Finite Group Databasebeta

← #8110594

Subgroups — #8110594

Order 512.

4632 conjugacy classes of subgroups.

The subgroup lattice has 1147 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59828C211yesmaximal, characteristic, complemented
2#59828C211yesmaximal, characteristic, complemented
3#59827C211yesmaximal, characteristic, complemented
4#59821C211yesmaximal, characteristic, complemented
5#53377C214yesmaximal, complemented
6#53208C214yesmaximal, complemented
7#46347C214yesmaximal, complemented
8#46057C214yesmaximal, complemented
9#45656C214yesmaximal, complemented
10#39746C212yesmaximal, complemented
11#39744C212yesmaximal, complemented
12#39737C212yesmaximal, complemented
13#39726C212yesmaximal
14#39635C212yesmaximal, complemented
15#39633C212yesmaximal, complemented
16#39606C212yesmaximal, complemented
17#39599C212yesmaximal, complemented
18#39200C212yesmaximal, complemented
19#39127C212yesmaximal, complemented
20#38965C212yesmaximal, complemented
21#38923C212yesmaximal, complemented
22#37384C214yesmaximal, complemented
23#37369C214yesmaximal, complemented
24#37288C214yesmaximal, complemented
25#36645C211yesmaximal, characteristic, complemented
26#36635C211yesmaximal, characteristic, complemented
27#36631C211yesmaximal, characteristic
28C2×#559C2212yes—
29C2×#557C2212yes—
30C2×#557C2212yes—
31C2×#556C2212yes—
32C2×#533C2212yes—
33C2×#529C2212yes—
34#2868C2211yescharacteristic
35#2868C2211yescharacteristic
36#2864C2212yes—
37#2863C2212yes—
38#2863C2212yes—
39#2862C2211yescharacteristic
40#2862C2212yes—
41#2861C2212yes—
42#2860C2212yes—
43#2860C2212yes—
44#2859C2211yescharacteristic
45#2859C2211yescharacteristic
46#2859C2212yes—
47#2859C2212yes—
48#2858C2211yescharacteristic
49#2857C2212yes—
50#2857C2211yescharacteristic
51#2857C2211yescharacteristic
52#2857C2211yescharacteristic
53#2857C2211yescharacteristic
54#2857C2212yes—
55#2857C2211yescharacteristic
56#2857C2212yes—
57#2856C2211yescharacteristic
58#2855C2212yes—
59#2855C2212yes—
60#2854C2212yes—
61#2854C2212yes—
62#2851C2212yes—
63#2850C2212yes—
64#2831C2218yes—
65#2802C2218yes—
66#2802C2218yes—
67#2790C2218yes—
68#2783C2218yes—
69#2777C2218yes—
70#2773C2218yes—
71#2772C2218yes—
72#2768C2218yes—
73#2768C2218yes—
74#2754C2218yes—
75#2748C2218yes—
76#2744C2218yes—
77#2743C2218yes—
78#2741C2218yes—
79#2740C2218yes—
80#2738C2218yes—
81#2729C2218yes—
82#2727C2214yes—
83#2726C2218yes—
84#2726C2214yes—
85#2726C2214yes—
86#2725C2218yes—
87#2724C2214yes—
88#2722C2218yes—
89#2721C2218yes—
90#2721C2218yes—
91#2707C2218yes—
92#2707C2218yes—
93#2704C2218yes—
94#2704C2218yes—
95#2695C2218yes—
96#2694C2218yes—
97#2694C2218yes—
98#2681C2218yes—
99#2658C2214yes—
100#2647C2214yes—
101#2629C2214yes—
102#2629C2214yes—
103#2625C2214yes—
104#2620C2214yes—
105#2592C2214yes—
106#2584C2214yes—
107#2582C2212yes—
108#2582C2214yes—
109#2582C2212yes—
110#2582C2212yes—
111#2562C2214yes—
112#2552C2212yes—
113#2552C2212yes—
114#2548C2212yes—
115#2547C2214yes—
116#2547C2212yes—
117#2547C2212yes—
118#2546C2212yes—
119#2546C2214yes—
120#2546C2212yes—
121#2545C2214yes—
122#2545C2214yes—
123#2542C2212yes—
124#2538C2214yes—
125#2538C2214yes—
126#2538C2212yes—
127#2512C2214yes—
128#2511C2214yes—
129#2511C2214yes—
130#2507C2214yes—
131#2507C2214yes—
132#2506C2214yes—
