Finite Group Databasebeta

← #7688605

Subgroups — #7688605

Order 512.

5059 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59817C211yesmaximal, characteristic, complemented
2#59486C214yesmaximal, complemented
3#59421C212yesmaximal, complemented
4#59418C212yesmaximal, complemented
5#59253C214yesmaximal, complemented
6#59064C212yesmaximal, complemented
7#45172C214yesmaximal, complemented
8#43827C218yesmaximal, complemented
9#40194C214yesmaximal, complemented
10#40073C214yesmaximal, complemented
11#39159C212yesmaximal, complemented
12#38977C212yesmaximal, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36560C211yesmaximal, characteristic, complemented
15#36446C212yesmaximal, complemented
16#36303C212yesmaximal, complemented
17#36288C212yesmaximal, complemented
18#36174C212yesmaximal, complemented
19#36127C211yesmaximal, characteristic
20#35900C214yesmaximal, complemented
21#34945C212yesmaximal, complemented
22#34945C211yesmaximal, characteristic, complemented
23#34334C212yesmaximal, complemented
24#34232C212yesmaximal, complemented
25C4×#559C211yesmaximal, characteristic, complemented
26C4×#556C211yesmaximal, characteristic, complemented
27C2×#559C2211yescharacteristic
28C2×#557C2212yes—
29C2×#556C2211yescharacteristic
30C2×D4×Q8C2212yes—
31C2×D4×Q8C2212yes—
32C2×#547C2212yes—
33C2×#532C2212yes—
34#2868C2211yescharacteristic
35#2862C2214yes—
36#2862C2212yes—
37#2859C2212yes—
38#2857C2212yes—
39#2850C2214yes—
40#2781C2218yes—
41#2765C2218yes—
42#2764C2218yes—
43#2758C2218yes—
44#2751C2218yes—
45#2745C2218yes—
46#2739C2218yes—
47#2708C2218yes—
48#2707C2218yes—
49#2702C2218yes—
50#2683C2214yes—
51#2653C2218yes—
52#2645C2214yes—
53#2612C2218yes—
54#2597C2218yes—
55#2582C2212yes—
56#2574C2218yes—
57#2573C2214yes—
58#2573C2218yes—
59#2571C2212yes—
60#2571C2211yescharacteristic
61#2570C2214yes—
62#2568C2211yescharacteristic
63#2568C2214yes—
64#2568C2212yes—
65#2568C2212yes—
66#2565C2214yes—
67#2560C2218yes—
68#2558C2218yes—
69#2551C2212yes—
70#2547C2212yes—
71#2547C2214yes—
72#2547C2211yescharacteristic
73#2546C2212yes—
74#2546C2212yes—
75#2538C2211yescharacteristic
76#2538C2212yes—
77#2538C2212yes—
78#2537C2212yes—
79#2537C2212yes—
80#2527C2218yes—
81#2526C2218yes—
82#2518C2218yes—
83#2514C2212yes—
84#2514C2214yes—
85#2511C2214yes—
86#2508C2214yes—
87#2506C2214yes—
88#2506C2214yes—
89#2505C2218yes—
90#2503C2214yes—
91#2495C2214yes—
92#2494C2214yes—
93#2494C2212yes—
94#2493C2218yes—
95#2492C2214yes—
96#2492C2214yes—
97#2492C2214yes—
98#2490C2214yes—
99#2489C2214yes—
100#2489C2218yes—
101#2489C2218yes—
102#2489C2214yes—
103#2488C2218yes—
104#2488C2218yes—
105#2452C2214yes—
106#2452C2214yes—
107#2447C2212yes—
108#2447C2214yes—
109#2447C2214yes—
110#2446C2214yes—
111#2442C2214yes—
112#2439C2214yes—
113#2436C2214yes—
114#2432C2214yes—
115#2432C2214yes—
116#2429C2214yes—
117#2427C2214yes—
118#2426C2214yes—
119#2422C2214yes—
120#2422C2214yes—
121#2421C2214yes—
122#2421C2214yes—
123#2421C2212yes—
124#2420C2214yes—
125#2419C2218yes—
126#2409C2214yes—
127#2401C2218yes—
128#2401C2214yes—
129#2374C2214yes—
130#2373C2214yes—
131#2369C2214yes—
132#2368C2218yes—
133#2367C2212yes—
134#2367C2212yes—
135#2367C2212yes—
136#2366C2211yescharacteristic
137#2366C2212yes—
138#2365C2211yescharacteristic
139#2365C2212yes—
140#2365C2212yes—
141#2365C2212yes—
142#2363C2214yes—
143#2363C2214yes—
144#2362C2212yes—
145#2360C2214yes—
146#2357C2212yes—
