Group #18076210 — subgroups

Subgroups — #18076210

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	#14563787	C₂	1	2	yes	maximal
2	#14561470	C₂	1	4	yes	maximal
3	C₁₉×#1744	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
5	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
7	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
8	C₄³×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#336	C₄	1	4	yes	—
10	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
11	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
12	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
13	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
14	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
15	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
16	C₂²×C₁₉⋊C₈	—	2	4	no	—
17	C₄×C₈×C₁₉	—	2	4	no	—
18	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
19	C₄⋊(C₁₉⋊C₈)	—	4	4	no	—
20	C₄⋊(C₁₉⋊C₈)	—	4	4	no	—
21	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
22	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
23	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
26	C₂×C₈×C₁₉	—	2	4	no	—
27	C₂×C₈×C₁₉	—	2	8	no	—
28	C₄²×C₁₉	—	2	4	no	—
29	C₄²×C₁₉	—	4	2	no	—
30	C₄²×C₁₉	D₈	1	2	yes	—
31	C₄²×C₁₉	SD₁₆	1	4	yes	—
32	C₄²×C₁₉	Q₁₆	1	2	yes	—
33	C₄²×C₁₉	#41	1	4	yes	—
34	C₂×C₁₉⋊C₈	—	4	4	no	—
35	C₂×C₁₉⋊C₈	—	4	4	no	—
36	C₂×C₁₉⋊C₈	—	4	4	no	—
37	#8787	—	19	1	no	maximal, Sylow
38	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₄×C₁₉	—	2	2	no	—
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	2	2	no	—
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	#106	1	4	yes	—
45	C₂×C₄×C₁₉	#107	1	4	yes	—
46	C₂×C₄×C₁₉	#117	1	2	yes	—
47	C₂×C₄×C₁₉	#124	1	2	yes	—
48	C₂×C₄×C₁₉	#125	1	2	yes	—
49	C₂×C₄×C₁₉	#131	1	4	yes	—
50	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
52	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
53	C₈×C₁₉	—	4	4	no	—
54	C₁₉⋊C₈	—	8	4	no	—
55	#1842	—	19	2	no	—
56	#1744	D₁₉	1	1	yes	characteristic
57	#1277	—	19	4	no	—
58	C₂²×C₁₉	#382	1	1	yes	characteristic
59	C₂²×C₁₉	#424	1	2	yes	—
60	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
61	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
62	C₂²×C₁₉	#430	1	2	yes	—
63	C₄×C₁₉	—	2	4	no	—
64	C₄×C₁₉	—	2	4	no	—
65	C₄×C₁₉	—	2	2	no	—
66	C₄×C₁₉	#433	1	4	yes	—
67	C₄×C₁₉	#486	1	2	yes	—
68	C₄×C₁₉	#487	1	2	yes	—
69	C₂×C₄⋊C₈	—	19	4	no	—
70	C₂×C₄⋊C₈	—	38	2	no	—
71	C₂×C₄⋊C₈	—	38	2	no	—
72	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
73	C₄³	C₂×D₁₉	1	1	yes	characteristic
74	#336	Dic₁₉	1	4	yes	—
75	C₂×C₁₉	#1570	1	2	yes	—
76	C₂×C₁₉	#1571	1	2	yes	—
77	C₂×C₁₉	#1832	1	1	yes	characteristic
78	C₂×C₁₉	#1834	1	1	yes	characteristic
79	C₂×C₁₉	#1838	1	1	yes	characteristic
80	C₂²×C₈	—	38	4	no	—
81	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
82	C₂×C₄²	Dic₃₈	1	2	yes	—
83	C₂×C₄²	D₇₆	1	1	yes	characteristic
84	C₂×C₄²	D₇₆	1	1	yes	characteristic
85	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
86	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
87	C₄⋊C₈	—	38	8	no	—
88	C₄⋊C₈	—	76	4	no	—
89	C₄⋊C₈	—	76	4	no	—
90	C₄×C₈	—	2	4	no	—
91	C₁₉	#8787	1	1	yes	characteristic, complemented, Sylow
92	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
93	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
94	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
95	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
96	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
97	C₂×C₈	—	2	8	no	—
98	C₂×C₈	—	2	4	no	—
99	C₂×C₈	—	76	4	no	—
100	C₂×C₈	—	76	4	no	—
101	C₂×C₈	—	76	4	no	—
102	C₄²	—	2	4	no	—
103	C₄²	—	4	2	no	—
104	C₄²	#64516	1	4	yes	—
105	C₄²	D₁₅₂	1	2	yes	—
106	C₄²	Dic₇₆	1	2	yes	—
107	C₄²	#64541	1	4	yes	—
108	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
109	C₂×C₄	—	2	2	no	—
110	C₂×C₄	—	2	2	no	—
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	#10597274	1	4	yes	—
115	C₂×C₄	#10597275	1	4	yes	—
116	C₂×C₄	#10597316	1	2	yes	—
117	C₂×C₄	#10597321	1	2	yes	—
118	C₂×C₄	C₂×#64516	1	2	yes	—
119	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
120	C₂×C₄	C₂×Dic₇₆	1	1	yes	characteristic
121	C₂×C₄	#10597372	1	2	yes	—
122	C₂×C₄	#10597394	1	4	yes	—
123	C₈	—	4	4	no	—
124	C₈	—	152	4	no	—
125	C₂²	#11926410	1	1	yes	characteristic
126	C₂²	#11926571	1	2	yes	—
127	C₂²	C₂×#10597274	1	1	yes	characteristic
128	C₂²	C₂×#10597275	1	1	yes	characteristic
129	C₂²	#11926593	1	2	yes	—
130	C₄	—	2	4	no	—
131	C₄	—	2	4	no	—
132	C₄	—	2	2	no	—
133	C₄	#11926605	1	4	yes	—
134	C₄	#11926891	1	2	yes	—
135	C₄	#11926895	1	2	yes	—
136	C₂	#14562406	1	2	yes	—
137	C₂	#14562410	1	2	yes	—
138	C₂	#14563755	1	1	yes	characteristic
139	C₂	#14563763	1	1	yes	characteristic
140	C₂	#14563776	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563787

