Finite Group Databasebeta

← #7654874

Subgroups — #7654874

Order 512.

5080 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42946C214yesmaximal, complemented
2#42089C218yesmaximal, complemented
3#39432C214yesmaximal, complemented
4#39377C212yesmaximal, complemented
5#39192C212yesmaximal, complemented
6#39157C212yesmaximal, complemented
7#39056C214yesmaximal, complemented
8#38941C212yesmaximal, complemented
9#37968C214yesmaximal, complemented
10#37758C214yesmaximal, complemented
11#37640C211yesmaximal, characteristic, complemented
12#37631C212yesmaximal, complemented
13#36564C212yesmaximal, complemented
14#36453C212yesmaximal, complemented
15#36194C212yesmaximal, complemented
16#36117C212yesmaximal, complemented
17#35989C214yesmaximal, complemented
18#35275C211yesmaximal, characteristic, complemented
19#35273C211yesmaximal, characteristic
20#35176C212yesmaximal, complemented
21#35170C212yesmaximal, complemented
22#34979C211yesmaximal, characteristic, complemented
23#34932C212yesmaximal, complemented
24#34214C211yesmaximal, characteristic, complemented
25#34155C211yesmaximal, characteristic, complemented
26#34127C211yesmaximal, characteristic, complemented
27C2×#544C2212yes—
28C2×#542C2214yes—
29C2×#537C2212yes—
30C2×#533C2211yescharacteristic
31C2×#532C2211yescharacteristic
32C2×#529C2214yes—
33C2×C4×#41C2211yescharacteristic
34#2868C2212yes—
35#2859C2212yes—
36#2857C2214yes—
37#2857C2214yes—
38#2857C2212yes—
39#2856C2212yes—
40#2855C2214yes—
41#2854C2214yes—
42#2838C2218yes—
43#2820C2214yes—
44#2772C2218yes—
45#2762C2218yes—
46#2746C2218yes—
47#2737C2218yes—
48#2725C2218yes—
49#2723C2218yes—
50#2718C2218yes—
51#2708C2218yes—
52#2689C2218yes—
53#2686C2218yes—
54#2681C2218yes—
55#2674C2218yes—
56#2667C2218yes—
57#2663C2218yes—
58#2660C2214yes—
59#2650C2218yes—
60#2645C2214yes—
61#2640C2214yes—
62#2628C2214yes—
63#2625C2214yes—
64#2624C2214yes—
65#2620C2214yes—
66#2620C2214yes—
67#2616C2214yes—
68#2611C2214yes—
69#2597C2218yes—
70#2586C2218yes—
71#2576C2218yes—
72#2571C2214yes—
73#2568C2211yescharacteristic
74#2567C2212yes—
75#2563C2214yes—
76#2559C2218yes—
77#2553C2218yes—
78#2552C2212yes—
79#2552C2212yes—
80#2551C2212yes—
81#2551C2212yes—
82#2549C2218yes—
83#2548C2212yes—
84#2547C2212yes—
85#2547C2211yescharacteristic
86#2546C2211yescharacteristic
87#2542C2212yes—
88#2542C2211yescharacteristic
89#2538C2212yes—
90#2538C2212yes—
91#2538C2212yes—
92#2538C2212yes—
93#2537C2212yes—
94#2537C2212yes—
95#2522C2218yes—
96#2521C2218yes—
97#2513C2214yes—
98#2512C2214yes—
99#2509C2214yes—
100#2507C2214yes—
101#2507C2214yes—
102#2501C2214yes—
103#2499C2212yes—
104#2497C2218yes—
105#2496C2214yes—
106#2496C2214yes—
107#2496C2214yes—
108#2494C2214yes—
109#2494C2214yes—
110#2492C2214yes—
111#2492C2214yes—
112#2491C2214yes—
113#2491C2214yes—
114#2489C2214yes—
115#2479C2218yes—
116#2477C2218yes—
117#2460C2218yes—
118#2454C2214yes—
119#2451C2214yes—
120#2448C2214yes—
121#2440C2214yes—
122#2440C2214yes—
123#2440C2214yes—
124#2439C2218yes—
125#2432C2212yes—
126#2429C2214yes—
127#2427C2214yes—
128#2427C2218yes—
129#2427C2214yes—
130#2425C2218yes—
131#2423C2214yes—
132#2422C2214yes—
133#2420C2214yes—
134#2416C2214yes—
135#2416C2214yes—
136#2415C2212yes—
137#2415C2212yes—
138#2395C2218yes—
139#2395C2214yes—
140#2372C2214yes—
141#2369C2214yes—
142#2369C2211yescharacteristic
143#2369C2211yescharacteristic
144#2366C2211yescharacteristic
145#2366C2211yescharacteristic
146#2363C2212yes—
147#2363C2212yes—
148#2363C2212yes—
149#2363C2212yes—
150#2361C2214yes—
