Subgroups — #17992579

Order 4736.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557663	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#10596925	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#346	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₇₄	C₄	1	1	yes	characteristic
5	C₂×#10596925	—	2	1	no	—
6	C₄⋊#64436	C₄	1	1	yes	characteristic
7	#11924465	—	2	1	no	—
8	#11924446	—	2	1	no	—
9	C₂×C₁₆×C₃₇	—	2	1	no	—
10	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₇₄	C₈	1	1	yes	characteristic
12	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
13	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
14	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₄⋊Dic₃₇	C₈	1	1	yes	characteristic
16	#10596936	—	2	1	no	—
17	C₄×Dic₃₇	—	2	1	no	—
18	C₂×#64436	—	2	1	no	—
19	C₁₆×C₃₇	—	2	2	no	—
20	#10596925	—	4	1	no	—
21	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₃₇	M₁₆	1	1	yes	characteristic
24	C₂×Dic₃₇	—	2	1	no	—
25	C₂×Dic₃₇	—	2	1	no	—
26	Dic₇₄	—	4	1	no	—
27	C₈×C₃₇	—	2	1	no	—
28	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
29	C₈×C₃₇	Q₁₆	1	1	yes	characteristic
30	#64436	—	4	1	no	—
31	C₂²×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₃₇	—	2	1	no	—
33	C₄×C₃₇	—	2	1	no	—
34	C₄×C₃₇	#103	1	1	yes	characteristic
35	C₄×C₃₇	#104	1	1	yes	characteristic
36	Dic₃₇	—	4	1	no	—
37	Dic₃₇	—	4	1	no	—
38	#1338	—	37	1	no	maximal, Sylow
39	C₂×C₃₇	Q₈⋊C₈	1	1	yes	characteristic
40	C₂×C₃₇	#349	1	1	yes	characteristic
41	C₂×C₃₇	#350	1	1	yes	characteristic
42	#446	—	37	1	no	—
43	C₄⋊C₁₆	—	37	1	no	—
44	#346	D₃₇	1	1	yes	characteristic
45	C₃₇	#1338	1	1	yes	characteristic, complemented, Sylow
46	C₄×Q₈	—	37	1	no	—
47	C₂×C₁₆	—	2	1	no	—
48	C₂×C₁₆	—	74	1	no	—
49	C₄⋊C₈	—	37	1	no	—
50	C₄⋊C₈	—	74	1	no	—
51	#97	—	74	1	no	—
52	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
53	C₂×Q₈	—	37	1	no	—
54	C₂×C₈	—	74	1	no	—
55	C₂×C₈	D₁₄₈	1	1	yes	characteristic
56	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
57	C₄⋊C₄	—	37	1	no	—
58	C₄⋊C₄	—	74	1	no	—
59	C₄²	—	74	1	no	—
60	C₄²	C₄×D₃₇	1	1	yes	characteristic
61	C₁₆	—	2	2	no	—
62	C₁₆	—	148	1	no	—
63	Q₈	—	148	1	no	—
64	C₂×C₄	—	74	1	no	—
65	C₂×C₄	—	74	1	no	—
66	C₂×C₄	C₈×D₃₇	1	1	yes	characteristic
67	C₂×C₄	#10596929	1	1	yes	characteristic
68	C₂×C₄	#10596938	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	148	1	no	—
71	C₈	#10596930	1	1	yes	characteristic
72	C₈	Dic₁₄₈	1	1	yes	characteristic
73	C₂²	#11924448	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	148	1	no	—
77	C₄	—	148	1	no	—
78	C₄	#11924461	1	1	yes	characteristic
79	C₄	#11924464	1	1	yes	characteristic
80	C₂	#14557265	1	1	yes	characteristic
81	C₂	#14557314	1	1	yes	characteristic
82	C₂	#14557318	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10596938
commutator	C₂×C₄×C₃₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₃₇
Fitting	C₃₇×#346	C₂
socle, prime radical	C₂²×C₃₇	C₂²⋊C₈
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	#346	D₃₇
hypocenter	C₃₇	#1338
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
45. C₃₇	#1338	semidirect

Maximal subgroups

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

subgroup	index
#14557663	2
C₄⋊#10596925	2
C₃₇×#346	2
#1338	37