Subgroups — D₈₇⋊D₄₇ #30654875

Order 16356.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×D₈₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×D₁₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₃₆₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₉×D₄₇	—	3	1	no	maximal, Hall
5	C₃×C₂₉×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₃₆₃	D₃	1	1	yes	characteristic, complemented
7	C₂₉×D₄₇	—	3	1	no	—
8	C₄₇×D₂₉	—	3	1	no	—
9	C₂₉×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×D₄₇	—	29	1	no	maximal, Hall
11	D₃×D₂₉	—	47	1	no	maximal, Hall
12	D₁₄₁	D₂₉	1	1	yes	characteristic, complemented
13	C₃×D₄₇	—	29	1	no	—
14	D₃×C₄₇	—	29	1	no	—
15	C₂×D₄₇	—	87	1	no	Hall
16	D₈₇	D₄₇	1	1	yes	characteristic, complemented
17	C₃×D₂₉	—	47	1	no	—
18	D₃×C₂₉	—	47	1	no	—
19	C₃×C₄₇	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
20	C₂×D₂₉	—	141	1	no	Hall
21	C₂×C₄₇	—	87	1	no	—
22	D₄₇	—	3	1	no	—
23	D₄₇	—	29	1	no	—
24	C₃×C₂₉	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
25	C₂×C₂₉	—	141	1	no	—
26	D₂₉	—	3	1	no	—
27	D₂₉	—	47	1	no	—
28	C₄₇	D₃×D₂₉	1	1	yes	characteristic, complemented, Sylow
29	C₂₉	D₃×D₄₇	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	1363	1	no	Hall
31	C₂×C₃	—	1363	1	no	—
32	D₃	—	29	1	no	—
33	D₃	—	47	1	no	—
34	C₂²	—	4089	1	no	Sylow
35	C₃	D₂₉×D₄₇	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	1363	1	no	—
37	C₂	—	87	1	no	—
38	C₂	—	141	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₂₉×C₄₇	C₂²
LCS	G ▷ C₃×C₂₉×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.