Group #26136757 — subgroups

Subgroups — C₂×Dic₄₇⋊C₃₂ #26136757

Order 12032.

230 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 147 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	C₂²×C₄₇⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	Dic₄₇⋊C₃₂	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄₇⋊C₁₆	C₄	1	1	yes	characteristic
6	C₂×C₈×Dic₄₇	C₄	1	1	yes	characteristic
7	C₂×C₄₇⋊C₃₂	—	2	2	no	—
8	C₂×C₄₇⋊C₃₂	C₂²	1	2	yes	—
9	C₁₆×Dic₄₇	C₄	1	2	yes	—
10	C₁₆×Dic₄₇	C₂²	1	2	yes	—
11	C₂²×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×C₃₂×C₄₇	—	2	2	no	—
13	C₂×C₃₂×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₄₇⋊C₈	C₈	1	1	yes	characteristic
15	C₂×C₄×Dic₄₇	C₈	1	1	yes	characteristic
16	C₂×C₄₇⋊C₁₆	—	2	2	no	—
17	C₂×C₄₇⋊C₁₆	C₂×C₄	1	2	yes	—
18	C₈×Dic₄₇	C₈	1	2	yes	—
19	C₈×Dic₄₇	C₂×C₄	1	2	yes	—
20	C₄₇⋊C₃₂	—	2	2	no	—
21	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
23	C₂×C₁₆×C₄₇	D₄	1	2	yes	—
24	C₂×C₁₆×C₄₇	Q₈	1	2	yes	—
25	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
26	C₃₂×C₄₇	—	2	2	no	—
27	C₂²×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
28	C₂²×Dic₄₇	C₁₆	1	1	yes	characteristic
29	C₂²×Dic₄₇	C₁₆	1	1	yes	characteristic
30	C₂×C₈×C₄₇	C₄⋊C₄	1	2	yes	—
31	C₂×C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
32	C₂×C₈×C₄₇	M₁₆	1	2	yes	—
33	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
34	C₄×Dic₄₇	C₁₆	1	2	yes	—
35	C₄×Dic₄₇	C₂×C₈	1	2	yes	—
36	C₂×C₄₇⋊C₈	—	2	2	no	—
37	C₂×C₄₇⋊C₈	C₂×C₈	1	2	yes	—
38	C₁₆×C₄₇	C₄⋊C₄	1	2	yes	—
39	C₁₆×C₄₇	C₂×D₄	1	1	yes	characteristic
40	C₁₆×C₄₇	C₂×Q₈	1	1	yes	characteristic
41	C₄₇⋊C₁₆	—	2	2	no	—
42	C₂³×C₄₇	C₂×C₁₆	1	1	yes	characteristic
43	C₂×C₄×C₄₇	C₄⋊C₈	1	2	yes	—
44	C₂×C₄×C₄₇	C₂×C₁₆	1	1	yes	characteristic
45	C₂×C₄×C₄₇	M₃₂	1	2	yes	—
46	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
47	C₂×Dic₄₇	—	2	2	no	—
48	C₂×Dic₄₇	C₃₂	1	4	yes	complemented
49	C₂×Dic₄₇	C₂×C₁₆	1	2	yes	—
50	C₂×Dic₄₇	C₂×C₁₆	1	2	yes	—
51	C₈×C₄₇	C₄⋊C₈	1	2	yes	—
52	C₈×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₈×C₄₇	C₂×M₁₆	1	1	yes	characteristic
54	C₄₇⋊C₈	—	2	2	no	—
55	C₂×C₄⋊C₃₂	—	47	1	no	maximal, Sylow
56	C₂²×C₄₇	C₄⋊C₁₆	1	2	yes	—
57	C₂²×C₄₇	C₂×C₃₂	1	2	yes	—
58	C₂²×C₄₇	M₆₄	1	2	yes	—
59	C₂²×C₄₇	C₂²×C₁₆	1	1	yes	characteristic
60	C₄×C₄₇	C₄⋊C₁₆	1	2	yes	—
61	C₄×C₄₇	C₂×C₄⋊C₈	1	1	yes	characteristic
62	C₄×C₄₇	C₂×M₃₂	1	1	yes	characteristic
63	Dic₄₇	—	2	2	no	—
