Group #18076251 — subgroups

Subgroups — #18076251

Order 4864.

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

normal subgroups only

This group has 220 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	#14562398	C₂	1	1	yes	maximal, characteristic
2	#14561927	C₂	1	1	yes	maximal, characteristic
3	#14561498	C₂	1	2	yes	maximal
4	#14561496	C₂	1	2	yes	maximal
5	C₁₉×#1568	C₂	1	1	yes	maximal, characteristic
6	#11926601	C₂²	1	2	yes	—
7	#11926597	C₂²	1	1	yes	characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	#11926297	—	2	1	no	—
10	#11926295	—	2	1	no	—
11	#11926266	C₄	1	4	yes	—
12	C₁₉×#432	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#335	—	2	1	no	—
15	C₁₉×#334	—	2	1	no	—
16	C₂²×C₈×C₁₉	Q₈	1	2	yes	—
17	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
18	C₁₉×C₄⋊C₈	—	2	2	no	—
19	C₁₉×C₂²⋊C₈	—	2	2	no	—
20	C₁₉×#97	—	2	2	no	—
21	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
22	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
25	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
26	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
27	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
28	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
29	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
30	#10597260	—	2	2	no	—
31	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
32	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
33	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
36	C₂×C₈×C₁₉	—	4	2	no	—
37	C₂×C₈×C₁₉	—	4	2	no	—
38	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
39	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
40	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₄²×C₁₉	#41	1	1	yes	characteristic
43	C₄²×C₁₉	#41	1	1	yes	characteristic
44	C₂×C₁₉⋊C₈	—	2	2	no	—
45	C₂×C₁₉⋊C₈	—	2	2	no	—
46	C₂×C₁₉⋊C₈	—	4	2	no	—
47	#8798	—	19	1	no	maximal, Sylow
48	C₂³×C₁₉	#125	1	1	yes	characteristic
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	4	1	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
54	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
55	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
56	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
58	C₈×C₁₉	—	2	2	no	—
59	C₈×C₁₉	—	2	2	no	—
60	C₈×C₁₉	—	8	2	no	—
61	C₁₉⋊C₈	—	4	2	no	—
62	C₁₉⋊C₈	—	4	2	no	—
63	C₁₉⋊C₈	—	8	2	no	—
64	#1568	—	19	1	no	—
65	#1568	D₁₉	1	1	yes	characteristic
66	#1452	—	19	1	no	—
67	#1287	—	19	2	no	—
68	#1287	—	19	2	no	—
69	C₂²×C₁₉	—	2	1	no	—
70	C₂²×C₁₉	—	2	1	no	—
71	C₂²×C₁₉	—	2	1	no	—
72	C₂²×C₁₉	#382	1	1	yes	characteristic
73	C₄×C₁₉	—	2	1	no	—
74	C₄×C₁₉	—	2	1	no	—
75	C₄×C₁₉	—	2	1	no	—
76	C₄×C₁₉	—	2	1	no	—
77	C₄×C₁₉	—	2	1	no	—
78	C₄×C₁₉	#430	1	2	yes	—
79	#432	—	19	2	no	—
80	#432	C₂×D₁₉	1	2	yes	—
81	#431	—	19	1	no	—
82	#431	—	19	1	no	—
83	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
84	#335	—	2	1	no	—
85	#335	—	38	1	no	—
86	#334	—	2	1	no	—
87	#334	—	38	1	no	—
88	#322	—	19	4	no	—
89	C₂×C₁₉	—	4	1	no	—
90	C₂×C₁₉	#1833	1	1	yes	characteristic
91	C₂×C₁₉	#1833	1	1	yes	characteristic
92	C₂×C₁₉	#1838	1	1	yes	characteristic
93	C₂²×C₈	Dic₃₈	1	2	yes	—
94	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
95	C₄⋊C₈	—	2	2	no	—
96	C₄⋊C₈	—	38	1	no	—
97	C₄⋊C₈	—	38	1	no	—
98	C₄⋊C₈	—	38	2	no	—
99	C₂²⋊C₈	—	2	2	no	—
100	C₂²⋊C₈	—	38	1	no	—
101	C₂²⋊C₈	—	38	1	no	—
102	C₂²⋊C₈	—	38	2	no	—
103	#97	—	2	2	no	—
104	#97	—	38	2	no	—
105	C₄×C₈	—	19	2	no	—
106	C₄×C₈	—	19	2	no	—
107	C₄×C₈	C₄×D₁₉	1	2	yes	—
108	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
109	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
110	C₁₉	#8798	1	1	yes	characteristic, complemented, Sylow
111	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
112	C₂²×C₄	#64543	1	1	yes	characteristic
113	C₂²×C₄	#64545	1	1	yes	characteristic
114	C₂×C₈	—	4	2	no	—
115	C₂×C₈	—	4	2	no	—
116	C₂×C₈	—	38	2	no	—
117	C₂×C₈	—	38	2	no	—
118	C₂×C₈	—	76	2	no	—
119	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
120	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
121	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
122	C₄²	#64543	1	1	yes	characteristic
123	C₄²	#64545	1	1	yes	characteristic
124	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
125	C₂³	#10597336	1	1	yes	characteristic
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	—	4	1	no	—
129	C₂×C₄	#10597336	1	1	yes	characteristic
130	C₂×C₄	#10597338	1	1	yes	characteristic
131	C₂×C₄	#10597338	1	1	yes	characteristic
132	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
133	C₂×C₄	#10597382	1	1	yes	characteristic
134	C₂×C₄	#10597393	1	1	yes	characteristic
135	C₈	—	2	2	no	—
136	C₈	—	2	2	no	—
137	C₈	—	8	2	no	—
138	C₈	—	76	2	no	—
139	C₈	—	76	2	no	—
140	C₈	—	152	2	no	—
141	C₂²	—	2	1	no	—
142	C₂²	—	2	1	no	—
143	C₂²	—	2	1	no	—
144	C₂²	#11926409	1	1	yes	characteristic
145	C₄	—	2	1	no	—
146	C₄	—	2	1	no	—
147	C₄	—	2	1	no	—
148	C₄	—	2	1	no	—
149	C₄	—	2	1	no	—
150	C₄	#11926592	1	2	yes	—
151	C₂	—	4	1	no	—
152	C₂	#14563758	1	1	yes	characteristic
153	C₂	#14563760	1	1	yes	characteristic
154	C₂	#14563775	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14562398

