Subgroups — C₂×D₉₂₃₁ #49147384

Order 36924.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₉₂₃₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₇×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃₀₇₇	—	3	1	no	maximal, Hall
4	C₃×C₁₇×C₁₈₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₇×C₁₈₁	D₃	1	1	yes	characteristic, complemented
6	D₃₀₇₇	—	3	2	no	—
7	C₁₇×C₁₈₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₅₄₃	—	17	1	no	maximal, Hall
9	C₂×C₃×C₁₈₁	D₁₇	1	1	yes	characteristic, complemented
10	D₅₄₃	—	17	2	no	—
11	C₂×D₁₈₁	—	51	1	no	Hall
12	C₃×C₁₈₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₈₁	D₅₁	1	1	yes	characteristic, complemented
14	D₁₈₁	—	51	2	no	—
15	C₂×D₅₁	—	181	1	no	maximal, Hall
16	C₁₈₁	C₂×D₅₁	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃×C₁₇	D₁₈₁	1	1	yes	characteristic, complemented
18	D₅₁	—	181	2	no	—
19	C₂×D₁₇	—	543	1	no	Hall
20	C₃×C₁₇	C₂×D₁₈₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₇	D₅₄₃	1	1	yes	characteristic, complemented
22	D₁₇	—	543	2	no	—
23	C₁₇	C₂×D₅₄₃	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₃	—	3077	1	no	Hall
25	C₂×C₃	D₃₀₇₇	1	1	yes	characteristic, complemented
26	D₃	—	3077	2	no	—
27	C₂²	—	9231	1	no	Sylow
28	C₃	C₂×D₃₀₇₇	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	9231	2	no	—
30	C₂	D₉₂₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₉₂₃₁
commutator, cosocle, hypocenter	C₃×C₁₇×C₁₈₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₇×C₁₈₁	C₂
LCS	G ▷ C₃×C₁₇×C₁₈₁
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.