Group #13076977 — subgroups

Subgroups — #13076977

Order 1408.

472 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 197 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×#66943	C₂	1	2	yes	maximal
2	C₁₁×#384	C₂	1	1	yes	maximal, characteristic
3	#10622598	C₂	1	4	yes	maximal
4	#10622590	C₂	1	2	yes	maximal
5	#10622586	C₂	1	4	yes	maximal
6	#10622548	C₂	1	1	yes	maximal, characteristic
7	C₄²×Dic₁₁	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
10	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₁	C₂²	1	2	yes	—
12	C₂×C₄⋊Dic₁₁	C₂²	1	4	yes	—
13	C₂×C₄⋊Dic₁₁	C₂²	1	4	yes	—
14	C₂×Dic₁₁⋊C₄	C₂²	1	4	yes	—
15	C₂×C₄×Dic₁₁	C₂²	1	2	yes	—
16	C₂×C₄×Dic₁₁	C₂²	1	2	yes	—
17	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic
19	#66943	—	2	8	no	—
20	C₁₁⋊#95	C₂²	1	8	yes	—
21	C₂²×C₄×C₁₁	C₂³	1	4	yes	—
22	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
24	C₂²×Dic₁₁	C₂³	1	4	yes	—
25	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
27	C₂²×Dic₁₁	C₂³	1	2	yes	—
28	C₁₁×C₄⋊C₄	—	2	4	no	—
29	C₁₁×C₄⋊C₄	—	2	8	no	—
30	C₄²×C₁₁	Q₈	1	4	yes	—
31	C₄⋊Dic₁₁	—	2	8	no	—
32	C₄⋊Dic₁₁	—	2	4	no	—
33	C₄⋊Dic₁₁	—	2	8	no	—
34	Dic₁₁⋊C₄	—	2	8	no	—
35	C₄×Dic₁₁	—	2	4	no	—
36	C₄×Dic₁₁	—	2	4	no	—
37	C₄×Dic₁₁	D₄	1	4	yes	—
38	C₄×Dic₁₁	Q₈	1	4	yes	—
39	#2859	—	11	1	no	maximal, Sylow
40	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
41	C₂×C₄×C₁₁	—	2	4	no	—
42	C₂×C₄×C₁₁	—	2	8	no	—
43	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₁₁	C₂×Q₈	1	4	yes	—
45	C₂×C₄×C₁₁	C₂×Q₈	1	2	yes	—
46	C₂×C₄×C₁₁	C₂×Q₈	1	2	yes	—
47	C₂×C₄×C₁₁	#41	1	4	yes	—
48	C₂×C₄×C₁₁	#41	1	4	yes	—
49	C₂×Dic₁₁	—	2	2	no	—
50	C₂×Dic₁₁	—	2	2	no	—
51	C₂×Dic₁₁	—	2	2	no	—
52	C₂×Dic₁₁	—	2	2	no	—
53	C₂×Dic₁₁	—	2	4	no	—
54	C₂×Dic₁₁	—	2	8	no	—
55	C₂×Dic₁₁	C₂×D₄	1	2	yes	—
56	C₂×Dic₁₁	C₂×D₄	1	2	yes	—
57	C₂×Dic₁₁	C₂×Q₈	1	4	yes	—
58	C₂×#125	—	11	2	no	—
59	#389	—	11	4	no	—
60	#389	—	11	4	no	—
61	#384	—	11	1	no	—
62	#384	D₁₁	1	1	yes	characteristic
63	#382	—	11	2	no	—
64	C₄³	—	11	1	no	—
65	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
66	C₂²×C₁₁	C₂²×Q₈	1	1	yes	characteristic
67	C₂²×C₁₁	C₂²×Q₈	1	1	yes	characteristic
68	C₂²×C₁₁	C₂×#41	1	2	yes	—
69	C₂²×C₁₁	C₂×#41	1	2	yes	—
70	C₄×C₁₁	—	4	4	no	—
71	C₄×C₁₁	#125	1	8	yes	complemented
