Group #18010926 — subgroups

Subgroups — D₃₇⋊(C₄⋊C₁₆) #18010926

Order 4736.

184 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 94 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	C₂×D₃₇⋊C₁₆	C₂	1	2	yes	maximal
2	#14558454	C₂	1	2	yes	maximal, complemented
3	C₄⋊#10596927	C₂	1	2	yes	maximal, complemented
4	C₄×C₈×D₃₇	C₂	1	1	yes	maximal, characteristic
5	D₃₇⋊C₁₆	—	2	4	no	—
6	C₂×#10596927	C₂²	1	4	yes	—
7	C₂×C₈×D₃₇	C₄	1	1	yes	characteristic
8	C₂×C₈×D₃₇	C₂²	1	1	yes	characteristic
9	C₄²×D₃₇	C₄	1	1	yes	characteristic
10	C₄×#64436	C₂²	1	1	yes	characteristic
11	C₈×Dic₃₇	C₄	1	1	yes	characteristic
12	C₈×Dic₃₇	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₃₇	C₄	1	1	yes	characteristic
14	C₂×C₄×D₃₇	C₈	1	1	yes	characteristic
15	C₂×C₄×D₃₇	C₈	1	1	yes	characteristic
16	C₂×C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
20	C₄×Dic₃₇	C₈	1	1	yes	characteristic
21	C₄×Dic₃₇	C₈	1	1	yes	characteristic
22	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
23	C₂×#64436	C₂×C₄	1	1	yes	characteristic
24	C₂×#64436	C₂³	1	1	yes	characteristic
25	C₈×D₃₇	—	2	2	no	—
26	C₈×D₃₇	D₄	1	2	yes	—
27	C₈×D₃₇	Q₈	1	2	yes	—
28	#10596927	—	2	4	no	—
29	C₂²×D₃₇	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
33	C₂×Dic₃₇	C₂×C₈	1	1	yes	characteristic
34	C₂×Dic₃₇	C₂×C₈	1	1	yes	characteristic
35	C₂×Dic₃₇	C₂×C₈	1	1	yes	characteristic
36	C₄×D₃₇	—	2	2	no	—
37	C₄×D₃₇	C₁₆	1	4	yes	complemented
38	C₄×D₃₇	C₄⋊C₄	1	2	yes	—
39	C₄×D₃₇	M₁₆	1	2	yes	—
40	C₈×C₃₇	—	2	1	no	—
41	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
42	#64436	—	2	1	no	—
43	#64436	C₂×D₄	1	1	yes	characteristic
44	#64436	C₂×Q₈	1	1	yes	characteristic
45	C₂²×C₃₇	C₂²×C₈	1	1	yes	characteristic
46	C₂×D₃₇	C₄⋊C₈	1	2	yes	—
47	C₂×D₃₇	C₂×C₁₆	1	2	yes	—
48	C₂×D₃₇	M₃₂	1	2	yes	—
49	C₄×C₃₇	—	2	1	no	—
50	C₄×C₃₇	C₂×C₁₆	1	2	yes	complemented
51	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₄×C₃₇	C₂×M₁₆	1	1	yes	characteristic
53	Dic₃₇	—	2	1	no	—
54	Dic₃₇	C₄⋊C₈	1	2	yes	—
55	Dic₃₇	C₂×C₁₆	1	2	yes	complemented
56	C₂×C₄⋊C₁₆	—	37	1	no	maximal, Sylow
57	C₂×C₃₇	C₂×C₄⋊C₈	1	1	yes	characteristic
58	C₂×C₃₇	C₂²×C₁₆	1	1	yes	characteristic
59	C₂×C₃₇	C₂×M₃₂	1	1	yes	characteristic
60	D₃₇	C₄⋊C₁₆	1	4	yes	complemented
61	C₂²×C₁₆	—	37	2	no	—
62	C₂×C₄×C₈	—	37	1	no	—
63	C₄⋊C₁₆	—	37	2	no	—
64	C₄⋊C₁₆	—	37	2	no	—
65	C₃₇	C₂×C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₈	—	37	1	no	—
67	C₂²×C₈	—	37	1	no	—
68	C₂×C₄²	—	37	1	no	—
69	C₂×C₁₆	—	37	4	no	—
70	C₂×C₁₆	—	74	4	no	—
71	C₄×C₈	—	37	1	no	—
72	C₄×C₈	—	37	1	no	—
73	C₄×C₈	—	37	1	no	—
74	C₄×C₈	#3866	1	1	yes	characteristic
75	C₂²×C₄	—	37	1	no	—
76	C₂²×C₄	—	37	1	no	—
77	C₂²×C₄	—	37	1	no	—
78	C₂×C₈	—	37	1	no	—
79	C₂×C₈	—	37	2	no	—
80	C₂×C₈	—	37	2	no	—
81	C₂×C₈	—	37	1	no	—
82	C₂×C₈	—	74	2	no	—
83	C₂×C₈	C₂×#3866	1	1	yes	characteristic
84	C₂×C₈	C₂×#3866	1	1	yes	characteristic
85	C₄²	—	37	1	no	—
86	C₄²	—	37	1	no	—
87	C₄²	—	37	1	no	—
88	C₄²	C₂×#3866	1	1	yes	characteristic
89	C₁₆	—	74	4	no	—
90	C₂³	—	37	1	no	—
91	C₂×C₄	—	37	1	no	—
92	C₂×C₄	—	37	1	no	—
93	C₂×C₄	—	37	4	no	—
94	C₂×C₄	—	37	2	no	—
95	C₂×C₄	—	37	2	no	—
96	C₂×C₄	—	37	1	no	—
97	C₂×C₄	—	74	2	no	—
98	C₂×C₄	D₃₇⋊C₈	1	1	yes	characteristic
99	C₂×C₄	D₃₇⋊C₈	1	1	yes	characteristic
100	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
101	C₈	—	2	1	no	—
102	C₈	—	37	1	no	—
103	C₈	—	37	1	no	—
104	C₈	—	74	1	no	—
105	C₈	C₄⋊#3866	1	2	yes	—
106	C₂²	—	37	2	no	—
107	C₂²	—	37	2	no	—
108	C₂²	—	37	2	no	—
109	C₂²	C₂×D₃₇⋊C₈	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	37	2	no	—
112	C₄	—	37	2	no	—
113	C₄	—	74	1	no	—
114	C₄	D₃₇⋊C₁₆	1	2	yes	complemented
115	C₄	C₂×C₄⋊#3866	1	1	yes	characteristic
116	C₄	D₃₇⋊M₁₆	1	1	yes	characteristic
117	C₂	—	37	4	no	—
118	C₂	D₃₇⋊(C₄⋊C₈)	1	1	yes	characteristic
119	C₂	C₂×D₃₇⋊C₁₆	1	1	yes	characteristic
120	C₂	D₃₇⋊M₃₂	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₃₇⋊C₁₆

