Group #14680935 — subgroups

Subgroups — #14680935

Order 2816.

3998 conjugacy classes of subgroups; only the 651 normal subgroups are shown.

normal subgroups only

This group has 3998 conjugacy classes of subgroups — too many to draw. Only its 651 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×#10622824	C₂	1	6	yes	maximal
2	#13066887	C₂	1	8	yes	maximal, complemented
3	C₂⁴×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₂³×Q₈×C₁₁	—	2	24	no	—
5	C₂³×Q₈×C₁₁	C₄	1	8	yes	complemented
6	C₂³×Q₈×C₁₁	C₂²	1	4	yes	—
7	C₂⁴×C₄×C₁₁	C₂²	1	3	yes	—
8	C₂²×C₂²⋊Dic₁₁	C₂²	1	4	yes	—
9	#10622824	—	2	24	no	—
10	C₂×C₁₁⋊#95	C₂²	1	24	yes	—
11	C₂⁵×C₁₁	C₂³	1	1	yes	characteristic
12	C₂²×Q₈×C₁₁	—	2	128	no	—
13	C₂²×Q₈×C₁₁	—	2	96	no	—
14	C₂²×Q₈×C₁₁	—	2	48	no	—
15	C₂²×Q₈×C₁₁	C₂×C₄	1	16	yes	—
16	C₂³×C₄×C₁₁	—	2	24	no	—
17	C₂³×C₄×C₁₁	C₂×C₄	1	12	yes	—
18	C₂³×C₄×C₁₁	D₄	1	24	yes	—
19	C₂³×C₄×C₁₁	C₂³	1	6	yes	—
20	C₂³×Dic₁₁	C₂³	1	8	yes	—
21	C₂×C₂²⋊Dic₁₁	—	2	24	no	—
22	C₁₁⋊#95	—	2	48	no	—
23	#14336	—	11	1	no	maximal, Sylow
24	C₂⁴×C₁₁	—	2	8	no	—
25	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
26	C₂⁴×C₁₁	C₂×D₄	1	12	yes	—
27	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
28	C₂×Q₈×C₁₁	—	2	128	no	—
29	C₂×Q₈×C₁₁	—	2	256	no	—
30	C₂×Q₈×C₁₁	—	2	96	no	—
31	C₂²×C₄×C₁₁	—	2	48	no	—
32	C₂²×C₄×C₁₁	—	2	96	no	—
33	C₂²×C₄×C₁₁	—	2	24	no	—
34	C₂²×C₄×C₁₁	C₂²⋊C₄	1	48	yes	—
35	C₂²×C₄×C₁₁	C₂²×C₄	1	12	yes	—
36	C₂²×C₄×C₁₁	C₂×D₄	1	24	yes	—
37	C₂²×Dic₁₁	—	2	24	no	—
38	C₂²×Dic₁₁	—	2	32	no	—
39	C₂²⋊Dic₁₁	—	4	16	no	—
40	C₂⁴×Q₈	D₁₁	1	1	yes	characteristic
41	C₂×#381	—	11	6	no	—
42	#1446	—	11	8	no	—
43	C₂³×C₁₁	—	2	8	no	—
44	C₂³×C₁₁	—	2	48	no	—
45	C₂³×C₁₁	C₂×C₂²⋊C₄	1	12	yes	—
46	C₂³×C₁₁	#120	1	16	yes	—
47	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
48	C₂³×C₁₁	C₂²×D₄	1	6	yes	—
49	C₂³×C₁₁	2₋¹⁺⁴	1	8	yes	—
50	Q₈×C₁₁	—	2	128	no	—
51	C₂×C₄×C₁₁	—	2	24	no	—
52	C₂×C₄×C₁₁	—	2	48	no	—
53	C₂×C₄×C₁₁	—	2	96	no	—
54	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	24	yes	—
55	C₂×Dic₁₁	—	4	8	no	—
56	C₂×Dic₁₁	—	4	48	no	—
57	C₂³×Q₈	—	2	24	no	—
58	C₂³×Q₈	Dic₁₁	1	8	yes	complemented
