Subgroups — (C₄₃⋊C₃)⋊(C₇⋊D₇) #27162442

Order 12642.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇⋊D₃₀₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	(C₄₃⋊C₃)⋊D₇	—	7	8	no	maximal
5	C₇×C₄₃⋊C₃	D₇	1	8	yes	complemented
6	D₃₀₁	—	7	8	no	—
7	C₇×C₄₃	C₃×D₇	1	8	yes	complemented
8	C₃×C₇⋊D₇	—	43	1	no	maximal, Hall
9	D₄₃⋊C₃	—	49	1	no	Hall
10	C₃×C₇²	—	43	1	no	Hall
11	C₄₃⋊C₃	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
12	C₇⋊D₇	—	43	1	no	Hall
13	D₄₃	—	49	1	no	Hall
14	C₇²	D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
15	C₄₃	C₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
16	C₃×D₇	—	301	8	no	—
17	C₃×C₇	—	43	8	no	—
18	D₇	—	301	8	no	—
19	C₇	(C₄₃⋊C₃)⋊D₇	1	8	yes	complemented
20	C₂×C₃	—	2107	1	no	Hall
21	C₃	—	43	1	no	Sylow
22	C₂	—	2107	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₄₃	C₂×C₃
LCS	G ▷ C₇²×C₄₃
UCS	C₁

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

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