Finite Group Databasebeta

← #8108048

Subgroups — #8108048

Order 512.

4483 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53137C212yesmaximal, complemented
2#53072C214yesmaximal, complemented
3#53033C212yesmaximal, complemented
4#53006C212yesmaximal, complemented
5#53005C212yesmaximal, complemented
6#45420C212yesmaximal, complemented
7#45410C212yesmaximal, complemented
8#45308C212yesmaximal, complemented
9#45226C212yesmaximal, complemented
10#45125C214yesmaximal, complemented
11#42981C212yesmaximal, complemented
12#42955C212yesmaximal, complemented
13#42867C214yesmaximal, complemented
14#42831C214yesmaximal, complemented
15#42771C214yesmaximal, complemented
16#42770C214yesmaximal, complemented
17#42686C212yesmaximal, complemented
18#42684C212yesmaximal, complemented
19#36210C212yesmaximal, complemented
20#36209C212yesmaximal, complemented
21#36129C212yesmaximal, complemented
22#36129C212yesmaximal, complemented
23#35297C212yesmaximal, complemented
24#35291C212yesmaximal, complemented
25#35279C211yesmaximal, characteristic, complemented
26#35279C211yesmaximal, characteristic, complemented
27#34547C211yesmaximal, characteristic
28C2×#533C2212yes—
29C22×C4⋊Q8C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic
31C2×C4×#41C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33#2862C2212yes—
34#2859C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40#2857C2212yes—
41#2844C2214yes—
42#2843C2214yes—
43#2838C2218yes—
44#2837C2218yes—
45#2833C2218yes—
46#2832C2218yes—
47#2826C2214yes—
48#2824C2214yes—
49#2807C2214yes—
50#2795C2214yes—
51#2794C2214yes—
52#2793C2218yes—
53#2789C2214yes—
54#2788C2218yes—
55#2785C2214yes—
56#2778C2218yes—
57#2775C2218yes—
58#2775C2218yes—
59#2773C2218yes—
60#2768C2218yes—
61#2763C2214yes—
62#2762C2218yes—
63#2759C2218yes—
64#2758C2218yes—
65#2756C2218yes—
66#2753C2218yes—
67#2742C2214yes—
68#2742C2214yes—
69#2666C2218yes—
70#2653C2218yes—
71#2649C2218yes—
72#2647C2218yes—
73#2645C2214yes—
74#2628C2212yes—
75#2628C2212yes—
76#2628C2212yes—
77#2628C2212yes—
78#2625C2214yes—
79#2625C2214yes—
80#2616C2214yes—
81#2612C2214yes—
82#2597C2218yes—
83#2584C2214yes—
84#2581C2214yes—
85#2578C2218yes—
86#2571C2214yes—
87#2568C2212yes—
88#2568C2212yes—
89#2567C2212yes—
90#2567C2212yes—
91#2563C2212yes—
92#2563C2212yes—
93#2562C2214yes—
94#2562C2214yes—
95#2550C2214yes—
96#2550C2214yes—
97#2542C2212yes—
98#2542C2212yes—
99#2536C2214yes—
100#2536C2214yes—
101#2532C2218yes—
102#2531C2218yes—
103#2523C2214yes—
104#2517C2214yes—
105#2514C2214yes—
106#2514C2214yes—
107#2509C2214yes—
108#2509C2214yes—
109#2508C2214yes—
110#2508C2214yes—
111#2508C2214yes—
112#2495C2214yes—
113#2495C2214yes—
114#2495C2214yes—
115#2495C2214yes—
116#2494C2214yes—
117#2494C2214yes—
118#2494C2214yes—
119#2492C2214yes—
120#2492C2214yes—
121#2489C2214yes—
122#2489C2214yes—
123#2489C2214yes—
124#2487C2212yes—
125#2487C2212yes—
126#2487C2212yes—
127#2487C2212yes—
128#2485C2214yes—
129#2485C2214yes—
130#2485C2214yes—
131#2485C2214yes—
132#2485C2214yes—
133#2453C2214yes—
134#2451C2214yes—
135#2451C2214yes—
136#2446C2214yes—
137#2446C2214yes—
138#2442C2214yes—
139#2442C2214yes—
140#2439C2214yes—
141#2439C2214yes—
142#2429C2214yes—
143#2429C2214yes—
144#2421C2214yes—
145#2421C2214yes—
146#2417C2214yes—
147#2417C2214yes—
148#2415C2214yes—
149#2415C2214yes—
150#2415C2214yes—
151#2409C2214yes—
152#2409C2212yes—
153#2409C2214yes—
154#2409C2212yes—
155#2409C2212yes—
156#2409C2212yes—
157#2399C2211yescharacteristic
158#2398C2211yescharacteristic
159#2398C2211yescharacteristic
160#2397C2211yescharacteristic
161#2396C2212yes—
162#2396C2211yescharacteristic
