Subgroups — #17992548

Order 4736.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557561	C₂	1	1	yes	maximal, characteristic
2	#14557315	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#349	C₂	1	1	yes	maximal, characteristic
4	C₂²×#64436	C₄	1	1	yes	characteristic
5	#11924495	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	M₁₆×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	C₈	1	2	yes	—
16	C₄⋊Dic₃₇	—	2	1	no	—
17	C₄×Dic₃₇	—	2	1	no	—
18	C₂×#64436	—	2	1	no	—
19	C₂×#64436	—	4	1	no	—
20	C₁₆×C₃₇	—	4	1	no	—
21	#10596925	—	4	1	no	—
22	C₂³×C₃₇	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₃₇	—	2	1	no	—
24	C₂×C₄×C₃₇	—	2	1	no	—
25	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₃₇	M₁₆	1	1	yes	characteristic
27	C₂×Dic₃₇	—	2	2	no	—
28	C₈×C₃₇	—	2	1	no	—
29	C₈×C₃₇	—	2	1	no	—
30	#64436	—	4	1	no	—
31	C₂²×C₃₇	—	2	1	no	—
32	C₂²×C₃₇	—	4	1	no	—
33	C₂²×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
34	C₄×C₃₇	—	2	1	no	—
35	C₄×C₃₇	#99	1	1	yes	characteristic
36	C₄×C₃₇	#101	1	1	yes	characteristic
37	Dic₃₇	—	4	2	no	—
38	#1328	—	37	1	no	maximal, Sylow
39	C₂×C₃₇	—	2	1	no	—
40	C₂×C₃₇	—	4	1	no	—
41	C₂×C₃₇	#324	1	1	yes	characteristic
42	#424	—	37	1	no	—
43	#349	—	37	1	no	—
44	#349	D₃₇	1	1	yes	characteristic
45	C₃₇	#1328	1	1	yes	characteristic, complemented, Sylow
46	C₂×M₁₆	C₂×D₃₇	1	1	yes	characteristic
47	C₂²×C₈	—	37	1	no	—
48	#117	—	37	1	no	—
49	M₃₂	—	2	1	no	—
50	M₃₂	—	74	1	no	—
51	C₄⋊C₈	—	74	1	no	—
52	C₄⋊C₈	—	74	1	no	—
53	C₂²×C₄	C₄×D₃₇	1	1	yes	characteristic
54	M₁₆	—	4	1	no	—
55	C₂×C₈	—	74	1	no	—
56	C₂×C₈	—	148	1	no	—
57	C₂×C₈	D₁₄₈	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
59	C₄⋊C₄	—	74	1	no	—
60	C₂²⋊C₄	—	37	2	no	—
61	C₄²	—	74	1	no	—
62	C₁₆	—	4	1	no	—
63	C₁₆	—	148	1	no	—
64	C₂³	C₈×D₃₇	1	1	yes	characteristic
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	74	2	no	—
68	C₂×C₄	#10596929	1	1	yes	characteristic
69	C₂×C₄	#10596938	1	1	yes	characteristic
70	C₈	—	2	1	no	—
71	C₈	—	2	1	no	—
72	C₈	—	148	1	no	—
73	C₂²	—	2	1	no	—
74	C₂²	—	4	1	no	—
75	C₂²	#11924448	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	148	2	no	—
78	C₄	#11924450	1	1	yes	characteristic
79	C₄	#11924454	1	1	yes	characteristic
80	C₂	—	2	1	no	—
81	C₂	—	4	1	no	—
82	C₂	#14557258	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11924450
commutator, prime radical	C₂³×C₃₇	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₃₇
Fitting	C₃₇×#349	C₂
socle	C₂×C₃₇	#324
cosocle	C₂×M₁₆×C₃₇	C₂²
hypercenter	#349	D₃₇
hypocenter	C₃₇	#1328
LCS	G ▷ C₂³×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
45. C₃₇	#1328	semidirect

Maximal subgroups

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

subgroup	index
#14557561	2
#14557315	2
C₃₇×#349	2
#1328	37