Group #14565844 — subgroups

Subgroups — #14565844

Order 2432.

132 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 49 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	#11926785	C₂	1	1	yes	maximal, characteristic
2	#11926582	C₂	1	1	yes	maximal, characteristic
3	#11926372	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926370	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926349	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926349	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	#10597372	—	2	1	no	—
10	#10597370	—	2	1	no	—
11	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	#10597275	C₂²	1	1	yes	characteristic
15	#10597275	C₂²	1	1	yes	characteristic
16	#10597275	C₂²	1	1	yes	characteristic
17	#10597274	—	2	1	no	—
18	#10597273	—	2	1	no	—
19	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
20	C₂×Dic₃₈	—	2	1	no	—
21	C₂×C₈×C₁₉	—	2	1	no	—
22	C₂×C₈×C₁₉	—	2	1	no	—
23	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²⋊Dic₁₉	—	4	1	no	—
26	C₂²⋊Dic₁₉	—	4	1	no	—
27	C₄⋊Dic₁₉	—	2	1	no	—
28	C₄⋊Dic₁₉	—	2	1	no	—
29	C₄⋊Dic₁₉	—	2	1	no	—
30	Dic₁₉⋊C₄	—	4	1	no	—
31	C₄×Dic₁₉	—	4	1	no	—
32	Dic₇₆	—	2	1	no	—
33	Dic₇₆	—	2	1	no	—
34	C₁₆×C₁₉	—	2	1	no	—
35	C₁₆×C₁₉	—	2	1	no	—
36	C₂³×C₁₉	D₈	1	1	yes	characteristic
37	C₂×C₄×C₁₉	—	2	1	no	—
38	C₂×C₄×C₁₉	—	2	1	no	—
39	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
40	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂×Dic₁₉	—	4	1	no	—
42	C₂×Dic₁₉	—	4	1	no	—
43	C₂×Dic₁₉	—	4	1	no	—
44	C₂×Dic₁₉	—	4	1	no	—
45	Dic₃₈	—	4	1	no	—
46	Dic₃₈	—	4	1	no	—
47	C₈×C₁₉	—	2	1	no	—
48	C₈×C₁₉	#41	1	1	yes	characteristic
49	C₈×C₁₉	#41	1	1	yes	characteristic
50	#2237	—	19	1	no	maximal, Sylow
51	C₂²×C₁₉	—	2	1	no	—
52	C₂²×C₁₉	—	2	1	no	—
53	C₂²×C₁₉	—	2	1	no	—
54	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
55	C₄×C₁₉	—	2	1	no	—
56	C₄×C₁₉	#123	1	1	yes	characteristic
57	C₄×C₁₉	#137	1	1	yes	characteristic
58	Dic₁₉	—	8	1	no	—
59	Dic₁₉	—	8	1	no	—
60	Dic₁₉	—	8	1	no	—
61	Dic₁₉	—	8	1	no	—
62	#467	—	19	1	no	—
63	#427	—	19	1	no	—
64	#367	—	19	1	no	—
65	#366	—	19	1	no	—
66	#358	—	19	1	no	—
67	#358	—	19	1	no	—
68	C₂²⋊C₁₆	D₁₉	1	1	yes	characteristic
69	C₂×C₁₉	—	4	1	no	—
70	C₂×C₁₉	#480	1	1	yes	characteristic
71	C₂×C₁₉	#508	1	1	yes	characteristic
72	C₂×C₁₉	#510	1	1	yes	characteristic
73	C₂×Q₁₆	—	19	1	no	—
74	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
75	C₂²⋊Q₈	—	38	1	no	—
76	#117	—	38	1	no	—
77	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
78	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
79	#107	—	19	1	no	—
80	#107	—	19	1	no	—
81	#107	—	19	1	no	—
82	#106	—	38	1	no	—
83	#103	—	38	1	no	—
84	C₁₉	#2237	1	1	yes	characteristic, complemented, Sylow
85	C₂×Q₈	—	38	1	no	—
86	C₂²×C₄	D₇₆	1	1	yes	characteristic
87	Q₁₆	—	38	1	no	—
88	Q₁₆	—	38	1	no	—
89	C₂×C₈	—	2	1	no	—
90	C₂×C₈	—	2	1	no	—
91	C₂×C₈	D₇₆	1	1	yes	characteristic
92	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
93	C₄⋊C₄	—	38	1	no	—
94	C₄⋊C₄	—	38	1	no	—
95	C₄⋊C₄	—	38	1	no	—
96	C₄⋊C₄	—	76	1	no	—
97	C₂²⋊C₄	—	76	1	no	—
98	C₂²⋊C₄	—	76	1	no	—
99	C₄²	—	76	1	no	—
100	C₁₆	—	2	1	no	—
101	C₁₆	—	2	1	no	—
102	C₂³	D₁₅₂	1	1	yes	characteristic
103	Q₈	—	76	1	no	—
104	Q₈	—	76	1	no	—
105	C₂×C₄	—	2	1	no	—
106	C₂×C₄	—	2	1	no	—
107	C₂×C₄	—	76	1	no	—
108	C₂×C₄	—	76	1	no	—
109	C₂×C₄	—	76	1	no	—
110	C₂×C₄	—	76	1	no	—
111	C₂×C₄	D₁₅₂	1	1	yes	characteristic
112	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
113	C₈	—	2	1	no	—
114	C₈	#64543	1	1	yes	characteristic
115	C₈	#64543	1	1	yes	characteristic
116	C₂²	—	2	1	no	—
117	C₂²	—	2	1	no	—
118	C₂²	—	2	1	no	—
119	C₂²	C₂×D₁₅₂	1	1	yes	characteristic
120	C₄	—	2	1	no	—
121	C₄	—	152	1	no	—
122	C₄	—	152	1	no	—
123	C₄	—	152	1	no	—
124	C₄	—	152	1	no	—
125	C₄	#10597332	1	1	yes	characteristic
126	C₄	#10597355	1	1	yes	characteristic
127	C₂	—	4	1	no	—
128	C₂	#11926858	1	1	yes	characteristic
129	C₂	#11926976	1	1	yes	characteristic
130	C₂	#11926987	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926785

