Group #18082387 — subgroups

Subgroups — #18082387

Order 4864.

542 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 191 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×#11926924	C₂	1	1	yes	maximal, characteristic
2	#14564595	C₂	1	4	yes	maximal
3	C₂×#11926265	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1844	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₇₆	—	2	2	no	—
6	C₂×#10597315	C₂²	1	2	yes	—
7	#11926924	—	2	2	no	—
8	#11926924	C₄	1	4	yes	complemented
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
10	#11926306	—	2	8	no	—
11	#11926265	—	2	2	no	—
12	C₂×C₁₉×#106	—	2	2	no	—
13	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#384	C₂²	1	2	yes	—
15	C₂²×Dic₃₈	—	2	2	no	—
16	C₂²×C₈×C₁₉	D₄	1	2	yes	—
17	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
18	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
20	C₂×C₄⋊Dic₁₉	—	2	4	no	—
21	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
22	C₂×Dic₇₆	—	2	8	no	—
23	C₂×Dic₇₆	—	4	4	no	—
24	C₂×Dic₇₆	—	4	4	no	—
25	#10597315	—	2	4	no	—
26	#10597315	—	2	2	no	—
27	#10597315	C₂×C₄	1	4	yes	—
28	C₁₉×#106	—	4	4	no	—
29	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
30	C₄×C₈×C₁₉	D₄	1	2	yes	—
31	C₄×C₁₉⋊C₈	—	2	2	no	—
32	C₄×C₁₉⋊C₈	—	2	2	no	—
33	C₂²×C₄×C₁₉	—	4	2	no	—
34	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
35	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
36	C₂²×Dic₁₉	—	4	2	no	—
37	C₂×Dic₃₈	—	2	4	no	—
38	C₂×Dic₃₈	—	4	4	no	—
39	C₂×Dic₃₈	—	4	4	no	—
40	C₂×Dic₃₈	—	4	2	no	—
41	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
42	C₂×C₈×C₁₉	D₈	1	4	yes	—
43	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
44	C₄⋊C₄×C₁₉	—	4	4	no	—
45	C₄⋊C₄×C₁₉	—	4	8	no	—
46	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
47	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₄²×C₁₉	#41	1	2	yes	—
49	C₄⋊Dic₁₉	—	2	8	no	—
50	C₄⋊Dic₁₉	—	4	4	no	—
51	C₂×C₁₉⋊C₈	—	2	4	no	—
52	C₂×C₁₉⋊C₈	—	2	8	no	—
53	Dic₇₆	—	4	16	no	—
54	#9839	—	19	1	no	maximal, Sylow
55	C₂³×C₁₉	#127	1	1	yes	characteristic
56	C₂×C₄×C₁₉	—	8	2	no	—
57	C₂×C₄×C₁₉	—	8	4	no	—
58	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
60	C₂×C₄×C₁₉	#121	1	2	yes	—
61	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
62	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
63	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
64	C₂×C₄×C₁₉	#137	1	8	yes	—
65	C₂×Dic₁₉	—	4	4	no	—
66	C₂×Dic₁₉	—	8	2	no	—
67	C₂×Dic₁₉	—	8	2	no	—
68	Dic₃₈	—	4	8	no	—
69	Dic₃₈	—	8	4	no	—
70	C₈×C₁₉	#102	1	8	yes	—
71	C₁₉⋊C₈	—	4	4	no	—
72	C₂×#494	—	19	1	no	—
73	#1990	—	19	4	no	—
74	#1844	D₁₉	1	1	yes	characteristic
75	C₂×#322	—	19	1	no	—
76	C₂²×C₁₉	#390	1	1	yes	characteristic
77	C₂²×C₁₉	#492	1	1	yes	characteristic