163#2396C2211yescharacteristic
164#2395C2212yes—
165#2395C2211yescharacteristic
166#2395C2211yescharacteristic
167#2392C2212yes—
168#2392C2212yes—
169#2392C2212yes—
170#2392C2211yescharacteristic
171#2392C2211yescharacteristic
172#2388C2211yescharacteristic
173#2388C2211yescharacteristic
174#2388C2212yes—
175#2370C2214yes—
176#2362C2214yes—
177#2360C2214yes—
178#2360C2214yes—
179#2356C2214yes—
180#2352C2214yes—
181#2352C2214yes—
182#2347C2214yes—
183#2346C2214yes—
184#2346C2214yes—
185Q8×C22⋊C4C2214yes—
186Q8×C22⋊C4C2214yes—
187#2323C2214yes—
188#2323C2214yes—
189#2323C2214yes—
190#2320C2214yes—
191#2317C2212yes—
192#2317C2212yes—
193#2311C2212yes—
194#2311C2212yes—
195C4×C4⋊Q8C2212yes—
196C4×C4⋊Q8C2212yes—
197#2285C2211yescharacteristic
198#2285C2212yes—
199#2285C2211yescharacteristic
200C42×D4C2212yes—
201C42×D4C2212yes—
202C4×#117C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×Q8C2312yes—
206C23×Q8C2312yes—
207#533—48no—
208C2×C4⋊Q8—44no—
209C2×C4⋊Q8—44no—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2312yes—
218C2×#125C2314yes—
219C2×#125C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C4×#41—44no—
229C4×#41—44no—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×D4C2312yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2312yes—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2312yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×#117C2312yes—
255C2×#117C2312yes—
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2312yes—
260C2×#117C2312yes—
261C2×#117C2314yes—
262C2×#117C2314yes—
263C2×#117C2311yescharacteristic
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2312yes—
268C22×C42C2311yescharacteristic
269C22×C42C2311yescharacteristic
270C22×C42C2311yescharacteristic
271C22×C42C2312yes—
272#401C2318yes—
273#401C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2318yes—
281#400C2318yes—
282#400C2311yescharacteristic
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#400C2311yescharacteristic
290#400C2318yes—
291#400C2312yes—
292#399C2314yes—
293#399C2314yes—
294#399C2314yes—
295#399C2312yes—
296#399C2314yes—
297#399C2311yescharacteristic
298#399C2311yescharacteristic
299#398C2312yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#398C2318yes—
307#398C2312yes—
308#398C2311yescharacteristic
309#398C2311yescharacteristic
310#398C2312yes—
311#397C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2318yes—
315#397C2318yes—
316#397C2318yes—
317#397C2318yes—
318#397C2318yes—
319#397C2312yes—
320#397C2312yes—
321#397C2311yescharacteristic
322#397C2312yes—
323#397C2311yescharacteristic
324#396C2318yes—
325#396C2318yes—
326#396C2312yes—
327#396C2312yes—
328#396C2312yes—
329#396C2312yes—
330#395C2314yes—
331#395C2314yes—
332#395C2314yes—
333#395C2314yes—
334#395C2318yes—
335#395C2318yes—
336#395C2318yes—
337#395C2311yescharacteristic
338#395C2311yescharacteristic
339#395C2312yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2312yes—
345#394C2318yes—
346#394C2312yes—
347#394C2312yes—
348#394C2312yes—
349#394C2312yes—
350#394C2311yescharacteristic
351#394C2311yescharacteristic
352#394C2312yes—
353#394C2312yes—
354#393C2314yes—
355#393C2314yes—
356#393C2314yes—
357#393C2314yes—
358#393C2318yes—
359#393C2318yes—
360#393C2311yescharacteristic
361#393C2311yescharacteristic
362#393C2312yes—
363#392C2311yescharacteristic
364#392C2311yescharacteristic
365#392C2312yes—
366#392C2312yes—
367#392C2312yes—
368#391C2314yes—
369#391C2314yes—
370#391C2314yes—
371#391C2314yes—
372#391C2314yes—
373#391C2314yes—
374#391C2314yes—
375#391C2314yes—
376#391C2314yes—
377#391C2318yes—
378#391C2318yes—
