Subgroups — D₅₇⋊D₄₇ #24924281

Order 10716.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×D₁₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₈₉₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₉×D₄₇	—	3	1	no	maximal, Hall
5	C₃×C₁₉×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₈₉₃	D₃	1	1	yes	characteristic, complemented
7	C₁₉×D₄₇	—	3	1	no	—
8	D₁₉×C₄₇	—	3	1	no	—
9	C₁₉×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×D₄₇	—	19	1	no	maximal, Hall
11	D₁₄₁	D₁₉	1	1	yes	characteristic, complemented
12	C₃×D₄₇	—	19	1	no	—
13	D₃×C₄₇	—	19	1	no	—
14	D₃×D₁₉	—	47	1	no	maximal, Hall
15	C₂×D₄₇	—	57	1	no	Hall
16	C₃×C₄₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
17	D₅₇	D₄₇	1	1	yes	characteristic, complemented
18	C₃×D₁₉	—	47	1	no	—
19	D₃×C₁₉	—	47	1	no	—
20	C₂×C₄₇	—	57	1	no	—
21	D₄₇	—	3	1	no	—
22	D₄₇	—	19	1	no	—
23	C₂×D₁₉	—	141	1	no	Hall
24	C₃×C₁₉	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
25	C₄₇	D₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₉	—	141	1	no	—
27	D₁₉	—	3	1	no	—
28	D₁₉	—	47	1	no	—
29	C₁₉	D₃×D₄₇	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	893	1	no	Hall
31	C₂×C₃	—	893	1	no	—
32	D₃	—	19	1	no	—
33	D₃	—	47	1	no	—
34	C₂²	—	2679	1	no	Sylow
35	C₃	D₁₉×D₄₇	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	57	1	no	—
37	C₂	—	893	1	no	—
38	C₂	—	141	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₉×C₄₇	C₂²
LCS	G ▷ C₃×C₁₉×C₄₇
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.