Group #11857066 — subgroups

Subgroups — #11857066

Order 1152.

1908 conjugacy classes of subgroups; only the 310 normal subgroups are shown.

normal subgroups only

This group has 1908 conjugacy classes of subgroups — too many to draw. Only its 310 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×C₉×#127	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#63502	C₂	1	12	yes	maximal, complemented
3	C₂×#63436	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄²×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#83185	—	3	1	no	maximal
6	C₂²×D₄×C₉	C₂²	1	6	yes	—
7	C₂²×#611	C₂²	1	16	yes	—
8	C₂²×D₃₆	C₂²	1	6	yes	—
9	C₉×#127	—	2	4	no	—
10	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
11	#63502	—	2	48	no	—
12	C₂×C₄×Dic₉	C₂²	1	6	yes	—
13	#63436	—	2	4	no	—
14	C₂×C₃×#127	D₃	1	1	yes	characteristic
15	C₂×#940	—	3	12	no	—
16	C₂×#874	—	3	1	no	—
17	C₄²×Dic₃	—	3	1	no	—
18	C₂⁴×C₉	C₂³	1	4	yes	—
19	C₂³×D₉	C₂³	1	4	yes	—
20	C₂×D₄×C₉	—	2	24	no	—
21	C₂×D₄×C₉	—	2	12	no	—
22	C₂²×C₄×C₉	C₂³	1	3	yes	—
23	C₂×#611	—	2	96	no	—
24	C₂²×Dic₉	C₂³	1	4	yes	—
25	C₂×D₃₆	—	2	24	no	—
26	C₂×D₃₆	—	2	12	no	—
27	C₄²×C₉	D₄	1	4	yes	complemented
28	C₄×Dic₉	D₄	1	24	yes	complemented
29	#2867	—	9	1	no	Sylow
30	C₂²×C₃×D₄	C₂×D₃	1	6	yes	—
31	C₂²×#67	—	3	16	no	—
32	C₂²×D₁₂	—	3	6	no	—
33	C₃×#127	—	2	4	no	—
34	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
35	#940	—	6	48	no	—
36	C₂×C₄×Dic₃	—	3	6	no	—
37	#874	—	6	4	no	—
38	C₂³×C₉	—	2	24	no	—
39	C₂³×C₉	—	2	4	no	—
40	C₂³×C₉	C₂⁴	1	1	yes	characteristic
41	C₂²×D₉	—	2	4	no	—
42	C₂²×D₉	—	2	24	no	—
43	D₄×C₉	—	4	24	no	—
44	C₂×C₄×C₉	C₂×D₄	1	12	yes	—
45	C₂×C₄×C₉	C₂×D₄	1	6	yes	—
46	#611	—	4	64	no	—
47	C₂×Dic₉	C₂×D₄	1	24	yes	—
48	D₃₆	—	4	24	no	—
49	C₂×#127	—	9	12	no	—
50	C₂×#127	—	9	1	no	—
51	C₂×#127	D₉	1	1	yes	characteristic, complemented
52	C₄³	—	9	1	no	—
53	C₂⁴×C₃	C₂²×D₃	1	4	yes	—
54	C₂³×D₃	—	3	4	no	—
55	C₂×C₃×D₄	—	2	24	no	—
56	C₂×C₃×D₄	—	2	12	no	—
57	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
58	C₂×#67	—	6	96	no	—
59	C₂²×Dic₃	—	3	4	no	—
60	C₂×D₁₂	—	6	24	no	—
61	C₂×D₁₂	—	6	12	no	—
62	C₃×C₄²	#67	1	4	yes	—
63	C₄×Dic₃	—	3	24	no	—
