Group #11771899 — subgroups

Subgroups — #11771899

Order 1152.

312 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 95 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	#10592815	C₂	1	1	yes	maximal, characteristic
2	C₃²×#341	C₂	1	1	yes	maximal, characteristic
3	#10589415	C₂	1	1	yes	maximal, characteristic
4	#67488	—	3	4	no	maximal
5	C₂×C₃²×M₁₆	—	2	1	no	—
6	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
7	#64133	—	2	1	no	—
8	C₂×#3746	C₄	1	1	yes	characteristic
9	#63645	C₄	1	1	yes	characteristic
10	#63643	—	2	1	no	—
11	C₂×C₃⋊(C₃⋊C₁₆)	—	2	1	no	—
12	#5116	—	3	4	no	—
13	C₃×#341	D₃	1	4	yes	—
14	#4549	—	3	4	no	—
15	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
16	C₂×#634	—	2	1	no	—
17	C₃²×M₁₆	—	2	2	no	—
18	C₃²×M₁₆	—	4	1	no	—
19	C₂×C₃²×C₈	—	4	1	no	—
20	C₂×C₃²×C₈	—	4	1	no	—
21	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
22	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
23	#3757	—	4	1	no	—
24	C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
25	#3750	—	4	1	no	—
26	#3746	—	4	1	no	—
27	C₃⋊(C₃⋊C₁₆)	—	4	1	no	—
28	#1350	—	9	1	no	Sylow
29	C₂×C₃×M₁₆	—	2	4	no	—
30	C₂²×C₃×C₈	C₂×D₃	1	4	yes	—
31	#924	—	6	4	no	—
32	C₂×Dic₁₂	—	3	4	no	—
33	#818	—	3	4	no	—
34	#816	—	6	4	no	—
35	C₂×C₃⋊C₁₆	—	6	4	no	—
36	C₂³×C₃²	SD₁₆	1	1	yes	characteristic
37	C₂×C₃²×C₄	—	2	1	no	—
38	C₂×C₃²×C₄	—	2	1	no	—
39	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
41	C₂×C₃⋊Dic₃	—	4	1	no	—
42	C₂×C₃⋊Dic₃	—	4	1	no	—
43	#634	—	4	1	no	—
44	#634	—	4	1	no	—
45	C₃²×C₈	—	2	1	no	—
46	C₃²×C₈	—	2	1	no	—
47	C₃²×C₈	—	4	2	no	—
48	#467	—	9	1	no	—
49	C₂²⋊C₁₆	—	9	1	no	—
50	#341	C₃⋊D₃	1	1	yes	characteristic
51	C₂²×C₃×C₄	#67	1	4	yes	—
52	C₂×Dic₆	—	6	4	no	—
53	C₃×M₁₆	—	2	8	no	—
54	C₃×M₁₆	—	4	4	no	—
55	C₂×C₃×C₈	—	4	4	no	—
56	C₂×C₃×C₈	—	4	4	no	—
57	C₂×C₃×C₈	C₄×D₃	1	4	yes	—
58	C₂×C₃×C₈	D₁₂	1	4	yes	—
59	#217	—	12	4	no	—
60	C₄⋊Dic₃	—	6	4	no	—
61	Dic₃⋊C₄	—	12	4	no	—
62	Dic₁₂	—	12	4	no	—
63	C₃⋊C₁₆	—	12	4	no	—
64	C₂²×C₃²	—	2	1	no	—
65	C₂²×C₃²	—	2	1	no	—
66	C₂²×C₃²	—	2	1	no	—
67	C₂²×C₃²	#102	1	1	yes	characteristic
68	C₃²×C₄	—	2	1	no	—
69	C₃²×C₄	#99	1	1	yes	characteristic
70	C₃²×C₄	#104	1	1	yes	characteristic
