Group #18069858 — subgroups

Subgroups — #18069858

Order 4864.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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	#14561969	C₂	1	2	yes	maximal
2	C₁₉×#1818	C₂	1	1	yes	maximal, characteristic
3	#11926601	—	2	2	no	—
4	#11926270	—	2	2	no	—
5	#11926268	C₄	1	4	yes	—
6	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×C₂²⋊C₈	C₄	1	1	yes	characteristic
8	C₂×C₁₉×C₂²⋊C₈	C₄	1	1	yes	characteristic
9	C₁₉×#336	—	2	2	no	—
10	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	—	2	1	no	—
12	C₂²×C₈×C₁₉	—	2	1	no	—
13	C₁₉×#117	—	4	1	no	—
14	C₁₉×#117	—	4	1	no	—
15	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₄⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
17	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₁₉	D₄	1	2	yes	—
19	C₁₉×C₂²⋊C₈	—	4	1	no	—
20	C₁₉×C₂²⋊C₈	—	4	1	no	—
21	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
22	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
23	#10597260	—	4	2	no	—
24	C₂⁴×C₁₉	C₄²	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	—	2	1	no	—
26	C₂²×C₄×C₁₉	—	2	1	no	—
27	C₂²×C₄×C₁₉	—	4	2	no	—
28	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
29	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
31	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₈×C₁₉	—	4	2	no	—
33	C₂×C₈×C₁₉	—	4	2	no	—
34	C₂×C₈×C₁₉	—	4	1	no	—
35	C₂×C₈×C₁₉	—	4	1	no	—
36	C₄⋊C₄×C₁₉	—	4	1	no	—
37	C₄⋊C₄×C₁₉	—	4	1	no	—
38	C₂²⋊C₄×C₁₉	—	4	2	no	—
39	C₄²×C₁₉	—	2	2	no	—
40	C₄²×C₁₉	—	2	2	no	—
41	C₂×C₁₉⋊C₈	—	4	4	no	—
42	#7325	—	19	1	no	maximal, Sylow
43	C₂³×C₁₉	—	2	1	no	—
44	C₂³×C₁₉	—	2	2	no	—
45	C₂³×C₁₉	—	4	1	no	—
46	C₂³×C₁₉	—	4	1	no	—
47	C₂³×C₁₉	#95	1	1	yes	characteristic
48	C₂×C₄×C₁₉	—	2	2	no	—
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	4	2	no	—
54	C₂×C₄×C₁₉	—	4	2	no	—
55	C₂×C₄×C₁₉	—	4	2	no	—
56	C₂×C₄×C₁₉	—	4	2	no	—
57	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
59	C₈×C₁₉	—	8	1	no	—
60	C₈×C₁₉	—	8	1	no	—
61	C₁₉⋊C₈	—	8	4	no	—
62	#1818	D₁₉	1	1	yes	characteristic
63	#1464	—	19	2	no	—
64	C₂²×C₁₉	—	2	1	no	—
65	C₂²×C₁₉	—	2	1	no	—
66	C₂²×C₁₉	—	4	1	no	—
67	C₂²×C₁₉	—	4	1	no	—
68	C₂²×C₁₉	—	4	1	no	—
69	C₂²×C₁₉	—	8	2	no	—
70	C₂²×C₁₉	#342	1	1	yes	characteristic
71	C₂²×C₁₉	#344	1	2	yes	—
72	C₄×C₁₉	—	2	1	no	—
73	C₄×C₁₉	—	2	1	no	—
74	C₄×C₁₉	—	4	1	no	—
75	C₄×C₁₉	—	4	2	no	—
76	C₄×C₁₉	—	4	2	no	—
77	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
78	#432	—	38	2	no	—
79	C₂×C₂²⋊C₈	Dic₁₉	1	1	yes	characteristic
80	C₂×C₂²⋊C₈	Dic₁₉	1	1	yes	characteristic
81	#336	—	2	2	no	—
82	#324	—	38	2	no	—
83	#323	—	19	4	no	—
84	C₂×C₁₉	—	2	2	no	—
85	C₂×C₁₉	—	8	1	no	—
86	C₂×C₁₉	#1306	1	1	yes	characteristic
87	C₂×C₁₉	#1391	1	1	yes	characteristic
88	C₂×C₁₉	#1392	1	1	yes	characteristic
89	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
90	C₂²×C₈	—	2	1	no	—
91	C₂²×C₈	—	2	1	no	—
92	#117	—	4	1	no	—
93	#117	—	4	1	no	—
94	C₂×C₄⋊C₄	Dic₃₈	1	1	yes	characteristic
95	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
96	C₂×C₂²⋊C₄	C₄×D₁₉	1	2	yes	—
97	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
98	C₄⋊C₈	—	76	2	no	—
99	C₂²⋊C₈	—	4	1	no	—
100	C₂²⋊C₈	—	4	1	no	—
101	C₂²⋊C₈	—	38	4	no	—
102	#97	—	76	2	no	—
103	C₁₉	#7325	1	1	yes	characteristic, complemented, Sylow
104	C₂⁴	C₄×Dic₁₉	1	1	yes	characteristic
105	C₂²×C₄	—	2	1	no	—
106	C₂²×C₄	—	2	1	no	—
107	C₂²×C₄	—	4	2	no	—
108	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
109	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
110	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
111	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
112	C₂×C₈	—	4	2	no	—
113	C₂×C₈	—	4	2	no	—
114	C₂×C₈	—	4	1	no	—
115	C₂×C₈	—	4	1	no	—
116	C₂×C₈	—	76	4	no	—
117	C₄⋊C₄	—	4	1	no	—
118	C₄⋊C₄	—	4	1	no	—
119	C₂²⋊C₄	—	4	2	no	—
120	C₄²	—	2	2	no	—
121	C₄²	—	2	2	no	—
122	C₂³	—	2	1	no	—
123	C₂³	—	2	2	no	—
124	C₂³	—	4	1	no	—
125	C₂³	—	4	1	no	—
126	C₂³	C₁₉⋊#95	1	1	yes	characteristic
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	2	1	no	—
131	C₂×C₄	—	2	2	no	—
132	C₂×C₄	—	4	2	no	—
133	C₂×C₄	—	4	2	no	—
134	C₂×C₄	—	4	2	no	—
135	C₂×C₄	—	4	2	no	—
136	C₂×C₄	#10597291	1	1	yes	characteristic
137	C₂×C₄	#10597291	1	1	yes	characteristic
138	C₈	—	8	1	no	—
139	C₈	—	8	1	no	—
140	C₈	—	152	4	no	—
141	C₂²	—	2	1	no	—
142	C₂²	—	2	1	no	—
143	C₂²	—	4	1	no	—
144	C₂²	—	4	1	no	—
145	C₂²	—	4	1	no	—
146	C₂²	—	8	2	no	—
147	C₂²	#11926311	1	1	yes	characteristic
148	C₂²	#11926314	1	2	yes	—
149	C₄	—	2	1	no	—
150	C₄	—	2	1	no	—
151	C₄	—	4	1	no	—
152	C₄	—	4	2	no	—
153	C₄	—	4	2	no	—
154	C₂	—	2	2	no	—
155	C₂	—	8	1	no	—
156	C₂	#14561543	1	1	yes	characteristic
157	C₂	#14561756	1	1	yes	characteristic
158	C₂	#14561758	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561969

