Group #14563018 — subgroups

Subgroups — #14563018

Order 2432.

150 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 57 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	#11926942	C₂	1	1	yes	maximal, characteristic
2	#11926840	C₂	1	1	yes	maximal, characteristic
3	#11926755	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₃₈	C₂	1	1	yes	maximal, characteristic
5	#11926292	C₂	1	1	yes	maximal, characteristic
6	#11926291	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#334	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₇₆	—	2	1	no	—
9	#10597315	C₂²	1	1	yes	characteristic
10	#10597315	C₂²	1	1	yes	characteristic
11	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
12	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	#10597275	—	2	1	no	—
16	#10597274	—	2	1	no	—
17	#10597274	—	2	1	no	—
18	#10597273	—	2	1	no	—
19	#10597273	—	2	1	no	—
20	Dic₁₉⋊C₈	—	2	1	no	—
21	C₈×Dic₁₉	—	2	1	no	—
22	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×Dic₃₈	—	2	1	no	—
24	C₂×Dic₃₈	—	2	1	no	—
25	C₂×Dic₃₈	D₄	1	1	yes	characteristic
26	C₂×C₈×C₁₉	—	2	1	no	—
27	C₂×C₈×C₁₉	—	2	1	no	—
28	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
29	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
30	C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₄⋊Dic₁₉	—	2	1	no	—
32	C₄⋊Dic₁₉	—	2	1	no	—
33	C₄⋊Dic₁₉	—	2	1	no	—
34	C₄⋊Dic₁₉	—	2	1	no	—
35	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
36	Dic₁₉⋊C₄	—	2	1	no	—
37	C₄×Dic₁₉	—	2	1	no	—
38	C₂×C₁₉⋊C₈	—	2	1	no	—
39	Dic₇₆	—	4	2	no	—
40	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
43	C₂×Dic₁₉	—	2	1	no	—
44	C₂×Dic₁₉	—	2	1	no	—
45	C₂×Dic₁₉	—	4	1	no	—
46	C₂×Dic₁₉	—	4	1	no	—
47	Dic₃₈	—	2	1	no	—
48	Dic₃₈	—	4	1	no	—
49	Dic₃₈	—	4	1	no	—
50	Dic₃₈	—	8	1	no	—
51	Dic₃₈	SD₁₆	1	2	yes	—
52	C₈×C₁₉	—	2	1	no	—
53	C₈×C₁₉	—	4	1	no	—
54	C₈×C₁₉	—	4	1	no	—
55	C₈×C₁₉	Q₁₆	1	2	yes	complemented
56	C₁₉⋊C₈	—	4	1	no	—
57	#1672	—	19	1	no	maximal, Sylow
58	C₂²×C₁₉	#121	1	1	yes	characteristic
59	C₄×C₁₉	—	2	1	no	—
60	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
61	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
62	C₄×C₁₉	#135	1	1	yes	characteristic
63	C₄×C₁₉	#137	1	1	yes	characteristic
64	Dic₁₉	—	2	2	no	—
65	Dic₁₉	—	4	1	no	—
66	Dic₁₉	—	8	1	no	—
67	Dic₁₉	—	8	1	no	—
68	#498	—	19	1	no	—
69	#477	—	19	1	no	—
70	#462	—	19	1	no	—
71	C₈×Q₈	—	19	1	no	—
72	#334	D₁₉	1	1	yes	characteristic
73	#333	—	19	1	no	—
74	#332	—	19	1	no	—
75	C₂×C₁₉	#462	1	1	yes	characteristic
76	C₂×C₁₉	#465	1	1	yes	characteristic
77	C₂×C₁₉	#471	1	1	yes	characteristic
78	C₂×Q₁₆	—	38	1	no	—
79	C₄⋊Q₈	—	19	1	no	—
80	C₄⋊Q₈	—	19	1	no	—
81	C₄×Q₈	—	19	1	no	—
82	#107	—	38	1	no	—
83	#106	—	38	1	no	—
84	#106	—	38	1	no	—
85	C₄⋊C₈	—	19	1	no	—
86	C₄⋊C₈	—	38	1	no	—
87	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
88	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
89	#103	—	38	1	no	—
90	#103	—	38	1	no	—
91	C₄×C₈	—	38	1	no	—
92	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
93	C₁₉	#1672	1	1	yes	characteristic, complemented, Sylow
94	C₂×Q₈	—	19	1	no	—
95	C₂×Q₈	—	38	1	no	—
96	C₂×Q₈	—	38	1	no	—
97	Q₁₆	—	76	2	no	—
98	C₂×C₈	—	2	1	no	—
99	C₂×C₈	—	2	1	no	—
100	C₂×C₈	—	38	1	no	—
101	C₂×C₈	D₇₆	1	1	yes	characteristic
102	C₂×C₈	D₇₆	1	1	yes	characteristic
103	C₄⋊C₄	—	19	1	no	—
104	C₄⋊C₄	—	38	1	no	—
105	C₄⋊C₄	—	38	1	no	—
106	C₄⋊C₄	—	38	1	no	—
107	C₄⋊C₄	—	38	1	no	—
108	C₄⋊C₄	—	38	1	no	—
109	C₄²	—	38	1	no	—
110	C₄²	C₂²×D₁₉	1	1	yes	characteristic
111	Q₈	—	19	2	no	—
112	Q₈	—	38	1	no	—
113	Q₈	—	76	1	no	—
114	Q₈	—	76	1	no	—
115	Q₈	—	152	1	no	—
116	C₂×C₄	—	38	1	no	—
117	C₂×C₄	—	38	1	no	—
118	C₂×C₄	—	76	1	no	—
119	C₂×C₄	—	76	1	no	—
120	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
121	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
122	C₂×C₄	#64545	1	1	yes	characteristic
123	C₈	—	2	1	no	—
124	C₈	—	4	1	no	—
125	C₈	—	4	1	no	—
126	C₈	—	76	1	no	—
127	C₈	Dic₇₆	1	2	yes	complemented
128	C₂²	#10597341	1	1	yes	characteristic
129	C₄	—	2	1	no	—
130	C₄	—	38	2	no	—
131	C₄	—	76	1	no	—
132	C₄	—	152	1	no	—
133	C₄	—	152	1	no	—
134	C₄	C₂×Dic₇₆	1	1	yes	characteristic
135	C₄	#10597355	1	1	yes	characteristic
136	C₄	SD₁₆×D₁₉	1	1	yes	characteristic
137	C₄	#10597362	1	1	yes	characteristic
138	C₂	#11926755	1	1	yes	characteristic
139	C₂	#11926774	1	1	yes	characteristic
140	C₂	#11926808	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926942

