Subgroups — Dic₇₉₃₁ #44540573

Order 31724.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₁×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₁×C₁₀₃	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₁₃₃	—	7	1	no	maximal, Hall
4	Dic₇₂₁	—	11	1	no	maximal, Hall
5	C₂×C₁₁×C₁₀₃	D₇	1	1	yes	characteristic
6	C₂×C₇×C₁₀₃	D₁₁	1	1	yes	characteristic
7	C₁₁×C₁₀₃	Dic₇	1	1	yes	characteristic, complemented, Hall
8	C₇×C₁₀₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
9	Dic₁₀₃	—	77	1	no	Hall
10	Dic₇₇	—	103	1	no	maximal, Hall
11	C₂×C₁₀₃	D₇₇	1	1	yes	characteristic
12	C₂×C₇×C₁₁	D₁₀₃	1	1	yes	characteristic
13	C₁₀₃	Dic₇₇	1	1	yes	characteristic, complemented, Sylow
14	C₇×C₁₁	Dic₁₀₃	1	1	yes	characteristic, complemented, Hall
15	Dic₁₁	—	721	1	no	Hall
16	Dic₇	—	1133	1	no	Hall
17	C₂×C₁₁	D₇₂₁	1	1	yes	characteristic
18	C₂×C₇	D₁₁₃₃	1	1	yes	characteristic
19	C₁₁	Dic₇₂₁	1	1	yes	characteristic, complemented, Sylow
20	C₇	Dic₁₁₃₃	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	7931	1	no	Sylow
22	C₂	D₇₉₃₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇₉₃₁
commutator, hypocenter	C₇×C₁₁×C₁₀₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₇×C₁₁×C₁₀₃	C₂
LCS	G ▷ C₇×C₁₁×C₁₀₃
UCS	C₁ ◁ C₂

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.