Subgroups — C₂×D₇×#11744749 #38760503

Order 25284.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#11744749	C₂	1	1	yes	maximal, characteristic, complemented
2	D₇×#11744749	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇×D₇×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇×#11744749	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×D₇×C₄₃	C₂×C₃	1	2	yes	complemented
6	C₂×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂²×#11744749	—	7	1	no	maximal
8	C₂×D₇×C₄₃⋊C₃	—	7	1	no	maximal
9	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×#11744749	—	7	2	no	—
11	C₂×#11744749	D₇	1	1	yes	characteristic, direct product factor
12	C₂×C₇×C₄₃⋊C₃	—	7	1	no	—
13	D₇×C₄₃⋊C₃	—	7	2	no	—
14	C₂²×C₇×C₄₃	—	7	1	no	—
15	C₂×D₇×C₄₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
16	#11744749	C₂×D₇	1	1	yes	characteristic, direct product factor
17	C₇×C₄₃⋊C₃	—	7	1	no	—
18	C₂×C₇×C₄₃	—	6	1	no	—
19	C₂×C₇×C₄₃	—	7	2	no	—
20	C₂×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
21	C₂×C₇×C₄₃	C₃×D₇	1	1	yes	characteristic, complemented
22	D₇×C₄₃	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
23	C₂×D₇×ΓL(1,𝔽₈)	—	43	1	no	maximal, Hall
24	C₂²×C₄₃⋊C₃	—	49	1	no	Hall
25	C₇×C₄₃	—	6	1	no	—
26	C₇×C₄₃	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
27	C₇×C₄₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented
28	C₂×C₇×ΓL(1,𝔽₈)	—	43	1	no	—
29	D₇×ΓL(1,𝔽₈)	—	43	2	no	—
30	C₂×C₄₃⋊C₃	—	7	1	no	—
31	C₂×C₄₃⋊C₃	—	49	2	no	—
32	C₂×C₇×D₇	C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
33	C₂²×C₄₃	—	7	1	no	Hall
34	C₇×ΓL(1,𝔽₈)	—	43	1	no	Hall
35	C₄₃⋊C₃	—	7	1	no	Hall
36	C₂×C₇²	C₂×C₄₃⋊C₃	1	1	yes	characteristic, complemented
37	C₇×D₇	C₂×C₄₃⋊C₃	1	2	yes	complemented
38	C₂×C₄₃	—	7	2	no	—
39	C₂×C₄₃	D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
40	C₂×C₃×D₇	—	301	1	no	—
41	C₂²×ΓL(1,𝔽₈)	—	301	1	no	—
42	C₇²	C₂²×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
43	C₄₃	C₂×D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃×C₇	—	301	1	no	—
45	C₃×D₇	—	301	2	no	—
46	C₂×ΓL(1,𝔽₈)	—	43	1	no	—
47	C₂×ΓL(1,𝔽₈)	—	301	2	no	—
48	C₂²×C₇	—	7	1	no	—
49	C₂×D₇	#11744749	1	1	yes	characteristic, direct product factor
50	C₃×C₇	—	301	1	no	—
51	ΓL(1,𝔽₈)	—	43	1	no	—
52	C₂×C₇	—	6	1	no	—
53	C₂×C₇	—	7	2	no	—
54	C₂×C₇	D₇×C₄₃⋊C₃	1	1	yes	characteristic, complemented
55	C₂×C₇	C₂×#11744749	1	1	yes	characteristic, complemented
56	D₇	C₂×#11744749	1	2	yes	direct product factor
57	C₂²×C₃	—	2107	1	no	Hall
58	C₇	—	6	1	no	—
59	C₇	C₂×D₇×C₄₃⋊C₃	1	1	yes	characteristic, complemented
60	C₇	C₂²×#11744749	1	1	yes	characteristic, complemented
61	C₂×C₃	—	301	1	no	—
62	C₂×C₃	—	2107	2	no	—
63	C₂²	—	7	1	no	Sylow
64	C₃	—	301	1	no	Sylow
65	C₂	—	7	2	no	—
66	C₂	D₇×#11744749	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₇×#11744749
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×C₇×#11744749	C₂	semidirect
2. D₇×#11744749	C₂	direct (N × H)
3. C₂×C₇×D₇×C₄₃	C₃	semidirect
4. C₇×#11744749	C₂²	semidirect
5. C₇×D₇×C₄₃	C₂×C₃	semidirect
6. C₂×C₇²×C₄₃	C₂×C₃	semidirect
9. C₇²×C₄₃	C₂²×C₃	semidirect
11. C₂×#11744749	D₇	direct (N × H)
15. C₂×D₇×C₄₃	ΓL(1,𝔽₈)	semidirect
16. #11744749	C₂×D₇	direct (N × H)
20. C₂×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	semidirect
21. C₂×C₇×C₄₃	C₃×D₇	semidirect
22. D₇×C₄₃	C₂×ΓL(1,𝔽₈)	semidirect
26. C₇×C₄₃	C₂²×ΓL(1,𝔽₈)	semidirect
27. C₇×C₄₃	C₂×C₃×D₇	semidirect
32. C₂×C₇×D₇	C₄₃⋊C₃	semidirect
36. C₂×C₇²	C₂×C₄₃⋊C₃	semidirect
37. C₇×D₇	C₂×C₄₃⋊C₃	semidirect
39. C₂×C₄₃	D₇×ΓL(1,𝔽₈)	semidirect
42. C₇²	C₂²×C₄₃⋊C₃	semidirect
43. C₄₃	C₂×D₇×ΓL(1,𝔽₈)	semidirect
49. C₂×D₇	#11744749	direct (N × H)
54. C₂×C₇	D₇×C₄₃⋊C₃	semidirect
55. C₂×C₇	C₂×#11744749	semidirect
56. D₇	C₂×#11744749	direct (N × H)
59. C₇	C₂×D₇×C₄₃⋊C₃	semidirect
60. C₇	C₂²×#11744749	semidirect
66. C₂	D₇×#11744749	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×#11744749	2
D₇×#11744749	2
C₂×C₇×D₇×C₄₃	3
C₂²×#11744749	7
C₂×D₇×C₄₃⋊C₃	7
C₂×D₇×ΓL(1,𝔽₈)	43

Subgroups — C2×D7×#11744749 #38760503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₇×#11744749 #38760503