151#2360C2214yes—
152#2360C2214yes—
153#2355C2211yescharacteristic
154#2355C2212yes—
155#2355C2211yescharacteristic
156#2355C2212yes—
157#2354C2214yes—
158#2352C2212yes—
159#2352C2212yes—
160Q8×C4⋊C4C2212yes—
161Q8×C4⋊C4C2212yes—
162D4×C4⋊C4C2211yescharacteristic
163D4×C4⋊C4C2211yescharacteristic
164#2347C2212yes—
165#2345C2214yes—
166#2343C2214yes—
167#2339C2212yes—
168#2330C2214yes—
169#2330C2214yes—
170#2323C2214yes—
171#2319C2214yes—
172#2317C2212yes—
173#2317C2212yes—
174#2311C2212yes—
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×#124C2212yes—
179C4×C22⋊Q8C2212yes—
180C4×C22⋊Q8C2212yes—
181C4×C22⋊Q8C2214yes—
182C4×#121C2214yes—
183#2297C2214yes—
184#2295C2212yes—
185#2293C2212yes—
186#2293C2212yes—
187#2290C2214yes—
188#2285C2211yescharacteristic
189#2285C2214yes—
190C2×#384C2211yescharacteristic
191#2283C2212yes—
192#2274C2212yes—
193C42×D4C2212yes—
194C42×D4C2212yes—
195C42×D4C2212yes—
196C4×#117C2211yescharacteristic
197C4×#117C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2311yescharacteristic
200C22×#41C2312yes—
201#544—48no—
202#542—416no—
203#537—48no—
204#533—28no—
205#532—28no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×#127C2311yescharacteristic
215#529—416no—
216C2×#126C2318yes—
217C2×#126C2318yes—
218C2×#125C2312yes—
219C2×#125C2314yes—
220C2×#125C2314yes—
221C2×#124C2312yes—
222C2×#124C2312yes—
223C2×#124C2314yes—
224C2×#124C2318yes—
225C2×#123C2318yes—
226C2×#123C2318yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2318yes—
236C2×C22⋊Q8C2318yes—
237C2×#121C2312yes—
238C2×#121C2312yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C2×#121C2314yes—
242C2×#121C2314yes—
243C2×#121C2318yes—
244C4×#41—28no—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2312yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2318yes—
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C2×#117C2312yes—
267C2×#117C2312yes—
268C2×#117C2311yescharacteristic
269C2×#117C2311yescharacteristic
270C2×#117C2311yescharacteristic
271C2×#117C2312yes—
272C2×#117C2314yes—
273C2×#117C2318yes—
274C22×C4⋊C4C2312yes—
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2312yes—
277C22×C4⋊C4C2312yes—
278C22×C4⋊C4C2312yes—
279C22×C42C2312yes—
280C22×C42C2314yes—
281C22×C42C2314yes—
282C22×C42C2311yescharacteristic
283#401C2318yes—
284#400C2314yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#399C2318yes—
291#399C2318yes—
292#399C2314yes—
293#399C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2314yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2314yes—
305#397C2318yes—
306#397C2314yes—
307#397C2318yes—
308#397C2314yes—
309#397C2318yes—
310#396C2318yes—
311#396C2318yes—
312#396C2318yes—
313#396C2318yes—
314#396C2318yes—
315#395C2318yes—
316#395C2318yes—
317#395C2318yes—
318#395C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2314yes—
325#394C2314yes—
326#394C2318yes—
327#394C2318yes—
328#393C2318yes—
329#393C2318yes—
330#393C2318yes—
331#391C2312yes—
332#391C2312yes—
333#391C2314yes—
334#391C2314yes—
335#391C2314yes—
336#391C2314yes—
337#391C2312yes—
338#391C2312yes—
339#391C2314yes—
340#391C2318yes—
341#391C2312yes—
342#391C2312yes—
343#391C2312yes—
344#391C2314yes—
345#391C2318yes—
346#390C2314yes—
347#390C2314yes—
348#390C2314yes—
349#390C2314yes—
350#390C2314yes—
351#390C2314yes—
352#390C2312yes—
353#390C2314yes—
354#390C2314yes—
355#390C2312yes—
356#390C2312yes—
357#390C2312yes—
358#390C2312yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2318yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2312yes—
