Group #18076268 — subgroups

Subgroups — #18076268

Order 4864.

258 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 91 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	#14563384	C₂	1	1	yes	maximal, characteristic
2	#14561479	C₂	1	2	yes	maximal
3	#14561468	C₂	1	1	yes	maximal, characteristic
4	#14561465	C₂	1	2	yes	maximal
5	C₁₉×#1276	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	C₂×#10597260	C₂²	1	1	yes	characteristic
8	C₂×#10597260	C₂²	1	1	yes	characteristic
9	#11926299	C₄	1	2	yes	—
10	#11926299	C₄	1	2	yes	—
11	C₁₉×#431	C₂²	1	2	yes	—
12	C₄³×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₁₉	—	2	2	no	—
14	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
16	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
19	C₁₉×C₄⋊C₈	—	2	2	no	—
20	C₁₉×C₂²⋊C₈	—	2	2	no	—
21	C₄×C₈×C₁₉	—	2	2	no	—
22	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
23	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
24	#10597260	—	2	2	no	—
25	#10597260	—	2	1	no	—
26	#10597260	—	2	1	no	—
27	C₄×C₁₉⋊C₈	—	2	2	no	—
28	C₂²×C₄×C₁₉	—	2	2	no	—
29	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	#41	1	2	yes	—
31	C₂×C₈×C₁₉	—	4	2	no	—
32	C₄²×C₁₉	—	2	2	no	—
33	C₄²×C₁₉	—	2	2	no	—
34	C₄²×C₁₉	—	4	4	no	—
35	C₄²×C₁₉	#41	1	2	yes	—
36	C₄²×C₁₉	#41	1	1	yes	characteristic
37	C₄²×C₁₉	#41	1	1	yes	characteristic
38	C₂×C₁₉⋊C₈	—	2	1	no	—
39	C₂×C₁₉⋊C₈	—	2	1	no	—
40	C₂×C₁₉⋊C₈	—	2	2	no	—
41	C₂×C₁₉⋊C₈	—	2	2	no	—
42	C₂×C₁₉⋊C₈	—	2	2	no	—
43	C₂×C₁₉⋊C₈	—	2	2	no	—
44	C₂×C₁₉⋊C₈	—	2	2	no	—
45	C₂×C₁₉⋊C₈	—	4	2	no	—
46	#8802	—	19	1	no	maximal, Sylow
47	C₂³×C₁₉	#117	1	1	yes	characteristic
48	C₂×C₄×C₁₉	—	2	4	no	—
49	C₂×C₄×C₁₉	—	4	2	no	—
50	C₂×C₄×C₁₉	—	4	2	no	—
51	C₂×C₄×C₁₉	—	4	2	no	—
52	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
53	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
54	C₂×C₄×C₁₉	#126	1	2	yes	—
55	C₂×C₄×C₁₉	#126	1	2	yes	—
56	C₂×C₄×C₁₉	#131	1	2	yes	—
57	C₂×C₄×C₁₉	#131	1	2	yes	—
58	C₈×C₁₉	—	8	2	no	—
59	C₁₉⋊C₈	—	4	1	no	—
60	C₁₉⋊C₈	—	4	2	no	—
61	C₁₉⋊C₈	—	4	1	no	—
62	C₁₉⋊C₈	—	8	2	no	—
63	#1745	—	19	1	no	—
64	#1281	—	19	2	no	—
65	#1276	—	19	1	no	—
66	#1276	D₁₉	1	1	yes	characteristic
67	#1275	—	19	2	no	—
68	C₂²×C₁₉	—	2	2	no	—
69	C₂²×C₁₉	#383	1	1	yes	characteristic
70	C₂²×C₁₉	#433	1	2	yes	—
71	C₄×C₁₉	—	2	2	no	—
72	C₄×C₁₉	—	2	2	no	—
73	C₄×C₁₉	—	4	4	no	—
74	C₄×C₁₉	#433	1	1	yes	characteristic
75	C₄×C₁₉	#433	1	2	yes	—
76	C₄×C₁₉	#433	1	1	yes	characteristic
77	#431	—	19	2	no	—
78	#431	C₂×D₁₉	1	2	yes	—
79	C₂×#97	—	19	1	no	—
80	C₂×#97	—	19	1	no	—
81	C₄³	C₂×D₁₉	1	1	yes	characteristic
82	#336	—	19	2	no	—
83	#336	—	19	2	no	—
84	C₂×C₁₉	—	2	2	no	—
85	C₂×C₁₉	#1840	1	1	yes	characteristic
86	C₂×C₁₉	#1841	1	2	yes	—
87	C₂²×C₈	—	19	1	no	—
88	C₂²×C₈	—	19	1	no	—
89	C₂²×C₈	—	19	2	no	—
90	C₂×C₄²	—	2	2	no	—
91	C₂×C₄²	C₄×D₁₉	1	2	yes	—
92	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
93	C₄⋊C₈	—	2	2	no	—
94	C₄⋊C₈	—	38	2	no	—
95	C₂²⋊C₈	—	2	2	no	—
96	C₂²⋊C₈	—	38	2	no	—
97	#97	—	38	2	no	—
98	#97	—	38	1	no	—
99	#97	—	38	1	no	—
100	C₄×C₈	—	2	2	no	—
101	C₄×C₈	—	38	2	no	—
102	C₁₉	#8802	1	1	yes	characteristic, complemented, Sylow
103	C₂²×C₄	—	2	2	no	—
104	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
105	C₂²×C₄	#64543	1	2	yes	—
106	C₂×C₈	—	4	2	no	—
107	C₂×C₈	—	38	1	no	—
108	C₂×C₈	—	38	1	no	—
109	C₂×C₈	—	38	2	no	—
110	C₂×C₈	—	38	2	no	—
111	C₂×C₈	—	38	2	no	—
112	C₂×C₈	—	38	2	no	—
113	C₂×C₈	—	38	2	no	—
114	C₂×C₈	—	76	2	no	—
115	C₄²	—	2	2	no	—
116	C₄²	—	2	2	no	—
117	C₄²	—	4	4	no	—
118	C₄²	#64541	1	2	yes	—
119	C₄²	#64543	1	1	yes	characteristic
120	C₄²	#64545	1	1	yes	characteristic
121	C₂³	#10597323	1	1	yes	characteristic
122	C₂×C₄	—	2	4	no	—
123	C₂×C₄	—	4	2	no	—
124	C₂×C₄	—	4	2	no	—
125	C₂×C₄	—	4	2	no	—
126	C₂×C₄	#10597318	1	1	yes	characteristic
127	C₂×C₄	#10597325	1	2	yes	—
128	C₂×C₄	#10597338	1	1	yes	characteristic
129	C₂×C₄	#10597344	1	2	yes	—
130	C₂×C₄	#10597347	1	2	yes	—
131	C₂×C₄	#10597353	1	2	yes	—
132	C₈	—	8	2	no	—
133	C₈	—	76	1	no	—
134	C₈	—	76	2	no	—
135	C₈	—	76	1	no	—
136	C₈	—	152	2	no	—
137	C₂²	—	2	2	no	—
138	C₂²	#11926411	1	1	yes	characteristic
139	C₂²	#11926602	1	2	yes	—
140	C₄	—	2	2	no	—
141	C₄	—	2	2	no	—
142	C₄	—	4	4	no	—
143	C₄	#11926603	1	1	yes	characteristic
144	C₄	#11926604	1	2	yes	—
145	C₄	#11926606	1	1	yes	characteristic
146	C₂	—	2	2	no	—
147	C₂	#14563779	1	1	yes	characteristic
148	C₂	#14563781	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563384

