Subgroups — #38760476

Order 25284.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27162424	C₂	1	2	yes	maximal, complemented
2	C₄₃×#64425	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₇⋊D₇)⋊D₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₄₃×#3862	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₄₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇×D₃₀₁	C₂×C₃	1	2	yes	complemented
7	AGL(1,𝔽₇)×D₄₃	—	7	2	no	maximal
8	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	ΓL(1,𝔽₈)⋊D₄₃	—	14	2	no	—
10	AGL(1,𝔽₇)×C₄₃	—	7	2	no	—
11	ΓL(1,𝔽₈)×D₄₃	—	7	2	no	—
12	D₇×D₄₃	—	7	2	no	—
13	ΓL(1,𝔽₈)×C₄₃	—	14	2	no	—
14	D₃₀₁	AGL(1,𝔽₇)	1	2	yes	complemented
15	C₇×D₄₃	—	7	2	no	—
16	D₇×C₄₃	—	7	2	no	—
17	D₇×C₄₃	—	42	1	no	—
18	#64422⋊C₂	—	43	1	no	maximal, Hall
19	C₂×C₃×D₄₃	—	49	1	no	Hall
20	C₇×C₄₃	—	6	1	no	—
21	C₇×C₄₃	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
22	#64425	D₄₃	1	1	yes	characteristic, complemented
23	#64422	—	43	2	no	—
24	C₂×C₃×C₄₃	—	49	1	no	—
25	C₃×D₄₃	—	98	2	no	—
26	D₇²	—	43	1	no	Hall
27	C₂×D₄₃	—	49	1	no	Hall
28	#3862	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
29	C₃×C₄₃	—	196	1	no	Hall
30	C₇⋊D₇	C₃×D₄₃	1	1	yes	characteristic, complemented
31	C₇×D₇	—	43	2	no	—
32	C₂×C₄₃	—	49	1	no	—
33	D₄₃	—	7	2	no	—
34	C₂×AGL(1,𝔽₇)	—	301	2	no	—
35	C₇²	C₂×C₃×D₄₃	1	1	yes	characteristic, complemented, Sylow
36	C₄₃	#64422⋊C₂	1	1	yes	characteristic, complemented, Sylow
37	C₂×ΓL(1,𝔽₈)	—	301	2	no	—
38	AGL(1,𝔽₇)	—	7	2	no	—
39	AGL(1,𝔽₇)	—	602	2	no	—
40	C₂×D₇	—	301	2	no	—
41	ΓL(1,𝔽₈)	—	14	2	no	—
42	C₂×C₇	—	301	2	no	—
43	D₇	—	7	2	no	—
44	D₇	—	42	1	no	—
45	D₇	—	43	2	no	—
46	C₂²×C₃	—	2107	1	no	Hall
47	C₇	—	6	1	no	—
48	C₇	AGL(1,𝔽₇)×D₄₃	1	2	yes	complemented
49	C₂×C₃	—	49	1	no	—
50	C₂×C₃	—	4214	2	no	—
51	C₂²	—	2107	1	no	Sylow
52	C₃	—	196	1	no	Sylow
53	C₂	—	301	2	no	—
54	C₂	—	49	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. #27162424	C₂	semidirect
2. C₄₃×#64425	C₂	semidirect
3. (C₇⋊D₇)⋊D₄₃	C₃	semidirect
4. C₄₃×#3862	C₂²	semidirect
5. C₄₃×C₇⋊D₇	C₂×C₃	semidirect
6. C₇×D₃₀₁	C₂×C₃	semidirect
8. C₇²×C₄₃	C₂²×C₃	semidirect
14. D₃₀₁	AGL(1,𝔽₇)	semidirect
21. C₇×C₄₃	C₂×AGL(1,𝔽₇)	semidirect
22. #64425	D₄₃	semidirect
28. #3862	C₂×D₄₃	semidirect
30. C₇⋊D₇	C₃×D₄₃	semidirect
35. C₇²	C₂×C₃×D₄₃	semidirect
36. C₄₃	#64422⋊C₂	semidirect
48. C₇	AGL(1,𝔽₇)×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#27162424	2
C₄₃×#64425	2
(C₇⋊D₇)⋊D₄₃	3
AGL(1,𝔽₇)×D₄₃	7
#64422⋊C₂	43