Group #14674745 — subgroups

Subgroups — #14674745

Order 2816.

182 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 75 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	#13070891	C₂	1	1	yes	maximal, characteristic
2	#13066797	C₂	1	4	yes	maximal
3	C₄×C₁₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#2247	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×Q₃₂	—	2	1	no	—
6	C₂×C₁₁×Q₃₂	C₂²	1	2	yes	—
7	C₁₁×#494	—	2	1	no	—
8	#10622295	—	2	1	no	—
9	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
10	#10622142	—	2	1	no	—
11	#10622142	C₂²	1	2	yes	—
12	C₂×C₁₁⋊C₃₂	C₂²	1	2	yes	—
13	C₂×C₁₁×Q₁₆	—	2	2	no	—
14	C₂×C₁₁×Q₁₆	—	4	1	no	—
15	C₁₁×C₄⋊Q₈	—	4	1	no	—
16	#66922	—	4	1	no	—
17	C₁₁×Q₃₂	—	2	4	no	—
18	C₁₁×Q₃₂	—	4	2	no	—
19	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
20	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
21	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
22	#66882	—	2	2	no	—
23	#66882	—	4	1	no	—
24	C₁₁⋊C₃₂	—	2	2	no	—
25	#13720	—	11	1	no	maximal, Sylow
26	C₂×Q₈×C₁₁	—	4	2	no	—
27	C₂×Dic₂₂	—	8	1	no	—
28	C₁₁×Q₁₆	—	4	2	no	—
29	C₁₁×Q₁₆	—	4	2	no	—
30	C₁₁×Q₁₆	—	8	2	no	—
31	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
32	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
33	C₁₁×C₄⋊C₄	—	8	1	no	—
34	C₁₁×C₄⋊C₄	—	8	1	no	—
35	C₄²×C₁₁	D₈	1	1	yes	characteristic
36	C₄⋊Dic₁₁	—	4	2	no	—
37	C₄⋊Dic₁₁	—	8	1	no	—
38	C₁₁×C₁₆	SD₁₆	1	2	yes	—
39	C₁₁×C₁₆	#41	1	2	yes	—
40	#2252	—	11	1	no	—
41	#2247	D₁₁	1	1	yes	characteristic
42	#1416	—	11	4	no	—
43	C₄×C₃₂	—	11	1	no	—
44	Q₈×C₁₁	—	8	2	no	—
45	Q₈×C₁₁	—	8	2	no	—
46	C₂×C₄×C₁₁	—	8	2	no	—
47	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
48	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
49	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
50	C₂×Dic₁₁	—	8	2	no	—
51	Dic₂₂	—	16	2	no	—
52	C₈×C₁₁	SD₃₂	1	2	yes	—
53	C₈×C₁₁	#124	1	1	yes	characteristic
54	C₈×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
55	C₂×Q₃₂	—	2	1	no	—
56	C₂×Q₃₂	C₂×D₁₁	1	2	yes	—
