Subgroups — #18010968

Order 4736.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558456	C₂	1	2	yes	maximal, complemented
2	#14558430	C₂	1	2	yes	maximal
3	#14558426	C₂	1	2	yes	maximal, complemented
4	C₄×#10596929	C₂	1	1	yes	maximal, characteristic
5	#11924610	C₂²	1	4	yes	—
6	C₂×#10596929	C₄	1	1	yes	characteristic
7	C₂×#10596929	C₂²	1	1	yes	characteristic
8	C₄²×D₃₇	C₄	1	1	yes	characteristic
9	#11924446	C₄	1	1	yes	characteristic
10	#11924446	C₂²	1	1	yes	characteristic
11	C₄×#64436	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₃₇	C₄	1	1	yes	characteristic
13	C₂×C₄×D₃₇	—	2	1	no	—
14	C₂×C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₃₇	—	2	1	no	—
19	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
20	C₂×#64436	C₂×C₄	1	1	yes	characteristic
21	C₂×#64436	C₂³	1	1	yes	characteristic
22	#10596929	—	2	2	no	—
23	#10596929	—	2	2	no	—
24	#10596927	—	2	4	no	—
25	C₂²×D₃₇	M₁₆	1	1	yes	characteristic
26	C₂×C₄×C₃₇	—	2	1	no	—
27	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
28	C₂×Dic₃₇	—	2	1	no	—
29	C₂×Dic₃₇	M₁₆	1	1	yes	characteristic
30	C₄×D₃₇	—	2	1	no	—
31	C₄×D₃₇	—	2	1	no	—
32	C₄×D₃₇	—	4	2	no	—
33	C₈×C₃₇	—	2	1	no	—
34	C₈×C₃₇	—	2	1	no	—
35	#64436	M₁₆	1	2	yes	—
36	#64436	#41	1	2	yes	—
37	C₂²×C₃₇	C₂×M₁₆	1	1	yes	characteristic
38	C₂×D₃₇	—	2	1	no	—
39	C₂×D₃₇	—	4	1	no	—
40	C₄×C₃₇	—	2	2	no	—
41	C₄×C₃₇	#117	1	1	yes	characteristic
42	C₄×C₃₇	C₂×M₁₆	1	1	yes	characteristic
43	Dic₃₇	—	2	1	no	—
44	Dic₃₇	—	4	1	no	—
45	#2165	—	37	1	no	maximal, Sylow
46	C₂×C₃₇	—	2	1	no	—
47	C₂×C₃₇	#432	1	1	yes	characteristic
48	D₃₇	—	4	1	no	—
49	C₄×M₁₆	—	37	1	no	—
50	#364	—	37	2	no	—
51	#349	—	37	2	no	—
52	#347	—	37	2	no	—
53	C₃₇	#2165	1	1	yes	characteristic, complemented, Sylow
54	C₂×M₁₆	—	37	1	no	—
55	C₂×M₁₆	—	37	1	no	—
56	C₂×C₄²	—	37	1	no	—
57	M₃₂	—	37	4	no	—
58	#97	—	37	1	no	—
59	#97	—	37	1	no	—
60	C₄×C₈	—	37	1	no	—
61	C₄×C₈	#3866	1	1	yes	characteristic
62	C₂²×C₄	—	37	1	no	—
63	C₂²×C₄	—	74	1	no	—
64	M₁₆	—	74	2	no	—
65	M₁₆	—	74	2	no	—
66	C₂×C₈	—	37	1	no	—
67	C₂×C₈	—	37	1	no	—
68	C₂×C₈	C₂×#3866	1	1	yes	characteristic
69	C₂×C₈	C₂×#3866	1	1	yes	characteristic
70	C₄²	—	37	1	no	—
71	C₄²	—	74	1	no	—
72	C₄²	C₂×#3866	1	1	yes	characteristic
73	C₁₆	—	74	4	no	—
74	C₂³	—	37	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	37	1	no	—
77	C₂×C₄	—	74	1	no	—
78	C₂×C₄	—	74	1	no	—
79	C₂×C₄	—	74	1	no	—
80	C₂×C₄	—	148	2	no	—
81	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	2	1	no	—
84	C₈	—	37	2	no	—
85	C₈	—	37	2	no	—
86	C₂²	—	74	1	no	—
87	C₂²	—	148	1	no	—
88	C₂²	D₃₇⋊M₁₆	1	1	yes	characteristic
89	C₄	—	2	2	no	—
90	C₄	—	74	1	no	—
91	C₄	—	148	1	no	—
92	C₄	#11924615	1	1	yes	characteristic
93	C₄	D₃₇⋊M₁₆	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	148	1	no	—
96	C₂	#14558556	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11924615
commutator	C₂×C₄×C₃₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×#3866
Fitting	C₄×C₈×C₃₇	C₄
socle	C₂×C₃₇	#432
prime radical	C₂²×D₃₇	M₁₆
cosocle	C₂×#64436	C₂³
hypercenter	C₄×C₈	#3866
hypocenter	C₃₇	#2165
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. #14558456	C₂	semidirect
3. #14558426	C₂	semidirect
53. C₃₇	#2165	semidirect

Maximal subgroups

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

subgroup	index
#14558456	2
#14558430	2
#14558426	2
C₄×#10596929	2
#2165	37