Subgroups — D₁₂₉⋊D₄₇ #37564654

Order 24252.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×D₁₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×D₁₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₀₂₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄₃×D₄₇	—	3	1	no	maximal, Hall
5	C₃×C₄₃×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₀₂₁	D₃	1	1	yes	characteristic, complemented
7	C₄₃×D₄₇	—	3	1	no	—
8	C₄₇×D₄₃	—	3	1	no	—
9	C₄₃×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×D₄₇	—	43	1	no	maximal, Hall
11	D₃×D₄₃	—	47	1	no	maximal, Hall
12	D₁₄₁	D₄₃	1	1	yes	characteristic, complemented
13	C₃×D₄₇	—	43	1	no	—
14	D₃×C₄₇	—	43	1	no	—
15	D₁₂₉	D₄₇	1	1	yes	characteristic, complemented
16	C₃×D₄₃	—	47	1	no	—
17	D₃×C₄₃	—	47	1	no	—
18	C₂×D₄₇	—	129	1	no	Hall
19	C₂×D₄₃	—	141	1	no	Hall
20	C₃×C₄₇	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₄₃	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₄₇	—	129	1	no	—
23	D₄₇	—	3	1	no	—
24	D₄₇	—	43	1	no	—
25	C₂×C₄₃	—	141	1	no	—
26	D₄₃	—	3	1	no	—
27	D₄₃	—	47	1	no	—
28	C₄₇	D₃×D₄₃	1	1	yes	characteristic, complemented, Sylow
29	C₄₃	D₃×D₄₇	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	2021	1	no	Hall
31	C₂×C₃	—	2021	1	no	—
32	D₃	—	43	1	no	—
33	D₃	—	47	1	no	—
34	C₂²	—	6063	1	no	Sylow
35	C₃	D₄₃×D₄₇	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	129	1	no	—
37	C₂	—	141	1	no	—
38	C₂	—	2021	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₄₃×C₄₇	C₂²
LCS	G ▷ C₃×C₄₃×C₄₇
UCS	C₁

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.