Group #18009446 — subgroups

Subgroups — #18009446

Order 4736.

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

normal subgroups only

This group has 164 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	C₄×C₄⋊#3866	C₂	1	1	yes	maximal, characteristic
3	#14557588	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊#3866	—	2	1	no	—
5	C₂×C₄×#3866	C₄	1	2	yes	—
6	#11924603	C₄	1	2	yes	complemented
7	#11924593	—	2	1	no	—
8	#11924591	—	2	1	no	—
9	(C₂×#3866)⋊C₄	—	2	1	no	—
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, complemented
14	#97×C₃₇	C₄	1	1	yes	characteristic, complemented
15	C₂²×#3866	—	2	2	no	—
16	C₂×C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×D₃₇	D₄	1	1	yes	characteristic
18	C₂×C₄×D₃₇	D₄	1	1	yes	characteristic
19	C₂×#64438	—	2	2	no	—
20	C₄⋊#3866	—	2	4	no	—
21	C₄×#3866	—	4	2	no	—
22	C₂×C₈×C₃₇	—	2	1	no	—
23	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₃₇	D₄	1	1	yes	characteristic
26	C₄×Dic₃₇	Q₈	1	1	yes	characteristic
27	C₂×#64436	—	2	1	no	—
28	C₂²×D₃₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×#3866	—	2	4	no	—
30	C₂×#3866	—	4	2	no	—
31	C₂×#3866	—	4	2	no	—
32	C₂×C₄×C₃₇	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
35	C₂×Dic₃₇	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×Dic₃₇	C₄⋊C₄	1	1	yes	characteristic
37	C₂×Dic₃₇	C₄⋊C₄	1	1	yes	characteristic
38	C₄×D₃₇	—	2	1	no	—
39	C₄×D₃₇	—	2	1	no	—
40	C₄×D₃₇	—	2	2	no	—
41	C₄×D₃₇	—	4	1	no	—
42	#64438	—	4	2	no	—
43	C₈×C₃₇	—	4	1	no	—
44	#64436	—	4	1	no	—
45	C₂²×C₃₇	#95	1	1	yes	characteristic
46	C₂×D₃₇	—	2	1	no	—
47	C₂×D₃₇	—	2	1	no	—
48	C₂×D₃₇	#100	1	1	yes	characteristic
49	C₂×D₃₇	#101	1	1	yes	characteristic
50	#3866	—	4	4	no	—
51	C₄×C₃₇	—	2	1	no	—
52	C₄×C₃₇	—	2	1	no	—
53	C₄×C₃₇	—	2	1	no	—
54	Dic₃₇	—	2	1	no	—
55	Dic₃₇	—	2	1	no	—
56	Dic₃₇	#104	1	2	yes	—
57	#1285	—	37	1	no	maximal, Sylow
58	C₂×C₃₇	H(3,ℤ/4)	1	1	yes	characteristic
59	C₂×C₃₇	#339	1	1	yes	characteristic
60	C₂×C₃₇	#343	1	1	yes	characteristic
61	D₃₇	—	2	1	no	—
62	D₃₇	—	2	1	no	—
63	#432	—	37	1	no	—
64	#432	—	37	1	no	—
65	C₄×C₄⋊C₄	—	37	1	no	—
66	C₃₇	#1285	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₄⋊C₄	—	74	1	no	—
68	C₂×C₄²	—	37	1	no	—
69	C₂×C₄²	—	37	2	no	—
70	C₄⋊C₈	—	37	2	no	—
71	C₄⋊C₈	—	74	1	no	—
72	C₂²⋊C₈	—	74	1	no	—
73	C₂²⋊C₈	—	74	1	no	—
74	#97	—	37	1	no	—
75	#97	—	74	1	no	—
76	#97	#3866	1	1	yes	characteristic, complemented
77	#95	—	74	1	no	—
78	C₂²×C₄	—	37	1	no	—
79	C₂²×C₄	—	37	1	no	—
80	C₂²×C₄	—	37	1	no	—
81	C₂²×C₄	—	74	2	no	—
82	C₂×C₈	—	2	1	no	—
83	C₂×C₈	—	74	2	no	—
84	C₂×C₈	—	74	1	no	—
85	C₄⋊C₄	—	74	4	no	—
86	C₄²	—	37	1	no	—
87	C₄²	—	37	1	no	—
88	C₄²	—	37	1	no	—
89	C₄²	—	148	2	no	—
90	C₄²	C₂×#3866	1	1	yes	characteristic
91	C₂³	—	37	1	no	—
92	C₂×C₄	—	37	1	no	—
93	C₂×C₄	—	37	1	no	—
94	C₂×C₄	—	37	1	no	—
95	C₂×C₄	—	74	2	no	—
96	C₂×C₄	—	74	1	no	—
97	C₂×C₄	—	74	1	no	—
98	C₂×C₄	—	74	4	no	—
99	C₂×C₄	—	148	1	no	—
100	C₂×C₄	—	148	2	no	—
101	C₂×C₄	—	148	2	no	—
102	C₂×C₄	C₄×#3866	1	1	yes	characteristic
103	C₂×C₄	C₄⋊#3866	1	1	yes	characteristic
104	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
105	C₈	—	4	1	no	—
106	C₈	—	148	1	no	—
107	C₈	—	148	2	no	—
108	C₂²	—	37	1	no	—
109	C₂²	—	37	1	no	—
110	C₂²	—	74	1	no	—
111	C₂²	—	74	1	no	—
112	C₂²	(C₂×#3866)⋊C₄	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	2	1	no	—
115	C₄	—	2	1	no	—
116	C₄	—	37	2	no	—
117	C₄	—	74	1	no	—
118	C₄	—	74	1	no	—
119	C₄	—	148	4	no	—
120	C₂	—	74	1	no	—
121	C₂	—	74	1	no	—
122	C₂	#14558400	1	1	yes	characteristic
123	C₂	#14558405	1	1	yes	characteristic
124	C₂	#14558412	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14558556