C₂

yes

maximal, characteristic

#14561479

C₂

yes

maximal

#14561468

C₂

yes

maximal, characteristic

#14561465

C₂

yes

maximal

C₁₉×#1276

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

C₂×#10597260

C₂²

yes

characteristic

C₂×#10597260

C₂²

yes

characteristic

#11926299

C₄

yes

—

#11926299

C₄

yes

—

C₁₉×#431

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

—

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

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

yes

C₄²×C₁₉

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

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#126

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

—

—

D₁₉

yes

characteristic

#1275

—

C₂²×C₁₉

—

C₂²×C₁₉

#383

yes

characteristic

C₂²×C₁₉

#433

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#433

yes

characteristic

C₄×C₁₉

#433

yes

—

C₄×C₁₉

yes

—

C₂×D₁₉

yes

—

C₂×#97

—

C₂×#97

—

C₄³

C₂×D₁₉

yes

characteristic

#336

—

#336

—

C₂×C₁₉

—

C₂×C₁₉

#1840

yes

characteristic

C₂×C₁₉

#1841

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

C₄×D₁₉

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

#97

—

100

C₄×C₈

—

101

C₄×C₈

—

102

C₁₉

#8802

yes

characteristic, complemented, Sylow

103

C₂²×C₄

—

104

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

105

C₂²×C₄

#64543

yes

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₄²

—

116

C₄²

—

117

C₄²

—

118

C₄²

#64541

yes

—

119

C₄²

#64543

yes

characteristic

120

C₄²

#64545

yes

characteristic

121

C₂³

#10597323

yes

characteristic

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

#10597318

yes

characteristic

127

C₂×C₄

#10597325

yes

—

128

C₂×C₄

#10597338

yes

characteristic

129

C₂×C₄

#10597344

yes

—

130

C₂×C₄

#10597347

yes

—

131

C₂×C₄

#10597353

yes

—

132

C₈

—

133

C₈

—

134

C₈

—

135

C₈

—

136

C₈

—

152

—

137

C₂²

—

138

C₂²

#11926411

yes

characteristic

139

C₂²

#11926602

yes

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

#11926603

yes

characteristic

144

C₄

#11926604

yes

—

145

C₄

#11926606

yes

characteristic

146

C₂

—

147

C₂

#14563779

yes

characteristic

148

C₂

#14563781

yes

—

	subgroup	G/H
center	C₂×C₄	#10597338
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1276	C₂
socle	C₂²×C₁₉	#383
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1276	D₁₉
hypocenter	C₁₉	#8802
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1276

subgroup

G/H

center

C₂×C₄

#10597338

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1276

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1276

N	H ≅ G/N	type
102. C₁₉	#8802	semidirect

H ≅ G/N

type

102. C₁₉

#8802

semidirect

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

subgroup	index
#14563384	2
#14561479	2
#14561468	2
#14561465	2
C₁₉×#1276	2
#8802	19

subgroup

index

C₁₉×#1276

Subgroups — #18076268

Conjugacy classes of subgroups

Complements

Maximal subgroups