Group #11783014 — subgroups

Subgroups — C₄×#63553 #11783014

Order 1152.

945 conjugacy classes of subgroups; only the 420 normal subgroups are shown.

normal subgroups only

This group has 945 conjugacy classes of subgroups — too many to draw. Only its 420 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	C₄²×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₃⋊C₈	C₂	1	2	yes	maximal
3	C₂×#63553	C₂	1	4	yes	maximal
4	C₄×C₈×Dic₃	—	3	2	no	maximal
5	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₃⋊Dic₃	C₄	1	4	yes	—
7	C₂×C₄×C₃⋊Dic₃	C₂²	1	2	yes	—
8	C₂²×C₃×C₃⋊C₈	C₂²	1	4	yes	—
9	C₃×C₄×C₃⋊C₈	C₄	1	8	yes	complemented
10	#63553	C₄	1	16	yes	direct product factor
11	C₂×C₃×C₄×C₈	—	3	2	no	—
12	C₂×C₈×Dic₃	—	3	8	no	—
13	C₄²×Dic₃	—	3	2	no	—
14	C₄²×Dic₃	—	6	1	no	—
15	C₂×C₄×C₃⋊C₈	D₃	1	2	yes	—
16	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
17	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
18	C₂²×C₃⋊Dic₃	C₂×C₄	1	4	yes	—
19	C₃²×C₄²	C₂×C₄	1	4	yes	—
20	C₄×C₃⋊Dic₃	C₈	1	16	yes	complemented
21	C₄×C₃⋊Dic₃	C₂×C₄	1	8	yes	—
22	C₂×C₃×C₃⋊C₈	C₂×C₄	1	16	yes	—
23	C₂×C₃×C₃⋊C₈	C₂×C₄	1	8	yes	—
24	C₄²×C₈	—	9	1	no	Sylow
25	C₂²×C₃×C₈	—	3	4	no	—
26	C₂×C₃×C₄²	—	2	1	no	—
27	C₂×C₃×C₄²	C₂×D₃	1	2	yes	—
28	C₂×C₄×Dic₃	—	3	8	no	—
29	C₂×C₄×Dic₃	—	3	4	no	—
30	C₂×C₄×Dic₃	—	6	4	no	—
31	C₂×C₄×Dic₃	—	6	2	no	—
32	C₂²×C₃⋊C₈	C₂×D₃	1	4	yes	—
33	C₃×C₄×C₈	—	3	8	no	—
34	C₈×Dic₃	—	3	32	no	—
35	C₄×C₃⋊C₈	Dic₃	1	8	yes	complemented
36	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₃²×C₄	C₄²	1	4	yes	—
38	C₂×C₃²×C₄	C₂×C₈	1	8	yes	—
39	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
40	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
41	C₂×C₃⋊Dic₃	C₄²	1	8	yes	—
42	C₂×C₃⋊Dic₃	C₂×C₈	1	16	yes	—
43	C₃×C₃⋊C₈	C₄²	1	16	yes	complemented
44	C₂×C₄×C₈	—	3	2	no	—
45	C₂×C₄×C₈	—	9	4	no	—
46	C₄³	—	9	1	no	—
47	C₂²×C₃×C₄	—	2	2	no	—
48	C₂²×C₃×C₄	—	2	1	no	—
49	C₂²×C₃×C₄	C₄×D₃	1	4	yes	—
50	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
51	C₂²×Dic₃	—	3	8	no	—
52	C₂²×Dic₃	—	6	4	no	—
53	C₂×C₃×C₈	—	3	16	no	—
54	C₂×C₃×C₈	—	3	8	no	—
55	C₃×C₄²	—	2	4	no	—
56	C₃×C₄²	C₄×D₃	1	4	yes	—
57	C₃×C₄²	C₂×Dic₃	1	4	yes	—
58	C₄×Dic₃	—	3	32	no	—
59	C₄×Dic₃	—	3	16	no	—
60	C₄×Dic₃	—	6	16	no	—
61	C₄×Dic₃	—	6	8	no	—
62	C₂×C₃⋊C₈	C₄×D₃	1	16	yes	—
63	C₂×C₃⋊C₈	C₂×Dic₃	1	8	yes	—
64	C₂²×C₃²	C₂×C₄²	1	2	yes	—