C₂

yes

maximal, characteristic

#11926582

C₂

yes

maximal, characteristic

#11926372

C₂

yes

maximal, characteristic, complemented

#11926370

C₂

yes

maximal, characteristic, complemented

#11926349

C₂

yes

maximal, characteristic, complemented

#11926349

C₂

yes

maximal, characteristic, complemented

C₁₉×C₂²⋊C₁₆

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

#10597372

—

#10597370

—

C₂×Dic₇₆

C₂²

yes

characteristic

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

#10597275

C₂²

yes

characteristic

#10597275

C₂²

yes

characteristic

#10597275

C₂²

yes

characteristic

#10597274

—

#10597273

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

Dic₇₆

—

Dic₇₆

—

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₂³×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

—

—

C₂²⋊C₁₆

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂²⋊Q₈

—

#117

—

C₂×C₁₆

C₂×D₁₉

yes

characteristic

C₂×C₁₆

C₂×D₁₉

yes

—

—

—

—

—

C₁₉

#2237

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

D₇₆

yes

characteristic

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

100

C₁₆

—

101

C₁₆

—

102

C₂³

D₁₅₂

yes

characteristic

103

Q₈

—

104

Q₈

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

D₁₅₂

yes

characteristic

112

C₂×C₄

C₂×D₇₆

yes

characteristic

113

C₈

—

114

C₈

#64543

yes

characteristic

115

C₈

#64543

yes

characteristic

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

C₂×D₁₅₂

yes

characteristic

120

C₄

—

121

C₄

—

152

—

122

C₄

—

152

—

123

C₄

—

152

—

124

C₄

—

152

—

125

C₄

#10597332

yes

characteristic

126

C₄

#10597355

yes

characteristic

127

C₂

—

128

C₂

#11926858

yes

characteristic

129

C₂

#11926976

yes

characteristic

130

C₂

#11926987

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₅₂
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×C₂²⋊C₁₆	C₂
socle	C₂²×C₁₉	C₂×D₈
prime radical	C₂³×C₁₉	D₈
hypercenter	C₂²⋊C₁₆	D₁₉
hypocenter	C₁₉	#2237
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

subgroup

G/H

center

C₂²

C₂×D₁₅₂

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×C₂²⋊C₁₆

C₂

socle

C₂²×C₁₉

C₂×D₈

prime radical

C₂³×C₁₉

D₈

hypercenter

C₂²⋊C₁₆

D₁₉

hypocenter

C₁₉

#2237

LCS

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

N	H ≅ G/N	type
3. #11926372	C₂	semidirect
4. #11926370	C₂	semidirect
5. #11926349	C₂	semidirect
6. #11926349	C₂	semidirect
84. C₁₉	#2237	semidirect

H ≅ G/N

type

3. #11926372

C₂

semidirect

4. #11926370

C₂

semidirect

5. #11926349

C₂

semidirect

6. #11926349

C₂

semidirect

84. C₁₉

#2237

semidirect

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

subgroup	index
#11926785	2
#11926582	2
#11926372	2
#11926370	2
#11926349	2
C₁₉×C₂²⋊C₁₆	2
#2237	19

subgroup

index

C₁₉×C₂²⋊C₁₆

Subgroups — #14565844

Conjugacy classes of subgroups

Complements

Maximal subgroups