yes—
339#391C2312yes—
340#391C2312yes—
341#391C2314yes—
342#391C2318yes—
343#391C2312yes—
344#391C2318yes—
345#391C2314yes—
346#391C2318yes—
347#391C2314yes—
348#391C2314yes—
349#391C2312yes—
350#390C2314yes—
351#390C2312yes—
352#390C2312yes—
353#389C2312yes—
354#389C2314yes—
355#389C2314yes—
356#389C2318yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2318yes—
361#389C2314yes—
362#389C2318yes—
363#389C2318yes—
364#389C2314yes—
365#389C2314yes—
366#389C2318yes—
367#389C2314yes—
368#389C2314yes—
369#389C2312yes—
370#389C2314yes—
371#389C2318yes—
372#389C2314yes—
373#389C2318yes—
374#389C2318yes—
375#389C2314yes—
376#389C2318yes—
377#389C2314yes—
378#389C2318yes—
379#389C2314yes—
380#389C2314yes—
381#389C2318yes—
382#389C2312yes—
383#389C2318yes—
384#389C2312yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2314yes—
393#388C2314yes—
394#388C2318yes—
395#388C2318yes—
396#388C2314yes—
397#388C2314yes—
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#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2314yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2314yes—
420#387C2314yes—
421#387C2314yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#386C2314yes—
426#386C2314yes—
427#385C2314yes—
428#385C2314yes—
429#385C2314yes—
430#385C2318yes—
431#385C2318yes—
432#385C2314yes—
433#385C2314yes—
434#385C2314yes—
435#384C2312yes—
436#384C2312yes—
437#384C2314yes—
438#384C2314yes—
439#384C2312yes—
440#384C2314yes—
441#383C2318yes—
442#383C2318yes—
443#382C2314yes—
444#382C2314yes—
445#382C2318yes—
446#382C2312yes—
447#382C2312yes—
448#382C2318yes—
449#382C2318yes—
450#382C2314yes—
451#382C2312yes—
452#380C2314yes—
453#380C2314yes—
454#380C2314yes—
455#380C2314yes—
456#380C2312yes—
457#380C2312yes—
458#380C2318yes—
459#380C2312yes—
460#380C2312yes—
461#380C2312yes—
462#380C2312yes—
463C4×C4⋊C4C2318yes—
464C4×C4⋊C4C2318yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2318yes—
468C4×C4⋊C4C2318yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2318yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2318yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493#376C2312yes—
494#376C2312yes—
495C43C2312yes—
496C43C2312yes—
497C2×#41—24no—
498C2×#41—42no—
499C2×#41—42no—
500C22×Q8—44no—
501C22×Q8—48no—
502C22×Q8C2412yes—
503C22×Q8C2412yes—
504C22×Q8C2414yes—
505C22×Q8C2412yes—
506C22×Q8C2412yes—
507C22×Q8C2414yes—
508C22×Q8C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C23×C4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2414yes—
522C4⋊Q8—28no—
523C4⋊Q8—28no—
524C4⋊Q8—28no—
525C4⋊Q8—44no—
526C4⋊Q8—44no—
527C4⋊Q8—42no—
528C4⋊Q8—42no—
529C4⋊Q8—44no—
530C4⋊Q8—48no—
531C4⋊Q8—42no—
532C4⋊Q8—42no—
533C4⋊Q8—48no—
534#126—416no—
535#125—216no—
536#125—44no—
537#125—44no—
538#125—48no—
539#125—416no—
540#124—44no—
541#124—44no—
542C22⋊Q8—28no—
543C22⋊Q8—28no—
544C22⋊Q8—44no—
545C22⋊Q8—44no—
546C22⋊Q8—44no—
547C22⋊Q8—44no—
548C22⋊Q8—48no—
549C22⋊Q8—48no—
550C22⋊Q8—44no—
551C22⋊Q8—44no—
552C4×Q8—28no—
553C4×Q8—28no—
554C4×Q8—42no—
555C4×Q8—42no—
556C4×Q8—44no—
557C4×Q8—44no—
558C4×Q8—48no—
559C4×Q8—48no—
560C4×Q8—48no—
561C4×Q8—48no—
562C4×D4—42no—
563C4×D4—42no—
564C4×D4—42no—
565C4×D4—42no—
566C4×D4—42no—
567C4×D4—42no—
568#117—28no—
569#117—42no—
570#117—42no—
571#117—42no—
572#117—44no—
573#117—44no—
574#117—44no—
575#117—44no—
576C2×C4⋊C4—44no—