147#2357C2212yes—
148#2356C2212yes—
149#2355C2212yes—
150#2355C2212yes—
151#2355C2211yescharacteristic
152#2355C2211yescharacteristic
153#2355C2211yescharacteristic
154#2354C2211yescharacteristic
155#2353C2218yes—
156#2349C2214yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2212yes—
159#2347C2212yes—
160#2346C2214yes—
161#2341C2214yes—
162Q8×C22⋊C4C2214yes—
163Q8×C22⋊C4C2214yes—
164#2339C2214yes—
165#2339C2214yes—
166#2333C2218yes—
167#2331C2214yes—
168#2329C2218yes—
169#2319C2214yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2211yescharacteristic
174C4×#127C2211yescharacteristic
175C4×#126C2214yes—
176C4×#124C2212yes—
177C4×#124C2212yes—
178C4×#124C2212yes—
179C4×#124C2212yes—
180C4×#124C2214yes—
181C4×#124C2214yes—
182C4×C22⋊Q8C2214yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2212yes—
185C4×#123C2214yes—
186#2295C2212yes—
187#2295C2214yes—
188C2×#391C2214yes—
189#2283C2214yes—
190#2283C2212yes—
191#2275C2214yes—
192C42×Q8C2212yes—
193C42×Q8C2211yescharacteristic
194C42×Q8C2211yescharacteristic
195C42×D4C2212yes—
196C42×D4C2211yescharacteristic
197C42×D4C2212yes—
198C4×#117C2212yes—
199C22×#41C2314yes—
200C23×Q8C2314yes—
201#559—28no—
202#557—48no—
203#556—28no—
204D4×Q8—216no—
205D4×Q8—48no—
206#547—48no—
207#532—216no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#126C2314yes—
218C2×#125C2314yes—
219C2×#125C2318yes—
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×#124C2312yes—
223C2×#124C2314yes—
224C2×#124C2312yes—
225C2×#123C2314yes—
226C2×#123C2318yes—
227C2×C22⋊Q8C2318yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2318yes—
234C2×#121C2314yes—
235C2×#121C2314yes—
236C2×#121C2314yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2312yes—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2311yescharacteristic
264C2×#117C2312yes—
265C2×#117C2312yes—
266C22×C4⋊C4C2314yes—
267C22×C42C2312yes—
268C22×C42C2314yes—
269#401C2318yes—
270#401C2314yes—
271#400C2318yes—
272#400C2318yes—
273#400C2314yes—
274#400C2318yes—
275#400C2318yes—
276#400C2314yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2314yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2314yes—
290#397C2314yes—
291#397C2318yes—
292#397C2314yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#396C2318yes—
297#396C2314yes—
298#396C2318yes—
299#396C2318yes—
300#395C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#393C2318yes—
306#393C2318yes—
307#393C2318yes—
308#391C2318yes—
309#391C2312yes—
310#391C2314yes—
311#391C2314yes—
312#391C2312yes—
313#391C2314yes—
314#391C2314yes—
315#391C2318yes—
316#391C2314yes—
317#391C2314yes—
318#391C2312yes—
319#391C2312yes—
320#391C2314yes—
321#391C2312yes—
322#391C2318yes—
323#391C2314yes—
324#391C2318yes—
325#391C2314yes—
326#391C2314yes—
327#391C2318yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2312yes—
332#391C2318yes—
333#391C2312yes—
334#390C2318yes—
335#390C2312yes—
336#390C2312yes—
337#390C2312yes—
338#390C2312yes—
339#390C2314yes—
340#390C2318yes—
341#390C2312yes—
342#390C2312yes—
343#390C2314yes—
344#390C2312yes—
345#389C2312yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2312yes—
350#389C2314yes—
351#389C2312yes—
352#389C2312yes—
353#389C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2314yes—
357#389C2318yes—
358#389C2312yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2312yes—
366#389C2314yes—
367#388C2314yes—
368#388C2314yes—