C₂

yes

maximal

#14561470

C₂

yes

maximal

C₁₉×#1744

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

Q₈

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₄×C₈×C₁₉

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

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

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₈

yes

—

C₄²×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

Q₁₆

yes

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8787

—

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×C₁₉

#106

yes

—

C₂×C₄×C₁₉

#107

yes

—

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#124

yes

—

C₂×C₄×C₁₉

#125

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

C₈×C₁₉

—

C₁₉⋊C₈

—

#1842

—

#1744

D₁₉

yes

characteristic

#1277

—

C₂²×C₁₉

#382

yes

characteristic

C₂²×C₁₉

#424

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#433

yes

—

C₄×C₁₉

#486

yes

—

C₄×C₁₉

#487

yes

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

C₄³

C₂×D₁₉

yes

characteristic

#336

Dic₁₉

yes

—

C₂×C₁₉

#1570

yes

—

C₂×C₁₉

#1571

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂²×C₈

C₂×Dic₁₉

yes

—

C₂×C₄²

Dic₃₈

yes

—

C₂×C₄²

D₇₆

yes

characteristic

C₂×C₄²

D₇₆

yes

characteristic

C₂×C₄²

C₂×Dic₁₉

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₁₉

#8787

yes

characteristic, complemented, Sylow

C₂²×C₄

C₄⋊Dic₁₉

yes

—

C₂²×C₄

C₄⋊Dic₁₉

yes

—

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

C₂²×C₄

C₂×D₇₆

yes

characteristic

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₄²

—

103

C₄²

—

104

C₄²

#64516

yes

—

105

C₄²

D₁₅₂

yes

—

106

C₄²

Dic₇₆

yes

—

107

C₄²

#64541

yes

—

108

C₂³

C₂×C₄⋊Dic₁₉

yes

characteristic

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

#10597274

yes

—

115

C₂×C₄

#10597275

yes

—

116

C₂×C₄

#10597316

yes

—

117

C₂×C₄

#10597321

yes

—

118

C₂×C₄

C₂×#64516

yes

—

119

C₂×C₄

C₂×D₁₅₂

yes

characteristic

120

C₂×C₄

C₂×Dic₇₆

yes

characteristic

121

C₂×C₄

#10597372

yes

—

122

C₂×C₄

#10597394

yes

—

123

C₈

—

124

C₈

—

152

—

125

C₂²

#11926410

yes

characteristic

126

C₂²

#11926571

yes

—

127

C₂²

C₂×#10597274

yes

characteristic

128

C₂²

C₂×#10597275

yes

characteristic

129

C₂²

#11926593

yes

—

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

#11926605

yes

—

134

C₄

#11926891

yes

—

135

C₄

#11926895

yes

—

136

C₂

#14562406

yes

—

137

C₂

#14562410

yes

—

138

C₂

#14563755

yes

characteristic

139

C₂

#14563763

yes

characteristic

140

C₂

#14563776

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	#8787
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
91. C₁₉	#8787	semidirect

H ≅ G/N

type

91. C₁₉

#8787

semidirect

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

subgroup	index
#14563787	2
#14561470	2
C₁₉×#1744	2
#8787	19

subgroup

index

#14563787

#14561470

C₁₉×#1744

#8787

Subgroups — #18076210

Conjugacy classes of subgroups

Complements

Maximal subgroups