Group #14565713 — subgroups

Subgroups — #14565713

Order 2432.

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

normal subgroups only

This group has 150 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	#11926985	C₂	1	2	yes	maximal
2	#11926662	C₂	1	1	yes	maximal, characteristic
3	#11926365	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926360	C₂	1	2	yes	maximal, complemented
5	C₁₉×#494	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₁₆×C₁₉	—	2	1	no	—
7	C₂×Q₁₆×C₁₉	C₂²	1	2	yes	—
8	C₁₉×C₄⋊Q₈	—	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	#10597286	—	2	2	no	—
13	#10597285	—	2	2	no	—
14	#10597276	C₂²	1	1	yes	characteristic
15	#10597269	C₂²	1	2	yes	—
16	#10597262	—	2	1	no	—
17	C₂×Q₈×C₁₉	—	2	2	no	—
18	#64541	—	2	1	no	—
19	Q₁₆×C₁₉	—	2	2	no	—
20	Q₁₆×C₁₉	—	2	2	no	—
21	Q₁₆×C₁₉	—	4	1	no	—
22	Q₁₆×C₁₉	—	4	1	no	—
23	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
25	C₄⋊C₄×C₁₉	—	4	2	no	—
26	C₄²×C₁₉	D₄	1	1	yes	characteristic
27	#64520	—	2	1	no	—
28	Dic₇₆	D₄	1	1	yes	characteristic
29	D₁₅₂	D₄	1	1	yes	characteristic
30	#64516	—	2	1	no	—
31	#64515	—	4	1	no	—
32	C₈×D₁₉	—	4	1	no	—
33	C₁₉⋊C₁₆	—	2	2	no	—
34	Q₈×C₁₉	—	4	2	no	—
35	Q₈×C₁₉	—	4	2	no	—
36	C₂×C₄×C₁₉	—	2	1	no	—
37	C₂×C₄×C₁₉	—	4	2	no	—
38	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂²⋊D₁₉	—	4	1	no	—
40	D₇₆	—	2	1	no	—
41	C₄×D₁₉	—	4	1	no	—
42	Dic₃₈	—	2	1	no	—
43	C₈×C₁₉	D₈	1	1	yes	characteristic
44	C₈×C₁₉	D₈	1	1	yes	characteristic
45	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₈×C₁₉	#41	1	1	yes	characteristic
47	C₁₉⋊C₈	—	4	1	no	—
48	#2214	—	19	1	no	maximal, Sylow
49	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
50	C₂×D₁₉	—	4	1	no	—
51	C₄×C₁₉	—	2	2	no	—
52	C₄×C₁₉	—	8	2	no	—
53	C₄×C₁₉	#121	1	1	yes	characteristic
54	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
55	Dic₁₉	—	4	1	no	—
56	#510	—	19	2	no	—
57	#494	D₁₉	1	1	yes	characteristic, complemented
58	#443	—	19	1	no	—
59	#364	—	19	1	no	—
60	#362	—	19	2	no	—
61	C₂×C₁₉	—	2	1	no	—
62	C₂×C₁₉	#459	1	1	yes	characteristic
63	D₁₉	—	8	1	no	—
64	#135	—	19	1	no	—
65	C₂×Q₁₆	—	2	1	no	—
66	C₂×Q₁₆	C₂×D₁₉	1	2	yes	—
67	#131	—	38	1	no	—
68	C₄⋊Q₈	—	2	1	no	—
69	Q₃₂	—	38	2	no	—
70	SD₃₂	—	38	2	no	—
71	M₃₂	—	19	2	no	—
72	#108	—	19	1	no	—
73	#104	—	38	1	no	—
74	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
75	C₁₉	#2214	1	1	yes	characteristic, complemented, Sylow
76	#41	—	38	1	no	—
77	C₂×Q₈	—	2	2	no	—
78	Q₁₆	—	2	2	no	—
79	Q₁₆	—	2	2	no	—
80	Q₁₆	—	4	1	no	—
81	Q₁₆	—	4	1	no	—
82	Q₁₆	—	19	1	no	—
83	SD₁₆	—	38	1	no	—
84	D₈	—	19	1	no	—
85	M₁₆	—	38	1	no	—
86	M₁₆	—	76	1	no	—
87	C₂×C₈	—	76	1	no	—
88	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
89	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
90	C₄⋊C₄	—	4	2	no	—
91	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
92	C₁₆	—	38	2	no	—
93	Q₈	—	4	2	no	—
94	Q₈	—	4	2	no	—
95	Q₈	—	38	1	no	—
96	D₄	—	38	1	no	—
97	D₄	—	76	1	no	—
98	C₂×C₄	—	2	1	no	—
99	C₂×C₄	—	4	2	no	—
100	C₂×C₄	—	76	1	no	—
101	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
102	C₈	—	76	1	no	—
103	C₈	#64525	1	1	yes	characteristic
104	C₈	#64525	1	1	yes	characteristic
105	C₈	D₄×D₁₉	1	1	yes	characteristic
106	C₈	#64543	1	1	yes	characteristic
107	C₂²	—	76	1	no	—
108	C₂²	#10597378	1	1	yes	characteristic
109	C₄	—	2	2	no	—
110	C₄	—	8	2	no	—
111	C₄	—	76	1	no	—
112	C₄	C₂×#64525	1	1	yes	characteristic
113	C₄	#10597384	1	1	yes	characteristic
114	C₂	—	2	1	no	—
115	C₂	—	152	1	no	—
116	C₂	#11926736	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926985

