Group #18070072 — subgroups

Subgroups — #18070072

Order 4864.

162 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 37 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	#14565080	C₂	1	1	yes	maximal, characteristic
2	#14561573	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1392	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597274	C₄	1	1	yes	characteristic
5	#11926545	—	2	1	no	—
6	#11926326	—	2	1	no	—
7	#11926312	—	2	1	no	—
8	#11926309	C₄	1	1	yes	characteristic
9	C₁₉×#413	—	2	1	no	—
10	C₁₉×#408	C₂²	1	1	yes	characteristic
11	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
12	C₂×M₁₆×C₁₉	—	4	1	no	—
13	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
14	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄⋊Dic₁₉	—	2	1	no	—
16	C₂×#64520	—	2	1	no	—
17	C₁₉×#101	—	4	1	no	—
18	C₁₉×#100	—	2	2	no	—
19	C₁₉×C₂²⋊C₈	—	4	1	no	—
20	#10597292	—	4	1	no	—
21	#10597289	—	4	1	no	—
22	#10597274	—	4	1	no	—
23	#10597269	—	4	1	no	—
24	#41×C₁₉	—	4	1	no	—
25	#41×C₁₉	—	4	1	no	—
26	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
27	C₂×D₄×C₁₉	—	2	1	no	—
28	C₂×D₄×C₁₉	SD₁₆	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	—	2	1	no	—
30	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×Dic₁₉	—	4	1	no	—
32	M₁₆×C₁₉	—	4	1	no	—
33	M₁₆×C₁₉	—	4	2	no	—
34	M₁₆×C₁₉	—	8	1	no	—
35	C₂×C₈×C₁₉	—	2	1	no	—
36	C₂×C₈×C₁₉	—	2	1	no	—
37	C₂×C₈×C₁₉	—	4	1	no	—
38	C₂×C₈×C₁₉	—	8	1	no	—
39	C₄⋊Dic₁₉	—	4	1	no	—
40	C₄⋊Dic₁₉	—	4	1	no	—
41	#64520	—	4	1	no	—
42	#64520	—	4	1	no	—
43	C₂×C₁₉⋊C₈	—	4	1	no	—
44	C₁₉⋊C₁₆	—	8	1	no	—
45	#7411	—	19	1	no	maximal, Sylow
46	C₂³×C₁₉	—	2	1	no	—
47	C₂³×C₁₉	#104	1	1	yes	characteristic
48	Q₈×C₁₉	—	4	1	no	—
49	D₄×C₁₉	—	4	1	no	—
50	D₄×C₁₉	—	8	1	no	—
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	2	1	no	—
54	C₂×C₄×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	—	4	1	no	—
56	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
58	C₂×Dic₁₉	—	8	1	no	—
59	C₂×Dic₁₉	—	16	1	no	—
60	C₈×C₁₉	—	4	1	no	—
61	C₈×C₁₉	—	4	1	no	—
62	C₈×C₁₉	—	8	2	no	—
63	C₁₉⋊C₈	—	8	1	no	—
64	#2079	—	19	1	no	—
65	#1392	D₁₉	1	1	yes	characteristic
66	#1321	—	19	1	no	—
67	C₂²×C₁₉	—	2	1	no	—
68	C₂²×C₁₉	—	4	1	no	—
69	C₂²×C₁₉	—	4	1	no	—
70	C₂²×C₁₉	—	8	1	no	—
71	C₂²×C₁₉	#327	1	1	yes	characteristic
72	C₄×C₁₉	—	2	1	no	—
73	C₄×C₁₉	—	4	1	no	—
74	C₄×C₁₉	#352	1	1	yes	characteristic
75	C₄×C₁₉	#354	1	1	yes	characteristic
76	Dic₁₉	—	16	1	no	—
77	C₂×#106	—	19	1	no	—
78	#417	—	38	1	no	—
79	#413	—	2	1	no	—
80	#408	C₂×D₁₉	1	1	yes	characteristic
81	#349	—	38	1	no	—
82	#343	—	38	1	no	—
83	#341	—	19	1	no	—
84	C₂×C₁₉	—	2	1	no	—
85	C₂×C₁₉	—	4	1	no	—
86	C₂×C₁₉	—	8	1	no	—
87	C₂×C₁₉	#1344	1	1	yes	characteristic
88	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
89	C₂×M₁₆	—	4	1	no	—
90	C₂×M₁₆	—	38	1	no	—
91	C₂×M₁₆	D₇₆	1	1	yes	characteristic
92	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
93	C₂×C₄⋊C₄	—	38	1	no	—
94	M₃₂	—	76	1	no	—
95	#106	—	76	1	no	—
96	#103	—	76	1	no	—
97	#102	—	76	1	no	—
98	#101	—	4	1	no	—
99	#100	—	2	2	no	—
100	C₂²⋊C₈	—	4	1	no	—
101	C₁₉	#7411	1	1	yes	characteristic, complemented, Sylow
102	#41	—	4	1	no	—
103	#41	—	4	1	no	—
104	C₂×Q₈	#64525	1	1	yes	characteristic
105	C₂×D₄	—	2	1	no	—
106	C₂×D₄	#64527	1	1	yes	characteristic
107	C₂²×C₄	—	2	1	no	—
108	C₂²×C₄	—	76	1	no	—
109	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
110	M₁₆	—	4	1	no	—
111	M₁₆	—	4	2	no	—
112	M₁₆	—	8	1	no	—
113	M₁₆	—	76	1	no	—
114	M₁₆	—	76	1	no	—
115	C₂×C₈	—	2	1	no	—
116	C₂×C₈	—	2	1	no	—
117	C₂×C₈	—	4	1	no	—
118	C₂×C₈	—	8	1	no	—
119	C₂×C₈	—	76	1	no	—
120	C₄⋊C₄	—	76	1	no	—
121	C₄⋊C₄	—	76	1	no	—
122	C₁₆	—	152	1	no	—
123	C₂³	—	2	1	no	—
124	C₂³	#10597262	1	1	yes	characteristic
125	Q₈	—	4	1	no	—
126	D₄	—	4	1	no	—
127	D₄	—	8	1	no	—
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	2	1	no	—
131	C₂×C₄	—	4	1	no	—
132	C₂×C₄	—	4	1	no	—
133	C₂×C₄	—	304	1	no	—
134	C₂×C₄	—	152	1	no	—
135	C₂×C₄	#10597263	1	1	yes	characteristic
136	C₂×C₄	#10597266	1	1	yes	characteristic
137	C₈	—	4	1	no	—
138	C₈	—	4	1	no	—
139	C₈	—	8	2	no	—
140	C₈	—	152	1	no	—
141	C₂²	—	2	1	no	—
142	C₂²	—	4	1	no	—
143	C₂²	—	4	1	no	—
144	C₂²	—	8	1	no	—
145	C₂²	#11926277	1	1	yes	characteristic
146	C₄	—	2	1	no	—
147	C₄	—	4	1	no	—
148	C₄	—	304	1	no	—
149	C₄	#11926333	1	1	yes	characteristic
150	C₄	#11926338	1	1	yes	characteristic
151	C₂	—	2	1	no	—
152	C₂	—	4	1	no	—
153	C₂	—	8	1	no	—
154	C₂	#14561634	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565080

