Subgroups — C₄₃⋊C₃×C₇⋊Dic₇ #38760350

Order 25284.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄₃×C₇⋊Dic₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₄₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic
5	Dic₇×C₄₃⋊C₃	—	7	8	no	maximal
6	C₇²×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₇×C₄₃⋊C₃	D₇	1	8	yes	—
8	Dic₇×C₄₃	—	7	8	no	—
9	C₇×C₄₃⋊C₃	Dic₇	1	8	yes	complemented
10	C₂×C₇×C₄₃	C₃×D₇	1	8	yes	—
11	C₃×C₇⋊Dic₇	—	43	1	no	maximal, Hall
12	C₄×C₄₃⋊C₃	—	49	1	no	Hall
13	C₇×C₄₃	C₃×Dic₇	1	8	yes	complemented
14	C₂×C₃×C₇²	—	43	1	no	—
15	C₂×C₄₃⋊C₃	C₇⋊D₇	1	1	yes	characteristic
16	C₇⋊Dic₇	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
17	C₄×C₄₃	—	49	1	no	Hall
18	C₃×C₇²	—	43	1	no	Hall
19	C₄₃⋊C₃	C₇⋊Dic₇	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₇²	C₂×C₄₃⋊C₃	1	1	yes	characteristic
21	C₂×C₄₃	C₃×C₇⋊D₇	1	1	yes	characteristic
22	C₃×Dic₇	—	301	8	no	—
23	C₇²	C₄×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₄₃	C₃×C₇⋊Dic₇	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃×C₇	—	43	8	no	—
26	Dic₇	—	7	8	no	—
27	C₃×C₇	—	43	8	no	—
28	C₂×C₇	D₇×C₄₃⋊C₃	1	8	yes	—
29	C₃×C₄	—	2107	1	no	Hall
30	C₇	Dic₇×C₄₃⋊C₃	1	8	yes	complemented
31	C₂×C₃	—	43	1	no	—
32	C₄	—	49	1	no	Sylow
33	C₃	—	43	1	no	Sylow
34	C₂	C₇⋊D₇×C₄₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₇⋊D₇×C₄₃⋊C₃
commutator, hypocenter	C₇²×C₄₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₇²×C₄₃	C₂×C₃
prime radical	C₂×C₇²×C₄₃⋊C₃	C₂
LCS	G ▷ C₇²×C₄₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₄₃×C₇⋊Dic₇	C₃	semidirect
3. C₇²×C₄₃⋊C₃	C₄	semidirect
6. C₇²×C₄₃	C₃×C₄	semidirect
9. C₇×C₄₃⋊C₃	Dic₇	semidirect
13. C₇×C₄₃	C₃×Dic₇	semidirect
16. C₇⋊Dic₇	C₄₃⋊C₃	direct (N × H)
19. C₄₃⋊C₃	C₇⋊Dic₇	direct (N × H)
23. C₇²	C₄×C₄₃⋊C₃	semidirect
24. C₄₃	C₃×C₇⋊Dic₇	semidirect
30. C₇	Dic₇×C₄₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇²×C₄₃⋊C₃	2
C₄₃×C₇⋊Dic₇	3
Dic₇×C₄₃⋊C₃	7
C₃×C₇⋊Dic₇	43

Subgroups — C43⋊C3×C7⋊Dic7 #38760350

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃⋊C₃×C₇⋊Dic₇ #38760350