57	#500	—	22	1	no	—
58	#494	—	2	1	no	—
59	C₂×C₃₂	—	11	2	no	—
60	#366	—	11	2	no	—
61	#366	—	22	1	no	—
62	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
63	C₂²×C₁₁	C₂×D₁₆	1	1	yes	characteristic
64	C₄×C₁₁	—	16	2	no	—
65	C₄×C₁₁	SD₆₄	1	2	yes	—
66	C₄×C₁₁	Q₆₄	1	2	yes	—
67	C₄×C₁₁	#486	1	1	yes	characteristic
68	C₄×C₁₁	C₂×SD₃₂	1	1	yes	characteristic
69	Dic₁₁	—	16	2	no	—
70	C₂×Q₁₆	—	2	2	no	—
71	C₂×Q₁₆	—	4	1	no	—
72	C₄⋊Q₈	—	4	1	no	—
73	C₄⋊Q₈	—	44	1	no	—
74	Q₃₂	—	2	4	no	—
75	Q₃₂	—	4	2	no	—
76	C₂×C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
77	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
78	#107	—	22	2	no	—
79	#107	—	44	1	no	—
80	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
81	C₃₂	—	22	2	no	—
82	C₂×C₁₁	#2240	1	1	yes	characteristic
83	C₂×C₁₁	C₂×SD₆₄	1	1	yes	characteristic
84	C₂×C₁₁	C₂×Q₆₄	1	1	yes	characteristic
85	C₂×Q₈	—	4	2	no	—
86	C₂×Q₈	—	88	1	no	—
87	Q₁₆	—	4	2	no	—
88	Q₁₆	—	4	2	no	—
89	Q₁₆	—	8	2	no	—
90	C₂×C₈	#4323	1	1	yes	characteristic
91	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
92	C₄⋊C₄	—	8	1	no	—
93	C₄⋊C₄	—	8	1	no	—
94	C₄⋊C₄	—	44	2	no	—
95	C₄⋊C₄	—	88	1	no	—
96	C₄²	#4323	1	1	yes	characteristic
97	C₁₆	#4324	1	2	yes	—
98	C₁₆	#4341	1	2	yes	—
99	C₁₁	#13720	1	1	yes	characteristic, complemented, Sylow
100	Q₈	—	8	2	no	—
101	Q₈	—	8	2	no	—
102	Q₈	—	176	2	no	—
103	C₂×C₄	—	8	2	no	—
104	C₂×C₄	—	88	2	no	—
105	C₂×C₄	#66890	1	1	yes	characteristic
106	C₂×C₄	#66890	1	1	yes	characteristic
107	C₂×C₄	C₂×#4323	1	1	yes	characteristic
108	C₈	#66891	1	2	yes	—
109	C₈	C₂×#4324	1	1	yes	characteristic
110	C₈	#66989	1	1	yes	characteristic
111	C₂²	C₂×#66890	1	1	yes	characteristic
112	C₄	—	16	2	no	—
113	C₄	—	176	2	no	—
114	C₄	#10622159	1	2	yes	—
115	C₄	#10622160	1	2	yes	—
116	C₄	#10622683	1	1	yes	characteristic
117	C₄	C₂×#66891	1	1	yes	characteristic
118	C₂	#13070839	1	1	yes	characteristic
119	C₂	C₂×#10622159	1	1	yes	characteristic
120	C₂	C₂×#10622160	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13070891

