Group #14563216 — subgroups

Subgroups — #14563216

Order 2432.

140 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 49 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	#11926894	C₂	1	1	yes	maximal, characteristic
2	#11926840	C₂	1	1	yes	maximal, characteristic
3	#11926826	C₂	1	1	yes	maximal, characteristic
4	#11926671	C₂	1	1	yes	maximal, characteristic
5	#11926294	C₂	1	1	yes	maximal, characteristic
6	#11926292	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#332	C₂	1	1	yes	maximal, characteristic
8	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	#10597315	C₂²	1	1	yes	characteristic
10	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
11	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	#10597292	—	2	1	no	—
14	#10597292	—	2	1	no	—
15	#10597275	—	2	1	no	—
16	#10597273	—	2	1	no	—
17	#10597272	—	2	1	no	—
18	Dic₁₉⋊C₈	—	2	1	no	—
19	#10597267	—	2	1	no	—
20	#10597265	—	2	1	no	—
21	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₁₉	—	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	C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₄⋊Dic₁₉	—	2	1	no	—
32	C₄⋊Dic₁₉	—	2	1	no	—
33	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
34	Dic₁₉⋊C₄	—	2	1	no	—
35	C₄×Dic₁₉	—	2	1	no	—
36	C₂×C₁₉⋊C₈	—	2	1	no	—
37	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
38	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
39	Q₈×C₁₉	—	4	1	no	—
40	Q₈×C₁₉	—	4	1	no	—
41	C₂×C₄×C₁₉	—	4	1	no	—
42	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
45	C₂×Dic₁₉	—	2	1	no	—
46	C₂×Dic₁₉	—	2	1	no	—
47	C₂×Dic₁₉	—	4	1	no	—
48	Dic₃₈	—	2	1	no	—
49	Dic₃₈	—	2	1	no	—
50	Dic₃₈	—	8	1	no	—
51	C₈×C₁₉	—	4	1	no	—
52	C₈×C₁₉	—	4	1	no	—
53	C₁₉⋊C₈	—	2	1	no	—
54	C₁₉⋊C₈	—	2	1	no	—
55	C₁₉⋊C₈	—	4	1	no	—
56	#1704	—	19	1	no	maximal, Sylow
57	C₂²×C₁₉	#121	1	1	yes	characteristic
58	C₄×C₁₉	—	2	1	no	—
59	C₄×C₁₉	—	8	1	no	—
60	C₄×C₁₉	#135	1	1	yes	characteristic
61	C₄×C₁₉	#137	1	1	yes	characteristic
62	C₄×C₁₉	#137	1	1	yes	characteristic
63	C₄×C₁₉	#137	1	1	yes	characteristic
64	Dic₁₉	—	4	1	no	—
65	Dic₁₉	—	4	1	no	—
66	Dic₁₉	—	8	1	no	—
67	#487	—	19	1	no	—
68	#477	—	19	1	no	—
69	#475	—	19	1	no	—
70	#446	—	19	1	no	—
71	#334	—	19	1	no	—
72	#333	—	19	1	no	—
73	#332	D₁₉	1	1	yes	characteristic
74	C₂×C₁₉	#464	1	1	yes	characteristic
75	C₂×C₁₉	#470	1	1	yes	characteristic
76	C₂×C₁₉	#471	1	1	yes	characteristic
77	C₄⋊Q₈	—	19	1	no	—
78	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
79	C₄×Q₈	—	19	1	no	—
80	#107	—	38	1	no	—
81	#106	—	38	1	no	—
82	C₄⋊C₈	—	19	1	no	—
83	C₄⋊C₈	—	38	1	no	—
84	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
85	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
86	#103	—	38	1	no	—
87	#103	—	38	1	no	—
88	#103	—	38	1	no	—
89	#103	—	38	1	no	—
90	#97	—	38	1	no	—
91	C₄×C₈	—	19	1	no	—
92	C₁₉	#1704	1	1	yes	characteristic, complemented, Sylow
93	C₂×Q₈	—	2	1	no	—
94	C₂×Q₈	—	19	1	no	—
95	C₂×Q₈	—	38	1	no	—
96	C₂×C₈	—	2	1	no	—
97	C₂×C₈	—	2	1	no	—
98	C₂×C₈	—	19	1	no	—
99	C₂×C₈	—	19	1	no	—
100	C₂×C₈	—	38	1	no	—
101	C₄⋊C₄	—	2	1	no	—
102	C₄⋊C₄	—	2	1	no	—
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	C₄²	—	38	1	no	—
108	C₄²	C₂²×D₁₉	1	1	yes	characteristic
109	Q₈	—	4	1	no	—
110	Q₈	—	4	1	no	—
111	Q₈	—	38	1	no	—
112	Q₈	—	38	1	no	—
113	Q₈	—	152	1	no	—
114	C₂×C₄	—	4	1	no	—
115	C₂×C₄	—	38	1	no	—
116	C₂×C₄	—	38	1	no	—
117	C₂×C₄	—	76	1	no	—
118	C₂×C₄	#64541	1	1	yes	characteristic
119	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
120	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
121	C₈	—	4	1	no	—
122	C₈	—	4	1	no	—
123	C₈	—	38	1	no	—
124	C₈	—	38	1	no	—
125	C₈	—	76	1	no	—
126	C₂²	#10597330	1	1	yes	characteristic
127	C₄	—	2	1	no	—
128	C₄	—	8	1	no	—
129	C₄	—	76	1	no	—
130	C₄	—	76	1	no	—
131	C₄	—	152	1	no	—
132	C₄	#10597358	1	1	yes	characteristic
133	C₄	#10597361	1	1	yes	characteristic
134	C₄	#10597361	1	1	yes	characteristic
135	C₄	#10597364	1	1	yes	characteristic
136	C₂	#11926765	1	1	yes	characteristic
137	C₂	#11926801	1	1	yes	characteristic
138	C₂	#11926810	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926894

