Group #14564421 — subgroups

Subgroups — #14564421

Order 2432.

196 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 97 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	#11926586	C₂	1	2	yes	maximal
2	C₂×#10597275	C₂	1	1	yes	maximal, characteristic
3	#11926499	C₂	1	1	yes	maximal, characteristic
4	#11926312	C₂	1	2	yes	maximal
5	C₂×C₁₉×#108	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	#10597372	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
10	C₂×#64520	C₂²	1	1	yes	characteristic
11	C₁₉×#108	C₄	1	4	yes	complemented
12	#10597275	—	2	1	no	—
13	#10597275	—	2	1	no	—
14	#10597275	—	2	2	no	—
15	#10597274	—	2	2	no	—
16	#10597272	—	2	1	no	—
17	C₈×Dic₁₉	—	2	1	no	—
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×Dic₁₉	—	2	2	no	—
20	M₁₆×C₁₉	—	2	2	no	—
21	M₁₆×C₁₉	C₂×C₄	1	4	yes	—
22	C₂×C₈×C₁₉	—	2	2	no	—
23	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₈×C₁₉	Q₈	1	2	yes	—
27	C₂²⋊Dic₁₉	—	2	1	no	—
28	C₄⋊Dic₁₉	—	2	2	no	—
29	C₄⋊Dic₁₉	—	2	2	no	—
30	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
31	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
32	C₄×Dic₁₉	—	2	1	no	—
33	#64520	—	2	1	no	—
34	#64520	Q₈	1	2	yes	—
35	C₂×C₁₉⋊C₈	—	2	1	no	—
36	C₂³×C₁₉	#41	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₁₉	C₂×Q₈	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	2	no	—
46	C₂×Dic₁₉	—	8	2	no	—
47	C₈×C₁₉	—	2	4	no	—
48	C₈×C₁₉	C₄⋊C₄	1	2	yes	—
49	C₈×C₁₉	C₄⋊C₄	1	2	yes	—
50	C₁₉⋊C₈	—	2	2	no	—
51	#1952	—	19	1	no	maximal, Sylow
52	C₂²×C₁₉	—	2	1	no	—
53	C₂²×C₁₉	—	2	1	no	—
54	C₂²×C₁₉	C₄×Q₈	1	1	yes	characteristic
55	C₂²×C₁₉	#121	1	1	yes	characteristic
56	C₂²×C₁₉	#125	1	1	yes	characteristic
57	C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
59	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
60	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
61	Dic₁₉	—	4	1	no	—
62	Dic₁₉	—	4	1	no	—
63	Dic₁₉	—	8	2	no	—
64	C₂×#108	D₁₉	1	1	yes	characteristic
65	#428	—	19	2	no	—
66	C₂×#107	—	19	1	no	—
67	#405	—	19	1	no	—
68	#343	—	19	2	no	—
69	C₂×C₁₉	—	2	1	no	—
70	C₂×C₁₉	—	2	1	no	—
71	C₂×C₁₉	#389	1	1	yes	characteristic
72	C₂×C₁₉	#472	1	1	yes	characteristic
73	C₂×C₁₉	#473	1	1	yes	characteristic
74	C₂×M₁₆	—	19	1	no	—
75	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
76	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
77	#117	—	19	1	no	—
78	C₂×C₄⋊C₄	—	19	2	no	—
79	#108	Dic₁₉	1	4	yes	complemented
80	#107	—	38	2	no	—
81	#107	—	38	1	no	—
82	#107	—	38	1	no	—
83	#106	—	38	2	no	—
84	#97	—	38	1	no	—
85	C₄×C₈	—	38	1	no	—
86	C₁₉	#1952	1	1	yes	characteristic, complemented, Sylow
87	C₂²×C₄	—	38	2	no	—
88	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
89	M₁₆	—	2	2	no	—
90	M₁₆	—	19	2	no	—
91	M₁₆	—	38	1	no	—
92	M₁₆	C₂×Dic₁₉	1	4	yes	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	38	1	no	—
95	C₂×C₈	Dic₃₈	1	2	yes	—
96	C₂×C₈	D₇₆	1	1	yes	characteristic
97	C₂×C₈	D₇₆	1	1	yes	characteristic
98	C₂×C₈	C₂×Dic₁₉	1	2	yes	—
99	C₄⋊C₄	—	19	1	no	—
100	C₄⋊C₄	—	19	1	no	—
101	C₄⋊C₄	—	38	2	no	—
102	C₄⋊C₄	—	38	2	no	—
103	C₂²⋊C₄	—	38	1	no	—
104	C₄²	—	38	1	no	—
105	C₂³	#64545	1	1	yes	characteristic
106	C₂×C₄	—	38	1	no	—
107	C₂×C₄	—	38	1	no	—
108	C₂×C₄	—	76	2	no	—
109	C₂×C₄	—	152	2	no	—
110	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
111	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
112	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
113	C₂×C₄	#64543	1	1	yes	characteristic
114	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
115	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
116	C₈	—	2	4	no	—
117	C₈	—	38	2	no	—
118	C₈	C₄⋊Dic₁₉	1	2	yes	—
119	C₈	C₄⋊Dic₁₉	1	2	yes	—
120	C₂²	—	2	1	no	—
121	C₂²	—	2	1	no	—
122	C₂²	#10597336	1	1	yes	characteristic
123	C₂²	#10597341	1	1	yes	characteristic
124	C₂²	Q₈×Dic₁₉	1	1	yes	characteristic
125	C₄	—	76	1	no	—
126	C₄	—	76	1	no	—
127	C₄	—	152	2	no	—
128	C₄	#10597334	1	1	yes	characteristic
129	C₄	#10597343	1	1	yes	characteristic
130	C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
131	C₄	D₄×Dic₁₉	1	1	yes	characteristic
132	C₂	—	2	1	no	—
133	C₂	—	2	1	no	—
134	C₂	#11926443	1	1	yes	characteristic
135	C₂	#11926815	1	1	yes	characteristic
136	C₂	#11926820	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926586

