Group #14564977 — subgroups

Subgroups — #14564977

Order 2432.

246 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 75 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	#11926587	C₂	1	2	yes	maximal
2	#11926413	C₂	1	1	yes	maximal, characteristic
3	#11926313	C₂	1	1	yes	maximal, characteristic
4	#11926303	C₂	1	2	yes	maximal
5	C₁₉×#544	C₂	1	1	yes	maximal, characteristic
6	C₁₉×C₄⋊Q₈	—	2	2	no	—
7	C₁₉×#125	—	2	2	no	—
8	C₁₉×C₂²⋊Q₈	—	2	2	no	—
9	C₁₉×#117	C₂²	1	2	yes	—
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×Dic₁₉⋊C₄	—	2	2	no	—
13	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
14	C₂×#64520	C₂²	1	2	yes	—
15	#10597265	—	2	2	no	—
16	#10597264	—	2	2	no	—
17	C₂×Q₈×C₁₉	—	2	2	no	—
18	C₂²×C₄×C₁₉	D₄	1	2	yes	—
19	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
20	C₂²×Dic₁₉	—	2	1	no	—
21	C₂²×Dic₁₉	—	2	1	no	—
22	C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₄⋊C₄×C₁₉	—	2	4	no	—
24	C₄⋊C₄×C₁₉	—	2	2	no	—
25	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
26	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
27	C₂²⋊C₄×C₁₉	—	2	2	no	—
28	C₄²×C₁₉	—	2	2	no	—
29	C₄⋊Dic₁₉	—	2	2	no	—
30	Dic₁₉⋊C₄	—	4	4	no	—
31	C₄×Dic₁₉	—	2	1	no	—
32	C₄×Dic₁₉	Q₈	1	2	yes	complemented
33	#64520	—	2	2	no	—
34	#64520	Q₈	1	4	yes	complemented
35	C₂×C₁₉⋊C₈	—	2	2	no	—
36	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
37	Q₈×C₁₉	—	8	2	no	—
38	C₂×C₄×C₁₉	—	2	2	no	—
39	C₂×C₄×C₁₉	—	2	2	no	—
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	4	2	no	—
42	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
44	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
46	C₂×Dic₁₉	—	2	2	no	—
47	C₂×Dic₁₉	—	2	2	no	—
48	C₂×Dic₁₉	—	2	2	no	—
49	C₂×Dic₁₉	—	4	2	no	—
50	C₂×Dic₁₉	—	4	1	no	—
51	C₁₉⋊C₈	—	2	4	no	—
52	#2060	—	19	1	no	maximal, Sylow
53	C₂²×C₁₉	—	2	1	no	—
54	C₂²×C₁₉	—	2	1	no	—
55	C₂²×C₁₉	#120	1	1	yes	characteristic
56	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
57	C₂²×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
58	C₄×C₁₉	—	4	2	no	—
59	C₄×C₁₉	—	4	2	no	—
60	C₄×C₁₉	—	4	2	no	—
61	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
62	C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
63	Dic₁₉	—	2	4	no	—
64	Dic₁₉	—	8	1	no	—
65	#544	D₁₉	1	1	yes	characteristic
66	#428	—	19	2	no	—
67	#384	—	19	1	no	—
68	#343	—	19	1	no	—
69	#339	—	19	2	no	—
70	C₂×C₁₉	—	2	1	no	—
71	C₂×C₁₉	—	2	1	no	—
72	C₂×C₁₉	#395	1	1	yes	characteristic
73	C₂×C₁₉	#453	1	1	yes	characteristic
74	C₂×C₁₉	#456	1	1	yes	characteristic
75	C₂×M₁₆	—	19	2	no	—
76	C₄⋊Q₈	—	2	2	no	—
77	#125	—	2	2	no	—
78	C₂²⋊Q₈	—	2	2	no	—
79	#117	C₂×D₁₉	1	2	yes	—
80	C₂×C₄⋊C₄	—	19	1	no	—
81	C₂×C₄⋊C₄	—	38	2	no	—
82	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
83	C₂×C₄²	—	19	1	no	—
84	#107	—	38	2	no	—
85	#106	—	38	2	no	—
86	C₁₉	#2060	1	1	yes	characteristic, complemented, Sylow
87	C₂×Q₈	—	2	2	no	—
88	C₂²×C₄	—	38	1	no	—
89	C₂²×C₄	—	38	1	no	—
90	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
91	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
92	M₁₆	—	19	4	no	—
93	M₁₆	—	38	2	no	—
94	C₂×C₈	—	38	2	no	—
95	C₄⋊C₄	—	2	2	no	—
96	C₄⋊C₄	—	2	4	no	—
97	C₄⋊C₄	—	2	2	no	—
98	C₄⋊C₄	—	38	2	no	—
99	C₄⋊C₄	—	76	4	no	—
100	C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
101	C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
102	C₂²⋊C₄	—	2	2	no	—
103	C₄²	—	2	2	no	—
104	C₄²	—	19	2	no	—
105	C₄²	—	38	1	no	—
106	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
107	Q₈	—	8	2	no	—
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	—	2	2	no	—
110	C₂×C₄	—	2	2	no	—
111	C₂×C₄	—	4	2	no	—
112	C₂×C₄	—	38	2	no	—
113	C₂×C₄	—	38	2	no	—
114	C₂×C₄	—	38	2	no	—
115	C₂×C₄	—	76	2	no	—
116	C₂×C₄	—	76	1	no	—
117	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
118	C₂×C₄	Q₈×D₁₉	1	2	yes	—
119	C₂×C₄	#64545	1	1	yes	characteristic
120	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
121	C₈	—	38	4	no	—
122	C₂²	—	2	1	no	—
123	C₂²	—	2	1	no	—
124	C₂²	#10597390	1	1	yes	characteristic
125	C₂²	#10597392	1	1	yes	characteristic
126	C₂²	#10597399	1	1	yes	characteristic
127	C₄	—	4	2	no	—
128	C₄	—	4	2	no	—
129	C₄	—	4	2	no	—
130	C₄	—	38	4	no	—
131	C₄	—	152	1	no	—
132	C₄	#10597390	1	2	yes	—
133	C₄	#10597392	1	2	yes	—
134	C₂	—	2	1	no	—
135	C₂	—	2	1	no	—
136	C₂	#11926463	1	1	yes	characteristic
137	C₂	#11926712	1	1	yes	characteristic
138	C₂	#11926727	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926587