369#388C2314yes—
370#388C2314yes—
371#388C2314yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2314yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2314yes—
381#388C2314yes—
382#388C2318yes—
383#388C2314yes—
384#388C2314yes—
385#388C2314yes—
386#388C2314yes—
387#388C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2314yes—
398#387C2318yes—
399#387C2314yes—
400#387C2314yes—
401#387C2314yes—
402#387C2318yes—
403#387C2318yes—
404#387C2314yes—
405#387C2314yes—
406#386C2318yes—
407#386C2314yes—
408#386C2318yes—
409#386C2318yes—
410#386C2318yes—
411#386C2318yes—
412#385C2314yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2314yes—
419#385C2314yes—
420#385C2318yes—
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2312yes—
424#384C2311yescharacteristic
425#384C2312yes—
426#384C2312yes—
427#384C2312yes—
428#383C2314yes—
429#383C2314yes—
430#383C2318yes—
431#382C2314yes—
432#382C2312yes—
433#382C2312yes—
434#382C2314yes—
435#382C2314yes—
436#382C2314yes—
437#382C2312yes—
438#382C2312yes—
439#382C2318yes—
440#382C2318yes—
441#382C2312yes—
442#382C2312yes—
443#381C2314yes—
444#381C2318yes—
445#381C2318yes—
446#381C2318yes—
447#381C2314yes—
448#380C2314yes—
449#380C2318yes—
450#380C2318yes—
451#380C2312yes—
452#380C2312yes—
453#380C2314yes—
454#380C2314yes—
455#380C2318yes—
456#380C2312yes—
457#380C2314yes—
458#380C2312yes—
459#380C2314yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2314yes—
500C4×C22⋊C4C2318yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2312yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517#376C2314yes—
518#376C2318yes—
519#376C2314yes—
520C2×#95C2318yes—
521C2×#95C2318yes—
522C43C2314yes—
523C43C2311yescharacteristic
524C43C2312yes—
525C43C2312yes—
526C2×#41—216no—
527C2×#41—48no—
528C2×#41—48no—
529C22×Q8—216no—
530C22×Q8—48no—
531C22×Q8—48no—
532C22×Q8C2411yescharacteristic
533C22×Q8C2411yescharacteristic
534C22×Q8C2414yes—
535C22×Q8C2412yes—
536C22×Q8C2412yes—
537C22×Q8C2418yes—
538C22×D4C2411yescharacteristic
539C22×D4C2412yes—
540C22×D4C2412yes—
541C22×D4C2418yes—
542C22×D4C2412yes—
543C23×C4C2414yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2418yes—
547C23×C4C2418yes—
548C23×C4C2414yes—
549C23×C4C2414yes—
550C23×C4C2412yes—
551C4⋊Q8—216no—
552C4⋊Q8—28no—
553C4⋊Q8—28no—
554C4⋊Q8—24no—
555C4⋊Q8—48no—
556C4⋊Q8—44no—
557C4⋊Q8—48no—
558C4⋊Q8#4118yescomplemented
559#127#4118yes—
560#126—216no—
561#125—48no—
562#125—416no—
563#124—28no—
564#124—216no—
565#124—28no—
566#124—28no—
567#124—44no—
568#123—216no—
569#123—416no—
570C22⋊Q8—216no—
571C22⋊Q8—232no—
572C22⋊Q8—28no—
573C22⋊Q8—416no—
574C22⋊Q8—44no—
575C22⋊Q8—48no—
576C22⋊Q8—48no—
577#121—216no—
578#121—216no—
579#121—48no—
580C4×Q8—28no—
581C4×Q8—24no—
582C4×Q8—28no—
583C4×Q8—24no—
584C4×Q8—24no—
585C4×Q8—24no—
586C4×Q8—28no—
587C4×Q8—24no—
588C4×Q8—44no—
589C4×Q8—48no—
590C4×Q8—42no—
591C4×Q8—48no—
592C4×Q8—48no—
593C4×D4—216no—
594C4×D4—216no—
595C4×D4—28no—
596C4×D4—28no—
597C4×D4—216no—
598C4×D4—28no—
599C4×D4—28no—
600C4×D4—24no—
601C4×D4—24no—
602C4×D4—28no—
603C4×D4—42no—
604C4×D4—44no—
605C4×D4—48no—
606C4×D4—44no—
607#117—28no—
608#117—28no—
609C2×C4⋊C4—48no—
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2411yescharacteristic
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C42—28no—
684C2×C42—48no—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2411yescharacteristic