C₂

yes

maximal

#11926662

C₂

yes

maximal, characteristic

#11926365

C₂

yes

maximal, characteristic, complemented

#11926360

C₂

yes

maximal, complemented

C₁₉×#494

C₂

yes

maximal, characteristic, complemented

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

C₂²

yes

—

C₁₉×C₄⋊Q₈

—

#10597350

C₂²

yes

characteristic

#10597347

—

C₄×C₈×C₁₉

C₂²

yes

—

—

C₂²

yes

characteristic

#10597269

C₂²

yes

—

#10597262

—

C₂×Q₈×C₁₉

—

#64541

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

#64520

—

Dic₇₆

D₄

yes

characteristic

D₁₅₂

D₄

yes

characteristic

#64516

—

#64515

—

C₈×D₁₉

—

C₁₉⋊C₁₆

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×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

—

—

C₂²×C₁₉

yes

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#121

yes

characteristic

C₄×C₁₉

C₂×D₈

yes

characteristic

Dic₁₉

—

#510

—

#494

D₁₉

yes

characteristic, complemented

#443

—

#364

—

#362

—

C₂×C₁₉

—

C₂×C₁₉

#459

yes

characteristic

D₁₉

—

#135

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₁₉

yes

—

#131

—

C₄⋊Q₈

—

Q₃₂

—

SD₃₂

—

M₃₂

—

#108

—

#104

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2214

yes

characteristic, complemented, Sylow

#41

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄²

C₂²⋊D₁₉

yes

characteristic

C₁₆

—

Q₈

—

Q₈

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

102

C₈

—

103

C₈

#64525

yes

characteristic

104

C₈

#64525

yes

characteristic

105

C₈

D₄×D₁₉

yes

characteristic

106

C₈

#64543

yes

characteristic

107

C₂²

—

108

C₂²

#10597378

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

C₂×#64525

yes

characteristic

113

C₄

#10597384

yes

characteristic

114

C₂

—

115

C₂

—

152

—

116

C₂

#11926736

yes

characteristic

	subgroup	G/H
center	C₂	#11926736
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#494	C₂
socle	C₂×C₁₉	#459
prime radical	#10597350	C₂²
hypercenter	#494	D₁₉
hypocenter	C₁₉	#2214
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #494

subgroup

G/H

center

C₂

#11926736

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#494

C₂

C₂×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #494

N	H ≅ G/N	type
3. #11926365	C₂	semidirect
4. #11926360	C₂	semidirect
5. C₁₉×#494	C₂	semidirect
57. #494	D₁₉	semidirect
75. C₁₉	#2214	semidirect

H ≅ G/N

type

3. #11926365

C₂

semidirect

4. #11926360

C₂

semidirect

5. C₁₉×#494

C₂

semidirect

57. #494

D₁₉

semidirect

75. C₁₉

#2214

semidirect

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

subgroup	index
#11926985	2
#11926662	2
#11926365	2
#11926360	2
C₁₉×#494	2
#2214	19

subgroup

index

C₁₉×#494

Subgroups — #14565713

Conjugacy classes of subgroups

Complements

Maximal subgroups