Group #18076191 — subgroups

Subgroups — #18076191

Order 4864.

262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 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	#14563387	C₂	1	1	yes	maximal, characteristic
2	#14562381	C₂	1	2	yes	maximal
3	#14561479	C₂	1	2	yes	maximal
4	#14561464	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1274	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	C₂×#10597260	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	#11926299	C₄	1	2	yes	—
10	#11926299	C₄	1	2	yes	—
11	#11926296	—	2	2	no	—
12	#11926294	—	2	2	no	—
13	C₁₉×#431	C₂²	1	2	yes	—
14	C₁₉×#376	C₂²	1	1	yes	characteristic
15	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
17	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
20	C₁₉×C₄⋊C₈	—	2	2	no	—
21	C₁₉×C₂²⋊C₈	—	2	2	no	—
22	C₄×C₈×C₁₉	—	2	2	no	—
23	C₁₉×#95	—	2	2	no	—
24	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
25	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
26	#10597260	—	2	2	no	—
27	C₄×C₁₉⋊C₈	—	2	2	no	—
28	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
29	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
30	C₄×C₁₉⋊C₈	Q₈	1	2	yes	—
31	C₂²×C₄×C₁₉	—	2	2	no	—
32	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	#41	1	2	yes	—
34	C₂×C₈×C₁₉	—	4	2	no	—
35	C₄²×C₁₉	—	2	2	no	—
36	C₄²×C₁₉	—	2	2	no	—
37	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
39	C₄²×C₁₉	#41	1	2	yes	—
40	C₂×C₁₉⋊C₈	—	2	2	no	—
41	C₂×C₁₉⋊C₈	—	2	2	no	—
42	C₂×C₁₉⋊C₈	—	2	1	no	—
43	C₂×C₁₉⋊C₈	—	2	1	no	—
44	C₂×C₁₉⋊C₈	—	2	2	no	—
45	C₂×C₁₉⋊C₈	—	2	2	no	—
46	C₂×C₁₉⋊C₈	—	4	2	no	—
47	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
48	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
49	#8782	—	19	1	no	maximal, Sylow
50	C₂³×C₁₉	#117	1	1	yes	characteristic
51	C₂×C₄×C₁₉	—	4	2	no	—
52	C₂×C₄×C₁₉	—	4	4	no	—
53	C₂×C₄×C₁₉	—	4	2	no	—
54	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
56	C₂×C₄×C₁₉	#124	1	2	yes	—
57	C₂×C₄×C₁₉	#125	1	2	yes	—
58	C₂×C₄×C₁₉	#131	1	2	yes	—
59	C₂×C₄×C₁₉	#131	1	2	yes	—
60	C₈×C₁₉	—	8	2	no	—
61	C₁₉⋊C₈	—	2	2	no	—
62	C₁₉⋊C₈	—	2	2	no	—
63	C₁₉⋊C₈	—	4	1	no	—
64	C₁₉⋊C₈	—	4	1	no	—
65	C₁₉⋊C₈	—	8	2	no	—
66	#1746	—	19	1	no	—
67	#1564	—	19	2	no	—
68	#1281	—	19	2	no	—
69	#1274	—	19	1	no	—
70	#1274	D₁₉	1	1	yes	characteristic
71	C₂²×C₁₉	—	2	2	no	—
72	C₂²×C₁₉	#382	1	1	yes	characteristic
73	C₂²×C₁₉	#433	1	2	yes	—
74	C₄×C₁₉	—	2	2	no	—
75	C₄×C₁₉	—	2	2	no	—
76	C₄×C₁₉	—	8	2	no	—
77	C₄×C₁₉	#424	1	2	yes	—
78	C₄×C₁₉	#433	1	1	yes	characteristic
79	C₄×C₁₉	#433	1	1	yes	characteristic
80	#431	—	19	2	no	—
81	#431	C₂×D₁₉	1	2	yes	—
82	C₂×#97	—	19	1	no	—
83	C₂×C₄×C₈	—	19	1	no	—
84	#376	C₂×D₁₉	1	1	yes	characteristic
85	#336	—	19	2	no	—
86	#336	—	19	2	no	—
87	#335	—	38	2	no	—
88	#334	—	38	2	no	—
89	C₂×C₁₉	—	2	2	no	—
90	C₂×C₁₉	#1832	1	1	yes	characteristic
91	C₂×C₁₉	#1833	1	2	yes	—
92	C₂²×C₈	—	19	2	no	—
93	C₂²×C₈	—	19	1	no	—
94	C₂²×C₈	—	19	1	no	—
95	C₂×C₄²	C₄×D₁₉	1	2	yes	—
96	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
97	C₄⋊C₈	—	2	2	no	—
98	C₄⋊C₈	—	38	2	no	—
99	C₂²⋊C₈	—	2	2	no	—
100	C₂²⋊C₈	—	38	2	no	—
101	#97	—	38	2	no	—
102	C₄×C₈	—	2	2	no	—
103	C₄×C₈	—	19	1	no	—
104	C₄×C₈	—	19	1	no	—
105	C₄×C₈	—	19	2	no	—
106	C₄×C₈	—	38	2	no	—
107	#95	—	2	2	no	—
108	C₁₉	#8782	1	1	yes	characteristic, complemented, Sylow
109	C₂²×C₄	—	2	2	no	—
110	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
111	C₂²×C₄	#64543	1	2	yes	—
112	C₂×C₈	—	4	2	no	—
113	C₂×C₈	—	19	2	no	—
114	C₂×C₈	—	19	2	no	—
115	C₂×C₈	—	38	2	no	—
116	C₂×C₈	—	38	2	no	—
117	C₂×C₈	—	38	1	no	—
118	C₂×C₈	—	38	1	no	—
119	C₂×C₈	—	38	2	no	—
120	C₂×C₈	—	38	2	no	—
121	C₂×C₈	—	76	2	no	—
122	C₄²	—	2	2	no	—
123	C₄²	—	2	2	no	—
124	C₄²	#64541	1	2	yes	—
125	C₄²	D₄×D₁₉	1	1	yes	characteristic
126	C₄²	Q₈×D₁₉	1	1	yes	characteristic
127	C₂³	#10597323	1	1	yes	characteristic
128	C₂×C₄	—	4	2	no	—
129	C₂×C₄	—	4	4	no	—
130	C₂×C₄	—	4	2	no	—
131	C₂×C₄	#10597318	1	1	yes	characteristic
132	C₂×C₄	#10597331	1	2	yes	—
133	C₂×C₄	#10597335	1	2	yes	—
134	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
135	C₂×C₄	#10597347	1	2	yes	—
136	C₂×C₄	#10597353	1	2	yes	—
137	C₈	—	8	2	no	—
138	C₈	—	38	2	no	—
139	C₈	—	38	2	no	—
140	C₈	—	76	1	no	—
141	C₈	—	76	1	no	—
142	C₈	—	152	2	no	—
143	C₂²	—	2	2	no	—
144	C₂²	#11926408	1	1	yes	characteristic
145	C₂²	#11926602	1	2	yes	—
146	C₄	—	2	2	no	—
147	C₄	—	2	2	no	—
148	C₄	—	8	2	no	—
149	C₄	#11926569	1	2	yes	—
150	C₄	#11926603	1	1	yes	characteristic
151	C₄	#11926606	1	1	yes	characteristic
152	C₂	—	2	2	no	—
153	C₂	#14563753	1	1	yes	characteristic
154	C₂	#14563757	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563387

