Group #14565905 — subgroups

Subgroups — #14565905

Order 2432.

178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 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×Dic₁₅₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597286	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597284	C₂	1	1	yes	maximal, characteristic
4	#11926927	C₂	1	1	yes	maximal, characteristic
5	#11926922	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926319	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×SD₃₂	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
10	#10597390	—	2	1	no	—
11	C₂×#64528	—	2	1	no	—
12	#10597382	—	2	1	no	—
13	C₂×#64526	—	2	1	no	—
14	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
15	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
16	C₁₉×SD₃₂	—	2	2	no	—
17	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	#10597286	—	2	2	no	—
19	#10597284	—	2	2	no	—
20	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
22	Dic₁₅₂	—	2	2	no	—
23	C₂×Q₈×C₁₉	—	2	1	no	—
24	C₂×D₄×C₁₉	—	2	1	no	—
25	C₂×Dic₃₈	—	2	1	no	—
26	C₂×Dic₃₈	—	2	1	no	—
27	Q₁₆×C₁₉	—	2	1	no	—
28	Q₁₆×C₁₉	—	2	1	no	—
29	D₈×C₁₉	—	2	1	no	—
30	D₈×C₁₉	—	2	1	no	—
31	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²⋊Dic₁₉	—	4	2	no	—
33	#64528	—	4	2	no	—
34	#64526	—	4	2	no	—
35	Dic₁₉⋊C₄	—	4	2	no	—
36	C₄×Dic₁₉	D₄	1	1	yes	characteristic
37	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
38	Dic₇₆	—	2	1	no	—
39	Dic₇₆	—	2	1	no	—
40	Dic₇₆	—	2	1	no	—
41	Dic₇₆	—	2	1	no	—
42	C₁₆×C₁₉	D₄	1	2	yes	—
43	C₁₉⋊C₁₆	D₄	1	2	yes	—
44	C₂³×C₁₉	—	4	1	no	—
45	Q₈×C₁₉	—	4	1	no	—
46	Q₈×C₁₉	—	4	1	no	—
47	D₄×C₁₉	—	4	1	no	—
48	D₄×C₁₉	—	4	1	no	—
49	C₂×C₄×C₁₉	—	4	1	no	—
50	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×Dic₁₉	—	4	1	no	—
52	C₂×Dic₁₉	—	4	1	no	—
53	C₂×Dic₁₉	D₈	1	2	yes	—
54	Dic₃₈	—	4	1	no	—
55	Dic₃₈	—	4	1	no	—
56	Dic₃₈	—	4	1	no	—
57	Dic₃₈	—	4	1	no	—
58	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₁₉⋊C₈	D₈	1	2	yes	—
61	#2251	—	19	1	no	maximal, Sylow
62	C₂²×C₁₉	—	8	1	no	—
63	C₂²×C₁₉	—	8	2	no	—
64	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
65	C₄×C₁₉	—	8	1	no	—
66	C₄×C₁₉	#127	1	1	yes	characteristic
67	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
68	Dic₁₉	—	2	2	no	—
69	Dic₁₉	—	8	1	no	—
70	Dic₁₉	—	8	1	no	—
71	C₂×Q₃₂	—	19	1	no	—
72	C₂×Q₃₂	—	19	1	no	—
73	C₂×SD₃₂	—	19	1	no	—
74	C₂×SD₃₂	D₁₉	1	1	yes	characteristic
75	#495	—	19	1	no	—
76	#494	—	19	1	no	—
77	#346	—	19	1	no	—
78	C₂×C₁₉	—	16	1	no	—
79	C₂×C₁₉	#493	1	1	yes	characteristic
80	C₂×C₁₉	#510	1	2	yes	—
81	C₂×Q₁₆	—	19	1	no	—
82	C₂×Q₁₆	—	19	1	no	—
83	C₂×Q₁₆	—	38	1	no	—
84	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic
85	C₂×SD₁₆	—	38	1	no	—
86	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
87	C₄⋊Q₈	—	38	1	no	—
88	#124	—	38	1	no	—
89	Q₃₂	—	38	2	no	—
90	Q₃₂	—	38	2	no	—
91	SD₃₂	—	2	2	no	—
92	SD₃₂	—	38	2	no	—
93	C₂×C₁₆	—	19	1	no	—
94	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
95	C₄×C₈	—	19	1	no	—
96	C₁₉	#2251	1	1	yes	characteristic, complemented, Sylow
97	C₂×Q₈	—	2	1	no	—
98	C₂×Q₈	—	38	1	no	—
99	C₂×Q₈	—	38	1	no	—
100	C₂×D₄	—	2	1	no	—
101	Q₁₆	—	2	1	no	—
102	Q₁₆	—	2	1	no	—
103	Q₁₆	—	38	1	no	—
104	Q₁₆	—	38	1	no	—
105	Q₁₆	—	38	1	no	—
106	Q₁₆	—	38	1	no	—
107	Q₁₆	—	76	2	no	—
108	SD₁₆	—	76	2	no	—
109	D₈	—	2	1	no	—
110	D₈	—	2	1	no	—
111	C₂×C₈	—	19	1	no	—
112	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
113	C₄⋊C₄	—	76	2	no	—
114	C₂²⋊C₄	—	76	2	no	—
115	C₄²	—	19	1	no	—
116	C₁₆	—	19	2	no	—
117	C₁₆	C₂²⋊D₁₉	1	2	yes	—
118	C₂³	—	4	1	no	—
119	Q₈	—	4	1	no	—
120	Q₈	—	4	1	no	—
121	Q₈	—	76	1	no	—
122	Q₈	—	76	1	no	—
123	Q₈	—	76	1	no	—
124	Q₈	—	76	1	no	—
125	D₄	—	4	1	no	—
126	D₄	—	4	1	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	—	19	2	no	—
129	C₂×C₄	—	76	1	no	—
130	C₂×C₄	—	76	1	no	—
131	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
132	C₈	—	19	2	no	—
133	C₈	D₄×D₁₉	1	1	yes	characteristic
134	C₈	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
135	C₂²	—	8	1	no	—
136	C₂²	—	8	2	no	—
137	C₂²	D₈×D₁₉	1	1	yes	characteristic
138	C₄	—	8	1	no	—
139	C₄	—	38	2	no	—
140	C₄	—	152	1	no	—
141	C₄	—	152	1	no	—
142	C₄	D₈×D₁₉	1	1	yes	characteristic
143	C₄	#10597386	1	1	yes	characteristic
144	C₂	—	16	1	no	—
145	C₂	#11926919	1	1	yes	characteristic
146	C₂	#11926983	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₁₅₂