C₂

yes

maximal

#14558454

C₂

yes

maximal, complemented

C₄⋊#10596927

C₂

yes

maximal, complemented

C₄×C₈×D₃₇

C₂

yes

maximal, characteristic

D₃₇⋊C₁₆

—

C₂×#10596927

C₂²

yes

—

C₂×C₈×D₃₇

C₄

yes

characteristic

C₂×C₈×D₃₇

C₂²

yes

characteristic

C₄²×D₃₇

C₄

yes

characteristic

C₄×#64436

C₂²

yes

characteristic

C₈×Dic₃₇

C₄

yes

characteristic

C₈×Dic₃₇

C₂²

yes

characteristic

C₄×C₈×C₃₇

C₄

yes

characteristic

C₂×C₄×D₃₇

C₈

yes

characteristic

C₂×C₄×D₃₇

C₈

yes

characteristic

C₂×C₄×D₃₇

C₂×C₄

yes

characteristic

C₂×C₈×C₃₇

C₂×C₄

yes

characteristic

C₂×C₈×C₃₇

C₂×C₄

yes

characteristic

C₄²×C₃₇

C₂×C₄

yes

characteristic

C₄×Dic₃₇

C₈

yes

characteristic

C₄×Dic₃₇

C₈

yes

characteristic

C₄×Dic₃₇

C₂×C₄

yes

characteristic

C₂×#64436

C₂×C₄

yes

characteristic

C₂×#64436

C₂³

yes

characteristic

C₈×D₃₇

—

C₈×D₃₇

D₄

yes

—

C₈×D₃₇

Q₈

yes

—

#10596927

—

C₂²×D₃₇

C₂×C₈

yes

characteristic

C₂×C₄×C₃₇

C₂×C₈

yes

characteristic

C₂×C₄×C₃₇

C₂×C₈

yes

characteristic

C₂×C₄×C₃₇

C₂²×C₄

yes

characteristic

C₂×Dic₃₇

C₂×C₈

yes

characteristic

C₂×Dic₃₇

C₂×C₈

yes

characteristic

C₂×Dic₃₇

C₂×C₈

yes

characteristic

C₄×D₃₇

—

C₄×D₃₇

C₁₆

yes

complemented

C₄×D₃₇

C₄⋊C₄

yes

—

C₄×D₃₇

M₁₆

yes

—

C₈×C₃₇

—

C₈×C₃₇

C₄⋊C₄

yes

—

#64436

—

#64436

C₂×D₄

yes

characteristic

#64436

C₂×Q₈

yes

characteristic

C₂²×C₃₇

C₂²×C₈

yes

characteristic

C₂×D₃₇

C₄⋊C₈

yes

—

C₂×D₃₇

C₂×C₁₆

yes

—

C₂×D₃₇

M₃₂

yes

—

C₄×C₃₇

—

C₄×C₃₇

C₂×C₁₆

yes

complemented

C₄×C₃₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₃₇

C₂×M₁₆

yes

characteristic

Dic₃₇

—

Dic₃₇

C₄⋊C₈

yes

—

Dic₃₇

C₂×C₁₆

yes

complemented

C₂×C₄⋊C₁₆

—

maximal, Sylow

C₂×C₃₇

C₂×C₄⋊C₈

yes

characteristic

C₂×C₃₇

C₂²×C₁₆

yes

characteristic

C₂×C₃₇

C₂×M₃₂

yes

characteristic

D₃₇

C₄⋊C₁₆

yes

complemented

C₂²×C₁₆

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₃₇

C₂×C₄⋊C₁₆

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#3866

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#3866