C₂

yes

maximal, characteristic

#14561927

C₂

yes

maximal, characteristic

#14561498

C₂

yes

maximal

#14561496

C₂

yes

maximal

C₁₉×#1568

C₂

yes

maximal, characteristic

#11926601

C₂²

yes

—

#11926597

C₂²

yes

characteristic

#11926597

C₂²

yes

—

—

C₄

yes

—

C₁₉×#432

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₁₉×#334

—

C₂²×C₈×C₁₉

Q₈

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×Q₈

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

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⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1568

—

#1568

D₁₉

yes

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#382

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#430

yes

—

#432

—

#432

C₂×D₁₉

yes

—

#431

—

#431

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

Dic₃₈

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

100

C₂²⋊C₈

—

101

C₂²⋊C₈

—

102

C₂²⋊C₈

—

103

#97

—

104

#97

—

105

C₄×C₈

—

106

C₄×C₈

—

107

C₄×C₈

C₄×D₁₉

yes

—

108

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

109

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

110

C₁₉

#8798

yes

characteristic, complemented, Sylow

111

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

112

C₂²×C₄

#64543

yes

characteristic

113

C₂²×C₄

#64545

yes

characteristic

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

Dic₁₉⋊C₄

yes

—

120

C₂×C₈

Dic₁₉⋊C₄

yes

—

121

C₄²

C₂×C₄×D₁₉

yes

characteristic

122

C₄²

#64543

yes

characteristic

123

C₄²

#64545

yes

characteristic

124

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

125

C₂³

#10597336

yes

characteristic

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

#10597336

yes

characteristic

130

C₂×C₄

#10597338

yes

characteristic

131

C₂×C₄

#10597338

yes

characteristic

132

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

133

C₂×C₄

#10597382

yes

characteristic

134

C₂×C₄

#10597393

yes

characteristic

135

C₈

—

136

C₈

—

137

C₈

—

138

C₈

—

139

C₈

—

140

C₈

—

152

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

#11926409

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

#11926592

yes

—

151

C₂

—

152

C₂

#14563758

yes

characteristic

153

C₂

#14563760

yes

characteristic

154

C₂

#14563775

yes

characteristic

	subgroup	G/H
center	C₂²	#11926409
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1568	C₂
socle	C₂²×C₁₉	#382
prime radical	C₂³×C₁₉	#125
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1568	D₁₉
hypocenter	C₁₉	#8798
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

subgroup

G/H

center

C₂²

#11926409

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1568

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

N	H ≅ G/N	type
110. C₁₉	#8798	semidirect

H ≅ G/N

type

110. C₁₉

#8798

semidirect

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

subgroup	index
#14562398	2
#14561927	2
#14561498	2
#14561496	2
C₁₉×#1568	2
#8798	19

subgroup

index

C₁₉×#1568

Subgroups — #18076251

Conjugacy classes of subgroups

Complements

Maximal subgroups