Group #18081932 — subgroups

Subgroups — #18081932

Order 4864.

370 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 119 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	#14563766	C₂	1	1	yes	maximal, characteristic
2	#14562199	C₂	1	4	yes	maximal
3	#14561927	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#3160	C₂	1	1	yes	maximal, characteristic
5	#11926597	C₂²	1	2	yes	—
6	#11926410	C₂²	1	2	yes	—
7	#11926307	—	2	2	no	—
8	#11926281	—	2	8	no	—
9	#11926266	—	2	2	no	—
10	C₁₉×#533	C₂²	1	2	yes	—
11	C₁₉×#500	C₄	1	2	yes	complemented
12	C₁₉×#499	—	2	2	no	—
13	C₁₉×#498	C₄	1	2	yes	complemented
14	C₁₉×#427	—	2	2	no	—
15	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	D₄	1	2	yes	—
17	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
18	C₁₉×#125	—	2	2	no	—
19	C₁₉×C₂²⋊Q₈	—	2	4	no	—
20	C₄×Q₈×C₁₉	—	2	4	no	—
21	C₁₉×#117	—	2	2	no	—
22	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
23	C₂×C₄⋊Dic₁₉	—	2	2	no	—
24	C₁₉×#107	—	2	4	no	—
25	C₁₉×#106	—	2	4	no	—
26	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₁₉	D₄	1	2	yes	—
29	C₁₉⋊#95	—	2	4	no	—
30	C₂²⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
31	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
32	C₄×C₁₉⋊C₈	—	2	2	no	—
33	C₂×Q₈×C₁₉	—	2	4	no	—
34	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
35	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
36	C₂²×Dic₁₉	—	4	2	no	—
37	C₂×C₈×C₁₉	—	2	4	no	—
38	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
39	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
40	C₄⋊C₄×C₁₉	—	2	4	no	—
41	C₄⋊C₄×C₁₉	—	2	4	no	—
42	C₄⋊C₄×C₁₉	—	4	4	no	—
43	C₂²⋊C₄×C₁₉	—	4	2	no	—
44	C₄²×C₁₉	—	4	2	no	—
45	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
46	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₄²×C₁₉	#41	1	2	yes	—
48	C₄⋊Dic₁₉	—	4	4	no	—
49	C₂×C₁₉⋊C₈	—	2	4	no	—
50	#9759	—	19	1	no	maximal, Sylow
51	C₂³×C₁₉	#127	1	1	yes	characteristic
52	Q₈×C₁₉	—	8	4	no	—
53	C₂×C₄×C₁₉	—	4	2	no	—
54	C₂×C₄×C₁₉	—	4	4	no	—
55	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
57	C₂×C₄×C₁₉	#121	1	2	yes	—
58	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
59	C₂×C₄×C₁₉	#137	1	4	yes	—
60	C₂×Dic₁₉	—	8	4	no	—
61	C₂×Dic₁₉	—	8	2	no	—
62	C₈×C₁₉	—	2	2	no	—
63	C₈×C₁₉	—	2	2	no	—
64	C₁₉⋊C₈	—	4	4	no	—
65	#3160	D₁₉	1	1	yes	characteristic
66	#1835	—	19	1	no	—
67	#1518	—	19	4	no	—
68	#1452	—	19	1	no	—
69	C₂²×C₁₉	—	2	2	no	—
70	C₂²×C₁₉	#390	1	1	yes	characteristic
71	C₂²×C₁₉	#497	1	2	yes	—
72	C₄×C₁₉	—	2	2	no	—
73	C₄×C₁₉	—	2	2	no	—
74	C₄×C₁₉	—	8	4	no	—
75	C₄×C₁₉	#419	1	2	yes	—
76	C₄×C₁₉	#491	1	2	yes	—
77	Dic₁₉	—	16	2	no	—
78	#533	C₂×D₁₉	1	2	yes	—
79	#500	Dic₁₉	1	2	yes	complemented
80	#499	—	2	2	no	—
81	#498	Dic₁₉	1	2	yes	complemented
82	#431	—	19	2	no	—
83	#427	—	2	2	no	—
84	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
85	#382	—	19	2	no	—
86	#340	—	38	2	no	—
87	#328	—	38	8	no	—
88	#322	—	38	2	no	—
89	C₂×C₁₉	—	2	2	no	—
90	C₂×C₁₉	#1960	1	1	yes	characteristic
91	C₂×C₁₉	#1976	1	2	yes	—
92	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
93	C₄⋊Q₈	C₂×Dic₁₉	1	4	yes	—
94	#125	—	2	2	no	—
95	C₂²⋊Q₈	—	2	4	no	—
96	C₄×Q₈	—	2	4	no	—
97	#117	—	2	2	no	—
98	C₂×C₄⋊C₄	—	38	2	no	—
99	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
100	#107	—	2	4	no	—
101	#106	—	2	4	no	—
102	C₄⋊C₈	—	38	2	no	—
103	C₂²⋊C₈	—	19	4	no	—
104	C₄×C₈	—	38	2	no	—
105	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
106	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
107	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
108	#95	—	38	4	no	—
109	C₁₉	#9759	1	1	yes	characteristic, complemented, Sylow
110	C₂×Q₈	—	2	4	no	—
111	C₂²×C₄	—	76	2	no	—
112	C₂²×C₄	D₄×D₁₉	1	2	yes	—
113	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
114	C₂×C₈	—	2	4	no	—
115	C₂×C₈	—	38	4	no	—
116	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
117	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
118	C₄⋊C₄	—	2	4	no	—
119	C₄⋊C₄	—	2	4	no	—
120	C₄⋊C₄	—	4	4	no	—
121	C₄⋊C₄	—	76	4	no	—
122	C₂²⋊C₄	—	4	2	no	—
123	C₄²	—	4	2	no	—
124	C₄²	#64543	1	2	yes	—
125	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
126	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
127	C₂³	#10597386	1	1	yes	characteristic
128	Q₈	—	8	4	no	—
129	C₂×C₄	—	4	2	no	—
130	C₂×C₄	—	4	4	no	—
131	C₂×C₄	—	152	4	no	—
132	C₂×C₄	—	152	2	no	—
133	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
134	C₂×C₄	#10597382	1	1	yes	characteristic
135	C₂×C₄	#10597384	1	2	yes	—
136	C₂×C₄	#10597388	1	4	yes	—
137	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
138	C₈	—	2	2	no	—
139	C₈	—	2	2	no	—
140	C₈	—	76	4	no	—
141	C₂²	—	2	2	no	—
142	C₂²	#11926447	1	1	yes	characteristic
143	C₂²	#11926936	1	2	yes	—
144	C₄	—	2	2	no	—
145	C₄	—	2	2	no	—
146	C₄	—	8	4	no	—
147	C₄	—	304	2	no	—
148	C₄	#11926553	1	2	yes	—
149	C₄	#11926912	1	2	yes	—
150	C₂	—	2	2	no	—
151	C₂	#14564456	1	1	yes	characteristic
152	C₂	#14564534	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563766

