Group #14565852 — subgroups

Subgroups — #14565852

Order 2432.

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

normal subgroups only

This group has 124 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
2	#11926366	C₂	1	2	yes	maximal, complemented
3	#11926360	C₂	1	2	yes	maximal, complemented
4	#11926326	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#470	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×C₂²⋊Q₈	—	2	1	no	—
9	C₂×#64520	—	2	1	no	—
10	C₁₉×#106	C₂²	1	1	yes	characteristic
11	C₁₉×#103	—	2	1	no	—
12	#10597276	—	2	1	no	—
13	#10597276	C₂²	1	2	yes	—
14	#10597269	C₂²	1	2	yes	—
15	C₂×Q₈×C₁₉	—	2	1	no	—
16	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
17	Q₁₆×C₁₉	—	2	2	no	—
18	M₁₆×C₁₉	—	2	2	no	—
19	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
21	C₄⋊C₄×C₁₉	—	2	1	no	—
22	C₄⋊C₄×C₁₉	—	4	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	SD₁₆	1	1	yes	characteristic
29	Q₈×C₁₉	—	4	1	no	—
30	Q₈×C₁₉	—	4	1	no	—
31	C₂×C₄×C₁₉	—	2	1	no	—
32	C₂×C₄×C₁₉	—	2	1	no	—
33	C₂×C₄×C₁₉	—	4	1	no	—
34	C₂×C₄×C₁₉	—	4	1	no	—
35	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₈×C₁₉	—	2	1	no	—
38	C₈×C₁₉	#41	1	2	yes	—
39	C₁₉⋊C₈	—	4	2	no	—
40	#2239	—	19	1	no	maximal, Sylow
41	C₂²×C₁₉	—	2	1	no	—
42	C₂²×C₁₉	—	4	1	no	—
43	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
44	C₄×C₁₉	—	2	1	no	—
45	C₄×C₁₉	—	8	1	no	—
46	C₄×C₁₉	—	8	1	no	—
47	C₄×C₁₉	#123	1	1	yes	characteristic
48	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
49	#470	D₁₉	1	1	yes	characteristic
50	#430	—	19	1	no	—
51	#365	—	19	2	no	—
52	#362	—	19	2	no	—
53	#349	—	19	1	no	—
54	C₂×C₁₉	—	2	1	no	—
55	C₂×C₁₉	—	4	1	no	—
56	C₂×C₁₉	#481	1	1	yes	characteristic
57	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic
58	C₂×M₁₆	—	38	1	no	—
59	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
60	C₂²⋊Q₈	—	2	1	no	—
61	M₃₂	—	19	2	no	—
62	#108	—	19	2	no	—
63	#108	—	38	1	no	—
64	#106	C₂×D₁₉	1	1	yes	characteristic
65	#103	—	2	1	no	—
66	C₁₉	#2239	1	1	yes	characteristic, complemented, Sylow
67	C₂×Q₈	—	2	1	no	—
68	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
69	Q₁₆	—	2	2	no	—
70	M₁₆	—	2	2	no	—
71	M₁₆	—	38	2	no	—
72	M₁₆	—	76	1	no	—
73	C₂×C₈	—	76	1	no	—
74	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
76	C₄⋊C₄	—	2	1	no	—
77	C₄⋊C₄	—	4	1	no	—
78	C₂²⋊C₄	—	4	1	no	—
79	C₁₆	—	38	2	no	—
80	C₂³	#64526	1	1	yes	characteristic
81	Q₈	—	4	1	no	—
82	Q₈	—	4	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	4	1	no	—
86	C₂×C₄	—	4	1	no	—
87	C₂×C₄	#64526	1	1	yes	characteristic
88	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	—	76	2	no	—
91	C₈	#64543	1	2	yes	—
92	C₂²	—	2	1	no	—
93	C₂²	—	4	1	no	—
94	C₂²	C₂×#64526	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	8	1	no	—
97	C₄	—	8	1	no	—
98	C₄	#10597381	1	1	yes	characteristic
99	C₄	#10597395	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	4	1	no	—
102	C₂	#11926860	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926593

C₂

yes

maximal, characteristic

#11926366

C₂

yes

maximal, complemented

#11926360

C₂

yes

maximal, complemented

#11926326

C₂

yes

maximal, characteristic

C₁₉×#470

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×C₂²⋊Q₈

—

C₂×#64520

—

C₁₉×#106

C₂²

yes

characteristic

C₁₉×#103

—

#10597276

—

#10597276

C₂²

yes

—

#10597269

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

Q₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

SD₁₆

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×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

—

#2239

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#481

yes

characteristic

C₂×Q₁₆

C₂×D₁₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂²⋊Q₈

—

M₃₂

—

#108

—

#108

—

#106

C₂×D₁₉

yes

characteristic

#103

—

C₁₉

#2239

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

Q₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

C₂³

#64526

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

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

C₂×#64526

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

—

102

C₂

#11926860

yes

characteristic

	subgroup	G/H
center	C₂	#11926860
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#470	C₂
socle	C₂×C₁₉	#481
prime radical	C₂³×C₁₉	SD₁₆
hypercenter	#470	D₁₉
hypocenter	C₁₉	#2239
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #470

subgroup

G/H

center

C₂

#11926860

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#470

C₂

socle

C₂×C₁₉

#481

prime radical

C₂³×C₁₉

SD₁₆

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #470

N	H ≅ G/N	type
2. #11926366	C₂	semidirect
3. #11926360	C₂	semidirect
66. C₁₉	#2239	semidirect

H ≅ G/N

type

2. #11926366

C₂

semidirect

3. #11926360

C₂

semidirect

66. C₁₉

#2239

semidirect

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

subgroup	index
#11926593	2
#11926366	2
#11926360	2
#11926326	2
C₁₉×#470	2
#2239	19

subgroup

index

C₁₉×#470

Subgroups — #14565852

Conjugacy classes of subgroups

Complements

Maximal subgroups