Group #13070031 — subgroups

Subgroups — #13070031

Order 1408.

258 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 79 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×#66885	C₂	1	2	yes	maximal
2	#10622552	C₂	1	1	yes	maximal, characteristic
3	#10622549	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#336	C₂	1	1	yes	maximal, characteristic, complemented
5	#10622189	C₂	1	2	yes	maximal, complemented
6	C₂²×D₄₄	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₁	C₂²	1	2	yes	—
8	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×(C₂×D₁₁)⋊C₄	—	2	2	no	—
10	C₂×C₄⋊Dic₁₁	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic
12	C₁₁⋊#95	—	2	2	no	—
13	#66885	—	2	4	no	—
14	C₂³×D₁₁	—	2	1	no	—
15	C₂²×C₄×C₁₁	D₄	1	2	yes	—
16	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
17	C₂²×Dic₁₁	—	2	2	no	—
18	C₂²×Dic₁₁	—	2	1	no	—
19	C₂×D₄₄	—	2	1	no	—
20	C₂×D₄₄	—	2	2	no	—
21	C₂×D₄₄	—	2	2	no	—
22	C₂×D₄₄	D₄	1	2	yes	—
23	C₂×C₈×C₁₁	—	2	2	no	—
24	C₂×C₈×C₁₁	—	2	2	no	—
25	C₂×C₈×C₁₁	—	2	2	no	—
26	C₄²×C₁₁	—	2	2	no	—
27	(C₂×D₁₁)⋊C₄	—	4	4	no	—
28	C₄⋊Dic₁₁	—	2	2	no	—
29	C₄⋊Dic₁₁	—	2	2	no	—
30	C₄⋊Dic₁₁	—	2	2	no	—
31	#2073	—	11	1	no	maximal, Sylow
32	C₂³×C₁₁	C₂×D₄	1	1	yes	characteristic
33	C₂²×D₁₁	—	2	2	no	—
34	C₂²×D₁₁	—	4	1	no	—
35	C₂²×D₁₁	—	4	1	no	—
36	C₂²×D₁₁	—	4	2	no	—
37	C₂²×D₁₁	—	4	2	no	—
38	C₂×C₄×C₁₁	—	2	2	no	—
39	C₂×C₄×C₁₁	—	2	2	no	—
40	C₂×C₄×C₁₁	—	2	2	no	—
41	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₁₁	#41	1	2	yes	—
43	C₂×C₄×C₁₁	#41	1	2	yes	—
44	C₂×C₄×C₁₁	#41	1	1	yes	characteristic
45	C₂×Dic₁₁	—	4	2	no	—
46	C₂×Dic₁₁	—	4	1	no	—
47	C₂×Dic₁₁	—	4	2	no	—
48	C₂×Dic₁₁	—	4	2	no	—
49	C₂×Dic₁₁	—	4	2	no	—
50	D₄₄	—	2	4	no	—
51	D₄₄	—	4	2	no	—
52	C₈×C₁₁	—	4	2	no	—
53	C₂×#102	—	11	2	no	—
54	#390	—	11	1	no	—
55	#382	—	11	1	no	—
56	#340	—	11	2	no	—
57	#336	D₁₁	1	1	yes	characteristic, complemented
58	C₂²×C₁₁	#121	1	1	yes	characteristic
59	C₂²×C₁₁	#123	1	1	yes	characteristic
60	C₂²×C₁₁	#124	1	1	yes	characteristic
61	C₂²×C₁₁	#135	1	2	yes	—
62	C₂²×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
63	C₂×D₁₁	—	4	2	no	—
64	C₂×D₁₁	—	4	4	no	—
