Group #13069367 — subgroups

Subgroups — #13069367

Order 1408.

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

normal subgroups only

This group has 200 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×#108	C₂	1	1	yes	maximal, characteristic
2	#10622732	C₂	1	2	yes	maximal
3	#10622719	C₂	1	1	yes	maximal, characteristic
4	C₂×#66879	C₂	1	1	yes	maximal, characteristic
5	#10622193	C₂	1	2	yes	maximal
6	C₂×C₁₁×M₁₆	C₂²	1	2	yes	—
7	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	#66979	C₂²	1	2	yes	—
9	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic
10	C₂²×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
11	C₁₁×#108	—	2	2	no	—
12	#66882	C₄	1	2	yes	complemented
13	#66881	C₄	1	2	yes	complemented
14	#66879	—	2	2	no	—
15	Dic₁₁⋊C₈	—	2	4	no	—
16	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
17	C₂²×Dic₁₁	—	2	1	no	—
18	C₁₁×M₁₆	—	2	2	no	—
19	C₁₁×M₁₆	—	2	2	no	—
20	C₂×C₈×C₁₁	—	2	2	no	—
21	C₂×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₁₁	D₄	1	2	yes	—
24	C₂×C₈×C₁₁	Q₈	1	2	yes	—
25	C₂²⋊Dic₁₁	—	2	2	no	—
26	C₄⋊Dic₁₁	C₂×C₄	1	4	yes	—
27	C₄×Dic₁₁	—	2	2	no	—
28	C₄×Dic₁₁	—	2	1	no	—
29	C₄×Dic₁₁	Q₈	1	2	yes	—
30	C₂×C₁₁⋊C₈	—	2	1	no	—
31	C₂×C₁₁⋊C₈	—	2	1	no	—
32	C₂×C₁₁⋊C₈	D₄	1	2	yes	—
33	#1946	—	11	1	no	maximal, Sylow
34	C₂³×C₁₁	#41	1	1	yes	characteristic
35	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₁₁	#41	1	1	yes	characteristic
41	C₂×Dic₁₁	—	2	4	no	—
42	C₂×Dic₁₁	—	2	2	no	—
43	C₂×Dic₁₁	—	4	2	no	—
44	C₈×C₁₁	—	4	2	no	—
45	C₈×C₁₁	C₄⋊C₄	1	2	yes	—
46	C₈×C₁₁	C₄⋊C₄	1	2	yes	—
47	C₁₁⋊C₈	—	2	2	no	—
48	C₂×#108	D₁₁	1	1	yes	characteristic
49	#427	—	11	1	no	—
50	#424	—	11	2	no	—
51	C₂×#97	—	11	1	no	—
52	#339	—	11	2	no	—
53	C₂²×C₁₁	—	2	2	no	—
54	C₂²×C₁₁	C₄×D₄	1	1	yes	characteristic
55	C₂²×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
56	C₂²×C₁₁	#125	1	1	yes	characteristic
57	C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
59	C₄×C₁₁	#121	1	1	yes	characteristic
60	C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
61	Dic₁₁	—	4	2	no	—
62	Dic₁₁	—	4	4	no	—
63	C₂×M₁₆	C₂×D₁₁	1	2	yes	—
64	C₂²×C₈	—	11	1	no	—
65	C₂²×C₈	C₂×D₁₁	1	1	yes	characteristic
66	#117	—	11	2	no	—
67	C₂×C₄²	—	11	1	no	—
68	#108	—	2	2	no	—
69	#107	—	11	2	no	—
70	#106	—	11	2	no	—
71	C₄⋊C₈	—	22	4	no	—
72	#97	—	22	2	no	—
73	C₂×C₁₁	—	2	1	no	—
74	C₂×C₁₁	—	2	1	no	—
75	C₂×C₁₁	#389	1	1	yes	characteristic
76	C₂×C₁₁	#444	1	2	yes	—
77	C₂²×C₄	—	22	1	no	—
78	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
79	M₁₆	—	2	2	no	—
80	M₁₆	—	2	2	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	11	2	no	—
83	C₂×C₈	—	22	1	no	—
84	C₂×C₈	—	22	1	no	—
85	C₂×C₈	Dic₂₂	1	2	yes	—
86	C₂×C₈	C₄×D₁₁	1	1	yes	characteristic
87	C₂×C₈	C₄×D₁₁	1	1	yes	characteristic
88	C₂×C₈	C₂²⋊D₁₁	1	2	yes	—
89	C₄⋊C₄	—	11	4	no	—
90	C₂²⋊C₄	—	22	2	no	—
91	C₄²	—	11	2	no	—
92	C₄²	—	22	2	no	—
93	C₄²	—	22	1	no	—
94	C₁₁	#1946	1	1	yes	characteristic, complemented, Sylow
95	C₂³	#4343	1	1	yes	characteristic
96	C₂×C₄	—	22	4	no	—
97	C₂×C₄	—	22	2	no	—
98	C₂×C₄	—	44	2	no	—
99	C₂×C₄	C₂×Dic₂₂	1	1	yes	characteristic
100	C₂×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
101	C₂×C₄	D₄×D₁₁	1	1	yes	characteristic
102	C₂×C₄	#4341	1	1	yes	characteristic
103	C₂×C₄	Q₈×D₁₁	1	1	yes	characteristic
104	C₂×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
105	C₈	—	4	2	no	—
106	C₈	—	22	2	no	—
107	C₈	Dic₁₁⋊C₄	1	2	yes	—
108	C₈	Dic₁₁⋊C₄	1	2	yes	—
109	C₂²	—	2	2	no	—
110	C₂²	#66943	1	1	yes	characteristic
111	C₂²	#66946	1	1	yes	characteristic
112	C₂²	#66999	1	1	yes	characteristic
113	C₄	—	44	2	no	—
114	C₄	—	44	4	no	—
115	C₄	#66940	1	1	yes	characteristic
116	C₄	#66941	1	1	yes	characteristic
117	C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
118	C₄	#66991	1	1	yes	characteristic
119	C₂	—	2	1	no	—
120	C₂	—	2	1	no	—
121	C₂	#10622507	1	2	yes	—
122	C₂	#10622586	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₁×#108

