Subgroups — C₂×C₇²×D₁₅₃ #44472627

Order 29988.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×D₁₅₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇²×C₉×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇²×D₅₁	—	3	1	no	maximal
4	C₇²×C₉×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇²×D₅₁	—	3	2	no	—
6	C₂×C₃×C₇²×C₁₇	D₃	1	1	yes	characteristic
7	C₂×C₇×D₁₅₃	C₇	1	8	yes	maximal, direct product factor
8	C₂×C₇²×D₁₇	—	9	1	no	Hall
9	C₃×C₇²×C₁₇	C₂×D₃	1	1	yes	characteristic
10	C₇×D₁₅₃	C₂×C₇	1	16	yes	direct product factor
11	C₂×C₇×C₉×C₁₇	C₂×C₇	1	8	yes	complemented
12	C₂×C₇²×D₉	—	17	1	no	maximal, Hall
13	C₂×C₇²×C₁₇	D₉	1	1	yes	characteristic, complemented
14	C₇²×D₁₇	—	9	2	no	—
15	C₂×C₇×D₅₁	—	3	8	no	—
16	C₇×C₉×C₁₇	C₂²×C₇	1	8	yes	complemented
17	C₂×C₇²×C₉	D₁₇	1	1	yes	characteristic, complemented
18	C₇²×D₉	—	17	2	no	—
19	C₇²×C₁₇	C₂×D₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₇×C₁₇	D₃×C₇	1	8	yes	—
21	C₇×D₅₁	—	3	16	no	—
22	C₂×D₁₅₃	C₇²	1	1	yes	characteristic, direct product factor, Hall
23	C₂×D₃×C₇²	—	51	1	no	—
24	C₂×C₇×D₁₇	—	9	8	no	—
25	C₇²×C₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
26	C₃×C₇×C₁₇	C₂×D₃×C₇	1	8	yes	—
27	C₂×C₉×C₁₇	C₂×C₇²	1	1	yes	characteristic, complemented
28	D₁₅₃	C₂×C₇²	1	2	yes	direct product factor
29	C₂×C₃×C₇²	D₅₁	1	1	yes	characteristic
30	D₃×C₇²	—	51	2	no	—
31	C₂×C₇×D₉	—	17	8	no	—
32	C₂×C₇×C₁₇	C₇×D₉	1	8	yes	complemented
33	C₇×D₁₇	—	9	16	no	—
34	C₂×D₅₁	—	3	1	no	—
35	C₂²×C₇²	—	153	1	no	Hall
36	C₉×C₁₇	C₂²×C₇²	1	1	yes	characteristic, complemented, Hall
37	C₃×C₇²	C₂×D₅₁	1	1	yes	characteristic
38	C₂×C₇×C₉	C₇×D₁₇	1	8	yes	complemented
39	C₇×D₉	—	17	16	no	—
40	C₇×C₁₇	C₂×C₇×D₉	1	8	yes	complemented
41	C₂×C₃×C₁₇	D₃×C₇²	1	1	yes	characteristic
42	D₅₁	—	3	2	no	—
43	C₂×C₇²	—	153	2	no	—
44	C₂×C₇²	D₁₅₃	1	1	yes	characteristic, direct product factor
45	C₂×D₃×C₇	—	51	8	no	—
46	C₂×D₁₇	—	9	1	no	Hall
47	C₇×C₉	C₂×C₇×D₁₇	1	8	yes	complemented
48	C₃×C₁₇	C₂×D₃×C₇²	1	1	yes	characteristic
49	C₇²	C₂×D₁₅₃	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₃×C₇	C₇×D₅₁	1	8	yes	—
51	D₃×C₇	—	51	16	no	—
52	C₂×D₉	—	17	1	no	Hall
53	C₂×C₁₇	C₇²×D₉	1	1	yes	characteristic, complemented
54	D₁₇	—	9	2	no	—
55	C₂²×C₇	—	153	8	no	—
56	C₃×C₇	C₂×C₇×D₅₁	1	8	yes	—
57	C₂×C₉	C₇²×D₁₇	1	1	yes	characteristic, complemented
58	D₉	—	17	2	no	—
59	C₁₇	C₂×C₇²×D₉	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₇	—	153	16	no	—
61	C₂×C₇	C₇×D₁₅₃	1	8	yes	direct product factor
62	C₂×D₃	—	51	1	no	—
63	C₉	C₂×C₇²×D₁₇	1	1	yes	characteristic, complemented, Sylow
64	C₇	C₂×C₇×D₁₅₃	1	8	yes	direct product factor
65	C₂×C₃	C₇²×D₅₁	1	1	yes	characteristic
66	D₃	—	51	2	no	—
67	C₂²	—	153	1	no	Sylow
68	C₃	C₂×C₇²×D₅₁	1	1	yes	characteristic
69	C₂	—	153	2	no	—
70	C₂	C₇²×D₁₅₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇²	D₁₅₃
commutator, cosocle, hypocenter	C₉×C₁₇	C₂²×C₇²
Frattini	C₃	C₂×C₇²×D₅₁
Fitting	C₂×C₇²×C₉×C₁₇	C₂
socle	C₂×C₃×C₇²×C₁₇	D₃
LCS	G ▷ C₉×C₁₇
UCS	C₁ ◁ C₂×C₇²

Complements

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

N	H ≅ G/N	type
1. C₇²×D₁₅₃	C₂	direct (N × H)
2. C₂×C₇²×C₉×C₁₇	C₂	semidirect
4. C₇²×C₉×C₁₇	C₂²	semidirect
7. C₂×C₇×D₁₅₃	C₇	direct (N × H)
10. C₇×D₁₅₃	C₂×C₇	direct (N × H)
11. C₂×C₇×C₉×C₁₇	C₂×C₇	semidirect
13. C₂×C₇²×C₁₇	D₉	semidirect
16. C₇×C₉×C₁₇	C₂²×C₇	semidirect
17. C₂×C₇²×C₉	D₁₇	semidirect
19. C₇²×C₁₇	C₂×D₉	semidirect
22. C₂×D₁₅₃	C₇²	direct (N × H)
25. C₇²×C₉	C₂×D₁₇	semidirect
27. C₂×C₉×C₁₇	C₂×C₇²	semidirect
28. D₁₅₃	C₂×C₇²	direct (N × H)
32. C₂×C₇×C₁₇	C₇×D₉	semidirect
36. C₉×C₁₇	C₂²×C₇²	semidirect
38. C₂×C₇×C₉	C₇×D₁₇	semidirect
40. C₇×C₁₇	C₂×C₇×D₉	semidirect
44. C₂×C₇²	D₁₅₃	direct (N × H)
47. C₇×C₉	C₂×C₇×D₁₇	semidirect
49. C₇²	C₂×D₁₅₃	direct (N × H)
53. C₂×C₁₇	C₇²×D₉	semidirect
57. C₂×C₉	C₇²×D₁₇	semidirect
59. C₁₇	C₂×C₇²×D₉	semidirect
61. C₂×C₇	C₇×D₁₅₃	direct (N × H)
63. C₉	C₂×C₇²×D₁₇	semidirect
64. C₇	C₂×C₇×D₁₅₃	direct (N × H)
70. C₂	C₇²×D₁₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇²×D₁₅₃	2
C₂×C₇²×C₉×C₁₇	2
C₂×C₇²×D₅₁	3
C₂×C₇×D₁₅₃	7
C₂×C₇²×D₉	17

Subgroups — C2×C72×D153 #44472627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇²×D₁₅₃ #44472627