Subgroups — C₂×C₁₁×C₁₇×C₃⋊D₁₅ #46778213

Order 33660.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₇×C₃⋊D₁₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×C₁₇×D₁₅	—	3	4	no	maximal
4	C₃²×C₅×C₁₁×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₁×C₁₇×C₃⋊D₃	—	5	1	no	maximal, Hall
6	C₁₁×C₁₇×D₁₅	—	3	8	no	—
7	C₂×C₃×C₅×C₁₁×C₁₇	D₃	1	4	yes	complemented
8	C₂×D₅×C₁₁×C₁₇	—	9	1	no	Hall
9	C₁₁×C₁₇×C₃⋊D₃	—	5	2	no	—
10	C₂×C₃²×C₁₁×C₁₇	D₅	1	1	yes	characteristic, complemented
11	C₂×C₁₇×C₃⋊D₁₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃×C₅×C₁₁×C₁₇	C₂×D₃	1	4	yes	complemented
13	C₂×D₃×C₁₁×C₁₇	—	15	4	no	—
14	C₂×C₁₁×C₃⋊D₁₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₅×C₁₁×C₁₇	C₃⋊D₃	1	1	yes	characteristic, complemented
16	D₅×C₁₁×C₁₇	—	9	2	no	—
17	C₃²×C₁₁×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃²×C₅×C₁₇	C₂×C₁₁	1	1	yes	characteristic, complemented
19	C₁₇×C₃⋊D₁₅	C₂×C₁₁	1	2	yes	direct product factor
20	C₂×C₃×C₁₁×C₁₇	D₁₅	1	4	yes	complemented
21	D₃×C₁₁×C₁₇	—	15	8	no	—
22	C₂×C₁₇×D₁₅	—	3	4	no	—
23	C₂×C₃²×C₅×C₁₁	C₂×C₁₇	1	1	yes	characteristic, complemented
24	C₁₁×C₃⋊D₁₅	C₂×C₁₇	1	2	yes	direct product factor
25	C₅×C₁₁×C₁₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
26	C₃²×C₅×C₁₇	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₁₁×C₁₇	—	45	1	no	Hall
28	C₂×C₁₁×D₁₅	—	3	4	no	—
29	C₂×C₁₇×C₃⋊D₃	—	5	1	no	Hall
30	C₃×C₁₁×C₁₇	C₂×D₁₅	1	4	yes	complemented
31	C₂×C₃×C₅×C₁₇	D₃×C₁₁	1	4	yes	complemented
32	C₁₇×D₁₅	—	3	8	no	—
33	C₃²×C₅×C₁₁	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
34	C₂×C₁₁×C₃⋊D₃	—	5	1	no	Hall
35	C₂×C₁₁×C₁₇	—	45	2	no	—
36	C₂×C₁₁×C₁₇	C₃⋊D₁₅	1	1	yes	characteristic, direct product factor
37	C₂×D₅×C₁₇	—	9	1	no	Hall
38	C₂×C₃×C₅×C₁₁	D₃×C₁₇	1	4	yes	complemented
39	C₁₁×D₁₅	—	3	8	no	—
40	C₂×C₃²×C₁₇	D₅×C₁₁	1	1	yes	characteristic, complemented
41	C₁₇×C₃⋊D₃	—	5	2	no	—
42	C₃×C₅×C₁₇	C₂×D₃×C₁₁	1	4	yes	complemented
43	C₂×D₅×C₁₁	—	9	1	no	Hall
44	C₂×D₃×C₁₇	—	15	4	no	—
45	C₂×C₃²×C₁₁	D₅×C₁₇	1	1	yes	characteristic, complemented
46	C₁₁×C₃⋊D₃	—	5	2	no	—
47	C₁₁×C₁₇	C₂×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor, Hall
48	C₂×C₃⋊D₁₅	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
