Group #11771103 — subgroups

Subgroups — #11771103

Order 1152.

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

normal subgroups only

This group has 285 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	C₉×#407	C₂	1	1	yes	maximal, characteristic
2	C₂×#63389	C₂	1	2	yes	maximal
3	#67688	—	3	1	no	maximal
4	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
5	C₂×C₉×M₁₆	C₄	1	2	yes	—
6	C₂²×C₉⋊C₈	—	2	2	no	—
7	C₉×C₂²⋊C₈	—	2	2	no	—
8	#63389	—	2	2	no	—
9	#63389	C₄	1	4	yes	—
10	C₃×#407	D₃	1	1	yes	characteristic
11	C₂×#830	—	3	2	no	—
12	C₂⁴×C₉	Q₈	1	1	yes	characteristic
13	C₂²×C₄×C₉	—	4	2	no	—
14	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₉	D₄	1	2	yes	—
17	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
18	C₉×M₁₆	—	4	2	no	—
19	C₂×C₈×C₉	—	2	2	no	—
20	C₂×C₉⋊C₈	—	2	4	no	—
21	C₂×C₉⋊C₈	—	4	4	no	—
22	#1298	—	9	1	no	Sylow
23	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
24	C₂×C₃×M₁₆	Dic₃	1	2	yes	—
25	C₂²×C₃⋊C₈	—	6	2	no	—
26	C₃×C₂²⋊C₈	—	2	2	no	—
27	#830	—	3	4	no	—
28	#830	—	6	2	no	—
29	C₂³×C₉	—	2	4	no	—
30	C₂³×C₉	—	4	1	no	—
31	C₂³×C₉	C₄⋊C₄	1	2	yes	—
32	C₂³×C₉	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₉	—	2	4	no	—
34	C₂×C₄×C₉	—	2	2	no	—
35	C₂×C₄×C₉	—	4	2	no	—
36	C₂×C₄×C₉	—	4	1	no	—
37	C₂×C₄×C₉	C₄²	1	1	yes	characteristic
38	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
39	C₂×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₈×C₉	—	4	2	no	—
41	C₉⋊C₈	—	4	4	no	—
42	#407	D₉	1	1	yes	characteristic
43	C₂×C₂²⋊C₈	—	9	2	no	—
44	C₂⁴×C₃	Dic₆	1	1	yes	characteristic
45	C₂²×C₃×C₄	—	4	2	no	—
46	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
47	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
48	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
49	C₂²×C₃×C₄	#67	1	2	yes	—
50	C₃×M₁₆	—	4	2	no	—
51	C₂×C₃×C₈	—	2	2	no	—
52	C₂×C₃⋊C₈	—	6	4	no	—
53	C₂×C₃⋊C₈	—	12	4	no	—
54	C₂²×C₉	—	2	2	no	—
55	C₂²×C₉	—	2	2	no	—
56	C₂²×C₉	—	2	2	no	—
57	C₂²×C₉	—	2	1	no	—
58	C₂²×C₉	—	4	4	no	—
59	C₂²×C₉	#95	1	1	yes	characteristic
60	C₂²×C₉	#108	1	4	yes	—
61	C₄×C₉	—	2	2	no	—
62	C₄×C₉	—	2	1	no	—
63	C₄×C₉	#99	1	2	yes	—