577C2×C4⋊C4—44no—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2412yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2411yescharacteristic
636C2×C22⋊C4C2411yescharacteristic
637C2×C22⋊C4C2411yescharacteristic
638C2×C22⋊C4C2411yescharacteristic
639C2×C22⋊C4C2411yescharacteristic
640C2×C22⋊C4C2411yescharacteristic
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C42—24no—
651C2×C42—24no—
652C2×C42—24no—
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2414yes—
657C2×C42C2414yes—
658C2×C42C2414yes—
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2414yes—
666C2×C42C2414yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2414yes—
670C2×C42C2414yes—
671C2×C42C2418yes—
672C2×C42C2418yes—
673C2×C42C2418yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2418yes—
677C2×C42C2411yescharacteristic
678#95C2412yes—
679#95C2414yes—
680#95C2414yes—
681#95C2412yes—
682#95C2412yes—
683#95C2412yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2418yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2418yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2418yes—
698#95C2414yes—
699#95C2418yes—
700#95C2418yes—
701#95C2418yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2414yes—
710#95C2418yes—
711#95C2418yes—
712#95C2414yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722C24C2511yescharacteristic
723C24C2511yescharacteristic
724C24C2511yescharacteristic
725#41—416no—
726C2×Q8—24no—
727C2×Q8—24no—
728C2×Q8—28no—
729C2×Q8—24no—
730C2×Q8—24no—
731C2×Q8—24no—
732C2×Q8—24no—
733C2×Q8—24no—
734C2×Q8—28no—
735C2×Q8—24no—
736C2×Q8—28no—
737C2×Q8—41no—
738C2×Q8—41no—
739C2×Q8—42no—
740C2×Q8—42no—
741C2×Q8—42no—
742C2×Q8—42no—
743C2×Q8—44no—
744C2×Q8—48no—
745C2×Q8—816no—
746C2×Q82−1+414yes—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—22no—
752C2×D4—41no—
753C2×D4—41no—
754C2×D4—41no—
755C2×D4—41no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—41no—
776C22×C4—41no—
777C22×C4—44no—
778C22×C4—48no—
779C22×C4C2514yes—
780C22×C4C2511yescharacteristic
781C22×C4C2514yes—
782C22×C4C2511yescharacteristic
783C22×C4C2511yescharacteristic
784C22×C4C2511yescharacteristic
785C22×C4C2514yes—
786C22×C4C2514yes—
787C22×C4C2518yes—
788C22×C4C2514yes—
789C22×C4C2514yes—
790C22×C4C2518yes—
791C22×C4C2511yescharacteristic
792C22×C4C2514yes—
793C22×C4C2511yescharacteristic
794C22×C4C2511yescharacteristic
795C22×C4C2511yescharacteristic
796C22×C4C2511yescharacteristic
797C22×C4C2514yes—
798C22×C4C2511yescharacteristic
799C22×C4C2511yescharacteristic
800C22×C4C2511yescharacteristic
801C4⋊C4—28no—
802C4⋊C4—28no—
803C4⋊C4—24no—
804C4⋊C4—28no—
805C4⋊C4—28no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—28no—
809C4⋊C4—28no—
810C4⋊C4—216no—
811C4⋊C4—216no—
812C4⋊C4—28no—
813C4⋊C4—28no—
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—28no—
820C4⋊C4—44no—
821C4⋊C4—44no—
822C4⋊C4—44no—
823C4⋊C4—41no—
824C4⋊C4—41no—
825C4⋊C4—41no—
826C4⋊C4—41no—
827C4⋊C4—41no—
828C4⋊C4—41no—
829C4⋊C4—42no—
830C4⋊C4—42no—
831C4⋊C4—42no—
832C4⋊C4—42no—
833C4⋊C4—48no—
834C4⋊C4—48no—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C4⋊C4—42no—
838C4⋊C4—42no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C4⋊C4—44no—
842C4⋊C4—48no—
843C4⋊C4—44no—
844C4⋊C4—48no—
845C4⋊C4—48no—
846C4⋊C4—48no—
847C4⋊C4—48no—
848C4⋊C4—48no—
849C4⋊C4—48no—
850C4⋊C4—48no—
851C4⋊C42−1+418yes—