59	C₂³×Q₈	C₂×D₁₁	1	4	yes	—
60	C₂⁴×C₄	C₂×D₁₁	1	3	yes	—
61	C₂²×C₂²⋊C₄	—	11	4	no	—
62	#381	—	22	24	no	—
63	C₂×#95	—	11	24	no	—
64	C₂²×C₁₁	—	2	24	no	—
65	C₂²×C₁₁	—	2	32	no	—
66	C₂²×C₁₁	#379	1	8	yes	—
67	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	3	yes	—
68	C₂²×C₁₁	#519	1	4	yes	—
69	C₂²×C₁₁	C₂×#120	1	4	yes	—
70	C₂²×C₁₁	#536	1	24	yes	—
71	C₄×C₁₁	—	2	24	no	—
72	Dic₁₁	—	8	8	no	—
73	C₂⁵	C₂²×D₁₁	1	1	yes	characteristic
74	C₂²×Q₈	—	2	128	no	—
75	C₂²×Q₈	—	2	96	no	—
76	C₂²×Q₈	—	2	48	no	—
77	C₂²×Q₈	C₂×Dic₁₁	1	16	yes	—
78	C₂³×C₄	—	2	24	no	—
79	C₂³×C₄	—	11	8	no	—
80	C₂³×C₄	C₂×Dic₁₁	1	12	yes	—
81	C₂³×C₄	C₂²⋊D₁₁	1	24	yes	—
82	C₂³×C₄	C₂²×D₁₁	1	6	yes	—
83	C₂×C₂²⋊C₄	—	22	24	no	—
84	#95	—	22	48	no	—
85	C₂×C₁₁	—	2	8	no	—
86	C₂×C₁₁	C₂×#379	1	1	yes	characteristic
87	C₂×C₁₁	#2310	1	6	yes	—
88	C₂×C₁₁	#2614	1	8	yes	—
89	C₂⁴	—	2	8	no	—
90	C₂⁴	C₂²×Dic₁₁	1	2	yes	—
91	C₂⁴	C₂×C₂²⋊D₁₁	1	12	yes	—
92	C₂⁴	C₂³×D₁₁	1	1	yes	characteristic
93	C₂×Q₈	—	2	128	no	—
94	C₂×Q₈	—	2	256	no	—
95	C₂×Q₈	—	2	96	no	—
96	C₂²×C₄	—	2	48	no	—
97	C₂²×C₄	—	2	96	no	—
98	C₂²×C₄	—	2	24	no	—
99	C₂²×C₄	—	22	32	no	—
100	C₂²×C₄	—	22	24	no	—
101	C₂²×C₄	C₂²⋊Dic₁₁	1	48	yes	—
102	C₂²×C₄	C₂²×Dic₁₁	1	12	yes	—
103	C₂²×C₄	C₂×C₂²⋊D₁₁	1	24	yes	—
104	C₂²⋊C₄	—	44	16	no	—
105	C₁₁	#14336	1	1	yes	characteristic, complemented, Sylow
106	C₂³	—	2	8	no	—
107	C₂³	—	2	48	no	—
108	C₂³	C₂×C₂²⋊Dic₁₁	1	12	yes	—
109	C₂³	#67006	1	16	yes	—
110	C₂³	#67040	1	8	yes	—
111	C₂³	C₂³×Dic₁₁	1	1	yes	characteristic
112	C₂³	C₂²×C₂²⋊D₁₁	1	6	yes	—
113	Q₈	—	2	128	no	—
114	C₂×C₄	—	2	24	no	—
115	C₂×C₄	—	2	48	no	—
116	C₂×C₄	—	2	96	no	—
117	C₂×C₄	—	44	48	no	—
118	C₂×C₄	—	44	8	no	—
119	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	24	yes	—
120	C₂²	—	2	24	no	—
121	C₂²	—	2	32	no	—
122	C₂²	#10622860	1	8	yes	—
123	C₂²	#10623343	1	4	yes	—
124	C₂²	#10623347	1	24	yes	—
125	C₂²	C₂²×C₂²⋊Dic₁₁	1	3	yes	—
126	C₂²	C₂×#67006	1	4	yes	—
127	C₄	—	2	24	no	—
128	C₄	—	88	8	no	—
129	C₂	—	2	8	no	—
130	C₂	C₂×#10622860	1	1	yes	characteristic
131	C₂	#13071202	1	6	yes	—
132	C₂	#13074335	1	8	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622824

