Group #18069958 — subgroups

Subgroups — #18069958

Order 4864.

178 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 47 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	#14561579	C₂	1	1	yes	maximal, characteristic
2	#14561579	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1847	C₂	1	1	yes	maximal, characteristic
4	#11926270	—	2	1	no	—
5	#11926270	—	2	1	no	—
6	C₂×C₁₉×#107	—	2	1	no	—
7	C₂×C₁₉×#106	—	2	1	no	—
8	C₂×C₁₉×#97	C₄	1	1	yes	characteristic
9	C₁₉×#384	C₄	1	1	yes	characteristic
10	C₁₉×#382	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	—	2	1	no	—
12	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
13	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
14	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
15	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₁₉×#107	—	4	2	no	—
18	C₁₉×#106	—	4	2	no	—
19	C₁₉×#97	—	2	1	no	—
20	C₁₉×#97	C₈	1	2	yes	complemented
21	C₁₉×#95	—	4	1	no	—
22	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
23	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
24	C₂²×C₄×C₁₉	—	2	1	no	—
25	C₂²×C₄×C₁₉	—	2	1	no	—
26	C₂²×C₄×C₁₉	—	2	1	no	—
27	C₂²×C₄×C₁₉	—	4	1	no	—
28	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₈×C₁₉	—	2	2	no	—
30	C₂×C₈×C₁₉	—	2	2	no	—
31	C₂×C₈×C₁₉	—	2	2	no	—
32	C₄⋊C₄×C₁₉	—	4	1	no	—
33	C₄⋊C₄×C₁₉	—	4	1	no	—
34	C₄⋊C₄×C₁₉	—	4	1	no	—
35	C₄⋊C₄×C₁₉	—	4	1	no	—
36	C₄⋊C₄×C₁₉	—	8	2	no	—
37	C₄²×C₁₉	—	2	1	no	—
38	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
39	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
40	C₂×C₁₉⋊C₈	—	8	1	no	—
41	C₂×C₁₉⋊C₈	—	8	1	no	—
42	#7372	—	19	1	no	maximal, Sylow
43	C₂³×C₁₉	#99	1	1	yes	characteristic
44	C₂×C₄×C₁₉	—	2	1	no	—
45	C₂×C₄×C₁₉	—	2	1	no	—
46	C₂×C₄×C₁₉	—	2	1	no	—
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	4	1	no	—
49	C₂×C₄×C₁₉	—	4	1	no	—
50	C₂×C₄×C₁₉	—	4	1	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	—	8	1	no	—
53	C₂×C₄×C₁₉	—	8	1	no	—
54	C₂×C₄×C₁₉	—	8	2	no	—
55	C₂×C₄×C₁₉	—	8	1	no	—
56	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
58	C₈×C₁₉	—	2	4	no	—
59	C₁₉⋊C₈	—	16	1	no	—
60	C₁₉⋊C₈	—	16	1	no	—
61	#1847	D₁₉	1	1	yes	characteristic
62	#1324	—	19	1	no	—
63	#1324	—	19	1	no	—
64	C₂²×C₁₉	—	2	1	no	—
65	C₂²×C₁₉	—	2	1	no	—
66	C₂²×C₁₉	#324	1	1	yes	characteristic
67	C₂²×C₁₉	#353	1	1	yes	characteristic
68	C₂²×C₁₉	#356	1	1	yes	characteristic
69	C₄×C₁₉	—	2	1	no	—
70	C₄×C₁₉	—	2	1	no	—
71	C₄×C₁₉	—	4	1	no	—
72	C₄×C₁₉	—	4	1	no	—
73	C₄×C₁₉	—	8	1	no	—
74	C₄×C₁₉	—	8	1	no	—
75	C₄×C₁₉	—	16	1	no	—
76	C₂×#107	—	2	1	no	—
77	C₂×#106	—	2	1	no	—
78	C₂×#97	Dic₁₉	1	1	yes	characteristic
79	#384	Dic₁₉	1	1	yes	characteristic
80	#382	C₂×D₁₉	1	1	yes	characteristic
81	#324	—	38	1	no	—
82	#324	—	38	1	no	—
83	C₂×C₁₉	—	2	1	no	—
84	C₂×C₁₉	—	2	1	no	—
85	C₂×C₁₉	#1325	1	1	yes	characteristic
86	C₂×C₁₉	#1406	1	1	yes	characteristic
87	C₂×C₁₉	#1407	1	1	yes	characteristic
88	C₂²×C₈	—	2	1	no	—
89	C₂×C₄⋊C₄	—	2	1	no	—
90	C₂×C₄⋊C₄	—	4	1	no	—
91	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
92	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
93	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
94	#107	—	4	2	no	—
95	#106	—	4	2	no	—
96	C₂²⋊C₈	—	76	1	no	—
97	C₂²⋊C₈	—	76	1	no	—
98	#97	—	2	1	no	—
99	#97	C₁₉⋊C₈	1	2	yes	complemented
100	#95	—	4	1	no	—
101	C₁₉	#7372	1	1	yes	characteristic, complemented, Sylow
102	C₂²×C₄	—	2	1	no	—
103	C₂²×C₄	—	2	1	no	—
104	C₂²×C₄	—	2	1	no	—
105	C₂²×C₄	—	4	1	no	—
106	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
107	C₂×C₈	—	2	2	no	—
108	C₂×C₈	—	2	2	no	—
109	C₂×C₈	—	2	2	no	—
110	C₂×C₈	—	152	1	no	—
111	C₂×C₈	—	152	1	no	—
112	C₄⋊C₄	—	4	1	no	—
113	C₄⋊C₄	—	4	1	no	—
114	C₄⋊C₄	—	4	1	no	—
115	C₄⋊C₄	—	4	1	no	—
116	C₄⋊C₄	—	8	2	no	—
117	C₄²	—	2	1	no	—
118	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
119	C₄²	#64520	1	1	yes	characteristic
120	C₂³	#10597291	1	1	yes	characteristic
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	4	1	no	—
126	C₂×C₄	—	4	1	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	—	4	1	no	—
129	C₂×C₄	—	8	1	no	—
130	C₂×C₄	—	8	1	no	—
131	C₂×C₄	—	8	2	no	—
132	C₂×C₄	—	8	1	no	—
133	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
134	C₂×C₄	#10597293	1	1	yes	characteristic
135	C₈	—	2	4	no	—
136	C₈	—	304	1	no	—
137	C₈	—	304	1	no	—
138	C₂²	—	2	1	no	—
139	C₂²	—	2	1	no	—
140	C₂²	#11926270	1	1	yes	characteristic
141	C₂²	#11926337	1	1	yes	characteristic
142	C₂²	#11926343	1	1	yes	characteristic
143	C₄	—	2	1	no	—
144	C₄	—	2	1	no	—
145	C₄	—	4	1	no	—
146	C₄	—	4	1	no	—
147	C₄	—	8	1	no	—
148	C₄	—	8	1	no	—
149	C₄	—	16	1	no	—
150	C₂	—	2	1	no	—
151	C₂	—	2	1	no	—
152	C₂	#14561581	1	1	yes	characteristic
153	C₂	#14561792	1	1	yes	characteristic
154	C₂	#14561795	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561579