49	C₂×C₅×C₁₇	C₁₁×C₃⋊D₃	1	1	yes	characteristic, complemented
50	D₅×C₁₇	—	9	2	no	—
51	C₃×C₅×C₁₁	C₂×D₃×C₁₇	1	4	yes	complemented
52	C₃²×C₁₇	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
53	C₂×D₃×C₁₁	—	15	4	no	—
54	C₂×C₅×C₁₁	C₁₇×C₃⋊D₃	1	1	yes	characteristic, complemented
55	D₅×C₁₁	—	9	2	no	—
56	C₂×C₃×C₁₇	C₁₁×D₁₅	1	4	yes	complemented
57	D₃×C₁₇	—	15	8	no	—
58	C₃²×C₁₁	C₂×D₅×C₁₇	1	1	yes	characteristic, complemented, Hall
59	C₂×C₃²×C₅	C₂×C₁₁×C₁₇	1	1	yes	characteristic, complemented
60	C₃⋊D₁₅	C₂×C₁₁×C₁₇	1	2	yes	direct product factor
61	C₅×C₁₇	C₂×C₁₁×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
62	C₂²×C₁₇	—	45	1	no	Hall
63	C₂×C₃×C₁₁	C₁₇×D₁₅	1	4	yes	complemented
64	D₃×C₁₁	—	15	8	no	—
65	C₂×D₁₅	—	3	4	no	—
66	C₅×C₁₁	C₂×C₁₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
67	C₃×C₁₇	C₂×C₁₁×D₁₅	1	4	yes	complemented
68	C₃²×C₅	C₂²×C₁₁×C₁₇	1	1	yes	characteristic, complemented, Hall
69	C₂²×C₁₁	—	45	1	no	Hall
70	C₂×C₃⋊D₃	—	5	1	no	Hall
71	C₂×C₁₇	—	45	2	no	—
72	C₂×C₁₇	C₁₁×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor
73	C₃×C₁₁	C₂×C₁₇×D₁₅	1	4	yes	complemented
74	C₂×C₃×C₅	D₃×C₁₁×C₁₇	1	4	yes	complemented
75	D₁₅	—	3	8	no	—
76	C₂×C₁₁	—	45	2	no	—
77	C₂×C₁₁	C₁₇×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor
78	C₂×D₅	—	9	1	no	Hall
79	C₂×C₃²	D₅×C₁₁×C₁₇	1	1	yes	characteristic, complemented
80	C₃⋊D₃	—	5	2	no	—
81	C₁₇	C₂×C₁₁×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor, Sylow
82	C₃×C₅	C₂×D₃×C₁₁×C₁₇	1	4	yes	complemented
83	C₂×D₃	—	15	4	no	—
84	C₁₁	C₂×C₁₇×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor, Sylow
85	C₂×C₅	C₁₁×C₁₇×C₃⋊D₃	1	1	yes	characteristic, complemented
86	D₅	—	9	2	no	—
87	C₃²	C₂×D₅×C₁₁×C₁₇	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	C₁₁×C₁₇×D₁₅	1	4	yes	complemented
89	D₃	—	15	8	no	—
90	C₅	C₂×C₁₁×C₁₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	45	1	no	Sylow
92	C₃	C₂×C₁₁×C₁₇×D₁₅	1	4	yes	complemented
93	C₂	—	45	2	no	—
94	C₂	C₁₁×C₁₇×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁×C₁₇	C₃⋊D₁₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂²×C₁₁×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₁₁×C₁₇	C₂
