Group #14562716 — subgroups

Subgroups — #14562716

Order 2432.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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	#11927260	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926736	C₂	1	2	yes	maximal, complemented
3	#11926293	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926273	C₂	1	2	yes	maximal, complemented
5	C₁₉×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×SD₁₆×C₁₉	—	2	2	no	—
7	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₁₉×#127	C₂²	1	1	yes	characteristic
9	#10597393	—	2	2	no	—
10	C₂×#64525	—	2	2	no	—
11	#10597341	—	2	2	no	—
12	#10597338	—	2	2	no	—
13	C₄×D₇₆	C₂²	1	2	yes	—
14	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	#10597289	—	2	2	no	—
16	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
17	C₂×Q₈×C₁₉	D₄	1	2	yes	—
18	C₂×D₄×C₁₉	—	2	2	no	—
19	C₂×D₄×C₁₉	—	2	1	no	—
20	C₂×D₇₆	—	2	2	no	—
21	C₂×D₇₆	D₄	1	2	yes	—
22	C₂×C₄×D₁₉	—	2	2	no	—
23	SD₁₆×C₁₉	—	4	4	no	—
24	C₂×C₈×C₁₉	—	2	1	no	—
25	C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	#64525	—	4	4	no	—
28	(C₂×D₁₉)⋊C₄	—	2	4	no	—
29	(C₂×D₁₉)⋊C₄	—	2	2	no	—
30	C₄⋊Dic₁₉	D₄	1	2	yes	—
31	C₄×Dic₁₉	—	2	2	no	—
32	C₂×C₁₉⋊C₈	—	2	2	no	—
33	C₂³×C₁₉	—	4	1	no	—
34	C₂²×D₁₉	—	2	2	no	—
35	Q₈×C₁₉	—	4	2	no	—
36	D₄×C₁₉	—	4	2	no	—
37	D₄×C₁₉	—	4	2	no	—
38	D₄×C₁₉	—	4	2	no	—
39	C₂×C₄×C₁₉	—	2	2	no	—
40	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
41	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂×Dic₁₉	—	2	2	no	—
43	D₇₆	—	2	2	no	—
44	D₇₆	—	2	2	no	—
45	D₇₆	—	8	2	no	—
46	C₄×D₁₉	—	4	2	no	—
47	C₄×D₁₉	—	4	2	no	—
48	C₈×C₁₉	—	2	2	no	—
49	C₁₉⋊C₈	—	4	2	no	—
50	#1624	—	19	1	no	maximal, Sylow
51	C₂²×C₁₉	—	8	2	no	—
52	C₂²×C₁₉	—	8	1	no	—
53	C₂²×C₁₉	#120	1	1	yes	characteristic
54	C₂×D₁₉	—	4	2	no	—
55	C₂×D₁₉	—	4	2	no	—
56	C₂×D₁₉	—	4	2	no	—
57	C₄×C₁₉	—	2	1	no	—
58	C₄×C₁₉	—	4	2	no	—
59	C₄×C₁₉	#135	1	2	yes	—
60	C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
61	Dic₁₉	—	4	2	no	—
62	#555	—	19	1	no	—
63	#492	D₁₉	1	1	yes	characteristic, complemented
64	#459	—	19	2	no	—
65	#333	—	19	1	no	—
66	D₄⋊C₈	—	19	2	no	—
67	C₂×C₁₉	—	16	1	no	—
68	C₂×C₁₉	#449	1	2	yes	—
69	C₂×C₁₉	#453	1	1	yes	characteristic
70	D₁₉	—	8	2	no	—
71	C₂×SD₁₆	—	2	2	no	—
72	C₂×D₈	—	38	2	no	—
73	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
74	#127	C₂×D₁₉	1	1	yes	characteristic
75	#124	—	38	2	no	—
76	#121	—	38	2	no	—
77	C₄×D₄	—	19	2	no	—
78	#117	—	38	2	no	—
79	C₄⋊C₈	—	19	2	no	—
80	#102	—	38	2	no	—
81	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
82	C₁₉	#1624	1	1	yes	characteristic, complemented, Sylow
83	C₂×Q₈	C₂²⋊D₁₉	1	2	yes	—
84	C₂×D₄	—	2	2	no	—
85	C₂×D₄	—	2	1	no	—
86	C₂×D₄	—	19	2	no	—
87	C₂×D₄	—	38	2	no	—
88	C₂²×C₄	—	38	2	no	—
89	SD₁₆	—	4	4	no	—
90	D₈	—	76	4	no	—
91	C₂×C₈	—	2	1	no	—
92	C₂×C₈	—	38	2	no	—
93	C₄⋊C₄	—	2	2	no	—
94	C₄⋊C₄	—	19	2	no	—
95	C₂²⋊C₄	—	38	4	no	—
96	C₂²⋊C₄	—	38	2	no	—
97	C₄²	—	38	2	no	—
98	C₄²	C₂²×D₁₉	1	1	yes	characteristic
99	C₂³	—	4	1	no	—
100	C₂³	—	38	2	no	—
101	Q₈	—	4	2	no	—
102	D₄	—	4	2	no	—
103	D₄	—	4	2	no	—
104	D₄	—	4	2	no	—
105	D₄	—	38	2	no	—
106	D₄	—	38	2	no	—
107	D₄	—	152	2	no	—
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	—	38	2	no	—
110	C₂×C₄	—	76	2	no	—
111	C₂×C₄	—	76	2	no	—
112	C₂×C₄	D₄×D₁₉	1	2	yes	—
113	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	76	2	no	—
116	C₂²	—	8	2	no	—
117	C₂²	—	8	1	no	—
118	C₂²	—	76	2	no	—
119	C₂²	—	76	2	no	—
120	C₂²	—	76	2	no	—
121	C₂²	#10597383	1	1	yes	characteristic
122	C₄	—	2	1	no	—
123	C₄	—	4	2	no	—
124	C₄	—	76	2	no	—
125	C₄	#10597360	1	2	yes	—
126	C₄	#10597362	1	2	yes	—
127	C₂	—	16	1	no	—
128	C₂	—	152	2	no	—
129	C₂	#11926688	1	2	yes	—
130	C₂	#11926711	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927260

