Finite Group Databasebeta

← #7671814

Subgroups — #7671814

Order 512.

4952 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59869C211yesmaximal, characteristic, complemented
3#59823C211yesmaximal, characteristic, complemented
4#59821C211yesmaximal, characteristic, complemented
5#59564C214yesmaximal, complemented
6#59235C212yesmaximal, complemented
7#59227C212yesmaximal, complemented
8#59055C212yesmaximal, complemented
9#59052C212yesmaximal, complemented
10#40130C214yesmaximal, complemented
11#40119C214yesmaximal, complemented
12#38828C214yesmaximal, complemented
13#38821C214yesmaximal, complemented
14#36631C211yesmaximal, characteristic
15#36460C212yesmaximal
16#36447C212yesmaximal, complemented
17#36391C214yesmaximal, complemented
18#36312C214yesmaximal, complemented
19#36300C212yesmaximal, complemented
20#36287C212yesmaximal, complemented
21#35635C214yesmaximal, complemented
22#35209C212yesmaximal, complemented
23#35209C212yesmaximal, complemented
24#34322C212yesmaximal, complemented
25#34317C212yesmaximal, complemented
26C4×#533C211yesmaximal, characteristic, complemented
27C4×#533C211yesmaximal, characteristic, complemented
28C2×#556C2212yes—
29C2×#554C2212yes—
30C2×#541C2214yes—
31C2×#533C2211yescharacteristic
32C2×#533C2211yescharacteristic
33C2×#529C2212yes—
34#2861C2212yes—
35#2860C2212yes—
36#2860C2212yes—
37#2860C2214yes—
38#2860C2214yes—
39#2859C2211yescharacteristic
40#2859C2214yes—
41#2859C2214yes—
42#2858C2211yescharacteristic
43#2857C2211yescharacteristic
44#2856C2211yescharacteristic
45#2854C2212yes—
46#2854C2212yes—
47#2850C2212yes—
48#2809C2214yes—
49#2806C2214yes—
50#2783C2218yes—
51#2781C2218yes—
52#2744C2218yes—
53#2744C2218yes—
54#2732C2214yes—
55#2732C2218yes—
56#2727C2214yes—
57#2721C2218yes—
58#2664C2218yes—
59#2664C2218yes—
60#2612C2218yes—
61#2609C2218yes—
62#2584C2214yes—
63#2582C2214yes—
64#2571C2214yes—
65#2571C2212yes—
66#2568C2214yes—
67#2567C2212yes—
68#2562C2214yes—
69#2559C2218yes—
70#2558C2218yes—
71#2556C2218yes—
72#2553C2218yes—
73#2552C2212yes—
74#2552C2214yes—
75#2552C2212yes—
76#2552C2212yes—
77#2548C2212yes—
78#2546C2212yes—
79#2546C2212yes—
80#2542C2214yes—
81#2542C2212yes—
82#2542C2212yes—
83#2538C2212yes—
84#2538C2212yes—
85#2538C2214yes—
86#2529C2218yes—
87#2529C2218yes—
88#2526C2218yes—
89#2521C2218yes—
90#2519C2218yes—
91#2519C2218yes—
92#2519C2218yes—
93#2513C2214yes—
94#2512C2214yes—
95#2512C2214yes—
96#2512C2214yes—
97#2508C2214yes—
98#2508C2214yes—
99#2508C2218yes—
100#2508C2214yes—
101#2507C2214yes—
102#2506C2218yes—
103#2506C2214yes—
104#2506C2214yes—
105#2500C2214yes—
106#2497C2214yes—
107#2496C2218yes—
108#2489C2214yes—
109#2489C2214yes—
110#2479C2218yes—
111#2474C2218yes—
112#2454C2214yes—
113#2454C2214yes—
114#2448C2214yes—
115#2448C2214yes—
116#2441C2214yes—
117#2429C2214yes—
118#2429C2214yes—
119#2426C2214yes—
120#2423C2218yes—
121#2423C2214yes—
122#2420C2214yes—
123#2417C2214yes—
124#2417C2214yes—
125#2415C2214yes—
126#2415C2214yes—
127#2373C2218yes—
128#2370C2214yes—
129#2369C2212yes—
130#2369C2212yes—
131#2367C2214yes—
132#2366C2212yes—
133#2365C2212yes—
134#2363C2214yes—
135#2362C2218yes—
136#2362C2214yes—
137#2360C2214yes—
138#2357C2214yes—
139#2355C2212yes—
140#2355C2212yes—
141#2354C2212yes—
142#2354C2214yes—