C₂

yes

maximal

#13066887

C₂

yes

maximal, complemented

C₂⁴×Q₈×C₁₁

C₂

yes

maximal, characteristic

C₂³×Q₈×C₁₁

—

C₂³×Q₈×C₁₁

C₄

yes

complemented

C₂³×Q₈×C₁₁

C₂²

yes

—

C₂⁴×C₄×C₁₁

C₂²

yes

—

C₂²×C₂²⋊Dic₁₁

C₂²

yes

—

#10622824

—

C₂×C₁₁⋊#95

C₂²

yes

—

C₂⁵×C₁₁

C₂³

yes

characteristic

C₂²×Q₈×C₁₁

—

128

—

C₂²×Q₈×C₁₁

—

C₂²×Q₈×C₁₁

—

C₂²×Q₈×C₁₁

C₂×C₄

yes

—

C₂³×C₄×C₁₁

—

C₂³×C₄×C₁₁

C₂×C₄

yes

—

C₂³×C₄×C₁₁

D₄

yes

—

C₂³×C₄×C₁₁

C₂³

yes

—

C₂³×Dic₁₁

C₂³

yes

—

C₂×C₂²⋊Dic₁₁

—

C₁₁⋊#95

—

#14336

—

maximal, Sylow

C₂⁴×C₁₁

—

C₂⁴×C₁₁

C₂²×C₄

yes

—

C₂⁴×C₁₁

C₂×D₄

yes

—

C₂⁴×C₁₁

C₂⁴

yes

characteristic

C₂×Q₈×C₁₁

—

128

—

C₂×Q₈×C₁₁

—

256

—

C₂×Q₈×C₁₁

—

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₁

C₂²×C₄

yes

—

C₂²×C₄×C₁₁

C₂×D₄

yes

—

C₂²×Dic₁₁

—

C₂²×Dic₁₁

—

C₂²⋊Dic₁₁

—

C₂⁴×Q₈

D₁₁

yes

characteristic

C₂×#381

—

#1446

—

C₂³×C₁₁

—

C₂³×C₁₁

—

C₂³×C₁₁

C₂×C₂²⋊C₄

yes

—

C₂³×C₁₁

#120

yes

—

C₂³×C₁₁

C₂³×C₄

yes

characteristic

C₂³×C₁₁

C₂²×D₄

yes

—

C₂³×C₁₁

2₋¹⁺⁴

yes

—

Q₈×C₁₁

—

128

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₂²⋊C₄

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂³×Q₈

—

C₂³×Q₈

Dic₁₁

yes

complemented

C₂³×Q₈

C₂×D₁₁

yes

—

C₂⁴×C₄

C₂×D₁₁

yes

—

C₂²×C₂²⋊C₄

—

#381

—

C₂×#95

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

#379

yes

—

C₂²×C₁₁

C₂²×C₂²⋊C₄

yes

—

C₂²×C₁₁

#519

yes

—

C₂²×C₁₁

C₂×#120

yes

—

C₂²×C₁₁

#536

yes

—

C₄×C₁₁

—

Dic₁₁

—

C₂⁵

C₂²×D₁₁

yes

characteristic

C₂²×Q₈

—

128

—

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×Q₈

C₂×Dic₁₁

yes

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂×Dic₁₁

yes

—

C₂³×C₄

C₂²⋊D₁₁

yes

—

C₂³×C₄

C₂²×D₁₁

yes

—

C₂×C₂²⋊C₄

—

#95

—

C₂×C₁₁

—

C₂×C₁₁

C₂×#379

yes

characteristic

C₂×C₁₁

#2310

yes

—

C₂×C₁₁

#2614

yes

—

C₂⁴

—

C₂⁴

C₂²×Dic₁₁

yes

