Subgroups — #17992630

Order 4736.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557902	C₂	1	1	yes	maximal, characteristic
2	#14557311	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#347	C₂	1	1	yes	maximal, characteristic
4	#11924536	C₄	1	1	yes	characteristic
5	#11924528	C₄	1	1	yes	characteristic
6	#11924476	—	2	1	no	—
7	#11924461	—	2	1	no	—
8	#11924461	—	2	1	no	—
9	M₃₂×C₃₇	—	2	1	no	—
10	#97×C₃₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₇₄	—	2	1	no	—
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	—	2	1	no	—
16	C₄⋊Dic₃₇	—	4	1	no	—
17	#10596936	—	4	1	no	—
18	C₁₆×C₃₇	—	2	2	no	—
19	#10596925	—	2	2	no	—
20	C₂×C₄×C₃₇	—	2	1	no	—
21	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×Dic₃₇	—	4	1	no	—
23	C₂×Dic₃₇	—	4	1	no	—
24	Dic₇₄	—	4	1	no	—
25	Dic₇₄	—	4	1	no	—
26	C₈×C₃₇	—	2	1	no	—
27	C₈×C₃₇	—	2	1	no	—
28	C₂²×C₃₇	#100	1	1	yes	characteristic
29	C₄×C₃₇	—	4	1	no	—
30	C₄×C₃₇	#104	1	1	yes	characteristic
31	C₄×C₃₇	#104	1	1	yes	characteristic
32	Dic₃₇	—	8	1	no	—
33	Dic₃₇	—	8	1	no	—
34	#1356	—	37	1	no	maximal, Sylow
35	C₂×C₃₇	—	2	1	no	—
36	C₂×C₃₇	#329	1	1	yes	characteristic
37	#491	—	37	1	no	—
38	#347	—	37	1	no	—
39	#347	D₃₇	1	1	yes	characteristic
40	C₃₇	#1356	1	1	yes	characteristic, complemented, Sylow
41	C₄⋊Q₈	—	37	1	no	—
42	#125	—	37	1	no	—
43	M₃₂	—	2	1	no	—
44	M₃₂	—	74	1	no	—
45	#103	—	74	1	no	—
46	#103	—	74	1	no	—
47	#97	C₂×D₃₇	1	1	yes	characteristic
48	C₂×Q₈	—	74	1	no	—
49	C₂×C₈	D₁₄₈	1	1	yes	characteristic
50	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
51	C₄⋊C₄	—	74	1	no	—
52	C₄⋊C₄	—	148	1	no	—
53	C₄⋊C₄	—	148	1	no	—
54	C₄²	C₄×D₃₇	1	1	yes	characteristic
55	C₁₆	—	2	2	no	—
56	C₁₆	—	74	2	no	—
57	Q₈	—	148	1	no	—
58	Q₈	—	148	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	148	1	no	—
61	C₂×C₄	—	148	1	no	—
62	C₂×C₄	#10596938	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	2	1	no	—
65	C₂²	#11924452	1	1	yes	characteristic
66	C₄	—	4	1	no	—
67	C₄	—	296	1	no	—
68	C₄	—	296	1	no	—
69	C₄	#11924462	1	1	yes	characteristic
70	C₄	#11924464	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#14557272	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14557272
commutator	C₄²×C₃₇	C₂×C₄
Frattini	#97	C₂×D₃₇
Fitting	C₃₇×#347	C₂
socle	C₂×C₃₇	#329
prime radical	C₂²×C₃₇	#100
cosocle	#97×C₃₇	C₂²
hypercenter	#347	D₃₇
hypocenter	C₃₇	#1356
LCS	G ▷ C₄²×C₃₇ ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #347

Complements

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

N	H ≅ G/N	type
40. C₃₇	#1356	semidirect

Maximal subgroups

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

subgroup	index
#14557902	2
#14557311	2
C₃₇×#347	2
#1356	37