Finite Group Databasebeta

← #8429415

Subgroups — #8429415

Order 512.

3953 conjugacy classes of subgroups.

The subgroup lattice has 1033 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59665C212yesmaximal, complemented
3#59426C212yesmaximal
4#59242C212yesmaximal, complemented
5#58643C218yesmaximal, complemented
6#53139C214yesmaximal, complemented
7#53093C214yesmaximal, complemented
8#52994C214yesmaximal
9#42689C214yesmaximal, complemented
10#42562C214yesmaximal, complemented
11#42461C214yesmaximal, complemented
12#39754C212yesmaximal, complemented
13#39515C212yesmaximal
14#39480C212yesmaximal, complemented
15#39157C212yesmaximal, complemented
16#38986C212yesmaximal, complemented
17#38978C212yesmaximal
18#37638C212yesmaximal, complemented
19#37637C212yesmaximal
20#37624C212yesmaximal, complemented
21#36598C211yesmaximal, characteristic, complemented
22#36563C211yesmaximal, characteristic, complemented
23#36194C211yesmaximal, characteristic
24#34950C211yesmaximal, characteristic, complemented
25#34945C211yesmaximal, characteristic
26#34941C211yesmaximal, characteristic
27#2868C2211yescharacteristic
28#2862C2212yes—
29#2859C2212yes—
30#2857C2212yes—
31#2841C2218yes—
32#2838C2218yes—
33#2836C2218yes—
34#2836C2218yes—
35#2833C2218yes—
36#2833C2218yes—
37#2831C2218yes—
38#2806C2214yes—
39#2802C2218yes—
40#2799C2218yes—
41#2798C2218yes—
42#2789C2218yes—
43#2787C2218yes—
44#2777C2218yes—
45#2774C2218yes—
46#2772C2218yes—
47#2769C2218yes—
48#2766C2218yes—
49#2762C2218yes—
50#2762C2218yes—
51#2759C2218yes—
52#2759C2218yes—
53#2758C2218yes—
54#2725C2218yes—
55#2690C2218yes—
56#2689C2218yes—
57#2666C2218yes—
58#2660C2214yes—
59#2655C2218yes—
60#2647C2214yes—
61#2647C2214yes—
62#2645C2214yes—
63#2645C2214yes—
64#2644C2214yes—
65#2637C2218yes—
66#2634C2218yes—
67#2629C2214yes—
68#2628C2214yes—
69#2625C2214yes—
70#2592C2214yes—
71#2586C2214yes—
72#2584C2214yes—
73#2584C2214yes—
74#2582C2214yes—
75#2582C2212yes—
76#2582C2211yescharacteristic
77#2582C2212yes—
78#2581C2214yes—
79#2574C2214yes—
80#2573C2214yes—
81#2571C2212yes—
82#2571C2211yescharacteristic
83#2571C2212yes—
84#2571C2214yes—
85#2571C2214yes—
86#2570C2214yes—
87#2570C2214yes—
88#2570C2214yes—
89#2568C2211yescharacteristic
90#2568C2212yes—
91#2567C2212yes—
92#2567C2211yescharacteristic
93#2567C2212yes—
94#2567C2211yescharacteristic
95#2567C2211yescharacteristic
96#2563C2212yes—
97#2563C2211yescharacteristic
98#2552C2212yes—
99#2552C2211yescharacteristic
100#2552C2212yes—
101#2552C2212yes—
102#2551C2211yescharacteristic
103#2550C2214yes—
104#2550C2214yes—
105#2547C2211yescharacteristic
106#2538C2212yes—
107#2538C2211yescharacteristic
108#2538C2211yescharacteristic
109#2524C2218yes—
110#2514C2214yes—
111#2514C2214yes—
112#2514C2214yes—
113#2514C2214yes—
114#2514C2214yes—
115#2514C2212yes—
116#2512C2214yes—
117#2511C2214yes—
118#2509C2214yes—
119#2509C2214yes—
120#2508C2214yes—
121#2508C2212yes—
122#2507C2214yes—
123#2507C2212yes—
124#2507C2214yes—
125#2507C2212yes—
126#2506C2214yes—
127#2506C2214yes—
128#2506C2214yes—
129#2499C2214yes—
130#2497C2212yes—
131#2497C2214yes—
132#2496C2214yes—
133#2496C2214yes—
134#2495C2214yes—
135#2495C2214yes—
136#2494C2214yes—
137#2494C2214yes—
138#2494C2212yes—
139#2492C2214yes—
140#2489C2214yes—
141#2489C2214yes—
142#2469C2218yes—
143#2454C2212yes—
144#2453C2214yes—
145#2453C2218yes—
146#2451C2214yes—
147#2451C2212yes—
148#2451C2212yes—
149#2448C2214yes—
150#2447C2212yes—
151#2446C2214yes—
152#2441C2214yes—
153#2439C2214yes—
154#2439C2214yes—
155#2423C2212yes—
156#2421C2212yes—
157#2401C2214yes—
158#2399C2214yes—
159#2396C2214yes—
160#2370C2214yes—
161#2369C2212yes—
162#2369C2212yes—
163#2369C2212yes—
164#2365C2212yes—
165#2365C2212yes—
166#2355C2214yes—
167#2355C2212yes—
168#2355C2212yes—
169#2355C2212yes—
170#2355C2212yes—
171#2354C2212yes—