64	C₂³×C₄	C₂×D₉	1	1	yes	characteristic
65	C₂×M₁₆	Dic₉	1	2	yes	—
66	C₂²×C₈	—	18	2	no	—
67	C₂²⋊C₈	—	2	2	no	—
68	C₂²⋊C₈	—	9	4	no	—
69	C₂²⋊C₈	—	18	2	no	—
70	C₂³×C₃	—	2	4	no	—
71	C₂³×C₃	—	4	1	no	—
72	C₂³×C₃	Dic₃⋊C₄	1	2	yes	—
73	C₂³×C₃	C₄⋊Dic₃	1	1	yes	characteristic
74	C₂×C₃×C₄	—	2	4	no	—
75	C₂×C₃×C₄	—	2	2	no	—
76	C₂×C₃×C₄	—	4	2	no	—
77	C₂×C₃×C₄	—	4	1	no	—
78	C₂×C₃×C₄	C₄×Dic₃	1	1	yes	characteristic
79	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
80	C₂×C₃×C₄	#217	1	1	yes	characteristic
81	C₃×C₈	—	4	2	no	—
82	C₃⋊C₈	—	12	4	no	—
83	C₂×C₉	—	2	4	no	—
84	C₂×C₉	—	4	1	no	—
85	C₂×C₉	#341	1	2	yes	—
86	C₂×C₉	#342	1	1	yes	characteristic
87	C₂⁴	Dic₁₈	1	1	yes	characteristic
88	C₂²×C₄	—	4	2	no	—
89	C₂²×C₄	C₄×D₉	1	2	yes	—
90	C₂²×C₄	D₃₆	1	1	yes	characteristic
91	C₂²×C₄	C₂×Dic₉	1	1	yes	characteristic
92	C₂²×C₄	#611	1	2	yes	—
93	M₁₆	—	4	2	no	—
94	C₂×C₈	—	2	2	no	—
95	C₂×C₈	—	18	4	no	—
96	C₂×C₈	—	36	4	no	—
97	C₂²×C₃	—	2	2	no	—
98	C₂²×C₃	—	2	2	no	—
99	C₂²×C₃	—	2	1	no	—
100	C₂²×C₃	—	2	2	no	—
101	C₂²×C₃	—	4	4	no	—
102	C₂²×C₃	#822	1	4	yes	—
103	C₂²×C₃	C₃⋊#95	1	1	yes	characteristic
104	C₃×C₄	—	2	2	no	—
105	C₃×C₄	—	2	1	no	—
106	C₃×C₄	#834	1	2	yes	—
107	C₉	#1298	1	1	yes	characteristic, complemented, Sylow
108	C₂³	—	2	4	no	—
109	C₂³	—	4	1	no	—
110	C₂³	Dic₉⋊C₄	1	2	yes	—
111	C₂³	C₄⋊Dic₉	1	1	yes	characteristic
112	C₂×C₄	—	2	4	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	4	2	no	—
115	C₂×C₄	—	4	1	no	—
116	C₂×C₄	C₄×Dic₉	1	1	yes	characteristic
117	C₂×C₄	(C₂×D₉)⋊C₄	1	2	yes	—
118	C₂×C₄	#3676	1	1	yes	characteristic
119	C₈	—	4	2	no	—
120	C₈	—	36	4	no	—
121	C₂×C₃	—	2	4	no	—
122	C₂×C₃	—	4	1	no	—
123	C₂×C₃	#4526	1	1	yes	characteristic
124	C₂×C₃	#4558	1	2	yes	—
125	C₂²	—	2	2	no	—
126	C₂²	—	2	2	no	—
127	C₂²	—	2	1	no	—
128	C₂²	—	2	2	no	—
129	C₂²	—	4	4	no	—
130	C₂²	#63381	1	4	yes	—
131	C₂²	C₉⋊#95	1	1	yes	characteristic
132	C₄	—	2	2	no	—
133	C₄	—	2	1	no	—
134	C₄	#63393	1	2	yes	—
135	C₃	#67688	1	1	yes	characteristic
136	C₂	—	2	4	no	—
137	C₂	—	4	1	no	—
138	C₂	#10588203	1	1	yes	characteristic
139	C₂	#10588231	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#407

