Subgroups — #38760449

Order 25284.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27162431	C₂	1	1	yes	maximal, characteristic, complemented
2	#27162406	C₂	1	1	yes	maximal, characteristic, complemented
3	#27162404	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄₃×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	#20263479	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇⋊D₃₀₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₄₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇²×D₄₃	C₂×C₃	1	1	yes	characteristic, complemented
9	#14268588⋊C₂	—	7	8	no	maximal
10	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	#14268594	—	7	8	no	—
12	#14268592	—	7	8	no	—
13	#14268588	—	7	8	no	—
14	D₇×D₄₃	—	7	8	no	—
15	#11744749	—	7	8	no	—
16	D₃₀₁	—	7	8	no	—
17	C₇×D₄₃	AGL(1,𝔽₇)	1	8	yes	complemented
18	D₇×C₄₃	—	7	8	no	—
19	C₂×#64424	—	43	1	no	maximal, Hall
20	C₂×D₄₃⋊C₃	—	49	1	no	Hall
21	C₇×C₄₃	C₂×AGL(1,𝔽₇)	1	8	yes	complemented
22	C₂×#3861	—	43	1	no	—
23	#64424	—	43	1	no	—
24	#64424	—	43	1	no	—
25	C₂×C₄₃⋊C₃	—	49	1	no	—
26	D₄₃⋊C₃	—	49	1	no	—
27	D₄₃⋊C₃	—	49	1	no	—
28	C₂×C₇⋊D₇	—	43	1	no	Hall
29	C₂×D₄₃	—	49	1	no	Hall
30	#3861	—	43	1	no	Hall
31	C₄₃⋊C₃	—	49	1	no	Hall
32	C₂×C₇²	—	43	1	no	—
33	C₇⋊D₇	—	43	1	no	—
34	C₇⋊D₇	D₄₃⋊C₃	1	1	yes	characteristic, complemented
35	C₂×C₄₃	—	49	1	no	—
36	D₄₃	—	49	1	no	—
37	D₄₃	#64424	1	1	yes	characteristic, complemented
38	C₂×AGL(1,𝔽₇)	—	301	8	no	—
39	C₇²	C₂×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
40	C₄₃	C₂×#64424	1	1	yes	characteristic, complemented, Sylow
41	C₂×ΓL(1,𝔽₈)	—	301	8	no	—
42	AGL(1,𝔽₇)	—	301	8	no	—
43	AGL(1,𝔽₇)	—	301	8	no	—
44	C₂×D₇	—	301	8	no	—
45	ΓL(1,𝔽₈)	—	301	8	no	—
46	C₂×C₇	—	43	8	no	—
47	D₇	—	7	8	no	—
48	D₇	—	301	8	no	—
49	C₂²×C₃	—	2107	1	no	Hall
50	C₇	#14268588⋊C₂	1	8	yes	complemented
51	C₂×C₃	—	2107	1	no	—
52	C₂×C₃	—	2107	1	no	—
53	C₂×C₃	—	2107	1	no	—
54	C₂²	—	2107	1	no	Sylow
55	C₃	—	2107	1	no	Sylow
56	C₂	—	43	1	no	—
57	C₂	—	49	1	no	—
58	C₂	—	2107	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. #27162431	C₂	semidirect
2. #27162406	C₂	semidirect
3. #27162404	C₂	semidirect
4. D₄₃×C₇⋊D₇	C₃	semidirect
5. #20263479	C₂²	semidirect
6. C₇⋊D₃₀₁	C₂×C₃	semidirect
7. C₄₃×C₇⋊D₇	C₂×C₃	semidirect
8. C₇²×D₄₃	C₂×C₃	semidirect
10. C₇²×C₄₃	C₂²×C₃	semidirect
17. C₇×D₄₃	AGL(1,𝔽₇)	semidirect
21. C₇×C₄₃	C₂×AGL(1,𝔽₇)	semidirect
34. C₇⋊D₇	D₄₃⋊C₃	semidirect
37. D₄₃	#64424	semidirect
39. C₇²	C₂×D₄₃⋊C₃	semidirect
40. C₄₃	C₂×#64424	semidirect
50. C₇	#14268588⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
#27162431	2
#27162406	2
#27162404	2
D₄₃×C₇⋊D₇	3
#14268588⋊C₂	7
C₂×#64424	43