Group #14565708 — subgroups

Subgroups — #14565708

Order 2432.

170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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	#11926980	C₂	1	2	yes	maximal, complemented
2	#11926662	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926365	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926357	C₂	1	2	yes	maximal, complemented
5	C₁₉×#493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₈×C₁₉	—	2	1	no	—
7	C₂×D₈×C₁₉	C₂²	1	2	yes	—
8	C₁₉×#127	—	2	1	no	—
9	#10597350	C₂²	1	1	yes	characteristic
10	#10597347	—	2	1	no	—
11	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	#10597284	—	2	2	no	—
13	#10597283	—	2	2	no	—
14	#10597276	C₂²	1	1	yes	characteristic
15	#10597269	C₂²	1	2	yes	—
16	#10597262	—	2	1	no	—
17	C₂×D₄×C₁₉	—	2	2	no	—
18	C₂×D₄×C₁₉	—	4	2	no	—
19	#64541	—	2	1	no	—
20	D₈×C₁₉	—	2	2	no	—
21	D₈×C₁₉	—	2	2	no	—
22	D₈×C₁₉	—	4	1	no	—
23	D₈×C₁₉	—	4	1	no	—
24	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
26	C₄²×C₁₉	D₄	1	1	yes	characteristic
27	#64520	—	2	1	no	—
28	Dic₇₆	D₄	1	1	yes	characteristic, complemented
29	D₁₅₂	D₄	1	1	yes	characteristic, complemented
30	#64516	—	2	1	no	—
31	#64515	—	4	1	no	—
32	C₈×D₁₉	—	4	1	no	—
33	C₁₉⋊C₁₆	—	2	2	no	—
34	C₂³×C₁₉	—	4	2	no	—
35	D₄×C₁₉	—	4	2	no	—
36	D₄×C₁₉	—	4	2	no	—
37	D₄×C₁₉	—	8	4	no	—
38	C₂×C₄×C₁₉	—	2	1	no	—
39	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂²⋊D₁₉	—	4	1	no	—
41	D₇₆	—	2	1	no	—
42	C₄×D₁₉	—	4	1	no	—
43	Dic₃₈	—	2	1	no	—
44	C₈×C₁₉	D₈	1	1	yes	characteristic
45	C₈×C₁₉	D₈	1	1	yes	characteristic
46	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₈×C₁₉	#41	1	1	yes	characteristic
48	C₁₉⋊C₈	—	4	1	no	—
49	#2213	—	19	1	no	maximal, Sylow
50	C₂²×C₁₉	—	8	4	no	—
51	C₂²×C₁₉	—	8	2	no	—
52	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
53	C₂×D₁₉	—	4	1	no	—
54	C₄×C₁₉	—	2	2	no	—
55	C₄×C₁₉	#121	1	1	yes	characteristic
56	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
57	Dic₁₉	—	4	1	no	—
58	#509	—	19	2	no	—
59	#493	D₁₉	1	1	yes	characteristic, complemented
60	#443	—	19	1	no	—
61	#364	—	19	1	no	—
62	#361	—	19	2	no	—
63	C₂×C₁₉	—	2	1	no	—
64	C₂×C₁₉	—	16	2	no	—
65	C₂×C₁₉	#459	1	1	yes	characteristic
66	D₁₉	—	8	1	no	—
67	#135	—	19	1	no	—
68	C₂×D₈	—	2	1	no	—
69	C₂×D₈	C₂×D₁₉	1	2	yes	—
70	#131	—	38	1	no	—
71	#127	—	2	1	no	—
72	SD₃₂	—	38	2	no	—
73	D₁₆	—	38	2	no	—
74	M₃₂	—	19	2	no	—
75	#108	—	19	1	no	—
76	#104	—	38	1	no	—
77	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
78	C₁₉	#2213	1	1	yes	characteristic, complemented, Sylow
79	#41	—	38	1	no	—
80	C₂×D₄	—	2	2	no	—
81	C₂×D₄	—	4	2	no	—
82	Q₁₆	—	19	1	no	—
83	SD₁₆	—	38	1	no	—
84	D₈	—	2	2	no	—
85	D₈	—	2	2	no	—
86	D₈	—	4	1	no	—
87	D₈	—	4	1	no	—
88	D₈	—	19	1	no	—
89	M₁₆	—	38	1	no	—
90	M₁₆	—	76	1	no	—
91	C₂×C₈	—	76	1	no	—
92	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
93	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
94	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
95	C₁₆	—	38	2	no	—
96	C₂³	—	4	2	no	—
97	Q₈	—	38	1	no	—
98	D₄	—	4	2	no	—
99	D₄	—	4	2	no	—
100	D₄	—	8	4	no	—
101	D₄	—	38	1	no	—
102	D₄	—	76	1	no	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	76	1	no	—
105	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
106	C₈	—	76	1	no	—
107	C₈	#64525	1	1	yes	characteristic
108	C₈	#64525	1	1	yes	characteristic
109	C₈	D₄×D₁₉	1	1	yes	characteristic
110	C₈	#64543	1	1	yes	characteristic
111	C₂²	—	8	4	no	—
112	C₂²	—	8	2	no	—
113	C₂²	—	76	1	no	—
114	C₂²	#10597378	1	1	yes	characteristic
115	C₄	—	2	2	no	—
116	C₄	—	76	1	no	—
117	C₄	C₂×#64525	1	1	yes	characteristic
118	C₄	#10597384	1	1	yes	characteristic
119	C₂	—	2	1	no	—
120	C₂	—	16	2	no	—
121	C₂	—	152	1	no	—
122	C₂	#11926736	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926980

