Subgroups — C₁₁⋊(Dic₄₃⋊C₇) #27210364

Order 13244.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₄₃⋊C₇	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₄₃⋊C₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₄₇₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
4	Dic₄₃⋊C₇	—	11	1	no	maximal, Hall
5	C₂×C₁₁×C₄₃	C₂×C₇	1	1	yes	characteristic
6	C₂×C₄₃⋊C₇	D₁₁	1	1	yes	characteristic
7	C₁₁×C₄₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×Dic₁₁	—	43	1	no	maximal, Hall
9	C₄₃⋊C₇	Dic₁₁	1	1	yes	characteristic, complemented, Hall
10	Dic₄₃	—	11	1	no	Hall
11	C₂×C₇×C₁₁	—	43	1	no	—
12	C₂×C₄₃	C₇×D₁₁	1	1	yes	characteristic
13	C₇×C₁₁	—	43	1	no	Hall
14	Dic₁₁	—	43	1	no	Hall
15	C₄₃	C₇×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
16	C₄×C₇	—	473	1	no	Hall
17	C₂×C₁₁	D₄₃⋊C₇	1	1	yes	characteristic
18	C₂×C₇	—	43	1	no	—
19	C₁₁	Dic₄₃⋊C₇	1	1	yes	characteristic, complemented, Sylow
20	C₇	—	43	1	no	Sylow
21	C₄	—	473	1	no	Sylow
22	C₂	C₁₁⋊(D₄₃⋊C₇)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₁₁⋊(D₄₃⋊C₇)
commutator, hypocenter	C₁₁×C₄₃	C₄×C₇
Fitting, socle	C₂×C₁₁×C₄₃	C₂×C₇
LCS	G ▷ C₁₁×C₄₃
UCS	C₁ ◁ C₂

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