Subgroups — #17992583

Order 4736.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557791	C₂	1	1	yes	maximal, characteristic
2	#14557315	C₂	1	1	yes	maximal, characteristic
3	C₃₇×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₄₈	C₄	1	1	yes	characteristic, complemented
5	#11924515	—	2	1	no	—
6	#11924476	—	2	1	no	—
7	#11924468	C₄	1	1	yes	characteristic, complemented
8	#11924461	—	2	1	no	—
9	C₂×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
10	#117×C₃₇	—	2	1	no	—
11	C₂²×C₄×C₃₇	D₄	1	1	yes	characteristic
12	C₂×Dic₇₄	—	2	1	no	—
13	M₁₆×C₃₇	—	4	1	no	—
14	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
16	C₄⋊C₄×C₃₇	—	4	1	no	—
17	C₂²⋊C₄×C₃₇	—	4	1	no	—
18	C₄²×C₃₇	—	2	2	no	—
19	C₂²⋊Dic₃₇	—	4	1	no	—
20	C₄⋊Dic₃₇	—	2	1	no	—
21	#10596936	—	4	1	no	—
22	Dic₁₄₈	—	4	1	no	—
23	#10596925	—	4	1	no	—
24	C₂³×C₃₇	D₈	1	1	yes	characteristic
25	C₂×C₄×C₃₇	—	2	1	no	—
26	C₂×C₄×C₃₇	—	2	1	no	—
27	C₂×C₄×C₃₇	—	4	2	no	—
28	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₃₇	SD₁₆	1	1	yes	characteristic
30	C₂×Dic₃₇	—	4	1	no	—
31	C₂×Dic₃₇	—	4	1	no	—
32	Dic₇₄	—	4	1	no	—
33	Dic₇₄	—	4	1	no	—
34	C₈×C₃₇	—	2	1	no	—
35	C₈×C₃₇	—	2	1	no	—
36	C₂²×C₃₇	—	2	1	no	—
37	C₂²×C₃₇	—	4	1	no	—
38	C₂²×C₃₇	#102	1	1	yes	characteristic
39	C₄×C₃₇	—	2	1	no	—
40	C₄×C₃₇	—	8	2	no	—
41	C₄×C₃₇	#99	1	1	yes	characteristic
42	C₄×C₃₇	#104	1	1	yes	characteristic
43	Dic₃₇	—	8	1	no	—
44	Dic₃₇	—	8	1	no	—
45	#1340	—	37	1	no	maximal, Sylow
46	C₂×C₃₇	—	2	1	no	—
47	C₂×C₃₇	—	4	1	no	—
48	C₂×C₃₇	#327	1	1	yes	characteristic
49	#470	—	37	1	no	—
50	#349	—	37	1	no	—
51	H(3,ℤ/4)	D₃₇	1	1	yes	characteristic
52	C₃₇	#1340	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₁₆	—	37	1	no	—
54	C₂×M₁₆	C₂×D₃₇	1	1	yes	characteristic
55	C₂²⋊Q₈	—	74	1	no	—
56	#117	—	2	1	no	—
57	M₃₂	—	74	1	no	—
58	#106	—	37	1	no	—
59	#103	—	74	1	no	—
60	C₂×Q₈	—	74	1	no	—
61	C₂²×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
62	Q₁₆	—	148	1	no	—
63	M₁₆	—	4	1	no	—
64	C₂×C₈	C₄×D₃₇	1	1	yes	characteristic
65	C₂×C₈	D₁₄₈	1	1	yes	characteristic
66	C₄⋊C₄	—	4	1	no	—
67	C₄⋊C₄	—	74	1	no	—
68	C₄⋊C₄	—	148	1	no	—
69	C₂²⋊C₄	—	4	1	no	—
70	C₂²⋊C₄	—	148	1	no	—
71	C₄²	—	2	2	no	—
72	C₁₆	—	148	1	no	—
73	C₂³	#10596939	1	1	yes	characteristic
74	Q₈	—	148	1	no	—
75	Q₈	—	148	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	4	2	no	—
79	C₂×C₄	—	148	1	no	—
80	C₂×C₄	—	148	1	no	—
81	C₂×C₄	#10596938	1	1	yes	characteristic
82	C₂×C₄	#10596941	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	2	1	no	—
85	C₂²	—	2	1	no	—
86	C₂²	—	4	1	no	—
87	C₂²	#11924456	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	8	2	no	—
90	C₄	—	296	1	no	—
91	C₄	—	296	1	no	—
92	C₄	#11924450	1	1	yes	characteristic
93	C₄	#11924464	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	4	1	no	—
96	C₂	#14557266	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14557266
commutator	C₂×C₈×C₃₇	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₃₇
Fitting	C₃₇×H(3,ℤ/4)	C₂
socle	C₂×C₃₇	#327
prime radical	C₂³×C₃₇	D₈
cosocle	C₂×M₁₆×C₃₇	C₂²
hypercenter	H(3,ℤ/4)	D₃₇
hypocenter	C₃₇	#1340
LCS	G ▷ C₂×C₈×C₃₇ ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ H(3,ℤ/4)

Complements

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

N	H ≅ G/N	type
4. C₂×Dic₁₄₈	C₄	semidirect
7. #11924468	C₄	semidirect
52. C₃₇	#1340	semidirect

Maximal subgroups

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

subgroup	index
#14557791	2
#14557315	2
C₃₇×H(3,ℤ/4)	2
#1340	37