Group #14563055 — subgroups

Subgroups — #14563055

Order 2432.

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

normal subgroups only

This group has 166 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	#11926821	C₂	1	1	yes	maximal, characteristic
2	#11926746	C₂	1	1	yes	maximal, characteristic
3	C₈×D₇₆	C₂	1	1	yes	maximal, characteristic
4	#11926295	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926290	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926290	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#487	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×#64527	—	2	1	no	—
11	C₂×C₈×D₁₉	—	2	1	no	—
12	C₄×D₇₆	C₂²	1	1	yes	characteristic
13	C₁₉×#103	—	2	1	no	—
14	C₁₉×#103	—	2	1	no	—
15	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	#10597292	—	2	1	no	—
17	(C₂×D₁₉)⋊C₈	—	2	1	no	—
18	#10597266	—	2	1	no	—
19	#10597264	—	2	1	no	—
20	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₁₉	—	2	1	no	—
24	C₂×Q₈×C₁₉	—	2	1	no	—
25	C₂×D₇₆	D₄	1	1	yes	characteristic
26	C₂×C₄×D₁₉	—	2	1	no	—
27	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
29	C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	#64527	—	4	2	no	—
35	(C₂×D₁₉)⋊C₄	—	2	1	no	—
36	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
37	C₂×C₁₉⋊C₈	—	2	1	no	—
38	C₂×C₁₉⋊C₈	—	2	1	no	—
39	C₂×C₁₉⋊C₈	—	2	1	no	—
40	C₈×D₁₉	—	4	2	no	—
41	C₂²×D₁₉	—	2	1	no	—
42	Q₈×C₁₉	—	4	1	no	—
43	Q₈×C₁₉	—	4	1	no	—
44	Q₈×C₁₉	—	4	1	no	—
45	Q₈×C₁₉	—	4	1	no	—
46	C₂×C₄×C₁₉	—	4	1	no	—
47	C₂×C₄×C₁₉	—	4	1	no	—
48	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
51	C₂×Dic₁₉	—	2	1	no	—
52	D₇₆	—	2	1	no	—
53	D₇₆	SD₁₆	1	2	yes	—
54	C₄×D₁₉	—	4	1	no	—
55	C₄×D₁₉	—	4	1	no	—
56	C₈×C₁₉	—	2	1	no	—
57	C₈×C₁₉	—	2	1	no	—
58	C₁₉⋊C₈	—	4	1	no	—
59	C₁₉⋊C₈	—	4	1	no	—
60	C₁₉⋊C₈	—	4	1	no	—
61	#1679	—	19	1	no	maximal, Sylow
62	C₂²×C₁₉	#121	1	1	yes	characteristic
63	C₂×D₁₉	—	2	2	no	—
64	C₂×D₁₉	—	4	1	no	—
65	C₂×D₁₉	—	4	1	no	—
66	C₄×C₁₉	—	2	1	no	—
67	C₄×C₁₉	—	8	1	no	—
68	C₄×C₁₉	—	8	1	no	—
69	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
70	C₄×C₁₉	#135	1	1	yes	characteristic
71	C₄×C₁₉	#135	1	1	yes	characteristic
72	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
73	Dic₁₉	—	4	1	no	—
74	#487	D₁₉	1	1	yes	characteristic, complemented
75	#474	—	19	1	no	—
76	#461	—	19	1	no	—
77	C₈×D₄	—	19	1	no	—
78	#334	—	19	1	no	—
79	#332	—	19	1	no	—
80	#332	—	19	1	no	—
81	C₂×C₁₉	#463	1	1	yes	characteristic
82	C₂×C₁₉	#465	1	1	yes	characteristic
83	C₂×C₁₉	#473	1	1	yes	characteristic
84	D₁₉	—	4	2	no	—
85	C₂×SD₁₆	—	38	1	no	—
86	C₂²×C₈	—	38	1	no	—
87	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
88	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
89	C₄×D₄	—	19	1	no	—
90	#107	—	38	1	no	—
91	C₄⋊C₈	—	19	1	no	—
92	C₄⋊C₈	—	19	1	no	—
93	C₄⋊C₈	—	19	1	no	—
94	#103	—	2	1	no	—
95	#103	—	2	1	no	—
96	#103	—	38	1	no	—
97	#102	—	38	1	no	—
98	C₂²⋊C₈	—	38	1	no	—
99	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
100	C₁₉	#1679	1	1	yes	characteristic, complemented, Sylow
101	C₂×Q₈	—	2	1	no	—
102	C₂×Q₈	—	2	1	no	—
103	C₂×D₄	—	19	1	no	—
104	C₂²×C₄	—	38	1	no	—
105	SD₁₆	—	76	2	no	—
106	C₂×C₈	—	38	1	no	—
107	C₂×C₈	—	38	1	no	—
108	C₂×C₈	—	38	1	no	—
109	C₂×C₈	—	76	2	no	—
110	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
111	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
112	C₄⋊C₄	—	2	1	no	—
113	C₄⋊C₄	—	2	1	no	—
114	C₄⋊C₄	—	2	1	no	—
115	C₄⋊C₄	—	2	1	no	—
116	C₄⋊C₄	—	19	1	no	—
117	C₂²⋊C₄	—	38	1	no	—
118	C₄²	C₂²×D₁₉	1	1	yes	characteristic
119	C₂³	—	38	1	no	—
120	Q₈	—	4	1	no	—
121	Q₈	—	4	1	no	—
122	Q₈	—	4	1	no	—
123	Q₈	—	4	1	no	—
124	D₄	—	19	2	no	—
125	D₄	—	38	1	no	—
126	C₂×C₄	—	4	1	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	—	38	1	no	—
129	C₂×C₄	—	76	1	no	—
130	C₂×C₄	—	76	1	no	—
131	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
132	C₂×C₄	#64543	1	1	yes	characteristic
133	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
134	C₈	—	2	1	no	—
135	C₈	—	2	1	no	—
136	C₈	—	76	1	no	—
137	C₈	—	76	1	no	—
138	C₈	—	76	1	no	—
139	C₂²	—	38	2	no	—
140	C₂²	—	76	1	no	—
141	C₂²	—	76	1	no	—
142	C₂²	#10597384	1	1	yes	characteristic
143	C₄	—	2	1	no	—
144	C₄	—	8	1	no	—
145	C₄	—	8	1	no	—
146	C₄	—	76	1	no	—
147	C₄	SD₁₆×D₁₉	1	1	yes	characteristic
148	C₄	#10597362	1	1	yes	characteristic
149	C₄	#10597395	1	1	yes	characteristic
150	C₄	#10597396	1	1	yes	characteristic
151	C₂	—	76	2	no	—
152	C₂	#11926756	1	1	yes	characteristic
153	C₂	#11926770	1	1	yes	characteristic
154	C₂	#11926816	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926821

