Subgroups — C₂²×C₄₃⋊#3862 #38760581

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	3	yes	maximal, direct product factor
2	C₂²×C₇²×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₃⋊#3862	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇²×C₄₃	C₂×C₃	1	3	yes	complemented
5	C₂²×#11744748	—	7	1	no	maximal
6	C₂²×#11744749	—	7	1	no	maximal
7	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×#11744749	—	7	3	no	—
9	C₂×#11744748	—	7	3	no	—
10	C₂²×C₇×C₄₃	—	3	2	no	—
11	C₂²×C₇×C₄₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
12	C₂²×C₇×C₄₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	#11744749	—	7	1	no	—
14	#11744748	—	7	1	no	—
15	C₂×C₇×C₄₃	—	3	6	no	—
16	C₂×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	1	3	yes	complemented
17	C₂×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	1	3	yes	complemented
18	C₂²×#3862	—	43	1	no	maximal, Hall
19	C₂²×C₄₃⋊C₃	—	49	1	no	Hall
20	C₇×C₄₃	—	3	2	no	—
21	C₇×C₄₃	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
22	C₇×C₄₃	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
23	C₂×#3862	—	43	3	no	—
24	C₂×C₄₃⋊C₃	—	49	3	no	—
25	C₂²×C₇²	C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
26	C₂²×C₄₃	#3862	1	1	yes	characteristic, complemented, Hall
27	#3862	—	43	1	no	Hall
28	C₄₃⋊C₃	—	49	1	no	Hall
29	C₂×C₇²	C₂×C₄₃⋊C₃	1	3	yes	complemented
30	C₂×C₄₃	C₂×#3862	1	3	yes	complemented
31	C₂²×ΓL(1,𝔽₈)	—	301	1	no	—
32	C₂²×ΓL(1,𝔽₈)	—	301	1	no	—
33	C₇²	C₂²×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
34	C₄₃	C₂²×#3862	1	1	yes	characteristic, complemented, Sylow
35	C₂×ΓL(1,𝔽₈)	—	301	3	no	—
36	C₂×ΓL(1,𝔽₈)	—	301	3	no	—
37	C₂²×C₇	—	3	2	no	—
38	C₂²×C₇	#11744748	1	1	yes	characteristic, complemented
39	C₂²×C₇	#11744749	1	1	yes	characteristic, complemented
40	ΓL(1,𝔽₈)	—	301	1	no	—
41	ΓL(1,𝔽₈)	—	301	1	no	—
42	C₂×C₇	—	3	6	no	—
43	C₂×C₇	C₂×#11744748	1	3	yes	complemented
44	C₂×C₇	C₂×#11744749	1	3	yes	complemented
45	C₂²×C₃	—	2107	1	no	Hall
46	C₇	—	3	2	no	—
47	C₇	C₂²×#11744749	1	1	yes	characteristic, complemented
48	C₇	C₂²×#11744748	1	1	yes	characteristic, complemented
49	C₂×C₃	—	2107	3	no	—
50	C₂²	C₄₃⋊#3862	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	—	2107	1	no	Sylow
52	C₂	C₂×C₄₃⋊#3862	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	C₄₃⋊#3862
commutator, cosocle, hypocenter	C₇²×C₄₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂²×C₇²×C₄₃	C₃
LCS	G ▷ C₇²×C₄₃
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃⋊#3862	C₂	direct (N × H)
2. C₂²×C₇²×C₄₃	C₃	semidirect
3. C₄₃⋊#3862	C₂²	direct (N × H)
4. C₂×C₇²×C₄₃	C₂×C₃	semidirect
7. C₇²×C₄₃	C₂²×C₃	semidirect
11. C₂²×C₇×C₄₃	ΓL(1,𝔽₈)	semidirect
12. C₂²×C₇×C₄₃	ΓL(1,𝔽₈)	semidirect
16. C₂×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	semidirect
17. C₂×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	semidirect
21. C₇×C₄₃	C₂²×ΓL(1,𝔽₈)	semidirect
22. C₇×C₄₃	C₂²×ΓL(1,𝔽₈)	semidirect
25. C₂²×C₇²	C₄₃⋊C₃	semidirect
26. C₂²×C₄₃	#3862	semidirect
29. C₂×C₇²	C₂×C₄₃⋊C₃	semidirect
30. C₂×C₄₃	C₂×#3862	semidirect
33. C₇²	C₂²×C₄₃⋊C₃	semidirect
34. C₄₃	C₂²×#3862	semidirect
38. C₂²×C₇	#11744748	semidirect
39. C₂²×C₇	#11744749	semidirect
43. C₂×C₇	C₂×#11744748	semidirect
44. C₂×C₇	C₂×#11744749	semidirect
47. C₇	C₂²×#11744749	semidirect
48. C₇	C₂²×#11744748	semidirect
50. C₂²	C₄₃⋊#3862	direct (N × H)
52. C₂	C₂×C₄₃⋊#3862	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
C₂²×C₇²×C₄₃	3
C₂²×#11744748	7
C₂²×#11744749	7
C₂²×#3862	43

Subgroups — C22×C43⋊#3862 #38760581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄₃⋊#3862 #38760581