Subgroups — C₂×C₄₇⋊(D₄₃⋊C₃) #37564646

Order 24252.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇⋊(D₄₃⋊C₃)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₄₇×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₀₂₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₄₇×C₄₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₄₃×C₄₇	C₂×C₃	1	1	yes	characteristic, complemented
6	D₂₀₂₁	C₂×C₃	1	2	yes	complemented
7	C₄₃×C₄₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×D₄₇	—	43	1	no	maximal, Hall
9	C₂×D₄₃⋊C₃	—	47	1	no	maximal, Hall
10	C₂×C₃×C₄₇	—	86	1	no	—
11	C₃×D₄₇	—	43	2	no	—
12	C₂×C₄₃⋊C₃	D₄₇	1	1	yes	characteristic, complemented
13	D₄₃⋊C₃	—	47	2	no	—
14	C₂×D₄₇	—	43	1	no	Hall
15	C₂×D₄₃	—	47	1	no	Hall
16	C₃×C₄₇	—	86	1	no	Hall
17	C₄₃⋊C₃	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₄₇	D₄₃⋊C₃	1	1	yes	characteristic, complemented
19	D₄₇	—	43	2	no	—
20	C₂×C₄₃	C₃×D₄₇	1	1	yes	characteristic, complemented
21	D₄₃	—	47	2	no	—
22	C₄₇	C₂×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₄₃	C₂×C₃×D₄₇	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	2021	1	no	Hall
25	C₂×C₃	—	86	1	no	—
26	C₂×C₃	—	2021	2	no	—
27	C₂²	—	2021	1	no	Sylow
28	C₃	—	86	1	no	Sylow
29	C₂	—	2021	2	no	—
30	C₂	C₄₇⋊(D₄₃⋊C₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₄₇⋊(D₄₃⋊C₃)
commutator, cosocle, hypocenter	C₄₃×C₄₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₄₃×C₄₇	C₂×C₃
LCS	G ▷ C₄₃×C₄₇
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.