C₂

yes

maximal, characteristic

#14561579

C₂

yes

maximal, characteristic

C₁₉×#1847

C₂

yes

maximal, characteristic

#11926270

—

#11926270

—

C₂×C₁₉×#107

—

C₂×C₁₉×#106

—

C₂×C₁₉×#97

C₄

yes

characteristic

C₁₉×#384

C₄

yes

characteristic

C₁₉×#382

C₂²

yes

characteristic

C₂²×C₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#107

—

C₁₉×#106

—

C₁₉×#97

—

C₁₉×#97

C₈

yes

complemented

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

#101

yes

characteristic

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1847

D₁₉

yes

characteristic

#1324

—

#1324

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂×#107

—

C₂×#106

—

C₂×#97

Dic₁₉

yes

characteristic

#384

Dic₁₉

yes

characteristic

#382

C₂×D₁₉

yes

characteristic

#324

—

#324

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

#107

—

#106

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

C₁₉⋊C₈

yes

complemented

100

#95

—

101

C₁₉

#7372

yes

characteristic, complemented, Sylow

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

152

—

111

C₂×C₈

—

152

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄²

—

118

C₄²

C₂×C₁₉⋊C₈

yes

characteristic

119

C₄²

#64520

yes

characteristic

120

C₂³

#10597291

yes

characteristic

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

134

C₂×C₄

#10597293

yes

characteristic

135

C₈

—

136

C₈

—

304

—

137

C₈

—

304

—

138

C₂²

—

139

C₂²

—

140

C₂²

#11926270

yes

characteristic

141

C₂²

#11926337

yes

characteristic

142

C₂²

#11926343

yes

characteristic

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₂

—

151

C₂

—

152

C₂

#14561581

yes

characteristic

153

C₂

#14561792

yes

characteristic

154

C₂

#14561795

yes

characteristic

	subgroup	G/H
center	C₂²	#11926337
commutator	C₄²×C₁₉	C₂×C₈
Frattini	#382	C₂×D₁₉
Fitting	C₁₉×#1847	C₂
socle	C₂²×C₁₉	#353
prime radical	C₂³×C₁₉	#99
cosocle	C₁₉×#382	C₂²
hypercenter	#1847	D₁₉
hypocenter	C₁₉	#7372
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #382 ◁ #1847

subgroup

G/H

center

C₂²

#11926337

commutator

C₄²×C₁₉

C₂×C₈

Frattini

#382

C₂×D₁₉

Fitting

C₁₉×#1847

C₂

C₂²×C₁₉

C₂³×C₁₉

C₁₉×#382

C₂²

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #382 ◁ #1847

N	H ≅ G/N	type
20. C₁₉×#97	C₈	semidirect
99. #97	C₁₉⋊C₈	semidirect
101. C₁₉	#7372	semidirect

H ≅ G/N

type

20. C₁₉×#97

C₈

semidirect

99. #97

C₁₉⋊C₈

semidirect

101. C₁₉

#7372

semidirect

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

subgroup	index
#14561579	2
C₁₉×#1847	2
#7372	19

subgroup

index

#14561579

C₁₉×#1847

#7372

Subgroups — #18069958

Conjugacy classes of subgroups

Complements

Maximal subgroups