Subgroups — #18002990

Order 4736.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11924532	C₂	1	12	yes	maximal, complemented
3	C₄²×Dic₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#127×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₁₄₈	C₂²	1	6	yes	—
6	C₂²×C₂²⋊D₃₇	C₂²	1	16	yes	—
7	#11924533	—	2	4	no	—
8	#11924532	—	2	48	no	—
9	C₂×C₄×Dic₃₇	C₂²	1	6	yes	—
10	C₂²×D₄×C₃₇	C₂²	1	6	yes	—
11	#127×C₃₇	—	2	4	no	—
12	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
13	C₂⁴×C₃₇	C₂³	1	4	yes	—
14	C₂³×D₃₇	C₂³	1	4	yes	—
15	C₂×D₄×C₃₇	—	2	24	no	—
16	C₂×D₄×C₃₇	—	2	12	no	—
17	C₂²×C₄×C₃₇	C₂³	1	3	yes	—
18	C₂×C₂²⋊D₃₇	—	2	96	no	—
19	C₂²×Dic₃₇	C₂³	1	4	yes	—
20	C₂×D₁₄₈	—	2	24	no	—
21	C₂×D₁₄₈	—	2	12	no	—
22	C₄²×C₃₇	D₄	1	4	yes	complemented
23	C₄×Dic₃₇	D₄	1	24	yes	complemented
24	C₂³×C₃₇	—	2	24	no	—
25	C₂³×C₃₇	—	2	4	no	—
26	C₂³×C₃₇	C₂⁴	1	1	yes	characteristic
27	C₂²×D₃₇	—	2	4	no	—
28	C₂²×D₃₇	—	2	24	no	—
29	D₄×C₃₇	—	4	24	no	—
30	C₂×C₄×C₃₇	C₂×D₄	1	12	yes	—
31	C₂×C₄×C₃₇	C₂×D₄	1	6	yes	—
32	C₂²⋊D₃₇	—	4	64	no	—
33	C₂×Dic₃₇	C₂×D₄	1	24	yes	—
34	D₁₄₈	—	4	24	no	—
35	C₂²×C₃₇	—	4	16	no	—
36	C₂²×C₃₇	—	4	12	no	—
37	C₂²×C₃₇	C₂²×D₄	1	6	yes	—
38	C₂²×C₃₇	C₂²×D₄	1	1	yes	characteristic
39	C₂×D₃₇	—	4	12	no	—
40	C₂×D₃₇	—	4	16	no	—
41	C₄×C₃₇	#127	1	12	yes	complemented
42	Dic₃₇	#127	1	16	yes	complemented
43	#2867	—	37	1	no	maximal, Sylow
44	C₂×C₃₇	—	8	4	no	—
45	C₂×C₃₇	C₂×#127	1	4	yes	—
46	C₂×C₃₇	C₂×#127	1	3	yes	—
47	D₃₇	—	8	4	no	—
48	C₂×#127	—	37	12	no	—
49	C₂×#127	—	37	1	no	—
50	C₂×#127	D₃₇	1	1	yes	characteristic, complemented
51	C₄³	—	37	1	no	—
52	C₃₇	#2867	1	1	yes	characteristic, complemented, Sylow
53	C₂²×D₄	—	37	16	no	—
54	C₂²×D₄	—	37	6	no	—
55	C₂²×D₄	C₂×D₃₇	1	6	yes	—
56	#127	—	2	4	no	—
57	#127	—	74	48	no	—
58	#127	—	74	4	no	—
59	C₂×C₄²	—	37	6	no	—
60	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
61	C₂⁴	—	37	4	no	—
62	C₂⁴	C₂²×D₃₇	1	4	yes	—
63	C₂×D₄	—	2	24	no	—
64	C₂×D₄	—	2	12	no	—
65	C₂×D₄	—	74	96	no	—
66	C₂×D₄	—	74	24	no	—
67	C₂×D₄	—	74	12	no	—
68	C₂²×C₄	—	37	4	no	—
69	C₂²×C₄	C₂²×D₃₇	1	3	yes	—
70	C₄²	—	37	24	no	—
71	C₄²	C₂²⋊D₃₇	1	4	yes	complemented
72	C₂³	—	2	24	no	—
73	C₂³	—	2	4	no	—
74	C₂³	—	74	24	no	—
75	C₂³	—	74	4	no	—
76	C₂³	C₂³×D₃₇	1	1	yes	characteristic
77	D₄	—	4	24	no	—
78	D₄	—	148	64	no	—
79	D₄	—	148	24	no	—
80	C₂×C₄	—	37	24	no	—
81	C₂×C₄	D₄×D₃₇	1	12	yes	—
82	C₂×C₄	C₂×C₂²⋊D₃₇	1	6	yes	—
83	C₂²	—	4	16	no	—
84	C₂²	—	4	12	no	—
85	C₂²	—	148	16	no	—
86	C₂²	—	148	12	no	—
87	C₂²	C₂×D₄×D₃₇	1	6	yes	—
88	C₂²	C₂²×C₂²⋊D₃₇	1	1	yes	characteristic
89	C₄	—	37	16	no	—
90	C₄	#11924532	1	12	yes	complemented
91	C₂	—	8	4	no	—
92	C₂	—	296	4	no	—
93	C₂	#127×D₃₇	1	4	yes	—
94	C₂	C₂×#11924532	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₃₇
commutator, socle, cosocle	C₂³×C₃₇	C₂⁴
Fitting	C₂×#127×C₃₇	C₂
hypercenter	C₂×#127	D₃₇
hypocenter	C₃₇	#2867
LCS	G ▷ C₂³×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂×#127

Complements

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

N	H ≅ G/N	type
1. C₂×#11924533	C₂	semidirect
2. C₂×#11924532	C₂	semidirect
3. C₄²×Dic₃₇	C₂	semidirect
4. C₂×#127×C₃₇	C₂	semidirect
22. C₄²×C₃₇	D₄	semidirect
23. C₄×Dic₃₇	D₄	semidirect
41. C₄×C₃₇	#127	semidirect
42. Dic₃₇	#127	semidirect
50. C₂×#127	D₃₇	semidirect
52. C₃₇	#2867	semidirect
71. C₄²	C₂²⋊D₃₇	semidirect
90. C₄	#11924532	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11924533	2
C₂×#11924532	2
C₄²×Dic₃₇	2
C₂×#127×C₃₇	2
#2867	37