Group #14669189 — subgroups

Subgroups — #14669189

Order 2816.

306 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 163 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×#10622144	C₂	1	2	yes	maximal
2	C₄×#66883	C₂	1	2	yes	maximal
3	#13066710	C₂	1	2	yes	maximal
4	C₂×C₁₁×#346	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
6	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×#66883	C₂²	1	4	yes	—
9	C₄×#4318	—	2	2	no	—
10	C₁₁×#346	C₄	1	4	yes	—
11	#10622190	—	2	2	no	—
12	#10622144	C₄	1	8	yes	complemented
13	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
14	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
15	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
16	C₂×#4318	—	2	4	no	—
17	C₂×C₁₁×C₁₆	—	2	2	no	—
18	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
19	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
20	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
21	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
22	C₄×C₈×C₁₁	Q₈	1	2	yes	—
23	#66883	—	2	4	no	—
24	#66883	C₂×C₄	1	8	yes	—
25	#66867	—	4	2	no	—
26	C₄×C₁₁⋊C₈	—	4	2	no	—
27	#12676	—	11	1	no	maximal, Sylow
28	C₂²×C₄×C₁₁	Q₁₆	1	2	yes	—
29	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
30	C₂×C₈×C₁₁	—	2	2	no	—
31	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
32	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
34	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₈×C₁₁	#41	1	2	yes	—
36	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
37	C₄²×C₁₁	D₈	1	2	yes	—
38	#4318	—	2	8	no	—
39	#4318	—	4	4	no	—
40	C₂×C₁₁⋊C₈	—	4	4	no	—
41	C₁₁×C₁₆	—	2	2	no	—
42	C₁₁×C₁₆	C₄²	1	4	yes	—
43	C₂×#368	—	11	2	no	—
44	C₂×#346	D₁₁	1	1	yes	characteristic
45	C₄×#108	—	11	2	no	—
46	#1381	—	11	2	no	—
47	C₂³×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
48	C₂×C₄×C₁₁	—	4	2	no	—
49	C₂×C₄×C₁₁	#107	1	4	yes	—
50	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
52	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
53	C₂×C₄×C₁₁	#135	1	2	yes	—
54	C₈×C₁₁	—	2	2	no	—
55	C₈×C₁₁	C₂×C₄²	1	1	yes	characteristic
56	C₈×C₁₁	#117	1	1	yes	characteristic
57	C₈×C₁₁	C₄×Q₈	1	2	yes	—
58	C₁₁⋊C₈	—	4	8	no	—
59	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
60	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
