Finite Group Databasebeta

← #7987165

Subgroups — #7987165

Order 512.

4643 conjugacy classes of subgroups.

The subgroup lattice has 1097 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59828C211yesmaximal, characteristic, complemented
2#59660C212yesmaximal
3#59321C212yesmaximal, complemented
4#59305C212yesmaximal, complemented
5#49148C218yesmaximal, complemented
6#46116C214yesmaximal, complemented
7#45331C214yesmaximal, complemented
8#45220C214yesmaximal, complemented
9#42921C214yesmaximal, complemented
10#42772C214yesmaximal, complemented
11#40048C214yesmaximal, complemented
12#39478C212yesmaximal, complemented
13#39173C212yesmaximal, complemented
14#38943C212yesmaximal, complemented
15#38923C212yesmaximal, complemented
16#36598C211yesmaximal, characteristic, complemented
17#36562C212yesmaximal, complemented
18#36449C212yesmaximal, complemented
19#36180C211yesmaximal, characteristic, complemented
20#36180C211yesmaximal, characteristic, complemented
21#35286C212yesmaximal, complemented
22#35208C212yesmaximal, complemented
23#34945C211yesmaximal, characteristic, complemented
24#34932C211yesmaximal, characteristic
25#34384C212yesmaximal, complemented
26C4×#556C211yesmaximal, characteristic, complemented
27C2×#557C2212yes—
28C2×#556C2211yescharacteristic
29C2×#554C2212yes—
30C2×#554C2212yes—
31C2×#529C2212yes—
32#2868C2211yescharacteristic
33#2863C2214yes—
34#2862C2212yes—
35#2859C2214yes—
36#2859C2214yes—
37#2857C2212yes—
38#2857C2212yes—
39#2839C2218yes—
40#2791C2218yes—
41#2790C2218yes—
42#2787C2218yes—
43#2782C2218yes—
44#2770C2218yes—
45#2770C2218yes—
46#2769C2218yes—
47#2767C2218yes—
48#2766C2218yes—
49#2747C2218yes—
50#2744C2218yes—
51#2728C2218yes—
52#2726C2214yes—
53#2722C2218yes—
54#2695C2218yes—
55#2690C2218yes—
56#2690C2218yes—
57#2666C2218yes—
58#2652C2218yes—
59#2647C2218yes—
60#2642C2214yes—
61#2625C2214yes—
62#2582C2212yes—
63#2582C2212yes—
64#2579C2218yes—
65#2578C2218yes—
66#2573C2214yes—
67#2571C2214yes—
68#2571C2212yes—
69#2571C2211yescharacteristic
70#2570C2214yes—
71#2568C2211yescharacteristic
72#2568C2212yes—
73#2567C2212yes—
74#2567C2212yes—
75#2566C2214yes—
76#2565C2214yes—
77#2565C2214yes—
78#2556C2218yes—
79#2556C2218yes—
80#2553C2214yes—
81#2552C2214yes—
82#2552C2212yes—
83#2552C2212yes—
84#2552C2212yes—
85#2552C2212yes—
86#2552C2211yescharacteristic
87#2552C2212yes—
88#2547C2211yescharacteristic
89#2547C2214yes—
90#2547C2211yescharacteristic
91#2546C2212yes—
92#2542C2211yescharacteristic
93#2538C2211yescharacteristic
94#2537C2211yescharacteristic
95#2536C2218yes—
96#2530C2218yes—
97#2514C2212yes—
98#2511C2214yes—
99#2511C2214yes—
100#2511C2214yes—
101#2508C2214yes—
102#2507C2214yes—
103#2506C2214yes—
104#2506C2214yes—
105#2502C2214yes—
106#2502C2214yes—
107#2502C2214yes—
108#2497C2214yes—
109#2496C2212yes—
110#2495C2214yes—
111#2494C2212yes—
112#2489C2214yes—
113#2489C2214yes—
114#2489C2212yes—
115#2485C2214yes—
116#2473C2218yes—
117#2462C2218yes—
118#2460C2218yes—
119#2453C2214yes—
120#2453C2214yes—
121#2447C2212yes—
122#2446C2214yes—
123#2446C2214yes—
124#2442C2214yes—
125#2442C2214yes—
126#2442C2214yes—
127#2442C2214yes—
128#2442C2218yes—
129#2440C2214yes—
130#2440C2214yes—
131#2440C2214yes—
132#2440C2214yes—
133#2429C2214yes—
