Group #13079355 — subgroups

Subgroups — #13079355

Order 1408.

446 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 125 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	#10623256	C₂	1	2	yes	maximal, complemented
2	C₁₁×#498	C₂	1	1	yes	maximal, characteristic, complemented
3	#10622701	C₂	1	2	yes	maximal, complemented
4	#10622482	C₂	1	4	yes	maximal, complemented
5	#10622478	C₂	1	4	yes	maximal, complemented
6	#10622308	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×#4313	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#4343	—	2	2	no	—
9	C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
10	#67000	—	2	2	no	—
11	C₂×D₈₈	C₂²	1	4	yes	—
12	C₂×#4313	C₂²	1	2	yes	—
13	#66948	—	2	2	no	—
14	#66948	C₂²	1	4	yes	—
15	#66946	—	2	2	no	—
16	#66946	C₂²	1	4	yes	—
17	#66927	C₂²	1	2	yes	—
18	C₄²×D₁₁	C₂²	1	1	yes	characteristic
19	C₁₁×#106	C₂²	1	4	yes	—
20	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
21	#66879	C₂²	1	2	yes	—
22	#66873	C₂²	1	8	yes	—
23	C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×Q₈×C₁₁	—	2	2	no	—
25	#4343	—	4	8	no	—
26	C₂×D₄₄	—	2	4	no	—
27	C₂×D₄₄	—	2	2	no	—
28	C₂×D₄₄	—	2	2	no	—
29	C₂×D₄₄	C₂³	1	4	yes	—
30	C₂×C₄×D₁₁	—	2	4	no	—
31	C₂×C₄×D₁₁	D₄	1	2	yes	—
32	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
33	C₂×C₈×C₁₁	C₂³	1	2	yes	—
34	C₁₁×C₄⋊C₄	—	2	2	no	—
35	C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
36	C₄²×C₁₁	C₂³	1	1	yes	characteristic
37	(C₂×D₁₁)⋊C₄	—	2	4	no	—
38	(C₂×D₁₁)⋊C₄	—	2	4	no	—
39	C₄×Dic₁₁	D₄	1	2	yes	—
40	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
41	C₂×C₁₁⋊C₈	C₂³	1	2	yes	—
42	D₈₈	—	2	8	no	—
43	#4313	—	2	4	no	—
44	#3184	—	11	1	no	maximal, Sylow
45	C₂²×D₁₁	—	2	4	no	—
46	C₂²×D₁₁	C₂×D₄	1	1	yes	characteristic
47	Q₈×C₁₁	—	4	4	no	—
48	C₂×C₄×C₁₁	—	2	4	no	—
49	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
50	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
51	C₂×Dic₁₁	C₂×D₄	1	1	yes	characteristic
52	C₂×Dic₁₁	C₂×D₄	1	2	yes	—
53	D₄₄	—	2	8	no	—
54	D₄₄	—	4	8	no	—
55	D₄₄	—	4	4	no	—
56	D₄₄	—	4	4	no	—
57	C₄×D₁₁	—	2	4	no	—
58	C₄×D₁₁	—	2	2	no	—
59	C₄×D₁₁	—	4	8	no	—
60	C₈×C₁₁	#41	1	4	yes	complemented
61	C₁₁⋊C₈	—	2	2	no	—
62	#532	—	11	2	no	—
63	#498	D₁₁	1	1	yes	characteristic, complemented
64	#493	—	11	1	no	—