C₂

yes

maximal, characteristic

#14562381

C₂

yes

maximal

#14561479

C₂

yes

maximal

#14561464

C₂

yes

maximal, characteristic

C₁₉×#1274

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

C₂×#10597260

C₂²

yes

characteristic

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926299

C₄

yes

—

#11926299

C₄

yes

—

#11926296

—

#11926294

—

C₁₉×#431

C₂²

yes

—

C₁₉×#376

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

D₄

yes

characteristic

C₄×C₁₉⋊C₈

D₄

yes

characteristic

C₄×C₁₉⋊C₈

Q₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#125

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

—

—

—

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

#382

yes

characteristic

C₂²×C₁₉

#433

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#424

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₂×D₁₉

yes

—

C₂×#97

—

C₂×C₄×C₈

—

#376

C₂×D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

#1832

yes

characteristic

C₂×C₁₉

#1833

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

C₄×D₁₉

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

100

C₂²⋊C₈

—

101

#97

—

102

C₄×C₈

—

103

C₄×C₈

—

104

C₄×C₈

—

105

C₄×C₈

—

106

C₄×C₈

—

107

#95

—

108

C₁₉

#8782

yes

characteristic, complemented, Sylow

109

C₂²×C₄

—

110

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

111

C₂²×C₄

#64543

yes

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₄²

—

123

C₄²

—

124

C₄²

#64541

yes

—

125

C₄²

D₄×D₁₉

yes

characteristic

126

C₄²

Q₈×D₁₉

yes

characteristic

127

C₂³

#10597323

yes

characteristic

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

#10597318

yes

characteristic

132

C₂×C₄

#10597331

yes

—

133

C₂×C₄

#10597335

yes

—

134

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

135

C₂×C₄

#10597347

yes

—

136

C₂×C₄

#10597353

yes

—

137

C₈

—

138

C₈

—

139

C₈

—

140

C₈

—

141

C₈

—

142

C₈

—

152

—

143

C₂²

—

144

C₂²

#11926408

yes

characteristic

145

C₂²

#11926602

yes

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

#11926569

yes

—

150

C₄

#11926603

yes

characteristic

151

C₄

#11926606

yes

characteristic

152

C₂

—

153

C₂

#14563753

yes

characteristic

154

C₂

#14563757

yes

—

	subgroup	G/H
center	C₂×C₄	#10597318
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1274	C₂
socle	C₂²×C₁₉	#382
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1274	D₁₉
hypocenter	C₁₉	#8782
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #376 ◁ #1274

subgroup

G/H

center

C₂×C₄

#10597318

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1274

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ #376 ◁ #1274

N	H ≅ G/N	type
108. C₁₉	#8782	semidirect

H ≅ G/N

type

108. C₁₉

#8782

semidirect

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

subgroup	index
#14563387	2
#14562381	2
#14561479	2
#14561464	2
C₁₉×#1274	2
#8782	19

subgroup

index

C₁₉×#1274

Subgroups — #18076191

Conjugacy classes of subgroups

Complements

Maximal subgroups