852C22⋊C4—28no—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—28no—
856C22⋊C4—28no—
857C22⋊C4—28no—
858C22⋊C4—44no—
859C22⋊C4—41no—
860C22⋊C4—41no—
861C22⋊C4—41no—
862C22⋊C4—41no—
863C22⋊C4—41no—
864C22⋊C4—41no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C42—22no—
874C42—22no—
875C42—22no—
876C42—22no—
877C42—22no—
878C42—22no—
879C42—22no—
880C42—22no—
881C42—22no—
882C42—28no—
883C42—28no—
884C42—28no—
885C42—28no—
886C42—24no—
887C42—24no—
888C42—28no—
889C42—44no—
890C42—44no—
891C42—48no—
892C42—48no—
893C42—48no—
894C42—42no—
895C42—42no—
896C42—48no—
897C42H(5,𝔽2)14yes—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—22no—
902C23—21no—
903C23—21no—
904C23—22no—
905C23—22no—
906C23—21no—
907C23—21no—
908C23—22no—
909C23—22no—
910C23—21no—
911C23—21no—
912C23#58512yes—
913C23C2611yescharacteristic
914Q8—44no—
915Q8—48no—
916Q8—48no—
917Q8—416no—
918Q8—84no—
919Q8—84no—
920Q8—88no—
921D4—44no—
922D4—44no—
923D4—44no—
924C2×C4—28no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—24no—
929C2×C4—21no—
930C2×C4—24no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—28no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—28no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—28no—
963C2×C4—24no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—28no—
968C2×C4—28no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—28no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—44no—
975C2×C4—44no—
976C2×C4—44no—
977C2×C4—44no—
978C2×C4—44no—
979C2×C4—44no—
980C2×C4—44no—
981C2×C4—44no—
982C2×C4—88no—
983C2×C4C2×H(5,𝔽2)12yes—
984C2×C4C2×H(5,𝔽2)12yes—
985C2×C4C2×H(5,𝔽2)12yes—
986C2×C4C2×2−1+412yes—
987C2×C4C2×2−1+412yes—
988C2×C4C2×2−1+418yes—
989C2×C4C2×2−1+412yes—
990C2×C4C2×2−1+414yes—
991C2×C4#58514yes—
992C22—24no—
993C22—22no—
994C22—41no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—42no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—41no—
1006C22—41no—
1007C22C22×H(5,𝔽2)11yescharacteristic
1008C22C22×2−1+412yes—
1009C22C22×2−1+411yescharacteristic
1010C22C2×#58512yes—
1011C22C2×#58511yescharacteristic
1012C4—28no—
1013C4—22no—
1014C4—22no—
1015C4—22no—
1016C4—22no—
1017C4—41no—
1018C4—41no—
1019C4—41no—
1020C4—48no—
1021C4—44no—
1022C4—41no—
1023C4—41no—
1024C4—41no—
1025C4—44no—
1026C4—44no—
1027C4—44no—
1028C4—44no—
1029C4—48no—
1030C4—44no—
1031C4—44no—
1032C4#355014yes—
1033C4#355114yes—
1034C2—42no—
1035C2—81no—
1036C2—81no—
1037C2C2×#355111yescharacteristic
1038C2C2×#355011yescharacteristic
1039C2#6281911yescharacteristic
1040C2#6303212yes—
1041C2#6303312yes—
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. #59925C2semidirect
2. #59869C2semidirect
3. #59249C2semidirect
4. #59144C2semidirect
5. #58664C2semidirect
6. #56834C2semidirect
7. #53008C2semidirect
8. #52961C2semidirect
10. #47419C2semidirect
11. #46346C2semidirect
12. #46331C2semidirect
13. #45351C2semidirect
14. #45226C2semidirect
15. #42708C2semidirect
16. #42707C2semidirect
17. #40190C2semidirect
18. #39724C2semidirect
19. #39599C2semidirect
20. #39216C2semidirect
21. #36481C2semidirect
22. #36450C2semidirect

Maximal subgroups

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

subgroupindex
#599252
#598692
#592492
#591442
#586642
#568342
#530082
#529612
#519882
#474192
#463462
#463312
#453512
#452262
#427082
#427072
#401902
#397242
#395992
#392162
#364812
#364502
#352792
#349792