372#389C2318yes—
373#389C2314yes—
374#389C2312yes—
375#389C2318yes—
376#389C2314yes—
377#389C2318yes—
378#389C2318yes—
379#389C2312yes—
380#389C2314yes—
381#389C2314yes—
382#389C2312yes—
383#389C2318yes—
384#389C2312yes—
385#389C2314yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#388C2318yes—
390#388C2318yes—
391#388C2314yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2314yes—
396#388C2314yes—
397#388C2318yes—
398#388C2314yes—
399#388C2318yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2314yes—
404#388C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2314yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2314yes—
413#387C2318yes—
414#387C2318yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#386C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2314yes—
423#386C2314yes—
424#386C2314yes—
425#386C2314yes—
426#386C2314yes—
427#386C2314yes—
428#385C2318yes—
429#385C2318yes—
430#385C2314yes—
431#385C2314yes—
432#385C2318yes—
433#385C2314yes—
434#385C2314yes—
435#385C2318yes—
436#384C2312yes—
437#384C2312yes—
438#384C2314yes—
439#384C2314yes—
440#384C2314yes—
441#384C2314yes—
442#384C2312yes—
443#384C2312yes—
444#384C2314yes—
445#384C2311yescharacteristic
446#384C2312yes—
447#384C2311yescharacteristic
448#383C2314yes—
449#382C2312yes—
450#382C2314yes—
451#382C2312yes—
452#382C2312yes—
453#382C2318yes—
454#382C2314yes—
455#382C2312yes—
456#381C2318yes—
457#381C2314yes—
458#380C2318yes—
459#380C2318yes—
460#380C2314yes—
461#380C2314yes—
462#380C2312yes—
463#380C2312yes—
464#380C2314yes—
465#380C2318yes—
466#380C2312yes—
467#380C2314yes—
468#380C2318yes—
469#380C2312yes—
470#380C2312yes—
471#380C2312yes—
472#380C2314yes—
473#380C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2318yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2318yes—
505C4×C22⋊C4C2312yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520#376C2314yes—
521#376C2312yes—
522#376C2312yes—
523C2×#95C2314yes—
524C43C2312yes—
525C43C2312yes—
526C2×#41—24no—
527C2×#41—24no—
528C2×#41—28no—
529C2×#41—44no—
530C2×#41—44no—
531C2×#41—42no—
532C22×Q8C2412yes—
533C22×Q8C2412yes—
534C22×Q8C2411yescharacteristic
535C22×Q8C2412yes—
536C22×Q8C2418yes—
537C22×D4C2412yes—
538C22×D4C2412yes—
539C22×D4C2412yes—
540C22×D4C2411yescharacteristic
541C22×D4C2418yes—
542C22×D4C2414yes—
543C22×D4C2412yes—
544C23×C4C2412yes—
545C23×C4C2414yes—
546C23×C4C2412yes—
547C23×C4C2414yes—
548C23×C4C2412yes—
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2414yes—
553C23×C4C2414yes—
554C23×C4C2414yes—
555C23×C4C2414yes—
556C4⋊Q8—24no—
557C4⋊Q8—24no—
558C4⋊Q8—24no—
559C4⋊Q8—48no—
560C4⋊Q8—48no—
561C4⋊Q8—48no—
562C4⋊Q8—48no—
563C4⋊Q8—44no—
564#127—24no—
565#126—416no—
566#126—416no—
567#125—216no—
568#125—28no—
569#125—48no—
570#124—28no—
571#124—28no—
572#124—48no—
573#124—416no—
574#123—416no—
575#123—416no—
576C22⋊Q8—28no—
577C22⋊Q8—28no—
578C22⋊Q8—28no—
579C22⋊Q8—28no—
580C22⋊Q8—48no—
581C22⋊Q8—416no—
582C22⋊Q8—416no—
583C22⋊Q8—48no—
584C22⋊Q8—48no—
585C22⋊Q8—48no—
586#121—216no—
587#121—28no—
588#121—28no—
589#121—416no—
590#121—48no—
591#121—48no—
592#121—48no—
593C4×Q8—24no—
594C4×Q8—24no—
595C4×Q8—28no—
596C4×Q8—28no—
597C4×Q8—48no—
598C4×Q8—48no—
599C4×D4—28no—
600C4×D4—28no—
601C4×D4—28no—
602C4×D4—28no—
603C4×D4—28no—
604C4×D4—28no—
605C4×D4—24no—
606C4×D4—24no—
607C4×D4—28no—
608C4×D4—28no—
609C4×D4—44no—
610C4×D4—44no—
611C4×D4—416no—
612#117—24no—
613#117—28no—
614#117—24no—
615#117—24no—
616#117—24no—
617#117—28no—
618#117—48no—