C₂

yes

maximal, characteristic

#11926840

C₂

yes

maximal, characteristic

#11926755

C₂

yes

maximal, characteristic

C₈×Dic₃₈

C₂

yes

maximal, characteristic

#11926292

C₂

yes

maximal, characteristic

#11926291

C₂

yes

maximal, characteristic

C₁₉×#334

C₂

yes

maximal, characteristic

C₂×Dic₇₆

—

#10597315

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₄×Dic₃₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

—

—

—

—

—

Dic₁₉⋊C₈

—

C₈×Dic₁₉

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

characteristic

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

SD₁₆

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

Q₁₆

yes

complemented

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₄×C₁₉

C₂×Q₁₆

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

#498

—

#477

—

#462

—

C₈×Q₈

—

#334

D₁₉

yes

characteristic

#333

—

#332

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄×Q₈

—

#107

—

#106

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₉

yes

characteristic

C₄⋊C₈

C₂×D₁₉

yes

characteristic

#103

—

#103

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1672

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

D₇₆

yes

characteristic

102

C₂×C₈

D₇₆

yes

characteristic

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄²

—

110

C₄²

C₂²×D₁₉

yes

characteristic

111

Q₈

—

112

Q₈

—

113

Q₈

—

114

Q₈

—

115

Q₈

—

152

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

C₂×D₇₆

yes

characteristic

121

C₂×C₄

D₄×D₁₉

yes

characteristic

122

C₂×C₄

#64545

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

126

C₈

—

127

C₈

Dic₇₆

yes

complemented

128

C₂²

#10597341

yes

characteristic

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

152

—

133

C₄

—

152

—

134

C₄

C₂×Dic₇₆

yes

characteristic

135

C₄

#10597355

yes

characteristic

136

C₄

SD₁₆×D₁₉

yes

characteristic

137

C₄

#10597362

yes

characteristic

138

C₂

#11926755

yes

characteristic

139

C₂

#11926774

yes

characteristic

140

C₂

#11926808

yes

characteristic

	subgroup	G/H
center	C₂²	#10597341
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#334	C₂
socle, prime radical	C₂²×C₁₉	#121
hypercenter	#334	D₁₉
hypocenter	C₁₉	#1672
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#10597341

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#334

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
55. C₈×C₁₉	Q₁₆	semidirect
93. C₁₉	#1672	semidirect
127. C₈	Dic₇₆	semidirect

H ≅ G/N

type

55. C₈×C₁₉

Q₁₆

semidirect

93. C₁₉

#1672

semidirect

127. C₈

Dic₇₆

semidirect

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

subgroup	index
#11926942	2
#11926840	2
#11926755	2
C₈×Dic₃₈	2
#11926292	2
#11926291	2
C₁₉×#334	2
#1672	19

subgroup

index

C₈×Dic₃₈

C₁₉×#334

Subgroups — #14563018

Conjugacy classes of subgroups

Complements

Maximal subgroups