Group #18081931 — subgroups

Subgroups — #18081931

Order 4864.

370 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 115 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	#14574149	C₂	1	1	yes	maximal, characteristic
2	#14563766	C₂	1	1	yes	maximal, characteristic
3	#14562200	C₂	1	4	yes	maximal
4	C₁₉×#1452	C₂	1	1	yes	maximal, characteristic
5	#11927101	C₂²	1	2	yes	—
6	#11926949	C₄	1	2	yes	complemented
7	#11926946	—	2	2	no	—
8	#11926942	C₄	1	2	yes	complemented
9	#11926582	—	2	2	no	—
10	#11926410	C₂²	1	2	yes	—
11	#11926307	—	2	2	no	—
12	#11926282	—	2	8	no	—
13	C₁₉×#431	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#322	—	2	2	no	—
16	C₂²×C₈×C₁₉	D₄	1	2	yes	—
17	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
18	#10597372	—	2	2	no	—
19	C₂×C₄⋊Dic₁₉	—	2	2	no	—
20	#10597370	—	2	4	no	—
21	#10597316	—	2	2	no	—
22	#10597315	C₂×C₄	1	4	yes	—
23	C₄×Dic₃₈	—	2	4	no	—
24	C₁₉×C₄⋊C₈	—	2	2	no	—
25	C₁₉×C₂²⋊C₈	D₄	1	4	yes	—
26	C₄×C₈×C₁₉	—	2	2	no	—
27	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₄×C₈×C₁₉	D₄	1	2	yes	—
30	C₁₉⋊#95	—	2	4	no	—
31	#10597275	—	2	4	no	—
32	#10597274	—	2	4	no	—
33	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
34	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
35	C₂²×Dic₁₉	—	4	2	no	—
36	C₂×Dic₃₈	—	2	4	no	—
37	C₂×C₈×C₁₉	—	2	4	no	—
38	C₂×C₈×C₁₉	—	2	4	no	—
39	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
40	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
41	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
42	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₄²×C₁₉	#41	1	2	yes	—
44	C₂²⋊Dic₁₉	—	4	2	no	—
45	C₄⋊Dic₁₉	—	2	4	no	—
46	C₄⋊Dic₁₉	—	2	4	no	—
47	C₄⋊Dic₁₉	—	4	4	no	—
48	Dic₁₉⋊C₄	—	4	4	no	—
49	C₄×Dic₁₉	—	4	2	no	—
50	#9759	—	19	1	no	maximal, Sylow
51	C₂³×C₁₉	#127	1	1	yes	characteristic
52	C₂×C₄×C₁₉	—	4	2	no	—
53	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
54	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
55	C₂×C₄×C₁₉	#121	1	2	yes	—
56	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#137	1	4	yes	—
58	C₂×Dic₁₉	—	4	4	no	—
59	C₂×Dic₁₉	—	8	4	no	—
60	C₂×Dic₁₉	—	8	2	no	—
61	Dic₃₈	—	8	4	no	—
62	C₈×C₁₉	—	2	2	no	—
63	C₈×C₁₉	—	2	2	no	—
64	C₈×C₁₉	—	4	4	no	—
65	#3160	—	19	1	no	—
66	#1835	—	19	1	no	—
67	#1518	—	19	4	no	—
68	#1452	D₁₉	1	1	yes	characteristic
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	#419	1	2	yes	—
75	C₄×C₁₉	#491	1	2	yes	—
76	Dic₁₉	—	8	4	no	—
77	Dic₁₉	—	16	2	no	—
78	#533	—	19	2	no	—
79	#500	—	19	2	no	—
80	#499	—	38	2	no	—
81	#498	—	19	2	no	—
82	#431	C₂×D₁₉	1	2	yes	—
83	#427	—	38	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	—	2	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	D₇₆	1	2	yes	—
93	C₄⋊Q₈	—	19	4	no	—
94	#125	—	38	2	no	—
95	C₂²⋊Q₈	—	38	4	no	—
96	C₄×Q₈	—	38	4	no	—
97	#117	—	38	2	no	—
98	C₂×C₄⋊C₄	—	38	2	no	—
99	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
100	#107	—	38	4	no	—
101	#106	—	38	4	no	—
102	C₄⋊C₈	—	2	2	no	—
103	C₂²⋊C₈	D₇₆	1	4	yes	—
104	C₄×C₈	—	2	2	no	—
105	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
106	C₄×C₈	C₄×D₁₉	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	—	38	4	no	—
111	C₂²×C₄	—	76	2	no	—
112	C₂²×C₄	C₂×D₇₆	1	2	yes	—
113	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
114	C₂×C₈	—	2	4	no	—
115	C₂×C₈	—	2	4	no	—
116	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
117	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
118	C₄⋊C₄	—	38	4	no	—
119	C₄⋊C₄	—	38	4	no	—
120	C₄⋊C₄	—	76	4	no	—
121	C₄⋊C₄	—	76	4	no	—
122	C₂²⋊C₄	—	76	2	no	—
123	C₄²	—	76	2	no	—
124	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
125	C₄²	#64541	1	2	yes	—
126	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
127	C₂³	#10597320	1	1	yes	characteristic
128	Q₈	—	152	4	no	—
129	C₂×C₄	—	4	2	no	—
130	C₂×C₄	—	76	4	no	—
131	C₂×C₄	—	152	4	no	—
132	C₂×C₄	—	152	2	no	—
133	C₂×C₄	C₄×D₇₆	1	2	yes	—
134	C₂×C₄	#10597321	1	1	yes	characteristic
135	C₂×C₄	#10597355	1	4	yes	—
136	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
137	C₂×C₄	#10597376	1	2	yes	—
138	C₈	—	2	2	no	—
139	C₈	—	2	2	no	—
140	C₈	—	4	4	no	—
141	C₂²	—	2	2	no	—
142	C₂²	#11926446	1	1	yes	characteristic
143	C₂²	#11926938	1	2	yes	—
144	C₄	—	2	2	no	—
145	C₄	—	2	2	no	—
146	C₄	—	304	2	no	—
147	C₄	—	152	4	no	—
148	C₄	#11926554	1	2	yes	—
149	C₄	#11926913	1	2	yes	—
150	C₂	—	2	2	no	—
151	C₂	#14564455	1	1	yes	characteristic
152	C₂	#14564533	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14574149