619#117—44no—
620#117—42no—
621#117—416no—
622C2×C4⋊C4—28no—
623C2×C4⋊C4—44no—
624C2×C4⋊C4—44no—
625C2×C4⋊C4—44no—
626C2×C4⋊C4—44no—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2412yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2418yes—
708C2×C42—28no—
709C2×C42—48no—
710C2×C42—48no—
711C2×C42#4118yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2414yes—
716C2×C42C2414yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2414yes—
729C2×C42C2418yes—
730C2×C42C2412yes—
731C2×C42C2418yes—
732C2×C42C2414yes—
733C2×C42C2414yes—
734C2×C42C2414yes—
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739#95C2412yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2412yes—
744#95C2412yes—
745#95C2412yes—
746#95C2412yes—
747#95C2412yes—
748#95C2412yes—
749#95C2412yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764#95C2414yes—
765#95C2418yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2418yes—
778#95C2418yes—
779C24C2514yes—
780C24C2511yescharacteristic
781C24C2512yes—
782#41—416no—
783#41—816no—
784C2×Q8—22no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—22no—
791C2×Q8—24no—
792C2×Q8—24no—
793C2×Q8—22no—
794C2×Q8—42no—
795C2×Q8—42no—
796C2×Q8—48no—
797C2×Q8—48no—
798C2×Q8—48no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—28no—
802C2×D4—216no—
803C2×D4—22no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—22no—
811C2×D4—24no—
812C2×D4—42no—
813C2×D4—48no—
814C2×D4—42no—
815C2×D4—44no—
816C2×D4—48no—
817C2×D4—42no—
818C2×D4—44no—
819C2×D4H(5,𝔽2)14yes—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—24no—
827C22×C4—28no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—28no—
832C22×C4—24no—
833C22×C4—28no—
834C22×C4—28no—
835C22×C4—24no—
836C22×C4—28no—
837C22×C4—24no—
838C22×C4—28no—
839C22×C4—24no—
840C22×C4—28no—
841C22×C4—28no—
842C22×C4—44no—
843C22×C4—42no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4C2×#4114yes—
854C22×C4C2×#4114yes—
855C22×C4C2×#4114yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2512yes—
860C22×C4C2512yes—
861C22×C4C2514yes—
862C22×C4C2514yes—
863C22×C4C2512yes—
864C22×C4C2514yes—
865C22×C4C2512yes—
866C22×C4C2514yes—
867C22×C4C2514yes—
868C22×C4C2518yes—
869C22×C4C2512yes—
870C22×C4C2511yescharacteristic
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C22×C4C2512yes—
874C22×C4C2512yes—
875C22×C4C2512yes—
876C22×C4C2511yescharacteristic
877C22×C4C2511yescharacteristic
878C22×C4C2511yescharacteristic
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—22no—
894C4⋊C4—28no—
895C4⋊C4—216no—
896C4⋊C4—24no—
897C4⋊C4—216no—
898C4⋊C4—28no—
899C4⋊C4—24no—
900C4⋊C4—22no—
901C4⋊C4—22no—
902C4⋊C4—28no—
903C4⋊C4—22no—
904C4⋊C4—28no—
905C4⋊C4—24no—
906C4⋊C4—22no—
907C4⋊C4—24no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—42no—
914C4⋊C4—44no—
915C4⋊C4—42no—
916C4⋊C4—48no—
917C4⋊C4—48no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—48no—
922C4⋊C4—48no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—48no—
926C4⋊C4H(5,𝔽2)14yes—
927C4⋊C42−1+414yes—
928C4⋊C42−1+414yes—
929C22⋊C4—24no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—216no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—24no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—42no—
948C22⋊C4—48no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—48no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—48no—
960C42—24no—
961C42—24no—
962C42—24no—
963C42—28no—
964C42—24no—
965C42—28no—
966C42—24no—
967C42—24no—
968C42—24no—
969C42—24no—
970C42—24no—
971C42—24no—
