Subgroups — C₂×D₇₉₃₁ #44540588

Order 31724.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₉₃₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₁₁×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₁×C₁₀₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₁₃₃	—	7	1	no	maximal, Hall
5	C₂×D₇₂₁	—	11	1	no	maximal, Hall
6	C₂×C₁₁×C₁₀₃	D₇	1	1	yes	characteristic, complemented
7	D₁₁₃₃	—	7	2	no	—
8	C₂×C₇×C₁₀₃	D₁₁	1	1	yes	characteristic, complemented
9	D₇₂₁	—	11	2	no	—
10	C₁₁×C₁₀₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₁₀₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂×D₁₀₃	—	77	1	no	Hall
13	C₂×D₇₇	—	103	1	no	maximal, Hall
14	C₂×C₁₀₃	D₇₇	1	1	yes	characteristic, complemented
15	D₁₀₃	—	77	2	no	—
16	C₂×C₇×C₁₁	D₁₀₃	1	1	yes	characteristic, complemented
17	D₇₇	—	103	2	no	—
18	C₁₀₃	C₂×D₇₇	1	1	yes	characteristic, complemented, Sylow
19	C₇×C₁₁	C₂×D₁₀₃	1	1	yes	characteristic, complemented, Hall
20	C₂×D₁₁	—	721	1	no	Hall
21	C₂×D₇	—	1133	1	no	Hall
22	C₂×C₁₁	D₇₂₁	1	1	yes	characteristic, complemented
23	D₁₁	—	721	2	no	—
24	C₂×C₇	D₁₁₃₃	1	1	yes	characteristic, complemented
25	D₇	—	1133	2	no	—
26	C₁₁	C₂×D₇₂₁	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₂×D₁₁₃₃	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	7931	1	no	Sylow
29	C₂	—	7931	2	no	—
30	C₂	D₇₉₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₇₉₃₁
commutator, cosocle, hypocenter	C₇×C₁₁×C₁₀₃	C₂²
Frattini	C₁	G
Fitting, socle	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.