Subgroups — C₂×D₆₁₂₃ #37587667

Order 24492.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₁₂₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₃×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₀₄₁	—	3	1	no	maximal, Hall
4	C₃×C₁₃×C₁₅₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₁₅₇	D₃	1	1	yes	characteristic, complemented
6	D₂₀₄₁	—	3	2	no	—
7	C₁₃×C₁₅₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₄₇₁	—	13	1	no	maximal, Hall
9	C₂×C₃×C₁₅₇	D₁₃	1	1	yes	characteristic, complemented
10	D₄₇₁	—	13	2	no	—
11	C₂×D₁₅₇	—	39	1	no	Hall
12	C₃×C₁₅₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₅₇	D₃₉	1	1	yes	characteristic, complemented
14	D₁₅₇	—	39	2	no	—
15	C₁₅₇	C₂×D₃₉	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₃₉	—	157	1	no	maximal, Hall
17	C₂×C₃×C₁₃	D₁₅₇	1	1	yes	characteristic, complemented
18	D₃₉	—	157	2	no	—
19	C₂×D₁₃	—	471	1	no	Hall
20	C₃×C₁₃	C₂×D₁₅₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₃	D₄₇₁	1	1	yes	characteristic, complemented
22	D₁₃	—	471	2	no	—
23	C₁₃	C₂×D₄₇₁	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₃	—	2041	1	no	Hall
25	C₂×C₃	D₂₀₄₁	1	1	yes	characteristic, complemented
26	D₃	—	2041	2	no	—
27	C₂²	—	6123	1	no	Sylow
28	C₃	C₂×D₂₀₄₁	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	6123	2	no	—
30	C₂	D₆₁₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₆₁₂₃
commutator, cosocle, hypocenter	C₃×C₁₃×C₁₅₇	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₁₅₇	C₂
LCS	G ▷ C₃×C₁₃×C₁₅₇
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.