—

C₂⁴

C₂×C₂²⋊D₁₁

yes

—

C₂⁴

C₂³×D₁₁

yes

characteristic

C₂×Q₈

—

128

—

C₂×Q₈

—

256

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

C₂²⋊Dic₁₁

yes

—

102

C₂²×C₄

C₂²×Dic₁₁

yes

—

103

C₂²×C₄

C₂×C₂²⋊D₁₁

yes

—

104

C₂²⋊C₄

—

105

C₁₁

#14336

yes

characteristic, complemented, Sylow

106

C₂³

—

107

C₂³

—

108

C₂³

C₂×C₂²⋊Dic₁₁

yes

—

109

C₂³

#67006

yes

—

110

C₂³

#67040

yes

—

111

C₂³

C₂³×Dic₁₁

yes

characteristic

112

C₂³

C₂²×C₂²⋊D₁₁

yes

—

113

Q₈

—

128

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

C₂×C₂²⋊Dic₁₁

yes

—

120

C₂²

—

121

C₂²

—

122

C₂²

#10622860

yes

—

123

C₂²

#10623343

yes

—

124

C₂²

#10623347

yes

—

125

C₂²

C₂²×C₂²⋊Dic₁₁

yes

—

126

C₂²

C₂×#67006

yes

—

127

C₄

—

128

C₄

—

129

C₂

—

130

C₂

C₂×#10622860

yes

characteristic

131

C₂

#13071202

yes

—

132

C₂

#13074335

yes

—

	subgroup	G/H
center, Frattini	C₂⁴	C₂³×D₁₁
commutator	C₂³×C₁₁	C₂³×C₄
Fitting	C₂⁴×Q₈×C₁₁	C₂
socle, cosocle	C₂⁴×C₁₁	C₂⁴
prime radical	C₂⁵×C₁₁	C₂³
hypercenter	C₂⁴×Q₈	D₁₁
hypocenter	C₁₁	#14336
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×Q₈

subgroup

G/H

center, Frattini

C₂⁴

C₂³×D₁₁

commutator

C₂³×C₁₁

C₂³×C₄

Fitting

C₂⁴×Q₈×C₁₁

C₂

socle, cosocle

C₂⁴×C₁₁

C₂⁴

prime radical

C₂⁵×C₁₁

C₂³

hypercenter

C₂⁴×Q₈

D₁₁

C₁₁

G ▷ C₂³×C₁₁ ▷ C₁₁

C₁ ◁ C₂⁴ ◁ C₂⁴×Q₈

N	H ≅ G/N	type
2. #13066887	C₂	semidirect
5. C₂³×Q₈×C₁₁	C₄	semidirect
58. C₂³×Q₈	Dic₁₁	semidirect
105. C₁₁	#14336	semidirect

H ≅ G/N

type

2. #13066887

C₂

semidirect

5. C₂³×Q₈×C₁₁

C₄

semidirect

58. C₂³×Q₈

Dic₁₁

semidirect

105. C₁₁

#14336

semidirect

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

subgroup	index
C₂×#10622824	2
#13066887	2
C₂⁴×Q₈×C₁₁	2
#14336	11

subgroup

index

C₂×#10622824

#13066887

C₂⁴×Q₈×C₁₁

#14336

Subgroups — #14680935

Conjugacy classes of subgroups

Complements

Maximal subgroups