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2414yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2414yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2411yescharacteristic
699C2×C42C2412yes—
700C2×C42C2411yescharacteristic
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2418yes—
705C2×C42C2414yes—
706C2×C42C2412yes—
707C2×C42C2418yes—
708C2×C42C2412yes—
709C2×C42C2411yescharacteristic
710C2×C42C2412yes—
711C2×C42C2414yes—
712C2×C42C2414yes—
713C2×C42C2414yes—
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2412yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2412yes—
736#95C2412yes—
737#95C2414yes—
738#95C2414yes—
739#95C2412yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2412yes—
744#95C2412yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2418yes—
749#95C2418yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2412yes—
754#95C2412yes—
755#95C2412yes—
756#95C2414yes—
757#95C2414yes—
758#95C2418yes—
759#95C2418yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2418yes—
764#95C2418yes—
765C24C2512yes—
766C24C2514yes—
767#41—832no—
768C2×Q8—22no—
769C2×Q8—22no—
770C2×Q8—22no—
771C2×Q8—24no—
772C2×Q8—28no—
773C2×Q8—216no—
774C2×Q8—24no—
775C2×Q8—22no—
776C2×Q8—28no—
777C2×Q8—24no—
778C2×Q8—22no—
779C2×Q8—24no—
780C2×Q8—22no—
781C2×Q8—28no—
782C2×Q8—24no—
783C2×Q8—48no—
784C2×Q8—48no—
785C2×Q8—832no—
786C2×Q8C2×#4118yes—
787C2×D4—216no—
788C2×D4—24no—
789C2×D4—22no—
790C2×D4—24no—
791C2×D4—22no—
792C2×D4—24no—
793C2×D4—24no—
794C2×D4—22no—
795C2×D4—42no—
796C2×D4—42no—
797C2×D4—48no—
798C2×D4—48no—
799C2×D4C2×#4118yes—
800C2×D4C2×#4118yes—
801C2×D4C2×#4118yes—
802C22×C4—28no—
803C22×C4—216no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—28no—
808C22×C4—28no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—28no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—216no—
815C22×C4—28no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—48no—
819C22×C4—48no—
820C22×C4—44no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—44no—
824C22×C4—48no—
825C22×C4—48no—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2514yes—
833C22×C4C2512yes—
834C22×C4C2511yescharacteristic
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2514yes—
839C22×C4C2514yes—
840C22×C4C2518yes—
841C22×C4C2512yes—
842C22×C4C2511yescharacteristic
843C22×C4C2514yes—
844C22×C4C2511yescharacteristic
845C22×C4C2511yescharacteristic
846C22×C4C2512yes—
847C22×C4C2511yescharacteristic
848C22×C4C2511yescharacteristic
849C22×C4C2511yescharacteristic
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—28no—
855C4⋊C4—28no—
856C4⋊C4—24no—
857C4⋊C4—24no—
858C4⋊C4—28no—
859C4⋊C4—28no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—216no—
864C4⋊C4—22no—
865C4⋊C4—28no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—22no—
869C4⋊C4—28no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—28no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—24no—
879C4⋊C4—48no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—44no—
883C4⋊C4—42no—
884C4⋊C4—44no—
885C4⋊C4—48no—
886C4⋊C4—42no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—44no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4C2×#4118yes—
895C4⋊C4C2×#4118yes—
896C4⋊C42−1+414yes—
897C22⋊C4—216no—
898C22⋊C4—216no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—216no—
904C22⋊C4—28no—
905C22⋊C4—24no—
906C22⋊C4—28no—
907C22⋊C4—28no—