71	C₃⋊Dic₃	—	8	1	no	—
72	C₃⋊Dic₃	—	8	1	no	—
73	C₂×Q₁₆	—	9	1	no	—
74	C₂×M₁₆	—	2	1	no	—
75	C₂²×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
76	C₂²⋊Q₈	—	18	1	no	—
77	C₂×C₁₆	—	18	1	no	—
78	#107	—	9	1	no	—
79	#103	—	18	1	no	—
80	C₂³×C₃	#215	1	4	yes	—
81	C₂×C₃×C₄	—	2	4	no	—
82	C₂×C₃×C₄	—	2	4	no	—
83	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	4	yes	—
84	C₂×C₃×C₄	#213	1	4	yes	—
85	C₂×Dic₃	—	12	4	no	—
86	C₂×Dic₃	—	12	4	no	—
87	Dic₆	—	12	4	no	—
88	Dic₆	—	12	4	no	—
89	C₃×C₈	—	2	4	no	—
90	C₃×C₈	—	2	4	no	—
91	C₃×C₈	—	4	8	no	—
92	C₂×C₃²	—	4	1	no	—
93	C₂×C₃²	#327	1	1	yes	characteristic
94	C₂×C₃²	#359	1	1	yes	characteristic
95	C₂×C₃²	#362	1	1	yes	characteristic
96	C₂×Q₈	—	18	1	no	—
97	C₂²×C₄	#638	1	1	yes	characteristic
98	Q₁₆	—	36	1	no	—
99	M₁₆	—	2	2	no	—
100	M₁₆	—	4	1	no	—
101	C₂×C₈	—	4	1	no	—
102	C₂×C₈	—	4	1	no	—
103	C₂×C₈	C₄×C₃⋊D₃	1	1	yes	characteristic
104	C₂×C₈	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
105	C₄⋊C₄	—	18	1	no	—
106	C₄⋊C₄	—	36	1	no	—
107	C₂²⋊C₄	—	36	1	no	—
108	C₁₆	—	36	1	no	—
109	C₂²×C₃	—	2	4	no	—
110	C₂²×C₃	—	2	4	no	—
111	C₂²×C₃	—	2	4	no	—
112	C₂²×C₃	#809	1	4	yes	—
113	C₃×C₄	—	2	4	no	—
114	C₃×C₄	#805	1	4	yes	—
115	C₃×C₄	#806	1	4	yes	—
116	Dic₃	—	24	4	no	—
117	Dic₃	—	24	4	no	—
118	C₃²	#1350	1	1	yes	characteristic, complemented, Sylow
119	C₂³	#3755	1	1	yes	characteristic
120	Q₈	—	36	1	no	—
121	Q₈	—	36	1	no	—
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	36	1	no	—
125	C₂×C₄	—	36	1	no	—
126	C₂×C₄	#3752	1	1	yes	characteristic
127	C₂×C₄	#3753	1	1	yes	characteristic
128	C₈	—	2	1	no	—
129	C₈	—	2	1	no	—
130	C₈	—	4	2	no	—
131	C₂×C₃	—	4	4	no	—
132	C₂×C₃	#4451	1	4	yes	—
133	C₂×C₃	#4496	1	4	yes	—
134	C₂×C₃	#4497	1	4	yes	—
135	C₂²	—	2	1	no	—
136	C₂²	—	2	1	no	—
137	C₂²	—	2	1	no	—
138	C₂²	#63636	1	1	yes	characteristic
139	C₄	—	2	1	no	—
140	C₄	—	72	1	no	—
141	C₄	—	72	1	no	—
142	C₄	#63632	1	1	yes	characteristic
143	C₄	#63633	1	1	yes	characteristic
144	C₃	#67488	1	4	yes	complemented
145	C₂	—	4	1	no	—
146	C₂	#10589317	1	1	yes	characteristic
147	C₂	#10589362	1	1	yes	characteristic
148	C₂	#10589363	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10592815

