Group #18069136 — subgroups

Subgroups — #18069136

Order 4864.

304 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 107 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	#14563488	C₂	1	2	yes	maximal
2	C₁₉×#1831	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
4	C₂×#10597260	C₄	1	4	yes	—
5	#11926299	—	2	2	no	—
6	C₂×C₁₉×C₄⋊C₈	C₄	1	2	yes	—
7	C₄³×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#336	—	2	2	no	—
9	C₂²×C₈×C₁₉	—	2	2	no	—
10	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
11	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄²×C₁₉	D₄	1	2	yes	—
13	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
14	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
15	C₂²×C₁₉⋊C₈	—	2	4	no	—
16	C₁₉×C₄⋊C₈	—	4	2	no	—
17	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
18	#10597260	—	4	4	no	—
19	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
21	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
23	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	—	4	2	no	—
25	C₂×C₈×C₁₉	—	4	4	no	—
26	C₄²×C₁₉	—	2	2	no	—
27	C₄²×C₁₉	—	2	1	no	—
28	C₄²×C₁₉	—	2	2	no	—
29	C₄²×C₁₉	—	2	1	no	—
30	C₄²×C₁₉	—	2	4	no	—
31	C₄²×C₁₉	—	2	2	no	—
32	C₄²×C₁₉	—	4	1	no	—
33	C₂×C₁₉⋊C₈	—	2	8	no	—
34	C₂×C₁₉⋊C₈	—	4	4	no	—
35	C₂×C₁₉⋊C₈	—	4	4	no	—
36	#7042	—	19	1	no	maximal, Sylow
37	C₂³×C₁₉	#95	1	1	yes	characteristic
38	C₂×C₄×C₁₉	—	2	2	no	—
39	C₂×C₄×C₁₉	—	2	1	no	—
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	—	2	1	no	—
46	C₂×C₄×C₁₉	—	2	2	no	—
47	C₂×C₄×C₁₉	#100	1	2	yes	—
48	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
49	C₂×C₄×C₁₉	#101	1	2	yes	—
50	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
51	C₂×C₄×C₁₉	#104	1	4	yes	—
52	C₂×C₄×C₁₉	#108	1	2	yes	—
53	C₈×C₁₉	—	8	2	no	—
54	C₁₉⋊C₈	—	4	8	no	—
55	#1831	D₁₉	1	1	yes	characteristic
56	#1767	—	19	2	no	—
57	C₂²×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
58	C₂²×C₁₉	#339	1	2	yes	—
59	C₂²×C₁₉	#341	1	1	yes	characteristic
60	C₂²×C₁₉	#343	1	2	yes	—
61	C₂²×C₁₉	#343	1	1	yes	characteristic
62	C₄×C₁₉	—	2	2	no	—
63	C₄×C₁₉	—	2	2	no	—
64	C₄×C₁₉	—	2	2	no	—
65	C₄×C₁₉	—	4	2	no	—
66	C₄×C₁₉	—	4	1	no	—
67	C₄×C₁₉	#329	1	2	yes	—
68	C₄×C₁₉	#330	1	2	yes	—
69	C₂×C₄⋊C₈	—	38	2	no	—
70	C₂×C₄⋊C₈	Dic₁₉	1	2	yes	—
71	C₂×#97	—	19	4	no	—
72	C₄³	C₂×D₁₉	1	1	yes	characteristic
73	#336	—	2	2	no	—
74	#336	—	38	2	no	—
75	C₂×C₁₉	#1285	1	2	yes	—
76	C₂×C₁₉	#1290	1	1	yes	characteristic
77	C₂×C₁₉	#1295	1	1	yes	characteristic
78	C₂×C₁₉	#1299	1	2	yes	—
79	C₂×C₁₉	#1309	1	1	yes	characteristic
80	C₂²×C₈	—	2	2	no	—
81	C₂²×C₈	—	38	4	no	—
82	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
83	C₂×C₄²	C₄×D₁₉	1	2	yes	—
84	C₂×C₄²	D₇₆	1	1	yes	characteristic
85	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
86	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
87	C₄⋊C₈	—	4	2	no	—
88	C₄⋊C₈	—	38	8	no	—
89	#97	—	76	4	no	—
90	C₁₉	#7042	1	1	yes	characteristic, complemented, Sylow
91	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
92	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
93	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
94	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
95	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
96	C₂×C₈	—	4	2	no	—
97	C₂×C₈	—	4	4	no	—
98	C₂×C₈	—	38	8	no	—
99	C₂×C₈	—	76	4	no	—
100	C₂×C₈	—	76	4	no	—
101	C₄²	—	2	2	no	—
102	C₄²	—	2	2	no	—
103	C₄²	—	2	2	no	—
104	C₄²	—	2	1	no	—
105	C₄²	—	2	1	no	—
106	C₄²	—	2	4	no	—
107	C₄²	—	4	1	no	—
108	C₂³	C₁₉⋊#95	1	1	yes	characteristic
109	C₂×C₄	—	2	2	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	#10597276	1	2	yes	—
119	C₂×C₄	#10597280	1	2	yes	—
120	C₂×C₄	#10597281	1	2	yes	—
121	C₂×C₄	#10597290	1	1	yes	characteristic
122	C₂×C₄	#10597293	1	1	yes	characteristic
123	C₂×C₄	#10597294	1	4	yes	—
124	C₈	—	8	2	no	—
125	C₈	—	76	8	no	—
126	C₂²	#11926301	1	1	yes	characteristic
127	C₂²	#11926303	1	2	yes	—
128	C₂²	#11926309	1	1	yes	characteristic
129	C₂²	#11926312	1	2	yes	—
130	C₂²	#11926313	1	1	yes	characteristic
131	C₄	—	2	2	no	—
132	C₄	—	2	2	no	—
133	C₄	—	2	2	no	—
134	C₄	—	4	1	no	—
135	C₄	—	4	2	no	—
136	C₄	#11926284	1	2	yes	—
137	C₄	#11926286	1	2	yes	—
138	C₂	#14561492	1	2	yes	—
139	C₂	#14561505	1	1	yes	characteristic
140	C₂	#14561516	1	1	yes	characteristic
141	C₂	#14561526	1	2	yes	—
142	C₂	C₁₉⋊#1309	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563488