134#2429C2214yes—
135#2427C2214yes—
136#2427C2214yes—
137#2427C2212yes—
138#2422C2212yes—
139#2421C2214yes—
140#2421C2214yes—
141#2421C2212yes—
142#2417C2214yes—
143#2401C2214yes—
144#2395C2214yes—
145#2383C2218yes—
146#2373C2214yes—
147#2367C2212yes—
148#2365C2212yes—
149#2365C2211yescharacteristic
150#2365C2212yes—
151#2362C2212yes—
152#2361C2214yes—
153#2361C2214yes—
154#2360C2214yes—
155#2360C2214yes—
156#2356C2212yes—
157#2355C2212yes—
158#2355C2212yes—
159#2355C2211yescharacteristic
160#2354C2211yescharacteristic
161#2352C2214yes—
162Q8×C4⋊C4C2212yes—
163D4×C4⋊C4C2212yes—
164D4×C4⋊C4C2214yes—
165D4×C4⋊C4C2212yes—
166D4×C4⋊C4C2212yes—
167D4×C4⋊C4C2212yes—
168#2347C2212yes—
169#2345C2214yes—
170#2330C2214yes—
171#2326C2214yes—
172#2322C2218yes—
173#2320C2214yes—
174#2317C2214yes—
175#2316C2214yes—
176#2314C2214yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×#126C2214yes—
182C4×#124C2212yes—
183C4×#124C2212yes—
184C4×#124C2214yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×#121C2212yes—
189#2295C2212yes—
190#2285C2212yes—
191C2×#384C2212yes—
192C2×#384C2212yes—
193#2283C2212yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2212yes—
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199#557—48no—
200#556—28no—
201#554—48no—
202#554—48no—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2312yes—
210#529—216no—
211C2×#126C2314yes—
212C2×#126C2314yes—
213C2×#125C2312yes—
214C2×#125C2314yes—
215C2×#125C2314yes—
216C2×#125C2314yes—
217C2×#125C2318yes—
218C2×#125C2318yes—
219C2×#124C2312yes—
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×#123C2314yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2318yes—
230C2×C22⋊Q8C2318yes—
231C2×#121C2312yes—
232C2×#121C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2314yes—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2314yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2318yes—
253C2×C4×D4C2311yescharacteristic
254C2×#117C2314yes—
255C2×#117C2312yes—
256C2×#117C2312yes—
257C22×C4⋊C4C2314yes—
258C22×C4⋊C4C2314yes—
259C22×C4⋊C4C2314yes—
260C22×C4⋊C4C2314yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2314yes—
263C22×C42C2312yes—
264C22×C42C2312yes—
265#401C2314yes—
266#400C2318yes—
267#400C2314yes—
268#400C2314yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2314yes—
273#400C2314yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#399C2314yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2314yes—
296#398C2318yes—
297#398C2318yes—
298#397C2314yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2314yes—
303#397C2314yes—
304#397C2314yes—
305#397C2314yes—
306#397C2318yes—
307#397C2314yes—
308#396C2318yes—
309#396C2318yes—
310#396C2314yes—
311#395C2318yes—
312#395C2318yes—
313#394C2318yes—
314#394C2314yes—
315#394C2314yes—
316#391C2314yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2312yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2312yes—
328#391C2312yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2312yes—
334#391C2312yes—
335#391C2312yes—
336#390C2312yes—
337#390C2312yes—
338#390C2312yes—
339#389C2312yes—
340#389C2314yes—
341#389C2312yes—
342#389C2314yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2312yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2312yes—
