Subgroups — #17992546

Order 4736.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557556	C₂	1	1	yes	maximal, characteristic
2	#14557315	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#349	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596934	C₄	1	1	yes	characteristic
5	C₂×C₄×Dic₃₇	C₄	1	1	yes	characteristic
6	#11924476	—	2	1	no	—
7	#11924465	—	2	1	no	—
8	#11924465	—	2	1	no	—
9	C₂×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
10	M₃₂×C₃₇	—	2	1	no	—
11	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂²×Dic₃₇	—	2	1	no	—
13	M₁₆×C₃₇	—	4	1	no	—
14	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
15	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
16	C₄×Dic₃₇	—	2	1	no	—
17	C₄×Dic₃₇	C₈	1	1	yes	characteristic
18	C₄×Dic₃₇	C₈	1	1	yes	characteristic
19	#10596934	—	4	1	no	—
20	C₂×#64436	—	2	1	no	—
21	C₁₆×C₃₇	—	4	1	no	—
22	#10596925	—	4	1	no	—
23	C₂³×C₃₇	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₃₇	—	2	1	no	—
25	C₂×C₄×C₃₇	—	2	1	no	—
26	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
28	C₂×Dic₃₇	—	2	1	no	—
29	C₂×Dic₃₇	—	2	1	no	—
30	C₂×Dic₃₇	—	4	2	no	—
31	C₈×C₃₇	—	2	1	no	—
32	C₈×C₃₇	—	2	1	no	—
33	#64436	—	4	1	no	—
34	C₂²×C₃₇	—	2	1	no	—
35	C₂²×C₃₇	—	4	1	no	—
36	C₂²×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
37	C₄×C₃₇	—	2	1	no	—
38	C₄×C₃₇	#99	1	1	yes	characteristic
39	C₄×C₃₇	#101	1	1	yes	characteristic
40	Dic₃₇	—	2	2	no	—
41	Dic₃₇	—	4	1	no	—
42	#1327	—	37	1	no	maximal, Sylow
43	C₂×C₃₇	—	2	1	no	—
44	C₂×C₃₇	—	4	1	no	—
45	C₂×C₃₇	#324	1	1	yes	characteristic
46	#423	—	37	1	no	—
47	#349	—	37	1	no	—
48	#349	D₃₇	1	1	yes	characteristic
49	C₃₇	#1327	1	1	yes	characteristic, complemented, Sylow
50	C₂×M₁₆	—	37	1	no	—
51	C₂×M₁₆	C₂×D₃₇	1	1	yes	characteristic
52	C₂×C₄²	—	37	1	no	—
53	M₃₂	—	2	1	no	—
54	M₃₂	—	74	1	no	—
55	C₄⋊C₈	—	74	1	no	—
56	C₄⋊C₈	—	74	1	no	—
57	C₂²×C₄	—	74	1	no	—
58	C₂²×C₄	C₄×D₃₇	1	1	yes	characteristic
59	M₁₆	—	4	1	no	—
60	M₁₆	—	148	1	no	—
61	C₂×C₈	—	74	1	no	—
62	C₂×C₈	D₁₄₈	1	1	yes	characteristic
63	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
64	C₄²	—	37	1	no	—
65	C₄²	—	37	1	no	—
66	C₄²	—	74	1	no	—
67	C₁₆	—	4	1	no	—
68	C₁₆	—	148	1	no	—
69	C₂³	#10596929	1	1	yes	characteristic
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	74	1	no	—
73	C₂×C₄	—	74	1	no	—
74	C₂×C₄	—	148	2	no	—
75	C₂×C₄	C₈×D₃₇	1	1	yes	characteristic
76	C₂×C₄	#10596938	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	2	1	no	—
79	C₈	—	148	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	4	1	no	—
82	C₂²	#11924448	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	74	2	no	—
85	C₄	—	148	1	no	—
86	C₄	#11924450	1	1	yes	characteristic
87	C₄	#11924454	1	1	yes	characteristic
88	C₂	—	2	1	no	—
89	C₂	—	4	1	no	—
90	C₂	#14557258	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11924450
commutator	C₂×C₄×C₃₇	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₃₇
Fitting	C₃₇×#349	C₂
socle	C₂×C₃₇	#324
prime radical	C₂³×C₃₇	M₁₆
cosocle	C₂×M₁₆×C₃₇	C₂²
hypercenter	#349	D₃₇
hypocenter	C₃₇	#1327
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

Complements

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

N	H ≅ G/N	type
49. C₃₇	#1327	semidirect

Maximal subgroups

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

subgroup	index
#14557556	2
#14557315	2
C₃₇×#349	2
#1327	37