Subgroups — D₁₇₁⋊D₂₃ #30628562

Order 15732.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×D₁₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×D₂₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×D₄₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅₇⋊D₂₃	—	3	1	no	maximal
5	C₉×C₁₉×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂₃×D₅₇	—	3	1	no	—
7	C₁₉×D₆₉	—	3	1	no	—
8	C₃×D₄₃₇	D₃	1	1	yes	characteristic
9	D₁₉×D₂₃	—	9	1	no	Hall
10	C₃×C₁₉×C₂₃	C₂×D₃	1	1	yes	characteristic
11	D₄₃₇	D₉	1	1	yes	characteristic, complemented
12	C₁₉×D₂₃	—	9	1	no	—
13	C₂₃×D₁₉	—	9	1	no	—
14	D₉×D₂₃	—	19	1	no	maximal, Hall
15	D₉×D₁₉	—	23	1	no	maximal, Hall
16	C₁₉×C₂₃	C₂×D₉	1	1	yes	characteristic, complemented, Hall
17	D₂₀₇	D₁₉	1	1	yes	characteristic, complemented
18	C₉×D₂₃	—	19	1	no	—
19	D₉×C₂₃	—	19	1	no	—
20	D₁₇₁	D₂₃	1	1	yes	characteristic, complemented
21	C₉×D₁₉	—	23	1	no	—
22	D₉×C₁₉	—	23	1	no	—
23	D₃×D₂₃	—	57	1	no	—
24	D₃×D₁₉	—	69	1	no	—
25	C₉×C₂₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
26	C₉×C₁₉	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
27	D₆₉	—	3	1	no	—
28	C₃×D₂₃	—	19	1	no	—
29	D₃×C₂₃	—	57	1	no	—
30	D₅₇	—	3	1	no	—
31	C₃×D₁₉	—	23	1	no	—
32	D₃×C₁₉	—	69	1	no	—
33	C₂×D₂₃	—	171	1	no	Hall
34	C₂×D₁₉	—	207	1	no	Hall
35	C₃×C₂₃	D₃×D₁₉	1	1	yes	characteristic
36	C₃×C₁₉	D₃×D₂₃	1	1	yes	characteristic
37	C₂×C₂₃	—	171	1	no	—
38	D₂₃	—	9	1	no	—
39	D₂₃	—	19	1	no	—
40	C₂×C₁₉	—	207	1	no	—
41	D₁₉	—	9	1	no	—
42	D₁₉	—	23	1	no	—
43	C₂×D₉	—	437	1	no	Hall
44	C₂₃	D₉×D₁₉	1	1	yes	characteristic, complemented, Sylow
45	C₁₉	D₉×D₂₃	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₉	—	437	1	no	—
47	D₉	—	19	1	no	—
48	D₉	—	23	1	no	—
49	C₂×D₃	—	1311	1	no	—
50	C₉	D₁₉×D₂₃	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	437	1	no	—
52	D₃	—	57	1	no	—
53	D₃	—	69	1	no	—
54	C₂²	—	3933	1	no	Sylow
55	C₃	D₅₇⋊D₂₃	1	1	yes	characteristic
56	C₂	—	171	1	no	—
57	C₂	—	437	1	no	—
58	C₂	—	207	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₉×C₂₃	C₂²
Frattini	C₃	D₅₇⋊D₂₃
socle	C₃×C₁₉×C₂₃	C₂×D₃
LCS	G ▷ C₉×C₁₉×C₂₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂₃×D₁₇₁	C₂	semidirect
2. C₁₉×D₂₀₇	C₂	semidirect
3. C₉×D₄₃₇	C₂	semidirect
5. C₉×C₁₉×C₂₃	C₂²	semidirect
11. D₄₃₇	D₉	semidirect
16. C₁₉×C₂₃	C₂×D₉	semidirect
17. D₂₀₇	D₁₉	semidirect
20. D₁₇₁	D₂₃	semidirect
25. C₉×C₂₃	C₂×D₁₉	semidirect
26. C₉×C₁₉	C₂×D₂₃	semidirect
44. C₂₃	D₉×D₁₉	semidirect
45. C₁₉	D₉×D₂₃	semidirect
50. C₉	D₁₉×D₂₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×D₁₇₁	2
C₁₉×D₂₀₇	2
C₉×D₄₃₇	2
D₅₇⋊D₂₃	3
D₉×D₂₃	19
D₉×D₁₉	23

Subgroups — D171⋊D23 #30628562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₇₁⋊D₂₃ #30628562