Subgroups — #17992628

Order 4736.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557898	C₂	1	1	yes	maximal, characteristic
2	#14557311	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#347	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924533	C₄	1	1	yes	characteristic
5	#11924528	C₄	1	1	yes	characteristic
6	#11924476	—	2	1	no	—
7	#11924458	—	2	1	no	—
8	#11924458	—	2	1	no	—
9	M₃₂×C₃₇	—	2	1	no	—
10	#97×C₃₇	C₂²	1	1	yes	characteristic
11	C₂×D₁₄₈	—	2	1	no	—
12	C₂×D₁₄₈	—	4	1	no	—
13	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
14	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
15	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
16	C₄⋊Dic₃₇	—	2	1	no	—
17	#10596936	—	4	1	no	—
18	C₁₆×C₃₇	—	2	2	no	—
19	#10596925	—	2	2	no	—
20	C₂²×D₃₇	—	4	1	no	—
21	C₂×C₄×C₃₇	—	2	1	no	—
22	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×Dic₃₇	—	4	1	no	—
24	D₁₄₈	—	4	1	no	—
25	D₁₄₈	—	4	1	no	—
26	D₁₄₈	—	8	2	no	—
27	C₈×C₃₇	—	2	1	no	—
28	C₈×C₃₇	—	2	1	no	—
29	C₂²×C₃₇	#100	1	1	yes	characteristic
30	C₂×D₃₇	—	8	2	no	—
31	C₂×D₃₇	—	8	1	no	—
32	C₄×C₃₇	—	4	1	no	—
33	C₄×C₃₇	#104	1	1	yes	characteristic
34	C₄×C₃₇	#104	1	1	yes	characteristic
35	Dic₃₇	—	8	1	no	—
36	#1355	—	37	1	no	maximal, Sylow
37	C₂×C₃₇	—	2	1	no	—
38	C₂×C₃₇	#329	1	1	yes	characteristic
39	D₃₇	—	16	1	no	—
40	#490	—	37	1	no	—
41	#347	—	37	1	no	—
42	#347	D₃₇	1	1	yes	characteristic, complemented
43	C₃₇	#1355	1	1	yes	characteristic, complemented, Sylow
44	#127	—	37	1	no	—
45	#125	—	37	1	no	—
46	M₃₂	—	2	1	no	—
47	M₃₂	—	74	1	no	—
48	#102	—	74	1	no	—
49	#102	—	74	1	no	—
50	#97	C₂×D₃₇	1	1	yes	characteristic
51	C₂×D₄	—	74	1	no	—
52	C₂×D₄	—	148	1	no	—
53	C₂×C₈	D₁₄₈	1	1	yes	characteristic
54	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
55	C₄⋊C₄	—	74	1	no	—
56	C₄⋊C₄	—	148	1	no	—
57	C₄²	C₄×D₃₇	1	1	yes	characteristic
58	C₁₆	—	2	2	no	—
59	C₁₆	—	74	2	no	—
60	C₂³	—	148	1	no	—
61	D₄	—	296	2	no	—
62	D₄	—	148	1	no	—
63	D₄	—	148	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	148	1	no	—
66	C₂×C₄	#10596938	1	1	yes	characteristic
67	C₈	—	2	1	no	—
68	C₈	—	2	1	no	—
69	C₂²	—	296	2	no	—
70	C₂²	—	296	1	no	—
71	C₂²	#11924452	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	296	1	no	—
74	C₄	#11924462	1	1	yes	characteristic
75	C₄	#11924464	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	592	1	no	—
78	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	#11924533	C₄
cosocle	#97×C₃₇	C₂²
hypercenter	#347	D₃₇
hypocenter	C₃₇	#1355
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
2. #14557311	C₂	semidirect
3. C₃₇×#347	C₂	semidirect
42. #347	D₃₇	semidirect
43. C₃₇	#1355	semidirect

Maximal subgroups

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

subgroup	index
#14557898	2
#14557311	2
C₃₇×#347	2
#1355	37