Group #18069228 — subgroups

Subgroups — #18069228

Order 4864.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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	#14565128	C₂	1	1	yes	maximal, characteristic
2	#14561505	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1322	C₂	1	1	yes	maximal, characteristic
4	#11926601	—	2	1	no	—
5	C₂×#10597275	C₄	1	1	yes	characteristic
6	#11926442	—	2	1	no	—
7	#11926307	—	2	1	no	—
8	#11926307	C₄	1	1	yes	characteristic
9	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
10	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
11	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
13	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
14	C₂×C₄⋊Dic₁₉	—	2	1	no	—
15	C₂×C₄⋊Dic₁₉	—	2	1	no	—
16	C₂×Dic₁₉⋊C₄	—	4	1	no	—
17	C₂×C₁₆×C₁₉	—	4	1	no	—
18	C₁₉×C₄⋊C₈	—	4	1	no	—
19	C₁₉⋊#95	—	4	1	no	—
20	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
21	#10597275	—	4	1	no	—
22	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
23	#10597260	—	2	2	no	—
24	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
27	C₂²×Dic₁₉	—	4	1	no	—
28	C₂²×Dic₁₉	—	4	1	no	—
29	C₂×C₈×C₁₉	—	2	1	no	—
30	C₂×C₈×C₁₉	—	2	1	no	—
31	C₂×C₈×C₁₉	—	4	1	no	—
32	C₂×C₈×C₁₉	—	4	1	no	—
33	C₄²×C₁₉	—	2	1	no	—
34	C₄²×C₁₉	—	2	1	no	—
35	C₄⋊Dic₁₉	—	2	2	no	—
36	C₄⋊Dic₁₉	—	4	1	no	—
37	C₄⋊Dic₁₉	—	4	1	no	—
38	C₄⋊Dic₁₉	—	4	1	no	—
39	Dic₁₉⋊C₄	—	8	2	no	—
40	C₂×C₁₉⋊C₈	—	4	2	no	—
41	C₁₆×C₁₉	—	8	1	no	—
42	#7081	—	19	1	no	maximal, Sylow
43	C₂³×C₁₉	#102	1	1	yes	characteristic
44	C₂×C₄×C₁₉	—	2	1	no	—
45	C₂×C₄×C₁₉	—	2	1	no	—
46	C₂×C₄×C₁₉	—	2	1	no	—
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	2	1	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	4	1	no	—
51	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
52	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
53	C₂×Dic₁₉	—	4	2	no	—
54	C₂×Dic₁₉	—	8	1	no	—
55	C₂×Dic₁₉	—	8	1	no	—
56	C₂×Dic₁₉	—	8	1	no	—
57	C₂×Dic₁₉	—	8	1	no	—
58	C₂×Dic₁₉	—	8	1	no	—
59	C₈×C₁₉	—	4	1	no	—
60	C₈×C₁₉	—	4	1	no	—
61	C₁₉⋊C₈	—	8	2	no	—
62	#2087	—	19	1	no	—
63	#1322	D₁₉	1	1	yes	characteristic
64	#1290	—	19	1	no	—
65	C₂²×C₁₉	—	2	1	no	—
66	C₂²×C₁₉	—	2	1	no	—
67	C₂²×C₁₉	#327	1	1	yes	characteristic
68	C₂²×C₁₉	#359	1	1	yes	characteristic
69	C₂²×C₁₉	#362	1	1	yes	characteristic
70	C₄×C₁₉	—	2	1	no	—
71	C₄×C₁₉	—	4	1	no	—
72	C₄×C₁₉	—	4	1	no	—
73	C₄×C₁₉	#352	1	1	yes	characteristic
74	C₄×C₁₉	#356	1	1	yes	characteristic
75	Dic₁₉	—	8	2	no	—
76	Dic₁₉	—	16	1	no	—
77	#432	—	38	1	no	—
78	C₂×#107	—	19	1	no	—
79	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
80	#389	—	38	1	no	—
81	C₂²⋊C₁₆	—	2	1	no	—
82	#340	—	19	1	no	—
83	#340	—	38	1	no	—
84	C₂×C₁₉	—	2	1	no	—
85	C₂×C₁₉	—	2	1	no	—
86	C₂×C₁₉	#1339	1	1	yes	characteristic
87	C₂×C₁₉	#1346	1	1	yes	characteristic
88	C₂×C₁₉	#1350	1	1	yes	characteristic
89	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
90	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
91	C₂×C₄⋊C₄	—	38	1	no	—
92	C₂×C₄⋊C₄	—	38	1	no	—
93	C₂×C₄⋊C₄	—	76	1	no	—
94	C₂×C₄²	D₇₆	1	1	yes	characteristic
95	C₂×C₁₆	—	4	1	no	—
96	#107	—	76	1	no	—
97	C₄⋊C₈	—	4	1	no	—
98	C₄⋊C₈	—	76	1	no	—
99	C₂²⋊C₈	—	76	1	no	—
100	#97	—	38	2	no	—
101	#95	—	76	1	no	—
102	C₁₉	#7081	1	1	yes	characteristic, complemented, Sylow
103	C₂²×C₄	—	76	1	no	—
104	C₂²×C₄	—	76	1	no	—
105	C₂²×C₄	#64516	1	1	yes	characteristic
106	C₂²×C₄	D₁₅₂	1	1	yes	characteristic
107	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
108	C₂×C₈	—	2	1	no	—
109	C₂×C₈	—	2	1	no	—
110	C₂×C₈	—	4	1	no	—
111	C₂×C₈	—	4	1	no	—
112	C₂×C₈	—	76	2	no	—
113	C₄⋊C₄	—	38	2	no	—
114	C₄⋊C₄	—	76	1	no	—
115	C₄⋊C₄	—	76	1	no	—
116	C₄⋊C₄	—	76	1	no	—
117	C₄⋊C₄	—	152	2	no	—
118	C₄²	—	2	1	no	—
119	C₄²	—	2	1	no	—
120	C₁₆	—	8	1	no	—
121	C₂³	#10597278	1	1	yes	characteristic
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	2	1	no	—
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	4	1	no	—
129	C₂×C₄	—	76	2	no	—
130	C₂×C₄	—	152	1	no	—
131	C₂×C₄	—	152	1	no	—
132	C₂×C₄	—	152	1	no	—
133	C₂×C₄	—	152	1	no	—
134	C₂×C₄	—	152	1	no	—
135	C₂×C₄	#10597263	1	1	yes	characteristic
136	C₂×C₄	#10597282	1	1	yes	characteristic
137	C₈	—	4	1	no	—
138	C₈	—	4	1	no	—
139	C₈	—	152	2	no	—
140	C₂²	—	2	1	no	—
141	C₂²	—	2	1	no	—
142	C₂²	#11926279	1	1	yes	characteristic
143	C₂²	#11926352	1	1	yes	characteristic
144	C₂²	#11926361	1	1	yes	characteristic
145	C₄	—	2	1	no	—
146	C₄	—	4	1	no	—
147	C₄	—	4	1	no	—
148	C₄	—	304	1	no	—
149	C₄	—	152	2	no	—
150	C₄	#11926333	1	1	yes	characteristic
151	C₄	#11926342	1	1	yes	characteristic
152	C₂	—	2	1	no	—
153	C₂	—	2	1	no	—
154	C₂	#14561621	1	1	yes	characteristic
155	C₂	#14561642	1	1	yes	characteristic
156	C₂	#14561654	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565128

