Group #18070153 — subgroups

Subgroups — #18070153

Order 4864.

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

normal subgroups only

This group has 174 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	#14565188	C₂	1	1	yes	maximal, characteristic
2	#14561561	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1391	C₂	1	1	yes	maximal, characteristic
4	#11926593	C₄	1	1	yes	characteristic, complemented
5	#11926570	—	2	1	no	—
6	#11926561	—	2	1	no	—
7	C₂²⋊(C₁₉⋊C₁₆)	—	2	1	no	—
8	#11926301	C₄	1	1	yes	characteristic, complemented
9	C₁₉×#410	—	2	1	no	—
10	C₁₉×#408	C₂²	1	1	yes	characteristic
11	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
12	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
14	C₁₉×#117	—	4	1	no	—
15	#10597372	—	2	1	no	—
16	C₂×#64520	—	2	1	no	—
17	C₁₉×#99	—	2	2	no	—
18	C₁₉×#99	—	4	1	no	—
19	C₁₉×C₂²⋊C₈	—	4	1	no	—
20	#10597294	—	4	2	no	—
21	#10597276	—	4	1	no	—
22	Dic₁₉⋊C₈	—	4	2	no	—
23	C₂×C₁₉⋊C₁₆	—	4	1	no	—
24	#41×C₁₉	—	4	1	no	—
25	#41×C₁₉	—	4	1	no	—
26	C₂×Q₈×C₁₉	Q₁₆	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	M₁₆×C₁₉	—	4	1	no	—
32	C₂×C₈×C₁₉	—	2	1	no	—
33	C₂×C₈×C₁₉	—	2	1	no	—
34	C₂×C₈×C₁₉	—	4	1	no	—
35	C₄⋊C₄×C₁₉	—	8	1	no	—
36	C₂²⋊C₄×C₁₉	—	4	2	no	—
37	C₄²×C₁₉	—	8	1	no	—
38	C₂²⋊Dic₁₉	—	4	1	no	—
39	C₄⋊Dic₁₉	—	4	1	no	—
40	C₄×Dic₁₉	—	2	2	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	#7438	—	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	—	8	2	no	—
57	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
59	C₂×Dic₁₉	—	4	2	no	—
60	C₈×C₁₉	—	4	1	no	—
61	C₈×C₁₉	—	4	1	no	—
62	C₁₉⋊C₈	—	8	1	no	—
63	#2098	—	19	1	no	—
64	#1391	D₁₉	1	1	yes	characteristic
65	#1315	—	19	1	no	—
66	C₂²×C₁₉	—	2	1	no	—
67	C₂²×C₁₉	—	4	1	no	—
68	C₂²×C₁₉	—	4	1	no	—
69	C₂²×C₁₉	—	8	1	no	—
70	C₂²×C₁₉	#328	1	1	yes	characteristic
71	C₄×C₁₉	—	2	1	no	—
72	C₄×C₁₉	—	4	1	no	—
73	C₄×C₁₉	—	16	2	no	—
74	C₄×C₁₉	#352	1	1	yes	characteristic
75	C₄×C₁₉	#353	1	1	yes	characteristic
76	Dic₁₉	—	8	2	no	—
77	#430	—	19	1	no	—
78	#424	—	38	1	no	—
79	#421	—	38	1	no	—
80	#410	—	2	1	no	—
81	#408	C₂×D₁₉	1	1	yes	characteristic
82	C₂²⋊C₁₆	—	38	1	no	—
83	H(3,ℤ/4)	—	19	1	no	—
84	C₂×C₁₉	—	2	1	no	—
85	C₂×C₁₉	—	4	1	no	—
86	C₂×C₁₉	—	8	1	no	—
87	C₂×C₁₉	#1352	1	1	yes	characteristic
88	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
89	C₂×M₁₆	—	38	1	no	—
90	C₂×M₁₆	C₄×D₁₉	1	1	yes	characteristic
91	C₂²×C₈	D₇₆	1	1	yes	characteristic
92	#117	—	4	1	no	—
93	#117	—	38	1	no	—
94	C₂×C₁₆	—	76	1	no	—
95	#108	—	76	1	no	—
96	C₄⋊C₈	—	76	2	no	—
97	#104	—	76	2	no	—
98	#99	—	2	2	no	—
99	#99	—	4	1	no	—
100	C₂²⋊C₈	—	4	1	no	—
101	C₁₉	#7438	1	1	yes	characteristic, complemented, Sylow
102	#41	—	4	1	no	—
103	#41	—	4	1	no	—
104	C₂×Q₈	#64528	1	1	yes	characteristic
105	C₂×D₄	—	2	1	no	—
106	C₂×D₄	#64526	1	1	yes	characteristic
107	C₂²×C₄	—	2	1	no	—
108	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
109	M₁₆	—	4	1	no	—
110	M₁₆	—	76	1	no	—
111	M₁₆	—	76	1	no	—
112	C₂×C₈	—	2	1	no	—
113	C₂×C₈	—	2	1	no	—
114	C₂×C₈	—	4	1	no	—
115	C₂×C₈	—	76	1	no	—
116	C₄⋊C₄	—	8	1	no	—
117	C₄⋊C₄	—	76	1	no	—
118	C₂²⋊C₄	—	4	2	no	—
119	C₂²⋊C₄	—	76	1	no	—
120	C₄²	—	8	1	no	—
121	C₄²	—	38	2	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	—	8	2	no	—
134	C₂×C₄	—	76	2	no	—
135	C₂×C₄	#10597263	1	1	yes	characteristic
136	C₂×C₄	#10597267	1	1	yes	characteristic
137	C₈	—	4	1	no	—
138	C₈	—	4	1	no	—
139	C₈	—	152	1	no	—
140	C₂²	—	2	1	no	—
141	C₂²	—	4	1	no	—
142	C₂²	—	4	1	no	—
143	C₂²	—	8	1	no	—
144	C₂²	#11926280	1	1	yes	characteristic
145	C₄	—	2	1	no	—
146	C₄	—	4	1	no	—
147	C₄	—	16	2	no	—
148	C₄	—	152	2	no	—
149	C₄	#11926333	1	1	yes	characteristic
150	C₄	#11926336	1	1	yes	characteristic
151	C₂	—	2	1	no	—
152	C₂	—	4	1	no	—
153	C₂	—	8	1	no	—
154	C₂	#14561658	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565188