356#389C2318yes—
357#389C2318yes—
358#389C2318yes—
359#389C2318yes—
360#389C2318yes—
361#389C2312yes—
362#389C2318yes—
363#389C2314yes—
364#389C2314yes—
365#389C2318yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2312yes—
370#389C2318yes—
371#389C2312yes—
372#389C2314yes—
373#389C2312yes—
374#388C2314yes—
375#388C2314yes—
376#388C2314yes—
377#388C2318yes—
378#388C2318yes—
379#388C2314yes—
380#388C2314yes—
381#388C2318yes—
382#388C2318yes—
383#388C2314yes—
384#388C2318yes—
385#388C2314yes—
386#388C2318yes—
387#388C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2314yes—
399#387C2314yes—
400#387C2314yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2314yes—
409#387C2318yes—
410#387C2314yes—
411#386C2318yes—
412#386C2314yes—
413#386C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2314yes—
419#385C2318yes—
420#385C2318yes—
421#385C2314yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2314yes—
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2312yes—
431#384C2314yes—
432#384C2314yes—
433#384C2314yes—
434#384C2312yes—
435#384C2312yes—
436#384C2314yes—
437#384C2314yes—
438#384C2312yes—
439#384C2312yes—
440#384C2312yes—
441#384C2314yes—
442#384C2314yes—
443#383C2314yes—
444#383C2314yes—
445#383C2318yes—
446#382C2312yes—
447#382C2314yes—
448#382C2312yes—
449#382C2314yes—
450#382C2314yes—
451#382C2312yes—
452#382C2318yes—
453#382C2312yes—
454#382C2314yes—
455#382C2318yes—
456#381C2314yes—
457#380C2312yes—
458#380C2314yes—
459#380C2318yes—
460#380C2318yes—
461#380C2314yes—
462#380C2318yes—
463#380C2312yes—
464#380C2318yes—
465#380C2314yes—
466#380C2314yes—
467#380C2312yes—
468#380C2312yes—
469#380C2312yes—
470#380C2312yes—
471#380C2314yes—
472#380C2312yes—
473#380C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C22⋊C4C2312yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519#376C2314yes—
520#376C2314yes—
521C43C2314yes—
522C43C2311yescharacteristic
523C43C2312yes—
524C22×Q8C2411yescharacteristic
525C22×Q8C2412yes—
526C22×Q8C2412yes—
527C22×Q8C2412yes—
528C22×Q8C2414yes—
529C22×D4C2414yes—
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2418yes—
539C23×C4C2418yes—
540C4⋊Q8—24no—
541C4⋊Q8—28no—
542C4⋊Q8—24no—
543C4⋊Q8—24no—
544C4⋊Q8—44no—
545C4⋊Q8—48no—
546C4⋊Q8—82no—
547#126—216no—
548#126—216no—
549#125—28no—
550#125—48no—
551#125—48no—
552#125—48no—
553#125—416no—
554#125—88no—
555#124—28no—
556#124—28no—
557#124—28no—
558#123—216no—
559C22⋊Q8—28no—
560C22⋊Q8—28no—
561C22⋊Q8—28no—
562C22⋊Q8—416no—
563C22⋊Q8—416no—
564C22⋊Q8—44no—
565C22⋊Q8—48no—
566C22⋊Q8—48no—
567#121—28no—
568#121—28no—
569C4×Q8—28no—
570C4×Q8—28no—
571C4×Q8—28no—
572C4×Q8—24no—
573C4×Q8—28no—
574C4×Q8—28no—
575C4×Q8—24no—
576C4×Q8—42no—
577C4×Q8—48no—
578C4×Q8—48no—
579C4×Q8—84no—
580C4×D4—24no—
581C4×D4—216no—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—48no—
587C4×D4—48no—
588C4×D4—88no—
589C4×D4#4118yes—
590#117—216no—
591#117—28no—
592#117—44no—
593C2×C4⋊C4—48no—
594C2×C4⋊C4—48no—
595C2×C4⋊C4—48no—
596C2×C4⋊C4—48no—
597C2×C4⋊C4—84no—
598C2×C4⋊C4—84no—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2412yes—
679C2×C42—28no—
680C2×C42—28no—
681C2×C42C2412yes—
682C2×C42C2414yes—