C₂

yes

maximal, characteristic, complemented

#11926736

C₂

yes

maximal, complemented

#11926293

C₂

yes

maximal, characteristic, complemented

#11926273

C₂

yes

maximal, complemented

C₁₉×#492

C₂

yes

maximal, characteristic, complemented

C₂×SD₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#127

C₂²

yes

—

—

—

—

C₄×D₇₆

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597289

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₇₆

—

C₂×D₇₆

D₄

yes

—

C₂×C₄×D₁₉

—

SD₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

#64525

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

D₄

yes

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1624

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#120

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#135

yes

—

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

Dic₁₉

—

#555

—

#492

D₁₉

yes

characteristic, complemented

#459

—

#333

—

D₄⋊C₈

—

C₂×C₁₉

—

C₂×C₁₉

#449

yes

—

C₂×C₁₉

#453

yes

characteristic

D₁₉

—

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

#127

C₂×D₁₉

yes

characteristic

#124

—

#121

—

C₄×D₄

—

#117

—

C₄⋊C₈

—

#102

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1624

yes

characteristic, complemented, Sylow

C₂×Q₈

C₂²⋊D₁₉

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

SD₁₆

—

D₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂²×D₁₉

yes

characteristic

C₂³

—

100

C₂³

—

101

Q₈

—

102

D₄

—

103

D₄

—

104

D₄

—

105

D₄

—

106

D₄

—

107

D₄

—

152

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

D₄×D₁₉

yes

—

113

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

114

C₈

—

115

C₈

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

#10597383

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

#10597360

yes

—

126

C₄

#10597362

yes

—

127

C₂

—

128

C₂

—

152

—

129

C₂

#11926688

yes

—

130

C₂

#11926711

yes

characteristic

	subgroup	G/H
center	C₂²	#10597383
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#492	C₂
socle	C₂²×C₁₉	#120
hypercenter	#492	D₁₉
hypocenter	C₁₉	#1624
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #492

subgroup

G/H

center

C₂²

#10597383

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#492

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #492

N	H ≅ G/N	type
1. #11927260	C₂	semidirect
2. #11926736	C₂	semidirect
3. #11926293	C₂	semidirect
4. #11926273	C₂	semidirect
5. C₁₉×#492	C₂	semidirect
63. #492	D₁₉	semidirect
82. C₁₉	#1624	semidirect

H ≅ G/N

type

1. #11927260

C₂

semidirect

2. #11926736

C₂

semidirect

3. #11926293

C₂

semidirect

4. #11926273

C₂

semidirect

5. C₁₉×#492

C₂

semidirect

63. #492

D₁₉

semidirect

82. C₁₉

#1624

semidirect

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

subgroup	index
#11927260	2
#11926736	2
#11926293	2
#11926273	2
C₁₉×#492	2
#1624	19

subgroup

index

C₁₉×#492

Subgroups — #14562716

Conjugacy classes of subgroups

Complements

Maximal subgroups