65	C₂×D₁₁	—	8	2	no	—
66	C₂×D₁₁	—	8	1	no	—
67	C₂×D₁₁	—	8	1	no	—
68	C₄×C₁₁	—	4	2	no	—
69	C₄×C₁₁	#123	1	2	yes	—
70	C₄×C₁₁	#126	1	2	yes	—
71	Dic₁₁	—	8	2	no	—
72	Dic₁₁	—	8	1	no	—
73	C₂²×D₄	—	11	1	no	—
74	C₂²×C₈	C₂×D₁₁	1	2	yes	—
75	C₂×C₄⋊C₄	—	11	1	no	—
76	C₂×C₄⋊C₄	—	11	2	no	—
77	C₂×C₂²⋊C₄	—	22	2	no	—
78	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
79	#102	—	22	4	no	—
80	#95	—	22	2	no	—
81	C₂×C₁₁	#397	1	1	yes	characteristic
82	C₂×C₁₁	#463	1	2	yes	—
83	C₂×C₁₁	#482	1	2	yes	—
84	C₂×C₁₁	#488	1	1	yes	characteristic
85	C₂×C₁₁	#490	1	1	yes	characteristic
86	D₁₁	—	8	2	no	—
87	C₂⁴	—	22	1	no	—
88	C₂×D₄	—	11	2	no	—
89	C₂×D₄	—	22	2	no	—
90	C₂×D₄	—	22	2	no	—
91	C₂×D₄	—	22	1	no	—
92	C₂²×C₄	—	22	2	no	—
93	C₂²×C₄	—	22	1	no	—
94	C₂²×C₄	D₄₄	1	2	yes	—
95	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	—	2	2	no	—
99	C₄⋊C₄	—	22	2	no	—
100	C₄⋊C₄	—	22	2	no	—
101	C₄⋊C₄	—	22	2	no	—
102	C₂²⋊C₄	—	44	4	no	—
103	C₄²	—	2	2	no	—
104	C₁₁	#2073	1	1	yes	characteristic, complemented, Sylow
105	C₂³	—	22	2	no	—
106	C₂³	—	44	1	no	—
107	C₂³	—	44	1	no	—
108	C₂³	—	44	2	no	—
109	C₂³	—	44	2	no	—
110	C₂³	C₂×D₄₄	1	1	yes	characteristic
111	D₄	—	22	4	no	—
112	D₄	—	44	2	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	44	1	no	—
117	C₂×C₄	—	44	2	no	—
118	C₂×C₄	—	44	2	no	—
119	C₂×C₄	—	44	2	no	—
120	C₂×C₄	—	44	2	no	—
121	C₂×C₄	#4339	1	2	yes	—
122	C₂×C₄	D₄×D₁₁	1	1	yes	characteristic
123	C₂×C₄	#4341	1	2	yes	—
124	C₂×C₄	#4343	1	1	yes	characteristic
125	C₈	—	4	2	no	—
126	C₂²	—	44	2	no	—
127	C₂²	—	44	4	no	—
128	C₂²	—	88	1	no	—
129	C₂²	—	88	1	no	—
130	C₂²	—	88	2	no	—
131	C₂²	#66928	1	1	yes	characteristic
132	C₂²	#66939	1	1	yes	characteristic
133	C₂²	#66948	1	1	yes	characteristic
134	C₂²	#66957	1	2	yes	—
135	C₂²	#66961	1	2	yes	—
136	C₄	—	4	2	no	—
137	C₄	—	88	1	no	—
138	C₄	—	88	2	no	—
139	C₄	#66936	1	2	yes	—
140	C₄	#66951	1	2	yes	—
141	C₂	—	88	2	no	—
142	C₂	#10622287	1	1	yes	characteristic
143	C₂	#10622310	1	1	yes	characteristic
144	C₂	#10622326	1	1	yes	characteristic
145	C₂	#10622350	1	2	yes	—
146	C₂	#10622457	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#66885

