Subgroups — C₂×C₃⋊D₂₃₁ #14583945

Order 2772.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊D₂₃₁	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₂₃₁	—	3	4	no	maximal
4	C₃²×C₇×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×C₁₁	D₃	1	4	yes	complemented
6	D₂₃₁	—	3	8	no	—
7	C₂×C₃⋊D₃₃	—	7	1	no	maximal, Hall
8	C₂×D₇₇	—	9	1	no	Hall
9	C₂×C₃⋊D₂₁	—	11	1	no	maximal, Hall
10	C₃×C₇×C₁₁	C₂×D₃	1	4	yes	complemented
11	C₂×C₃²×C₁₁	D₇	1	1	yes	characteristic, complemented
12	C₃⋊D₃₃	—	7	2	no	—
13	C₂×C₇×C₁₁	C₃⋊D₃	1	1	yes	characteristic, complemented
14	D₇₇	—	9	2	no	—
15	C₂×D₃₃	—	21	4	no	—
16	C₂×C₃²×C₇	D₁₁	1	1	yes	characteristic, complemented
17	C₃⋊D₂₁	—	11	2	no	—
18	C₃²×C₁₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
19	C₂×D₂₁	—	33	4	no	—
20	C₇×C₁₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₁₁	D₂₁	1	4	yes	complemented
22	D₃₃	—	21	8	no	—
23	C₃²×C₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
24	C₂×D₁₁	—	63	1	no	Hall
25	C₂×C₃×C₇	D₃₃	1	4	yes	complemented
26	D₂₁	—	33	8	no	—
27	C₂×C₃⋊D₃	—	77	1	no	Hall
28	C₃×C₁₁	C₂×D₂₁	1	4	yes	complemented
29	C₂×D₇	—	99	1	no	Hall
30	C₂×C₁₁	C₃⋊D₂₁	1	1	yes	characteristic, complemented
31	D₁₁	—	63	2	no	—
32	C₃×C₇	C₂×D₃₃	1	4	yes	complemented
33	C₂×C₃²	D₇₇	1	1	yes	characteristic, complemented
34	C₃⋊D₃	—	77	2	no	—
35	C₂×C₇	C₃⋊D₃₃	1	1	yes	characteristic, complemented
36	D₇	—	99	2	no	—
37	C₂×D₃	—	231	4	no	—
38	C₁₁	C₂×C₃⋊D₂₁	1	1	yes	characteristic, complemented, Sylow
39	C₃²	C₂×D₇₇	1	1	yes	characteristic, complemented, Sylow
40	C₇	C₂×C₃⋊D₃₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₂₃₁	1	4	yes	complemented
42	D₃	—	231	8	no	—
43	C₂²	—	693	1	no	Sylow
44	C₃	C₂×D₂₃₁	1	4	yes	complemented
45	C₂	—	693	2	no	—
46	C₂	C₃⋊D₂₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊D₂₃₁
commutator, cosocle, hypocenter	C₃²×C₇×C₁₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₁₁	C₂
LCS	G ▷ C₃²×C₇×C₁₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₇×C₁₁	C₂	semidirect
2. C₃⋊D₂₃₁	C₂	direct (N × H)
4. C₃²×C₇×C₁₁	C₂²	semidirect
5. C₂×C₃×C₇×C₁₁	D₃	semidirect
10. C₃×C₇×C₁₁	C₂×D₃	semidirect
11. C₂×C₃²×C₁₁	D₇	semidirect
13. C₂×C₇×C₁₁	C₃⋊D₃	semidirect
16. C₂×C₃²×C₇	D₁₁	semidirect
18. C₃²×C₁₁	C₂×D₇	semidirect
20. C₇×C₁₁	C₂×C₃⋊D₃	semidirect
21. C₂×C₃×C₁₁	D₂₁	semidirect
23. C₃²×C₇	C₂×D₁₁	semidirect
25. C₂×C₃×C₇	D₃₃	semidirect
28. C₃×C₁₁	C₂×D₂₁	semidirect
30. C₂×C₁₁	C₃⋊D₂₁	semidirect
32. C₃×C₇	C₂×D₃₃	semidirect
33. C₂×C₃²	D₇₇	semidirect
35. C₂×C₇	C₃⋊D₃₃	semidirect
38. C₁₁	C₂×C₃⋊D₂₁	semidirect
39. C₃²	C₂×D₇₇	semidirect
40. C₇	C₂×C₃⋊D₃₃	semidirect
41. C₂×C₃	D₂₃₁	semidirect
44. C₃	C₂×D₂₃₁	semidirect
46. C₂	C₃⋊D₂₃₁	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×C₃²×C₇×C₁₁	2
C₃⋊D₂₃₁	2
C₂×D₂₃₁	3
C₂×C₃⋊D₃₃	7
C₂×C₃⋊D₂₁	11

Subgroups — C2×C3⋊D231 #14583945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊D₂₃₁ #14583945