65	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
66	C₂²×C₃²	C₂²×C₈	1	4	yes	—
67	C₃²×C₄	C₄×C₈	1	8	yes	complemented
68	C₃²×C₄	C₂×C₄²	1	4	yes	—
69	C₃⋊Dic₃	C₄×C₈	1	16	yes	complemented
70	C₂²×C₈	—	3	4	no	—
71	C₂×C₄²	—	9	4	no	—
72	C₂×C₄²	—	9	2	no	—
73	C₂×C₄²	D₃²	1	1	yes	characteristic
74	C₄×C₈	—	3	8	no	—
75	C₄×C₈	—	9	16	no	—
76	C₂³×C₃	—	2	1	no	—
77	C₂³×C₃	C₂×C₄×D₃	1	2	yes	—
78	C₂×C₃×C₄	—	2	8	no	—
79	C₂×C₃×C₄	—	2	4	no	—
80	C₂×C₃×C₄	—	2	4	no	—
81	C₂×C₃×C₄	—	2	2	no	—
82	C₂×C₃×C₄	D₃×C₈	1	16	yes	—
83	C₂×C₃×C₄	C₄×Dic₃	1	8	yes	—
84	C₂×C₃×C₄	C₂×C₄×D₃	1	8	yes	—
85	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
86	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
87	C₂×Dic₃	—	3	16	no	—
88	C₂×Dic₃	—	3	32	no	—
89	C₂×Dic₃	—	6	8	no	—
90	C₂×Dic₃	—	6	16	no	—
91	C₃×C₈	—	3	16	no	—
92	C₃⋊C₈	C₄×Dic₃	1	16	yes	complemented
93	C₂×C₃²	C₄³	1	1	yes	characteristic
94	C₂×C₃²	C₂×C₄×C₈	1	4	yes	—
95	C₂×C₃²	C₂×C₄×C₈	1	2	yes	—
96	C₂²×C₄	—	9	4	no	—
97	C₂²×C₄	#624	1	2	yes	—
98	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
99	C₂×C₈	—	3	16	no	—
100	C₂×C₈	—	3	8	no	—
101	C₄²	—	9	16	no	—
102	C₄²	—	9	8	no	—
103	C₄²	D₃×Dic₃	1	4	yes	—
104	C₂²×C₃	—	2	4	no	—
105	C₂²×C₃	—	2	2	no	—
106	C₂²×C₃	—	2	1	no	—
107	C₂²×C₃	C₄²×D₃	1	4	yes	—
108	C₂²×C₃	C₂×D₃×C₈	1	8	yes	—
109	C₂²×C₃	C₂×C₄×Dic₃	1	2	yes	—
110	C₃×C₄	—	2	8	no	—
111	C₃×C₄	—	2	4	no	—
112	C₃×C₄	C₈×Dic₃	1	16	yes	complemented
113	C₃×C₄	C₄²×D₃	1	4	yes	—
114	C₃×C₄	C₂×C₄×Dic₃	1	4	yes	—
115	Dic₃	—	3	32	no	—
116	Dic₃	—	6	16	no	—
117	C₃²	C₄²×C₈	1	1	yes	characteristic, complemented, Sylow
118	C₂³	C₂×#624	1	1	yes	characteristic
119	C₂×C₄	—	9	16	no	—
120	C₂×C₄	—	9	8	no	—
121	C₂×C₄	#3710	1	8	yes	—
122	C₂×C₄	Dic₃²	1	4	yes	—
123	C₂×C₄	C₄×D₃²	1	4	yes	—
124	C₂×C₄	C₂×D₃×Dic₃	1	2	yes	—
125	C₈	—	3	16	no	—
126	C₂×C₃	—	2	1	no	—
127	C₂×C₃	—	2	2	no	—
128	C₂×C₃	—	2	4	no	—
129	C₂×C₃	C₄×D₃×C₈	1	8	yes	—
130	C₂×C₃	C₄²×Dic₃	1	2	yes	—
131	C₂×C₃	C₂×C₈×Dic₃	1	4	yes	—
132	C₂²	C₂×#3710	1	4	yes	—
133	C₂²	C₄×#624	1	2	yes	—
134	C₂²	C₂×Dic₃²	1	1	yes	characteristic
135	C₄	—	9	16	no	—
136	C₄	#63553	1	8	yes	direct product factor
137	C₄	C₄×D₃×Dic₃	1	4	yes	—
138	C₃	—	2	1	no	—
139	C₃	C₄×C₈×Dic₃	1	2	yes	complemented
140	C₂	C₄×#3710	1	4	yes	—
141	C₂	C₂×#63553	1	2	yes	—
142	C₂	C₄×Dic₃²	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄²×C₃⋊Dic₃