C₂

yes

maximal, characteristic

#14561505

C₂

yes

maximal, characteristic

C₁₉×#1322

C₂

yes

maximal, characteristic

#11926601

—

C₂×#10597275

C₄

yes

—

—

C₄

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×C₂²⋊C₁₆

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×Dic₁₉⋊C₄

—

C₂×C₁₆×C₁₉

—

C₁₉×C₄⋊C₈

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

#10597275

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2087

—

#1322

D₁₉

yes

characteristic

#1290

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

#432

—

C₂×#107

—

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

#389

—

C₂²⋊C₁₆

—

#340

—

#340

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

C₄×D₁₉

yes

characteristic

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

D₇₆

yes

characteristic

C₂×C₁₆

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

100

#97

—

101

#95

—

102

C₁₉

#7081

yes

characteristic, complemented, Sylow

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

#64516

yes

characteristic

106

C₂²×C₄

D₁₅₂

yes

characteristic

107

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

152

—

118

C₄²

—

119

C₄²

—

120

C₁₆

—

121

C₂³

#10597278

yes

characteristic

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

152

—

131

C₂×C₄

—

152

—

132

C₂×C₄

—

152

—

133

C₂×C₄

—

152

—

134

C₂×C₄

—

152

—

135

C₂×C₄

#10597263

yes

characteristic

136

C₂×C₄

#10597282

yes

characteristic

137

C₈

—

138

C₈

—

139

C₈

—

152

—

140

C₂²

—

141

C₂²

—

142

C₂²

#11926279

yes

characteristic

143

C₂²

#11926352

yes

characteristic

144

C₂²

#11926361

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

304

—

149

C₄

—

152

—

150

C₄

#11926333

yes

characteristic

151

C₄

#11926342

yes

characteristic

152

C₂

—

153

C₂

—

154

C₂

#14561621

yes

characteristic

155

C₂

#14561642

yes

characteristic

156

C₂

#14561654

yes

characteristic

	subgroup	G/H
center	C₂²	#11926279
commutator	C₂²×C₈×C₁₉	C₂×C₄
Frattini	C₂×C₄⋊C₈	C₂×D₁₉
Fitting	C₁₉×#1322	C₂
socle	C₂²×C₁₉	#327
prime radical	C₂³×C₁₉	#102
cosocle	C₂×C₁₉×C₄⋊C₈	C₂²
hypercenter	#1322	D₁₉
hypocenter	C₁₉	#7081
LCS	G ▷ C₂²×C₈×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #1322

subgroup

G/H

center

C₂²

#11926279

commutator

C₂²×C₈×C₁₉

C₂×C₄

Frattini

C₂×C₄⋊C₈

C₂×D₁₉

Fitting

C₁₉×#1322

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₁₉×C₄⋊C₈

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₈×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #1322

N	H ≅ G/N	type
102. C₁₉	#7081	semidirect

H ≅ G/N

type

102. C₁₉

#7081

semidirect

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

subgroup	index
#14565128	2
#14561505	2
C₁₉×#1322	2
#7081	19

subgroup

index

#14565128

#14561505

C₁₉×#1322

#7081

Subgroups — #18069228

Conjugacy classes of subgroups

Complements

Maximal subgroups