Group #14668499 — subgroups

Subgroups — #14668499

Order 2816.

360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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	#13070871	C₂	1	2	yes	maximal, complemented
2	#13070865	C₂	1	2	yes	maximal, complemented
3	#13068222	C₂	1	1	yes	maximal, characteristic, complemented
4	#13066533	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1712	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#493	—	2	2	no	—
7	C₁₁×#493	C₂²	1	2	yes	—
8	C₂×#66891	—	2	4	no	—
9	C₂×#66890	—	2	4	no	—
10	#10622312	C₂²	1	1	yes	characteristic
11	#10622308	C₂²	1	1	yes	characteristic
12	#10622307	—	2	2	no	—
13	C₈²×C₁₁	C₂²	1	1	yes	characteristic
14	C₄×C₁₁⋊C₁₆	C₂²	1	2	yes	—
15	C₂×C₁₁×D₈	—	2	2	no	—
16	C₂×C₁₁×D₈	—	2	2	no	—
17	C₂×C₁₁×D₈	—	4	4	no	—
18	C₁₁×#127	—	2	2	no	—
19	C₂×Dic₄₄	—	2	2	no	—
20	C₂×D₈₈	—	2	2	no	—
21	#66927	—	2	1	no	—
22	#66922	—	2	1	no	—
23	C₄×C₈×C₁₁	D₄	1	2	yes	—
24	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
25	#66891	—	4	8	no	—
26	#66890	—	4	8	no	—
27	#66885	—	4	4	no	—
28	C₂×C₁₁⋊C₁₆	D₄	1	4	yes	—
29	#12519	—	11	1	no	maximal, Sylow
30	C₂×D₄×C₁₁	—	4	2	no	—
31	C₂×D₄×C₁₁	—	4	4	no	—
32	C₂×D₄₄	—	4	1	no	—
33	C₂×D₄₄	—	4	2	no	—
34	C₂×Dic₂₂	—	4	1	no	—
35	C₁₁×D₈	—	4	4	no	—
36	C₁₁×D₈	—	4	4	no	—
37	C₁₁×D₈	—	8	8	no	—
38	C₂×C₈×C₁₁	D₈	1	4	yes	—
39	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
40	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
41	C₄⋊Dic₁₁	—	4	2	no	—
42	Dic₄₄	—	4	4	no	—
43	D₈₈	—	4	4	no	—
44	C₁₁⋊C₁₆	D₈	1	8	yes	complemented
45	#2248	—	11	2	no	—
46	#2246	—	11	2	no	—
47	#1712	D₁₁	1	1	yes	characteristic, complemented
48	#1709	—	11	1	no	—
49	#1311	—	11	1	no	—
50	C₂³×C₁₁	—	8	2	no	—
51	C₂²×D₁₁	—	8	1	no	—
52	D₄×C₁₁	—	8	2	no	—
53	D₄×C₁₁	—	8	2	no	—
54	D₄×C₁₁	—	8	8	no	—
55	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
56	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
57	C₂×Dic₁₁	—	8	1	no	—
58	D₄₄	—	8	2	no	—
59	D₄₄	—	8	4	no	—
60	Dic₂₂	—	8	2	no	—
61	C₈×C₁₁	—	2	4	no	—