133#2506C2214yes—
134#2502C2214yes—
135#2497C2214yes—
136#2492C2214yes—
137#2486C2214yes—
138#2485C2214yes—
139#2454C2214yes—
140#2454C2214yes—
141#2453C2214yes—
142#2453C2214yes—
143#2453C2214yes—
144#2453C2214yes—
145#2452C2214yes—
146#2451C2214yes—
147#2448C2214yes—
148#2448C2214yes—
149#2448C2214yes—
150#2447C2214yes—
151#2447C2214yes—
152#2446C2214yes—
153#2446C2214yes—
154#2441C2214yes—
155#2441C2214yes—
156#2440C2214yes—
157#2429C2214yes—
158#2429C2214yes—
159#2427C2214yes—
160#2426C2214yes—
161#2423C2214yes—
162#2423C2214yes—
163#2417C2214yes—
164#2415C2214yes—
165#2378C2218yes—
166#2365C2212yes—
167#2365C2212yes—
168#2354C2212yes—
169Q8×C4⋊C4C2212yes—
170Q8×C4⋊C4C2212yes—
171Q8×C4⋊C4C2212yes—
172D4×C4⋊C4C2212yes—
173D4×C4⋊C4C2212yes—
174#2327C2214yes—
175#2326C2214yes—
176#2324C2214yes—
177#2323C2214yes—
178#2323C2214yes—
179#2316C2214yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2212yes—
185C4×C4⋊Q8C2212yes—
186C4×C4⋊Q8C2211yescharacteristic
187C4×C4⋊Q8C2211yescharacteristic
188C4×#127C2211yescharacteristic
189C4×#125C2212yes—
190C4×#124C2212yes—
191C4×C22⋊Q8C2212yes—
192C4×C22⋊Q8C2212yes—
193C4×#121C2212yes—
194C4×#121C2212yes—
195#2295C2212yes—
196#2295C2212yes—
197#2293C2212yes—
198#2293C2212yes—
199#2285C2212yes—
200#2285C2212yes—
201#2283C2212yes—
202C2×C43C2211yescharacteristic
203#559—48no—
204#557—48no—
205#557—48no—
206#556—48no—
207#533—48no—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2314yes—
219C2×C4⋊Q8C2314yes—
220C2×#127C2311yescharacteristic
221#529—48no—
222C2×#126C2314yes—
223C2×#126C2318yes—
224C2×#125C2312yes—
225C2×#125C2314yes—
226C2×#125C2314yes—
227C2×#125C2314yes—
228C2×#125C2312yes—
229C2×#125C2318yes—
230C2×#125C2318yes—
231C2×#124C2312yes—
232C2×#124C2314yes—
233C2×#124C2312yes—
234C2×#124C2314yes—
235C2×#124C2314yes—
236C2×#123C2314yes—
237C2×#123C2318yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2318yes—
247C2×#121C2312yes—
248C2×#121C2312yes—
249C2×#121C2312yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2314yes—
258C2×C4×Q8C2314yes—
259C2×C4×Q8C2314yes—
260C2×C4×Q8C2314yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×#117C2314yes—
268C2×#117C2314yes—
269C2×#117C2314yes—
270C22×C4⋊C4C2314yes—
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#399C2318yes—
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#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2318yes—
311#397C2318yes—
312#396C2318yes—
313#396C2318yes—
314#396C2318yes—
315#396C2318yes—
316#396C2318yes—
317#396C2318yes—
318#396C2318yes—
319#396C2318yes—
320#396C2318yes—
321#395C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#393C2318yes—
326#391C2314yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2312yes—
332#391C2314yes—
333#391C2312yes—
334#391C2312yes—
335#391C2312yes—
336#391C2314yes—
337#391C2314yes—
338#391C2312yes—
339#391C2314yes—
340#391C2314yes—
341#391C2314yes—
342#391C2314yes—
343#391C2318yes—
344#391C2312yes—
345#391C2312yes—
346#391C2312yes—
347#391C2312yes—
348#391C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2312yes—
352#390C2314yes—
353#390C2318yes—
354#390C2314yes—
355#390C2312yes—
356#390C2312yes—
357#390C2312yes—
358#390C2312yes—
359#390C2312yes—
360#390C2312yes—
361#390C2312yes—
362#390C2314yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2314yes—