C₂

yes

maximal, characteristic

#10622732

C₂

yes

maximal

#10622719

C₂

yes

maximal, characteristic

C₂×#66879

C₂

yes

maximal, characteristic

#10622193

C₂

yes

maximal

C₂×C₁₁×M₁₆

C₂²

yes

—

C₂²×C₈×C₁₁

C₂²

yes

characteristic

#66979

C₂²

yes

—

C₂×C₄×Dic₁₁

C₂²

yes

characteristic

C₂²×C₁₁⋊C₈

C₂²

yes

characteristic

C₁₁×#108

—

#66882

C₄

yes

complemented

#66881

C₄

yes

complemented

#66879

—

Dic₁₁⋊C₈

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂²×Dic₁₁

—

C₁₁×M₁₆

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂×C₄

yes

characteristic

C₂×C₈×C₁₁

C₂×C₄

yes

characteristic

C₂×C₈×C₁₁

D₄

yes

—

C₂×C₈×C₁₁

Q₈

yes

—

C₂²⋊Dic₁₁

—

C₄⋊Dic₁₁

C₂×C₄

yes

—

C₄×Dic₁₁

—

C₄×Dic₁₁

—

C₄×Dic₁₁

Q₈

yes

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

D₄

yes

—

—

C₂³×C₁₁

yes

C₂×C₄×C₁₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₁

#41

yes

characteristic

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₈×C₁₁

—

C₈×C₁₁

C₄⋊C₄

yes

—

C₈×C₁₁

C₄⋊C₄

yes

—

C₁₁⋊C₈

—

C₂×#108

D₁₁

yes

characteristic

#427

—

#424

—

C₂×#97

—

#339

—

C₂²×C₁₁

—

C₂²×C₁₁

C₄×D₄

yes

characteristic

C₂²×C₁₁

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₁

#125

yes

characteristic

C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₁

C₄×Q₈

yes

characteristic

C₄×C₁₁

#121

yes

characteristic

C₄×C₁₁

C₄⋊Q₈

yes

characteristic

Dic₁₁

—

Dic₁₁

—

C₂×M₁₆

C₂×D₁₁

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₁

yes

characteristic

#117

—

C₂×C₄²

—

#108

—

#107

—

#106

—

C₄⋊C₈

—

#97

—

C₂×C₁₁

—

C₂×C₁₁

—

C₂×C₁₁

#389

yes

characteristic

C₂×C₁₁

#444

yes

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₁

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₂₂

yes

—

C₂×C₈

C₄×D₁₁

yes

characteristic

C₂×C₈

C₄×D₁₁

yes

characteristic

C₂×C₈

C₂²⋊D₁₁

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₁₁

#1946

yes

characteristic, complemented, Sylow

C₂³

#4343

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₂₂

yes

characteristic

100

C₂×C₄

C₂×C₄×D₁₁

yes

characteristic

101

C₂×C₄

D₄×D₁₁

yes

characteristic

102

C₂×C₄

#4341

yes

characteristic

103

C₂×C₄

Q₈×D₁₁

yes

characteristic

104

C₂×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

Dic₁₁⋊C₄

yes

—

108

C₈

Dic₁₁⋊C₄

yes

—

109

C₂²

—

110

C₂²

#66943

yes

characteristic

111

C₂²

#66946

yes

characteristic

112

C₂²

#66999

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

#66940

yes

characteristic

116

C₄

#66941

yes

characteristic

117

C₄

C₂×Dic₁₁⋊C₄

yes

characteristic

118

C₄

#66991

yes

characteristic

119

C₂

—

120

C₂

—

121

C₂

#10622507

yes

—

122

C₂

#10622586

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₁
Fitting	C₂×C₁₁×#108	C₂
socle	C₂²×C₁₁	C₄×D₄
prime radical	C₂³×C₁₁	#41
cosocle	C₂²×C₄×C₁₁	C₂³
hypercenter	C₂×#108	D₁₁
hypocenter	C₁₁	#1946
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₁₁

commutator

C₂×C₄×C₁₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₁

Fitting

C₂×C₁₁×#108

C₂

socle

C₂²×C₁₁

C₄×D₄

prime radical

C₂³×C₁₁

#41

cosocle

C₂²×C₄×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
12. #66882	C₄	semidirect
13. #66881	C₄	semidirect
94. C₁₁	#1946	semidirect

H ≅ G/N

type

12. #66882

C₄

semidirect

13. #66881

C₄

semidirect

94. C₁₁

#1946

semidirect

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

subgroup	index
C₂×C₁₁×#108	2
#10622732	2
#10622719	2
C₂×#66879	2
#10622193	2
#1946	11

subgroup

index

C₂×C₁₁×#108

Subgroups — #13069367

Conjugacy classes of subgroups

Complements

Maximal subgroups