Group #13070109 — subgroups

Subgroups — #13070109

Order 1408.

224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#66882	C₂	1	1	yes	maximal, characteristic
3	#10622541	C₂	1	2	yes	maximal
4	#10622189	C₂	1	2	yes	maximal
5	#10622189	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₁	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₁₁	C₂²	1	2	yes	—
11	C₂×Dic₁₁⋊C₄	—	2	2	no	—
12	C₁₁×C₄⋊C₈	—	2	2	no	—
13	C₁₁⋊#95	—	2	2	no	—
14	#66882	—	2	2	no	—
15	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
18	C₂²×Dic₁₁	—	2	2	no	—
19	C₂²×Dic₁₁	—	2	2	no	—
20	C₂×C₈×C₁₁	—	2	1	no	—
21	C₂×C₈×C₁₁	—	2	2	no	—
22	C₂×C₈×C₁₁	—	2	2	no	—
23	C₂×C₈×C₁₁	D₄	1	2	yes	—
24	C₄²×C₁₁	—	2	1	no	—
25	C₄²×C₁₁	—	2	1	no	—
26	C₄⋊Dic₁₁	—	2	2	no	—
27	C₄⋊Dic₁₁	—	2	2	no	—
28	C₄⋊Dic₁₁	—	2	2	no	—
29	C₄⋊Dic₁₁	Q₈	1	4	yes	—
30	Dic₁₁⋊C₄	—	4	4	no	—
31	#2087	—	11	1	no	maximal, Sylow
32	C₂³×C₁₁	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₁₁	—	2	1	no	—
34	C₂×C₄×C₁₁	—	2	1	no	—
35	C₂×C₄×C₁₁	—	2	1	no	—
36	C₂×C₄×C₁₁	—	2	2	no	—
37	C₂×C₄×C₁₁	Q₁₆	1	2	yes	—
38	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₁	C₂×Q₈	1	2	yes	—
40	C₂×C₄×C₁₁	#41	1	1	yes	characteristic
41	C₂×C₄×C₁₁	#41	1	2	yes	—
42	C₂×Dic₁₁	—	2	4	no	—
43	C₂×Dic₁₁	—	4	2	no	—
44	C₂×Dic₁₁	—	4	2	no	—
45	C₂×Dic₁₁	—	4	2	no	—
46	C₂×Dic₁₁	—	4	2	no	—
47	C₂×Dic₁₁	—	4	2	no	—
48	C₈×C₁₁	—	2	2	no	—
49	C₈×C₁₁	—	4	1	no	—
50	C₂×#107	—	11	1	no	—
51	C₂×C₄⋊C₈	D₁₁	1	1	yes	characteristic
52	#389	—	11	2	no	—
53	#340	—	11	1	no	—
54	#340	—	11	2	no	—
55	C₂²×C₁₁	#121	1	1	yes	characteristic
56	C₂²×C₁₁	C₂²⋊Q₈	1	2	yes	—
57	C₂²×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
58	C₂²×C₁₁	#135	1	1	yes	characteristic
59	C₂²×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
60	C₄×C₁₁	—	2	2	no	—
61	C₄×C₁₁	—	4	1	no	—
62	C₄×C₁₁	#123	1	1	yes	characteristic
63	C₄×C₁₁	#125	1	2	yes	—
64	C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
65	Dic₁₁	—	4	4	no	—
66	Dic₁₁	—	8	2	no	—
67	C₂²×C₈	C₂×D₁₁	1	1	yes	characteristic
68	C₂²×C₈	C₂×D₁₁	1	1	yes	characteristic
69	C₂×C₄⋊C₄	—	11	2	no	—
70	C₂×C₄⋊C₄	—	11	2	no	—
71	C₂×C₄⋊C₄	—	22	2	no	—
72	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
73	#107	—	22	2	no	—
74	C₄⋊C₈	—	2	2	no	—
75	#95	—	22	2	no	—
76	C₂×C₁₁	#398	1	1	yes	characteristic
77	C₂×C₁₁	#467	1	1	yes	characteristic
78	C₂×C₁₁	#469	1	1	yes	characteristic
79	C₂×C₁₁	#477	1	2	yes	—
80	C₂×C₁₁	#478	1	2	yes	—
81	C₂²×C₄	—	22	2	no	—
82	C₂²×C₄	—	22	2	no	—
83	C₂²×C₄	D₄₄	1	1	yes	characteristic
84	C₂²×C₄	D₄₄	1	1	yes	characteristic
85	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
86	C₂×C₈	—	2	2	no	—
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	2	1	no	—
89	C₂×C₈	C₂²⋊D₁₁	1	2	yes	—
90	C₄⋊C₄	—	11	4	no	—
91	C₄⋊C₄	—	22	2	no	—
92	C₄⋊C₄	—	22	2	no	—
93	C₄⋊C₄	—	22	2	no	—
94	C₄⋊C₄	—	44	4	no	—
95	C₄²	—	2	1	no	—
96	C₄²	—	2	1	no	—
97	C₁₁	#2087	1	1	yes	characteristic, complemented, Sylow
98	C₂³	C₂×D₄₄	1	1	yes	characteristic
99	C₂×C₄	—	2	1	no	—
100	C₂×C₄	—	2	1	no	—
101	C₂×C₄	—	2	2	no	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	22	4	no	—
104	C₂×C₄	—	44	2	no	—
105	C₂×C₄	—	44	2	no	—
106	C₂×C₄	—	44	2	no	—
107	C₂×C₄	—	44	2	no	—
108	C₂×C₄	—	44	2	no	—
109	C₂×C₄	Dic₄₄	1	2	yes	—
110	C₂×C₄	#4339	1	1	yes	characteristic
111	C₂×C₄	#4341	1	2	yes	—
112	C₂×C₄	Q₈×D₁₁	1	2	yes	—
113	C₂×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	4	1	no	—
116	C₂²	#66950	1	2	yes	—
117	C₂²	#66957	1	1	yes	characteristic
118	C₂²	C₂×Dic₄₄	1	1	yes	characteristic
119	C₂²	#66961	1	2	yes	—
120	C₂²	#66983	1	1	yes	characteristic
121	C₄	—	2	2	no	—
122	C₄	—	4	1	no	—
123	C₄	—	44	4	no	—
124	C₄	—	88	2	no	—
125	C₄	#66942	1	2	yes	—
126	C₄	#66988	1	1	yes	characteristic
127	C₄	#66997	1	1	yes	characteristic
128	C₂	#10622460	1	2	yes	—
129	C₂	#10622463	1	2	yes	—
130	C₂	#10622596	1	1	yes	characteristic
131	C₂	#10622729	1	1	yes	characteristic
132	C₂	#10622748	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₁×C₄⋊C₈

