Group #14565847 — subgroups

Subgroups — #14565847

Order 2432.

134 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 45 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	#11926593	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926366	C₂	1	2	yes	maximal, complemented
3	#11926357	C₂	1	2	yes	maximal, complemented
4	#11926326	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#469	C₂	1	1	yes	maximal, characteristic
6	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#121	—	2	1	no	—
9	C₂×#64520	—	2	1	no	—
10	C₁₉×#106	C₂²	1	1	yes	characteristic
11	C₁₉×#102	—	2	1	no	—
12	#10597276	—	2	1	no	—
13	#10597276	C₂²	1	2	yes	—
14	#10597269	C₂²	1	2	yes	—
15	C₂×D₄×C₁₉	—	2	1	no	—
16	C₂×D₄×C₁₉	—	4	1	no	—
17	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
18	D₈×C₁₉	—	2	2	no	—
19	M₁₆×C₁₉	—	2	2	no	—
20	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₁₉	—	2	1	no	—
23	C₂²⋊C₄×C₁₉	—	4	1	no	—
24	#64520	—	2	2	no	—
25	#64520	—	4	1	no	—
26	C₂×C₁₉⋊C₈	—	4	1	no	—
27	C₁₉⋊C₁₆	—	2	2	no	—
28	C₂³×C₁₉	—	4	1	no	—
29	C₂³×C₁₉	SD₁₆	1	1	yes	characteristic
30	D₄×C₁₉	—	4	1	no	—
31	D₄×C₁₉	—	4	1	no	—
32	D₄×C₁₉	—	8	2	no	—
33	C₂×C₄×C₁₉	—	2	1	no	—
34	C₂×C₄×C₁₉	—	2	1	no	—
35	C₂×C₄×C₁₉	—	4	1	no	—
36	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₈×C₁₉	—	2	1	no	—
39	C₈×C₁₉	#41	1	2	yes	—
40	C₁₉⋊C₈	—	4	2	no	—
41	#2238	—	19	1	no	maximal, Sylow
42	C₂²×C₁₉	—	2	1	no	—
43	C₂²×C₁₉	—	4	1	no	—
44	C₂²×C₁₉	—	8	1	no	—
45	C₂²×C₁₉	—	8	1	no	—
46	C₂²×C₁₉	—	8	1	no	—
47	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
48	C₄×C₁₉	—	2	1	no	—
49	C₄×C₁₉	—	8	1	no	—
50	C₄×C₁₉	#123	1	1	yes	characteristic
51	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
52	#469	D₁₉	1	1	yes	characteristic
53	#430	—	19	1	no	—
54	#365	—	19	2	no	—
55	#361	—	19	2	no	—
56	#349	—	19	1	no	—
57	C₂×C₁₉	—	2	1	no	—
58	C₂×C₁₉	—	4	1	no	—
59	C₂×C₁₉	—	16	1	no	—
60	C₂×C₁₉	#481	1	1	yes	characteristic
61	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
62	C₂×M₁₆	—	38	1	no	—
63	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
64	#121	—	2	1	no	—
65	M₃₂	—	19	2	no	—
66	#108	—	19	2	no	—
67	#108	—	38	1	no	—
68	#106	C₂×D₁₉	1	1	yes	characteristic
69	#102	—	2	1	no	—
70	C₁₉	#2238	1	1	yes	characteristic, complemented, Sylow
71	C₂×D₄	—	2	1	no	—
72	C₂×D₄	—	4	1	no	—
73	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
74	D₈	—	2	2	no	—
75	M₁₆	—	2	2	no	—
76	M₁₆	—	38	2	no	—
77	M₁₆	—	76	1	no	—
78	C₂×C₈	—	76	1	no	—
79	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
80	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
81	C₄⋊C₄	—	2	1	no	—
82	C₂²⋊C₄	—	4	1	no	—
83	C₁₆	—	38	2	no	—
84	C₂³	—	4	1	no	—
85	C₂³	#64526	1	1	yes	characteristic
86	D₄	—	4	1	no	—
87	D₄	—	4	1	no	—
88	D₄	—	8	2	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	4	1	no	—
92	C₂×C₄	#64526	1	1	yes	characteristic
93	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	—	76	2	no	—
96	C₈	#64543	1	2	yes	—
97	C₂²	—	2	1	no	—
98	C₂²	—	4	1	no	—
99	C₂²	—	8	1	no	—
100	C₂²	—	8	1	no	—
101	C₂²	—	8	1	no	—
102	C₂²	C₂×#64526	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	8	1	no	—
105	C₄	#10597381	1	1	yes	characteristic
106	C₄	#10597395	1	1	yes	characteristic
107	C₂	—	2	1	no	—
108	C₂	—	4	1	no	—
109	C₂	—	16	1	no	—
110	C₂	#11926860	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926593

C₂

yes

maximal, characteristic, complemented

#11926366

C₂

yes

maximal, complemented

#11926357

C₂

yes

maximal, complemented

#11926326

C₂

yes

maximal, characteristic, complemented

C₁₉×#469

C₂

yes

maximal, characteristic

C₂×D₈×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#121

—

C₂×#64520

—

C₁₉×#106

C₂²

yes

characteristic

C₁₉×#102

—

#10597276

—

#10597276

C₂²

yes

—

#10597269

C₂²

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

D₈×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

—

C₂³×C₁₉

SD₁₆

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

SD₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

#41

yes

—

C₁₉⋊C₈

—

#2238

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#481

yes

characteristic

C₂×D₈

C₂×D₁₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

#121

—

M₃₂

—

#108

—

#108

—

#106

C₂×D₁₉

yes

characteristic

#102

—

C₁₉

#2238

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

D₈

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

C₂³

—

C₂³

#64526

yes

characteristic

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#64526

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

C₈

—

C₈

—

C₈

#64543

yes

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

—

101

C₂²

—

102

C₂²

C₂×#64526

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

#10597381

yes

characteristic

106

C₄

#10597395

yes

characteristic

107

C₂

—

108

C₂

—

109

C₂

—

110

C₂

#11926860

yes

characteristic

	subgroup	G/H
center	C₂	#11926860
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting, prime radical	C₁₉×#469	C₂
socle	C₂×C₁₉	#481
hypercenter	#469	D₁₉
hypocenter	C₁₉	#2238
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #469

subgroup

G/H

center

C₂

#11926860

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting, prime radical

C₁₉×#469

C₂

C₂×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #469

N	H ≅ G/N	type
1. #11926593	C₂	semidirect
2. #11926366	C₂	semidirect
3. #11926357	C₂	semidirect
4. #11926326	C₂	semidirect
70. C₁₉	#2238	semidirect

H ≅ G/N

type

1. #11926593

C₂

semidirect

2. #11926366

C₂

semidirect

3. #11926357

C₂

semidirect

4. #11926326

C₂

semidirect

70. C₁₉

#2238

semidirect

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

subgroup	index
#11926593	2
#11926366	2
#11926357	2
#11926326	2
C₁₉×#469	2
#2238	19

subgroup

index

C₁₉×#469

Subgroups — #14565847

Conjugacy classes of subgroups

Complements

Maximal subgroups