Group #18076299 — subgroups

Subgroups — #18076299

Order 4864.

362 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 179 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	#14563752	C₂	1	2	yes	maximal
2	C₂×#11926297	C₂	1	2	yes	maximal
3	C₂×#11926295	C₂	1	2	yes	maximal
4	C₁₉×#1744	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
6	#11926299	—	2	4	no	—
7	#11926297	—	2	4	no	—
8	#11926295	—	2	4	no	—
9	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₄³×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#336	C₄	1	4	yes	—
13	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
14	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₉	D₄	1	2	yes	—
17	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
18	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×C₁₉⋊C₈	—	2	4	no	—
20	C₄×C₈×C₁₉	D₄	1	2	yes	—
21	C₄×C₈×C₁₉	D₄	1	2	yes	—
22	C₄×C₈×C₁₉	Q₈	1	2	yes	—
23	C₄×C₈×C₁₉	Q₈	1	2	yes	—
24	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
25	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
26	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
27	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₈×C₁₉	—	2	4	no	—
31	C₂×C₈×C₁₉	—	2	4	no	—
32	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
33	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
34	C₄²×C₁₉	—	2	4	no	—
35	C₄²×C₁₉	—	2	4	no	—
36	C₄²×C₁₉	—	4	2	no	—
37	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
40	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₁₉⋊C₈	—	4	4	no	—
42	C₂×C₁₉⋊C₈	—	4	8	no	—
43	#8811	—	19	1	no	maximal, Sylow
44	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	—	2	2	no	—
46	C₂×C₄×C₁₉	—	2	4	no	—
47	C₂×C₄×C₁₉	—	2	4	no	—
48	C₂×C₄×C₁₉	—	2	4	no	—
49	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
52	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
53	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
54	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
55	C₂×C₄×C₁₉	#131	1	4	yes	—
56	C₂×C₄×C₁₉	#135	1	4	yes	—
57	C₈×C₁₉	—	2	4	no	—
58	C₈×C₁₉	—	2	4	no	—
59	C₁₉⋊C₈	—	8	4	no	—
60	#1831	—	19	2	no	—
61	#1744	D₁₉	1	1	yes	characteristic
62	C₂×#335	—	19	2	no	—
63	C₂×#334	—	19	2	no	—
64	C₂²×C₁₉	#384	1	1	yes	characteristic
65	C₂²×C₁₉	#424	1	2	yes	—
66	C₂²×C₁₉	#427	1	2	yes	—
67	C₂²×C₁₉	#430	1	2	yes	—
68	C₄×C₁₉	—	2	1	no	—
69	C₄×C₁₉	—	2	1	no	—
70	C₄×C₁₉	—	4	4	no	—
71	C₄×C₁₉	#424	1	2	yes	—
72	C₄×C₁₉	#424	1	2	yes	—
73	C₄×C₁₉	#495	1	2	yes	—
74	C₄×C₁₉	#499	1	2	yes	—
75	C₂×C₄⋊C₈	—	19	4	no	—
76	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
77	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
78	C₄³	C₂×D₁₉	1	1	yes	characteristic
79	#336	—	38	4	no	—
80	#336	Dic₁₉	1	4	yes	—
81	#335	—	38	4	no	—
82	#334	—	38	4	no	—
83	C₂×C₁₉	#1572	1	4	yes	—
84	C₂×C₁₉	#1843	1	1	yes	characteristic
85	C₂×C₁₉	#1846	1	1	yes	characteristic
86	C₂×C₁₉	#1849	1	1	yes	characteristic
87	C₂²×C₈	—	38	4	no	—
88	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
89	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
90	C₂×C₄²	Dic₃₈	1	2	yes	—
91	C₂×C₄²	D₇₆	1	2	yes	—
92	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
93	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
94	C₄⋊C₈	—	38	4	no	—
95	C₄⋊C₈	—	38	4	no	—
96	C₄×C₈	Dic₃₈	1	2	yes	—
97	C₄×C₈	Dic₃₈	1	2	yes	—
98	C₄×C₈	D₇₆	1	2	yes	—
99	C₄×C₈	D₇₆	1	2	yes	—
100	C₁₉	#8811	1	1	yes	characteristic, complemented, Sylow
101	C₂²×C₄	C₄⋊Dic₁₉	1	4	yes	—
102	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
103	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
104	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
105	C₂×C₈	—	2	4	no	—
106	C₂×C₈	—	2	4	no	—
107	C₂×C₈	—	76	4	no	—
108	C₂×C₈	—	76	8	no	—
109	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
110	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
111	C₄²	—	2	4	no	—
112	C₄²	—	2	4	no	—
113	C₄²	—	4	2	no	—
114	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
115	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
116	C₄²	C₂×D₇₆	1	1	yes	characteristic
117	C₄²	C₂×D₇₆	1	1	yes	characteristic
118	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	2	4	no	—
121	C₂×C₄	—	2	4	no	—
122	C₂×C₄	—	2	4	no	—
123	C₂×C₄	#10597315	1	1	yes	characteristic
124	C₂×C₄	#10597315	1	1	yes	characteristic
125	C₂×C₄	#10597315	1	1	yes	characteristic
126	C₂×C₄	#10597320	1	1	yes	characteristic
127	C₂×C₄	#10597350	1	4	yes	—
128	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
129	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
130	C₂×C₄	#10597394	1	4	yes	—
131	C₈	—	2	4	no	—
132	C₈	—	2	4	no	—
133	C₈	—	152	4	no	—
134	C₂²	#11926414	1	1	yes	characteristic
135	C₂²	#11926571	1	2	yes	—
136	C₂²	#11926582	1	2	yes	—
137	C₂²	#11926593	1	2	yes	—
138	C₄	—	2	1	no	—
139	C₄	—	2	1	no	—
140	C₄	—	4	4	no	—
141	C₄	#11926571	1	2	yes	—
142	C₄	#11926571	1	2	yes	—
143	C₄	#11926928	1	2	yes	—
144	C₄	#11926946	1	2	yes	—
145	C₂	#14562415	1	4	yes	—
146	C₂	#14563789	1	1	yes	characteristic
147	C₂	#14563799	1	1	yes	characteristic
148	C₂	#14563810	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563752

