Group #14669188 — subgroups

Subgroups — #14669188

Order 2816.

306 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 135 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×#10622131	C₂	1	2	yes	maximal
2	C₂×#10622140	C₂	1	1	yes	maximal, characteristic
3	#108×Dic₁₁	C₂	1	2	yes	maximal
4	#13066710	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1381	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₁₁×#108	C₂²	1	2	yes	—
8	M₁₆×Dic₁₁	—	2	2	no	—
9	C₂×#66883	C₂²	1	2	yes	—
10	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
11	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
12	#10622196	—	2	2	no	—
13	#10622140	C₄	1	4	yes	—
14	#10622131	C₄	1	8	yes	complemented
15	C₂×C₁₁×M₁₆	—	2	2	no	—
16	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
17	C₂×C₄×Dic₁₁	D₄	1	1	yes	characteristic
18	C₂×#4318	—	2	2	no	—
19	C₂²×C₁₁⋊C₈	D₄	1	1	yes	characteristic
20	C₂×C₁₁×C₁₆	—	2	2	no	—
21	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
22	C₁₁×#108	—	2	2	no	—
23	C₁₁×#108	C₂×C₄	1	4	yes	—
24	#66883	—	2	2	no	—
25	#66883	C₂×C₄	1	4	yes	—
26	#66879	—	4	2	no	—
27	C₈×Dic₁₁	—	4	2	no	—
28	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
29	C₈×Dic₁₁	Q₈	1	2	yes	—
30	C₂×C₁₁⋊C₁₆	C₂×C₄	1	4	yes	—
31	C₂×C₁₁⋊C₁₆	C₂×C₄	1	2	yes	—
32	#12676	—	11	1	no	maximal, Sylow
33	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
34	C₂²×Dic₁₁	Q₁₆	1	2	yes	—
35	C₁₁×M₁₆	—	2	4	no	—
36	C₁₁×M₁₆	—	4	2	no	—
37	C₂×C₈×C₁₁	—	4	2	no	—
38	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
40	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₈×C₁₁	#41	1	2	yes	—
42	C₄×Dic₁₁	C₄⋊C₄	1	2	yes	—
43	C₄×Dic₁₁	D₈	1	2	yes	—
44	#4318	—	2	4	no	—
45	#4318	—	4	2	no	—
46	C₂×C₁₁⋊C₈	—	2	2	no	—
47	C₂×C₁₁⋊C₈	—	4	2	no	—
48	C₂×C₁₁⋊C₈	C₄⋊C₄	1	2	yes	—
49	C₁₁×C₁₆	—	2	2	no	—
50	C₁₁⋊C₁₆	C₄²	1	4	yes	—
51	C₂×#368	—	11	2	no	—
52	C₂×#346	—	11	1	no	—
53	C₄×#108	—	11	2	no	—
54	#1381	—	11	1	no	—
55	#1381	D₁₁	1	1	yes	characteristic
56	C₂³×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
57	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
59	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
60	C₂×C₄×C₁₁	#135	1	2	yes	—
61	C₂×Dic₁₁	—	4	2	no	—
62	C₂×Dic₁₁	#107	1	4	yes	—
63	C₈×C₁₁	—	4	4	no	—
64	C₈×C₁₁	C₂×C₄²	1	1	yes	characteristic
65	C₈×C₁₁	#117	1	1	yes	characteristic
66	C₈×C₁₁	C₄×Q₈	1	2	yes	—
67	C₁₁⋊C₈	—	2	2	no	—
68	C₁₁⋊C₈	—	4	4	no	—