72	C₄×C₁₁	C₄⋊Q₈	1	4	yes	—
73	Dic₁₁	—	2	2	no	—
74	Dic₁₁	—	2	2	no	—
75	Dic₁₁	—	2	4	no	—
76	Dic₁₁	—	4	4	no	—
77	#125	—	22	8	no	—
78	C₂×C₄⋊C₄	—	11	2	no	—
79	C₂×C₄⋊C₄	—	11	4	no	—
80	C₂×C₄⋊C₄	—	11	4	no	—
81	C₂×C₄⋊C₄	—	11	4	no	—
82	C₂×C₄⋊C₄	C₂×D₁₁	1	2	yes	—
83	C₂×C₄⋊C₄	C₂×D₁₁	1	4	yes	—
84	C₂×C₄²	—	11	1	no	—
85	C₂×C₄²	—	11	1	no	—
86	C₂×C₄²	—	11	2	no	—
87	C₂×C₄²	—	11	2	no	—
88	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
89	#95	—	11	8	no	—
90	C₂×C₁₁	C₂×#125	1	2	yes	—
91	C₂×C₁₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
92	C₂×C₁₁	#532	1	1	yes	characteristic
93	C₂×C₁₁	#532	1	1	yes	characteristic
94	C₂×C₁₁	#533	1	2	yes	—
95	C₂²×C₄	—	11	2	no	—
96	C₂²×C₄	—	11	1	no	—
97	C₂²×C₄	—	11	1	no	—
98	C₂²×C₄	—	11	4	no	—
99	C₂²×C₄	C₂²×D₁₁	1	4	yes	—
100	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
101	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
102	C₄⋊C₄	—	2	4	no	—
103	C₄⋊C₄	—	2	8	no	—
104	C₄⋊C₄	—	22	8	no	—
105	C₄⋊C₄	—	22	8	no	—
106	C₄⋊C₄	—	22	4	no	—
107	C₄⋊C₄	—	22	8	no	—
108	C₄²	—	11	4	no	—
109	C₄²	—	11	4	no	—
110	C₄²	—	22	4	no	—
111	C₄²	—	22	4	no	—
112	C₄²	Dic₂₂	1	4	yes	—
113	C₁₁	#2859	1	1	yes	characteristic, complemented, Sylow
114	C₂³	C₂³×D₁₁	1	1	yes	characteristic
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	2	8	no	—
117	C₂×C₄	—	11	2	no	—
118	C₂×C₄	—	11	2	no	—
119	C₂×C₄	—	11	4	no	—
120	C₂×C₄	—	22	2	no	—
121	C₂×C₄	—	22	2	no	—
122	C₂×C₄	—	22	2	no	—
123	C₂×C₄	—	22	2	no	—
124	C₂×C₄	—	22	4	no	—
125	C₂×C₄	—	22	8	no	—
126	C₂×C₄	C₂×Dic₂₂	1	2	yes	—
127	C₂×C₄	C₂×Dic₂₂	1	4	yes	—
128	C₂×C₄	D₄×D₁₁	1	2	yes	—
129	C₂×C₄	#4341	1	4	yes	—
130	C₂×C₄	Q₈×D₁₁	1	2	yes	—
131	C₂×C₄	#4343	1	4	yes	—
132	C₂²	C₂²×Dic₂₂	1	1	yes	characteristic
133	C₂²	C₂×D₄×D₁₁	1	1	yes	characteristic
134	C₂²	C₂×#4341	1	2	yes	—
135	C₂²	C₂×Q₈×D₁₁	1	1	yes	characteristic
136	C₂²	C₂×#4343	1	2	yes	—
137	C₄	—	4	4	no	—
138	C₄	—	22	2	no	—
139	C₄	—	22	2	no	—
140	C₄	—	22	4	no	—
141	C₄	—	44	4	no	—
142	C₄	#66941	1	4	yes	—
143	C₄	#66943	1	8	yes	complemented
144	C₂	C₂×#66941	1	1	yes	characteristic
145	C₂	C₂×#66943	1	2	yes	—
146	C₂	#10623247	1	1	yes	characteristic
147	C₂	#10623256	1	1	yes	characteristic
148	C₂	#10623259	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#66943