C₂

yes

maximal

#10622552

C₂

yes

maximal, characteristic

#10622549

C₂

yes

maximal, characteristic, complemented

C₁₁×#336

C₂

yes

maximal, characteristic, complemented

#10622189

C₂

yes

maximal, complemented

C₂²×D₄₄

C₂²

yes

characteristic

C₂²×C₈×C₁₁

C₂²

yes

—

C₂×C₄²×C₁₁

C₂²

yes

characteristic

C₂×(C₂×D₁₁)⋊C₄

—

C₂×C₄⋊Dic₁₁

C₂²

yes

—

C₂×C₄⋊Dic₁₁

C₂²

yes

characteristic

C₁₁⋊#95

—

#66885

—

C₂³×D₁₁

—

C₂²×C₄×C₁₁

D₄

yes

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂²×Dic₁₁

—

C₂²×Dic₁₁

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×D₄₄

D₄

yes

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₄²×C₁₁

—

(C₂×D₁₁)⋊C₄

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

#2073

—

maximal, Sylow

C₂³×C₁₁

C₂×D₄

yes

characteristic

C₂²×D₁₁

—

C₂²×D₁₁

—

C₂²×D₁₁

—

C₂²×D₁₁

—

C₂²×D₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₁

#41

yes

—

C₂×C₄×C₁₁

#41

yes

—

C₂×C₄×C₁₁

#41

yes

characteristic

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

D₄₄

—

D₄₄

—

C₈×C₁₁

—

—

—

—

—

D₁₁

yes

characteristic, complemented

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₂²×C₁₁

yes

—

C₂²×C₁₁

AGL(1,ℤ/8)

yes

—

C₂×D₁₁

—

C₂×D₁₁

—

C₂×D₁₁

—

C₂×D₁₁

—

C₂×D₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#123

yes

—

C₄×C₁₁

#126

yes

—

Dic₁₁

—

Dic₁₁

—

C₂²×D₄

—

C₂²×C₈

C₂×D₁₁

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₁₁

yes

characteristic

#102

—

#95

—

C₂×C₁₁

#397

yes

characteristic

C₂×C₁₁

#463

yes

—

C₂×C₁₁

#482

yes

—

C₂×C₁₁

yes

C₂×C₁₁

yes

D₁₁

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₄₄

yes

—

C₂²×C₄

C₂²×D₁₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₂²⋊C₄

—

103

C₄²

—

104

C₁₁

#2073

yes

characteristic, complemented, Sylow

105

C₂³

—

106

C₂³

—

107

C₂³

—

108

C₂³

—

109

C₂³

—

110

C₂³

C₂×D₄₄

yes

characteristic

111

D₄

—

112

D₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

#4339

yes

—

122

C₂×C₄

D₄×D₁₁

yes

characteristic

123

C₂×C₄

#4341

yes

—

124

C₂×C₄

#4343

yes

characteristic

125

C₈

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

#66928

yes

characteristic

132

C₂²

#66939

yes

characteristic

133

C₂²

#66948

yes

characteristic

134

C₂²

#66957

yes

—

135

C₂²

#66961

yes

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

#66936

yes

—

140

C₄

#66951

yes

—

141

C₂

—

142

C₂

#10622287

yes

characteristic

143

C₂

#10622310

yes

characteristic

144

C₂

#10622326

yes

characteristic

145

C₂

#10622350

yes

—

146

C₂

#10622457

yes

—

	subgroup	G/H
center	C₂³	C₂×D₄₄
commutator, cosocle	C₂²×C₄×C₁₁	C₂³
Frattini	C₂²×C₄	C₂²×D₁₁
Fitting	C₁₁×#336	C₂
socle	C₂³×C₁₁	C₂×D₄
prime radical	C₂²×D₄₄	C₂²
hypercenter	#336	D₁₁
hypocenter	C₁₁	#2073
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

subgroup

G/H

center

C₂³

C₂×D₄₄

commutator, cosocle

C₂²×C₄×C₁₁

C₂³

Frattini

C₂²×C₄

C₂²×D₁₁

Fitting

C₁₁×#336

C₂

socle

C₂³×C₁₁

C₂×D₄

prime radical

C₂²×D₄₄

C₂²

D₁₁

C₁₁

G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

N	H ≅ G/N	type
3. #10622549	C₂	semidirect
4. C₁₁×#336	C₂	semidirect
5. #10622189	C₂	semidirect
57. #336	D₁₁	semidirect
104. C₁₁	#2073	semidirect

H ≅ G/N

type

3. #10622549

C₂

semidirect

4. C₁₁×#336

C₂

semidirect

5. #10622189

C₂

semidirect

57. #336

D₁₁

semidirect

104. C₁₁

#2073

semidirect

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

subgroup	index
C₂×#66885	2
#10622552	2
#10622549	2
C₁₁×#336	2
#10622189	2
#2073	11

subgroup

index

C₁₁×#336

Subgroups — #13070031

Conjugacy classes of subgroups

Complements

Maximal subgroups