143#2351C2214yes—
144Q8×C4⋊C4C2212yes—
145Q8×C4⋊C4C2212yes—
146Q8×C4⋊C4C2214yes—
147D4×C4⋊C4C2212yes—
148#2346C2214yes—
149#2346C2214yes—
150#2346C2218yes—
151#2344C2214yes—
152#2334C2218yes—
153#2332C2218yes—
154#2323C2214yes—
155#2323C2214yes—
156C4×C4⋊Q8C2211yescharacteristic
157C4×C4⋊Q8C2211yescharacteristic
158C4×C4⋊Q8C2211yescharacteristic
159C4×C4⋊Q8C2211yescharacteristic
160C4×C4⋊Q8C2211yescharacteristic
161C4×C4⋊Q8C2211yescharacteristic
162C4×C4⋊Q8C2211yescharacteristic
163C4×C4⋊Q8C2211yescharacteristic
164C4×C4⋊Q8C2211yescharacteristic
165C4×#127C2211yescharacteristic
166C4×#125C2214yes—
167C4×#125C2212yes—
168C4×#125C2212yes—
169C4×#125C2212yes—
170C4×#125C2212yes—
171C4×#124C2214yes—
172C4×#124C2212yes—
173C4×C22⋊Q8C2212yes—
174C4×C22⋊Q8C2212yes—
175C4×C22⋊Q8C2212yes—
176C4×C22⋊Q8C2212yes—
177C4×C22⋊Q8C2212yes—
178C4×C22⋊Q8C2212yes—
179C4×C22⋊Q8C2212yes—
180C4×C22⋊Q8C2212yes—
181C4×#121C2212yes—
182C4×#121C2212yes—
183#2296C2212yes—
184#2296C2212yes—
185#2295C2214yes—
186#2295C2212yes—
187#2295C2212yes—
188#2295C2212yes—
189#2295C2212yes—
190#2293C2212yes—
191#2293C2214yes—
192#2293C2212yes—
193#2285C2211yescharacteristic
194#2285C2211yescharacteristic
195#2274C2214yes—
196C42×Q8C2212yes—
197C42×Q8C2212yes—
198C42×Q8C2212yes—
199C42×Q8C2212yes—
200C4×#117C2212yes—
201C4×#117C2212yes—
202C2×C43C2211yescharacteristic
203#556—216no—
204#554—216no—
205#541—416no—
206#533—28no—
207#533—28no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#127C2311yescharacteristic
215#529—48no—
216C2×#126C2318yes—
217C2×#126C2314yes—
218C2×#126C2318yes—
219C2×#126C2318yes—
220C2×#125C2312yes—
221C2×#125C2312yes—
222C2×#125C2314yes—
223C2×#125C2314yes—
224C2×#125C2312yes—
225C2×#125C2318yes—
226C2×#125C2318yes—
227C2×#124C2314yes—
228C2×#124C2312yes—
229C2×#124C2312yes—
230C2×#123C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2318yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2314yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×#121C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2314yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×#117C2314yes—
266C2×#117C2312yes—
267C2×#117C2314yes—
268C2×#117C2312yes—
269C2×#117C2312yes—
270C2×#117C2318yes—
271C2×#117C2312yes—
272C22×C4⋊C4C2314yes—
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278C22×C42C2311yescharacteristic
279C22×C42C2311yescharacteristic
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#399C2318yes—
286#399C2318yes—
287#399C2318yes—
288#399C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#395C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#391C2312yes—
313#391C2312yes—
314#391C2312yes—
315#391C2312yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2318yes—
325#391C2318yes—
326#391C2312yes—
327#390C2312yes—
328#390C2312yes—
329#390C2312yes—
330#390C2312yes—
331#390C2312yes—
332#390C2312yes—
333#390C2312yes—
334#390C2312yes—
335#390C2312yes—
336#390C2312yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C2314yes—
341#390C2314yes—
342#390C2318yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2314yes—
363#389C2314yes—
364#389C2312yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2318yes—
369#389C2314yes—
370#389C2314yes—
371#389C2318yes—
372#389C2318yes—