64	Dic₄₇	C₂×C₃₂	1	4	yes	complemented
65	C₂²×C₃₂	—	47	1	no	—
66	C₂²×C₃₂	D₄₇	1	1	yes	characteristic
67	C₂×C₄×C₁₆	—	47	1	no	—
68	C₄⋊C₃₂	—	47	4	no	—
69	C₂×C₄₇	C₄⋊C₃₂	1	4	yes	complemented
70	C₂×C₄₇	C₂×C₄⋊C₁₆	1	1	yes	characteristic
71	C₂×C₄₇	C₂²×C₃₂	1	1	yes	characteristic
72	C₂×C₄₇	C₂×M₆₄	1	1	yes	characteristic
73	C₂²×C₁₆	—	47	1	no	—
74	C₂²×C₁₆	C₂×D₄₇	1	1	yes	characteristic
75	C₂×C₄×C₈	—	47	1	no	—
76	C₂×C₃₂	—	2	2	no	—
77	C₂×C₃₂	—	47	2	no	—
78	C₂×C₃₂	—	94	2	no	—
79	C₂×C₃₂	C₂×D₄₇	1	2	yes	—
80	C₄×C₁₆	—	47	2	no	—
81	C₄×C₁₆	—	47	2	no	—
82	C₄₇	C₂×C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
83	C₂²×C₈	—	47	1	no	—
84	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
85	C₂×C₄²	—	47	1	no	—
86	C₂×C₁₆	—	47	2	no	—
87	C₂×C₁₆	—	94	2	no	—
88	C₂×C₁₆	Dic₉₄	1	2	yes	—
89	C₂×C₁₆	C₄×D₄₇	1	1	yes	characteristic
90	C₂×C₁₆	C₂²⋊D₄₇	1	2	yes	—
91	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
92	C₄×C₈	—	47	2	no	—
93	C₄×C₈	—	47	2	no	—
94	C₃₂	—	2	2	no	—
95	C₃₂	—	94	2	no	—
96	C₂²×C₄	—	47	1	no	—
97	C₂²×C₄	—	47	1	no	—
98	C₂²×C₄	C₈×D₄₇	1	1	yes	characteristic
99	C₂×C₈	—	47	2	no	—
100	C₂×C₈	—	94	2	no	—
101	C₂×C₈	C₈×D₄₇	1	1	yes	characteristic
102	C₂×C₈	#10625324	1	2	yes	—
103	C₂×C₈	Dic₄₇⋊C₄	1	2	yes	—
104	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
105	C₄²	—	47	2	no	—
106	C₄²	—	47	2	no	—
107	C₁₆	—	94	2	no	—
108	C₁₆	Dic₄₇⋊C₄	1	2	yes	—
109	C₁₆	C₂×Dic₉₄	1	1	yes	characteristic
110	C₁₆	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
111	C₂³	C₁₆×D₄₇	1	1	yes	characteristic
112	C₂×C₄	—	47	2	no	—
113	C₂×C₄	—	47	4	no	—
114	C₂×C₄	—	47	2	no	—
115	C₂×C₄	—	94	2	no	—
116	C₂×C₄	Dic₄₇⋊C₈	1	2	yes	—
117	C₂×C₄	C₁₆×D₄₇	1	1	yes	characteristic
118	C₂×C₄	#13093963	1	2	yes	—
119	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
120	C₈	—	94	2	no	—
121	C₈	Dic₄₇⋊C₈	1	2	yes	—
122	C₈	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
123	C₈	C₂×#10625324	1	1	yes	characteristic
124	C₂²	Dic₄₇⋊C₁₆	1	2	yes	—
125	C₂²	C₃₂×D₄₇	1	2	yes	—
126	C₂²	#15688956	1	2	yes	—
127	C₂²	C₂×C₁₆×D₄₇	1	1	yes	characteristic
128	C₄	—	47	4	no	—
129	C₄	—	94	2	no	—
130	C₄	Dic₄₇⋊C₁₆	1	2	yes	—
131	C₄	C₂×Dic₄₇⋊C₈	1	1	yes	characteristic
132	C₄	C₂×#13093963	1	1	yes	characteristic
133	C₂	Dic₄₇⋊C₃₂	1	4	yes	direct product factor
134	C₂	C₂×Dic₄₇⋊C₁₆	1	1	yes	characteristic
135	C₂	C₂×C₃₂×D₄₇	1	1	yes	characteristic
136	C₂	C₂×#15688956	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄₇⋊C₃₂

