Group #18071906 — subgroups

Subgroups — #18071906

Order 4864.

518 conjugacy classes of subgroups; only the 291 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 291 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	#14563380	C₂	1	2	yes	maximal
2	C₄×#10597272	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926266	C₂	1	2	yes	maximal
4	C₂×#11926265	C₂	1	1	yes	maximal, characteristic
5	C₂×C₈²×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597272	C₄	1	4	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
10	#11926298	C₄	1	8	yes	—
11	#11926266	C₄	1	8	yes	complemented
12	#11926265	C₄	1	4	yes	complemented
13	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₈²×C₁₉	C₄	1	4	yes	complemented
16	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
17	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
19	C₂×C₄×Dic₁₉	C₂×C₄	1	4	yes	—
20	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
21	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
22	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
23	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
24	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
25	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
26	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
27	#10597272	—	2	8	no	—
28	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
29	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
30	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
31	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
33	C₂²×Dic₁₉	C₄²	1	4	yes	—
34	C₂×C₈×C₁₉	—	2	8	no	—
35	C₂×C₈×C₁₉	C₄²	1	8	yes	—
36	C₂×C₈×C₁₉	C₄²	1	4	yes	—
37	C₂×C₈×C₁₉	M₁₆	1	8	yes	—
38	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
39	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
40	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	C₄×Dic₁₉	—	2	4	no	—
42	C₄×Dic₁₉	—	2	8	no	—
43	C₂×C₁₉⋊C₈	—	2	4	no	—
44	C₂×C₁₉⋊C₈	—	2	8	no	—
45	C₂×C₁₉⋊C₈	C₄²	1	4	yes	—
46	C₂×C₁₉⋊C₈	C₄²	1	8	yes	—
47	#7844	—	19	1	no	maximal, Sylow
48	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
51	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
52	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
53	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
54	C₂×C₄×C₁₉	#131	1	8	yes	—
55	C₂×Dic₁₉	—	2	4	no	—
56	C₂×Dic₁₉	—	2	8	no	—
57	C₈×C₁₉	—	2	8	no	—
58	C₈×C₁₉	#97	1	8	yes	—
59	C₁₉⋊C₈	—	2	4	no	—
60	C₁₉⋊C₈	—	2	8	no	—
61	#1744	—	19	2	no	—
62	C₄×#97	—	19	1	no	—
63	C₂×#322	—	19	1	no	—