172Q8×C4⋊C4C2212yes—
173Q8×C4⋊C4C2212yes—
174#2347C2214yes—
175#2330C2214yes—
176#2320C2214yes—
177#2314C2214yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2211yescharacteristic
185C4×#125C2212yes—
186C4×#124C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189#2295C2212yes—
190#2295C2212yes—
191#2295C2212yes—
192#2293C2212yes—
193#2285C2212yes—
194#2285C2212yes—
195#2283C2212yes—
196C42×Q8C2211yescharacteristic
197C42×Q8C2211yescharacteristic
198C42×D4C2211yescharacteristic
199C2×C4⋊Q8C2311yescharacteristic
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2311yescharacteristic
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×#126C2318yes—
208C2×#125C2312yes—
209C2×#125C2314yes—
210C2×#125C2314yes—
211C2×#125C2318yes—
212C2×#124C2312yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2314yes—
216C2×C4×Q8C2312yes—
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×#117C2314yes—
233C2×#117C2314yes—
234C22×C42C2312yes—
235#401C2318yes—
236#401C2318yes—
237#401C2318yes—
238#401C2314yes—
239#400C2318yes—
240#400C2314yes—
241#400C2318yes—
242#400C2318yes—
243#400C2314yes—
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#400C2318yes—
251#400C2318yes—
252#400C2314yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2314yes—
258#400C2318yes—
259#399C2314yes—
260#399C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2314yes—
265#398C2318yes—
266#398C2318yes—
267#398C2314yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2314yes—
273#398C2314yes—
274#398C2318yes—
275#398C2314yes—
276#398C2318yes—
277#398C2318yes—
278#398C2314yes—
279#397C2314yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2314yes—
284#397C2314yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#396C2314yes—
289#396C2314yes—
290#396C2318yes—
291#396C2318yes—
292#396C2314yes—
293#396C2318yes—
294#395C2314yes—
295#395C2318yes—
296#395C2318yes—
297#395C2314yes—
298#395C2314yes—
299#395C2314yes—
300#395C2318yes—
301#395C2318yes—
302#395C2314yes—
303#393C2314yes—
304#393C2318yes—
305#393C2318yes—
306#391C2314yes—
307#391C2312yes—
308#391C2314yes—
309#391C2312yes—
310#391C2312yes—
311#391C2314yes—
312#391C2314yes—
313#391C2314yes—
314#391C2314yes—
315#391C2312yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2314yes—
320#391C2314yes—
321#391C2312yes—
322#391C2312yes—
323#391C2314yes—
324#391C2318yes—
325#391C2312yes—
326#391C2314yes—
327#391C2318yes—
328#391C2312yes—
329#391C2312yes—
330#391C2314yes—
331#391C2314yes—
332#391C2318yes—
333#391C2318yes—
334#390C2312yes—
335#390C2314yes—
336#390C2312yes—
337#390C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2314yes—
342#389C2312yes—
343#389C2312yes—
344#389C2314yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2314yes—
350#389C2312yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2314yes—
365#389C2312yes—
366#389C2314yes—
367#389C2312yes—
368#389C2314yes—
369#389C2318yes—
370#389C2318yes—
371#389C2314yes—
372#389C2312yes—
373#389C2318yes—
374#389C2318yes—
375#389C2312yes—
376#389C2314yes—
377#389C2318yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2318yes—
382#389C2314yes—
383#389C2314yes—
384#389C2312yes—
385#389C2312yes—
386#389C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2314yes—
390#388C2314yes—
391#388C2314yes—
392#388C2314yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#387C2314yes—
398#387C2314yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2314yes—
411#387C2318yes—
412#387C2314yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2314yes—
418#387C2314yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#385C2314yes—
426#385C2314yes—
427#384C2311yescharacteristic
428#384C2312yes—
429#384C2312yes—
430#384C2312yes—
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2314yes—
434#384C2314yes—
435#384C2312yes—
436#384C2312yes—
437#384C2312yes—