62	C₈×C₁₁	C₂×D₈	1	4	yes	—
63	C₂×SD₃₂	—	22	4	no	—
64	C₂×D₁₆	—	22	4	no	—
65	#494	—	11	1	no	—
66	#493	—	2	2	no	—
67	#493	—	11	1	no	—
68	#493	C₂×D₁₁	1	2	yes	—
69	#486	—	22	2	no	—
70	C₄×C₁₆	—	11	2	no	—
71	C₈²	C₂×D₁₁	1	1	yes	characteristic
72	C₂²×C₁₁	—	16	2	no	—
73	C₂²×C₁₁	—	16	4	no	—
74	C₂²×C₁₁	#493	1	1	yes	characteristic
75	C₂×D₁₁	—	16	1	no	—
76	C₂×D₁₁	—	16	2	no	—
77	C₄×C₁₁	#493	1	2	yes	—
78	C₄×C₁₁	#509	1	4	yes	—
79	Dic₁₁	—	16	1	no	—
80	C₂×Q₁₆	—	22	2	no	—
81	C₂×D₈	—	2	2	no	—
82	C₂×D₈	—	2	2	no	—
83	C₂×D₈	—	4	4	no	—
84	C₂×D₈	—	22	2	no	—
85	C₄⋊Q₈	—	22	1	no	—
86	#127	—	2	2	no	—
87	#127	—	22	1	no	—
88	SD₃₂	—	44	8	no	—
89	D₁₆	—	44	8	no	—
90	C₂×C₁₆	—	11	4	no	—
91	#102	—	44	4	no	—
92	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
93	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
94	C₂×C₁₁	—	32	2	no	—
95	C₂×C₁₁	#1712	1	1	yes	characteristic
96	C₂×C₁₁	#2250	1	2	yes	—
97	D₁₁	—	32	1	no	—
98	C₂×Q₈	—	44	1	no	—
99	C₂×D₄	—	4	4	no	—
100	C₂×D₄	—	4	2	no	—
101	C₂×D₄	—	44	2	no	—
102	C₂×D₄	—	44	1	no	—
103	Q₁₆	—	44	4	no	—
104	D₈	—	4	4	no	—
105	D₈	—	4	4	no	—
106	D₈	—	8	8	no	—
107	D₈	—	44	4	no	—
108	C₂×C₈	#4323	1	4	yes	—
109	C₂×C₈	D₄×D₁₁	1	2	yes	—
110	C₄⋊C₄	—	44	2	no	—
111	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
112	C₁₆	—	11	8	no	—
113	C₁₁	#12519	1	1	yes	characteristic, complemented, Sylow
114	C₂³	—	8	2	no	—
115	C₂³	—	88	1	no	—
116	Q₈	—	88	2	no	—
117	D₄	—	8	8	no	—
118	D₄	—	8	2	no	—
119	D₄	—	8	2	no	—
120	D₄	—	88	4	no	—
121	D₄	—	88	2	no	—
122	C₂×C₄	—	88	1	no	—
123	C₂×C₄	C₂×#4323	1	2	yes	—
124	C₂×C₄	#66993	1	1	yes	characteristic
125	C₈	—	2	4	no	—
126	C₈	D₈×D₁₁	1	4	yes	—
127	C₂²	—	16	4	no	—
128	C₂²	—	16	2	no	—
129	C₂²	—	176	2	no	—
130	C₂²	—	176	1	no	—
131	C₂²	#10622686	1	1	yes	characteristic
132	C₄	—	176	1	no	—
133	C₄	#10622760	1	4	yes	—
134	C₄	#10622764	1	2	yes	—
135	C₂	—	32	2	no	—
136	C₂	—	352	1	no	—
137	C₂	#13068230	1	1	yes	characteristic
138	C₂	#13070880	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13070871