C₂

yes

maximal, characteristic

#13066797

C₂

yes

maximal

C₄×C₁₁⋊C₃₂

C₂

yes

maximal, characteristic

C₁₁×#2247

C₂

yes

maximal, characteristic

C₂×C₁₁×Q₃₂

—

C₂×C₁₁×Q₃₂

C₂²

yes

—

C₁₁×#494

—

#10622295

—

C₄×C₁₁×C₁₆

C₂²

yes

characteristic

#10622142

—

#10622142

C₂²

yes

—

C₂×C₁₁⋊C₃₂

C₂²

yes

—

C₂×C₁₁×Q₁₆

—

C₂×C₁₁×Q₁₆

—

C₁₁×C₄⋊Q₈

—

#66922

—

C₁₁×Q₃₂

—

C₁₁×Q₃₂

—

C₂×C₁₁×C₁₆

D₄

yes

characteristic

C₂×C₁₁×C₁₆

C₂³

yes

characteristic

C₄×C₈×C₁₁

D₄

yes

characteristic

#66882

—

#66882

—

C₁₁⋊C₃₂

—

#13720

—

maximal, Sylow

C₂×Q₈×C₁₁

—

C₂×Dic₂₂

—

C₁₁×Q₁₆

—

C₁₁×Q₁₆

—

C₁₁×Q₁₆

—

C₂×C₈×C₁₁

D₈

yes

characteristic

C₂×C₈×C₁₁

C₂×D₄

yes

characteristic

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₄²×C₁₁

D₈

yes

characteristic

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₁₁×C₁₆

SD₁₆

yes

—

C₁₁×C₁₆

#41

yes

—

#2252

—

#2247

D₁₁

yes

characteristic

#1416

—

C₄×C₃₂

—

Q₈×C₁₁

—

Q₈×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

D₁₆

yes

characteristic

C₂×C₄×C₁₁

D₁₆

yes

characteristic

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

C₂×Dic₁₁

—

Dic₂₂

—

C₈×C₁₁

SD₃₂

yes

—

C₈×C₁₁

#124

yes

characteristic

C₈×C₁₁

C₂×SD₁₆

yes

characteristic

C₂×Q₃₂

—

C₂×Q₃₂

C₂×D₁₁

yes

—

#500

—

#494

—

C₂×C₃₂

—

#366

—

#366

—

C₄×C₁₆

C₂×D₁₁

yes

characteristic

C₂²×C₁₁

C₂×D₁₆

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

SD₆₄

yes

—

C₄×C₁₁

Q₆₄

yes

—

C₄×C₁₁

#486

yes

characteristic

C₄×C₁₁

C₂×SD₃₂

yes

characteristic

Dic₁₁

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

Q₃₂

—

Q₃₂

—

C₂×C₁₆

C₂²⋊D₁₁

yes

characteristic

C₂×C₁₆

C₂²×D₁₁

yes

characteristic

#107

—

#107

—

C₄×C₈

C₂²⋊D₁₁

yes

characteristic

C₃₂

—

C₂×C₁₁

#2240

yes

characteristic

C₂×C₁₁

C₂×SD₆₄

yes

characteristic

C₂×C₁₁

C₂×Q₆₄

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

C₂×C₈

#4323

yes

characteristic

C₂×C₈

C₂×C₂²⋊D₁₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

#4323

yes

characteristic

C₁₆

#4324

yes

—

C₁₆

#4341

yes

—

C₁₁

#13720

yes

characteristic, complemented, Sylow

100

Q₈

—

101

Q₈

—

102

Q₈

—

176

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

#66890

yes

characteristic

106

C₂×C₄

#66890

yes

characteristic

107

C₂×C₄

C₂×#4323

yes

characteristic

108

C₈

#66891

yes

—

109

C₈

C₂×#4324

yes

characteristic

110

C₈

#66989

yes

characteristic

111

C₂²

C₂×#66890

yes

characteristic

112

C₄

—

113

C₄

—

176

—

114

C₄

#10622159

yes

—

115

C₄

#10622160

yes

—

116

C₄

#10622683

yes

characteristic

117

C₄

C₂×#66891

yes

characteristic

118

C₂

#13070839

yes

characteristic

119

C₂

C₂×#10622159

yes

characteristic

120

C₂

C₂×#10622160

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#66890
commutator, cosocle	C₂×C₁₁×C₁₆	C₂³
Frattini	C₂×C₁₆	C₂²×D₁₁
Fitting	C₁₁×#2247	C₂
socle, prime radical	C₂²×C₁₁	C₂×D₁₆
hypercenter	#2247	D₁₁
hypocenter	C₁₁	#13720
LCS	G ▷ C₂×C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2247

subgroup

G/H

center

C₂²

C₂×#66890

commutator, cosocle

C₂×C₁₁×C₁₆

C₂³

Frattini

C₂×C₁₆

C₂²×D₁₁

Fitting

C₁₁×#2247

C₂

socle, prime radical

C₂²×C₁₁

C₂×D₁₆

D₁₁

C₁₁

G ▷ C₂×C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2247

N	H ≅ G/N	type
99. C₁₁	#13720	semidirect

H ≅ G/N

type

99. C₁₁

#13720

semidirect

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

subgroup	index
#13070891	2
#13066797	2
C₄×C₁₁⋊C₃₂	2
C₁₁×#2247	2
#13720	11

subgroup

index

#13070891

#13066797

C₄×C₁₁⋊C₃₂

C₁₁×#2247

#13720

Subgroups — #14674745

Conjugacy classes of subgroups

Complements

Maximal subgroups