C₂

yes

maximal

C₁₉×#1831

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×#10597260

C₄

yes

—

#11926299

—

C₂×C₁₉×C₄⋊C₈

C₄

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

Q₈

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#100

yes

—

C₂×C₄×C₁₉

#100

yes

characteristic

C₂×C₄×C₁₉

#101

yes

—

C₂×C₄×C₁₉

#101

yes

characteristic

C₂×C₄×C₁₉

#104

yes

—

C₂×C₄×C₁₉

#108

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1831

D₁₉

yes

characteristic

#1767

—

C₂²×C₁₉

H(3,ℤ/4)

yes

characteristic

C₂²×C₁₉

#339

yes

—

C₂²×C₁₉

#341

yes

characteristic

C₂²×C₁₉

#343

yes

—

C₂²×C₁₉

#343

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#329

yes

—

C₄×C₁₉

#330

yes

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

Dic₁₉

yes

—

C₂×#97

—

C₄³

C₂×D₁₉

yes

characteristic

#336

—

#336

—

C₂×C₁₉

#1285

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#1309

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

Dic₃₈

yes

characteristic

C₂×C₄²

C₄×D₁₉

yes

—

C₂×C₄²

D₇₆

yes

characteristic

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

C₂×C₄²

C₂²⋊D₁₉

yes

—

C₄⋊C₈

—

C₄⋊C₈

—

#97

—

C₁₉

#7042

yes

characteristic, complemented, Sylow

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

C₂²×C₄

Dic₁₉⋊C₄

yes

—

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₄²

—

102

C₄²

—

103

C₄²

—

104

C₄²

—

105

C₄²

—

106

C₄²

—

107

C₄²

—

108

C₂³

C₁₉⋊#95

yes

characteristic

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

#10597276

yes

—

119

C₂×C₄

#10597280

yes

—

120

C₂×C₄

#10597281

yes

—

121

C₂×C₄

#10597290

yes

characteristic

122

C₂×C₄

#10597293

yes

characteristic

123

C₂×C₄

#10597294

yes

—

124

C₈

—

125

C₈

—

126

C₂²

#11926301

yes

characteristic

127

C₂²

#11926303

yes

—

128

C₂²

#11926309

yes

characteristic

129

C₂²

#11926312

yes

—

130

C₂²

#11926313

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

#11926284

yes

—

137

C₄

#11926286

yes

—

138

C₂

#14561492

yes

—

139

C₂

#14561505

yes

characteristic

140

C₂

#14561516

yes

characteristic

141

C₂

#14561526

yes

—

142

C₂

C₁₉⋊#1309

yes

characteristic

	subgroup	G/H
center	C₂³	C₁₉⋊#95
commutator	C₂²×C₄×C₁₉	C₄²
Frattini	C₄³	C₂×D₁₉
Fitting	C₁₉×#1831	C₂
socle, prime radical	C₂³×C₁₉	#95
cosocle	C₄³×C₁₉	C₂²
hypercenter	#1831	D₁₉
hypocenter	C₁₉	#7042
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

subgroup

G/H

center

C₂³

C₁₉⋊#95

commutator

C₂²×C₄×C₁₉

C₄²

Frattini

C₄³

C₂×D₁₉

Fitting

C₁₉×#1831

C₂

socle, prime radical

C₂³×C₁₉

#95

cosocle

C₄³×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

N	H ≅ G/N	type
90. C₁₉	#7042	semidirect

H ≅ G/N

type

90. C₁₉

#7042

semidirect

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

subgroup	index
#14563488	2
C₁₉×#1831	2
#7042	19

subgroup

index

#14563488

C₁₉×#1831

#7042

Subgroups — #18069136

Conjugacy classes of subgroups

Complements

Maximal subgroups