Group #18069620 — subgroups

Subgroups — #18069620

Order 4864.

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

normal subgroups only

This group has 308 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	#14563660	C₂	1	2	yes	maximal
2	C₁₉×#2112	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597274	—	2	2	no	—
4	#11926404	—	2	2	no	—
5	#11926307	C₄	1	4	yes	complemented
6	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×M₃₂	C₄	1	2	yes	complemented
8	C₁₉×C₂²⋊C₁₆	—	2	2	no	—
9	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	—	4	2	no	—
11	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
13	C₂²×C₈×C₁₉	D₄	1	2	yes	—
14	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
15	C₂×C₂²⋊Dic₁₉	—	4	2	no	—
16	C₂×C₄⋊Dic₁₉	—	2	4	no	—
17	C₁₉×M₃₂	—	4	2	no	—
18	C₂×C₁₆×C₁₉	—	2	2	no	—
19	C₁₉⋊#95	—	4	2	no	—
20	#10597274	—	4	4	no	—
21	C₂⁴×C₁₉	D₈	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	—	4	1	no	—
23	C₂²×C₄×C₁₉	—	4	1	no	—
24	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
25	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
27	C₂²×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
28	C₂²×Dic₁₉	—	4	4	no	—
29	C₂×C₈×C₁₉	—	2	2	no	—
30	C₂×C₈×C₁₉	—	2	4	no	—
31	C₂×C₈×C₁₉	—	4	2	no	—
32	C₂×C₈×C₁₉	—	4	1	no	—
33	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
34	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
36	C₂²⋊Dic₁₉	—	8	4	no	—
37	C₄⋊Dic₁₉	—	4	4	no	—
38	C₄⋊Dic₁₉	—	4	4	no	—
39	C₁₆×C₁₉	—	4	2	no	—
40	#7233	—	19	1	no	maximal, Sylow
41	C₂³×C₁₉	—	2	4	no	—
42	C₂³×C₁₉	—	4	1	no	—
43	C₂³×C₁₉	#102	1	2	yes	—
44	C₂³×C₁₉	#107	1	1	yes	characteristic
45	C₂×C₄×C₁₉	—	2	2	no	—
46	C₂×C₄×C₁₉	—	2	1	no	—
47	C₂×C₄×C₁₉	—	2	2	no	—
48	C₂×C₄×C₁₉	—	2	1	no	—
49	C₂×C₄×C₁₉	—	4	2	no	—
50	C₂×C₄×C₁₉	—	4	1	no	—
51	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
52	C₂×C₄×C₁₉	#103	1	2	yes	—
53	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
54	C₂×Dic₁₉	—	8	4	no	—
55	C₂×Dic₁₉	—	8	4	no	—
56	C₂×Dic₁₉	—	8	4	no	—
57	C₈×C₁₉	—	2	1	no	—
58	C₈×C₁₉	—	2	2	no	—
59	C₈×C₁₉	#99	1	2	yes	—
60	#2112	D₁₉	1	1	yes	characteristic
61	#1807	—	19	2	no	—
62	C₂²×C₁₉	—	2	2	no	—
63	C₂²×C₁₉	—	2	2	no	—
64	C₂²×C₁₉	—	2	1	no	—
65	C₂²×C₁₉	—	2	2	no	—
66	C₂²×C₁₉	—	4	4	no	—
67	C₂²×C₁₉	#340	1	1	yes	characteristic
68	C₂²×C₁₉	#360	1	4	yes	—
69	C₄×C₁₉	—	2	2	no	—
70	C₄×C₁₉	—	2	1	no	—
71	C₄×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
72	C₄×C₁₉	#342	1	1	yes	characteristic
73	Dic₁₉	—	16	4	no	—
74	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
75	C₂×M₃₂	Dic₁₉	1	2	yes	complemented
76	C₂×#106	—	38	2	no	—
77	#380	—	38	2	no	—
78	C₂²⋊C₁₆	—	2	2	no	—
79	#340	—	19	4	no	—
80	C₂×C₁₉	—	2	4	no	—
81	C₂×C₁₉	—	4	1	no	—
82	C₂×C₁₉	#1289	1	1	yes	characteristic
83	C₂×C₁₉	#1386	1	2	yes	—
84	C₂³×C₄	D₇₆	1	1	yes	characteristic
85	C₂²×C₈	—	4	2	no	—
86	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
87	C₂²×C₈	C₄×D₁₉	1	2	yes	—
88	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
89	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
90	C₂×C₄⋊C₄	—	38	4	no	—
91	C₂×C₂²⋊C₄	—	76	2	no	—
92	M₃₂	—	4	2	no	—
93	C₂×C₁₆	—	2	2	no	—
94	#106	—	76	4	no	—
95	#95	—	76	2	no	—
96	C₁₉	#7233	1	1	yes	characteristic, complemented, Sylow
97	C₂⁴	D₁₅₂	1	1	yes	characteristic
98	C₂²×C₄	—	4	1	no	—
99	C₂²×C₄	—	4	1	no	—
100	C₂²×C₄	—	76	4	no	—
101	C₂²×C₄	#64516	1	2	yes	—
102	C₂²×C₄	Dic₇₆	1	1	yes	characteristic
103	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
104	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
105	C₂×C₈	—	2	4	no	—
106	C₂×C₈	—	2	2	no	—
107	C₂×C₈	—	4	1	no	—
108	C₂×C₈	—	4	2	no	—
109	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
110	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
111	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
112	C₄⋊C₄	—	76	4	no	—
113	C₄⋊C₄	—	76	4	no	—
114	C₂²⋊C₄	—	152	4	no	—
115	C₁₆	—	4	2	no	—
116	C₂³	—	2	4	no	—
117	C₂³	—	4	1	no	—
118	C₂³	#10597275	1	1	yes	characteristic
119	C₂³	#10597278	1	2	yes	—
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	4	2	no	—
125	C₂×C₄	—	4	1	no	—
126	C₂×C₄	—	152	4	no	—
127	C₂×C₄	—	152	4	no	—
128	C₂×C₄	—	152	4	no	—
129	C₂×C₄	#10597273	1	2	yes	—
130	C₂×C₄	#10597274	1	1	yes	characteristic
131	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
132	C₈	—	2	1	no	—
133	C₈	—	2	2	no	—
134	C₈	#10597291	1	2	yes	—
135	C₂²	—	2	2	no	—
136	C₂²	—	2	2	no	—
137	C₂²	—	2	2	no	—
138	C₂²	—	2	1	no	—
139	C₂²	—	4	4	no	—
140	C₂²	#11926307	1	1	yes	characteristic
141	C₂²	#11926355	1	4	yes	—
142	C₄	—	2	2	no	—
143	C₄	—	2	1	no	—
144	C₄	—	304	4	no	—
145	C₄	#11926301	1	1	yes	characteristic
146	C₄	#11926311	1	1	yes	characteristic
147	C₂	—	2	4	no	—
148	C₂	—	4	1	no	—
149	C₂	#14561503	1	1	yes	characteristic
150	C₂	#14561741	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563660