C₂

yes

maximal, complemented

#13070865

C₂

yes

maximal, complemented

#13068222

C₂

yes

maximal, characteristic, complemented

#13066533

C₂

yes

maximal, characteristic, complemented

C₁₁×#1712

C₂

yes

maximal, characteristic, complemented

C₁₁×#493

—

C₁₁×#493

C₂²

yes

—

C₂×#66891

—

C₂×#66890

—

#10622312

C₂²

yes

characteristic

#10622308

C₂²

yes

characteristic

#10622307

—

C₈²×C₁₁

C₂²

yes

characteristic

C₄×C₁₁⋊C₁₆

C₂²

yes

—

C₂×C₁₁×D₈

—

C₂×C₁₁×D₈

—

C₂×C₁₁×D₈

—

C₁₁×#127

—

C₂×Dic₄₄

—

C₂×D₈₈

—

#66927

—

#66922

—

C₄×C₈×C₁₁

D₄

yes

—

C₄×C₈×C₁₁

C₂³

yes

—

—

—

C₂×C₁₁⋊C₁₆

D₄

yes

—

#12519

—

maximal, Sylow

C₂×D₄×C₁₁

—

C₂×D₄×C₁₁

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×Dic₂₂

—

C₁₁×D₈

—

C₁₁×D₈

—

C₁₁×D₈

—

C₂×C₈×C₁₁

D₈

yes

—

C₂×C₈×C₁₁

C₂×D₄

yes

—

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄⋊Dic₁₁

—

Dic₄₄

—

D₈₈

—

C₁₁⋊C₁₆

D₈

yes

—

—

D₁₁

yes

characteristic, complemented

#1709

—

#1311

—

C₂³×C₁₁

—

C₂²×D₁₁

—

D₄×C₁₁

—

D₄×C₁₁

—

D₄×C₁₁

—

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

C₂×D₈

yes

—

C₂×Dic₁₁

—

D₄₄

—

D₄₄

—

Dic₂₂

—

C₈×C₁₁

—

C₈×C₁₁

C₂×D₈

yes

—

C₂×SD₃₂

—

C₂×D₁₆

—

—

—

—

C₂×D₁₁

yes

—

#486

—

C₄×C₁₆

—

C₈²

C₂×D₁₁

yes

characteristic

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

#493

yes

characteristic

C₂×D₁₁

—

C₂×D₁₁

—

C₄×C₁₁

#493

yes

—

C₄×C₁₁

#509

yes

—

Dic₁₁

—

C₂×Q₁₆

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

—

#127

—

#127

—

SD₃₂

—

D₁₆

—

C₂×C₁₆

—

#102

—

C₄×C₈

C₂²⋊D₁₁

yes

—

C₄×C₈

C₂²×D₁₁

yes

characteristic

C₂×C₁₁

—

C₂×C₁₁

#1712

yes

characteristic

C₂×C₁₁

#2250

yes

—

D₁₁

—

C₂×Q₈

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂×D₄

—

103

Q₁₆

—

104

D₈

—

105

D₈

—

106

D₈

—

107

D₈

—

108

C₂×C₈

#4323

yes

—

109

C₂×C₈

D₄×D₁₁

yes

—

110

C₄⋊C₄

—

111

C₄²

C₂×C₂²⋊D₁₁

yes

characteristic

112

C₁₆

—

113

C₁₁

#12519

yes

characteristic, complemented, Sylow

114

C₂³

—

115

C₂³

—

116

Q₈

—

117

D₄

—

118

D₄

—

119

D₄

—

120

D₄

—

121

D₄

—

122

C₂×C₄

—

123

C₂×C₄

C₂×#4323

yes

—

124

C₂×C₄

#66993

yes

characteristic

125

C₈

—

126

C₈

D₈×D₁₁

yes

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

176

—

130

C₂²

—

176

—

131

C₂²

#10622686

yes

characteristic

132

C₄

—

176

—

133

C₄

#10622760

yes

—

134

C₄

#10622764

yes

—

135

C₂

—

136

C₂

—

352

—

137

C₂

#13068230

yes

characteristic

138

C₂

#13070880

yes

—

	subgroup	G/H
center	C₂²	#10622686
commutator, cosocle	C₄×C₈×C₁₁	C₂³
Frattini	C₄×C₈	C₂²×D₁₁
Fitting	C₁₁×#1712	C₂
socle	C₂²×C₁₁	#493
hypercenter	#1712	D₁₁
hypocenter	C₁₁	#12519
LCS	G ▷ C₄×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1712

subgroup

G/H

center

C₂²

#10622686

commutator, cosocle

C₄×C₈×C₁₁

C₂³

Frattini

C₄×C₈

C₂²×D₁₁

Fitting

C₁₁×#1712

C₂

C₂²×C₁₁

D₁₁

C₁₁

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

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1712

N	H ≅ G/N	type
1. #13070871	C₂	semidirect
2. #13070865	C₂	semidirect
3. #13068222	C₂	semidirect
4. #13066533	C₂	semidirect
5. C₁₁×#1712	C₂	semidirect
44. C₁₁⋊C₁₆	D₈	semidirect
47. #1712	D₁₁	semidirect
113. C₁₁	#12519	semidirect

H ≅ G/N

type

1. #13070871

C₂

semidirect

2. #13070865

C₂

semidirect

3. #13068222

C₂

semidirect

4. #13066533

C₂

semidirect

5. C₁₁×#1712

C₂

semidirect

44. C₁₁⋊C₁₆

D₈

semidirect

47. #1712

D₁₁

semidirect

113. C₁₁

#12519

semidirect

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

subgroup	index
#13070871	2
#13070865	2
#13068222	2
#13066533	2
C₁₁×#1712	2
#12519	11

subgroup

index

C₁₁×#1712

Subgroups — #14668499

Conjugacy classes of subgroups

Complements

Maximal subgroups