64	C₂×#322	—	19	2	no	—
65	C₂×C₈²	D₁₉	1	1	yes	characteristic
66	C₂²×C₁₉	C₄³	1	1	yes	characteristic
67	C₂²×C₁₉	C₄×M₁₆	1	2	yes	—
68	C₂²×C₁₉	#405	1	4	yes	—
69	C₄×C₁₉	C₂×#97	1	2	yes	—
70	C₄×C₁₉	C₄×M₁₆	1	2	yes	—
71	C₄×C₁₉	#405	1	4	yes	—
72	C₄×C₁₉	#405	1	4	yes	—
73	Dic₁₉	—	4	4	no	—
74	C₂×#97	—	19	4	no	—
75	C₂×C₄×C₈	—	19	1	no	—
76	C₂×C₄×C₈	—	19	2	no	—
77	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
78	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
79	C₄³	—	19	1	no	—
80	#336	—	19	8	no	—
81	#322	—	19	4	no	—
82	#322	—	19	8	no	—
83	C₈²	Dic₁₉	1	4	yes	complemented
84	C₂×C₁₉	#1453	1	4	yes	—
85	C₂×C₁₉	C₄×#97	1	1	yes	characteristic
86	C₂×C₁₉	#1726	1	2	yes	—
87	C₂²×C₈	—	19	4	no	—
88	C₂²×C₈	—	19	2	no	—
89	C₂²×C₈	C₄×D₁₉	1	4	yes	—
90	C₂²×C₈	C₄×D₁₉	1	2	yes	—
91	C₂×C₄²	—	19	4	no	—
92	C₂×C₄²	—	19	2	no	—
93	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
94	#97	—	38	8	no	—
95	C₄×C₈	—	19	4	no	—
96	C₄×C₈	—	19	4	no	—
97	C₄×C₈	—	19	4	no	—
98	C₄×C₈	C₄×D₁₉	1	4	yes	—
99	C₄×C₈	C₄×D₁₉	1	2	yes	—
100	C₄×C₈	C₂×Dic₁₉	1	4	yes	—
101	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
102	C₁₉	#7844	1	1	yes	characteristic, complemented, Sylow
103	C₂²×C₄	—	19	4	no	—
104	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
105	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
106	C₂×C₈	—	2	8	no	—
107	C₂×C₈	—	19	4	no	—
108	C₂×C₈	—	19	8	no	—
109	C₂×C₈	—	38	4	no	—
110	C₂×C₈	—	38	8	no	—
111	C₂×C₈	#64515	1	8	yes	—
112	C₂×C₈	C₄×Dic₁₉	1	8	yes	—
113	C₂×C₈	C₄×Dic₁₉	1	4	yes	—
114	C₄²	—	38	4	no	—
115	C₄²	—	38	8	no	—
116	C₄²	C₂×C₄×D₁₉	1	2	yes	—
117	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
118	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
119	C₂³	C₄²×D₁₉	1	1	yes	characteristic
120	C₂×C₄	—	38	4	no	—
121	C₂×C₄	—	38	8	no	—
122	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
123	C₂×C₄	C₄²×D₁₉	1	2	yes	—
124	C₂×C₄	C₂×#64515	1	4	yes	—
125	C₂×C₄	#10597347	1	8	yes	—
126	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
127	C₂×C₄	C₂×C₄×Dic₁₉	1	2	yes	—
128	C₈	—	2	8	no	—
129	C₈	—	38	4	no	—
130	C₈	—	38	8	no	—
131	C₈	#10597272	1	8	yes	—
132	C₂²	C₄²×Dic₁₉	1	1	yes	characteristic
133	C₂²	C₄×#64515	1	2	yes	—
134	C₂²	#11926498	1	4	yes	—
135	C₄	—	76	4	no	—
136	C₄	C₂×#10597272	1	2	yes	—
137	C₄	C₄×#64515	1	2	yes	—
138	C₄	#11926498	1	4	yes	—
139	C₄	#11926499	1	4	yes	—
140	C₂	#14561929	1	4	yes	—
141	C₂	C₄×#10597272	1	1	yes	characteristic
142	C₂	#14563321	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563380

