Group #14563305 — subgroups

Subgroups — #14563305

Order 2432.

198 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 61 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	#11926947	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926923	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926918	C₂	1	1	yes	maximal, characteristic
4	#11926892	C₂	1	1	yes	maximal, characteristic
5	#11926891	C₂	1	1	yes	maximal, characteristic
6	#11926266	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#500	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×#64528	—	2	2	no	—
11	C₂×#64527	—	2	2	no	—
12	#10597320	C₂²	1	1	yes	characteristic
13	#10597315	C₂²	1	1	yes	characteristic
14	C₁₉×#107	—	2	2	no	—
15	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	#10597278	—	2	2	no	—
17	#10597266	—	2	2	no	—
18	#10597264	—	2	2	no	—
19	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Q₈×C₁₉	—	2	1	no	—
22	C₂×Q₈×C₁₉	—	2	1	no	—
23	C₂×D₇₆	—	2	1	no	—
24	C₂×D₇₆	—	2	1	no	—
25	C₂×D₇₆	—	2	1	no	—
26	C₂×Dic₃₈	—	2	1	no	—
27	C₂×C₈×C₁₉	D₄	1	2	yes	—
28	C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₄²×C₁₉	C₂³	1	1	yes	characteristic
33	#64528	—	4	4	no	—
34	#64527	—	4	4	no	—
35	C₄⋊Dic₁₉	—	2	1	no	—
36	C₄⋊Dic₁₉	—	2	1	no	—
37	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
38	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
39	C₂²×D₁₉	—	4	1	no	—
40	Q₈×C₁₉	—	4	2	no	—
41	Q₈×C₁₉	—	4	2	no	—
42	C₂×C₄×C₁₉	—	4	1	no	—
43	C₂×C₄×C₁₉	—	4	1	no	—
44	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₂×Dic₁₉	—	4	1	no	—
48	D₇₆	—	4	2	no	—
49	D₇₆	—	4	2	no	—
50	D₇₆	—	4	2	no	—
51	Dic₃₈	—	4	2	no	—
52	C₈×C₁₉	—	2	2	no	—
53	C₁₉⋊C₈	—	2	2	no	—
54	C₁₉⋊C₈	D₈	1	4	yes	—
55	#1722	—	19	1	no	maximal, Sylow
56	C₂²×C₁₉	#127	1	1	yes	characteristic
57	C₂×D₁₉	—	8	1	no	—
58	C₂×D₁₉	—	8	1	no	—
59	C₂×D₁₉	—	8	1	no	—
60	C₄×C₁₉	—	8	1	no	—
61	C₄×C₁₉	—	8	1	no	—
62	C₄×C₁₉	C₂×D₈	1	2	yes	—
63	C₄×C₁₉	#137	1	2	yes	—
64	C₄×C₁₉	#137	1	2	yes	—
65	Dic₁₉	—	8	1	no	—
66	#500	—	19	1	no	—
67	#500	D₁₉	1	1	yes	characteristic, complemented
68	#494	—	19	1	no	—
69	#492	—	19	1	no	—
70	#486	—	19	1	no	—
71	#486	—	19	1	no	—
72	#322	—	19	1	no	—
73	C₂×C₁₉	#493	1	1	yes	characteristic
74	C₂×C₁₉	#497	1	1	yes	characteristic
75	C₂×C₁₉	#497	1	1	yes	characteristic
76	D₁₉	—	16	1	no	—
77	C₂×Q₁₆	—	38	2	no	—
78	C₂×SD₁₆	—	38	2	no	—
79	C₄⋊Q₈	—	19	1	no	—
80	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
81	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
82	#127	—	19	1	no	—
83	#107	—	2	2	no	—
84	#107	—	38	2	no	—
85	#102	—	38	2	no	—
86	#102	—	38	2	no	—
87	C₄×C₈	—	19	1	no	—
88	C₄×C₈	—	19	1	no	—
89	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
90	C₁₉	#1722	1	1	yes	characteristic, complemented, Sylow
91	C₂×Q₈	—	2	1	no	—
92	C₂×Q₈	—	2	1	no	—
93	C₂×Q₈	—	38	1	no	—
94	C₂×D₄	—	38	1	no	—
95	C₂×D₄	—	38	1	no	—
96	C₂×D₄	—	38	1	no	—
97	Q₁₆	—	76	4	no	—
98	SD₁₆	—	76	4	no	—
99	C₂×C₈	—	19	2	no	—
100	C₂×C₈	—	19	2	no	—
101	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
102	C₄⋊C₄	—	2	1	no	—
103	C₄⋊C₄	—	2	1	no	—
104	C₄⋊C₄	—	2	1	no	—
105	C₄⋊C₄	—	2	1	no	—
106	C₄⋊C₄	—	38	1	no	—
107	C₄⋊C₄	—	38	1	no	—
108	C₄²	C₂²×D₁₉	1	1	yes	characteristic
109	C₂³	—	76	1	no	—
110	Q₈	—	4	2	no	—
111	Q₈	—	4	2	no	—
112	Q₈	—	76	2	no	—
113	D₄	—	76	2	no	—
114	D₄	—	76	2	no	—
115	D₄	—	76	2	no	—
116	C₂×C₄	—	4	1	no	—
117	C₂×C₄	—	4	1	no	—
118	C₂×C₄	—	76	1	no	—
119	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
120	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
121	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
122	C₈	—	2	2	no	—
123	C₈	—	19	4	no	—
124	C₈	—	38	2	no	—
125	C₂²	—	152	1	no	—
126	C₂²	—	152	1	no	—
127	C₂²	—	152	1	no	—
128	C₂²	#10597386	1	1	yes	characteristic
129	C₄	—	8	1	no	—
130	C₄	—	8	1	no	—
131	C₄	—	152	1	no	—
132	C₄	D₈×D₁₉	1	2	yes	—
133	C₄	#10597364	1	2	yes	—
134	C₄	#10597388	1	2	yes	—
135	C₂	—	304	1	no	—
136	C₂	#11926919	1	1	yes	characteristic
137	C₂	#11926936	1	1	yes	characteristic
138	C₂	#11926937	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926947