61	C₂×#108	—	11	4	no	—
62	C₄×M₁₆	—	22	2	no	—
63	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
64	#368	—	11	8	no	—
65	#346	Dic₁₁	1	4	yes	—
66	#341	—	22	2	no	—
67	C₂²×C₁₁	—	2	2	no	—
68	C₂²×C₁₁	C₂×#107	1	1	yes	characteristic
69	C₂²×C₁₁	C₄×Q₁₆	1	2	yes	—
70	C₄×C₁₁	—	2	4	no	—
71	C₄×C₁₁	C₄×C₄⋊C₄	1	1	yes	characteristic
72	C₄×C₁₁	#427	1	1	yes	characteristic
73	C₄×C₁₁	C₄×D₈	1	2	yes	—
74	C₂×M₁₆	—	22	4	no	—
75	C₂²×C₈	D₄₄	1	1	yes	characteristic
76	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
77	C₂×C₄²	D₄₄	1	1	yes	characteristic
78	C₂×C₁₆	—	2	2	no	—
79	C₂×C₁₆	C₄×D₁₁	1	4	yes	—
80	C₂×C₁₆	C₂×Dic₁₁	1	2	yes	—
81	C₂×C₁₆	C₂×Dic₁₁	1	2	yes	—
82	#108	—	11	8	no	—
83	#108	—	22	4	no	—
84	#97	—	44	2	no	—
85	C₄×C₈	—	44	2	no	—
86	C₄×C₈	Dic₂₂	1	2	yes	—
87	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
88	C₂×C₁₁	—	2	2	no	—
89	C₂×C₁₁	C₄×#107	1	1	yes	characteristic
90	C₂×C₁₁	#2161	1	2	yes	—
91	C₂²×C₄	Dic₄₄	1	2	yes	—
92	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
93	M₁₆	—	22	8	no	—
94	M₁₆	—	44	4	no	—
95	C₂×C₈	—	2	2	no	—
96	C₂×C₈	—	44	4	no	—
97	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
98	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
99	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
100	C₂×C₈	#4339	1	2	yes	—
101	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
102	C₄²	D₈₈	1	2	yes	—
103	C₄²	C₄⋊Dic₁₁	1	2	yes	—
104	C₁₆	—	2	2	no	—
105	C₁₆	C₄×Dic₁₁	1	4	yes	—
106	C₁₁	#12676	1	1	yes	characteristic, complemented, Sylow
107	C₂³	C₂×Dic₄₄	1	1	yes	characteristic
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	#66882	1	4	yes	—
110	C₂×C₄	C₄×D₄₄	1	2	yes	—
111	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
112	C₂×C₄	#66957	1	2	yes	—
113	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	44	8	no	—
116	C₈	C₄×Dic₂₂	1	2	yes	—
117	C₈	C₂×C₄×Dic₁₁	1	1	yes	characteristic
118	C₈	#66979	1	1	yes	characteristic
119	C₂²	—	2	2	no	—
120	C₂²	C₄×Dic₄₄	1	2	yes	—
121	C₂²	C₂×#66882	1	1	yes	characteristic
122	C₄	—	2	4	no	—
123	C₄	C₄×D₈₈	1	2	yes	—
124	C₄	C₄×C₄⋊Dic₁₁	1	1	yes	characteristic
125	C₄	#10622719	1	1	yes	characteristic
126	C₂	—	2	2	no	—
127	C₂	C₄×#66882	1	1	yes	characteristic
128	C₂	#13070411	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622144

