Subgroups — C₂×#27162405 #38760512

Order 25284.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20263480	C₂	1	1	yes	maximal, characteristic, complemented
2	#27162405	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇⋊D₃₀₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#20263480	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×#14268593	—	7	8	no	maximal
8	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×#11744748	—	7	8	no	—
10	#14268593	—	7	16	no	—
11	C₂×D₃₀₁	—	7	8	no	—
12	#11744748	—	7	8	no	—
13	C₂×C₇×C₄₃	AGL(1,𝔽₇)	1	8	yes	complemented
14	D₃₀₁	—	7	16	no	—
15	C₂×#64424	—	43	1	no	maximal, Hall
16	C₂×D₄₃⋊C₃	—	49	1	no	Hall
17	C₇×C₄₃	C₂×AGL(1,𝔽₇)	1	8	yes	complemented
18	C₂×#3861	—	43	1	no	—
19	#64424	—	43	2	no	—
20	C₂×C₄₃⋊C₃	—	49	1	no	—
21	D₄₃⋊C₃	—	49	2	no	—
22	C₂×C₇⋊D₇	—	43	1	no	Hall
23	C₂×D₄₃	—	49	1	no	Hall
24	#3861	—	43	1	no	Hall
25	C₄₃⋊C₃	—	49	1	no	Hall
26	C₂×C₇²	D₄₃⋊C₃	1	1	yes	characteristic, complemented
27	C₇⋊D₇	—	43	2	no	—
28	C₂×C₄₃	#64424	1	1	yes	characteristic, complemented
29	D₄₃	—	49	2	no	—
30	C₂×AGL(1,𝔽₇)	—	301	8	no	—
31	C₇²	C₂×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
32	C₄₃	C₂×#64424	1	1	yes	characteristic, complemented, Sylow
33	C₂×ΓL(1,𝔽₈)	—	301	8	no	—
34	AGL(1,𝔽₇)	—	301	16	no	—
35	C₂×D₇	—	301	8	no	—
36	ΓL(1,𝔽₈)	—	301	8	no	—
37	C₂×C₇	#14268593	1	8	yes	complemented
38	D₇	—	301	16	no	—
39	C₂²×C₃	—	2107	1	no	Hall
40	C₇	C₂×#14268593	1	8	yes	complemented
41	C₂×C₃	—	2107	2	no	—
42	C₂×C₃	—	2107	1	no	—
43	C₂²	—	2107	1	no	Sylow
44	C₃	—	2107	1	no	Sylow
45	C₂	—	2107	2	no	—
46	C₂	#27162405	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#27162405
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×#20263480	C₂	semidirect
2. #27162405	C₂	direct (N × H)
3. C₂×C₇⋊D₃₀₁	C₃	semidirect
4. #20263480	C₂²	semidirect
5. C₇⋊D₃₀₁	C₂×C₃	semidirect
6. C₂×C₇²×C₄₃	C₂×C₃	semidirect
8. C₇²×C₄₃	C₂²×C₃	semidirect
13. C₂×C₇×C₄₃	AGL(1,𝔽₇)	semidirect
17. C₇×C₄₃	C₂×AGL(1,𝔽₇)	semidirect
26. C₂×C₇²	D₄₃⋊C₃	semidirect
28. C₂×C₄₃	#64424	semidirect
31. C₇²	C₂×D₄₃⋊C₃	semidirect
32. C₄₃	C₂×#64424	semidirect
37. C₂×C₇	#14268593	semidirect
40. C₇	C₂×#14268593	semidirect
46. C₂	#27162405	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×#20263480	2
#27162405	2
C₂×C₇⋊D₃₀₁	3
C₂×#14268593	7
C₂×#64424	43

Subgroups — C2×#27162405 #38760512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27162405 #38760512