Subgroups — (C₃⋊D₃)⋊D₆₃₇ #37524296

Order 22932.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₃×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₉₁₁	C₂	1	2	yes	maximal, complemented
3	D₃×D₆₃₇	—	3	2	no	maximal
4	C₃²×C₁₃×C₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₉₁₁	D₃	1	2	yes	complemented
6	D₃×C₁₃×C₄₉	—	3	2	no	—
7	D₃×C₁₃×C₄₉	—	6	1	no	—
8	C₃×D₆₃₇	—	3	2	no	—
9	(C₃⋊D₃)⋊D₉₁	—	7	1	no	maximal
10	C₂×D₆₃₇	—	9	1	no	Hall
11	C₃×C₁₃×C₄₉	—	2	1	no	—
12	C₃×C₁₃×C₄₉	C₂×D₃	1	2	yes	complemented
13	(C₃⋊D₃)⋊D₄₉	—	13	1	no	maximal, Hall
14	C₇×C₁₃×C₃⋊D₃	D₇	1	1	yes	characteristic
15	C₃×D₂₇₃	—	7	2	no	—
16	C₂×C₁₃×C₄₉	—	9	1	no	—
17	D₆₃₇	—	3	2	no	—
18	D₃×D₉₁	—	21	2	no	—
19	C₃⋊D₃×C₄₉	D₁₃	1	1	yes	characteristic, complemented
20	C₃×D₁₄₇	—	13	2	no	—
21	C₃²×C₇×C₁₃	C₂×D₇	1	1	yes	characteristic
22	C₁₃×C₄₉	D₃²	1	1	yes	characteristic, complemented, Hall
23	D₃×D₄₉	—	39	2	no	—
24	D₂₇₃	—	7	2	no	—
25	D₃×C₇×C₁₃	—	3	2	no	—
26	D₃×C₇×C₁₃	—	6	1	no	—
27	C₃×D₉₁	—	21	2	no	—
28	(C₃⋊D₃)⋊D₁₃	—	49	1	no	Hall
29	C₃²×C₄₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×D₉₁	—	63	1	no	—
31	D₁₄₇	—	13	2	no	—
32	C₃×D₄₉	—	39	2	no	—
33	D₃×C₄₉	—	3	2	no	—
34	D₃×C₄₉	—	6	1	no	—
35	C₃×C₇×C₁₃	—	2	1	no	—
36	C₃×C₇×C₁₃	D₃×D₇	1	2	yes	—
37	(C₃⋊D₃)⋊D₇	—	91	1	no	—
38	C₁₃×C₃⋊D₃	D₄₉	1	1	yes	characteristic, complemented
39	C₃×D₃₉	—	49	2	no	—
40	C₂×D₄₉	—	117	1	no	Hall
41	C₂×C₇×C₁₃	—	9	1	no	—
42	D₉₁	—	21	2	no	—
43	D₃×D₁₃	—	147	2	no	—
44	C₃×C₄₉	—	2	1	no	—
45	C₃×C₄₉	D₃×D₁₃	1	2	yes	complemented
46	C₇×C₃⋊D₃	D₉₁	1	1	yes	characteristic
47	C₃×D₂₁	—	91	2	no	—
48	C₃²×C₁₃	C₂×D₄₉	1	1	yes	characteristic, complemented, Hall
49	C₂×C₄₉	—	9	1	no	—
50	D₄₉	—	39	2	no	—
51	C₇×C₁₃	(C₃⋊D₃)⋊D₇	1	1	yes	characteristic
52	D₃×D₇	—	273	2	no	—
53	D₃₉	—	49	2	no	—
54	C₃×D₁₃	—	147	2	no	—
55	D₃×C₁₃	—	3	2	no	—
56	D₃×C₁₃	—	6	1	no	—
57	C₃²×C₇	C₂×D₉₁	1	1	yes	characteristic
58	C₂×D₁₃	—	441	1	no	Hall
59	C₄₉	(C₃⋊D₃)⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
60	D₂₁	—	91	2	no	—
61	C₃×D₇	—	273	2	no	—
62	D₃×C₇	—	3	2	no	—
63	D₃×C₇	—	6	1	no	—
64	C₃×C₁₃	—	2	1	no	—
65	C₃×C₁₃	D₃×D₄₉	1	2	yes	complemented
66	D₃²	—	637	1	no	Hall
67	C₂×D₇	—	819	1	no	—
68	C₂×C₁₃	—	9	1	no	—
69	D₁₃	—	147	2	no	—
70	C₃×C₇	—	2	1	no	—
71	C₃×C₇	D₃×D₉₁	1	2	yes	—
72	C₃⋊D₃	D₆₃₇	1	1	yes	characteristic, complemented
73	C₃×D₃	—	637	2	no	—
74	C₂×C₇	—	9	1	no	—
75	D₇	—	273	2	no	—
76	C₁₃	(C₃⋊D₃)⋊D₄₉	1	1	yes	characteristic, complemented, Sylow
77	C₂×D₃	—	1911	2	no	—
78	C₃²	C₂×D₆₃₇	1	1	yes	characteristic, complemented, Sylow
79	C₇	(C₃⋊D₃)⋊D₉₁	1	1	yes	characteristic
80	C₂×C₃	—	1911	2	no	—
81	D₃	—	3	2	no	—
82	D₃	—	6	1	no	—
83	D₃	—	637	2	no	—
84	C₂²	—	5733	1	no	Sylow
85	C₃	—	2	1	no	—
86	C₃	D₃×D₆₃₇	1	2	yes	complemented
87	C₂	—	9	1	no	—
88	C₂	—	1911	2	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃²×C₁₃×C₄₉	C₂²
Frattini	C₇	(C₃⋊D₃)⋊D₉₁
socle	C₃²×C₇×C₁₃	C₂×D₇
LCS	G ▷ C₃²×C₁₃×C₄₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃⋊D₃×C₄₉	C₂	semidirect
2. C₃×D₁₉₁₁	C₂	semidirect
4. C₃²×C₁₃×C₄₉	C₂²	semidirect
5. D₁₉₁₁	D₃	semidirect
12. C₃×C₁₃×C₄₉	C₂×D₃	semidirect
19. C₃⋊D₃×C₄₉	D₁₃	semidirect
22. C₁₃×C₄₉	D₃²	semidirect
29. C₃²×C₄₉	C₂×D₁₃	semidirect
38. C₁₃×C₃⋊D₃	D₄₉	semidirect
45. C₃×C₄₉	D₃×D₁₃	semidirect
48. C₃²×C₁₃	C₂×D₄₉	semidirect
59. C₄₉	(C₃⋊D₃)⋊D₁₃	semidirect
65. C₃×C₁₃	D₃×D₄₉	semidirect
72. C₃⋊D₃	D₆₃₇	semidirect
76. C₁₃	(C₃⋊D₃)⋊D₄₉	semidirect
78. C₃²	C₂×D₆₃₇	semidirect
86. C₃	D₃×D₆₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₃⋊D₃×C₄₉	2
C₃×D₁₉₁₁	2
D₃×D₆₃₇	3
(C₃⋊D₃)⋊D₉₁	7
(C₃⋊D₃)⋊D₄₉	13

Subgroups — (C3⋊D3)⋊D637 #37524296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₃⋊D₃)⋊D₆₃₇ #37524296