C₂

yes

maximal, characteristic

C₂×#63389

C₂

yes

maximal

#67688

—

maximal

C₂³×C₄×C₉

C₂²

yes

characteristic

C₂×C₉×M₁₆

C₄

yes

—

C₂²×C₉⋊C₈

—

C₉×C₂²⋊C₈

—

#63389

—

#63389

C₄

yes

—

C₃×#407

D₃

yes

characteristic

C₂×#830

—

C₂⁴×C₉

Q₈

yes

characteristic

C₂²×C₄×C₉

—

C₂²×C₄×C₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₉

C₂×C₄

yes

—

C₂²×C₄×C₉

D₄

yes

—

C₂²×C₄×C₉

D₄

yes

characteristic

C₉×M₁₆

—

C₂×C₈×C₉

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

—

#1298

—

Sylow

C₂³×C₃×C₄

C₂×D₃

yes

characteristic

C₂×C₃×M₁₆

Dic₃

yes

—

C₂²×C₃⋊C₈

—

C₃×C₂²⋊C₈

—

#830

—

#830

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

C₄⋊C₄

yes

—

C₂³×C₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₄²

yes

characteristic

C₂×C₄×C₉

C₂²⋊C₄

yes

—

C₂×C₄×C₉

C₂²⋊C₄

yes

characteristic

C₈×C₉

—

C₉⋊C₈

—

#407

D₉

yes

characteristic

C₂×C₂²⋊C₈

—

C₂⁴×C₃

Dic₆

yes

characteristic

C₂²×C₃×C₄

—

C₂²×C₃×C₄

C₄×D₃

yes

—

C₂²×C₃×C₄

D₁₂

yes

characteristic

C₂²×C₃×C₄

C₂×Dic₃

yes

characteristic

C₂²×C₃×C₄

#67

yes

—

C₃×M₁₆

—

C₂×C₃×C₈

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

#95

yes

characteristic

C₂²×C₉

#108

yes

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

#99

yes

—

C₂³×C₄

C₂×D₉

yes

characteristic

C₂×M₁₆

Dic₉

yes

—

C₂²×C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂³×C₃

—

C₂³×C₃

—

C₂³×C₃

Dic₃⋊C₄

yes

—

C₂³×C₃

C₄⋊Dic₃

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₄×Dic₃

yes

characteristic

C₂×C₃×C₄

(C₂×D₃)⋊C₄

yes

—

C₂×C₃×C₄

#217

yes

characteristic

C₃×C₈

—

C₃⋊C₈

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

#341

yes

—

C₂×C₉

#342

yes

characteristic

C₂⁴

Dic₁₈

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₄×D₉

yes

—

C₂²×C₄

D₃₆

yes

characteristic

C₂²×C₄

C₂×Dic₉

yes

characteristic

C₂²×C₄

#611

yes

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

—

100

C₂²×C₃

—

101

C₂²×C₃

—

102

C₂²×C₃

#822

yes

—

103

C₂²×C₃

C₃⋊#95

yes

characteristic

104

C₃×C₄

—

105

C₃×C₄

—

106

C₃×C₄

#834

yes

—

107

C₉

#1298

yes

characteristic, complemented, Sylow

108

C₂³

—

109

C₂³

—

110

C₂³

Dic₉⋊C₄

yes

—

111

C₂³

C₄⋊Dic₉

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

C₄×Dic₉

yes

characteristic

117

C₂×C₄

(C₂×D₉)⋊C₄

yes

—

118

C₂×C₄

#3676

yes

characteristic

119

C₈

—

120

C₈

—

121

C₂×C₃

—

122

C₂×C₃

—

123

C₂×C₃

#4526

yes

characteristic

124

C₂×C₃

#4558

yes

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

#63381

yes

—

131

C₂²

C₉⋊#95

yes

characteristic

132

C₄

—

133

C₄

—

134

C₄

#63393

yes

—

135

C₃

#67688

yes

characteristic

136

C₂

—

137

C₂

—

138

C₂

#10588203

yes

characteristic

139

C₂

#10588231

yes

—

	subgroup	G/H
center	C₂×C₄	#3676
commutator	C₂×C₄×C₉	C₄²
Frattini	C₂³×C₃×C₄	C₂×D₃
Fitting	C₉×#407	C₂
socle	C₂²×C₃	C₃⋊#95
prime radical	C₂⁴×C₃	Dic₆
cosocle	C₂³×C₄×C₉	C₂²
hypercenter	#407	D₉
hypocenter	C₉	#1298
LCS	G ▷ C₂×C₄×C₉ ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #407

subgroup

G/H

center

C₂×C₄

#3676

commutator

C₂×C₄×C₉

C₄²

Frattini

C₂³×C₃×C₄

C₂×D₃

C₂

C₂²×C₃

C₂⁴×C₃

Dic₆

cosocle

C₂³×C₄×C₉

C₂²

D₉

C₉

G ▷ C₂×C₄×C₉ ▷ C₂²×C₉ ▷ C₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #407

N	H ≅ G/N	type
107. C₉	#1298	semidirect

H ≅ G/N

type

107. C₉

#1298

semidirect

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

subgroup	index
C₉×#407	2
C₂×#63389	2
#67688	3

subgroup

index

C₉×#407

C₂×#63389

#67688

Subgroups — #11771103

Conjugacy classes of subgroups

Complements

Maximal subgroups