Subgroups — #17992537

Order 4736.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557559	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊#10596925	C₂	1	1	yes	maximal, characteristic
3	C₃₇×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596934	C₄	1	1	yes	characteristic
5	#11924495	C₄	1	1	yes	characteristic
6	C₂×#10596925	—	2	1	no	—
7	#11924465	—	2	1	no	—
8	#11924465	—	2	1	no	—
9	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
10	C₂×C₁₆×C₃₇	—	2	1	no	—
11	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₃₇	—	4	1	no	—
13	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
14	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
15	C₂²⋊Dic₃₇	—	2	1	no	—
16	C₄⋊Dic₃₇	C₈	1	1	yes	characteristic
17	C₄⋊Dic₃₇	C₈	1	1	yes	characteristic
18	C₄×Dic₃₇	—	2	1	no	—
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	C₈×C₃₇	—	2	1	no	—
31	C₈×C₃₇	—	2	1	no	—
32	#64436	—	4	1	no	—
33	C₂²×C₃₇	—	2	1	no	—
34	C₂²×C₃₇	—	2	1	no	—
35	C₂²×C₃₇	—	2	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	—	4	1	no	—
41	Dic₃₇	—	4	1	no	—
42	#1323	—	37	1	no	maximal, Sylow
43	C₂×C₃₇	—	4	1	no	—
44	C₂×C₃₇	#324	1	1	yes	characteristic
45	C₂×C₃₇	#350	1	1	yes	characteristic
46	C₂×C₃₇	#350	1	1	yes	characteristic
47	#424	—	37	1	no	—
48	C₂²⋊C₁₆	—	37	1	no	—
49	C₂²⋊C₁₆	D₃₇	1	1	yes	characteristic
50	C₃₇	#1323	1	1	yes	characteristic, complemented, Sylow
51	C₂×M₁₆	—	37	1	no	—
52	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
53	#117	—	37	1	no	—
54	C₂×C₁₆	—	2	1	no	—
55	C₂×C₁₆	—	74	1	no	—
56	C₄⋊C₈	—	74	1	no	—
57	C₄⋊C₈	—	74	1	no	—
58	C₂²×C₄	C₄×D₃₇	1	1	yes	characteristic
59	M₁₆	—	148	1	no	—
60	C₂×C₈	—	4	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	C₄⋊C₄	—	37	1	no	—
65	C₄⋊C₄	—	37	1	no	—
66	C₂²⋊C₄	—	74	1	no	—
67	C₄²	—	74	1	no	—
68	C₁₆	—	4	1	no	—
69	C₁₆	—	148	1	no	—
70	C₂³	#10596929	1	1	yes	characteristic
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	74	1	no	—
74	C₂×C₄	—	74	1	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	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	#11924448	1	1	yes	characteristic
84	C₄	—	2	1	no	—
85	C₄	—	148	1	no	—
86	C₄	—	148	1	no	—
87	C₄	#11924450	1	1	yes	characteristic
88	C₄	#11924454	1	1	yes	characteristic
89	C₂	—	4	1	no	—
90	C₂	#14557258	1	1	yes	characteristic
91	C₂	#14557316	1	1	yes	characteristic
92	C₂	#14557318	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10596938
commutator	C₂×C₄×C₃₇	C₂×C₈
Frattini	C₂²×C₈	C₂×D₃₇
Fitting	C₃₇×C₂²⋊C₁₆	C₂
socle	C₂²×C₃₇	C₂²⋊C₈
prime radical	C₂³×C₃₇	M₁₆
cosocle	C₂²×C₈×C₃₇	C₂²
hypercenter	C₂²⋊C₁₆	D₃₇
hypocenter	C₃₇	#1323
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

Complements

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

N	H ≅ G/N	type
50. C₃₇	#1323	semidirect

Maximal subgroups

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

subgroup	index
#14557559	2
C₂²⋊#10596925	2
C₃₇×C₂²⋊C₁₆	2
#1323	37