Subgroups — C₂×C₈×C₁₁×C₇₁ #72190834

Order 12496.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₁×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₈×C₁₁×C₇₁	C₂	1	2	yes	maximal, direct product factor
3	C₂²×C₁₁×C₇₁	C₄	1	1	yes	characteristic
4	C₄×C₁₁×C₇₁	C₄	1	1	yes	characteristic
5	C₄×C₁₁×C₇₁	C₂²	1	1	yes	characteristic
6	C₂×C₁₁×C₇₁	C₈	1	2	yes	direct product factor
7	C₂×C₁₁×C₇₁	C₂×C₄	1	1	yes	characteristic
8	C₂×C₈×C₇₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₁×C₇₁	C₂×C₈	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₄×C₇₁	C₂×C₁₁	1	1	yes	characteristic
11	C₈×C₇₁	C₂×C₁₁	1	2	yes	direct product factor
12	C₂²×C₇₁	C₄×C₁₁	1	1	yes	characteristic
13	C₄×C₇₁	C₄×C₁₁	1	1	yes	characteristic
14	C₄×C₇₁	C₂²×C₁₁	1	1	yes	characteristic
15	C₂×C₈×C₁₁	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₇₁	C₈×C₁₁	1	2	yes	direct product factor
17	C₂×C₇₁	C₂×C₄×C₁₁	1	1	yes	characteristic
18	C₂×C₄×C₁₁	C₂×C₇₁	1	1	yes	characteristic
19	C₈×C₁₁	C₂×C₇₁	1	2	yes	direct product factor
20	C₇₁	C₂×C₈×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²×C₁₁	C₄×C₇₁	1	1	yes	characteristic
22	C₄×C₁₁	C₄×C₇₁	1	1	yes	characteristic
23	C₄×C₁₁	C₂²×C₇₁	1	1	yes	characteristic
24	C₂×C₁₁	C₈×C₇₁	1	2	yes	direct product factor
25	C₂×C₁₁	C₂×C₄×C₇₁	1	1	yes	characteristic
26	C₂×C₈	C₁₁×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₁₁	C₂×C₈×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₄	C₂×C₁₁×C₇₁	1	1	yes	characteristic
29	C₈	C₂×C₁₁×C₇₁	1	2	yes	direct product factor
30	C₂²	C₄×C₁₁×C₇₁	1	1	yes	characteristic
31	C₄	C₄×C₁₁×C₇₁	1	1	yes	characteristic
32	C₄	C₂²×C₁₁×C₇₁	1	1	yes	characteristic
33	C₂	C₈×C₁₁×C₇₁	1	2	yes	direct product factor
34	C₂	C₂×C₄×C₁₁×C₇₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₁₁×C₇₁
socle, prime radical	C₂²×C₁₁×C₇₁	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈×C₁₁×C₇₁	C₂	direct (N × H)
6. C₂×C₁₁×C₇₁	C₈	direct (N × H)
8. C₂×C₈×C₇₁	C₁₁	direct (N × H)
9. C₁₁×C₇₁	C₂×C₈	direct (N × H)
11. C₈×C₇₁	C₂×C₁₁	direct (N × H)
15. C₂×C₈×C₁₁	C₇₁	direct (N × H)
16. C₂×C₇₁	C₈×C₁₁	direct (N × H)
19. C₈×C₁₁	C₂×C₇₁	direct (N × H)
20. C₇₁	C₂×C₈×C₁₁	direct (N × H)
24. C₂×C₁₁	C₈×C₇₁	direct (N × H)
26. C₂×C₈	C₁₁×C₇₁	direct (N × H)
27. C₁₁	C₂×C₈×C₇₁	direct (N × H)
29. C₈	C₂×C₁₁×C₇₁	direct (N × H)
33. C₂	C₈×C₁₁×C₇₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₁₁×C₇₁	2
C₈×C₁₁×C₇₁	2
C₂×C₈×C₇₁	11
C₂×C₈×C₁₁	71

Subgroups — C2×C8×C11×C71 #72190834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×C₁₁×C₇₁ #72190834