78	C₂²×C₁₉	#493	1	1	yes	characteristic
79	C₂²×C₁₉	#497	1	4	yes	—
80	C₄×C₁₉	—	16	2	no	—
81	C₄×C₁₉	C₂×#102	1	2	yes	—
82	C₄×C₁₉	#441	1	4	yes	—
83	C₄×C₁₉	#470	1	4	yes	—
84	C₄×C₁₉	#486	1	2	yes	—
85	Dic₁₉	—	8	4	no	—
86	C₂²×Q₁₆	—	38	2	no	—
87	C₂×C₄⋊Q₈	—	19	2	no	—
88	#494	—	19	4	no	—
89	#494	—	38	2	no	—
90	C₂×#106	—	2	2	no	—
91	C₂×C₄×C₈	—	19	2	no	—
92	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
93	#384	C₂×D₁₉	1	2	yes	—
94	#340	—	38	8	no	—
95	#322	—	38	2	no	—
96	C₂×C₁₉	#1716	1	2	yes	—
97	C₂×C₁₉	#1722	1	2	yes	—
98	C₂×C₁₉	#1957	1	1	yes	characteristic
99	C₂×C₁₉	#1971	1	2	yes	—
100	C₂²×Q₈	—	38	2	no	—
101	C₂×Q₁₆	—	38	8	no	—
102	C₂×Q₁₆	—	76	4	no	—
103	C₂×Q₁₆	—	76	4	no	—
104	C₂²×C₈	—	19	4	no	—
105	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
106	C₄⋊Q₈	—	19	4	no	—
107	C₄⋊Q₈	—	38	2	no	—
108	C₄⋊Q₈	—	38	4	no	—
109	C₂×C₄⋊C₄	—	2	4	no	—
110	C₂×C₄⋊C₄	—	2	2	no	—
111	C₂×C₄⋊C₄	—	38	4	no	—
112	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
113	#106	—	4	4	no	—
114	C₄×C₈	—	38	2	no	—
115	C₄×C₈	—	38	2	no	—
116	C₄×C₈	C₄×D₁₉	1	2	yes	—
117	C₄×C₈	D₇₆	1	2	yes	—
118	C₁₉	#9839	1	1	yes	characteristic, complemented, Sylow
119	C₂×Q₈	—	38	4	no	—
120	C₂×Q₈	—	76	2	no	—
121	C₂×Q₈	—	76	4	no	—
122	C₂×Q₈	—	76	4	no	—
123	C₂²×C₄	—	4	2	no	—
124	C₂²×C₄	—	76	2	no	—
125	C₂²×C₄	D₄×D₁₉	1	2	yes	—
126	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
127	Q₁₆	—	76	16	no	—
128	C₂×C₈	—	38	4	no	—
129	C₂×C₈	—	38	8	no	—
130	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
131	C₂×C₈	#64525	1	4	yes	—
132	C₂×C₈	#64527	1	4	yes	—
133	C₄⋊C₄	—	4	4	no	—
134	C₄⋊C₄	—	4	8	no	—
135	C₄⋊C₄	—	38	8	no	—
136	C₄⋊C₄	—	76	4	no	—
137	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
138	C₄²	C₂×D₇₆	1	1	yes	characteristic
139	C₄²	#64545	1	2	yes	—
140	C₂³	#10597386	1	1	yes	characteristic
141	Q₈	—	76	8	no	—
142	Q₈	—	152	4	no	—
143	C₂×C₄	—	8	2	no	—
144	C₂×C₄	—	8	4	no	—
145	C₂×C₄	—	76	4	no	—
146	C₂×C₄	—	152	2	no	—
147	C₂×C₄	—	152	2	no	—
148	C₂×C₄	#10597339	1	2	yes	—
149	C₂×C₄	#10597341	1	2	yes	—
150	C₂×C₄	#10597361	1	8	yes	—
151	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
152	C₂×C₄	C₂×#64525	1	2	yes	—
153	C₂×C₄	C₂×#64527	1	2	yes	—
154	C₂×C₄	#10597393	1	1	yes	characteristic
155	C₈	—	76	4	no	—
156	C₈	#10597266	1	8	yes	—
157	C₂²	#11926445	1	1	yes	characteristic
158	C₂²	#11926918	1	1	yes	characteristic
159	C₂²	#11926920	1	1	yes	characteristic
160	C₂²	#11926935	1	4	yes	—
161	C₄	—	16	2	no	—
162	C₄	—	152	4	no	—
163	C₄	C₂×#10597266	1	2	yes	—
164	C₄	#11926650	1	4	yes	—
165	C₄	#11926803	1	4	yes	—
166	C₄	#11926892	1	2	yes	—
167	C₂	#14563269	1	2	yes	—
168	C₂	#14563304	1	2	yes	—
169	C₂	#14564440	1	1	yes	characteristic
170	C₂	#14564504	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926924