C₂

yes

maximal, characteristic

C₂×C₁₆×Dic₄₇

C₂

yes

maximal, characteristic

Dic₄₇⋊C₃₂

C₂

yes

maximal, direct product factor

C₂²×C₃₂×C₄₇

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₁₆

C₄

yes

characteristic

C₂×C₈×Dic₄₇

C₄

yes

characteristic

C₂×C₄₇⋊C₃₂

—

C₂×C₄₇⋊C₃₂

C₂²

yes

—

C₁₆×Dic₄₇

C₄

yes

—

C₁₆×Dic₄₇

C₂²

yes

—

C₂²×C₁₆×C₄₇

C₂²

yes

characteristic

C₂×C₃₂×C₄₇

—

C₂×C₃₂×C₄₇

C₂²

yes

—

C₂²×C₄₇⋊C₈

C₈

yes

characteristic

C₂×C₄×Dic₄₇

C₈

yes

characteristic

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

C₂×C₄

yes

—

C₈×Dic₄₇

C₈

yes

—

C₈×Dic₄₇

C₂×C₄

yes

—

C₄₇⋊C₃₂

—

C₂²×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₁₆×C₄₇

C₂×C₄

yes

characteristic

C₂×C₁₆×C₄₇

D₄

yes

—

C₂×C₁₆×C₄₇

Q₈

yes

—

C₂×C₁₆×C₄₇

C₂³

yes

characteristic

C₃₂×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂²×Dic₄₇

C₁₆

yes

characteristic

C₂²×Dic₄₇

C₁₆

yes

characteristic

C₂×C₈×C₄₇

C₄⋊C₄

yes

—

C₂×C₈×C₄₇

C₂×C₈

yes

characteristic

C₂×C₈×C₄₇

M₁₆

yes

—

C₂×C₈×C₄₇

C₂²×C₄

yes

characteristic

C₄×Dic₄₇

C₁₆

yes

—

C₄×Dic₄₇

C₂×C₈

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂×C₈

yes

—

C₁₆×C₄₇

C₄⋊C₄

yes

—

C₁₆×C₄₇

C₂×D₄

yes

characteristic

C₁₆×C₄₇

C₂×Q₈

yes

characteristic

C₄₇⋊C₁₆

—

C₂³×C₄₇

C₂×C₁₆

yes

characteristic

C₂×C₄×C₄₇

C₄⋊C₈

yes

—

C₂×C₄×C₄₇

C₂×C₁₆

yes

characteristic

C₂×C₄×C₄₇

M₃₂

yes

—

C₂×C₄×C₄₇

C₂²×C₈

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

C₃₂

yes

complemented

C₂×Dic₄₇

C₂×C₁₆

yes

—

C₂×Dic₄₇

C₂×C₁₆

yes

—

C₈×C₄₇

C₄⋊C₈

yes

—

C₈×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₈×C₄₇

C₂×M₁₆

yes

characteristic

C₄₇⋊C₈

—

C₂×C₄⋊C₃₂

—

maximal, Sylow

C₂²×C₄₇

C₄⋊C₁₆

yes

—

C₂²×C₄₇

C₂×C₃₂

yes

—

C₂²×C₄₇

M₆₄

yes

—

C₂²×C₄₇

C₂²×C₁₆

yes

characteristic

C₄×C₄₇

C₄⋊C₁₆

yes

—

C₄×C₄₇

C₂×C₄⋊C₈

yes

characteristic

C₄×C₄₇

C₂×M₃₂

yes

characteristic

Dic₄₇

—

Dic₄₇

C₂×C₃₂

yes

complemented

C₂²×C₃₂

—

C₂²×C₃₂

D₄₇

yes

characteristic

C₂×C₄×C₁₆

—

C₄⋊C₃₂

—

C₂×C₄₇

C₄⋊C₃₂

yes

complemented

C₂×C₄₇

C₂×C₄⋊C₁₆

yes

characteristic

C₂×C₄₇

C₂²×C₃₂

yes

characteristic

C₂×C₄₇

C₂×M₆₄

yes

characteristic

C₂²×C₁₆

—

C₂²×C₁₆

C₂×D₄₇

yes

characteristic

C₂×C₄×C₈

—

C₂×C₃₂

—

C₂×C₃₂

—

C₂×C₃₂

—

C₂×C₃₂

C₂×D₄₇

yes

—

C₄×C₁₆

—

C₄×C₁₆

—

C₄₇

C₂×C₄⋊C₃₂

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₄×D₄₇

yes

characteristic

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

Dic₉₄

yes

—

C₂×C₁₆

C₄×D₄₇

yes

characteristic

C₂×C₁₆

C₂²⋊D₄₇

yes

—

C₂×C₁₆

C₂²×D₄₇

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₃₂