C₂

yes

maximal, characteristic

#14563766

C₂

yes

maximal, characteristic

#14562200

C₂

yes

maximal

C₁₉×#1452

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

—

#11926949

C₄

yes

complemented

#11926946

—

#11926942

C₄

yes

complemented

#11926582

—

#11926410

C₂²

yes

—

#11926307

—

#11926282

—

C₁₉×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597372

—

C₂×C₄⋊Dic₁₉

—

#10597370

—

#10597316

—

#10597315

C₂×C₄

yes

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

D₄

yes

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

—

C₁₉⋊#95

—

#10597275

—

#10597274

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

—

C₂³×C₁₉

yes

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

—

C₂×Dic₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

—

—

—

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

#390

yes

characteristic

C₂²×C₁₉

#497

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#419

yes

—

C₄×C₁₉

#491

yes

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

C₂×D₁₉

yes

—

#427

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

#1960

yes

characteristic

C₂×C₁₉

#1976

yes

—

C₂²×C₈

D₇₆

yes

—

C₄⋊Q₈

—

#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

D₇₆

yes

—

104

C₄×C₈

—

105

C₄×C₈

C₄×D₁₉

yes

characteristic

106

C₄×C₈

C₄×D₁₉

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

C₂×D₇₆

yes

—

113

C₂²×C₄

C₂×D₇₆

yes

characteristic

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

117

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₂²⋊C₄

—

123

C₄²

—

124

C₄²

C₂×C₄×D₁₉

yes

characteristic

125

C₄²

#64541

yes

—

126

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

127

C₂³

#10597320

yes

characteristic

128

Q₈

—

152

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

152

—

132

C₂×C₄

—

152

—

133

C₂×C₄

C₄×D₇₆

yes

—

134

C₂×C₄

#10597321

yes

characteristic

135

C₂×C₄

#10597355

yes

—

136

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

137

C₂×C₄

#10597376

yes

—

138

C₈

—

139

C₈

—

140

C₈

—

141

C₂²

—

142

C₂²

#11926446

yes

characteristic

143

C₂²

#11926938

yes

—

144

C₄

—

145

C₄

—

146

C₄

—

304

—

147

C₄

—

152

—

148

C₄

#11926554

yes

—

149

C₄

#11926913

yes

—

150

C₂

—

151

C₂

#14564455

yes

characteristic

152

C₂

#14564533

yes

—

	subgroup	G/H
center	C₂²	#11926446
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1452	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1452	D₁₉
hypocenter	C₁₉	#9759
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1452

subgroup

G/H

center

C₂²

#11926446

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1452

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1452

N	H ≅ G/N	type
6. #11926949	C₄	semidirect
8. #11926942	C₄	semidirect
109. C₁₉	#9759	semidirect

H ≅ G/N

type

6. #11926949

C₄

semidirect

8. #11926942

C₄

semidirect

109. C₁₉

#9759

semidirect

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

subgroup	index
#14574149	2
#14563766	2
#14562200	2
C₁₉×#1452	2
#9759	19

subgroup

index

C₁₉×#1452

Subgroups — #18081931

Conjugacy classes of subgroups

Complements

Maximal subgroups