C₂

yes

maximal, characteristic

C₄×C₄⋊#3866

C₂

yes

maximal, characteristic

#14557588

C₂

yes

maximal, characteristic

C₂×C₄⋊#3866

—

C₂×C₄×#3866

C₄

yes

—

#11924603

C₄

yes

—

—

—

C₄²×D₃₇

C₂²

yes

—

—

C₄

yes

characteristic, complemented

#97×C₃₇

C₄

yes

characteristic, complemented

C₂²×#3866

—

C₂×C₄×D₃₇

C₂×C₄

yes

characteristic

C₂×C₄×D₃₇

D₄

yes

characteristic

C₂×C₄×D₃₇

D₄

yes

—

—

—

C₂×C₈×C₃₇

—

C₄²×C₃₇

C₂×C₄

yes

characteristic

C₄×Dic₃₇

C₂×C₄

yes

characteristic

C₄×Dic₃₇

D₄

yes

characteristic

C₄×Dic₃₇

Q₈

yes

characteristic

C₂×#64436

—

C₂²×D₃₇

C₂²⋊C₄

yes

—

—

—

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

C₄⋊C₄

yes

characteristic

C₂×Dic₃₇

C₄⋊C₄

yes

characteristic

C₄×D₃₇

—

C₄×D₃₇

—

C₄×D₃₇

—

C₄×D₃₇

—

#64438

—

C₈×C₃₇

—

#64436

—

C₂²×C₃₇

#95

yes

characteristic

C₂×D₃₇

—

C₂×D₃₇

—

C₂×D₃₇

yes

C₂×D₃₇

yes

—

C₄×C₃₇

—

C₄×C₃₇

—

C₄×C₃₇

—

Dic₃₇

—

Dic₃₇

—

Dic₃₇

#104

yes

—

—

C₂×C₃₇

yes

C₂×C₃₇

yes

C₂×C₃₇

yes

D₃₇

—

D₃₇

—

#432

—

#432

—

C₄×C₄⋊C₄

—

C₃₇

#1285

yes

characteristic, complemented, Sylow

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

—

—

yes

characteristic, complemented

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

148

—

C₄²

C₂×#3866

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

148

—

100

C₂×C₄

—

148

—

101

C₂×C₄

—

148

—

102

C₂×C₄

C₄×#3866

yes

characteristic

103

C₂×C₄

C₄⋊#3866

yes

characteristic

104

C₂×C₄

C₂²⋊#3866

yes

characteristic

105

C₈

—

106

C₈

—

148

—

107

C₈

—

148

—

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₂²

—

112

C₂²

(C₂×#3866)⋊C₄

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

148

—

120

C₂

—

121

C₂

—

122

C₂

#14558400

yes

characteristic

123

C₂

#14558405

yes

characteristic

124

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	C₂²⋊C₄
cosocle	C₄²×D₃₇	C₂²
hypercenter	#97	#3866
hypocenter	C₃₇	#1285
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

C₂²⋊C₄

cosocle

C₄²×D₃₇

C₂²

C₃₇

G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
6. #11924603	C₄	semidirect
13. #11924447	C₄	semidirect
14. #97×C₃₇	C₄	semidirect
66. C₃₇	#1285	semidirect
76. #97	#3866	semidirect

H ≅ G/N

type

6. #11924603

C₄

semidirect

13. #11924447

C₄

semidirect

14. #97×C₃₇

C₄

semidirect

66. C₃₇

#1285

semidirect

76. #97

#3866

semidirect

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

subgroup	index
#14558556	2
C₄×C₄⋊#3866	2
#14557588	2
#1285	37

subgroup

index

#14558556

C₄×C₄⋊#3866

#14557588

#1285

Subgroups — #18009446

Conjugacy classes of subgroups

Complements

Maximal subgroups