65	#486	—	11	2	no	—
66	#469	—	11	4	no	—
67	#442	—	11	4	no	—
68	C₄×M₁₆	—	11	1	no	—
69	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
70	C₂×D₁₁	—	2	1	no	—
71	C₂×D₁₁	—	2	2	no	—
72	C₂×D₁₁	—	4	4	no	—
73	C₂×D₁₁	—	4	4	no	—
74	C₂×D₁₁	—	4	4	no	—
75	C₄×C₁₁	—	4	4	no	—
76	C₄×C₁₁	AGL(1,ℤ/8)	1	4	yes	—
77	C₄×C₁₁	C₂×#41	1	2	yes	—
78	Dic₁₁	—	2	1	no	—
79	Dic₁₁	—	2	2	no	—
80	C₂×#41	—	22	2	no	—
81	C₂×D₈	—	11	4	no	—
82	C₂×M₁₆	—	11	2	no	—
83	C₄⋊Q₈	C₂×D₁₁	1	2	yes	—
84	#127	—	11	2	no	—
85	#124	—	22	2	no	—
86	#121	—	11	4	no	—
87	#121	—	22	2	no	—
88	C₄×D₄	—	11	4	no	—
89	C₄×D₄	—	22	2	no	—
90	C₂×C₄²	—	11	1	no	—
91	#106	C₂×D₁₁	1	4	yes	—
92	#102	—	11	8	no	—
93	#97	—	11	2	no	—
94	C₄×C₈	—	11	1	no	—
95	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
96	C₂×C₁₁	#532	1	1	yes	characteristic
97	C₂×C₁₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
98	D₁₁	—	4	1	no	—
99	D₁₁	—	8	4	no	—
100	#41	—	44	8	no	—
101	C₂×Q₈	—	2	2	no	—
102	C₂×D₄	—	11	4	no	—
103	C₂×D₄	—	22	4	no	—
104	C₂×D₄	—	22	2	no	—
105	C₂×D₄	—	22	2	no	—
106	C₂²×C₄	—	11	2	no	—
107	C₂²×C₄	—	11	1	no	—
108	C₂²×C₄	—	22	4	no	—
109	D₈	—	22	8	no	—
110	M₁₆	—	22	4	no	—
111	C₂×C₈	—	11	2	no	—
112	C₂×C₈	C₂²×D₁₁	1	2	yes	—
113	C₄⋊C₄	—	2	2	no	—
114	C₄⋊C₄	C₂²×D₁₁	1	4	yes	—
115	C₂²⋊C₄	—	22	4	no	—
116	C₂²⋊C₄	—	22	4	no	—
117	C₄²	—	11	2	no	—
118	C₄²	—	11	1	no	—
119	C₄²	C₂²×D₁₁	1	1	yes	characteristic
120	C₁₁	#3184	1	1	yes	characteristic, complemented, Sylow
121	C₂³	—	11	1	no	—
122	C₂³	—	22	4	no	—
123	Q₈	—	4	4	no	—
124	D₄	—	22	8	no	—
125	D₄	—	44	8	no	—
126	D₄	—	44	4	no	—
127	D₄	—	44	4	no	—
128	C₂×C₄	—	2	4	no	—
129	C₂×C₄	—	11	1	no	—
130	C₂×C₄	—	11	2	no	—
131	C₂×C₄	—	22	4	no	—
132	C₂×C₄	—	22	2	no	—
133	C₂×C₄	—	44	8	no	—
134	C₂×C₄	D₄×D₁₁	1	2	yes	—
135	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
136	C₈	—	22	2	no	—
137	C₈	#4343	1	4	yes	complemented
138	C₂²	—	22	1	no	—
139	C₂²	—	22	2	no	—
140	C₂²	—	44	4	no	—
141	C₂²	—	44	4	no	—
142	C₂²	—	44	4	no	—
143	C₂²	C₂×D₄×D₁₁	1	1	yes	characteristic
144	C₄	—	4	4	no	—
145	C₄	—	22	1	no	—
146	C₄	—	22	2	no	—
147	C₄	#66967	1	4	yes	—
148	C₄	C₂×#4343	1	2	yes	—
149	C₂	—	44	1	no	—
150	C₂	—	88	4	no	—
151	C₂	#10623256	1	1	yes	characteristic
152	C₂	C₂×#66967	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#10623256

