Group #14565177 — subgroups

Subgroups — #14565177

Order 2432.

254 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 95 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	C₂×#10597274	C₂	1	2	yes	maximal
2	C₂×#10597273	C₂	1	2	yes	maximal
3	#11926450	C₂	1	1	yes	maximal, characteristic
4	#11926414	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₉	—	2	2	no	—
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	C₁₉⋊#95	—	2	2	no	—
13	#10597274	—	2	4	no	—
14	#10597273	—	2	4	no	—
15	C₂²×C₄×C₁₉	D₄	1	2	yes	—
16	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
17	C₂²×Dic₁₉	—	2	1	no	—
18	C₂²×Dic₁₉	—	2	1	no	—
19	C₂²×Dic₁₉	—	2	2	no	—
20	C₂×Dic₃₈	—	2	2	no	—
21	C₂×Dic₃₈	—	2	2	no	—
22	C₂×Dic₃₈	—	2	1	no	—
23	C₂×Dic₃₈	Q₈	1	2	yes	—
24	C₂×C₈×C₁₉	—	2	2	no	—
25	C₂×C₈×C₁₉	—	2	2	no	—
26	C₂×C₈×C₁₉	D₄	1	4	yes	—
27	C₄²×C₁₉	—	2	2	no	—
28	C₄⋊Dic₁₉	—	2	2	no	—
29	C₄⋊Dic₁₉	—	2	2	no	—
30	C₄⋊Dic₁₉	—	2	2	no	—
31	C₄⋊Dic₁₉	—	4	4	no	—
32	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₁₉	—	2	2	no	—
34	C₂×C₄×C₁₉	—	2	2	no	—
35	C₂×C₄×C₁₉	SD₁₆	1	4	yes	—
36	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
37	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₁₉	#41	1	2	yes	—
39	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
40	C₂×Dic₁₉	—	2	2	no	—
41	C₂×Dic₁₉	—	4	1	no	—
42	C₂×Dic₁₉	—	4	1	no	—
43	C₂×Dic₁₉	—	4	2	no	—
44	C₂×Dic₁₉	—	4	1	no	—
45	C₂×Dic₁₉	—	4	4	no	—
46	C₂×Dic₁₉	—	4	2	no	—
47	Dic₃₈	—	2	4	no	—
48	Dic₃₈	—	4	2	no	—
49	C₈×C₁₉	—	2	4	no	—
50	#2096	—	19	1	no	maximal, Sylow
51	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
52	C₂²×C₁₉	#123	1	1	yes	characteristic
53	C₂²×C₁₉	#127	1	1	yes	characteristic
54	C₂²×C₁₉	C₂×SD₁₆	1	2	yes	—
55	C₂²×C₁₉	#137	1	2	yes	—
56	C₄×C₁₉	—	2	4	no	—
57	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
58	C₄×C₁₉	#123	1	2	yes	—
59	Dic₁₉	—	4	2	no	—
60	Dic₁₉	—	8	2	no	—
61	Dic₁₉	—	8	1	no	—
62	C₂×#106	—	19	2	no	—
63	C₂×#103	—	19	2	no	—
64	#391	—	19	1	no	—
65	#384	—	19	1	no	—
66	#336	D₁₉	1	1	yes	characteristic
67	C₂×C₁₉	#399	1	1	yes	characteristic
68	C₂×C₁₉	#475	1	2	yes	—
69	C₂×C₁₉	#483	1	2	yes	—
70	C₂×C₁₉	#492	1	1	yes	characteristic
71	C₂×C₁₉	#497	1	1	yes	characteristic
72	C₂²×Q₈	—	19	1	no	—
73	C₂²×C₈	C₂×D₁₉	1	2	yes	—
74	C₂×C₄⋊C₄	—	19	2	no	—
75	C₂×C₄⋊C₄	—	19	1	no	—
76	C₂×C₄⋊C₄	—	38	2	no	—
77	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
78	#106	—	38	4	no	—
79	#103	—	38	4	no	—
80	#95	—	38	2	no	—
81	C₁₉	#2096	1	1	yes	characteristic, complemented, Sylow
82	C₂×Q₈	—	19	2	no	—
83	C₂×Q₈	—	38	1	no	—
84	C₂×Q₈	—	38	2	no	—
85	C₂×Q₈	—	38	2	no	—
86	C₂²×C₄	—	38	1	no	—
87	C₂²×C₄	—	38	1	no	—
88	C₂²×C₄	—	38	2	no	—
89	C₂²×C₄	D₇₆	1	2	yes	—
90	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	D₇₆	1	4	yes	—
94	C₄⋊C₄	—	38	2	no	—
95	C₄⋊C₄	—	38	2	no	—
96	C₄⋊C₄	—	38	2	no	—
97	C₄⋊C₄	—	76	4	no	—
98	C₄²	—	2	2	no	—
99	C₂³	C₂×D₇₆	1	1	yes	characteristic
100	Q₈	—	38	4	no	—
101	Q₈	—	76	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	38	2	no	—
105	C₂×C₄	—	76	1	no	—
106	C₂×C₄	—	76	1	no	—
107	C₂×C₄	—	76	2	no	—
108	C₂×C₄	—	76	1	no	—
109	C₂×C₄	—	76	4	no	—
110	C₂×C₄	—	76	2	no	—
111	C₂×C₄	#64516	1	4	yes	—
112	C₂×C₄	C₂×D₇₆	1	2	yes	—
113	C₂×C₄	#64543	1	1	yes	characteristic
114	C₂×C₄	#64543	1	2	yes	—
115	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
116	C₈	—	2	4	no	—
117	C₂²	#10597320	1	1	yes	characteristic
118	C₂²	#10597332	1	1	yes	characteristic
119	C₂²	#10597343	1	1	yes	characteristic
120	C₂²	C₂×#64516	1	2	yes	—
121	C₂²	#10597355	1	2	yes	—
122	C₄	—	2	4	no	—
123	C₄	—	76	2	no	—
124	C₄	—	152	2	no	—
125	C₄	—	152	1	no	—
126	C₄	#10597332	1	2	yes	—
127	C₄	#10597343	1	2	yes	—
128	C₂	#11926481	1	1	yes	characteristic
129	C₂	#11926830	1	2	yes	—
130	C₂	#11926875	1	2	yes	—
131	C₂	#11926917	1	1	yes	characteristic
132	C₂	#11926938	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597274