C₂

yes

maximal

C₁₉×#2112

C₂

yes

maximal, characteristic

C₂×#10597274

—

#11926404

—

#11926307

C₄

yes

complemented

C₂³×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×M₃₂

C₄

yes

complemented

C₁₉×C₂²⋊C₁₆

—

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₁₉⋊#95

—

#10597274

—

C₂⁴×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

—

C₂²×C₄×C₁₉

Q₁₆

yes

characteristic

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₁₆×C₁₉

—

#7233

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#102

yes

—

C₂³×C₁₉

#107

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#95

yes

characteristic

C₂×C₄×C₁₉

#103

yes

—

C₂×C₄×C₁₉

#106

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#99

yes

—

#2112

D₁₉

yes

characteristic

#1807

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#340

yes

characteristic

C₂²×C₁₉

#360

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂³×C₈

C₂×D₁₉

yes

characteristic

C₂×M₃₂

Dic₁₉

yes

complemented

C₂×#106

—

#380

—

C₂²⋊C₁₆

—

#340

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1289

yes

characteristic

C₂×C₁₉

#1386

yes

—

C₂³×C₄

D₇₆

yes

characteristic

C₂²×C₈

—

C₂²×C₈

Dic₃₈

yes

characteristic

C₂²×C₈

C₄×D₁₉

yes

—

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

C₂²×C₈

C₂²⋊D₁₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

M₃₂

—

C₂×C₁₆

—

#106

—

#95

—

C₁₉

#7233

yes

characteristic, complemented, Sylow

C₂⁴

D₁₅₂

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

#64516

yes

—

102

C₂²×C₄

Dic₇₆

yes

characteristic

103

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

104

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

C₄×Dic₁₉

yes

characteristic

110

C₂×C₈

Dic₁₉⋊C₄

yes

—

111

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₂²⋊C₄

—

152

—

115

C₁₆

—

116

C₂³

—

117

C₂³

—

118

C₂³

#10597275

yes

characteristic

119

C₂³

#10597278

yes

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

152

—

127

C₂×C₄

—

152

—

128

C₂×C₄

—

152

—

129

C₂×C₄

#10597273

yes

—

130

C₂×C₄

#10597274

yes

characteristic

131

C₂×C₄

C₁₉⋊#95

yes

characteristic

132

C₈

—

133

C₈

—

134

C₈

#10597291

yes

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

#11926307

yes

characteristic

141

C₂²

#11926355

yes

—

142

C₄

—

143

C₄

—

144

C₄

—

304

—

145

C₄

#11926301

yes

characteristic

146

C₄

#11926311

yes

characteristic

147

C₂

—

148

C₂

—

149

C₂

#14561503

yes

characteristic

150

C₂

#14561741

yes

—

	subgroup	G/H
center	C₂²	#11926307
commutator	C₂×C₈×C₁₉	C₄²
Frattini	C₂³×C₈	C₂×D₁₉
Fitting	C₁₉×#2112	C₂
socle	C₂²×C₁₉	#340
prime radical	C₂⁴×C₁₉	D₈
cosocle	C₂³×C₈×C₁₉	C₂²
hypercenter	#2112	D₁₉
hypocenter	C₁₉	#7233
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #2112

subgroup

G/H

center

C₂²

#11926307

commutator

C₂×C₈×C₁₉

C₄²

Frattini

C₂³×C₈

C₂×D₁₉

Fitting

C₁₉×#2112

C₂

socle

C₂²×C₁₉

#340

prime radical

C₂⁴×C₁₉

D₈

cosocle

C₂³×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #2112

N	H ≅ G/N	type
5. #11926307	C₄	semidirect
7. C₂×C₁₉×M₃₂	C₄	semidirect
75. C₂×M₃₂	Dic₁₉	semidirect
96. C₁₉	#7233	semidirect

H ≅ G/N

type

5. #11926307

C₄

semidirect

7. C₂×C₁₉×M₃₂

C₄

semidirect

75. C₂×M₃₂

Dic₁₉

semidirect

96. C₁₉

#7233

semidirect

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

subgroup	index
#14563660	2
C₁₉×#2112	2
#7233	19

subgroup

index

#14563660

C₁₉×#2112

#7233

Subgroups — #18069620

Conjugacy classes of subgroups

Complements

Maximal subgroups