Subgroups — C₂×C₃⋊(C₇⋊D₂₈₇) #37563178

Order 24108.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₇⋊D₂₈₇)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇²×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇⋊D₂₈₇	—	3	1	no	maximal, Hall
4	C₃×C₇²×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇⋊D₂₈₇	—	3	2	no	—
6	C₂×C₇²×C₄₁	D₃	1	1	yes	characteristic, complemented
7	C₂×D₈₆₁	—	7	8	no	maximal
8	C₇²×C₄₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₇×C₄₁	D₇	1	8	yes	complemented
10	D₈₆₁	—	7	16	no	—
11	C₂×D₂₈₇	—	21	8	no	—
12	C₃×C₇×C₄₁	C₂×D₇	1	8	yes	complemented
13	C₂×C₃⋊(C₇⋊D₇)	—	41	1	no	maximal, Hall
14	C₂×C₇×C₄₁	D₂₁	1	8	yes	complemented
15	D₂₈₇	—	21	16	no	—
16	C₂×D₁₂₃	—	49	1	no	Hall
17	C₂×C₃×C₇²	D₄₁	1	1	yes	characteristic, complemented
18	C₃⋊(C₇⋊D₇)	—	41	2	no	—
19	C₇×C₄₁	C₂×D₂₁	1	8	yes	complemented
20	C₂×C₃×C₄₁	C₇⋊D₇	1	1	yes	characteristic, complemented
21	D₁₂₃	—	49	2	no	—
22	C₂×C₇⋊D₇	—	123	1	no	Hall
23	C₂×D₄₁	—	147	1	no	Hall
24	C₃×C₇²	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
25	C₃×C₄₁	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇²	D₁₂₃	1	1	yes	characteristic, complemented
27	C₇⋊D₇	—	123	2	no	—
28	C₂×D₂₁	—	287	8	no	—
29	C₂×C₄₁	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented
30	D₄₁	—	147	2	no	—
31	C₇²	C₂×D₁₂₃	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃×C₇	D₂₈₇	1	8	yes	complemented
33	D₂₁	—	287	16	no	—
34	C₄₁	C₂×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Sylow
35	C₂×D₇	—	861	8	no	—
36	C₃×C₇	C₂×D₂₈₇	1	8	yes	complemented
37	C₂×C₇	D₈₆₁	1	8	yes	complemented
38	D₇	—	861	16	no	—
39	C₂×D₃	—	2009	1	no	Hall
40	C₇	C₂×D₈₆₁	1	8	yes	complemented
41	C₂×C₃	C₇⋊D₂₈₇	1	1	yes	characteristic, complemented
42	D₃	—	2009	2	no	—
43	C₂²	—	6027	1	no	Sylow
44	C₃	C₂×C₇⋊D₂₈₇	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	6027	2	no	—
46	C₂	C₃⋊(C₇⋊D₂₈₇)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊(C₇⋊D₂₈₇)
commutator, cosocle, hypocenter	C₃×C₇²×C₄₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇²×C₄₁	C₂
LCS	G ▷ C₃×C₇²×C₄₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₇⋊D₂₈₇)	C₂	direct (N × H)
2. C₂×C₃×C₇²×C₄₁	C₂	semidirect
4. C₃×C₇²×C₄₁	C₂²	semidirect
6. C₂×C₇²×C₄₁	D₃	semidirect
8. C₇²×C₄₁	C₂×D₃	semidirect
9. C₂×C₃×C₇×C₄₁	D₇	semidirect
12. C₃×C₇×C₄₁	C₂×D₇	semidirect
14. C₂×C₇×C₄₁	D₂₁	semidirect
17. C₂×C₃×C₇²	D₄₁	semidirect
19. C₇×C₄₁	C₂×D₂₁	semidirect
20. C₂×C₃×C₄₁	C₇⋊D₇	semidirect
24. C₃×C₇²	C₂×D₄₁	semidirect
25. C₃×C₄₁	C₂×C₇⋊D₇	semidirect
26. C₂×C₇²	D₁₂₃	semidirect
29. C₂×C₄₁	C₃⋊(C₇⋊D₇)	semidirect
31. C₇²	C₂×D₁₂₃	semidirect
32. C₂×C₃×C₇	D₂₈₇	semidirect
34. C₄₁	C₂×C₃⋊(C₇⋊D₇)	semidirect
36. C₃×C₇	C₂×D₂₈₇	semidirect
37. C₂×C₇	D₈₆₁	semidirect
40. C₇	C₂×D₈₆₁	semidirect
41. C₂×C₃	C₇⋊D₂₈₇	semidirect
44. C₃	C₂×C₇⋊D₂₈₇	semidirect
46. C₂	C₃⋊(C₇⋊D₂₈₇)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃⋊(C₇⋊D₂₈₇)	2
C₂×C₃×C₇²×C₄₁	2
C₂×C₇⋊D₂₈₇	3
C₂×D₈₆₁	7
C₂×C₃⋊(C₇⋊D₇)	41

Subgroups — C2×C3⋊(C7⋊D287) #37563178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊(C₇⋊D₂₈₇) #37563178