Subgroups — C₄×C₇×C₁₁×C₈₁ #72202170

Order 24948.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₁×C₈₁	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×C₁₁×C₂₇	C₃	1	1	yes	maximal, characteristic
3	C₇×C₁₁×C₈₁	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇×C₁₁×C₂₇	C₂×C₃	1	1	yes	characteristic
5	C₄×C₁₁×C₈₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₄×C₇×C₈₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇×C₁₁×C₂₇	C₃×C₄	1	1	yes	characteristic
8	C₄×C₇×C₉×C₁₁	C₉	1	1	yes	characteristic
9	C₂×C₁₁×C₈₁	C₂×C₇	1	1	yes	characteristic
10	C₂×C₇×C₉×C₁₁	C₂×C₉	1	1	yes	characteristic
11	C₄×C₁₁×C₂₇	C₃×C₇	1	1	yes	characteristic
12	C₂×C₇×C₈₁	C₂×C₁₁	1	1	yes	characteristic
13	C₃×C₄×C₇×C₁₁	C₂₇	1	1	yes	characteristic
14	C₁₁×C₈₁	C₄×C₇	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₇×C₂₇	C₃×C₁₁	1	1	yes	characteristic
16	C₇×C₉×C₁₁	C₄×C₉	1	1	yes	characteristic
17	C₂×C₁₁×C₂₇	C₂×C₃×C₇	1	1	yes	characteristic
18	C₇×C₈₁	C₄×C₁₁	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×C₇×C₁₁	C₂×C₂₇	1	1	yes	characteristic
20	C₄×C₉×C₁₁	C₇×C₉	1	1	yes	characteristic
21	C₂×C₇×C₂₇	C₂×C₃×C₁₁	1	1	yes	characteristic
22	C₄×C₈₁	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
23	C₄×C₇×C₁₁	C₈₁	1	1	yes	characteristic, direct product factor, Hall
24	C₁₁×C₂₇	C₃×C₄×C₇	1	1	yes	characteristic
25	C₄×C₇×C₉	C₉×C₁₁	1	1	yes	characteristic
26	C₃×C₇×C₁₁	C₄×C₂₇	1	1	yes	characteristic
27	C₂×C₉×C₁₁	C₂×C₇×C₉	1	1	yes	characteristic
28	C₇×C₂₇	C₃×C₄×C₁₁	1	1	yes	characteristic
29	C₂×C₈₁	C₂×C₇×C₁₁	1	1	yes	characteristic
30	C₂×C₇×C₁₁	C₂×C₈₁	1	1	yes	characteristic
31	C₃×C₄×C₁₁	C₇×C₂₇	1	1	yes	characteristic
32	C₂×C₇×C₉	C₂×C₉×C₁₁	1	1	yes	characteristic
33	C₄×C₂₇	C₃×C₇×C₁₁	1	1	yes	characteristic
34	C₉×C₁₁	C₄×C₇×C₉	1	1	yes	characteristic
35	C₃×C₄×C₇	C₁₁×C₂₇	1	1	yes	characteristic
36	C₈₁	C₄×C₇×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
37	C₇×C₁₁	C₄×C₈₁	1	1	yes	characteristic, direct product factor, Hall
38	C₂×C₃×C₁₁	C₂×C₇×C₂₇	1	1	yes	characteristic
39	C₇×C₉	C₄×C₉×C₁₁	1	1	yes	characteristic
40	C₂×C₂₇	C₂×C₃×C₇×C₁₁	1	1	yes	characteristic
41	C₄×C₁₁	C₇×C₈₁	1	1	yes	characteristic, direct product factor, Hall
42	C₂×C₃×C₇	C₂×C₁₁×C₂₇	1	1	yes	characteristic
43	C₄×C₉	C₇×C₉×C₁₁	1	1	yes	characteristic
44	C₃×C₁₁	C₄×C₇×C₂₇	1	1	yes	characteristic
45	C₄×C₇	C₁₁×C₈₁	1	1	yes	characteristic, direct product factor, Hall
46	C₂₇	C₃×C₄×C₇×C₁₁	1	1	yes	characteristic
47	C₂×C₁₁	C₂×C₇×C₈₁	1	1	yes	characteristic
48	C₃×C₇	C₄×C₁₁×C₂₇	1	1	yes	characteristic
49	C₂×C₉	C₂×C₇×C₉×C₁₁	1	1	yes	characteristic
50	C₂×C₇	C₂×C₁₁×C₈₁	1	1	yes	characteristic
51	C₃×C₄	C₇×C₁₁×C₂₇	1	1	yes	characteristic
52	C₁₁	C₄×C₇×C₈₁	1	1	yes	characteristic, direct product factor, Sylow
53	C₉	C₄×C₇×C₉×C₁₁	1	1	yes	characteristic
54	C₇	C₄×C₁₁×C₈₁	1	1	yes	characteristic, direct product factor, Sylow
55	C₂×C₃	C₂×C₇×C₁₁×C₂₇	1	1	yes	characteristic
56	C₄	C₇×C₁₁×C₈₁	1	1	yes	characteristic, direct product factor, Sylow
57	C₃	C₄×C₇×C₁₁×C₂₇	1	1	yes	characteristic
58	C₂	C₂×C₇×C₁₁×C₈₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₂₇	C₂×C₃×C₇×C₁₁
socle, prime radical	C₂×C₃×C₇×C₁₁	C₂×C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×C₁₁×C₈₁	C₄	direct (N × H)
5. C₄×C₁₁×C₈₁	C₇	direct (N × H)
6. C₄×C₇×C₈₁	C₁₁	direct (N × H)
14. C₁₁×C₈₁	C₄×C₇	direct (N × H)
18. C₇×C₈₁	C₄×C₁₁	direct (N × H)
22. C₄×C₈₁	C₇×C₁₁	direct (N × H)
23. C₄×C₇×C₁₁	C₈₁	direct (N × H)
36. C₈₁	C₄×C₇×C₁₁	direct (N × H)
37. C₇×C₁₁	C₄×C₈₁	direct (N × H)
41. C₄×C₁₁	C₇×C₈₁	direct (N × H)
45. C₄×C₇	C₁₁×C₈₁	direct (N × H)
52. C₁₁	C₄×C₇×C₈₁	direct (N × H)
54. C₇	C₄×C₁₁×C₈₁	direct (N × H)
56. C₄	C₇×C₁₁×C₈₁	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×C₇×C₁₁×C₈₁	2
C₄×C₇×C₁₁×C₂₇	3
C₄×C₁₁×C₈₁	7
C₄×C₇×C₈₁	11

Subgroups — C4×C7×C11×C81 #72202170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×C₁₁×C₈₁ #72202170