69	C₂²×C₁₆	—	11	1	no	—
70	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
71	C₂×#108	—	11	2	no	—
72	C₂×#108	C₂×D₁₁	1	2	yes	—
73	C₄×M₁₆	—	22	2	no	—
74	C₂×C₄×C₈	—	11	1	no	—
75	#368	—	11	8	no	—
76	#346	—	11	4	no	—
77	#341	—	22	2	no	—
78	C₂²×C₁₁	—	2	2	no	—
79	C₂²×C₁₁	C₂×#107	1	1	yes	characteristic
80	C₂²×C₁₁	C₄×Q₁₆	1	2	yes	—
81	C₄×C₁₁	C₄×C₄⋊C₄	1	1	yes	characteristic
82	C₄×C₁₁	#427	1	1	yes	characteristic
83	C₄×C₁₁	C₄×D₈	1	2	yes	—
84	Dic₁₁	—	2	4	no	—
85	C₂×M₁₆	—	2	2	no	—
86	C₂×M₁₆	—	22	2	no	—
87	C₂²×C₈	—	11	1	no	—
88	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
89	C₂×C₄²	—	11	1	no	—
90	C₂×C₁₆	—	2	2	no	—
91	C₂×C₁₆	—	11	2	no	—
92	C₂×C₁₆	—	11	4	no	—
93	C₂×C₁₆	C₄×D₁₁	1	2	yes	—
94	#108	—	2	2	no	—
95	#108	—	11	4	no	—
96	#108	—	22	2	no	—
97	#108	C₄×D₁₁	1	4	yes	—
98	#97	—	44	2	no	—
99	C₄×C₈	—	11	2	no	—
100	C₄×C₈	—	11	2	no	—
101	C₄×C₈	—	44	2	no	—
102	C₂×C₁₁	—	2	2	no	—
103	C₂×C₁₁	C₄×#107	1	1	yes	characteristic
104	C₂×C₁₁	#2161	1	2	yes	—
105	C₂²×C₄	—	11	2	no	—
106	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
107	M₁₆	—	2	4	no	—
108	M₁₆	—	4	2	no	—
109	M₁₆	—	22	4	no	—
110	M₁₆	—	44	2	no	—
111	C₂×C₈	—	4	2	no	—
112	C₂×C₈	—	11	2	no	—
113	C₂×C₈	—	22	2	no	—
114	C₂×C₈	—	44	2	no	—
115	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
116	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
117	C₂×C₈	#4341	1	2	yes	—
118	C₂×C₈	Q₈×D₁₁	1	1	yes	characteristic
119	C₄²	—	11	2	no	—
120	C₄²	—	11	2	no	—
121	C₁₆	—	2	2	no	—
122	C₁₆	—	11	4	no	—
123	C₁₁	#12676	1	1	yes	characteristic, complemented, Sylow
124	C₂³	Q₁₆×D₁₁	1	1	yes	characteristic
125	C₂×C₄	—	11	4	no	—
126	C₂×C₄	—	44	2	no	—
127	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	2	yes	—
128	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
129	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
130	C₂×C₄	#66969	1	2	yes	—
131	C₈	—	4	4	no	—
132	C₈	—	22	2	no	—
133	C₈	—	44	4	no	—
134	C₈	C₄²×D₁₁	1	1	yes	characteristic
135	C₈	#66930	1	1	yes	characteristic
136	C₈	#66940	1	2	yes	—
137	C₂²	—	2	2	no	—
138	C₂²	#10622403	1	2	yes	—
139	C₂²	D₁₁×#107	1	1	yes	characteristic
140	C₄	—	22	4	no	—
141	C₄	#10622262	1	1	yes	characteristic
142	C₄	#10622369	1	2	yes	—
143	C₄	#10622473	1	1	yes	characteristic
144	C₂	—	2	2	no	—
145	C₂	#13068508	1	1	yes	characteristic
146	C₂	#13070409	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622131