373#389C2318yes—
374#389C2314yes—
375#389C2318yes—
376#389C2318yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2318yes—
381#389C2312yes—
382#389C2318yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2314yes—
395#388C2318yes—
396#388C2318yes—
397#388C2314yes—
398#388C2318yes—
399#388C2314yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2314yes—
409#388C2314yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2314yes—
422#387C2314yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#386C2314yes—
431#386C2314yes—
432#386C2318yes—
433#386C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2314yes—
437#385C2314yes—
438#385C2314yes—
439#385C2314yes—
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#384C2311yescharacteristic
444#384C2311yescharacteristic
445#384C2311yescharacteristic
446#384C2314yes—
447#384C2314yes—
448#384C2314yes—
449#384C2314yes—
450#384C2318yes—
451#382C2312yes—
452#382C2312yes—
453#382C2314yes—
454#382C2318yes—
455#382C2318yes—
456#382C2314yes—
457#382C2312yes—
458#382C2318yes—
459#382C2318yes—
460#381C2318yes—
461#380C2312yes—
462#380C2312yes—
463#380C2314yes—
464#380C2314yes—
465#380C2312yes—
466#380C2312yes—
467#380C2318yes—
468#380C2318yes—
469#380C2312yes—
470#380C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2318yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2318yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2318yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2314yes—
513C4×C4⋊C4C2312yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2318yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2314yes—
523#376C2318yes—
524#376C2314yes—
525#376C2314yes—
526C43C2311yescharacteristic
527C43C2311yescharacteristic
528C43C2311yescharacteristic
529C43C2314yes—
530C43C2311yescharacteristic
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2314yes—
534C43C2311yescharacteristic
535C43C2311yescharacteristic
536C22×Q8C2412yes—
537C22×Q8C2412yes—
538C22×Q8C2412yes—
539C22×Q8C2412yes—
540C22×Q8C2412yes—
541C22×D4C2412yes—
542C22×D4C2412yes—
543C22×D4C2414yes—
544C22×D4C2412yes—
545C23×C4C2414yes—
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2418yes—
553C23×C4C2411yescharacteristic
554C4⋊Q8—24no—
555C4⋊Q8—24no—
556C4⋊Q8—24no—
557C4⋊Q8—48no—
558C4⋊Q8#4118yes—
559C4⋊Q8#4118yes—
560#127—24no—
561#126—232no—
562#126—48no—
563#126—416no—
564#126—416no—
565#125—28no—
566#125—28no—
567#125—216no—
568#125—44no—
569#125—48no—
570#125—416no—
571#125—416no—
572#124—216no—
573#124—44no—
574#124—44no—
575#123—48no—
576C22⋊Q8—28no—
577C22⋊Q8—28no—
578C22⋊Q8—232no—
579C22⋊Q8—28no—
580C22⋊Q8—28no—
581C22⋊Q8—216no—
582C22⋊Q8—216no—
583C22⋊Q8—44no—
584C22⋊Q8—48no—
585C22⋊Q8—48no—
586#121—28no—
587#121—44no—
588#121—44no—
589C4×Q8—28no—
590C4×Q8—28no—
591C4×Q8—216no—
592C4×Q8—28no—
593C4×Q8—28no—
594C4×Q8—28no—
595C4×Q8—28no—
596C4×Q8—28no—
597C4×Q8—28no—
598C4×Q8—28no—
599C4×Q8—44no—
600C4×Q8—44no—
601C4×Q8—44no—
602C4×Q8—44no—
603C4×Q8—48no—
604C4×D4—216no—
605C4×D4—28no—
606C4×D4—28no—
607C4×D4—48no—
608C4×D4—44no—
609C4×D4—48no—
610#117—28no—
611#117—28no—
612#117—28no—
613#117—216no—
614#117—216no—
615#117—44no—
616#117—416no—
617C2×C4⋊C4—216no—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2414yes—
695C2×C42—24no—
