Subgroups — C₂×#27162408 #38760515

Order 25284.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#3861	C₂	1	1	yes	maximal, characteristic, complemented
2	#27162408	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇⋊D₃₀₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₄₃×#3861	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇⋊D₃₀₁	C₂×C₃	1	2	yes	complemented
6	C₂×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×ΓL(1,𝔽₈)⋊D₄₃	—	7	1	no	maximal
8	C₂×ΓL(1,𝔽₈)⋊D₄₃	—	7	7	no	maximal
9	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×ΓL(1,𝔽₈)×C₄₃	—	7	1	no	—
11	C₂×ΓL(1,𝔽₈)×C₄₃	—	14	7	no	—
12	ΓL(1,𝔽₈)⋊D₄₃	—	7	2	no	—
13	ΓL(1,𝔽₈)⋊D₄₃	—	7	14	no	—
14	C₂×D₃₀₁	—	7	1	no	—
15	C₂×D₃₀₁	—	7	7	no	—
16	ΓL(1,𝔽₈)×C₄₃	—	7	1	no	—
17	ΓL(1,𝔽₈)×C₄₃	—	14	7	no	—
18	C₂×C₇×C₄₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
19	C₂×C₇×C₄₃	AGL(1,𝔽₇)	1	7	yes	complemented
20	D₃₀₁	—	7	2	no	—
21	D₃₀₁	—	7	14	no	—
22	C₂×#64424	—	43	1	no	maximal, Hall
23	C₂×C₃×D₄₃	—	49	1	no	Hall
24	C₇×C₄₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
25	C₇×C₄₃	C₂×AGL(1,𝔽₇)	1	7	yes	complemented
26	C₂×#3861	D₄₃	1	1	yes	characteristic, complemented
27	#64424	—	43	2	no	—
28	C₂×C₃×C₄₃	—	98	1	no	—
29	C₃×D₄₃	—	49	2	no	—
30	C₂×C₇⋊D₇	—	43	1	no	Hall
31	C₂×D₄₃	—	49	1	no	Hall
32	#3861	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
33	C₃×C₄₃	—	98	1	no	Hall
34	C₂×C₇²	C₃×D₄₃	1	1	yes	characteristic, complemented
35	C₇⋊D₇	—	43	2	no	—
36	C₂×C₄₃	#64424	1	1	yes	characteristic, complemented
37	D₄₃	—	49	2	no	—
38	C₂×AGL(1,𝔽₇)	—	301	1	no	—
39	C₂×AGL(1,𝔽₇)	—	301	7	no	—
40	C₇²	C₂×C₃×D₄₃	1	1	yes	characteristic, complemented, Sylow
41	C₄₃	C₂×#64424	1	1	yes	characteristic, complemented, Sylow
42	C₂×ΓL(1,𝔽₈)	—	7	1	no	—
43	C₂×ΓL(1,𝔽₈)	—	14	7	no	—
44	AGL(1,𝔽₇)	—	301	2	no	—
45	AGL(1,𝔽₇)	—	301	14	no	—
46	C₂×D₇	—	301	1	no	—
47	C₂×D₇	—	301	7	no	—
48	ΓL(1,𝔽₈)	—	7	1	no	—
49	ΓL(1,𝔽₈)	—	14	7	no	—
50	C₂×C₇	ΓL(1,𝔽₈)⋊D₄₃	1	1	yes	characteristic, complemented
51	C₂×C₇	ΓL(1,𝔽₈)⋊D₄₃	1	7	yes	complemented
52	D₇	—	301	2	no	—
53	D₇	—	301	14	no	—
54	C₂²×C₃	—	2107	1	no	Hall
55	C₇	C₂×ΓL(1,𝔽₈)⋊D₄₃	1	1	yes	characteristic, complemented
56	C₇	C₂×ΓL(1,𝔽₈)⋊D₄₃	1	7	yes	complemented
57	C₂×C₃	—	2107	2	no	—
58	C₂×C₃	—	98	1	no	—
59	C₂²	—	2107	1	no	Sylow
60	C₃	—	98	1	no	Sylow
61	C₂	—	2107	2	no	—
62	C₂	#27162408	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#27162408
commutator, cosocle, hypocenter	C₇²×C₄₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₄₃	C₂×C₃
LCS	G ▷ C₇²×C₄₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#3861	C₂	semidirect
2. #27162408	C₂	direct (N × H)
3. C₂×C₇⋊D₃₀₁	C₃	semidirect
4. C₄₃×#3861	C₂²	semidirect
5. C₇⋊D₃₀₁	C₂×C₃	semidirect
6. C₂×C₇²×C₄₃	C₂×C₃	semidirect
9. C₇²×C₄₃	C₂²×C₃	semidirect
18. C₂×C₇×C₄₃	AGL(1,𝔽₇)	semidirect
19. C₂×C₇×C₄₃	AGL(1,𝔽₇)	semidirect
24. C₇×C₄₃	C₂×AGL(1,𝔽₇)	semidirect
25. C₇×C₄₃	C₂×AGL(1,𝔽₇)	semidirect
26. C₂×#3861	D₄₃	semidirect
32. #3861	C₂×D₄₃	semidirect
34. C₂×C₇²	C₃×D₄₃	semidirect
36. C₂×C₄₃	#64424	semidirect
40. C₇²	C₂×C₃×D₄₃	semidirect
41. C₄₃	C₂×#64424	semidirect
50. C₂×C₇	ΓL(1,𝔽₈)⋊D₄₃	semidirect
51. C₂×C₇	ΓL(1,𝔽₈)⋊D₄₃	semidirect
55. C₇	C₂×ΓL(1,𝔽₈)⋊D₄₃	semidirect
56. C₇	C₂×ΓL(1,𝔽₈)⋊D₄₃	semidirect
62. C₂	#27162408	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×C₄₃×#3861	2
#27162408	2
C₂×C₇⋊D₃₀₁	3
C₂×ΓL(1,𝔽₈)⋊D₄₃	7
C₂×#64424	43

Subgroups — C2×#27162408 #38760515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27162408 #38760515