Subgroups — C₂×#27162412 #38760533

Order 25284.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#3862	C₂	1	1	yes	maximal, characteristic, complemented
2	#27162412	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇⋊D₃₀₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₄₃×#3862	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	2	no	maximal
8	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×ΓL(1,𝔽₈)×C₄₃	—	14	2	no	—
10	ΓL(1,𝔽₈)⋊D₄₃	—	7	4	no	—
11	C₂×D₃₀₁	—	7	2	no	—
12	C₂×D₃₀₁	—	21	2	no	—
13	ΓL(1,𝔽₈)×C₄₃	—	14	2	no	—
14	C₂×C₇×C₄₃	—	3	2	no	—
15	C₂×C₇×C₄₃	AGL(1,𝔽₇)	1	2	yes	complemented
16	D₃₀₁	—	7	4	no	—
17	D₃₀₁	—	21	4	no	—
18	C₂×#64425	—	43	1	no	maximal, Hall
19	C₂×C₃×D₄₃	—	49	1	no	Hall
20	C₇×C₄₃	—	3	2	no	—
21	C₇×C₄₃	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
22	C₂×#3862	D₄₃	1	1	yes	characteristic, complemented
23	#64425	—	43	2	no	—
24	C₂×C₃×C₄₃	—	98	1	no	—
25	C₃×D₄₃	—	49	2	no	—
26	C₂×C₇⋊D₇	—	43	1	no	Hall
27	C₂×D₄₃	—	49	1	no	Hall
28	#3862	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
29	C₃×C₄₃	—	98	1	no	Hall
30	C₂×C₇²	C₃×D₄₃	1	1	yes	characteristic, complemented
31	C₇⋊D₇	—	43	2	no	—
32	C₂×C₄₃	#64425	1	1	yes	characteristic, complemented
33	D₄₃	—	49	2	no	—
34	C₂×AGL(1,𝔽₇)	—	301	2	no	—
35	C₇²	C₂×C₃×D₄₃	1	1	yes	characteristic, complemented, Sylow
36	C₄₃	C₂×#64425	1	1	yes	characteristic, complemented, Sylow
37	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
38	AGL(1,𝔽₇)	—	301	4	no	—
39	C₂×D₇	—	301	2	no	—
40	C₂×D₇	—	903	2	no	—
41	ΓL(1,𝔽₈)	—	14	2	no	—
42	C₂×C₇	—	3	2	no	—
43	C₂×C₇	ΓL(1,𝔽₈)⋊D₄₃	1	2	yes	complemented
44	D₇	—	301	4	no	—
45	D₇	—	903	4	no	—
46	C₂²×C₃	—	2107	1	no	Hall
47	C₇	—	3	2	no	—
48	C₇	C₂×ΓL(1,𝔽₈)⋊D₄₃	1	2	yes	complemented
49	C₂×C₃	—	2107	2	no	—
50	C₂×C₃	—	98	1	no	—
51	C₂²	—	2107	1	no	Sylow
52	C₃	—	98	1	no	Sylow
53	C₂	—	2107	2	no	—
54	C₂	#27162412	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#27162412
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×#3862	C₂	semidirect
2. #27162412	C₂	direct (N × H)
3. C₂×C₇⋊D₃₀₁	C₃	semidirect
4. C₄₃×#3862	C₂²	semidirect
5. C₇⋊D₃₀₁	C₂×C₃	semidirect
6. C₂×C₇²×C₄₃	C₂×C₃	semidirect
8. C₇²×C₄₃	C₂²×C₃	semidirect
15. C₂×C₇×C₄₃	AGL(1,𝔽₇)	semidirect
21. C₇×C₄₃	C₂×AGL(1,𝔽₇)	semidirect
22. C₂×#3862	D₄₃	semidirect
28. #3862	C₂×D₄₃	semidirect
30. C₂×C₇²	C₃×D₄₃	semidirect
32. C₂×C₄₃	#64425	semidirect
35. C₇²	C₂×C₃×D₄₃	semidirect
36. C₄₃	C₂×#64425	semidirect
43. C₂×C₇	ΓL(1,𝔽₈)⋊D₄₃	semidirect
48. C₇	C₂×ΓL(1,𝔽₈)⋊D₄₃	semidirect
54. C₂	#27162412	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×#3862	2
#27162412	2
C₂×C₇⋊D₃₀₁	3
C₂×ΓL(1,𝔽₈)⋊D₄₃	7
C₂×#64425	43

Subgroups — C2×#27162412 #38760533

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27162412 #38760533