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₂×C₁₁×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₇×C₃⋊D₁₅	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₁₁×C₁₇	C₂	semidirect
4. C₃²×C₅×C₁₁×C₁₇	C₂²	semidirect
7. C₂×C₃×C₅×C₁₁×C₁₇	D₃	semidirect
10. C₂×C₃²×C₁₁×C₁₇	D₅	semidirect
11. C₂×C₁₇×C₃⋊D₁₅	C₁₁	direct (N × H)
12. C₃×C₅×C₁₁×C₁₇	C₂×D₃	semidirect
14. C₂×C₁₁×C₃⋊D₁₅	C₁₇	direct (N × H)
15. C₂×C₅×C₁₁×C₁₇	C₃⋊D₃	semidirect
17. C₃²×C₁₁×C₁₇	C₂×D₅	semidirect
18. C₂×C₃²×C₅×C₁₇	C₂×C₁₁	semidirect
19. C₁₇×C₃⋊D₁₅	C₂×C₁₁	direct (N × H)
20. C₂×C₃×C₁₁×C₁₇	D₁₅	semidirect
23. C₂×C₃²×C₅×C₁₁	C₂×C₁₇	semidirect
24. C₁₁×C₃⋊D₁₅	C₂×C₁₇	direct (N × H)
25. C₅×C₁₁×C₁₇	C₂×C₃⋊D₃	semidirect
26. C₃²×C₅×C₁₇	C₂²×C₁₁	semidirect
30. C₃×C₁₁×C₁₇	C₂×D₁₅	semidirect
31. C₂×C₃×C₅×C₁₇	D₃×C₁₁	semidirect
33. C₃²×C₅×C₁₁	C₂²×C₁₇	semidirect
36. C₂×C₁₁×C₁₇	C₃⋊D₁₅	direct (N × H)
38. C₂×C₃×C₅×C₁₁	D₃×C₁₇	semidirect
40. C₂×C₃²×C₁₇	D₅×C₁₁	semidirect
42. C₃×C₅×C₁₇	C₂×D₃×C₁₁	semidirect
45. C₂×C₃²×C₁₁	D₅×C₁₇	semidirect
47. C₁₁×C₁₇	C₂×C₃⋊D₁₅	direct (N × H)
48. C₂×C₃⋊D₁₅	C₁₁×C₁₇	direct (N × H)
49. C₂×C₅×C₁₇	C₁₁×C₃⋊D₃	semidirect
51. C₃×C₅×C₁₁	C₂×D₃×C₁₇	semidirect
52. C₃²×C₁₇	C₂×D₅×C₁₁	semidirect
54. C₂×C₅×C₁₁	C₁₇×C₃⋊D₃	semidirect
56. C₂×C₃×C₁₇	C₁₁×D₁₅	semidirect
58. C₃²×C₁₁	C₂×D₅×C₁₇	semidirect
59. C₂×C₃²×C₅	C₂×C₁₁×C₁₇	semidirect
60. C₃⋊D₁₅	C₂×C₁₁×C₁₇	direct (N × H)
61. C₅×C₁₇	C₂×C₁₁×C₃⋊D₃	semidirect
63. C₂×C₃×C₁₁	C₁₇×D₁₅	semidirect
66. C₅×C₁₁	C₂×C₁₇×C₃⋊D₃	semidirect
67. C₃×C₁₇	C₂×C₁₁×D₁₅	semidirect
68. C₃²×C₅	C₂²×C₁₁×C₁₇	semidirect
72. C₂×C₁₇	C₁₁×C₃⋊D₁₅	direct (N × H)
73. C₃×C₁₁	C₂×C₁₇×D₁₅	semidirect
74. C₂×C₃×C₅	D₃×C₁₁×C₁₇	semidirect
77. C₂×C₁₁	C₁₇×C₃⋊D₁₅	direct (N × H)
79. C₂×C₃²	D₅×C₁₁×C₁₇	semidirect
81. C₁₇	C₂×C₁₁×C₃⋊D₁₅	direct (N × H)
82. C₃×C₅	C₂×D₃×C₁₁×C₁₇	semidirect
84. C₁₁	C₂×C₁₇×C₃⋊D₁₅	direct (N × H)
85. C₂×C₅	C₁₁×C₁₇×C₃⋊D₃	semidirect
87. C₃²	C₂×D₅×C₁₁×C₁₇	semidirect
88. C₂×C₃	C₁₁×C₁₇×D₁₅	semidirect
90. C₅	C₂×C₁₁×C₁₇×C₃⋊D₃	semidirect
92. C₃	C₂×C₁₁×C₁₇×D₁₅	semidirect
94. C₂	C₁₁×C₁₇×C₃⋊D₁₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₁₇×C₃⋊D₁₅	2
C₂×C₃²×C₅×C₁₁×C₁₇	2
C₂×C₁₁×C₁₇×D₁₅	3
C₂×C₁₁×C₁₇×C₃⋊D₃	5
C₂×C₁₇×C₃⋊D₁₅	11
C₂×C₁₁×C₃⋊D₁₅	17

Subgroups — C2×C11×C17×C3⋊D15 #46778213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×C₁₇×C₃⋊D₁₅ #46778213