C₂

yes

maximal, characteristic

#14562199

C₂

yes

maximal

#14561927

C₂

yes

maximal, characteristic

C₁₉×#3160

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

#11926410

C₂²

yes

—

#11926307

—

#11926281

—

#11926266

—

C₁₉×#533

C₂²

yes

—

C₁₉×#500

C₄

yes

complemented

C₁₉×#499

—

C₁₉×#498

C₄

yes

complemented

C₁₉×#427

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₁₉×#107

—

C₁₉×#106

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#3160

D₁₉

yes

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

#390

yes

characteristic

C₂²×C₁₉

#497

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#419

yes

—

C₄×C₁₉

#491

yes

—

Dic₁₉

—

#533

C₂×D₁₉

yes

—

#500

Dic₁₉

yes

complemented

#499

—

#498

Dic₁₉

yes

complemented

#431

—

#427

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

#1960

yes

characteristic

C₂×C₁₉

#1976

yes

—

C₂²×C₈

C₂²⋊D₁₉

yes

—

C₄⋊Q₈

C₂×Dic₁₉

yes

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

100

#107

—

101

#106

—

102

C₄⋊C₈

—

103

C₂²⋊C₈

—

104

C₄×C₈

—

105

C₄×C₈

C₂×Dic₁₉

yes

characteristic

106

C₄×C₈

C₂×Dic₁₉

yes

characteristic

107

C₄×C₈

C₂²⋊D₁₉

yes

—

108

#95

—

109

C₁₉

#9759

yes

characteristic, complemented, Sylow

110

C₂×Q₈

—

111

C₂²×C₄

—

112

C₂²×C₄

D₄×D₁₉

yes

—

113

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

C₂²⋊Dic₁₉

yes

—

117

C₂×C₈

C₂²⋊Dic₁₉

yes

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₂²⋊C₄

—

123

C₄²

—

124

C₄²

#64543

yes

—

125

C₄²

C₂²×Dic₁₉

yes

characteristic

126

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

127

C₂³

#10597386

yes

characteristic

128

Q₈

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

152

—

132

C₂×C₄

—

152

—

133

C₂×C₄

D₄×Dic₁₉

yes

—

134

C₂×C₄

#10597382

yes

characteristic

135

C₂×C₄

#10597384

yes

—

136

C₂×C₄

#10597388

yes

—

137

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

138

C₈

—

139

C₈

—

140

C₈

—

141

C₂²

—

142

C₂²

#11926447

yes

characteristic

143

C₂²

#11926936

yes

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

304

—

148

C₄

#11926553

yes

—

149

C₄

#11926912

yes

—

150

C₂

—

151

C₂

#14564456

yes

characteristic

152

C₂

#14564534

yes

—

	subgroup	G/H
center	C₂²	#11926447
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3160	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3160	D₁₉
hypocenter	C₁₉	#9759
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3160

subgroup

G/H

center

C₂²

#11926447

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3160

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3160

N	H ≅ G/N	type
11. C₁₉×#500	C₄	semidirect
13. C₁₉×#498	C₄	semidirect
79. #500	Dic₁₉	semidirect
81. #498	Dic₁₉	semidirect
109. C₁₉	#9759	semidirect

H ≅ G/N

type

11. C₁₉×#500

C₄

semidirect

13. C₁₉×#498

C₄

semidirect

79. #500

Dic₁₉

semidirect

81. #498

Dic₁₉

semidirect

109. C₁₉

#9759

semidirect

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

subgroup	index
#14563766	2
#14562199	2
#14561927	2
C₁₉×#3160	2
#9759	19

subgroup

index

C₁₉×#3160

Subgroups — #18081932

Conjugacy classes of subgroups

Complements

Maximal subgroups