C₂

yes

maximal

C₄×#66883

C₂

yes

maximal

#13066710

C₂

yes

maximal

C₂×C₁₁×#346

C₂

yes

maximal, characteristic

C₂²×C₁₁×C₁₆

C₂²

yes

characteristic

C₂²×C₁₁×C₁₆

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66883

C₂²

yes

—

C₄×#4318

—

C₁₁×#346

C₄

yes

—

#10622190

—

#10622144

C₄

yes

complemented

C₂²×C₈×C₁₁

D₄

yes

characteristic

C₂²×C₈×C₁₁

C₂³

yes

characteristic

C₂×C₄²×C₁₁

D₄

yes

characteristic

C₂×#4318

—

C₂×C₁₁×C₁₆

—

C₂×C₁₁×C₁₆

C₂×C₄

yes

—

C₂×C₁₁×C₁₆

C₂×C₄

yes

—

C₂×C₁₁×C₁₆

C₂×C₄

yes

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

Q₈

yes

—

#66883

—

#66883

C₂×C₄

yes

—

#66867

—

C₄×C₁₁⋊C₈

—

#12676

—

maximal, Sylow

C₂²×C₄×C₁₁

Q₁₆

yes

—

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

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

—

C₄²×C₁₁

C₄⋊C₄

yes

—

C₄²×C₁₁

D₈

yes

—

#4318

—

#4318

—

C₂×C₁₁⋊C₈

—

C₁₁×C₁₆

—

C₁₁×C₁₆

C₄²

yes

—

C₂×#368

—

C₂×#346

D₁₁

yes

characteristic

C₄×#108

—

#1381

—

C₂³×C₁₁

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#107

yes

—

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

—

C₈×C₁₁

—

C₈×C₁₁

C₂×C₄²

yes

characteristic

C₈×C₁₁

#117

yes

characteristic

C₈×C₁₁

C₄×Q₈

yes

—

C₁₁⋊C₈

—

C₂²×C₁₆

C₂×D₁₁

yes

characteristic

C₂²×C₁₆

C₂×D₁₁

yes

characteristic

C₂×#108

—

C₄×M₁₆

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

#368

—

#346

Dic₁₁

yes

—

#341

—

C₂²×C₁₁

—

C₂²×C₁₁

C₂×#107

yes

characteristic

C₂²×C₁₁

C₄×Q₁₆

yes

—

C₄×C₁₁

—

C₄×C₁₁

C₄×C₄⋊C₄

yes

characteristic

C₄×C₁₁

#427

yes

characteristic

C₄×C₁₁

C₄×D₈

yes

—

C₂×M₁₆

—

C₂²×C₈

D₄₄

yes

characteristic

C₂²×C₈

C₂²×D₁₁

yes

characteristic

C₂×C₄²

D₄₄

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

C₄×D₁₁

yes

—

C₂×C₁₆

C₂×Dic₁₁

yes

—

C₂×C₁₆

C₂×Dic₁₁

yes

—

#108

—

#108

—

#97

—

C₄×C₈

—

C₄×C₈

Dic₂₂

yes

—

C₄×C₈

C₂×Dic₁₁

yes

—

C₂×C₁₁

—

C₂×C₁₁

C₄×#107

yes

characteristic

C₂×C₁₁

#2161

yes

—

C₂²×C₄

Dic₄₄

yes

—

C₂²×C₄

C₂×D₄₄

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄⋊Dic₁₁

yes

—

C₂×C₈

C₂×Dic₂₂

yes

characteristic

C₂×C₈

C₂×C₄×D₁₁

yes

—

100

C₂×C₈

#4339

yes

—

101

C₂×C₈

C₂²×Dic₁₁

yes

characteristic

102

C₄²

D₈₈

yes

—

103

C₄²

C₄⋊Dic₁₁

yes

—

104

C₁₆

—

105

C₁₆

C₄×Dic₁₁

yes

—

106

C₁₁

#12676

yes

characteristic, complemented, Sylow

107

C₂³

C₂×Dic₄₄

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

#66882

yes

—

110

C₂×C₄

C₄×D₄₄

yes

—

111

C₂×C₄

C₂×D₈₈

yes

characteristic

112

C₂×C₄

#66957

yes

—

113

C₂×C₄

C₂×C₄⋊Dic₁₁

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

C₄×Dic₂₂

yes

—

117

C₈

C₂×C₄×Dic₁₁

yes

characteristic

118

C₈

#66979

yes

characteristic

119

C₂²

—

120

C₂²

C₄×Dic₄₄

yes

—

121

C₂²

C₂×#66882

yes

characteristic

122

C₄

—

123

C₄

C₄×D₈₈

yes

—

124

C₄

C₄×C₄⋊Dic₁₁

yes

characteristic

125

C₄

#10622719

yes

characteristic

126

C₂

—

127

C₂

C₄×#66882

yes

characteristic

128

C₂

#13070411

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₈₈
commutator	C₈×C₁₁	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₂×C₁₁×#346	C₂
socle	C₂²×C₁₁	C₂×#107
prime radical	C₂³×C₁₁	C₂×Q₁₆
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	C₂×#346	D₁₁
hypocenter	C₁₁	#12676
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

subgroup

G/H

center

C₂×C₄

C₂×D₈₈

commutator

C₈×C₁₁

C₂×C₄²

Frattini

C₂²×C₈

C₂²×D₁₁

Fitting

C₂×C₁₁×#346

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 ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

N	H ≅ G/N	type
12. #10622144	C₄	semidirect
106. C₁₁	#12676	semidirect

H ≅ G/N

type

12. #10622144

C₄

semidirect

106. C₁₁

#12676

semidirect

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

subgroup	index
C₂×#10622144	2
C₄×#66883	2
#13066710	2
C₂×C₁₁×#346	2
#12676	11

subgroup

index

C₂×C₁₁×#346

Subgroups — #14669189

Conjugacy classes of subgroups

Complements

Maximal subgroups