379#391C2314yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2318yes—
384#391C2318yes—
385#391C2314yes—
386#390C2314yes—
387#390C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2318yes—
397#389C2318yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2318yes—
404#389C2314yes—
405#389C2314yes—
406#389C2318yes—
407#389C2314yes—
408#389C2318yes—
409#389C2318yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#387C2318yes—
431#387C2318yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#387C2318yes—
444#386C2314yes—
445#386C2314yes—
446#386C2314yes—
447#386C2314yes—
448#386C2318yes—
449#386C2318yes—
450#385C2314yes—
451#385C2314yes—
452#385C2314yes—
453#385C2314yes—
454#385C2318yes—
455#385C2318yes—
456#384C2312yes—
457#384C2312yes—
458#384C2314yes—
459#384C2314yes—
460#383C2318yes—
461#383C2318yes—
462#383C2318yes—
463#382C2314yes—
464#382C2314yes—
465#382C2318yes—
466#382C2318yes—
467#382C2314yes—
468#382C2318yes—
469#382C2314yes—
470#382C2314yes—
471#382C2314yes—
472#382C2312yes—
473#382C2312yes—
474#380C2312yes—
475#380C2314yes—
476#380C2314yes—
477#380C2314yes—
478#380C2314yes—
479#380C2314yes—
480#380C2314yes—
481#380C2314yes—
482#380C2314yes—
483#380C2314yes—
484#380C2314yes—
485#380C2314yes—
486#380C2314yes—
487#380C2318yes—
488#380C2318yes—
489#380C2314yes—
490#380C2312yes—
491#380C2312yes—
492#380C2314yes—
493#380C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2318yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2312yes—
522C4×C22⋊C4C2312yes—
523C4×C22⋊C4C2312yes—
524C4×C22⋊C4C2311yescharacteristic
525C4×C22⋊C4C2311yescharacteristic
526C4×C22⋊C4C2312yes—
527C4×C22⋊C4C2312yes—
528C4×C22⋊C4C2312yes—
529C4×C22⋊C4C2312yes—
530C4×C22⋊C4C2312yes—
531#376C2311yescharacteristic
532#376C2318yes—
533#376C2311yescharacteristic
534C43C2312yes—
535C2×#41—24no—
536C2×#41—24no—
537C2×#41—42no—
538C2×#41—42no—
539C2×#41—44no—
540C22×Q8—44no—
541C22×Q8—44no—
542C22×Q8—48no—
543C22×Q8—48no—
544C22×Q8C2414yes—
545C22×Q8C2414yes—
546C22×Q8C2411yescharacteristic
547C22×Q8C2411yescharacteristic
548C22×Q8C2414yes—
549C22×Q8C2414yes—
550C22×D4C2411yescharacteristic
551C22×D4C2411yescharacteristic
552C22×D4C2411yescharacteristic
553C22×D4C2412yes—
554C22×D4C2412yes—
555C22×D4C2412yes—
556C22×D4C2411yescharacteristic
557C23×C4C2411yescharacteristic
558C23×C4C2411yescharacteristic
559C23×C4C2412yes—
560C23×C4C2411yescharacteristic
561C23×C4C2412yes—
562C23×C4C2411yescharacteristic
563C23×C4C2412yes—
564C23×C4C2411yescharacteristic
565C23×C4C2411yescharacteristic
566C23×C4C2411yescharacteristic
567C23×C4C2411yescharacteristic
568C23×C4C2411yescharacteristic
569C23×C4C2414yes—
570C23×C4C2414yes—
571C4⋊Q8—28no—
572C4⋊Q8—28no—
573C4⋊Q8—44no—
574C4⋊Q8—44no—
575C4⋊Q8—44no—
576C4⋊Q8—44no—
577C4⋊Q8—44no—
578C4⋊Q8—44no—
579#125—48no—
580#125—48no—
581C22⋊Q8—48no—
582C22⋊Q8—48no—
583C22⋊Q8—48no—
584C22⋊Q8—48no—
585C22⋊Q8—48no—
586C22⋊Q8—48no—
587C22⋊Q8—48no—
588C22⋊Q8—48no—
589C4×Q8—42no—
590C4×Q8—42no—
591C4×Q8—42no—
592C4×Q8—42no—
593C4×Q8—48no—
594C4×Q8—48no—
595C4×Q8—48no—
596C4×Q8—48no—
597C4×D4—28no—
598C4×D4—28no—
599C4×D4—44no—
600C4×D4—44no—
601C4×D4—44no—
602C4×D4—44no—
603C4×D4—42no—
604C4×D4—42no—
605C4×D4—42no—
606C4×D4—42no—
607C4×D4—44no—
608C4×D4—44no—
609C4×D4—42no—
610C4×D4—42no—
611C4×D4—42no—
612C4×D4—42no—
613#117—28no—
614#117—28no—
615#117—44no—
616#117—44no—
617#117—42no—
618#117—42no—
619#117—42no—
620#117—42no—
621#117—48no—
622#117—48no—
623C2×C4⋊C4—44no—
624C2×C4⋊C4—44no—
625C2×C4⋊C4—44no—
626C2×C4⋊C4—44no—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2418yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2411yescharacteristic
