Subgroups — C₂×C₃⋊D₃₀₀₃ #49115031

Order 36036.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃₀₀₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃₀₀₃	—	3	4	no	maximal
4	C₃²×C₇×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃₀₀₃	—	3	8	no	—
6	C₂×C₃×C₇×C₁₁×C₁₃	D₃	1	4	yes	complemented
7	C₂×C₃⋊D₄₂₉	—	7	1	no	maximal, Hall
8	C₂×D₁₀₀₁	—	9	1	no	Hall
9	C₂×C₃⋊D₂₇₃	—	11	1	no	maximal, Hall
10	C₃×C₇×C₁₁×C₁₃	C₂×D₃	1	4	yes	complemented
11	C₂×C₃⋊D₂₃₁	—	13	1	no	maximal, Hall
12	C₃⋊D₄₂₉	—	7	2	no	—
13	C₂×C₃²×C₁₁×C₁₃	D₇	1	1	yes	characteristic, complemented
14	D₁₀₀₁	—	9	2	no	—
15	C₂×C₇×C₁₁×C₁₃	C₃⋊D₃	1	1	yes	characteristic, complemented
16	C₂×D₄₂₉	—	21	4	no	—
17	C₂×C₃²×C₇×C₁₃	D₁₁	1	1	yes	characteristic, complemented
18	C₃⋊D₂₇₃	—	11	2	no	—
19	C₂×C₃²×C₇×C₁₁	D₁₃	1	1	yes	characteristic, complemented
20	C₃⋊D₂₃₁	—	13	2	no	—
21	C₃²×C₁₁×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	C₂×D₂₇₃	—	33	4	no	—
23	C₇×C₁₁×C₁₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
24	C₂×D₂₃₁	—	39	4	no	—
25	C₂×C₃×C₁₁×C₁₃	D₂₁	1	4	yes	complemented
26	D₄₂₉	—	21	8	no	—
27	C₃²×C₇×C₁₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
28	C₃²×C₇×C₁₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
29	C₂×D₁₄₃	—	63	1	no	Hall
30	C₂×C₃×C₇×C₁₃	D₃₃	1	4	yes	complemented
31	D₂₇₃	—	33	8	no	—
32	C₂×C₃⋊D₃₉	—	77	1	no	Hall
33	C₂×C₃×C₇×C₁₁	D₃₉	1	4	yes	complemented
34	D₂₃₁	—	39	8	no	—
35	C₃×C₁₁×C₁₃	C₂×D₂₁	1	4	yes	complemented
36	C₂×C₃⋊D₃₃	—	91	1	no	Hall
37	C₂×D₉₁	—	99	1	no	Hall
38	C₂×D₇₇	—	117	1	no	Hall
39	C₂×C₁₁×C₁₃	C₃⋊D₂₁	1	1	yes	characteristic, complemented
40	D₁₄₃	—	63	2	no	—
41	C₃×C₇×C₁₃	C₂×D₃₃	1	4	yes	complemented
42	C₂×C₃⋊D₂₁	—	143	1	no	Hall
43	C₂×C₃²×C₁₃	D₇₇	1	1	yes	characteristic, complemented
44	C₃⋊D₃₉	—	77	2	no	—
45	C₃×C₇×C₁₁	C₂×D₃₉	1	4	yes	complemented
46	C₂×C₃²×C₁₁	D₉₁	1	1	yes	characteristic, complemented
47	C₃⋊D₃₃	—	91	2	no	—
48	C₂×C₇×C₁₃	C₃⋊D₃₃	1	1	yes	characteristic, complemented
49	D₉₁	—	99	2	no	—
50	C₂×D₃₉	—	231	4	no	—
51	C₂×C₇×C₁₁	C₃⋊D₃₉	1	1	yes	characteristic, complemented
52	D₇₇	—	117	2	no	—
53	C₁₁×C₁₃	C₂×C₃⋊D₂₁	1	1	yes	characteristic, complemented, Hall
54	C₂×D₃₃	—	273	4	no	—
55	C₂×C₃²×C₇	D₁₄₃	1	1	yes	characteristic, complemented
56	C₃⋊D₂₁	—	143	2	no	—
57	C₃²×C₁₃	C₂×D₇₇	1	1	yes	characteristic, complemented, Hall
58	C₃²×C₁₁	C₂×D₉₁	1	1	yes	characteristic, complemented, Hall
59	C₇×C₁₃	C₂×C₃⋊D₃₃	1	1	yes	characteristic, complemented, Hall
60	C₂×D₂₁	—	429	4	no	—
61	C₂×C₃×C₁₃	D₂₃₁	1	4	yes	complemented
62	D₃₉	—	231	8	no	—
63	C₇×C₁₁	C₂×C₃⋊D₃₉	1	1	yes	characteristic, complemented, Hall
64	C₂×C₃×C₁₁	D₂₇₃	1	4	yes	complemented
65	D₃₃	—	273	8	no	—
66	C₃²×C₇	C₂×D₁₄₃	1	1	yes	characteristic, complemented, Hall
67	C₂×D₁₃	—	693	1	no	Hall
68	C₂×D₁₁	—	819	1	no	Hall
69	C₂×C₃×C₇	D₄₂₉	1	4	yes	complemented
70	D₂₁	—	429	8	no	—
71	C₃×C₁₃	C₂×D₂₃₁	1	4	yes	complemented
72	C₂×C₃⋊D₃	—	1001	1	no	Hall
