Group #18009460 — subgroups

Subgroups — #18009460

Order 4736.

136 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558556	C₂	1	1	yes	maximal, characteristic
2	D₃₇⋊(C₄⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#14557588	C₂	1	1	yes	maximal, characteristic
4	C₂×D₃₇⋊C₈	C₄	1	2	yes	—
5	#11924603	—	2	1	no	—
6	#11924603	—	2	1	no	—
7	C₄⋊#64438	—	2	1	no	—
8	#11924593	—	2	1	no	—
9	#11924591	C₄	1	2	yes	—
10	C₄²×D₃₇	C₂²	1	1	yes	characteristic
11	#11924465	—	2	1	no	—
12	#11924448	—	2	1	no	—
13	#11924447	C₄	1	1	yes	characteristic
14	#97×C₃₇	C₄	1	1	yes	characteristic
15	C₂×C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×D₃₇	D₄	1	1	yes	characteristic
17	C₂×C₄×D₃₇	Q₈	1	1	yes	characteristic
18	C₂×#64438	—	2	2	no	—
19	C₂×#64438	—	2	2	no	—
20	D₃₇⋊C₈	—	4	2	no	—
21	C₂×C₈×C₃₇	—	2	1	no	—
22	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₃₇	D₄	1	1	yes	characteristic
25	C₄×Dic₃₇	D₄	1	1	yes	characteristic
26	C₂×#64436	—	2	1	no	—
27	C₂²×D₃₇	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₃₇	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
31	C₂×Dic₃₇	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×Dic₃₇	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×Dic₃₇	C₄⋊C₄	1	1	yes	characteristic
34	C₄×D₃₇	—	2	2	no	—
35	C₄×D₃₇	—	2	1	no	—
36	C₄×D₃₇	—	2	1	no	—
37	C₄×D₃₇	—	4	1	no	—
38	#64438	—	4	2	no	—
39	#64438	—	4	2	no	—
40	C₈×C₃₇	—	4	1	no	—
41	#64436	—	4	1	no	—
42	C₂²×C₃₇	#95	1	1	yes	characteristic
43	C₂×D₃₇	—	2	1	no	—
44	C₂×D₃₇	—	2	1	no	—
45	C₂×D₃₇	#108	1	2	yes	—
46	C₄×C₃₇	—	2	1	no	—
47	C₄×C₃₇	—	2	1	no	—
48	C₄×C₃₇	—	2	1	no	—
49	Dic₃₇	—	2	1	no	—
50	Dic₃₇	—	2	1	no	—
51	Dic₃₇	#100	1	1	yes	characteristic
52	Dic₃₇	#101	1	1	yes	characteristic
53	#1290	—	37	1	no	maximal, Sylow
54	C₂×C₃₇	H(3,ℤ/4)	1	1	yes	characteristic
55	C₂×C₃₇	#341	1	1	yes	characteristic
56	C₂×C₃₇	#343	1	1	yes	characteristic
57	D₃₇	—	2	2	no	—
58	#432	—	37	1	no	—
59	#432	—	37	1	no	—
60	C₂×C₄⋊C₈	—	37	1	no	—
61	C₃₇	#1290	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₈	—	37	2	no	—
63	C₂×C₄²	—	37	1	no	—
64	C₄⋊C₈	—	74	1	no	—
65	C₄⋊C₈	—	74	1	no	—
66	C₄⋊C₈	—	74	1	no	—
67	C₄⋊C₈	—	74	1	no	—
68	C₂²⋊C₈	—	74	1	no	—
69	C₂²⋊C₈	—	74	1	no	—
70	#97	—	37	2	no	—
71	#97	—	37	1	no	—
72	#97	#3866	1	1	yes	characteristic
73	C₂²×C₄	—	37	1	no	—
74	C₂²×C₄	—	37	1	no	—
75	C₂²×C₄	—	37	1	no	—
76	C₂×C₈	—	2	1	no	—
77	C₂×C₈	—	74	2	no	—
78	C₂×C₈	—	74	2	no	—
79	C₂×C₈	—	74	1	no	—
80	C₂×C₈	—	148	2	no	—
81	C₄²	—	37	1	no	—
82	C₄²	—	37	1	no	—
83	C₄²	—	37	1	no	—
84	C₄²	C₂×#3866	1	1	yes	characteristic
85	C₂³	—	37	1	no	—
86	C₂×C₄	—	37	1	no	—
87	C₂×C₄	—	37	1	no	—
88	C₂×C₄	—	37	1	no	—
89	C₂×C₄	—	74	1	no	—
90	C₂×C₄	—	74	1	no	—
91	C₂×C₄	—	74	2	no	—
92	C₂×C₄	—	148	1	no	—
93	C₂×C₄	C₄×#3866	1	1	yes	characteristic
94	C₂×C₄	C₄⋊#3866	1	1	yes	characteristic
95	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
96	C₈	—	4	1	no	—
97	C₈	—	148	1	no	—
98	C₈	—	148	2	no	—
99	C₈	—	148	2	no	—
100	C₂²	—	37	2	no	—
101	C₂²	—	74	1	no	—
102	C₂²	—	74	1	no	—
103	C₂²	(C₂×#3866)⋊C₄	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	2	1	no	—
106	C₄	—	2	1	no	—
107	C₄	—	37	1	no	—
108	C₄	—	37	1	no	—
109	C₄	—	74	1	no	—
110	C₄	—	74	1	no	—
111	C₂	—	74	2	no	—
112	C₂	#14558400	1	1	yes	characteristic
113	C₂	#14558408	1	1	yes	characteristic
114	C₂	#14558412	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14558556