C₂

yes

maximal, complemented

#11926662

C₂

yes

maximal, characteristic, complemented

#11926365

C₂

yes

maximal, characteristic, complemented

#11926357

C₂

yes

maximal, complemented

C₁₉×#493

C₂

yes

maximal, characteristic, complemented

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

C₂²

yes

—

C₁₉×#127

—

#10597350

C₂²

yes

characteristic

#10597347

—

C₄×C₈×C₁₉

C₂²

yes

—

—

C₂²

yes

characteristic

#10597269

C₂²

yes

—

#10597262

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

#64541

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

#64520

—

Dic₇₆

D₄

yes

characteristic, complemented

D₁₅₂

D₄

yes

characteristic, complemented

#64516

—

#64515

—

C₈×D₁₉

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²⋊D₁₉

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

D₈

yes

characteristic

C₈×C₁₉

D₈

yes

characteristic

C₈×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

#41

yes

characteristic

C₁₉⋊C₈

—

#2213

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

AGL(1,ℤ/8)

yes

characteristic

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#121

yes

characteristic

C₄×C₁₉

C₂×D₈

yes

characteristic

Dic₁₉

—

#509

—

#493

D₁₉

yes

characteristic, complemented

#443

—

#364

—

#361

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#459

yes

characteristic

D₁₉

—

#135

—

C₂×D₈

—

C₂×D₈

C₂×D₁₉

yes

—

#131

—

#127

—

SD₃₂

—

D₁₆

—

M₃₂

—

#108

—

#104

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2213

yes

characteristic, complemented, Sylow

#41

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

SD₁₆

—

D₈

—

D₈

—

D₈

—

D₈

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄²

C₂²⋊D₁₉

yes

characteristic

C₁₆

—

C₂³

—

Q₈

—

D₄

—

D₄

—

100

D₄

—

101

D₄

—

102

D₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

106

C₈

—

107

C₈

#64525

yes

characteristic

108

C₈

#64525

yes

characteristic

109

C₈

D₄×D₁₉

yes

characteristic

110

C₈

#64543

yes

characteristic

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

#10597378

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

C₂×#64525

yes

characteristic

118

C₄

#10597384

yes

characteristic

119

C₂

—

120

C₂

—

121

C₂

—

152

—

122

C₂

#11926736

yes

characteristic

	subgroup	G/H
center	C₂	#11926736
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#493	C₂
socle	C₂×C₁₉	#459
hypercenter	#493	D₁₉
hypocenter	C₁₉	#2213
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #493

subgroup

G/H

center

C₂

#11926736

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#493

C₂

C₂×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #493

N	H ≅ G/N	type
1. #11926980	C₂	semidirect
2. #11926662	C₂	semidirect
3. #11926365	C₂	semidirect
4. #11926357	C₂	semidirect
5. C₁₉×#493	C₂	semidirect
28. Dic₇₆	D₄	semidirect
29. D₁₅₂	D₄	semidirect
59. #493	D₁₉	semidirect
78. C₁₉	#2213	semidirect

H ≅ G/N

type

1. #11926980

C₂

semidirect

2. #11926662

C₂

semidirect

3. #11926365

C₂

semidirect

4. #11926357

C₂

semidirect

5. C₁₉×#493

C₂

semidirect

28. Dic₇₆

D₄

semidirect

29. D₁₅₂

D₄

semidirect

59. #493

D₁₉

semidirect

78. C₁₉

#2213

semidirect

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

subgroup	index
#11926980	2
#11926662	2
#11926365	2
#11926357	2
C₁₉×#493	2
#2213	19

subgroup

index

C₁₉×#493

Subgroups — #14565708

Conjugacy classes of subgroups

Complements

Maximal subgroups