C₂

yes

maximal

C₁₉×#1818

C₂

yes

maximal, characteristic

#11926601

—

#11926270

—

#11926268

C₄

yes

—

C₂×C₁₉×#117

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

C₄

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

C₄

yes

characteristic

C₁₉×#336

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂⁴×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

#7325

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#95

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

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

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1818

D₁₉

yes

characteristic

#1464

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#342

yes

characteristic

C₂²×C₁₉

#344

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂×#117

C₂×D₁₉

yes

characteristic

#432

—

C₂×C₂²⋊C₈

Dic₁₉

yes

characteristic

C₂×C₂²⋊C₈

Dic₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

#117

—

#117

—

C₂×C₄⋊C₄

Dic₃₈

yes

characteristic

C₂×C₄⋊C₄

D₇₆

yes

characteristic

C₂×C₂²⋊C₄

C₄×D₁₉

yes

—

C₂×C₄²

C₂²⋊D₁₉

yes

—

C₄⋊C₈

—

C₂²⋊C₈

—

100

C₂²⋊C₈

—

101

C₂²⋊C₈

—

102

#97

—

103

C₁₉

#7325

yes

characteristic, complemented, Sylow

104

C₂⁴

C₄×Dic₁₉

yes

characteristic

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

Dic₁₉⋊C₄

yes

—

109

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

110

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

111

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₂²⋊C₄

—

120

C₄²

—

121

C₄²

—

122

C₂³

—

123

C₂³

—

124

C₂³

—

125

C₂³

—

126

C₂³

C₁₉⋊#95

yes

characteristic

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

#10597291

yes

characteristic

137

C₂×C₄

#10597291

yes

characteristic

138

C₈

—

139

C₈

—

140

C₈

—

152

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

#11926311

yes

characteristic

148

C₂²

#11926314

yes

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

—

154

C₂

—

155

C₂

—

156

C₂

#14561543

yes

characteristic

157

C₂

#14561756

yes

characteristic

158

C₂

#14561758

yes

characteristic

	subgroup	G/H
center	C₂²	#11926311
commutator, prime radical	C₂⁴×C₁₉	C₄²
Frattini	C₂×#117	C₂×D₁₉
Fitting	C₁₉×#1818	C₂
socle	C₂²×C₁₉	#342
cosocle	C₂×C₁₉×#117	C₂²
hypercenter	#1818	D₁₉
hypocenter	C₁₉	#7325
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#117 ◁ #1818

subgroup

G/H

center

C₂²

#11926311

commutator, prime radical

C₂⁴×C₁₉

C₄²

Frattini

C₂×#117

C₂×D₁₉

Fitting

C₁₉×#1818

C₂

socle

C₂²×C₁₉

#342

cosocle

C₂×C₁₉×#117

C₂²

D₁₉

C₁₉

G ▷ C₂⁴×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#117 ◁ #1818

N	H ≅ G/N	type
103. C₁₉	#7325	semidirect

H ≅ G/N

type

103. C₁₉

#7325

semidirect

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

subgroup	index
#14561969	2
C₁₉×#1818	2
#7325	19

subgroup

index

#14561969

C₁₉×#1818

#7325

Subgroups — #18069858

Conjugacy classes of subgroups

Complements

Maximal subgroups