C₂

yes

maximal, characteristic

#14564595

C₂

yes

maximal

C₂×#11926265

C₂

yes

maximal, characteristic

C₁₉×#1844

C₂

yes

maximal, characteristic

C₂²×Dic₇₆

—

C₂×#10597315

C₂²

yes

—

#11926924

—

#11926924

C₄

yes

complemented

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926306

—

#11926265

—

C₂×C₁₉×#106

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#384

C₂²

yes

—

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

D₄

yes

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

#10597315

—

#10597315

—

#10597315

C₂×C₄

yes

—

C₁₉×#106

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

D₈

yes

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

#102

yes

—

C₁₉⋊C₈

—

C₂×#494

—

#1990

—

#1844

D₁₉

yes

characteristic

C₂×#322

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₂×#102

yes

—

C₄×C₁₉

#441

yes

—

C₄×C₁₉

#470

yes

—

C₄×C₁₉

#486

yes

—

Dic₁₉

—

C₂²×Q₁₆

—

C₂×C₄⋊Q₈

—

#494

—

#494

—

C₂×#106

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#384

C₂×D₁₉

yes

—

#340

—

#322

—

C₂×C₁₉

#1716

yes

—

C₂×C₁₉

#1722

yes

—

C₂×C₁₉

#1957

yes

characteristic

C₂×C₁₉

#1971

yes

—

100

C₂²×Q₈

—

101

C₂×Q₁₆

—

102

C₂×Q₁₆

—

103

C₂×Q₁₆

—

104

C₂²×C₈

—

105

C₂²×C₈

C₂²⋊D₁₉

yes

—

106

C₄⋊Q₈

—

107

C₄⋊Q₈

—

108

C₄⋊Q₈

—

109

C₂×C₄⋊C₄

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄²

C₂²×D₁₉

yes

characteristic

113

#106

—

114

C₄×C₈

—

115

C₄×C₈

—

116

C₄×C₈

C₄×D₁₉

yes

—

117

C₄×C₈

D₇₆

yes

—

118

C₁₉

#9839

yes

characteristic, complemented, Sylow

119

C₂×Q₈

—

120

C₂×Q₈

—

121

C₂×Q₈

—

122

C₂×Q₈

—

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

D₄×D₁₉

yes

—

126

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

127

Q₁₆

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

131

C₂×C₈

#64525

yes

—

132

C₂×C₈

#64527

yes

—

133

C₄⋊C₄

—

134

C₄⋊C₄

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄²

C₂×C₄×D₁₉

yes

characteristic

138

C₄²

C₂×D₇₆

yes

characteristic

139

C₄²

#64545

yes

—

140

C₂³

#10597386

yes

characteristic

141

Q₈

—

142

Q₈

—

152

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

152

—

147

C₂×C₄

—

152

—

148

C₂×C₄

#10597339

yes

—

149

C₂×C₄

#10597341

yes

—

150

C₂×C₄

#10597361

yes

—

151

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

152

C₂×C₄

C₂×#64525

yes

—

153

C₂×C₄

C₂×#64527

yes

—

154

C₂×C₄

#10597393

yes

characteristic

155

C₈

—

156

C₈

#10597266

yes

—

157

C₂²

#11926445

yes

characteristic

158

C₂²

#11926918

yes

characteristic

159

C₂²

#11926920

yes

characteristic

160

C₂²

#11926935

yes

—

161

C₄

—

162

C₄

—

152

—

163

C₄

C₂×#10597266

yes

—

164

C₄

#11926650

yes

—

165

C₄

#11926803

yes

—

166

C₄

#11926892

yes

—

167

C₂

#14563269

yes

—

168

C₂

#14563304

yes

—

169

C₂

#14564440

yes

characteristic

170

C₂

#14564504

yes

—

	subgroup	G/H
center	C₂³	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1844	C₂
socle, prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1844	D₁₉
hypocenter	C₁₉	#9839
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1844

subgroup

G/H

center

C₂³

#10597386

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1844

C₂

socle, prime radical

C₂³×C₁₉

#127

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1844

N	H ≅ G/N	type
8. #11926924	C₄	semidirect
118. C₁₉	#9839	semidirect

H ≅ G/N

type

8. #11926924

C₄

semidirect

118. C₁₉

#9839

semidirect

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

subgroup	index
C₂×#11926924	2
#14564595	2
C₂×#11926265	2
C₁₉×#1844	2
#9839	19

subgroup

index

C₁₉×#1844

Subgroups — #18082387

Conjugacy classes of subgroups

Complements

Maximal subgroups