C₂

yes

maximal, characteristic

#11926746

C₂

yes

maximal, characteristic

C₈×D₇₆

C₂

yes

maximal, characteristic

#11926295

C₂

yes

maximal, characteristic, complemented

#11926290

C₂

yes

maximal, characteristic, complemented

#11926290

C₂

yes

maximal, characteristic, complemented

C₁₉×#487

C₂

yes

maximal, characteristic, complemented

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×#64527

—

C₂×C₈×D₁₉

—

C₄×D₇₆

C₂²

yes

characteristic

C₁₉×#103

—

C₁₉×#103

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597292

—

(C₂×D₁₉)⋊C₈

—

#10597266

—

#10597264

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₇₆

D₄

yes

characteristic

C₂×C₄×D₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

#64527

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₈×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

D₇₆

—

D₇₆

SD₁₆

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×SD₁₆

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

#487

D₁₉

yes

characteristic, complemented

#474

—

#461

—

C₈×D₄

—

#334

—

#332

—

#332

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂×SD₁₆

—

C₂²×C₈

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

C₄×D₄

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

—

—

—

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

100

C₁₉

#1679

yes

characteristic, complemented, Sylow

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×D₄

—

104

C₂²×C₄

—

105

SD₁₆

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

111

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₂²⋊C₄

—

118

C₄²

C₂²×D₁₉

yes

characteristic

119

C₂³

—

120

Q₈

—

121

Q₈

—

122

Q₈

—

123

Q₈

—

124

D₄

—

125

D₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

D₄×D₁₉

yes

characteristic

132

C₂×C₄

#64543

yes

characteristic

133

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

134

C₈

—

135

C₈

—

136

C₈

—

137

C₈

—

138

C₈

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

#10597384

yes

characteristic

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

SD₁₆×D₁₉

yes

characteristic

148

C₄

#10597362

yes

characteristic

149

C₄

#10597395

yes

characteristic

150

C₄

#10597396

yes

characteristic

151

C₂

—

152

C₂

#11926756

yes

characteristic

153

C₂

#11926770

yes

characteristic

154

C₂

#11926816

yes

characteristic

	subgroup	G/H
center	C₂²	#10597384
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#487	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂×D₇₆	D₄
hypercenter	#487	D₁₉
hypocenter	C₁₉	#1679
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #487

subgroup

G/H

center

C₂²

#10597384

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#487

C₂

socle

C₂²×C₁₉

#121

prime radical

C₂×D₇₆

D₄

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #487

N	H ≅ G/N	type
4. #11926295	C₂	semidirect
5. #11926290	C₂	semidirect
6. #11926290	C₂	semidirect
7. C₁₉×#487	C₂	semidirect
74. #487	D₁₉	semidirect
100. C₁₉	#1679	semidirect

H ≅ G/N

type

4. #11926295

C₂

semidirect

5. #11926290

C₂

semidirect

6. #11926290

C₂

semidirect

7. C₁₉×#487

C₂

semidirect

74. #487

D₁₉

semidirect

100. C₁₉

#1679

semidirect

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

subgroup	index
#11926821	2
#11926746	2
C₈×D₇₆	2
#11926295	2
#11926290	2
C₁₉×#487	2
#1679	19

subgroup

index

C₈×D₇₆

C₁₉×#487

Subgroups — #14563055

Conjugacy classes of subgroups

Complements

Maximal subgroups