C₂

yes

maximal, characteristic

#14561573

C₂

yes

maximal, characteristic

C₁₉×#1392

C₂

yes

maximal, characteristic

C₂×#10597274

C₄

yes

—

—

—

C₄

yes

characteristic

C₁₉×#413

—

C₁₉×#408

C₂²

yes

characteristic

C₂×#41×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×#64520

—

C₁₉×#101

—

C₁₉×#100

—

C₁₉×C₂²⋊C₈

—

—

—

—

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

D₈

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

SD₁₆

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₁₉⋊C₁₆

—

#7411

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#104

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2079

—

#1392

D₁₉

yes

characteristic

#1321

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#327

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

—

—

—

C₂×D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1344

yes

characteristic

C₂×#41

C₂²⋊D₁₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

D₇₆

yes

characteristic

C₂²×C₈

C₄×D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

M₃₂

—

—

—

—

—

—

100

C₂²⋊C₈

—

101

C₁₉

#7411

yes

characteristic, complemented, Sylow

102

#41

—

103

#41

—

104

C₂×Q₈

#64525

yes

characteristic

105

C₂×D₄

—

106

C₂×D₄

#64527

yes

characteristic

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

110

M₁₆

—

111

M₁₆

—

112

M₁₆

—

113

M₁₆

—

114

M₁₆

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₁₆

—

152

—

123

C₂³

—

124

C₂³

#10597262

yes

characteristic

125

Q₈

—

126

D₄

—

127

D₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

304

—

134

C₂×C₄

—

152

—

135

C₂×C₄

#10597263

yes

characteristic

136

C₂×C₄

#10597266

yes

characteristic

137

C₈

—

138

C₈

—

139

C₈

—

140

C₈

—

152

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

#11926277

yes

characteristic

146

C₄

—

147

C₄

—

148

C₄

—

304

—

149

C₄

#11926333

yes

characteristic

150

C₄

#11926338

yes

characteristic

151

C₂

—

152

C₂

—

153

C₂

—

154

C₂

#14561634

yes

characteristic

	subgroup	G/H
center	C₂	#14561634
commutator	C₂²×C₈×C₁₉	C₂×C₄
Frattini	#408	C₂×D₁₉
Fitting	C₁₉×#1392	C₂
socle	C₂×C₁₉	#1344
prime radical	C₂×#41×C₁₉	D₄
cosocle	C₁₉×#408	C₂²
hypercenter	#1392	D₁₉
hypocenter	C₁₉	#7411
LCS	G ▷ C₂²×C₈×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #408 ◁ #1392

subgroup

G/H

center

C₂

#14561634

commutator

C₂²×C₈×C₁₉

C₂×C₄

Frattini

#408

C₂×D₁₉

Fitting

C₁₉×#1392

C₂

socle

C₂×C₁₉

#1344

prime radical

C₂×#41×C₁₉

D₄

cosocle

C₁₉×#408

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₈×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #408 ◁ #1392

N	H ≅ G/N	type
101. C₁₉	#7411	semidirect

H ≅ G/N

type

101. C₁₉

#7411

semidirect

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

subgroup	index
#14565080	2
#14561573	2
C₁₉×#1392	2
#7411	19

subgroup

index

#14565080

#14561573

C₁₉×#1392

#7411

Subgroups — #18070072

Conjugacy classes of subgroups

Complements

Maximal subgroups