C₂

yes

maximal, characteristic

C₃²×#341

C₂

yes

maximal, characteristic

#10589415

C₂

yes

maximal, characteristic

#67488

—

maximal

C₂×C₃²×M₁₆

—

C₂²×C₃²×C₈

C₂²

yes

characteristic

#64133

—

C₂×#3746

C₄

yes

characteristic

#63645

C₄

yes

characteristic

#63643

—

C₂×C₃⋊(C₃⋊C₁₆)

—

#5116

—

C₃×#341

D₃

yes

—

#4549

—

C₂²×C₃²×C₄

D₄

yes

characteristic

C₂×#634

—

C₃²×M₁₆

—

C₃²×M₁₆

—

C₂×C₃²×C₈

—

C₂×C₃²×C₈

—

C₂×C₃²×C₈

C₂×C₄

yes

characteristic

C₂×C₃²×C₈

D₄

yes

characteristic

#3757

—

C₄⋊(C₃⋊Dic₃)

—

#3750

—

#3746

—

C₃⋊(C₃⋊C₁₆)

—

#1350

—

Sylow

C₂×C₃×M₁₆

—

C₂²×C₃×C₈

C₂×D₃

yes

—

#924

—

C₂×Dic₁₂

—

#818

—

#816

—

C₂×C₃⋊C₁₆

—

C₂³×C₃²

SD₁₆

yes

characteristic

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

C₂²⋊C₄

yes

characteristic

C₂×C₃²×C₄

D₈

yes

characteristic

C₂×C₃⋊Dic₃

—

C₂×C₃⋊Dic₃

—

#634

—

#634

—

C₃²×C₈

—

C₃²×C₈

—

C₃²×C₈

—

#467

—

C₂²⋊C₁₆

—

#341

C₃⋊D₃

yes

characteristic

C₂²×C₃×C₄

#67

yes

—

C₂×Dic₆

—

C₃×M₁₆

—

C₃×M₁₆

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₄×D₃

yes

—

C₂×C₃×C₈

D₁₂

yes

—

#217

—

C₄⋊Dic₃

—

Dic₃⋊C₄

—

Dic₁₂

—

C₃⋊C₁₆

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

#102

yes

characteristic

C₃²×C₄

—

C₃²×C₄

yes

C₃²×C₄

yes

C₃⋊Dic₃

—

C₃⋊Dic₃

—

C₂×Q₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×C₃⋊D₃

yes

characteristic

C₂²⋊Q₈

—

C₂×C₁₆

—

#107

—

#103

—

C₂³×C₃

#215

yes

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

(C₂×D₃)⋊C₄

yes

—

C₂×C₃×C₄

#213

yes

—

C₂×Dic₃

—

C₂×Dic₃

—

Dic₆

—

Dic₆

—

C₃×C₈

—

C₃×C₈

—

C₃×C₈

—

C₂×C₃²

—

C₂×C₃²

yes

C₂×C₃²

yes

C₂×C₃²

yes

C₂×Q₈

—

C₂²×C₄

#638

yes

characteristic

Q₁₆

—

M₁₆

—

100

M₁₆

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

C₄×C₃⋊D₃

yes

characteristic

104

C₂×C₈

C₄⋊(C₃⋊D₃)

yes

characteristic

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₂²⋊C₄

—

108

C₁₆

—

109

C₂²×C₃

—

110

C₂²×C₃

—

111

C₂²×C₃

—

112

C₂²×C₃

#809

yes

—

113

C₃×C₄

—

114

C₃×C₄

#805

yes

—

115

C₃×C₄

#806

yes

—

116

Dic₃

—

117

Dic₃

—

118

C₃²

#1350

yes

characteristic, complemented, Sylow

119

C₂³

#3755

yes

characteristic

120

Q₈

—

121

Q₈

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

#3752

yes

characteristic

127

C₂×C₄

#3753

yes

characteristic

128

C₈

—

129

C₈

—

130

C₈

—

131

C₂×C₃

—

132

C₂×C₃

#4451

yes

—

133

C₂×C₃

#4496

yes

—

134

C₂×C₃

#4497

yes

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

#63636

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

#63632

yes

characteristic

143

C₄

#63633

yes

characteristic

144

C₃

#67488

yes

complemented

145

C₂

—

146

C₂

#10589317

yes

characteristic

147

C₂

#10589362

yes

characteristic

148

C₂

#10589363

yes

characteristic

	subgroup	G/H
center	C₂²	#63636
commutator	C₂×C₃²×C₈	C₂×C₄
Frattini	C₂²×C₈	C₂×C₃⋊D₃
Fitting	C₃²×#341	C₂
socle	C₂²×C₃²	#102
prime radical	C₂³×C₃²	SD₁₆
cosocle	C₂²×C₃²×C₈	C₂²
hypercenter	#341	C₃⋊D₃
hypocenter	C₃²	#1350
LCS	G ▷ C₂×C₃²×C₈ ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #341

subgroup

G/H

center

C₂²

#63636

commutator

C₂×C₃²×C₈

C₂×C₄

Frattini

C₂²×C₈

C₂×C₃⋊D₃

Fitting

C₃²×#341

C₂

socle

C₂²×C₃²

#102

prime radical

C₂³×C₃²

SD₁₆

cosocle

C₂²×C₃²×C₈

C₂²

C₃⋊D₃

C₃²

G ▷ C₂×C₃²×C₈ ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #341

N	H ≅ G/N	type
118. C₃²	#1350	semidirect
144. C₃	#67488	semidirect

H ≅ G/N

type

118. C₃²

#1350

semidirect

144. C₃

#67488

semidirect

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

subgroup	index
#10592815	2
C₃²×#341	2
#10589415	2
#67488	3

subgroup

index

#10592815

C₃²×#341

#10589415

#67488

Subgroups — #11771899

Conjugacy classes of subgroups

Complements

Maximal subgroups