Subgroups — C₃×D₁₇×D₇₇ #30628129

Order 15708.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₃₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₇×D₇₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₁₁×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₇×D₇₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₇×C₁₁×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₃₀₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₇×D₇₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×C₁₁×D₁₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×D₁₁×D₁₇	—	7	1	no	maximal, Hall
10	C₃×D₇×D₁₇	—	11	1	no	maximal, Hall
11	C₇×C₁₁×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₃×D₁₈₇	—	7	1	no	—
13	C₃×C₁₇×D₁₁	—	7	1	no	—
14	C₃×C₁₁×D₁₇	D₇	1	1	yes	characteristic, complemented
15	C₂×C₃×D₇₇	—	17	1	no	maximal, Hall
16	D₁₁×D₁₇	—	7	1	no	Hall
17	C₃×D₁₁₉	—	11	1	no	—
18	C₃×D₇×C₁₇	—	11	1	no	—
19	C₃×C₇×D₁₇	D₁₁	1	1	yes	characteristic, complemented
20	C₃×C₁₁×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
21	D₇×D₁₇	—	11	1	no	Hall
22	C₂×C₃×C₇×C₁₁	—	17	1	no	—
23	C₃×D₇₇	—	17	1	no	—
24	C₃×D₇₇	D₁₇	1	1	yes	characteristic, direct product factor
25	D₁₈₇	—	7	1	no	—
26	C₁₁×D₁₇	C₃×D₇	1	1	yes	characteristic, complemented
27	C₁₇×D₁₁	—	7	1	no	—
28	C₃×C₇×C₁₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
29	C₂×D₇₇	—	17	1	no	Hall
30	D₁₁₉	—	11	1	no	—
31	C₇×D₁₇	C₃×D₁₁	1	1	yes	characteristic, complemented
32	D₇×C₁₇	—	11	1	no	—
33	C₃×C₇×C₁₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×D₁₇	—	77	1	no	Hall
35	C₁₁×C₁₇	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
36	C₂×C₇×C₁₁	—	17	1	no	—
37	D₇₇	—	17	1	no	—
38	D₇₇	C₃×D₁₇	1	1	yes	characteristic, direct product factor
39	C₂×C₃×D₁₁	—	119	1	no	Hall
40	C₇×C₁₇	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
41	C₂×C₃×C₁₇	—	77	1	no	—
42	C₃×D₁₇	—	77	1	no	—
43	C₃×D₁₇	D₇₇	1	1	yes	characteristic, direct product factor
44	C₂×C₃×D₇	—	187	1	no	Hall
45	C₇×C₁₁	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
46	C₂×D₁₇	—	77	1	no	Hall
47	C₂×C₃×C₁₁	—	17	1	no	—
48	C₃×D₁₁	—	7	1	no	—
49	C₃×D₁₁	—	119	1	no	—
50	C₃×C₁₇	C₂×D₇₇	1	1	yes	characteristic, complemented, Hall
51	C₂×D₁₁	—	119	1	no	Hall
52	C₂×C₃×C₇	—	17	1	no	—
53	C₃×D₇	—	11	1	no	—
54	C₃×D₇	—	187	1	no	—
55	C₂×C₁₇	—	77	1	no	—
56	D₁₇	—	77	1	no	—
57	D₁₇	C₃×D₇₇	1	1	yes	characteristic, direct product factor
58	C₃×C₁₁	D₇×D₁₇	1	1	yes	characteristic, complemented, Hall
59	C₂×D₇	—	187	1	no	Hall
60	C₂×C₁₁	—	17	1	no	—
61	D₁₁	—	7	1	no	—
62	D₁₁	—	119	1	no	—
63	C₃×C₇	D₁₁×D₁₇	1	1	yes	characteristic, complemented, Hall
64	C₁₇	C₂×C₃×D₇₇	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₇	—	17	1	no	—
66	D₇	—	11	1	no	—
67	D₇	—	187	1	no	—
68	C₂²×C₃	—	1309	1	no	Hall
69	C₁₁	C₃×D₇×D₁₇	1	1	yes	characteristic, complemented, Sylow
70	C₇	C₃×D₁₁×D₁₇	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	17	1	no	—
72	C₂×C₃	—	1309	1	no	—
73	C₂×C₃	—	77	1	no	—
74	C₂²	—	1309	1	no	Sylow
75	C₃	D₁₇×D₇₇	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	17	1	no	—
77	C₂	—	1309	1	no	—
78	C₂	—	77	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₁₇×D₇₇
commutator, cosocle, hypocenter	C₇×C₁₁×C₁₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₁₇	C₂²
LCS	G ▷ C₇×C₁₁×C₁₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₃₀₉	C₂	semidirect
2. C₃×C₁₇×D₇₇	C₂	semidirect
3. C₃×C₇×C₁₁×D₁₇	C₂	semidirect
4. D₁₇×D₇₇	C₃	direct (N × H)
5. C₃×C₇×C₁₁×C₁₇	C₂²	semidirect
6. D₁₃₀₉	C₂×C₃	semidirect
7. C₁₇×D₇₇	C₂×C₃	semidirect
8. C₇×C₁₁×D₁₇	C₂×C₃	semidirect
11. C₇×C₁₁×C₁₇	C₂²×C₃	semidirect
14. C₃×C₁₁×D₁₇	D₇	semidirect
19. C₃×C₇×D₁₇	D₁₁	semidirect
20. C₃×C₁₁×C₁₇	C₂×D₇	semidirect
24. C₃×D₇₇	D₁₇	direct (N × H)
26. C₁₁×D₁₇	C₃×D₇	semidirect
28. C₃×C₇×C₁₇	C₂×D₁₁	semidirect
31. C₇×D₁₇	C₃×D₁₁	semidirect
33. C₃×C₇×C₁₁	C₂×D₁₇	semidirect
35. C₁₁×C₁₇	C₂×C₃×D₇	semidirect
38. D₇₇	C₃×D₁₇	direct (N × H)
40. C₇×C₁₇	C₂×C₃×D₁₁	semidirect
43. C₃×D₁₇	D₇₇	direct (N × H)
45. C₇×C₁₁	C₂×C₃×D₁₇	semidirect
50. C₃×C₁₇	C₂×D₇₇	semidirect
57. D₁₇	C₃×D₇₇	direct (N × H)
58. C₃×C₁₁	D₇×D₁₇	semidirect
63. C₃×C₇	D₁₁×D₁₇	semidirect
64. C₁₇	C₂×C₃×D₇₇	semidirect
69. C₁₁	C₃×D₇×D₁₇	semidirect
70. C₇	C₃×D₁₁×D₁₇	semidirect
75. C₃	D₁₇×D₇₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₁₃₀₉	2
C₃×C₁₇×D₇₇	2
C₃×C₇×C₁₁×D₁₇	2
D₁₇×D₇₇	3
C₃×D₁₁×D₁₇	7
C₃×D₇×D₁₇	11
C₂×C₃×D₇₇	17

Subgroups — C3×D17×D77 #30628129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₁₇×D₇₇ #30628129