C₂

yes

maximal, characteristic

#11926840

C₂

yes

maximal, characteristic

#11926826

C₂

yes

maximal, characteristic

#11926671

C₂

yes

maximal, characteristic

#11926294

C₂

yes

maximal, characteristic

#11926292

C₂

yes

maximal, characteristic

C₁₉×#332

C₂

yes

maximal, characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₄×Dic₃₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

—

—

—

—

—

Dic₁₉⋊C₈

—

#10597267

—

#10597265

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

characteristic

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

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

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

—

—

D₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

C₄×Q₈

—

#107

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₉

yes

characteristic

C₄⋊C₈

C₂×D₁₉

yes

—

—

—

—

—

C₄×C₈

—

C₁₉

#1704

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄²

—

108

C₄²

C₂²×D₁₉

yes

characteristic

109

Q₈

—

110

Q₈

—

111

Q₈

—

112

Q₈

—

113

Q₈

—

152

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

#64541

yes

characteristic

119

C₂×C₄

D₄×D₁₉

yes

characteristic

120

C₂×C₄

D₄×D₁₉

yes

characteristic

121

C₈

—

122

C₈

—

123

C₈

—

124

C₈

—

125

C₈

—

126

C₂²

#10597330

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

152

—

132

C₄

#10597358

yes

characteristic

133

C₄

#10597361

yes

characteristic

134

C₄

#10597361

yes

characteristic

135

C₄

#10597364

yes

characteristic

136

C₂

#11926765

yes

characteristic

137

C₂

#11926801

yes

characteristic

138

C₂

#11926810

yes

characteristic

	subgroup	G/H
center	C₂²	#10597330
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#332	C₂
socle, prime radical	C₂²×C₁₉	#121
hypercenter	#332	D₁₉
hypocenter	C₁₉	#1704
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #332

subgroup

G/H

center

C₂²

#10597330

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#332

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #332

N	H ≅ G/N	type
92. C₁₉	#1704	semidirect

H ≅ G/N

type

92. C₁₉

#1704

semidirect

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

subgroup	index
#11926894	2
#11926840	2
#11926826	2
#11926671	2
#11926294	2
#11926292	2
C₁₉×#332	2
#1704	19

subgroup

index

C₁₉×#332

Subgroups — #14563216

Conjugacy classes of subgroups

Complements

Maximal subgroups