972C42—24no—
973C42—24no—
974C42—24no—
975C42—24no—
976C42—44no—
977C42—44no—
978C42—44no—
979C42—44no—
980C42—42no—
981C42—48no—
982C42—48no—
983C42C2×#4114yes—
984C42C2×#4114yes—
985C42C2×#4114yes—
986C42C2×#4114yes—
987C23—22no—
988C23—21no—
989C23—22no—
990C23—21no—
991C23—22no—
992C23—21no—
993C23—21no—
994C23—22no—
995C23—21no—
996C23—22no—
997C23—22no—
998C23—21no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23C22×#4112yes—
1007C23C2×H(5,𝔽2)14yes—
1008C23C2611yescharacteristic
1009Q8—48no—
1010Q8—44no—
1011Q8—48no—
1012Q8—84no—
1013Q8—168no—
1014D4—28no—
1015D4—48no—
1016D4—48no—
1017D4—48no—
1018D4—84no—
1019D4—816no—
1020D4—88no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—28no—
1034C2×C4—28no—
1035C2×C4—28no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—28no—
1054C2×C4—28no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—28no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—416no—
1079C2×C4—48no—
1080C2×C4—48no—
1081C2×C4—416no—
1082C2×C4—48no—
1083C2×C4—88no—
1084C2×C4—88no—
1085C2×C4—88no—
1086C2×C4—164no—
1087C2×C4C22×#4112yes—
1088C2×C4C22×#4112yes—
1089C2×C4C22×#4112yes—
1090C2×C4C22×#4112yes—
1091C2×C4C22×#4112yes—
1092C2×C4C22×#4112yes—
1093C2×C4C2×H(5,𝔽2)14yes—
1094C2×C4C2×H(5,𝔽2)12yes—
1095C2×C4C2×H(5,𝔽2)12yes—
1096C2×C4C2×2−1+414yes—
1097C2×C4C2×2−1+414yes—
1098C2×C4C2×2−1+412yes—
1099C2×C4C2×2−1+412yes—
1100C2×C4#58512yes—
1101C2×C4#58512yes—
1102C22—24no—
1103C22—24no—
1104C22—22no—
1105C22—24no—
1106C22—22no—
1107C22—22no—
1108C22—42no—
1109C22—41no—
1110C22—41no—
1111C22—41no—
1112C22—42no—
1113C22—41no—
1114C22—42no—
1115C22—42no—
1116C22—44no—
1117C22—44no—
1118C22—44no—
1119C22—44no—
1120C22—44no—
1121C22—44no—
1122C22—44no—
1123C22C23×#4111yescharacteristic
1124C22C22×H(5,𝔽2)11yescharacteristic
1125C22C22×H(5,𝔽2)11yescharacteristic
1126C22C22×2−1+411yescharacteristic
1127C22C22×2−1+411yescharacteristic
1128C22C2×#58511yescharacteristic
1129C22C2×#58511yescharacteristic
1130C4—24no—
1131C4—24no—
1132C4—24no—
1133C4—22no—
1134C4—22no—
1135C4—22no—
1136C4—44no—
1137C4—42no—
1138C4—44no—
1139C4—48no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—42no—
1144C4—42no—
1145C4—44no—
1146C4—44no—
1147C4—42no—
1148C4—44no—
1149C4—42no—
1150C4#346114yes—
1151C4#349414yes—
1152C4#351114yes—
1153C2—44no—
1154C2—42no—
1155C2—84no—
1156C2C2×#346111yescharacteristic
1157C2C2×#349411yescharacteristic
1158C2C2×#351111yescharacteristic
1159C2#6301311yescharacteristic
1160C2#6301411yescharacteristic
1161C2#6302511yescharacteristic
1162C2#6303711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35273C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42946C2semidirect
2. #42089C2semidirect
3. #39432C2semidirect
4. #39377C2semidirect
5. #39192C2semidirect
6. #39157C2semidirect
7. #39056C2semidirect
8. #38941C2semidirect
9. #37968C2semidirect
10. #37758C2semidirect
11. #37640C2semidirect
12. #37631C2semidirect
13. #36564C2semidirect
14. #36453C2semidirect
15. #36194C2semidirect
16. #36117C2semidirect
17. #35989C2semidirect
18. #35275C2semidirect
20. #35176C2semidirect
21. #35170C2semidirect
22. #34979C2semidirect
23. #34932C2semidirect
24. #34214C2semidirect
25. #34155C2semidirect
26. #34127C2semidirect

Maximal subgroups

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

subgroupindex
#429462
#420892
#394322
#393772
#391922
#391572
#390562
#389412
#379682
#377582
#376402
#376312
#365642
#364532
#361942
#361172
#359892
#352752
#352732
#351762
#351702
#349792
#349322
#342142
#341552
#341272