C₂

yes

maximal

C₄×#10597272

C₂

yes

maximal, characteristic

C₂×#11926266

C₂

yes

maximal

C₂×#11926265

C₂

yes

maximal, characteristic

C₂×C₈²×C₁₉

C₂

yes

maximal, characteristic

C₂×#10597272

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₄²×Dic₁₉

C₂²

yes

characteristic

#11926298

C₄

yes

—

#11926266

C₄

yes

complemented

#11926265

C₄

yes

complemented

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₈²×C₁₉

C₄

yes

complemented

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

—

C₂×C₄×Dic₁₉

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

#10597272

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

—

C₂²×Dic₁₉

C₄²

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

—

C₂×C₈×C₁₉

C₄²

yes

—

C₂×C₈×C₁₉

M₁₆

yes

—

C₄²×C₁₉

C₂²×C₄

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₄²

yes

—

C₂×C₁₉⋊C₈

C₄²

yes

—

#7844

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄²

yes

—

C₂×C₄×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄²

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#97

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1744

—

C₄×#97

—

C₂×#322

—

C₂×#322

—

C₂×C₈²

D₁₉

yes

characteristic

C₂²×C₁₉

C₄³

yes

characteristic

C₂²×C₁₉

C₄×M₁₆

yes

—

C₂²×C₁₉

#405

yes

—

C₄×C₁₉

C₂×#97

yes

—

C₄×C₁₉

C₄×M₁₆

yes

—

C₄×C₁₉

#405

yes

—

C₄×C₁₉

#405

yes

—

Dic₁₉

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄×C₈

C₂×D₁₉

yes

—

C₄³

—

#336

—

#322

—

#322

—

C₈²

Dic₁₉

yes

complemented

C₂×C₁₉

#1453

yes

—

C₂×C₁₉

C₄×#97

yes

characteristic

C₂×C₁₉

#1726

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₄×D₁₉

yes

—

C₂²×C₈

C₄×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₁₉

yes

—

C₄×C₈

C₄×D₁₉

yes

—

100

C₄×C₈

C₂×Dic₁₉

yes

—

101

C₄×C₈

C₂×Dic₁₉

yes

—

102

C₁₉

#7844

yes

characteristic, complemented, Sylow

103

C₂²×C₄

—

104

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

105

C₂²×C₄

C₂×C₄×D₁₉

yes

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

#64515

yes

—

112

C₂×C₈

C₄×Dic₁₉

yes

—

113

C₂×C₈

C₄×Dic₁₉

yes

—

114

C₄²

—

115

C₄²

—

116

C₄²

C₂×C₄×D₁₉

yes

—

117

C₄²

C₂×C₄×D₁₉

yes

characteristic

118

C₄²

C₂²×Dic₁₉

yes

characteristic

119

C₂³

C₄²×D₁₉

yes

characteristic

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

C₄²×D₁₉

yes

characteristic

123

C₂×C₄

C₄²×D₁₉

yes

—

124

C₂×C₄

C₂×#64515

yes

—

125

C₂×C₄

#10597347

yes

—

126

C₂×C₄

C₂×C₄×Dic₁₉

yes

characteristic

127

C₂×C₄

C₂×C₄×Dic₁₉

yes

—

128

C₈

—

129

C₈

—

130

C₈

—

131

C₈

#10597272

yes

—

132

C₂²

C₄²×Dic₁₉

yes

characteristic

133

C₂²

C₄×#64515

yes

—

134

C₂²

#11926498

yes

—

135

C₄

—

136

C₄

C₂×#10597272

yes

—

137

C₄

C₄×#64515

yes

—

138

C₄

#11926498

yes

—

139

C₄

#11926499

yes

—

140

C₂

#14561929

yes

—

141

C₂

C₄×#10597272

yes

characteristic

142

C₂

#14563321

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₉
commutator	C₂²×C₁₉	C₄³
Fitting	C₂×C₈²×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×C₈²	D₁₉
hypocenter	C₁₉	#7844
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₈²

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₁₉

commutator

C₂²×C₁₉

C₄³

Fitting

C₂×C₈²×C₁₉

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₄²

cosocle

C₂×C₄²×C₁₉

C₂³

hypercenter

C₂×C₈²

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄² ◁ C₂×C₈²

N	H ≅ G/N	type
11. #11926266	C₄	semidirect
12. #11926265	C₄	semidirect
15. C₈²×C₁₉	C₄	semidirect
83. C₈²	Dic₁₉	semidirect
102. C₁₉	#7844	semidirect

H ≅ G/N

type

11. #11926266

C₄

semidirect

12. #11926265

C₄

semidirect

15. C₈²×C₁₉

C₄

semidirect

83. C₈²

Dic₁₉

semidirect

102. C₁₉

#7844

semidirect

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

subgroup	index
#14563380	2
C₄×#10597272	2
C₂×#11926266	2
C₂×#11926265	2
C₂×C₈²×C₁₉	2
#7844	19

subgroup

index

C₂×C₈²×C₁₉

Subgroups — #18071906

Conjugacy classes of subgroups

Complements

Maximal subgroups