Subgroups — #17992739

Order 4736.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557949	C₂	1	1	yes	maximal, characteristic
2	C₂×#11924442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924542	C₄	1	1	yes	characteristic
5	#11924476	C₄	1	1	yes	characteristic
6	#11924475	—	2	1	no	—
7	C₁₆×D₃₇	—	2	1	no	—
8	#11924442	—	2	1	no	—
9	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
10	C₃₂×C₃₇	—	2	1	no	—
11	#10596962	C₈	1	1	yes	characteristic
12	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
13	#10596934	C₈	1	1	yes	characteristic
14	#10596929	—	2	1	no	—
15	C₈×D₃₇	—	2	1	no	—
16	C₁₆×C₃₇	D₄	1	1	yes	characteristic
17	C₁₆×C₃₇	D₄	1	1	yes	characteristic
18	#10596925	—	2	1	no	—
19	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
20	C₂²⋊D₃₇	—	2	1	no	—
21	D₁₄₈	C₁₆	1	1	yes	characteristic
22	C₄×D₃₇	—	2	1	no	—
23	Dic₇₄	C₁₆	1	1	yes	characteristic
24	C₈×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₃₇	M₁₆	1	1	yes	characteristic
26	#64436	—	2	1	no	—
27	C₂²×C₃₇	M₃₂	1	1	yes	characteristic
28	C₂×D₃₇	—	2	1	no	—
29	C₄×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
30	C₄×C₃₇	C₂×C₁₆	1	1	yes	characteristic
31	Dic₃₇	—	2	1	no	—
32	#1401	—	37	1	no	maximal, Sylow
33	C₂×C₃₇	—	2	1	no	—
34	C₂×C₃₇	C₂²⋊C₁₆	1	1	yes	characteristic
35	D₃₇	—	4	1	no	—
36	#504	—	37	1	no	—
37	M₆₄	D₃₇	1	1	yes	characteristic, complemented
38	C₂×C₃₂	—	37	1	no	—
39	C₃₇	#1401	1	1	yes	characteristic, complemented, Sylow
40	#131	—	37	1	no	—
41	M₃₂	—	37	1	no	—
42	M₃₂	—	74	1	no	—
43	C₂×C₁₆	—	74	1	no	—
44	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
45	C₃₂	—	2	1	no	—
46	C₃₂	—	74	1	no	—
47	#41	—	37	1	no	—
48	M₁₆	—	37	1	no	—
49	M₁₆	—	74	1	no	—
50	C₂×C₈	—	74	1	no	—
51	C₂×C₈	C₄×D₃₇	1	1	yes	characteristic
52	C₁₆	—	74	1	no	—
53	C₁₆	D₁₄₈	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₃₇	1	1	yes	characteristic
55	Q₈	—	37	1	no	—
56	D₄	—	37	1	no	—
57	D₄	—	74	1	no	—
58	C₂×C₄	—	74	1	no	—
59	C₂×C₄	C₈×D₃₇	1	1	yes	characteristic
60	C₈	—	74	1	no	—
61	C₈	#10596929	1	1	yes	characteristic
62	C₈	#10596938	1	1	yes	characteristic
63	C₂²	—	74	1	no	—
64	C₂²	#11924475	1	1	yes	characteristic
65	C₄	—	74	1	no	—
66	C₄	#11924448	1	1	yes	characteristic
67	C₄	C₁₆×D₃₇	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	148	1	no	—
70	C₂	#14557312	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂²⋊D₃₇
commutator	C₄×C₃₇	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₃₇
Fitting	C₃₇×M₆₄	C₂
socle	C₂×C₃₇	C₂²⋊C₁₆
prime radical	#10596962	C₈
cosocle	C₂×C₁₆×C₃₇	C₂²
hypercenter	M₆₄	D₃₇
hypocenter	C₃₇	#1401
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
2. C₂×#11924442	C₂	semidirect
3. C₃₇×M₆₄	C₂	semidirect
37. M₆₄	D₃₇	semidirect
39. C₃₇	#1401	semidirect

Maximal subgroups

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

subgroup	index
#14557949	2
C₂×#11924442	2
C₃₇×M₆₄	2
#1401	37