696C2×C42—24no—
697C2×C42—24no—
698C2×C42—24no—
699C2×C42—24no—
700C2×C42—42no—
701C2×C42—42no—
702C2×C42C2414yes—
703C2×C42C2414yes—
704C2×C42C2414yes—
705C2×C42C2414yes—
706C2×C42C2418yes—
707C2×C42C2414yes—
708C2×C42C2411yescharacteristic
709C2×C42C2414yes—
710C2×C42C2414yes—
711C2×C42C2414yes—
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2414yes—
720C2×C42C2414yes—
721C2×C42C2414yes—
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2418yes—
735C2×C42C2414yes—
736C2×C42C2414yes—
737C2×C42C2418yes—
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2418yes—
757#95C2414yes—
758#95C2414yes—
759#95C2418yes—
760#95C2414yes—
761#95C2418yes—
762#95C2414yes—
763#95C2418yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2418yes—
776#95C2418yes—
777#95C2418yes—
778#95C2418yes—
779#95C2418yes—
780#95C2414yes—
781#95C2414yes—
782C24C2514yes—
783C24C2511yescharacteristic
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—24no—
793C2×Q8—42no—
794C2×Q8—42no—
795C2×Q8—42no—
796C2×Q8—42no—
797C2×Q8C2×#4118yes—
798C2×Q8C2×#4118yes—
799C2×D4—28no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—44no—
808C2×D4—42no—
809C2×D4—44no—
810C2×D4—42no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—28no—
822C22×C4—28no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—28no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—216no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—48no—
836C22×C4—48no—
837C22×C42−1+414yes—
838C22×C4C2511yescharacteristic
839C22×C4C2514yes—
840C22×C4C2514yes—
841C22×C4C2511yescharacteristic
842C22×C4C2511yescharacteristic
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2514yes—
847C22×C4C2511yescharacteristic
848C22×C4C2514yes—
849C22×C4C2514yes—
850C22×C4C2514yes—
851C22×C4C2514yes—
852C22×C4C2511yescharacteristic
853C22×C4C2511yescharacteristic
854C22×C4C2514yes—
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C22×C4C2511yescharacteristic
862C22×C4C2511yescharacteristic
863C4⋊C4—24no—
864C4⋊C4—216no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—28no—
874C4⋊C4—28no—
875C4⋊C4—216no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—28no—
879C4⋊C4—216no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—28no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—28no—
894C4⋊C4—24no—
895C4⋊C4—24no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—48no—
899C4⋊C4—42no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—44no—
905C4⋊C4—48no—
906C4⋊C4—42no—
907C4⋊C4—44no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—48no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—48no—
914C4⋊C4C2×#4118yes—
915C4⋊C4C2×#4118yes—
916C4⋊C4C2×#4118yes—
917C4⋊C4C2×#4118yes—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—216no—
922C22⋊C4—216no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—216no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—44no—
940C42—22no—
941C42—22no—
942C42—22no—
943C42—22no—
944C42—22no—
945C42—22no—
946C42—28no—
947C42—28no—
948C42—216no—
949C42—28no—
950C42—28no—
951C42—22no—
952C42—22no—
953C42—22no—
954C42—28no—
955C42—28no—
956C42—28no—
957C42—22no—
958C42—22no—
959C42—22no—
960C42—22no—
961C42—22no—
962C42—22no—
963C42—22no—
964C42—28no—
965C42—28no—
966C42—22no—
967C42—22no—