C₂

yes

maximal

C₁₁×#384

C₂

yes

maximal, characteristic

#10622598

C₂

yes

maximal

#10622590

C₂

yes

maximal

#10622586

C₂

yes

maximal

#10622548

C₂

yes

maximal, characteristic

C₄²×Dic₁₁

C₂

yes

maximal, characteristic

C₂×C₁₁×C₄⋊C₄

C₂²

yes

—

C₂×C₁₁×C₄⋊C₄

C₂²

yes

—

C₂×C₄²×C₁₁

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₁

C₂²

yes

—

C₂×C₄⋊Dic₁₁

C₂²

yes

—

C₂×C₄⋊Dic₁₁

C₂²

yes

—

C₂×Dic₁₁⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₁

C₂²

yes

—

C₂×C₄×Dic₁₁

C₂²

yes

—

C₂×C₄×Dic₁₁

C₂²

yes

characteristic

C₂×C₄×Dic₁₁

C₂²

yes

characteristic

#66943

—

C₁₁⋊#95

C₂²

yes

—

C₂²×C₄×C₁₁

C₂³

yes

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂²×C₄×C₁₁

C₂³

yes

—

C₂²×Dic₁₁

C₂³

yes

—

C₂²×Dic₁₁

C₂³

yes

characteristic

C₂²×Dic₁₁

C₂³

yes

characteristic

C₂²×Dic₁₁

C₂³

yes

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₄²×C₁₁

Q₈

yes

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

Dic₁₁⋊C₄

—

C₄×Dic₁₁

—

C₄×Dic₁₁

—

C₄×Dic₁₁

D₄

yes

—

C₄×Dic₁₁

Q₈

yes

—

#2859

—

maximal, Sylow

C₂³×C₁₁

C₂⁴

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×D₄

yes

—

C₂×C₄×C₁₁

C₂×Q₈

yes

—

C₂×C₄×C₁₁

C₂×Q₈

yes

—

C₂×C₄×C₁₁

C₂×Q₈

yes

—

C₂×C₄×C₁₁

#41

yes

—

C₂×C₄×C₁₁

#41

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

C₂×D₄

yes

—

C₂×Dic₁₁

C₂×D₄

yes

—

C₂×Dic₁₁

C₂×Q₈

yes

—

—

—

—

—

D₁₁

yes

characteristic

#382

—

C₄³

—

C₂²×C₁₁

C₂²×D₄

yes

characteristic

C₂²×C₁₁

C₂²×Q₈

yes

characteristic

C₂²×C₁₁

C₂²×Q₈

yes

characteristic

C₂²×C₁₁

C₂×#41

yes

—

C₂²×C₁₁

C₂×#41

yes

—

C₄×C₁₁

—

C₄×C₁₁

#125

yes

complemented

C₄×C₁₁

C₄⋊Q₈

yes

—

Dic₁₁

—

Dic₁₁

—

Dic₁₁

—

Dic₁₁

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₁

yes

—

C₂×C₄⋊C₄

C₂×D₁₁

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₁

yes

characteristic

#95

—

C₂×C₁₁

C₂×#125

yes

—

C₂×C₁₁

C₂×C₄⋊Q₈

yes

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂×C₁₁

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₁

yes

—

100

C₂²×C₄

C₂²×D₁₁

yes

characteristic

101

C₂²×C₄

C₂²×D₁₁

yes

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₄²

—

112

C₄²

Dic₂₂

yes

—

113

C₁₁

#2859

yes

characteristic, complemented, Sylow

114

C₂³

C₂³×D₁₁

yes

characteristic

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

C₂×Dic₂₂

yes

—

127

C₂×C₄

C₂×Dic₂₂

yes

—

128

C₂×C₄

D₄×D₁₁

yes

—

129

C₂×C₄

#4341

yes

—

130

C₂×C₄

Q₈×D₁₁

yes

—

131

C₂×C₄

#4343

yes

—

132

C₂²

C₂²×Dic₂₂

yes

characteristic

133

C₂²

C₂×D₄×D₁₁

yes

characteristic

134

C₂²

C₂×#4341

yes

—

135

C₂²

C₂×Q₈×D₁₁

yes

characteristic

136

C₂²

C₂×#4343

yes

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

#66941

yes

—

143

C₄

#66943

yes

complemented

144

C₂

C₂×#66941

yes

characteristic

145

C₂

C₂×#66943

yes

—

146

C₂

#10623247

yes

characteristic

147

C₂

#10623256

yes

characteristic

148

C₂

#10623259

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₁
commutator, socle, prime radical, cosocle	C₂³×C₁₁	C₂⁴
Fitting	C₁₁×#384	C₂
hypercenter	#384	D₁₁
hypocenter	C₁₁	#2859
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₁

commutator, socle, prime radical, cosocle

C₂³×C₁₁

C₂⁴

Fitting

C₁₁×#384

C₂

D₁₁

C₁₁

G ▷ C₂³×C₁₁ ▷ C₁₁

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
71. C₄×C₁₁	#125	semidirect
113. C₁₁	#2859	semidirect
143. C₄	#66943	semidirect

H ≅ G/N

type

71. C₄×C₁₁

#125

semidirect

113. C₁₁

#2859

semidirect

143. C₄

#66943

semidirect

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

subgroup	index
C₂×#66943	2
C₁₁×#384	2
#10622598	2
#10622590	2
#10622586	2
#10622548	2
C₄²×Dic₁₁	2
#2859	11

subgroup

index

C₁₁×#384

C₄²×Dic₁₁

Subgroups — #13076977

Conjugacy classes of subgroups

Complements

Maximal subgroups