Subgroups — #38760464

Order 25284.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27162417	C₂	1	2	yes	maximal, complemented
2	#27162407	C₂	1	1	yes	maximal, characteristic, complemented
3	D₇²×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#20263480	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₄₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇×D₇×C₄₃	C₂×C₃	1	2	yes	complemented
7	C₂×#14268591	—	7	2	no	maximal
8	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×#11744748	—	7	2	no	—
10	#14268591	—	7	2	no	—
11	#14268591	—	7	2	no	—
12	#14268591	—	14	3	no	—
13	C₂×D₇×C₄₃	—	7	2	no	—
14	#11744748	—	7	2	no	—
15	#11744748	—	14	3	no	—
16	C₂×C₇×C₄₃	—	7	2	no	—
17	D₇×C₄₃	—	7	2	no	—
18	D₇×C₄₃	—	14	3	no	—
19	D₇×C₄₃	AGL(1,𝔽₇)	1	2	yes	complemented
20	#64423⋊C₂	—	43	1	no	maximal, Hall
21	C₂²×C₄₃⋊C₃	—	49	1	no	Hall
22	C₇×C₄₃	—	2	3	no	—
23	C₇×C₄₃	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
24	#64424	—	43	1	no	—
25	#64423	—	43	2	no	—
26	C₂×C₄₃⋊C₃	—	49	2	no	—
27	C₂×C₄₃⋊C₃	—	49	1	no	—
28	D₇²	C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
29	C₂²×C₄₃	—	49	1	no	Hall
30	#3861	—	43	1	no	Hall
31	C₄₃⋊C₃	—	49	1	no	Hall
32	C₇⋊D₇	C₂×C₄₃⋊C₃	1	1	yes	characteristic, complemented
33	C₇×D₇	C₂×C₄₃⋊C₃	1	2	yes	complemented
34	C₂×C₄₃	—	7	2	no	—
35	C₂×C₄₃	—	49	1	no	—
36	C₂×AGL(1,𝔽₇)	—	301	2	no	—
37	C₇²	C₂²×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
38	C₄₃	#64423⋊C₂	1	1	yes	characteristic, complemented, Sylow
39	C₂×ΓL(1,𝔽₈)	—	301	2	no	—
40	AGL(1,𝔽₇)	—	301	2	no	—
41	AGL(1,𝔽₇)	—	301	2	no	—
42	AGL(1,𝔽₇)	—	602	3	no	—
43	C₂×D₇	—	7	2	no	—
44	ΓL(1,𝔽₈)	—	301	2	no	—
45	ΓL(1,𝔽₈)	—	602	3	no	—
46	C₂×C₇	—	7	2	no	—
47	D₇	—	7	2	no	—
48	D₇	—	14	3	no	—
49	D₇	#14268591	1	2	yes	complemented
50	C₂²×C₃	—	2107	1	no	Hall
51	C₇	—	2	3	no	—
52	C₇	C₂×#14268591	1	2	yes	complemented
53	C₂×C₃	—	2107	2	no	—
54	C₂×C₃	—	2107	1	no	—
55	C₂²	—	49	1	no	Sylow
56	C₃	—	2107	1	no	Sylow
57	C₂	—	7	2	no	—
58	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. #27162417	C₂	semidirect
2. #27162407	C₂	semidirect
3. D₇²×C₄₃	C₃	semidirect
4. #20263480	C₂²	semidirect
5. C₄₃×C₇⋊D₇	C₂×C₃	semidirect
6. C₇×D₇×C₄₃	C₂×C₃	semidirect
8. C₇²×C₄₃	C₂²×C₃	semidirect
19. D₇×C₄₃	AGL(1,𝔽₇)	semidirect
23. C₇×C₄₃	C₂×AGL(1,𝔽₇)	semidirect
28. D₇²	C₄₃⋊C₃	semidirect
32. C₇⋊D₇	C₂×C₄₃⋊C₃	semidirect
33. C₇×D₇	C₂×C₄₃⋊C₃	semidirect
37. C₇²	C₂²×C₄₃⋊C₃	semidirect
38. C₄₃	#64423⋊C₂	semidirect
49. D₇	#14268591	semidirect
52. C₇	C₂×#14268591	semidirect

Maximal subgroups

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

subgroup	index
#27162417	2
#27162407	2
D₇²×C₄₃	3
C₂×#14268591	7
#64423⋊C₂	43