C₂

yes

maximal, characteristic, complemented

C₂×#10597286

C₂

yes

maximal, characteristic, complemented

C₂×#10597284

C₂

yes

maximal, characteristic

#11926927

C₂

yes

maximal, characteristic

#11926922

C₂

yes

maximal, characteristic, complemented

#11926319

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×SD₃₂

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂×D₈×C₁₉

C₂²

yes

—

—

—

—

C₂×Dic₇₆

C₂²

yes

characteristic

C₂×Dic₇₆

C₂²

yes

characteristic

C₁₉×SD₃₂

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

#10597286

—

#10597284

—

C₈×Dic₁₉

C₂²

yes

characteristic

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic

Dic₁₅₂

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

#64528

—

#64526

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

Dic₇₆

—

Dic₇₆

—

Dic₇₆

—

Dic₇₆

—

C₁₆×C₁₉

D₄

yes

—

C₁₉⋊C₁₆

D₄

yes

—

C₂³×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

D₈

yes

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

C₂×D₄

yes

characteristic

C₁₉⋊C₈

D₈

yes

—

#2251

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

#127

yes

characteristic

C₄×C₁₉

C₂×D₈

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×Q₃₂

—

C₂×Q₃₂

—

C₂×SD₃₂

—

C₂×SD₃₂

D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

#493

yes

characteristic

C₂×C₁₉

#510

yes

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₁₉

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

—

#124

—

Q₃₂

—

Q₃₂

—

SD₃₂

—

SD₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

characteristic

C₄×C₈

—

C₁₉

#2251

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

100

C₂×D₄

—

101

Q₁₆

—

102

Q₁₆

—

103

Q₁₆

—

104

Q₁₆

—

105

Q₁₆

—

106

Q₁₆

—

107

Q₁₆

—

108

SD₁₆

—

109

D₈

—

110

D₈

—

111

C₂×C₈

—

112

C₂×C₈

C₂²×D₁₉

yes

characteristic

113

C₄⋊C₄

—

114

C₂²⋊C₄

—

115

C₄²

—

116

C₁₆

—

117

C₁₆

C₂²⋊D₁₉

yes

—

118

C₂³

—

119

Q₈

—

120

Q₈

—

121

Q₈

—

122

Q₈

—

123

Q₈

—

124

Q₈

—

125

D₄

—

126

D₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

D₄×D₁₉

yes

characteristic

132

C₈

—

133

C₈

D₄×D₁₉

yes

characteristic

134

C₈

C₂×C₂²⋊D₁₉

yes

characteristic

135

C₂²

—

136

C₂²

—

137

C₂²

D₈×D₁₉

yes

characteristic

138

C₄

—

139

C₄

—

140

C₄

—

152

—

141

C₄

—

152

—

142

C₄

D₈×D₁₉

yes

characteristic

143

C₄

#10597386

yes

characteristic

144

C₂

—

145

C₂

#11926919

yes

characteristic

146

C₂

#11926983

yes

—

	subgroup	G/H
center	C₂²	D₈×D₁₉
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₂×C₁₉×SD₃₂	C₂
socle	C₂²×C₁₉	C₂×D₈
prime radical	C₂×D₈×C₁₉	C₂²
hypercenter	C₂×SD₃₂	D₁₉
hypocenter	C₁₉	#2251
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×SD₃₂

subgroup

G/H

center

C₂²

D₈×D₁₉

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₂×C₁₉×SD₃₂

C₂

socle

C₂²×C₁₉

C₂×D₈

prime radical

C₂×D₈×C₁₉

C₂²

hypercenter

C₂×SD₃₂

D₁₉

hypocenter

C₁₉

#2251

LCS

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×SD₃₂

N	H ≅ G/N	type
1. C₂×Dic₁₅₂	C₂	semidirect
2. C₂×#10597286	C₂	semidirect
5. #11926922	C₂	semidirect
6. #11926319	C₂	semidirect
96. C₁₉	#2251	semidirect

H ≅ G/N

type

1. C₂×Dic₁₅₂

C₂

semidirect

2. C₂×#10597286

C₂

semidirect

5. #11926922

C₂

semidirect

6. #11926319

C₂

semidirect

96. C₁₉

#2251

semidirect

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

subgroup	index
C₂×Dic₁₅₂	2
C₂×#10597286	2
C₂×#10597284	2
#11926927	2
#11926922	2
#11926319	2
C₂×C₁₉×SD₃₂	2
#2251	19

subgroup

index

C₂×Dic₁₅₂

C₂×C₁₉×SD₃₂

Subgroups — #14565905

Conjugacy classes of subgroups

Complements

Maximal subgroups