C₂

yes

maximal

#11926413

C₂

yes

maximal, characteristic

#11926313

C₂

yes

maximal, characteristic

#11926303

C₂

yes

maximal

C₁₉×#544

C₂

yes

maximal, characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×#117

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

#10597265

—

#10597264

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

Q₈

yes

complemented

#64520

—

#64520

Q₈

yes

complemented

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#2060

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#120

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

C₄⋊Q₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

C₄⋊Q₈

yes

—

Dic₁₉

—

Dic₁₉

—

#544

D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

#117

C₂×D₁₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₄²

—

#107

—

#106

—

C₁₉

#2060

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

C₂²⋊D₁₉

yes

—

101

C₄⋊C₄

C₂²⋊D₁₉

yes

—

102

C₂²⋊C₄

—

103

C₄²

—

104

C₄²

—

105

C₄²

—

106

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

107

Q₈

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

Q₈×D₁₉

yes

characteristic

118

C₂×C₄

Q₈×D₁₉

yes

—

119

C₂×C₄

#64545

yes

characteristic

120

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

121

C₈

—

122

C₂²

—

123

C₂²

—

124

C₂²

#10597390

yes

characteristic

125

C₂²

#10597392

yes

characteristic

126

C₂²

#10597399

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

152

—

132

C₄

#10597390

yes

—

133

C₄

#10597392

yes

—

134

C₂

—

135

C₂

—

136

C₂

#11926463

yes

characteristic

137

C₂

#11926712

yes

characteristic

138

C₂

#11926727

yes

characteristic

	subgroup	G/H
center	C₂²	#10597399
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#544	C₂
socle	C₂²×C₁₉	#120
prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#544	D₁₉
hypocenter	C₁₉	#2060
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #544

subgroup

G/H

center

C₂²

#10597399

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#544

C₂

socle

C₂²×C₁₉

#120

prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #544

N	H ≅ G/N	type
32. C₄×Dic₁₉	Q₈	semidirect
34. #64520	Q₈	semidirect
86. C₁₉	#2060	semidirect

H ≅ G/N

type

32. C₄×Dic₁₉

Q₈

semidirect

34. #64520

Q₈

semidirect

86. C₁₉

#2060

semidirect

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

subgroup	index
#11926587	2
#11926413	2
#11926313	2
#11926303	2
C₁₉×#544	2
#2060	19

subgroup

index

C₁₉×#544

Subgroups — #14564977

Conjugacy classes of subgroups

Complements

Maximal subgroups