yes

characteristic

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₃₇⋊C₈

yes

characteristic

C₂×C₄

D₃₇⋊C₈

yes

characteristic

100

C₂×C₄

C₂²×#3866

yes

characteristic

101

C₈

—

102

C₈

—

103

C₈

—

104

C₈

—

105

C₈

C₄⋊#3866

yes

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₂×D₃₇⋊C₈

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

D₃₇⋊C₁₆

yes

complemented

115

C₄

C₂×C₄⋊#3866

yes

characteristic

116

C₄

D₃₇⋊M₁₆

yes

characteristic

117

C₂

—

118

C₂

D₃₇⋊(C₄⋊C₈)

yes

characteristic

119

C₂

C₂×D₃₇⋊C₁₆

yes

characteristic

120

C₂

D₃₇⋊M₃₂

yes

characteristic

	subgroup	G/H
center	C₂×C₈	C₂×#3866
commutator	C₂×C₃₇	C₂²×C₁₆
Frattini	C₂×C₄	C₂²×#3866
Fitting	C₄×C₈×C₃₇	C₄
socle	C₂²×C₃₇	C₂²×C₈
prime radical	C₂²×D₃₇	C₂×C₈
cosocle	C₂×#64436	C₂³
hypercenter	C₄×C₈	#3866
hypocenter	C₃₇	C₂×C₄⋊C₁₆
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

subgroup

G/H

center

C₂×C₈

C₂×#3866

commutator

C₂×C₃₇

C₂²×C₁₆

Frattini

C₂×C₄

C₂²×#3866

Fitting

C₄×C₈×C₃₇

C₄

socle

C₂²×C₃₇

C₂²×C₈

prime radical

C₂²×D₃₇

C₂×C₈

C₂³

C₄×C₈

C₃₇

C₂×C₄⋊C₁₆

LCS

G ▷ C₂×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₈

N	H ≅ G/N	type
2. #14558454	C₂	semidirect
3. C₄⋊#10596927	C₂	semidirect
37. C₄×D₃₇	C₁₆	semidirect
50. C₄×C₃₇	C₂×C₁₆	semidirect
55. Dic₃₇	C₂×C₁₆	semidirect
60. D₃₇	C₄⋊C₁₆	semidirect
65. C₃₇	C₂×C₄⋊C₁₆	semidirect
114. C₄	D₃₇⋊C₁₆	semidirect

H ≅ G/N

type

2. #14558454

C₂

semidirect

3. C₄⋊#10596927

C₂

semidirect

37. C₄×D₃₇

C₁₆

semidirect

50. C₄×C₃₇

C₂×C₁₆

semidirect

55. Dic₃₇

C₂×C₁₆

semidirect

60. D₃₇

C₄⋊C₁₆

semidirect

65. C₃₇

C₂×C₄⋊C₁₆

semidirect

114. C₄

D₃₇⋊C₁₆

semidirect

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

subgroup	index
C₂×D₃₇⋊C₁₆	2
#14558454	2
C₄⋊#10596927	2
C₄×C₈×D₃₇	2
C₂×C₄⋊C₁₆	37

subgroup

index

C₂×D₃₇⋊C₁₆

#14558454

C₄⋊#10596927

C₄×C₈×D₃₇

C₂×C₄⋊C₁₆

Subgroups — D₃₇⋊(C₄⋊C₁₆) #18010926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D37⋊(C4⋊C16) #18010926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₇⋊(C₄⋊C₁₆) #18010926