C₂

yes

maximal, characteristic

#14561561

C₂

yes

maximal, characteristic

C₁₉×#1391

C₂

yes

maximal, characteristic

#11926593

C₄

yes

characteristic, complemented

#11926570

—

#11926561

—

C₂²⋊(C₁₉⋊C₁₆)

—

#11926301

C₄

yes

characteristic, complemented

C₁₉×#410

—

C₁₉×#408

C₂²

yes

characteristic

C₂×#41×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₁₉×#117

—

#10597372

—

C₂×#64520

—

C₁₉×#99

—

C₁₉×#99

—

C₁₉×C₂²⋊C₈

—

#10597294

—

#10597276

—

Dic₁₉⋊C₈

—

C₂×C₁₉⋊C₁₆

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

Q₁₆

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

SD₁₆

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₁₉⋊C₁₆

—

#7438

—

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

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2098

—

#1391

D₁₉

yes

characteristic

#1315

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#328

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

—

—

—

—

C₂×D₁₉

yes

characteristic

C₂²⋊C₁₆

—

H(3,ℤ/4)

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1352

yes

characteristic

C₂×#41

C₂²⋊D₁₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₄×D₁₉

yes

characteristic

C₂²×C₈

D₇₆

yes

characteristic

#117

—

#117

—

C₂×C₁₆

—

#108

—

C₄⋊C₈

—

#104

—

#99

—

#99

—

100

C₂²⋊C₈

—

101

C₁₉

#7438

yes

characteristic, complemented, Sylow

102

#41

—

103

#41

—

104

C₂×Q₈

#64528

yes

characteristic

105

C₂×D₄

—

106

C₂×D₄

#64526

yes

characteristic

107

C₂²×C₄

—

108

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

109

M₁₆

—

110

M₁₆

—

111

M₁₆

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₂²⋊C₄

—

119

C₂²⋊C₄

—

120

C₄²

—

121

C₄²

—

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

—

134

C₂×C₄

—

135

C₂×C₄

#10597263

yes

characteristic

136

C₂×C₄

#10597267

yes

characteristic

137

C₈

—

138

C₈

—

139

C₈

—

152

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

#11926280

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

152

—

149

C₄

#11926333

yes

characteristic

150

C₄

#11926336

yes

characteristic

151

C₂

—

152

C₂

—

153

C₂

—

154

C₂

#14561658

yes

characteristic

	subgroup	G/H
center	C₄	#11926336
commutator	C₂×M₁₆×C₁₉	C₂×C₄
Frattini	#408	C₂×D₁₉
Fitting	C₁₉×#1391	C₂
socle	C₂×C₁₉	#1352
prime radical	C₂×#41×C₁₉	D₄
cosocle	C₁₉×#408	C₂²
hypercenter	#1391	D₁₉
hypocenter	C₁₉	#7438
LCS	G ▷ C₂×M₁₆×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #408 ◁ #1391

subgroup

G/H

center

C₄

#11926336

commutator

C₂×M₁₆×C₁₉

C₂×C₄

Frattini

#408

C₂×D₁₉

Fitting

C₁₉×#1391

C₂

socle

C₂×C₁₉

#1352

prime radical

C₂×#41×C₁₉

D₄

cosocle

C₁₉×#408

C₂²

D₁₉

C₁₉

G ▷ C₂×M₁₆×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #408 ◁ #1391

N	H ≅ G/N	type
4. #11926593	C₄	semidirect
8. #11926301	C₄	semidirect
101. C₁₉	#7438	semidirect

H ≅ G/N

type

4. #11926593

C₄

semidirect

8. #11926301

C₄

semidirect

101. C₁₉

#7438

semidirect

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

subgroup	index
#14565188	2
#14561561	2
C₁₉×#1391	2
#7438	19

subgroup

index

#14565188

#14561561

C₁₉×#1391

#7438

Subgroups — #18070153

Conjugacy classes of subgroups

Complements

Maximal subgroups