683C2×C42C2414yes—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2412yes—
689C2×C42C2411yescharacteristic
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2414yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2414yes—
700C2×C42C2418yes—
701C2×C42C2418yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2414yes—
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709#95C2412yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2412yes—
718#95C2412yes—
719#95C2412yes—
720#95C2412yes—
721#95C2412yes—
722#95C2412yes—
723#95C2414yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2418yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2412yes—
737#95C2412yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2418yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750#95C2414yes—
751#95C2414yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757C24C2512yes—
758C24C2512yes—
759C2×Q8—22no—
760C2×Q8—24no—
761C2×Q8—24no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—28no—
766C2×Q8—24no—
767C2×Q8—22no—
768C2×Q8—24no—
769C2×Q8—24no—
770C2×Q8—24no—
771C2×Q8—22no—
772C2×Q8—44no—
773C2×Q8—44no—
774C2×D4—28no—
775C2×D4—28no—
776C2×D4—22no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—22no—
780C2×D4—44no—
781C2×D4C2×#4114yes—
782C2×D42−1+414yes—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—48no—
801C22×C4—48no—
802C22×C4—48no—
803C22×C4—48no—
804C22×C4—48no—
805C22×C4—48no—
806C22×C4C2×#4118yes—
807C22×C4C2512yes—
808C22×C4C2511yescharacteristic
809C22×C4C2512yes—
810C22×C4C2512yes—
811C22×C4C2514yes—
812C22×C4C2512yes—
813C22×C4C2512yes—
814C22×C4C2514yes—
815C22×C4C2512yes—
816C22×C4C2512yes—
817C22×C4C2514yes—
818C22×C4C2514yes—
819C22×C4C2512yes—
820C22×C4C2518yes—
821C22×C4C2514yes—
822C22×C4C2514yes—
823C22×C4C2512yes—
824C22×C4C2511yescharacteristic
825C22×C4C2511yescharacteristic
826C22×C4C2511yescharacteristic
827C22×C4C2512yes—
828C22×C4C2511yescharacteristic
829C22×C4C2511yescharacteristic
830C22×C4C2511yescharacteristic
831C4⋊C4—22no—
832C4⋊C4—28no—
833C4⋊C4—24no—
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—24no—
837C4⋊C4—28no—
838C4⋊C4—28no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—28no—
844C4⋊C4—28no—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—28no—
848C4⋊C4—28no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—24no—
855C4⋊C4—28no—
856C4⋊C4—24no—
857C4⋊C4—28no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—28no—
863C4⋊C4—22no—
864C4⋊C4—48no—
865C4⋊C4—48no—
866C4⋊C4—48no—
867C4⋊C4—48no—
868C4⋊C4—42no—
869C4⋊C4—42no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—48no—
875C4⋊C4—42no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—42no—
879C4⋊C4—48no—
880C4⋊C4—44no—
881C4⋊C4—48no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4C2×#4114yes—
888C4⋊C42−1+414yes—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—24no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—24no—
900C22⋊C4—24no—
901C22⋊C4—24no—
902C22⋊C4—24no—
903C22⋊C4—28no—
904C22⋊C4—44no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4C2×#4118yes—
911C42—24no—
912C42—24no—
913C42—24no—
914C42—28no—
915C42—28no—
916C42—24no—
917C42—28no—
918C42—28no—
919C42—24no—
920C42—24no—
921C42—24no—
922C42—22no—
923C42—22no—
924C42—24no—
925C42—28no—