C₂

yes

maximal

C₂×#10597275

C₂

yes

maximal, characteristic

#11926499

C₂

yes

maximal, characteristic

#11926312

C₂

yes

maximal

C₂×C₁₉×#108

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

#10597372

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×#64520

C₂²

yes

characteristic

C₁₉×#108

C₄

yes

—

—

—

—

—

C₈×Dic₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

Q₈

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

—

#64520

—

#64520

Q₈

yes

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

#41

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₄⋊C₄

yes

—

C₈×C₁₉

C₄⋊C₄

yes

—

C₁₉⋊C₈

—

#1952

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₄×Q₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₄⋊Q₈

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×#108

D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

#108

Dic₁₉

yes

—

—

—

—

—

C₄×C₈

—

C₁₉

#1952

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

C₂×Dic₁₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₃₈

yes

—

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

C₂×Dic₁₉

yes

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₂²⋊C₄

—

104

C₄²

—

105

C₂³

#64545

yes

characteristic

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

152

—

110

C₂×C₄

C₂×Dic₃₈

yes

characteristic

111

C₂×C₄

C₂×D₇₆

yes

characteristic

112

C₂×C₄

D₄×D₁₉

yes

characteristic

113

C₂×C₄

#64543

yes

characteristic

114

C₂×C₄

Q₈×D₁₉

yes

characteristic

115

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

116

C₈

—

117

C₈

—

118

C₈

C₄⋊Dic₁₉

yes

—

119

C₈

C₄⋊Dic₁₉

yes

—

120

C₂²

—

121

C₂²

—

122

C₂²

#10597336

yes

characteristic

123

C₂²

#10597341

yes

characteristic

124

C₂²

Q₈×Dic₁₉

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

—

152

—

128

C₄

#10597334

yes

characteristic

129

C₄

#10597343

yes

characteristic

130

C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

131

C₄

D₄×Dic₁₉

yes

characteristic

132

C₂

—

133

C₂

—

134

C₂

#11926443

yes

characteristic

135

C₂

#11926815

yes

characteristic

136

C₂

#11926820

yes

characteristic

	subgroup	G/H
center	C₂²	#10597341
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#108	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂³×C₁₉	#41
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#108	D₁₉
hypocenter	C₁₉	#1952
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂²

#10597341

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#108

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
11. C₁₉×#108	C₄	semidirect
79. #108	Dic₁₉	semidirect
86. C₁₉	#1952	semidirect

H ≅ G/N

type

11. C₁₉×#108

C₄

semidirect

79. #108

Dic₁₉

semidirect

86. C₁₉

#1952

semidirect

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

subgroup	index
#11926586	2
C₂×#10597275	2
#11926499	2
#11926312	2
C₂×C₁₉×#108	2
#1952	19

subgroup

index

C₂×C₁₉×#108

Subgroups — #14564421

Conjugacy classes of subgroups

Complements

Maximal subgroups