438#384C2312yes—
439#384C2314yes—
440#384C2312yes—
441#383C2314yes—
442#383C2318yes—
443#383C2318yes—
444#383C2318yes—
445#382C2312yes—
446#382C2314yes—
447#382C2312yes—
448#382C2314yes—
449#382C2314yes—
450#382C2314yes—
451#382C2314yes—
452#382C2314yes—
453#382C2318yes—
454#382C2312yes—
455#382C2318yes—
456#382C2312yes—
457#382C2314yes—
458#381C2314yes—
459#380C2314yes—
460#380C2312yes—
461#380C2314yes—
462#380C2312yes—
463#380C2312yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2312yes—
468#380C2312yes—
469#380C2312yes—
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2318yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514#376C2314yes—
515#376C2314yes—
516C43C2312yes—
517C43C2311yescharacteristic
518C43C2312yes—
519C22×Q8C2411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×Q8C2412yes—
522C22×Q8C2412yes—
523C22×Q8C2412yes—
524C22×Q8C2414yes—
525C22×Q8C2414yes—
526C22×D4C2411yescharacteristic
527C23×C4C2412yes—
528C23×C4C2412yes—
529C23×C4C2412yes—
530C4⋊Q8—24no—
531C4⋊Q8—24no—
532C4⋊Q8—24no—
533C4⋊Q8—28no—
534C4⋊Q8—44no—
535C4⋊Q8—44no—
536C4⋊Q8—44no—
537C4⋊Q8—82no—
538#126—88no—
539#125—48no—
540#125—44no—
541#125—48no—
542#125—88no—
543#124—44no—
544C22⋊Q8—44no—
545C22⋊Q8—44no—
546C22⋊Q8—84no—
547C4×Q8—24no—
548C4×Q8—24no—
549C4×Q8—28no—
550C4×Q8—24no—
551C4×Q8—24no—
552C4×Q8—44no—
553C4×Q8—44no—
554C4×Q8—48no—
555C4×Q8—48no—
556C4×Q8—42no—
557C4×Q8—42no—
558C4×Q8—84no—
559C4×Q8—84no—
560C4×D4—24no—
561C4×D4—24no—
562C4×D4—42no—
563#117—48no—
564#117—48no—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C42—28no—
642C2×C42C2412yes—
643C2×C42C2414yes—
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646C2×C42C2414yes—
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2411yescharacteristic
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2412yes—
653C2×C42C2412yes—
654C2×C42C2414yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2418yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2418yes—
663C2×C42C2418yes—
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2418yes—
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671#95C2414yes—
672#95C2414yes—
673#95C2414yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2412yes—
680#95C2412yes—
681#95C2412yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2412yes—
689#95C2414yes—
690#95C2412yes—
691#95C2412yes—
692#95C2412yes—
693#95C2412yes—
694#95C2412yes—
695#95C2418yes—
696#95C2414yes—
697#95C2414yes—
698#95C2418yes—
699#95C2414yes—
700#95C2418yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2414yes—
708#95C2418yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2418yes—
715#95C2414yes—
716#95C2418yes—
717#95C2414yes—
718#95C2414yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727C24C2512yes—
728C2×Q8—22no—
729C2×Q8—22no—
730C2×Q8—22no—
731C2×Q8—24no—
732C2×Q8—22no—
733C2×Q8—24no—
734C2×Q8—24no—
735C2×Q8—24no—
736C2×Q8—28no—
737C2×Q8—24no—
738C2×Q8—22no—
739C2×Q8—22no—
740C2×Q8—42no—
741C2×Q8—42no—
742C2×Q8—42no—
743C2×Q8—44no—
744C2×Q8—44no—
745C2×Q8—42no—
746C2×Q8—44no—
747C2×Q8—44no—
748C2×Q8—44no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—22no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4C2512yes—
762C22×C4C2512yes—
763C22×C4C2512yes—
764C22×C4C2514yes—
765C22×C4C2512yes—
766C22×C4C2514yes—
767C22×C4C2514yes—
768C22×C4C2518yes—
769C22×C4C2512yes—
770C22×C4C2512yes—
771C22×C4C2512yes—
772C22×C4C2512yes—
773C22×C4C2512yes—
774C22×C4C2512yes—
775C22×C4C2512yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2511yescharacteristic
779C22×C4C2514yes—
780C22×C4C2511yescharacteristic
781C22×C4C2511yescharacteristic
782C22×C4C2511yescharacteristic
783C22×C4C2511yescharacteristic
784C22×C4C2511yescharacteristic
785C22×C4C2511yescharacteristic
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—22no—