C₂

yes

maximal, characteristic, complemented

#11926923

C₂

yes

maximal, characteristic, complemented

#11926918

C₂

yes

maximal, characteristic

#11926892

C₂

yes

maximal, characteristic

#11926891

C₂

yes

maximal, characteristic

#11926266

C₂

yes

maximal, characteristic, complemented

C₁₉×#500

C₂

yes

maximal, characteristic, complemented

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

—

—

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₁₉×#107

—

C₄×C₈×C₁₉

C₂²

yes

—

—

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

#64528

—

#64527

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

D₈

yes

—

—

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×D₈

yes

—

C₄×C₁₉

#137

yes

—

C₄×C₁₉

#137

yes

—

Dic₁₉

—

#500

—

#500

D₁₉

yes

characteristic, complemented

—

—

—

—

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

C₂×D₁₉

yes

—

—

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1722

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

SD₁₆

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

C₂²⋊D₁₉

yes

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄²

C₂²×D₁₉

yes

characteristic

109

C₂³

—

110

Q₈

—

111

Q₈

—

112

Q₈

—

113

D₄

—

114

D₄

—

115

D₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

D₄×D₁₉

yes

characteristic

120

C₂×C₄

D₄×D₁₉

yes

characteristic

121

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

122

C₈

—

123

C₈

—

124

C₈

—

125

C₂²

—

152

—

126

C₂²

—

152

—

127

C₂²

—

152

—

128

C₂²

#10597386

yes

characteristic

129

C₄

—

130

C₄

—

131

C₄

—

152

—

132

C₄

D₈×D₁₉

yes

—

133

C₄

#10597364

yes

—

134

C₄

#10597388

yes

—

135

C₂

—

304

—

136

C₂

#11926919

yes

characteristic

137

C₂

#11926936

yes

characteristic

138

C₂

#11926937

yes

characteristic

	subgroup	G/H
center	C₂²	#10597386
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#500	C₂
socle	C₂²×C₁₉	#127
prime radical	#10597320	C₂²
hypercenter	#500	D₁₉
hypocenter	C₁₉	#1722
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #500

subgroup

G/H

center

C₂²

#10597386

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#500

C₂

C₂²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #500

N	H ≅ G/N	type
1. #11926947	C₂	semidirect
2. #11926923	C₂	semidirect
6. #11926266	C₂	semidirect
7. C₁₉×#500	C₂	semidirect
67. #500	D₁₉	semidirect
90. C₁₉	#1722	semidirect

H ≅ G/N

type

1. #11926947

C₂

semidirect

2. #11926923

C₂

semidirect

6. #11926266

C₂

semidirect

7. C₁₉×#500

C₂

semidirect

67. #500

D₁₉

semidirect

90. C₁₉

#1722

semidirect

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

subgroup	index
#11926947	2
#11926923	2
#11926918	2
#11926892	2
#11926891	2
#11926266	2
C₁₉×#500	2
#1722	19

subgroup

index

C₁₉×#500

Subgroups — #14563305

Conjugacy classes of subgroups

Complements

Maximal subgroups