C₂

yes

maximal, characteristic

C₂×#66882

C₂

yes

maximal, characteristic

#10622541

C₂

yes

maximal

#10622189

C₂

yes

maximal

#10622189

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₁

C₂²

yes

characteristic

C₂²×C₈×C₁₁

C₂²

yes

characteristic

C₂×C₄²×C₁₁

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₁

C₂²

yes

—

C₂×C₄⋊Dic₁₁

C₂²

yes

—

C₂×Dic₁₁⋊C₄

—

C₁₁×C₄⋊C₈

—

C₁₁⋊#95

—

#66882

—

C₂²×C₄×C₁₁

D₄

yes

characteristic

C₂²×C₄×C₁₁

D₄

yes

characteristic

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂²×Dic₁₁

—

C₂²×Dic₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

D₄

yes

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

Q₈

yes

—

Dic₁₁⋊C₄

—

#2087

—

maximal, Sylow

C₂³×C₁₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

Q₁₆

yes

—

C₂×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₁

C₂×Q₈

yes

—

C₂×C₄×C₁₁

#41

yes

characteristic

C₂×C₄×C₁₁

#41

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₈×C₁₁

—

C₈×C₁₁

—

C₂×#107

—

C₂×C₄⋊C₈

D₁₁

yes

—

—

—

C₂²×C₁₁

#121

yes

characteristic

C₂²×C₁₁

C₂²⋊Q₈

yes

—

C₂²×C₁₁

C₂×Q₁₆

yes

C₂²×C₁₁

yes

C₂²×C₁₁

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#123

yes

characteristic

C₄×C₁₁

#125

yes

—

C₄×C₁₁

C₄⋊Q₈

yes

characteristic

Dic₁₁

—

Dic₁₁

—

C₂²×C₈

C₂×D₁₁

yes

characteristic

C₂²×C₈

C₂×D₁₁

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₁₁

yes

characteristic

#107

—

C₄⋊C₈

—

#95

—

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂×C₁₁

yes

—

C₂×C₁₁

#478

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₄₄

yes

characteristic

C₂²×C₄

D₄₄

yes

characteristic

C₂²×C₄

C₂²×D₁₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₁

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₁₁

#2087

yes

characteristic, complemented, Sylow

C₂³

C₂×D₄₄

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

Dic₄₄

yes

—

110

C₂×C₄

#4339

yes

characteristic

111

C₂×C₄

#4341

yes

—

112

C₂×C₄

Q₈×D₁₁

yes

—

113

C₂×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

114

C₈

—

115

C₈

—

116

C₂²

#66950

yes

—

117

C₂²

#66957

yes

characteristic

118

C₂²

C₂×Dic₄₄

yes

characteristic

119

C₂²

#66961

yes

—

120

C₂²

#66983

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

#66942

yes

—

126

C₄

#66988

yes

characteristic

127

C₄

#66997

yes

characteristic

128

C₂

#10622460

yes

—

129

C₂

#10622463

yes

—

130

C₂

#10622596

yes

characteristic

131

C₂

#10622729

yes

characteristic

132

C₂

#10622748

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₄₄
commutator, cosocle	C₂²×C₄×C₁₁	C₂³
Frattini	C₂²×C₄	C₂²×D₁₁
Fitting	C₂×C₁₁×C₄⋊C₈	C₂
socle, prime radical	C₂³×C₁₁	C₂×D₄
hypercenter	C₂×C₄⋊C₈	D₁₁
hypocenter	C₁₁	#2087
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

subgroup

G/H

center

C₂³

C₂×D₄₄

commutator, cosocle

C₂²×C₄×C₁₁

C₂³

Frattini

C₂²×C₄

C₂²×D₁₁

Fitting

C₂×C₁₁×C₄⋊C₈

C₂

socle, prime radical

C₂³×C₁₁

C₂×D₄

hypercenter

C₂×C₄⋊C₈

D₁₁

hypocenter

C₁₁

#2087

LCS

G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
97. C₁₁	#2087	semidirect

H ≅ G/N

type

97. C₁₁

#2087

semidirect

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

subgroup	index
C₂×C₁₁×C₄⋊C₈	2
C₂×#66882	2
#10622541	2
#10622189	2
#2087	11

subgroup

index

C₂×C₁₁×C₄⋊C₈

Subgroups — #13070109

Conjugacy classes of subgroups

Complements

Maximal subgroups