375#389C2314yes—
376#389C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#389C2314yes—
382#389C2314yes—
383#389C2312yes—
384#389C2314yes—
385#389C2318yes—
386#389C2314yes—
387#389C2318yes—
388#389C2318yes—
389#389C2314yes—
390#389C2318yes—
391#389C2314yes—
392#389C2312yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2312yes—
399#389C2318yes—
400#389C2312yes—
401#389C2312yes—
402#389C2312yes—
403#389C2312yes—
404#389C2312yes—
405#389C2312yes—
406#389C2312yes—
407#389C2312yes—
408#389C2312yes—
409#389C2314yes—
410#389C2318yes—
411#389C2318yes—
412#389C2318yes—
413#389C2314yes—
414#389C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2314yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2318yes—
433#388C2318yes—
434#387C2314yes—
435#387C2314yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2318yes—
449#387C2318yes—
450#387C2318yes—
451#387C2318yes—
452#387C2318yes—
453#386C2318yes—
454#386C2314yes—
455#386C2314yes—
456#385C2318yes—
457#385C2318yes—
458#385C2318yes—
459#385C2314yes—
460#385C2314yes—
461#385C2318yes—
462#385C2318yes—
463#384C2311yescharacteristic
464#384C2312yes—
465#384C2311yescharacteristic
466#384C2311yescharacteristic
467#384C2311yescharacteristic
468#384C2311yescharacteristic
469#384C2311yescharacteristic
470#384C2312yes—
471#384C2312yes—
472#384C2314yes—
473#384C2312yes—
474#384C2312yes—
475#384C2312yes—
476#384C2312yes—
477#384C2314yes—
478#384C2314yes—
479#383C2314yes—
480#382C2312yes—
481#382C2312yes—
482#382C2314yes—
483#382C2314yes—
484#382C2312yes—
485#382C2312yes—
486#381C2314yes—
487#381C2318yes—
488#380C2312yes—
489#380C2312yes—
490#380C2314yes—
491#380C2314yes—
492#380C2318yes—
493#380C2318yes—
494#380C2312yes—
495#380C2312yes—
496#380C2312yes—
497#380C2312yes—
498#380C2312yes—
499#380C2312yes—
500#380C2312yes—
501#380C2312yes—
502#380C2314yes—
503#380C2314yes—
504#380C2314yes—
505#380C2314yes—
506#380C2318yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2314yes—
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2312yes—
519C4×C4⋊C4C2312yes—
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2312yes—
522C4×C4⋊C4C2314yes—
523C4×C4⋊C4C2314yes—
524C4×C22⋊C4C2314yes—
525C4×C22⋊C4C2314yes—
526C4×C22⋊C4C2314yes—
527#376C2314yes—
528C43C2311yescharacteristic
529C43C2311yescharacteristic
530C43C2311yescharacteristic
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2311yescharacteristic
534C43C2311yescharacteristic
535C43C2311yescharacteristic
536C22×Q8C2412yes—
537C22×Q8C2412yes—
538C22×Q8C2412yes—
539C22×Q8C2412yes—
540C22×Q8C2412yes—
541C22×Q8C2414yes—
542C22×D4C2412yes—
543C22×D4C2412yes—
544C22×D4C2414yes—
545C22×D4C2412yes—
546C23×C4C2414yes—
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2411yescharacteristic
553C23×C4C2411yescharacteristic
554C23×C4C2418yes—
555C4⋊Q8—24no—
556C4⋊Q8—24no—
557C4⋊Q8—24no—
558C4⋊Q8—24no—
559C4⋊Q8—24no—
560C4⋊Q8—28no—
561C4⋊Q8—44no—
562C4⋊Q8—44no—
563C4⋊Q8—44no—
564C4⋊Q8—44no—
565C4⋊Q8—48no—
566C4⋊Q8—48no—
567#127—24no—
568#126—48no—
569#126—416no—
570#125—44no—
571#125—44no—
572#125—48no—
573#125—48no—
574#125—48no—
575#125—416no—
576#125—416no—
577#124—28no—
578#124—44no—
579#124—48no—
580#124—48no—
581#124—48no—
582#123—48no—
583#123—416no—
584C22⋊Q8—28no—
585C22⋊Q8—416no—