926C42—24no—
927C42—24no—
928C42—22no—
929C42—44no—
930C42—48no—
931C42—42no—
932C42—48no—
933C42—42no—
934C42—44no—
935C42—41no—
936C42C2×#4114yes—
937C42H(5,𝔽2)14yes—
938C422−1+414yes—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23C22×#4114yes—
952C23C2×2−1+414yes—
953C23C2611yescharacteristic
954Q8—48no—
955Q8—48no—
956Q8—44no—
957Q8—48no—
958Q8—88no—
959D4—28no—
960D4—28no—
961D4—416no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—21no—
969C2×C4—22no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—216no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—28no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—21no—
993C2×C4—22no—
994C2×C4—21no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—21no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—28no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—28no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—48no—
1022C2×C4—48no—
1023C2×C4—48no—
1024C2×C4—48no—
1025C2×C4—48no—
1026C2×C4—168no—
1027C2×C4—168no—
1028C2×C4C22×#4112yes—
1029C2×C4C22×#4114yes—
1030C2×C4C22×#4112yes—
1031C2×C4C22×#4112yes—
1032C2×C4C2×H(5,𝔽2)12yes—
1033C2×C4C2×H(5,𝔽2)12yes—
1034C2×C4C2×H(5,𝔽2)12yes—
1035C2×C4C2×2−1+412yes—
1036C2×C4C2×2−1+414yes—
1037C2×C4C2×2−1+412yes—
1038C2×C4C2×2−1+412yes—
1039C2×C4C2×2−1+412yes—
1040C2×C4C2×2−1+412yes—
1041C2×C4#58512yes—
1042C22—24no—
1043C22—24no—
1044C22—24no—
1045C22—24no—
1046C22—24no—
1047C22—24no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22C23×#4111yescharacteristic
1057C22C22×H(5,𝔽2)11yescharacteristic
1058C22C22×2−1+411yescharacteristic
1059C22C22×2−1+411yescharacteristic
1060C22C22×2−1+411yescharacteristic
1061C22C2×#58511yescharacteristic
1062C22H(7,𝔽2)11yescharacteristic
1063C4—22no—
1064C4—24no—
1065C4—22no—
1066C4—24no—
1067C4—22no—
1068C4—42no—
1069C4—42no—
1070C4—44no—
1071C4—42no—
1072C4—44no—
1073C4—42no—
1074C4—41no—
1075C4—42no—
1076C4—42no—
1077C4—42no—
1078C4—44no—
1079C4—44no—
1080C4—42no—
1081C4—44no—
1082C4—44no—
1083C4—48no—
1084C4#351114yes—
1085C4#351514yes—
1086C4#355214yes—
1087C2—44no—
1088C2—44no—
1089C2C2×#355211yescharacteristic
1090C2C2×#351511yescharacteristic
1091C2C2×#351111yescharacteristic
1092C2#6294511yescharacteristic
1093C2#6296111yescharacteristic
1094C2#6300011yescharacteristic
1095C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2537C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59828C2semidirect
3. #59321C2semidirect
4. #59305C2semidirect
5. #49148C2semidirect
6. #46116C2semidirect
7. #45331C2semidirect
8. #45220C2semidirect
9. #42921C2semidirect
10. #42772C2semidirect
11. #40048C2semidirect
12. #39478C2semidirect
13. #39173C2semidirect
14. #38943C2semidirect
15. #38923C2semidirect
16. #36598C2semidirect
17. #36562C2semidirect
18. #36449C2semidirect
19. #36180C2semidirect
20. #36180C2semidirect
21. #35286C2semidirect
22. #35208C2semidirect
23. #34945C2semidirect
25. #34384C2semidirect
26. C4×#556C2semidirect

Maximal subgroups

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

subgroupindex
#598282
#596602
#593212
#593052
#491482
#461162
#453312
#452202
#429212
#427722
#400482
#394782
#391732
#389432
#389232
#365982
#365622
#364492
#361802
#352862
#352082
#349452
#349322
#343842
C4×#5562