73	C₃×C₁₁	C₂×D₂₇₃	1	4	yes	complemented
74	C₂×D₇	—	1287	1	no	Hall
75	C₂×C₁₃	C₃⋊D₂₃₁	1	1	yes	characteristic, complemented
76	D₁₃	—	693	2	no	—
77	C₂×C₁₁	C₃⋊D₂₇₃	1	1	yes	characteristic, complemented
78	D₁₁	—	819	2	no	—
79	C₃×C₇	C₂×D₄₂₉	1	4	yes	complemented
80	C₂×C₃²	D₁₀₀₁	1	1	yes	characteristic, complemented
81	C₃⋊D₃	—	1001	2	no	—
82	C₂×C₇	C₃⋊D₄₂₉	1	1	yes	characteristic, complemented
83	D₇	—	1287	2	no	—
84	C₁₃	C₂×C₃⋊D₂₃₁	1	1	yes	characteristic, complemented, Sylow
85	C₂×D₃	—	3003	4	no	—
86	C₁₁	C₂×C₃⋊D₂₇₃	1	1	yes	characteristic, complemented, Sylow
87	C₃²	C₂×D₁₀₀₁	1	1	yes	characteristic, complemented, Sylow
88	C₇	C₂×C₃⋊D₄₂₉	1	1	yes	characteristic, complemented, Sylow
89	C₂×C₃	D₃₀₀₃	1	4	yes	complemented
90	D₃	—	3003	8	no	—
91	C₂²	—	9009	1	no	Sylow
92	C₃	C₂×D₃₀₀₃	1	4	yes	complemented
93	C₂	—	9009	2	no	—
94	C₂	C₃⋊D₃₀₀₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊D₃₀₀₃
commutator, cosocle, hypocenter	C₃²×C₇×C₁₁×C₁₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₁₁×C₁₃	C₂
LCS	G ▷ C₃²×C₇×C₁₁×C₁₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₃₀₀₃	C₂	direct (N × H)
2. C₂×C₃²×C₇×C₁₁×C₁₃	C₂	semidirect
4. C₃²×C₇×C₁₁×C₁₃	C₂²	semidirect
6. C₂×C₃×C₇×C₁₁×C₁₃	D₃	semidirect
10. C₃×C₇×C₁₁×C₁₃	C₂×D₃	semidirect
13. C₂×C₃²×C₁₁×C₁₃	D₇	semidirect
15. C₂×C₇×C₁₁×C₁₃	C₃⋊D₃	semidirect
17. C₂×C₃²×C₇×C₁₃	D₁₁	semidirect
19. C₂×C₃²×C₇×C₁₁	D₁₃	semidirect
21. C₃²×C₁₁×C₁₃	C₂×D₇	semidirect
23. C₇×C₁₁×C₁₃	C₂×C₃⋊D₃	semidirect
25. C₂×C₃×C₁₁×C₁₃	D₂₁	semidirect
27. C₃²×C₇×C₁₃	C₂×D₁₁	semidirect
28. C₃²×C₇×C₁₁	C₂×D₁₃	semidirect
30. C₂×C₃×C₇×C₁₃	D₃₃	semidirect
33. C₂×C₃×C₇×C₁₁	D₃₉	semidirect
35. C₃×C₁₁×C₁₃	C₂×D₂₁	semidirect
39. C₂×C₁₁×C₁₃	C₃⋊D₂₁	semidirect
41. C₃×C₇×C₁₃	C₂×D₃₃	semidirect
43. C₂×C₃²×C₁₃	D₇₇	semidirect
45. C₃×C₇×C₁₁	C₂×D₃₉	semidirect
46. C₂×C₃²×C₁₁	D₉₁	semidirect
48. C₂×C₇×C₁₃	C₃⋊D₃₃	semidirect
51. C₂×C₇×C₁₁	C₃⋊D₃₉	semidirect
53. C₁₁×C₁₃	C₂×C₃⋊D₂₁	semidirect
55. C₂×C₃²×C₇	D₁₄₃	semidirect
57. C₃²×C₁₃	C₂×D₇₇	semidirect
58. C₃²×C₁₁	C₂×D₉₁	semidirect
59. C₇×C₁₃	C₂×C₃⋊D₃₃	semidirect
61. C₂×C₃×C₁₃	D₂₃₁	semidirect
63. C₇×C₁₁	C₂×C₃⋊D₃₉	semidirect
64. C₂×C₃×C₁₁	D₂₇₃	semidirect
66. C₃²×C₇	C₂×D₁₄₃	semidirect
69. C₂×C₃×C₇	D₄₂₉	semidirect
71. C₃×C₁₃	C₂×D₂₃₁	semidirect
73. C₃×C₁₁	C₂×D₂₇₃	semidirect
75. C₂×C₁₃	C₃⋊D₂₃₁	semidirect
77. C₂×C₁₁	C₃⋊D₂₇₃	semidirect
79. C₃×C₇	C₂×D₄₂₉	semidirect
80. C₂×C₃²	D₁₀₀₁	semidirect
82. C₂×C₇	C₃⋊D₄₂₉	semidirect
84. C₁₃	C₂×C₃⋊D₂₃₁	semidirect
86. C₁₁	C₂×C₃⋊D₂₇₃	semidirect
87. C₃²	C₂×D₁₀₀₁	semidirect
88. C₇	C₂×C₃⋊D₄₂₉	semidirect
89. C₂×C₃	D₃₀₀₃	semidirect
92. C₃	C₂×D₃₀₀₃	semidirect
94. C₂	C₃⋊D₃₀₀₃	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⋊D₃₀₀₃	2
C₂×C₃²×C₇×C₁₁×C₁₃	2
C₂×D₃₀₀₃	3
C₂×C₃⋊D₄₂₉	7
C₂×C₃⋊D₂₇₃	11
C₂×C₃⋊D₂₃₁	13

Subgroups — C2×C3⋊D3003 #49115031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊D₃₀₀₃ #49115031