64	C₂²×C₉	—	4	16	no	—
65	C₂²×C₉	—	4	12	no	—
66	C₂²×C₉	C₂²×D₄	1	6	yes	—
67	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
68	C₂×D₉	—	4	12	no	—
69	C₂×D₉	—	4	16	no	—
70	C₄×C₉	#127	1	12	yes	complemented
71	Dic₉	#127	1	16	yes	complemented
72	C₂²×D₄	—	9	16	no	—
73	C₂²×D₄	—	9	6	no	—
74	C₂²×D₄	C₂×D₉	1	6	yes	—
75	#127	—	2	4	no	—
76	#127	—	18	48	no	—
77	#127	—	18	4	no	—
78	C₂×C₄²	—	9	6	no	—
79	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
80	C₂³×C₃	—	2	24	no	—
81	C₂³×C₃	—	2	4	no	—
82	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
83	C₂²×D₃	—	6	24	no	—
84	C₂²×D₃	—	6	4	no	—
85	C₃×D₄	—	4	24	no	—
86	C₂×C₃×C₄	D₃×D₄	1	12	yes	—
87	C₂×C₃×C₄	C₂×#67	1	6	yes	—
88	#67	—	12	64	no	—
89	C₂×Dic₃	—	3	24	no	—
90	D₁₂	—	12	24	no	—
91	C₂×C₉	—	8	4	no	—
92	C₂×C₉	C₂×#127	1	4	yes	—
93	C₂×C₉	C₂×#127	1	3	yes	—
94	D₉	—	8	4	no	—
95	C₂⁴	—	9	4	no	—
96	C₂⁴	C₂²×D₉	1	4	yes	—
97	C₂×D₄	—	2	24	no	—
98	C₂×D₄	—	2	12	no	—
99	C₂×D₄	—	18	96	no	—
100	C₂×D₄	—	18	24	no	—
101	C₂×D₄	—	18	12	no	—
102	C₂²×C₄	—	9	4	no	—
103	C₂²×C₄	C₂²×D₉	1	3	yes	—
104	C₄²	—	9	24	no	—
105	C₄²	#611	1	4	yes	complemented
106	C₂²×C₃	—	4	16	no	—
107	C₂²×C₃	—	4	12	no	—
108	C₂²×C₃	C₂×D₃×D₄	1	6	yes	—
109	C₂²×C₃	C₂²×#67	1	1	yes	characteristic
110	C₂×D₃	—	12	16	no	—
111	C₂×D₃	—	12	12	no	—
112	C₃×C₄	#940	1	12	yes	—
113	Dic₃	—	3	16	no	—
114	C₉	#2867	1	1	yes	characteristic, complemented, Sylow
115	C₂³	—	2	24	no	—
116	C₂³	—	2	4	no	—
117	C₂³	—	18	24	no	—
118	C₂³	—	18	4	no	—
119	C₂³	C₂³×D₉	1	1	yes	characteristic
120	D₄	—	4	24	no	—
121	D₄	—	36	64	no	—
122	D₄	—	36	24	no	—
123	C₂×C₄	—	9	24	no	—
124	C₂×C₄	D₄×D₉	1	12	yes	—
125	C₂×C₄	C₂×#611	1	6	yes	—
126	C₂×C₃	—	8	4	no	—
127	C₂×C₃	D₃×#127	1	4	yes	—
128	C₂×C₃	C₂×#940	1	3	yes	—
129	D₃	—	24	4	no	—
130	C₂²	—	4	16	no	—
131	C₂²	—	4	12	no	—
132	C₂²	—	36	16	no	—
133	C₂²	—	36	12	no	—
134	C₂²	C₂×D₄×D₉	1	6	yes	—
135	C₂²	C₂²×#611	1	1	yes	characteristic
136	C₄	—	9	16	no	—
137	C₄	#63502	1	12	yes	complemented
138	C₃	#83185	1	1	yes	characteristic
139	C₂	—	8	4	no	—
140	C₂	—	72	4	no	—
141	C₂	D₉×#127	1	4	yes	—
142	C₂	C₂×#63502	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₉×#127