968C42—22no—
969C42—22no—
970C42—28no—
971C42—28no—
972C42—41no—
973C42—41no—
974C42—41no—
975C42—41no—
976C42—48no—
977C42—44no—
978C42—44no—
979C42—48no—
980C42C2×#4114yes—
981C42C2×#4114yes—
982C42H(5,𝔽2)14yes—
983C422−1+414yes—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23C2×2−1+412yes—
998C23C2611yescharacteristic
999Q8—216no—
1000Q8—48no—
1001Q8—48no—
1002Q8—48no—
1003Q8—84no—
1004D4—48no—
1005D4—48no—
1006D4—84no—
1007D4—88no—
1008C2×C4—28no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—24no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—24no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—24no—
1025C2×C4—21no—
1026C2×C4—24no—
1027C2×C4—28no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—21no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—44no—
1068C2×C4—44no—
1069C2×C4—44no—
1070C2×C4—44no—
1071C2×C4—416no—
1072C2×C4—44no—
1073C2×C4—816no—
1074C2×C4C22×#4118yes—
1075C2×C4C22×#4112yes—
1076C2×C4C22×#4112yes—
1077C2×C4C22×#4118yes—
1078C2×C4C22×#4112yes—
1079C2×C4C22×#4112yes—
1080C2×C4C22×#4112yes—
1081C2×C4C22×#4112yes—
1082C2×C4C2×H(5,𝔽2)12yes—
1083C2×C4C2×H(5,𝔽2)12yes—
1084C2×C4C2×H(5,𝔽2)12yes—
1085C2×C4C2×2−1+412yes—
1086C2×C4C2×2−1+412yes—
1087C2×C4C2×2−1+412yes—
1088C2×C4C2×2−1+412yes—
1089C2×C4C2×2−1+412yes—
1090C2×C4#58512yes—
1091C2×C4#58512yes—
1092C22—22no—
1093C22—22no—
1094C22—22no—
1095C22—41no—
1096C22—41no—
1097C22—41no—
1098C22—41no—
1099C22—44no—
1100C22—44no—
1101C22—44no—
1102C22—44no—
1103C22—44no—
1104C22—44no—
1105C22—44no—
1106C22C23×#4111yescharacteristic
1107C22C23×#4111yescharacteristic
1108C22C22×H(5,𝔽2)11yescharacteristic
1109C22C22×2−1+411yescharacteristic
1110C22C22×2−1+411yescharacteristic
1111C22C2×#58511yescharacteristic
1112C22C2×#58511yescharacteristic
1113C4—28no—
1114C4—22no—
1115C4—28no—
1116C4—22no—
1117C4—22no—
1118C4—22no—
1119C4—22no—
1120C4—22no—
1121C4—22no—
1122C4—41no—
1123C4—41no—
1124C4—44no—
1125C4—44no—
1126C4—44no—
1127C4—44no—
1128C4—41no—
1129C4—44no—
1130C4—44no—
1131C4—44no—
1132C4—41no—
1133C4—44no—
1134C4—44no—
1135C4#348314yes—
1136C4#351514yes—
1137C4#352314yes—
1138C2—42no—
1139C2—84no—
1140C2C2×#348311yescharacteristic
1141C2C2×#351511yescharacteristic
1142C2#6278111yescharacteristic
1143C2C2×#352311yescharacteristic
1144C2#6278811yescharacteristic
1145C2#6283511yescharacteristic
1146C2#6283511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2856C22
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. #59869C2semidirect
3. #59823C2semidirect
4. #59821C2semidirect
5. #59564C2semidirect
6. #59235C2semidirect
7. #59227C2semidirect
8. #59055C2semidirect
9. #59052C2semidirect
10. #40130C2semidirect
11. #40119C2semidirect
12. #38828C2semidirect
13. #38821C2semidirect
16. #36447C2semidirect
17. #36391C2semidirect
18. #36312C2semidirect
19. #36300C2semidirect
20. #36287C2semidirect
21. #35635C2semidirect
22. #35209C2semidirect
23. #35209C2semidirect
24. #34322C2semidirect
25. #34317C2semidirect
26. C4×#533C2semidirect
27. C4×#533C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#598692
#598232
#598212
#595642
#592352
#592272
#590552
#590522
#401302
#401192
#388282
#388212
#366312
#364602
#364472
#363912
#363122
#363002
#362872
#356352
#352092
#343222
#343172
C4×#5332