—

C₃₂

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₈×D₄₇

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

C₈×D₄₇

yes

characteristic

102

C₂×C₈

#10625324

yes

—

103

C₂×C₈

Dic₄₇⋊C₄

yes

—

104

C₂×C₈

C₂×C₄×D₄₇

yes

characteristic

105

C₄²

—

106

C₄²

—

107

C₁₆

—

108

C₁₆

Dic₄₇⋊C₄

yes

—

109

C₁₆

C₂×Dic₉₄

yes

characteristic

110

C₁₆

C₂×C₂²⋊D₄₇

yes

characteristic

111

C₂³

C₁₆×D₄₇

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

Dic₄₇⋊C₈

yes

—

117

C₂×C₄

C₁₆×D₄₇

yes

characteristic

118

C₂×C₄

#13093963

yes

—

119

C₂×C₄

C₂×C₈×D₄₇

yes

characteristic

120

C₈

—

121

C₈

Dic₄₇⋊C₈

yes

—

122

C₈

C₂×Dic₄₇⋊C₄

yes

characteristic

123

C₈

C₂×#10625324

yes

characteristic

124

C₂²

Dic₄₇⋊C₁₆

yes

—

125

C₂²

C₃₂×D₄₇

yes

—

126

C₂²

#15688956

yes

—

127

C₂²

C₂×C₁₆×D₄₇

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

Dic₄₇⋊C₁₆

yes

—

131

C₄

C₂×Dic₄₇⋊C₈

yes

characteristic

132

C₄

C₂×#13093963

yes

characteristic

133

C₂

Dic₄₇⋊C₃₂

yes

direct product factor

134

C₂

C₂×Dic₄₇⋊C₁₆

yes

characteristic

135

C₂

C₂×C₃₂×D₄₇

yes

characteristic

136

C₂

C₂×#15688956

yes

characteristic

	subgroup	G/H
center	C₂²×C₁₆	C₂×D₄₇
commutator	C₂×C₄₇	C₂²×C₃₂
Frattini	C₂×C₁₆	C₂²×D₄₇
Fitting	C₂²×C₃₂×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	C₂×C₁₆
cosocle	C₂×C₁₆×C₄₇	C₂³
hypercenter	C₂²×C₃₂	D₄₇
hypocenter	C₄₇	C₂×C₄⋊C₃₂
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₁₆ ◁ C₂²×C₃₂

subgroup

G/H

center

C₂²×C₁₆

C₂×D₄₇

commutator

C₂×C₄₇

C₂²×C₃₂

Frattini

C₂×C₁₆

C₂²×D₄₇

Fitting

C₂²×C₃₂×C₄₇

C₂

socle, prime radical

C₂³×C₄₇

C₂×C₁₆

cosocle

C₂×C₁₆×C₄₇

C₂³

hypercenter

C₂²×C₃₂

D₄₇

hypocenter

C₄₇

C₂×C₄⋊C₃₂

LCS

G ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂²×C₁₆ ◁ C₂²×C₃₂

N	H ≅ G/N	type
3. Dic₄₇⋊C₃₂	C₂	direct (N × H)
48. C₂×Dic₄₇	C₃₂	semidirect
64. Dic₄₇	C₂×C₃₂	semidirect
69. C₂×C₄₇	C₄⋊C₃₂	semidirect
82. C₄₇	C₂×C₄⋊C₃₂	semidirect
133. C₂	Dic₄₇⋊C₃₂	direct (N × H)

H ≅ G/N

type

3. Dic₄₇⋊C₃₂

C₂

direct (N × H)

48. C₂×Dic₄₇

C₃₂

semidirect

64. Dic₄₇

C₂×C₃₂

semidirect

69. C₂×C₄₇

C₄⋊C₃₂

semidirect

82. C₄₇

C₂×C₄⋊C₃₂

semidirect

133. C₂

Dic₄₇⋊C₃₂

direct (N × H)

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

subgroup	index
C₂²×C₄₇⋊C₃₂	2
C₂×C₁₆×Dic₄₇	2
Dic₄₇⋊C₃₂	2
C₂²×C₃₂×C₄₇	2
C₂×C₄⋊C₃₂	47

subgroup

index

C₂²×C₄₇⋊C₃₂

C₂×C₁₆×Dic₄₇

Dic₄₇⋊C₃₂

C₂²×C₃₂×C₄₇

C₂×C₄⋊C₃₂

Subgroups — C₂×Dic₄₇⋊C₃₂ #26136757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×Dic47⋊C32 #26136757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₄₇⋊C₃₂ #26136757