789C4⋊C4—22no—
790C4⋊C4—22no—
791C4⋊C4—24no—
792C4⋊C4—22no—
793C4⋊C4—24no—
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—28no—
797C4⋊C4—24no—
798C4⋊C4—24no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—28no—
804C4⋊C4—24no—
805C4⋊C4—28no—
806C4⋊C4—24no—
807C4⋊C4—28no—
808C4⋊C4—22no—
809C4⋊C4—24no—
810C4⋊C4—22no—
811C4⋊C4—22no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4—42no—
818C4⋊C4—42no—
819C4⋊C4—44no—
820C4⋊C4—44no—
821C4⋊C4—44no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—42no—
825C4⋊C4—42no—
826C4⋊C4—48no—
827C4⋊C4—42no—
828C4⋊C4—48no—
829C4⋊C4—48no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C4⋊C4—48no—
834C4⋊C4—44no—
835C4⋊C4—48no—
836C4⋊C4—48no—
837C4⋊C4—44no—
838C4⋊C4—48no—
839C4⋊C4—44no—
840C4⋊C4—48no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—48no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C22⋊C4—24no—
850C22⋊C4—24no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—48no—
854C22⋊C4—42no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—48no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C42—24no—
863C42—24no—
864C42—24no—
865C42—24no—
866C42—24no—
867C42—28no—
868C42—24no—
869C42—24no—
870C42—24no—
871C42—28no—
872C42—22no—
873C42—22no—
874C42—28no—
875C42—24no—
876C42—24no—
877C42—22no—
878C42—24no—
879C42—48no—
880C42—42no—
881C42—42no—
882C42—48no—
883C42—42no—
884C42—42no—
885C42—48no—
886C42—48no—
887C42—41no—
888C422−1+414yes—
889C422−1+414yes—
890C422−1+414yes—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23C2611yescharacteristic
899Q8—48no—
900Q8—44no—
901Q8—44no—
902Q8—48no—
903Q8—84no—
904Q8—88no—
905Q8—88no—
906D4—44no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—28no—
932C2×C4—24no—
933C2×C4—21no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—28no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—28no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—48no—
971C2×C4—48no—
972C2×C4—84no—
973C2×C4C2×2−1+412yes—
974C2×C4C2×2−1+412yes—
975C2×C4C2×2−1+412yes—
976C2×C4C2×2−1+412yes—
977C2×C4C2×2−1+412yes—
978C2×C4C2×2−1+412yes—
979C2×C4C2×2−1+412yes—
980C2×C4C2×2−1+412yes—
981C2×C4C2×2−1+412yes—
982C2×C4#58512yes—
983C2×C4#58512yes—
984C2×C4#58512yes—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—42no—
989C22—42no—
990C22—42no—
991C22—42no—
992C22C22×2−1+411yescharacteristic
993C22C22×2−1+411yescharacteristic
994C22C22×2−1+411yescharacteristic
995C22C2×#58511yescharacteristic
996C22C2×#58511yescharacteristic
997C22C2×#58511yescharacteristic
998C22H(7,𝔽2)11yescharacteristic
999C4—22no—
1000C4—22no—
1001C4—22no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—44no—
1007C4—41no—
1008C4—44no—
1009C4—44no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—44no—
1014C4—44no—
1015C4—42no—
1016C4—42no—
1017C4—42no—
1018C4—44no—
1019C4—42no—
1020C4—48no—
1021C4#355514yes—
1022C4#355514yes—
1023C4#355514yes—
1024C2—82no—
1025C2C2×#355511yescharacteristic
1026C2C2×#355511yescharacteristic
1027C2C2×#355511yescharacteristic
1028C2#6292611yescharacteristic
1029C2#6292911yescharacteristic
1030C2#6296211yescharacteristic
1031C2#6303111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59871C2semidirect
2. #59665C2semidirect
4. #59242C2semidirect
5. #58643C2semidirect
6. #53139C2semidirect
7. #53093C2semidirect
9. #42689C2semidirect
10. #42562C2semidirect
11. #42461C2semidirect
12. #39754C2semidirect
14. #39480C2semidirect
15. #39157C2semidirect
16. #38986C2semidirect
18. #37638C2semidirect
20. #37624C2semidirect
21. #36598C2semidirect
22. #36563C2semidirect
24. #34950C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#596652
#594262
#592422
#586432
#531392
#530932
#529942
#426892
#425622
#424612
#397542
#395152
#394802
#391572
#389862
#389782
#376382
#376372
#376242
#365982
#365632
#361942
#349502
#349452
#349412