C₂

yes

maximal, characteristic

D₃₇⋊(C₄⋊C₈)

C₂

yes

maximal, characteristic

#14557588

C₂

yes

maximal, characteristic

C₂×D₃₇⋊C₈

C₄

yes

—

—

—

—

—

C₄

yes

—

C₄²×D₃₇

C₂²

yes

—

—

C₄

yes

characteristic

#97×C₃₇

C₄

yes

characteristic

C₂×C₄×D₃₇

C₂×C₄

yes

characteristic

C₂×C₄×D₃₇

D₄

yes

characteristic

C₂×C₄×D₃₇

Q₈

yes

characteristic

C₂×#64438

—

C₂×#64438

—

D₃₇⋊C₈

—

C₂×C₈×C₃₇

—

C₄²×C₃₇

C₂×C₄

yes

characteristic

C₄×Dic₃₇

C₂×C₄

yes

characteristic

C₄×Dic₃₇

D₄

yes

characteristic

C₄×Dic₃₇

D₄

yes

characteristic

C₂×#64436

—

C₂²×D₃₇

C₄⋊C₄

yes

characteristic

C₂×C₄×C₃₇

C₄²

yes

characteristic

C₂×C₄×C₃₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₃₇

C₄⋊C₄

yes

characteristic

C₂×Dic₃₇

C₂²⋊C₄

yes

characteristic

C₂×Dic₃₇

C₂²⋊C₄

yes

characteristic

C₂×Dic₃₇

C₄⋊C₄

yes

characteristic

C₄×D₃₇

—

C₄×D₃₇

—

C₄×D₃₇

—

C₄×D₃₇

—

#64438

—

#64438

—

C₈×C₃₇

—

#64436

—

C₂²×C₃₇

#95

yes

characteristic

C₂×D₃₇

—

C₂×D₃₇

—

C₂×D₃₇

#108

yes

—

C₄×C₃₇

—

C₄×C₃₇

—

C₄×C₃₇

—

Dic₃₇

—

Dic₃₇

—

Dic₃₇

yes

Dic₃₇

yes

—

C₂×C₃₇

yes

C₂×C₃₇

yes

C₂×C₃₇

yes

D₃₇

—

#432

—

#432

—

C₂×C₄⋊C₈

—

C₃₇

#1290

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

—

—

yes

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

148

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#3866

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

148

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊#3866

yes

characteristic

C₈

—

C₈

—

148

—

C₈

—

148

—

C₈

—

148

—

100

C₂²

—

101

C₂²

—

102

C₂²

—

103

C₂²

(C₂×#3866)⋊C₄

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₂

—

112

C₂

#14558400

yes

characteristic

113

C₂

#14558408

yes

characteristic

114

C₂

#14558412

yes

characteristic

	subgroup	G/H
center	C₂²	(C₂×#3866)⋊C₄
commutator	C₂×C₄×C₃₇	C₄²
Frattini	C₄²	C₂×#3866
Fitting	#97×C₃₇	C₄
socle	C₂²×C₃₇	#95
prime radical	C₂²×D₃₇	C₄⋊C₄
cosocle	C₄²×D₃₇	C₂²
hypercenter	#97	#3866
hypocenter	C₃₇	#1290
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

(C₂×#3866)⋊C₄

commutator

C₂×C₄×C₃₇

C₄²

Frattini

C₄²

C₂×#3866

Fitting

#97×C₃₇

C₄

socle

C₂²×C₃₇

#95

prime radical

C₂²×D₃₇

C₄⋊C₄

cosocle

C₄²×D₃₇

C₂²

C₃₇

G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
61. C₃₇	#1290	semidirect

H ≅ G/N

type

61. C₃₇

#1290

semidirect

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

subgroup	index
#14558556	2
D₃₇⋊(C₄⋊C₈)	2
#14557588	2
#1290	37

subgroup

index

#14558556

D₃₇⋊(C₄⋊C₈)

#14557588

#1290

Subgroups — #18009460

Conjugacy classes of subgroups

Complements

Maximal subgroups