C₂

yes

maximal

C₂×#11926297

C₂

yes

maximal

C₂×#11926295

C₂

yes

maximal

C₁₉×#1744

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926299

—

#11926297

—

#11926295

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

Q₈

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8811

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1831

—

#1744

D₁₉

yes

characteristic

C₂×#335

—

C₂×#334

—

C₂²×C₁₉

#384

yes

characteristic

C₂²×C₁₉

#424

yes

—

C₂²×C₁₉

#427

yes

—

C₂²×C₁₉

#430

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#424

yes

—

C₄×C₁₉

#424

yes

—

C₄×C₁₉

#495

yes

—

C₄×C₁₉

#499

yes

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₄³

C₂×D₁₉

yes

characteristic

#336

—

#336

Dic₁₉

yes

—

#335

—

#334

—

C₂×C₁₉

#1572

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂²×C₈

C₂×Dic₁₉

yes

—

C₂²×C₈

C₂×Dic₁₉

yes

—

C₂×C₄²

Dic₃₈

yes

—

C₂×C₄²

D₇₆

yes

—

C₂×C₄²

C₂×Dic₁₉

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

Dic₃₈

yes

—

C₄×C₈

Dic₃₈

yes

—

C₄×C₈

D₇₆

yes

—

C₄×C₈

D₇₆

yes

—

100

C₁₉

#8811

yes

characteristic, complemented, Sylow

101

C₂²×C₄

C₄⋊Dic₁₉

yes

—

102

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

103

C₂²×C₄

C₂×D₇₆

yes

characteristic

104

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

C₄⋊Dic₁₉

yes

—

110

C₂×C₈

C₄⋊Dic₁₉

yes

—

111

C₄²

—

112

C₄²

—

113

C₄²

—

114

C₄²

C₂×Dic₃₈

yes

characteristic

115

C₄²

C₂×Dic₃₈

yes

characteristic

116

C₄²

C₂×D₇₆

yes

characteristic

117

C₄²

C₂×D₇₆

yes

characteristic

118

C₂³

C₂×C₄⋊Dic₁₉

yes

characteristic

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

#10597315

yes

characteristic

124

C₂×C₄

#10597315

yes

characteristic

125

C₂×C₄

#10597315

yes

characteristic

126

C₂×C₄

#10597320

yes

characteristic

127

C₂×C₄

#10597350

yes

—

128

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

129

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

130

C₂×C₄

#10597394

yes

—

131

C₈

—

132

C₈

—

133

C₈

—

152

—

134

C₂²

#11926414

yes

characteristic

135

C₂²

#11926571

yes

—

136

C₂²

#11926582

yes

—

137

C₂²

#11926593

yes

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

#11926571

yes

—

142

C₄

#11926571

yes

—

143

C₄

#11926928

yes

—

144

C₄

#11926946

yes

—

145

C₂

#14562415

yes

—

146

C₂

#14563789

yes

characteristic

147

C₂

#14563799

yes

characteristic

148

C₂

#14563810

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₇₆
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1744	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1744	D₁₉
hypocenter	C₁₉	#8811
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1744

subgroup

G/H

center

C₂²×C₄

C₂×D₇₆

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1744

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1744

N	H ≅ G/N	type
100. C₁₉	#8811	semidirect

H ≅ G/N

type

100. C₁₉

#8811

semidirect

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

subgroup	index
#14563752	2
C₂×#11926297	2
C₂×#11926295	2
C₁₉×#1744	2
#8811	19

subgroup

index

C₁₉×#1744

Subgroups — #18076299

Conjugacy classes of subgroups

Complements

Maximal subgroups