586C22⋊Q8—48no—
587C22⋊Q8—44no—
588C22⋊Q8—48no—
589C22⋊Q8—44no—
590C22⋊Q8—44no—
591C22⋊Q8—44no—
592C22⋊Q8—48no—
593#121—28no—
594#121—44no—
595#121—44no—
596C4×Q8—28no—
597C4×Q8—28no—
598C4×Q8—28no—
599C4×Q8—28no—
600C4×Q8—28no—
601C4×Q8—48no—
602C4×Q8—48no—
603C4×Q8—48no—
604C4×Q8—48no—
605C4×Q8—48no—
606C4×Q8—48no—
607C4×D4—28no—
608C4×D4—28no—
609C4×D4—48no—
610C4×D4—48no—
611C4×D4—44no—
612C4×D4—48no—
613#117—48no—
614#117—48no—
615#117—48no—
616C2×C4⋊C4—48no—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2412yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C42—24no—
700C2×C42—24no—
701C2×C42—24no—
702C2×C42—24no—
703C2×C42—24no—
704C2×C42—42no—
705C2×C42—42no—
706C2×C42C2411yescharacteristic
707C2×C42C2414yes—
708C2×C42C2414yes—
709C2×C42C2414yes—
710C2×C42C2411yescharacteristic
711C2×C42C2414yes—
712C2×C42C2411yescharacteristic
713C2×C42C2414yes—
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2418yes—
732C2×C42C2418yes—
733C2×C42C2418yes—
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2418yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2418yes—
773#95C2418yes—
774#95C2418yes—
775#95C2418yes—
776#95C2418yes—
777#95C2418yes—
778#95C2418yes—
779#95C2418yes—
780C24C2514yes—
781C24C2511yescharacteristic
782C2×Q8—24no—
783C2×Q8—24no—
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—24no—
794C2×Q8—24no—
795C2×Q8—24no—
796C2×Q8—24no—
797C2×Q8—28no—
798C2×Q8—44no—
799C2×Q8—44no—
800C2×D4—28no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—44no—
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—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—28no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—28no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—48no—
836C22×C4—48no—
837C22×C4—48no—
838C22×C42−1+414yes—
839C22×C4C2511yescharacteristic
840C22×C4C2514yes—
841C22×C4C2511yescharacteristic
842C22×C4C2511yescharacteristic
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2514yes—
847C22×C4C2514yes—
848C22×C4C2514yes—
849C22×C4C2511yescharacteristic
850C22×C4C2514yes—
851C22×C4C2514yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C22×C4C2511yescharacteristic
862C22×C4C2511yescharacteristic
863C22×C4C2511yescharacteristic
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—28no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—28no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—28no—
894C4⋊C4—24no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—42no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—48no—
905C4⋊C4—44no—
906C4⋊C4—48no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—42no—
911C4⋊C4—44no—
912C4⋊C4—48no—
913C4⋊C4—48no—
914C4⋊C4—48no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—44no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—44no—
921C4⋊C4—42no—
922C4⋊C4—44no—
923C4⋊C4—42no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—44no—
941C22⋊C4—48no—
942C22⋊C4—44no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C42—22no—
947C42—22no—
948C42—22no—
949C42—22no—
950C42—22no—
951C42—22no—
952C42—28no—
953C42—28no—
954C42—28no—
955C42—28no—
956C42—28no—
957C42—22no—
958C42—22no—
959C42—22no—
960C42—22no—
961C42—22no—
962C42—22no—
963C42—22no—
964C42—22no—
965C42—22no—
966C42—22no—
967C42—22no—