C₂

yes

maximal

C₂×#10622140

C₂

yes

maximal, characteristic

#108×Dic₁₁

C₂

yes

maximal

#13066710

C₂

yes

maximal, characteristic

C₁₁×#1381

C₂

yes

maximal, characteristic

C₂²×C₁₁×C₁₆

C₂²

yes

characteristic

C₂×C₁₁×#108

C₂²

yes

—

M₁₆×Dic₁₁

—

C₂×#66883

C₂²

yes

—

C₂×C₈×Dic₁₁

C₂²

yes

characteristic

C₂²×C₁₁⋊C₁₆

C₂²

yes

characteristic

#10622196

—

#10622140

C₄

yes

—

#10622131

C₄

yes

complemented

C₂×C₁₁×M₁₆

—

C₂²×C₈×C₁₁

C₂³

yes

characteristic

C₂×C₄×Dic₁₁

D₄

yes

characteristic

C₂×#4318

—

C₂²×C₁₁⋊C₈

D₄

yes

characteristic

C₂×C₁₁×C₁₆

—

C₂×C₁₁×C₁₆

C₂×C₄

yes

—

C₁₁×#108

—

C₁₁×#108

C₂×C₄

yes

—

#66883

—

#66883

C₂×C₄

yes

—

#66879

—

C₈×Dic₁₁

—

C₈×Dic₁₁

C₂×C₄

yes

—

C₈×Dic₁₁

Q₈

yes

—

C₂×C₁₁⋊C₁₆

C₂×C₄

yes

—

C₂×C₁₁⋊C₁₆

C₂×C₄

yes

—

#12676

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×Dic₁₁

Q₁₆

yes

—

C₁₁×M₁₆

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₁

C₂²×C₄

yes

—

C₂×C₈×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₁

#41

yes

—

C₄×Dic₁₁

C₄⋊C₄

yes

—

C₄×Dic₁₁

D₈

yes

—

#4318

—

#4318

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

C₄⋊C₄

yes

—

C₁₁×C₁₆

—

C₁₁⋊C₁₆

C₄²

yes

—

—

—

—

—

D₁₁

yes

characteristic

C₂³×C₁₁

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₄×D₄

yes

—

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

C₂×C₄×C₁₁

#135

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

#107

yes

—

C₈×C₁₁

—

C₈×C₁₁

C₂×C₄²

yes

characteristic

C₈×C₁₁

#117

yes

characteristic

C₈×C₁₁

C₄×Q₈

yes

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

C₂²×C₁₆

—

C₂²×C₁₆

C₂×D₁₁

yes

characteristic

C₂×#108

—

C₂×#108

C₂×D₁₁

yes

—

C₄×M₁₆

—

C₂×C₄×C₈

—

#368

—

#346

—

#341

—

C₂²×C₁₁

—

C₂²×C₁₁

C₂×#107

yes

characteristic

C₂²×C₁₁

C₄×Q₁₆

yes

—

C₄×C₁₁

C₄×C₄⋊C₄

yes

characteristic

C₄×C₁₁

#427

yes

characteristic

C₄×C₁₁

C₄×D₈

yes

—

Dic₁₁

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂²×D₁₁

yes

characteristic

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₄×D₁₁

yes

—

—

—

—

C₄×D₁₁

yes

—

#97

—

C₄×C₈

—

100

C₄×C₈

—

101

C₄×C₈

—

102

C₂×C₁₁

—

103

C₂×C₁₁

C₄×#107

yes

characteristic

104

C₂×C₁₁

#2161

yes

—

105

C₂²×C₄

—

106

C₂²×C₄

D₄×D₁₁

yes

characteristic

107

M₁₆

—

108

M₁₆

—

109

M₁₆

—

110

M₁₆

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

C₂×C₄×D₁₁

yes

characteristic

116

C₂×C₈

C₂×C₄×D₁₁

yes

—

117

C₂×C₈

#4341

yes

—

118

C₂×C₈

Q₈×D₁₁

yes

characteristic

119

C₄²

—

120

C₄²

—

121

C₁₆

—

122

C₁₆

—

123

C₁₁

#12676

yes

characteristic, complemented, Sylow

124

C₂³

Q₁₆×D₁₁

yes

characteristic

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

(C₂²⋊D₁₁)⋊C₄

yes

—

128

C₂×C₄

C₄⋊C₄×D₁₁

yes

characteristic

129

C₂×C₄

D₈×D₁₁

yes

characteristic

130

C₂×C₄

#66969

yes

—

131

C₈

—

132

C₈

—

133

C₈

—

134

C₈

C₄²×D₁₁

yes

characteristic

135

C₈

#66930

yes

characteristic

136

C₈

#66940

yes

—

137

C₂²

—

138

C₂²

#10622403

yes

—

139

C₂²

D₁₁×#107

yes

characteristic

140

C₄

—

141

C₄

#10622262

yes

characteristic

142

C₄

#10622369

yes

—

143

C₄

#10622473

yes

characteristic

144

C₂

—

145

C₂

#13068508

yes

characteristic

146

C₂

#13070409

yes

—

	subgroup	G/H
center	C₂×C₄	D₈×D₁₁
commutator	C₈×C₁₁	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#1381	C₂
socle	C₂²×C₁₁	C₂×#107
prime radical	C₂³×C₁₁	C₂×Q₁₆
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#1381	D₁₁
hypocenter	C₁₁	#12676
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1381

subgroup

G/H

center

C₂×C₄

D₈×D₁₁

commutator

C₈×C₁₁

C₂×C₄²

Frattini

C₂²×C₈

C₂²×D₁₁

Fitting

C₁₁×#1381

C₂

socle

C₂²×C₁₁

C₂×#107

prime radical

C₂³×C₁₁

C₂×Q₁₆

cosocle

C₂²×C₈×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1381

N	H ≅ G/N	type
14. #10622131	C₄	semidirect
123. C₁₁	#12676	semidirect

H ≅ G/N

type

14. #10622131

C₄

semidirect

123. C₁₁

#12676

semidirect

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

subgroup	index
C₂×#10622131	2
C₂×#10622140	2
#108×Dic₁₁	2
#13066710	2
C₁₁×#1381	2
#12676	11

subgroup

index

#108×Dic₁₁

C₁₁×#1381

Subgroups — #14669188

Conjugacy classes of subgroups

Complements

Maximal subgroups