678C2×C22⋊C4C2411yescharacteristic
679C2×C22⋊C4C2411yescharacteristic
680C2×C22⋊C4C2411yescharacteristic
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2411yescharacteristic
685C2×C22⋊C4C2411yescharacteristic
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2412yes—
692C2×C22⋊C4C2412yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2412yes—
695C2×C22⋊C4C2412yes—
696C2×C22⋊C4C2412yes—
697C2×C22⋊C4C2412yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C42—24no—
705C2×C42—24no—
706C2×C42—24no—
707C2×C42—28no—
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2412yes—
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2414yes—
716C2×C42C2414yes—
717C2×C42C2411yescharacteristic
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2418yes—
729C2×C42C2418yes—
730C2×C42C2418yes—
731C2×C42C2418yes—
732C2×C42C2411yescharacteristic
733#95C2412yes—
734#95C2411yescharacteristic
735#95C2412yes—
736#95C2411yescharacteristic
737#95C2411yescharacteristic
738#95C2411yescharacteristic
739#95C2412yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2412yes—
744#95C2412yes—
745#95C2412yes—
746#95C2412yes—
747#95C2412yes—
748#95C2412yes—
749#95C2412yes—
750#95C2412yes—
751#95C2412yes—
752#95C2412yes—
753#95C2412yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2414yes—
759#95C2418yes—
760#95C2414yes—
761#95C2418yes—
762#95C2414yes—
763#95C2414yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774#95C2418yes—
775#95C2418yes—
776#95C2418yes—
777#95C2418yes—
778#95C2418yes—
779C24C2512yes—
780C24C2511yescharacteristic
781C24C2511yescharacteristic
782C24C2511yescharacteristic
783#41—416no—
784#41—416no—
785C2×Q8—28no—
786C2×Q8—28no—
787C2×Q8—22no—
788C2×Q8—22no—
789C2×Q8—28no—
790C2×Q8—28no—
791C2×Q8—28no—
792C2×Q8—28no—
793C2×Q8—41no—
794C2×Q8—41no—
795C2×Q8—42no—
796C2×Q8—44no—
797C2×Q8—44no—
798C2×Q8—48no—
799C2×Q8—48no—
800C2×Q8—816no—
801C2×Q8—816no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—22no—
805C2×D4—22no—
806C2×D4—22no—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—22no—
810C2×D4—41no—
811C2×D4—41no—
812C2×D4—41no—
813C2×D4—41no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—42no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—24no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—24no—
832C22×C4—22no—
833C22×C4—24no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—48no—
853C22×C4—48no—
854C22×C42−1+414yes—
855C22×C42−1+414yes—
856C22×C4C2511yescharacteristic
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2512yes—
860C22×C4C2511yescharacteristic
861C22×C4C2511yescharacteristic
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2518yes—
865C22×C4C2518yes—
866C22×C4C2518yes—
867C22×C4C2518yes—
868C22×C4C2511yescharacteristic
869C22×C4C2512yes—
870C22×C4C2512yes—
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C22×C4C2511yescharacteristic
877C22×C4C2511yescharacteristic
878C22×C4C2511yescharacteristic
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—41no—
900C4⋊C4—41no—
901C4⋊C4—41no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—41no—
905C4⋊C4—41no—
906C4⋊C4—41no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—48no—
914C4⋊C4—48no—
915C4⋊C4—48no—
916C4⋊C4—48no—
917C4⋊C4—48no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—48no—
922C4⋊C4—48no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—24no—
926C22⋊C4—24no—
927C22⋊C4—24no—
928C22⋊C4—24no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—48no—
932C22⋊C4—42no—
933C22⋊C4—42no—
934C22⋊C4—41no—
935C22⋊C4—41no—
936C22⋊C4—41no—
937C22⋊C4—41no—
938C22⋊C4—42no—
939C22⋊C4—41no—
940C22⋊C4—41no—
