Group #14565342 — subgroups

Subgroups — #14565342

Order 2432.

228 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 93 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	C₂²×C₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926582	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926348	C₂	1	2	yes	maximal, complemented
4	#11926345	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#135	C₂	1	1	yes	maximal, characteristic
6	C₂×#41×C₁₉	—	2	1	no	—
7	C₁₉×#135	—	2	2	no	—
8	C₁₉×#135	C₄	1	4	yes	complemented
9	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×SD₁₆×C₁₉	—	2	1	no	—
11	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	#10597372	—	2	1	no	—
14	#10597275	C₂²	1	2	yes	—
15	#10597274	—	2	1	no	—
16	C₂×C₁₉⋊C₁₆	—	2	2	no	—
17	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
18	#41×C₁₉	—	2	4	no	—
19	#41×C₁₉	—	4	2	no	—
20	C₂×Q₈×C₁₉	—	2	1	no	—
21	C₂×D₄×C₁₉	—	2	1	no	—
22	C₂×D₄×C₁₉	—	4	1	no	—
23	C₂²×C₄×C₁₉	—	4	1	no	—
24	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
25	Q₁₆×C₁₉	—	2	1	no	—
26	Q₁₆×C₁₉	C₂×C₄	1	2	yes	—
27	SD₁₆×C₁₉	—	2	4	no	—
28	D₈×C₁₉	—	2	1	no	—
29	D₈×C₁₉	C₂×C₄	1	2	yes	—
30	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
32	C₂×C₈×C₁₉	D₄	1	2	yes	—
33	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
34	C₂²⋊Dic₁₉	—	4	1	no	—
35	C₄⋊Dic₁₉	—	2	2	no	—
36	C₄×Dic₁₉	—	4	1	no	—
37	C₁₉⋊C₁₆	—	2	2	no	—
38	C₂³×C₁₉	—	4	1	no	—
39	C₂³×C₁₉	D₈	1	1	yes	characteristic
40	Q₈×C₁₉	—	2	2	no	—
41	Q₈×C₁₉	—	4	1	no	—
42	D₄×C₁₉	—	2	2	no	—
43	D₄×C₁₉	—	4	4	no	—
44	D₄×C₁₉	—	4	1	no	—
45	C₂×C₄×C₁₉	—	4	1	no	—
46	C₂×C₄×C₁₉	—	4	4	no	—
47	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
48	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
49	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
50	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×Dic₁₉	—	4	2	no	—
52	C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
53	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
54	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
55	#2138	—	19	1	no	maximal, Sylow
56	C₂²×C₁₉	—	2	2	no	—
57	C₂²×C₁₉	—	4	2	no	—
58	C₂²×C₁₉	—	8	2	no	—
59	C₂²×C₁₉	#102	1	2	yes	—
60	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
61	C₄×C₁₉	—	4	2	no	—
62	C₄×C₁₉	#102	1	2	yes	—
63	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
64	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
65	Dic₁₉	—	8	2	no	—
66	C₂×#135	D₁₉	1	1	yes	characteristic
67	C₂²×C₁₆	—	19	1	no	—
68	#427	—	19	1	no	—
69	#358	—	19	2	no	—
70	#357	—	19	2	no	—
71	C₂×C₁₉	—	2	2	no	—
72	C₂×C₁₉	—	8	2	no	—
73	C₂×C₁₉	C₂×#102	1	1	yes	characteristic
74	C₂×C₁₉	#508	1	2	yes	—
75	C₂×#41	—	2	1	no	—
76	#135	—	2	2	no	—
77	#135	Dic₁₉	1	4	yes	complemented
78	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic
79	C₂×SD₁₆	—	2	1	no	—
80	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
81	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
82	#117	—	38	1	no	—
83	C₂×C₁₆	—	19	2	no	—
84	C₂×C₁₆	—	38	2	no	—
85	#107	—	19	2	no	—
86	#106	—	38	1	no	—
87	C₁₉	#2138	1	1	yes	characteristic, complemented, Sylow
88	#41	—	2	4	no	—
89	#41	—	4	2	no	—
90	C₂×Q₈	—	2	1	no	—
91	C₂×D₄	—	2	1	no	—
92	C₂×D₄	—	4	1	no	—
93	C₂²×C₄	—	4	1	no	—
94	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
95	Q₁₆	—	2	1	no	—
96	Q₁₆	C₂×Dic₁₉	1	2	yes	—
97	SD₁₆	—	2	4	no	—
98	D₈	—	2	1	no	—
99	D₈	C₂×Dic₁₉	1	2	yes	—
100	C₂×C₈	C₂×Dic₁₉	1	2	yes	—
101	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
102	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
103	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
104	C₄⋊C₄	—	38	2	no	—
105	C₂²⋊C₄	—	76	1	no	—
106	C₄²	—	76	1	no	—
107	C₁₆	—	38	2	no	—
108	C₂³	—	4	1	no	—
109	C₂³	#64525	1	1	yes	characteristic
110	Q₈	—	2	2	no	—
111	Q₈	—	4	1	no	—
112	D₄	—	2	2	no	—
113	D₄	—	4	4	no	—
114	D₄	—	4	1	no	—
115	C₂×C₄	—	4	1	no	—
116	C₂×C₄	—	4	4	no	—
117	C₂×C₄	—	76	2	no	—
118	C₂×C₄	#64525	1	1	yes	characteristic
119	C₂×C₄	#64526	1	2	yes	—
120	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
121	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
122	C₈	C₂²⋊Dic₁₉	1	2	yes	—
123	C₈	C₂²×Dic₁₉	1	1	yes	characteristic
124	C₈	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
125	C₂²	—	2	2	no	—
126	C₂²	—	4	2	no	—
127	C₂²	—	8	2	no	—
128	C₂²	#10597289	1	2	yes	—
129	C₂²	C₂×#64525	1	1	yes	characteristic
130	C₄	—	4	2	no	—
131	C₄	—	152	2	no	—
132	C₄	#10597289	1	2	yes	—
133	C₄	C₂×#64526	1	1	yes	characteristic
134	C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
135	C₂	—	2	2	no	—
136	C₂	—	8	2	no	—
137	C₂	C₂×#10597289	1	1	yes	characteristic
138	C₂	#11926974	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₁₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#11926582