C₂

yes

maximal, characteristic

C₂×C₃×C₄×C₃⋊C₈

C₂

yes

maximal

C₂×#63553

C₂

yes

maximal

C₄×C₈×Dic₃

—

maximal

C₂×C₃²×C₄²

C₂²

yes

characteristic

C₂×C₄×C₃⋊Dic₃

C₄

yes

—

C₂×C₄×C₃⋊Dic₃

C₂²

yes

—

C₂²×C₃×C₃⋊C₈

C₂²

yes

—

C₃×C₄×C₃⋊C₈

C₄

yes

complemented

#63553

C₄

yes

direct product factor

C₂×C₃×C₄×C₈

—

C₂×C₈×Dic₃

—

C₄²×Dic₃

—

C₄²×Dic₃

—

C₂×C₄×C₃⋊C₈

D₃

yes

—

C₂²×C₃²×C₄

C₂×C₄

yes

—

C₂²×C₃²×C₄

C₂³

yes

characteristic

C₂²×C₃⋊Dic₃

C₂×C₄

yes

—

C₃²×C₄²

C₂×C₄

yes

—

C₄×C₃⋊Dic₃

C₈

yes

complemented

C₄×C₃⋊Dic₃

C₂×C₄

yes

—

C₂×C₃×C₃⋊C₈

C₂×C₄

yes

—

C₂×C₃×C₃⋊C₈

C₂×C₄

yes

—

C₄²×C₈

—

Sylow

C₂²×C₃×C₈

—

C₂×C₃×C₄²

—

C₂×C₃×C₄²

C₂×D₃

yes

—

C₂×C₄×Dic₃

—

C₂×C₄×Dic₃

—

C₂×C₄×Dic₃

—

C₂×C₄×Dic₃

—

C₂²×C₃⋊C₈

C₂×D₃

yes

—

C₃×C₄×C₈

—

C₈×Dic₃

—

C₄×C₃⋊C₈

Dic₃

yes

complemented

C₂³×C₃²

C₂²×C₄

yes

characteristic

C₂×C₃²×C₄

C₄²

yes

—

C₂×C₃²×C₄

C₂×C₈

yes

—

C₂×C₃²×C₄

C₂²×C₄

yes

—

C₂×C₃²×C₄

C₂²×C₄

yes

—

C₂×C₃⋊Dic₃

C₄²

yes

—

C₂×C₃⋊Dic₃

C₂×C₈

yes

—

C₃×C₃⋊C₈

C₄²

yes

complemented

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₄³

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

C₄×D₃

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

—

C₂²×Dic₃

—

C₂²×Dic₃

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₃×C₄²

—

C₃×C₄²

C₄×D₃

yes

—

C₃×C₄²

C₂×Dic₃

yes

—

C₄×Dic₃

—

C₄×Dic₃

—

C₄×Dic₃

—

C₄×Dic₃

—

C₂×C₃⋊C₈

C₄×D₃

yes

—

C₂×C₃⋊C₈

C₂×Dic₃

yes

—

C₂²×C₃²

C₂×C₄²

yes

—

C₂²×C₃²

C₂×C₄²

yes

characteristic

C₂²×C₃²

C₂²×C₈

yes

—

C₃²×C₄

C₄×C₈

yes

complemented

C₃²×C₄

C₂×C₄²

yes

—

C₃⋊Dic₃

C₄×C₈

yes

complemented

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

D₃²

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₂³×C₃

—

C₂³×C₃

C₂×C₄×D₃

yes

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

D₃×C₈

yes

—

C₂×C₃×C₄

C₄×Dic₃

yes

—

C₂×C₃×C₄

C₂×C₄×D₃

yes

—

C₂×C₃×C₄

C₂×C₄×D₃

yes

—

C₂×C₃×C₄

C₂²×Dic₃

yes

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×Dic₃

—

C₃×C₈

—

C₃⋊C₈

C₄×Dic₃

yes

complemented

C₂×C₃²

C₄³

yes

characteristic

C₂×C₃²

C₂×C₄×C₈

yes

—

C₂×C₃²

C₂×C₄×C₈

yes

—

C₂²×C₄

—

C₂²×C₄

#624

yes

—

C₂²×C₄

C₂×D₃²

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

101

C₄²

—

102

C₄²

—

103

C₄²

D₃×Dic₃

yes

—

104

C₂²×C₃

—

105

C₂²×C₃

—

106

C₂²×C₃

—

107

C₂²×C₃

C₄²×D₃

yes

—

108

C₂²×C₃

C₂×D₃×C₈

yes

—

109

C₂²×C₃

C₂×C₄×Dic₃

yes

—

110