C₂

yes

maximal, characteristic, complemented

C₂×#63502

C₂

yes

maximal, complemented

C₂×#63436

C₂

yes

maximal, characteristic, complemented

C₄²×Dic₉

C₂

yes

maximal, characteristic, complemented

#83185

—

maximal

C₂²×D₄×C₉

C₂²

yes

—

C₂²×#611

C₂²

yes

—

C₂²×D₃₆

C₂²

yes

—

C₉×#127

—

C₂×C₄²×C₉

C₂²

yes

characteristic

#63502

—

C₂×C₄×Dic₉

C₂²

yes

—

#63436

—

C₂×C₃×#127

D₃

yes

characteristic

C₂×#940

—

C₂×#874

—

C₄²×Dic₃

—

C₂⁴×C₉

C₂³

yes

—

C₂³×D₉

C₂³

yes

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂²×C₄×C₉

C₂³

yes

—

C₂×#611

—

C₂²×Dic₉

C₂³

yes

—

C₂×D₃₆

—

C₂×D₃₆

—

C₄²×C₉

D₄

yes

complemented

C₄×Dic₉

D₄

yes

complemented

#2867

—

Sylow

C₂²×C₃×D₄

C₂×D₃

yes

—

C₂²×#67

—

C₂²×D₁₂

—

C₃×#127

—

C₂×C₃×C₄²

C₂×D₃

yes

characteristic

#940

—

C₂×C₄×Dic₃

—

#874

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

C₂⁴

yes

characteristic

C₂²×D₉

—

C₂²×D₉

—

D₄×C₉

—

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

C₂×D₄

yes

—

#611

—

C₂×Dic₉

C₂×D₄

yes

—

D₃₆

—

C₂×#127

—

C₂×#127

—

C₂×#127

D₉

yes

characteristic, complemented

C₄³

—

C₂⁴×C₃

C₂²×D₃

yes

—

C₂³×D₃

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂²×C₃×C₄

C₂²×D₃

yes

—

C₂×#67

—

C₂²×Dic₃

—

C₂×D₁₂

—

C₂×D₁₂

—

C₃×C₄²

#67

yes

—

C₄×Dic₃

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

C₂²×D₄

yes

—

C₂²×C₉

C₂²×D₄

yes

characteristic

C₂×D₉

—

C₂×D₉

—

C₄×C₉

yes

Dic₉

yes

C₂²×D₄

—

C₂²×D₄

—

C₂²×D₄

C₂×D₉

yes

—

#127

—

#127

—

#127

—

C₂×C₄²

—

C₂×C₄²

C₂×D₉

yes

characteristic

C₂³×C₃

—

C₂³×C₃

—

C₂³×C₃

C₂³×D₃

yes

characteristic

C₂²×D₃

—

C₂²×D₃

—

C₃×D₄

—

C₂×C₃×C₄

D₃×D₄

yes

—

C₂×C₃×C₄

C₂×#67

yes

—

#67

—

C₂×Dic₃

—

D₁₂

—

C₂×C₉

—

C₂×C₉

C₂×#127

yes

—

C₂×C₉

C₂×#127

yes

—

D₉

—

C₂⁴

—

C₂⁴

C₂²×D₉

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂²×C₄

—

103

C₂²×C₄

C₂²×D₉

yes

—

104

C₄²

—

105

C₄²

#611

yes

complemented

106

C₂²×C₃

—

107

C₂²×C₃

—

108

C₂²×C₃

C₂×D₃×D₄

yes

—

109

C₂²×C₃

C₂²×#67

yes

characteristic

110

C₂×D₃

—

111

C₂×D₃

—

112

C₃×C₄

#940

yes

—

113

Dic₃

—

114

C₉

#2867

yes

characteristic, complemented, Sylow

115

C₂³

—

116

C₂³

—

117

C₂³

—

118

C₂³

—

119

C₂³

C₂³×D₉

yes

characteristic

120

D₄

—

121

D₄

—

122

D₄

—

123

C₂×C₄

—

124

C₂×C₄

D₄×D₉

yes

—

125

C₂×C₄

C₂×#611

yes

—

126

C₂×C₃

—

127

C₂×C₃

D₃×#127

yes

—

128

C₂×C₃

C₂×#940

yes

—

129

D₃

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

C₂×D₄×D₉

yes

—

135

C₂²

C₂²×#611

yes

characteristic

136

C₄

—

137

C₄

#63502

yes

complemented

138

C₃

#83185

yes

characteristic

139

C₂

—

140

C₂

—

141

C₂

D₉×#127

yes

—

142

C₂

C₂×#63502

yes

—

	subgroup	G/H
center	C₂³	C₂³×D₉
commutator, cosocle	C₂³×C₉	C₂⁴
Frattini, socle	C₂³×C₃	C₂³×D₃
Fitting	C₂×C₉×#127	C₂
hypercenter	C₂×#127	D₉
hypocenter	C₉	#2867
LCS	G ▷ C₂³×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂×#127

subgroup

G/H

center

C₂³

C₂³×D₉

commutator, cosocle

C₂³×C₉

C₂⁴

Frattini, socle

C₂³×C₃

C₂³×D₃

Fitting

C₂×C₉×#127

C₂

D₉

C₉

G ▷ C₂³×C₉ ▷ C₉

C₁ ◁ C₂³ ◁ C₂×#127

N	H ≅ G/N	type
1. C₂×C₉×#127	C₂	semidirect
2. C₂×#63502	C₂	semidirect
3. C₂×#63436	C₂	semidirect
4. C₄²×Dic₉	C₂	semidirect
27. C₄²×C₉	D₄	semidirect
28. C₄×Dic₉	D₄	semidirect
51. C₂×#127	D₉	semidirect
70. C₄×C₉	#127	semidirect
71. Dic₉	#127	semidirect
105. C₄²	#611	semidirect
114. C₉	#2867	semidirect
137. C₄	#63502	semidirect

H ≅ G/N

type

1. C₂×C₉×#127

C₂

semidirect

2. C₂×#63502

C₂

semidirect

3. C₂×#63436

C₂

semidirect

4. C₄²×Dic₉

C₂

semidirect

27. C₄²×C₉

D₄

semidirect

28. C₄×Dic₉

D₄

semidirect

51. C₂×#127

D₉

semidirect

70. C₄×C₉

#127

semidirect

71. Dic₉

#127

semidirect

105. C₄²

#611

semidirect

114. C₉

#2867

semidirect

137. C₄

#63502

semidirect

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

subgroup	index
C₂×C₉×#127	2
C₂×#63502	2
C₂×#63436	2
C₄²×Dic₉	2
#83185	3

subgroup

index

C₂×C₉×#127

C₂×#63502

C₂×#63436

C₄²×Dic₉

#83185

Subgroups — #11857066

Conjugacy classes of subgroups

Complements

Maximal subgroups