C₂

yes

maximal

C₂×#10597273

C₂

yes

maximal

#11926450

C₂

yes

maximal, characteristic

#11926414

C₂

yes

maximal, characteristic

C₁₉×#336

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₁₉⋊#95

—

#10597274

—

#10597273

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

Q₈

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

#2096

—

maximal, Sylow

C₂²×C₁₉

C₂²⋊Q₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₂×SD₁₆

yes

—

C₂²×C₁₉

#137

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

#123

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#483

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

—

C₂²×C₈

C₂×D₁₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

—

—

—

C₁₉

#2096

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₇₆

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₇₆

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₂³

C₂×D₇₆

yes

characteristic

100

Q₈

—

101

Q₈

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

#64516

yes

—

112

C₂×C₄

C₂×D₇₆

yes

—

113

C₂×C₄

#64543

yes

characteristic

114

C₂×C₄

#64543

yes

—

115

C₂×C₄

Q₈×D₁₉

yes

characteristic

116

C₈

—

117

C₂²

#10597320

yes

characteristic

118

C₂²

#10597332

yes

characteristic

119

C₂²

#10597343

yes

characteristic

120

C₂²

C₂×#64516

yes

—

121

C₂²

#10597355

yes

—

122

C₄

—

123

C₄

—

124

C₄

—

152

—

125

C₄

—

152

—

126

C₄

#10597332

yes

—

127

C₄

#10597343

yes

—

128

C₂

#11926481

yes

characteristic

129

C₂

#11926830

yes

—

130

C₂

#11926875

yes

—

131

C₂

#11926917

yes

characteristic

132

C₂

#11926938

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₇₆
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#336	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#336	D₁₉
hypocenter	C₁₉	#2096
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

subgroup

G/H

center

C₂³

C₂×D₇₆

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#336

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

N	H ≅ G/N	type
81. C₁₉	#2096	semidirect

H ≅ G/N

type

81. C₁₉

#2096

semidirect

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

subgroup	index
C₂×#10597274	2
C₂×#10597273	2
#11926450	2
#11926414	2
C₁₉×#336	2
#2096	19

subgroup

index

C₁₉×#336

Subgroups — #14565177

Conjugacy classes of subgroups

Complements

Maximal subgroups