C₃×C₄

—

111

C₃×C₄

—

112

C₃×C₄

C₈×Dic₃

yes

complemented

113

C₃×C₄

C₄²×D₃

yes

—

114

C₃×C₄

C₂×C₄×Dic₃

yes

—

115

Dic₃

—

116

Dic₃

—

117

C₃²

C₄²×C₈

yes

characteristic, complemented, Sylow

118

C₂³

C₂×#624

yes

characteristic

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

#3710

yes

—

122

C₂×C₄

Dic₃²

yes

—

123

C₂×C₄

C₄×D₃²

yes

—

124

C₂×C₄

C₂×D₃×Dic₃

yes

—

125

C₈

—

126

C₂×C₃

—

127

C₂×C₃

—

128

C₂×C₃

—

129

C₂×C₃

C₄×D₃×C₈

yes

—

130

C₂×C₃

C₄²×Dic₃

yes

—

131

C₂×C₃

C₂×C₈×Dic₃

yes

—

132

C₂²

C₂×#3710

yes

—

133

C₂²

C₄×#624

yes

—

134

C₂²

C₂×Dic₃²

yes

characteristic

135

C₄

—

136

C₄

#63553

yes

direct product factor

137

C₄

C₄×D₃×Dic₃

yes

—

138

C₃

—

139

C₃

C₄×C₈×Dic₃

yes

complemented

140

C₂

C₄×#3710

yes

—

141

C₂

C₂×#63553

yes

—

142

C₂

C₄×Dic₃²

yes

characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄²	D₃²
commutator, hypocenter	C₃²	C₄²×C₈
Frattini	C₂²×C₄	C₂×D₃²
Fitting	C₂×C₃²×C₄²	C₂²
socle, prime radical	C₂³×C₃²	C₂²×C₄
cosocle	C₂²×C₃²×C₄	C₂³
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₄²

subgroup

G/H

center, hypercenter

C₂×C₄²

D₃²

commutator, hypocenter

C₃²

C₄²×C₈

Frattini

C₂²×C₄

C₂×D₃²

Fitting

C₂×C₃²×C₄²

C₂²

socle, prime radical

C₂³×C₃²

C₂²×C₄

cosocle

C₂²×C₃²×C₄

C₂³

LCS

G ▷ C₃²

UCS

C₁ ◁ C₂×C₄²

N	H ≅ G/N	type
9. C₃×C₄×C₃⋊C₈	C₄	semidirect
10. #63553	C₄	direct (N × H)
20. C₄×C₃⋊Dic₃	C₈	semidirect
35. C₄×C₃⋊C₈	Dic₃	semidirect
43. C₃×C₃⋊C₈	C₄²	semidirect
67. C₃²×C₄	C₄×C₈	semidirect
69. C₃⋊Dic₃	C₄×C₈	semidirect
92. C₃⋊C₈	C₄×Dic₃	semidirect
112. C₃×C₄	C₈×Dic₃	semidirect
117. C₃²	C₄²×C₈	semidirect
136. C₄	#63553	direct (N × H)
139. C₃	C₄×C₈×Dic₃	semidirect

H ≅ G/N

type

9. C₃×C₄×C₃⋊C₈

C₄

semidirect

10. #63553

C₄

direct (N × H)

20. C₄×C₃⋊Dic₃

C₈

semidirect

35. C₄×C₃⋊C₈

Dic₃

semidirect

43. C₃×C₃⋊C₈

C₄²

semidirect

67. C₃²×C₄

C₄×C₈

semidirect

69. C₃⋊Dic₃

C₄×C₈

semidirect

92. C₃⋊C₈

C₄×Dic₃

semidirect

112. C₃×C₄

C₈×Dic₃

semidirect

117. C₃²

C₄²×C₈

semidirect

136. C₄

#63553

direct (N × H)

139. C₃

C₄×C₈×Dic₃

semidirect

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

subgroup	index
C₄²×C₃⋊Dic₃	2
C₂×C₃×C₄×C₃⋊C₈	2
C₂×#63553	2
C₄×C₈×Dic₃	3

subgroup

index

C₄²×C₃⋊Dic₃

C₂×C₃×C₄×C₃⋊C₈

C₂×#63553

C₄×C₈×Dic₃

Subgroups — C₄×#63553 #11783014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C4×#63553 #11783014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#63553 #11783014