908C22⋊C4—24no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—48no—
915C22⋊C4—42no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C42—24no—
924C42—24no—
925C42—24no—
926C42—28no—
927C42—24no—
928C42—24no—
929C42—28no—
930C42—24no—
931C42—28no—
932C42—24no—
933C42—28no—
934C42—24no—
935C42—22no—
936C42—24no—
937C42—24no—
938C42—24no—
939C42—22no—
940C42—24no—
941C42—22no—
942C42—44no—
943C42—44no—
944C42—41no—
945C42—42no—
946C42—42no—
947C42—44no—
948C42—44no—
949C42—48no—
950C42—42no—
951C42—48no—
952C42C2×#4114yes—
953C42C2×#4114yes—
954C42H(5,𝔽2)14yes—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23C22×#4118yes—
969C23C2611yescharacteristic
970Q8—216no—
971Q8—44no—
972Q8—44no—
973Q8—48no—
974Q8—416no—
975Q8—816no—
976D4—216no—
977D4—216no—
978D4—48no—
979D4—44no—
980D4—816no—
981C2×C4—24no—
982C2×C4—21no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—24no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—28no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—28no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—28no—
1030C2×C4—24no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—48no—
1040C2×C4—416no—
1041C2×C4—48no—
1042C2×C4—84no—
1043C2×C4—88no—
1044C2×C4—816no—
1045C2×C4—88no—
1046C2×C4—816no—
1047C2×C4C22×#4112yes—
1048C2×C4C22×#4118yes—
1049C2×C4C22×#4112yes—
1050C2×C4C22×#4112yes—
1051C2×C4C22×#4112yes—
1052C2×C4C22×#4112yes—
1053C2×C4C22×#4112yes—
1054C2×C4C2×H(5,𝔽2)12yes—
1055C2×C4C2×H(5,𝔽2)12yes—
1056C2×C4C2×H(5,𝔽2)12yes—
1057C2×C4C2×2−1+414yes—
1058C2×C4C2×2−1+412yes—
1059C2×C4#58512yes—
1060C2×C4#58512yes—
1061C22—28no—
1062C22—28no—
1063C22—28no—
1064C22—44no—
1065C22—44no—
1066C22—44no—
1067C22—44no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22C23×#4111yescharacteristic
1076C22C23×#4111yescharacteristic
1077C22C22×H(5,𝔽2)11yescharacteristic
1078C22C22×2−1+411yescharacteristic
1079C22C2×#58511yescharacteristic
1080C22C2×#58511yescharacteristic
1081C222−1+611yescharacteristic
1082C4—22no—
1083C4—22no—
1084C4—24no—
1085C4—28no—
1086C4—22no—
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—42no—
1091C4—44no—
1092C4—41no—
1093C4—42no—
1094C4—42no—
1095C4—44no—
1096C4—44no—
1097C4—48no—
1098C4—42no—
1099C4—42no—
1100C4—44no—
1101C4—42no—
1102C4—42no—
1103C4#348214yes—
1104C4#351414yes—
1105C4#351414yes—
1106C2—48no—
1107C2—82no—
1108C2C2×#348211yescharacteristic
1109C2C2×#351411yescharacteristic
1110C2C2×#351411yescharacteristic
1111C2#6294611yescharacteristic
1112C2#6299111yescharacteristic
1113C2#6300711yescharacteristic
1114C2#6302511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59817C2semidirect
2. #59486C2semidirect
3. #59421C2semidirect
4. #59418C2semidirect
5. #59253C2semidirect
6. #59064C2semidirect
7. #45172C2semidirect
8. #43827C2semidirect
9. #40194C2semidirect
10. #40073C2semidirect
11. #39159C2semidirect
12. #38977C2semidirect
13. #36598C2semidirect
14. #36560C2semidirect
15. #36446C2semidirect
16. #36303C2semidirect
17. #36288C2semidirect
18. #36174C2semidirect
20. #35900C2semidirect
21. #34945C2semidirect
22. #34945C2semidirect
23. #34334C2semidirect
24. #34232C2semidirect
25. C4×#559C2semidirect
26. C4×#556C2semidirect
558. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598172
#594862
#594212
#594182
#592532
#590642
#451722
#438272
#401942
#400732
#391592
#389772
#365982
#365602
#364462
#363032
#362882
#361742
#361272
#359002
#349452
#343342
#342322
C4×#5592
C4×#5562