968C42—22no—
969C42—22no—
970C42—22no—
971C42—41no—
972C42—41no—
973C42—41no—
974C42—41no—
975C42—48no—
976C42—48no—
977C42—48no—
978C42H(5,𝔽2)14yes—
979C42H(5,𝔽2)14yes—
980C422−1+414yes—
981C422−1+414yes—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—21no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23C2×2−1+412yes—
996C23C2611yescharacteristic
997Q8—48no—
998Q8—48no—
999Q8—48no—
1000Q8—48no—
1001Q8—48no—
1002Q8—88no—
1003D4—48no—
1004D4—48no—
1005D4—84no—
1006D4—88no—
1007C2×C4—21no—
1008C2×C4—21no—
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—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—28no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
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—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—44no—
1068C2×C4—44no—
1069C2×C4—44no—
1070C2×C4—44no—
1071C2×C4—44no—
1072C2×C4—44no—
1073C2×C4—416no—
1074C2×C4—168no—
1075C2×C4C2×H(5,𝔽2)12yes—
1076C2×C4C2×H(5,𝔽2)12yes—
1077C2×C4C2×H(5,𝔽2)12yes—
1078C2×C4C2×H(5,𝔽2)12yes—
1079C2×C4C2×H(5,𝔽2)12yes—
1080C2×C4C2×H(5,𝔽2)12yes—
1081C2×C4C2×2−1+412yes—
1082C2×C4C2×2−1+412yes—
1083C2×C4C2×2−1+412yes—
1084C2×C4C2×2−1+412yes—
1085C2×C4C2×2−1+412yes—
1086C2×C4C2×2−1+412yes—
1087C2×C4C2×2−1+412yes—
1088C2×C4C2×2−1+412yes—
1089C2×C4#58512yes—
1090C2×C4#58512yes—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—41no—
1095C22—41no—
1096C22—41no—
1097C22—41no—
1098C22—44no—
1099C22—44no—
1100C22—44no—
1101C22—44no—
1102C22—44no—
1103C22—44no—
1104C22—44no—
1105C22C22×H(5,𝔽2)11yescharacteristic
1106C22C22×H(5,𝔽2)11yescharacteristic
1107C22C22×2−1+411yescharacteristic
1108C22C22×2−1+411yescharacteristic
1109C22C22×2−1+411yescharacteristic
1110C22C2×#58511yescharacteristic
1111C22C2×#58511yescharacteristic
1112C4—22no—
1113C4—22no—
1114C4—22no—
1115C4—22no—
1116C4—22no—
1117C4—22no—
1118C4—22no—
1119C4—44no—
1120C4—41no—
1121C4—44no—
1122C4—44no—
1123C4—41no—
1124C4—44no—
1125C4—44no—
1126C4—44no—
1127C4—44no—
1128C4—44no—
1129C4—44no—
1130C4—44no—
1131C4—41no—
1132C4—44no—
1133C4—41no—
1134C4#354814yes—
1135C4#355214yes—
1136C4#355414yes—
1137C2—42no—
1138C2—84no—
1139C2C2×#355211yescharacteristic
1140C2C2×#355411yescharacteristic
1141C2C2×#354811yescharacteristic
1142C2#6283011yescharacteristic
1143C2#6283511yescharacteristic
1144C2#6283711yescharacteristic
1145C2#6283711yescharacteristic
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. #59828C2semidirect
2. #59828C2semidirect
3. #59827C2semidirect
4. #59821C2semidirect
5. #53377C2semidirect
6. #53208C2semidirect
7. #46347C2semidirect
8. #46057C2semidirect
9. #45656C2semidirect
10. #39746C2semidirect
11. #39744C2semidirect
12. #39737C2semidirect
14. #39635C2semidirect
15. #39633C2semidirect
16. #39606C2semidirect
17. #39599C2semidirect
18. #39200C2semidirect
19. #39127C2semidirect
20. #38965C2semidirect
21. #38923C2semidirect
22. #37384C2semidirect
23. #37369C2semidirect
24. #37288C2semidirect
25. #36645C2semidirect
26. #36635C2semidirect

Maximal subgroups

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

subgroupindex
#598282
#598272
#598212
#533772
#532082
#463472
#460572
#456562
#397462
#397442
#397372
#397262
#396352
#396332
#396062
#395992
#392002
#391272
#389652
#389232
#373842
#373692
#372882
#366452
#366352
#366312