C₂

yes

maximal, complemented

C₁₁×#498

C₂

yes

maximal, characteristic, complemented

#10622701

C₂

yes

maximal, complemented

#10622482

C₂

yes

maximal, complemented

#10622478

C₂

yes

maximal, complemented

#10622308

C₂

yes

maximal, characteristic, complemented

C₄×#4313

C₂

yes

maximal, characteristic, complemented

C₂×#4343

—

C₁₁×C₄⋊Q₈

C₂²

yes

—

#67000

—

C₂×D₈₈

C₂²

yes

—

C₂×#4313

C₂²

yes

—

#66948

—

#66948

C₂²

yes

—

#66946

—

#66946

C₂²

yes

—

#66927

C₂²

yes

—

C₄²×D₁₁

C₂²

yes

characteristic

C₁₁×#106

C₂²

yes

—

C₄×C₈×C₁₁

C₂²

yes

characteristic

#66879

C₂²

yes

—

#66873

C₂²

yes

—

C₄×C₁₁⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₁

—

#4343

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×D₄₄

C₂³

yes

—

C₂×C₄×D₁₁

—

C₂×C₄×D₁₁

D₄

yes

—

C₂×C₄×D₁₁

C₂³

yes

characteristic

C₂×C₈×C₁₁

C₂³

yes

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

C₂³

yes

—

C₄²×C₁₁

C₂³

yes

characteristic

(C₂×D₁₁)⋊C₄

—

(C₂×D₁₁)⋊C₄

—

C₄×Dic₁₁

D₄

yes

—

C₄×Dic₁₁

C₂³

yes

characteristic

C₂×C₁₁⋊C₈

C₂³

yes

—

D₈₈

—

#4313

—

#3184

—

maximal, Sylow

C₂²×D₁₁

—

C₂²×D₁₁

C₂×D₄

yes

characteristic

Q₈×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×D₄

yes

—

C₂×C₄×C₁₁

C₂⁴

yes

characteristic

C₂×Dic₁₁

C₂×D₄

yes

characteristic

C₂×Dic₁₁

C₂×D₄

yes

—

D₄₄

—

D₄₄

—

D₄₄

—

D₄₄

—

C₄×D₁₁

—

C₄×D₁₁

—

C₄×D₁₁

—

C₈×C₁₁

#41

yes

complemented

C₁₁⋊C₈

—

#532

—

#498

D₁₁

yes

characteristic, complemented

—

—

—

—

C₄×M₁₆

—

C₂²×C₁₁

C₂²×D₄

yes

characteristic

C₂×D₁₁

—

C₂×D₁₁

—

C₂×D₁₁

—

C₂×D₁₁

—

C₂×D₁₁

—

C₄×C₁₁

—

C₄×C₁₁

AGL(1,ℤ/8)

yes

—

C₄×C₁₁

C₂×#41

yes

—

Dic₁₁

—

Dic₁₁

—

C₂×#41

—

C₂×D₈

—

C₂×M₁₆

—

C₄⋊Q₈

C₂×D₁₁

yes

—

—

—

—

—

C₄×D₄

—

C₄×D₄

—

C₂×C₄²

—

#106

C₂×D₁₁

yes

—

#102

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₁₁

yes

C₂×C₁₁

yes

C₂×C₁₁

yes

—

D₁₁

—

D₁₁

—

100

#41

—

101

C₂×Q₈

—

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

D₈

—

110

M₁₆

—

111

C₂×C₈

—

112

C₂×C₈

C₂²×D₁₁

yes

—

113

C₄⋊C₄

—

114

C₄⋊C₄

C₂²×D₁₁

yes

—

115

C₂²⋊C₄

—

116

C₂²⋊C₄

—

117

C₄²

—

118

C₄²

—

119

C₄²

C₂²×D₁₁

yes

characteristic

120

C₁₁

#3184

yes

characteristic, complemented, Sylow

121

C₂³

—

122

C₂³

—

123

Q₈

—

124

D₄

—

125

D₄

—

126

D₄

—

127

D₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

D₄×D₁₁

yes

—

135

C₂×C₄

C₂³×D₁₁

yes

characteristic

136

C₈

—

137

C₈

#4343

yes

complemented

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

C₂×D₄×D₁₁

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

#66967

yes

—

148

C₄

C₂×#4343

yes

—

149

C₂

—

150

C₂

—

151

C₂

#10623256

yes

characteristic

152

C₂

C₂×#66967

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₁
commutator, cosocle	C₂×C₄×C₁₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₁
Fitting	C₁₁×#498	C₂
socle	C₂²×C₁₁	C₂²×D₄
hypercenter	#498	D₁₁
hypocenter	C₁₁	#3184
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

subgroup

G/H

center

C₂²

C₂×D₄×D₁₁

commutator, cosocle

C₂×C₄×C₁₁

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₁

Fitting

C₁₁×#498

C₂

socle

C₂²×C₁₁

C₂²×D₄

D₁₁

C₁₁

G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #498

N	H ≅ G/N	type
1. #10623256	C₂	semidirect
2. C₁₁×#498	C₂	semidirect
3. #10622701	C₂	semidirect
4. #10622482	C₂	semidirect
5. #10622478	C₂	semidirect
6. #10622308	C₂	semidirect
7. C₄×#4313	C₂	semidirect
60. C₈×C₁₁	#41	semidirect
63. #498	D₁₁	semidirect
120. C₁₁	#3184	semidirect
137. C₈	#4343	semidirect

H ≅ G/N

type

1. #10623256

C₂

semidirect

2. C₁₁×#498

C₂

semidirect

3. #10622701

C₂

semidirect

4. #10622482

C₂

semidirect

5. #10622478

C₂

semidirect

6. #10622308

C₂

semidirect

7. C₄×#4313

C₂

semidirect

60. C₈×C₁₁

#41

semidirect

63. #498

D₁₁

semidirect

120. C₁₁

#3184

semidirect

137. C₈

#4343

semidirect

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

subgroup	index
#10623256	2
C₁₁×#498	2
#10622701	2
#10622482	2
#10622478	2
#10622308	2
C₄×#4313	2
#3184	11

subgroup

index

C₁₁×#498

Subgroups — #13079355

Conjugacy classes of subgroups

Complements

Maximal subgroups