C₂

yes

maximal, characteristic, complemented

#11926348

C₂

yes

maximal, complemented

#11926345

C₂

yes

maximal, complemented

C₂×C₁₉×#135

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

—

C₁₉×#135

—

C₁₉×#135

C₄

yes

complemented

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

#10597372

—

#10597275

C₂²

yes

—

#10597274

—

C₂×C₁₉⋊C₁₆

—

C₂×C₁₉⋊C₁₆

C₂²

yes

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

Q₁₆×C₁₉

—

Q₁₆×C₁₉

C₂×C₄

yes

—

SD₁₆×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

—

C₂³×C₁₉

D₈

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₈×C₁₉

C₂²⋊C₄

yes

—

C₈×C₁₉

C₂²×C₄

yes

characteristic

C₈×C₁₉

C₂×D₄

yes

characteristic

#2138

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#102

yes

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

#102

yes

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

Dic₁₉

—

C₂×#135

D₁₉

yes

characteristic

C₂²×C₁₆

—

#427

—

#358

—

#357

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#102

yes

characteristic

C₂×C₁₉

#508

yes

—

C₂×#41

—

#135

—

#135

Dic₁₉

yes

complemented

C₂×Q₁₆

C₂×D₁₉

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

C₂×D₁₉

yes

characteristic

C₂²×C₈

C₂×D₁₉

yes

characteristic

#117

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

—

#106

—

C₁₉

#2138

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

Q₁₆

—

Q₁₆

C₂×Dic₁₉

yes

—

SD₁₆

—

D₈

—

D₈

C₂×Dic₁₉

yes

—

100

C₂×C₈

C₂×Dic₁₉

yes

—

101

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

102

C₂×C₈

C₂²⋊D₁₉

yes

—

103

C₂×C₈

C₂²×D₁₉

yes

characteristic

104

C₄⋊C₄

—

105

C₂²⋊C₄

—

106

C₄²

—

107

C₁₆

—

108

C₂³

—

109

C₂³

#64525

yes

characteristic

110

Q₈

—

111

Q₈

—

112

D₄

—

113

D₄

—

114

D₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

#64525

yes

characteristic

119

C₂×C₄

#64526

yes

—

120

C₂×C₄

C₂²⋊Dic₁₉

yes

—

121

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

122

C₈

C₂²⋊Dic₁₉

yes

—

123

C₈

C₂²×Dic₁₉

yes

characteristic

124

C₈

C₂×C₂²⋊D₁₉

yes

characteristic

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

#10597289

yes

—

129

C₂²

C₂×#64525

yes

characteristic

130

C₄

—

131

C₄

—

152

—

132

C₄

#10597289

yes

—

133

C₄

C₂×#64526

yes

characteristic

134

C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

135

C₂

—

136

C₂

—

137

C₂

C₂×#10597289

yes

characteristic

138

C₂

#11926974

yes

—

	subgroup	G/H
center	C₂×C₄	#64525
commutator	C₈×C₁₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₉
Fitting, prime radical	C₂×C₁₉×#135	C₂
socle	C₂²×C₁₉	C₂×D₈
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	C₂×#135	D₁₉
hypocenter	C₁₉	#2138
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#135

subgroup

G/H

center

C₂×C₄

#64525

commutator

C₈×C₁₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₁₉

Fitting, prime radical

C₂×C₁₉×#135

C₂

socle

C₂²×C₁₉

C₂×D₈

cosocle

C₂×C₈×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#135

N	H ≅ G/N	type
1. C₂²×C₁₉⋊C₁₆	C₂	semidirect
2. #11926582	C₂	semidirect
3. #11926348	C₂	semidirect
4. #11926345	C₂	semidirect
8. C₁₉×#135	C₄	semidirect
77. #135	Dic₁₉	semidirect
87. C₁₉	#2138	semidirect

H ≅ G/N

type

1. C₂²×C₁₉⋊C₁₆

C₂

semidirect

2. #11926582

C₂

semidirect

3. #11926348

C₂

semidirect

4. #11926345

C₂

semidirect

8. C₁₉×#135

C₄

semidirect

77. #135

Dic₁₉

semidirect

87. C₁₉

#2138

semidirect

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

subgroup	index
C₂²×C₁₉⋊C₁₆	2
#11926582	2
#11926348	2
#11926345	2
C₂×C₁₉×#135	2
#2138	19

subgroup

index

C₂²×C₁₉⋊C₁₆

C₂×C₁₉×#135

Subgroups — #14565342

Conjugacy classes of subgroups

Complements

Maximal subgroups