941C22⋊C4—48no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—48no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C42—22no—
957C42—22no—
958C42—24no—
959C42—22no—
960C42—22no—
961C42—22no—
962C42—24no—
963C42—24no—
964C42—22no—
965C42—22no—
966C42—22no—
967C42—22no—
968C42—28no—
969C42—28no—
970C42—24no—
971C42—24no—
972C42—24no—
973C42—24no—
974C42—24no—
975C42—24no—
976C42—48no—
977C42—48no—
978C42—48no—
979C42—48no—
980C42H(5,𝔽2)14yes—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—21no—
991C23—22no—
992C23—22no—
993C23—21no—
994C23—21no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23C2×2−1+412yes—
1002C23C2×2−1+412yes—
1003C23C2611yescharacteristic
1004Q8—44no—
1005Q8—44no—
1006Q8—416no—
1007Q8—416no—
1008Q8—88no—
1009Q8—88no—
1010D4—44no—
1011D4—44no—
1012D4—44no—
1013D4—48no—
1014D4—48no—
1015D4—44no—
1016D4—48no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—28no—
1022C2×C4—28no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—28no—
1034C2×C4—28no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—28no—
1038C2×C4—28no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—28no—
1055C2×C4—28no—
1056C2×C4—28no—
1057C2×C4—28no—
1058C2×C4—28no—
1059C2×C4—28no—
1060C2×C4—22no—
1061C2×C4—28no—
1062C2×C4—28no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—48no—
1072C2×C4—44no—
1073C2×C4—44no—
1074C2×C4—44no—
1075C2×C4—44no—
1076C2×C4—48no—
1077C2×C4—44no—
1078C2×C4—44no—
1079C2×C4—48no—
1080C2×C4—44no—
1081C2×C4—88no—
1082C2×C4—88no—
1083C2×C4C2×H(5,𝔽2)12yes—
1084C2×C4C2×H(5,𝔽2)12yes—
1085C2×C4C2×H(5,𝔽2)12yes—
1086C2×C4C2×2−1+412yes—
1087C2×C4C2×2−1+412yes—
1088C2×C4C2×2−1+412yes—
1089C2×C4C2×2−1+412yes—
1090C2×C4#58514yes—
1091C2×C4#58514yes—
1092C22—22no—
1093C22—22no—
1094C22—24no—
1095C22—24no—
1096C22—41no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22—42no—
1101C22—42no—
1102C22—41no—
1103C22—42no—
1104C22—42no—
1105C22—41no—
1106C22—42no—
1107C22—41no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22C22×H(5,𝔽2)11yescharacteristic
1115C22C22×2−1+411yescharacteristic
1116C22C22×2−1+411yescharacteristic
1117C22C2×#58512yes—
1118C22C2×#58512yes—
1119C4—22no—
1120C4—22no—
1121C4—42no—
1122C4—41no—
1123C4—41no—
1124C4—41no—
1125C4—42no—
1126C4—41no—
1127C4—48no—
1128C4—41no—
1129C4—42no—
1130C4—41no—
1131C4—41no—
1132C4—48no—
1133C4—42no—
1134C4—42no—
1135C4—48no—
1136C4—48no—
1137C4—42no—
1138C4—42no—
1139C4#353814yes—
1140C4#354014yes—
1141C4#355114yes—
1142C2—42no—
1143C2—42no—
1144C2—81no—
1145C2—82no—
1146C2C2×#353811yescharacteristic
1147C2C2×#354011yescharacteristic
1148C2C2×#355111yescharacteristic
1149C2#6283812yes—
1150C2#6283812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34547C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53137C2semidirect
2. #53072C2semidirect
3. #53033C2semidirect
4. #53006C2semidirect
5. #53005C2semidirect
6. #45420C2semidirect
7. #45410C2semidirect
8. #45308C2semidirect
9. #45226C2semidirect
10. #45125C2semidirect
11. #42981C2semidirect
12. #42955C2semidirect
13. #42867C2semidirect
14. #42831C2semidirect
15. #42771C2semidirect
16. #42770C2semidirect
17. #42686C2semidirect
18. #42684C2semidirect
19. #36210C2semidirect
20. #36209C2semidirect
21. #36129C2semidirect
22. #36129C2semidirect
23. #35297C2semidirect
24. #35291C2semidirect
25. #35279C2semidirect
26. #35279C2semidirect

Maximal subgroups

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

subgroupindex
#531372
#530722
#530332
#530062
#530052
#454202
#454102
#453082
#452262
#451252
#429812
#429552
#428672
#428312
#427712
#427702
#426862
#426842
#362102
#362092
#361292
#352972
#352912
#352792
#345472