Subgroups — D₆₁×D₁₅₃ #49152608

Order 37332.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₉₃₃₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×D₁₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₁₇×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅₁×D₆₁	—	3	1	no	maximal
5	C₉×C₁₇×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃₁₁₁	—	3	1	no	—
7	C₆₁×D₅₁	—	3	1	no	—
8	C₃×C₁₇×D₆₁	D₃	1	1	yes	characteristic
9	D₁₇×D₆₁	—	9	1	no	Hall
10	C₃×C₁₇×C₆₁	C₂×D₃	1	1	yes	characteristic
11	D₉×D₆₁	—	17	1	no	maximal, Hall
12	D₁₀₃₇	—	9	1	no	—
13	C₁₇×D₆₁	D₉	1	1	yes	characteristic, complemented
14	D₁₇×C₆₁	—	9	1	no	—
15	D₅₄₉	—	17	1	no	—
16	C₉×D₆₁	D₁₇	1	1	yes	characteristic, complemented
17	D₉×C₆₁	—	17	1	no	—
18	C₁₇×C₆₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
19	D₃×D₆₁	—	51	1	no	—
20	C₂×D₁₅₃	—	61	1	no	maximal, Hall
21	C₉×C₆₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
22	D₁₈₃	—	51	1	no	—
23	C₃×D₆₁	D₅₁	1	1	yes	characteristic
24	D₃×C₆₁	—	51	1	no	—
25	C₂×C₉×C₁₇	—	61	1	no	—
26	D₁₅₃	—	61	1	no	—
27	D₁₅₃	D₆₁	1	1	yes	characteristic, direct product factor
28	C₂×D₆₁	—	153	1	no	Hall
29	C₂×D₅₁	—	183	1	no	—
30	C₃×C₆₁	C₂×D₅₁	1	1	yes	characteristic
31	C₉×C₁₇	C₂×D₆₁	1	1	yes	characteristic, complemented, Hall
32	C₂×C₆₁	—	153	1	no	—
33	D₆₁	—	153	1	no	—
34	D₆₁	D₁₅₃	1	1	yes	characteristic, direct product factor
35	C₂×C₃×C₁₇	—	61	1	no	—
36	D₅₁	—	3	1	no	—
37	D₅₁	—	183	1	no	—
38	C₂×D₁₇	—	549	1	no	Hall
39	C₆₁	C₂×D₁₅₃	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₁₇	D₃×D₆₁	1	1	yes	characteristic
41	C₂×D₉	—	1037	1	no	Hall
42	C₂×C₁₇	—	61	1	no	—
43	D₁₇	—	9	1	no	—
44	D₁₇	—	549	1	no	—
45	C₂×C₉	—	61	1	no	—
46	D₉	—	1037	1	no	—
47	D₉	—	17	1	no	—
48	C₁₇	D₉×D₆₁	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₃	—	3111	1	no	—
50	C₉	D₁₇×D₆₁	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	61	1	no	—
52	D₃	—	3111	1	no	—
53	D₃	—	51	1	no	—
54	C₂²	—	9333	1	no	Sylow
55	C₃	D₅₁×D₆₁	1	1	yes	characteristic
56	C₂	—	61	1	no	—
57	C₂	—	9333	1	no	—
58	C₂	—	153	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₇×C₆₁	C₂²
Frattini	C₃	D₅₁×D₆₁
socle	C₃×C₁₇×C₆₁	C₂×D₃
LCS	G ▷ C₉×C₁₇×C₆₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₉₃₃₃	C₂	semidirect
2. C₆₁×D₁₅₃	C₂	semidirect
3. C₉×C₁₇×D₆₁	C₂	semidirect
5. C₉×C₁₇×C₆₁	C₂²	semidirect
13. C₁₇×D₆₁	D₉	semidirect
16. C₉×D₆₁	D₁₇	semidirect
18. C₁₇×C₆₁	C₂×D₉	semidirect
21. C₉×C₆₁	C₂×D₁₇	semidirect
27. D₁₅₃	D₆₁	direct (N × H)
31. C₉×C₁₇	C₂×D₆₁	semidirect
34. D₆₁	D₁₅₃	direct (N × H)
39. C₆₁	C₂×D₁₅₃	semidirect
48. C₁₇	D₉×D₆₁	semidirect
50. C₉	D₁₇×D₆₁	semidirect

Maximal subgroups

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

subgroup	index
D₉₃₃₃	2
C₆₁×D₁₅₃	2
C₉×C₁₇×D₆₁	2
D₅₁×D₆₁	3
D₉×D₆₁	17
C₂×D₁₅₃	61

Subgroups — D61×D153 #49152608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₆₁×D₁₅₃ #49152608