Group #18069260 — subgroups

Subgroups — #18069260

Order 4864.

152 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 51 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	#14561699	C₂	1	2	yes	maximal, complemented
2	C₁₉×#1709	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₁₉⋊C₁₆)	—	2	2	no	—
4	C₁₉×#494	C₄	1	1	yes	characteristic
5	C₁₉×#493	C₄	1	1	yes	characteristic
6	C₁₉×#486	—	2	2	no	—
7	C₈²×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×Q₁₆×C₁₉	—	4	1	no	—
9	C₂×D₈×C₁₉	—	4	1	no	—
10	C₁₉×C₄⋊Q₈	—	2	1	no	—
11	C₁₉×#127	—	2	1	no	—
12	C₁₉×#102	—	4	2	no	—
13	C₁₉×#102	—	4	2	no	—
14	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₄×C₈×C₁₉	D₄	1	2	yes	—
16	C₂×C₁₉⋊C₁₆	—	4	2	no	—
17	C₂×Q₈×C₁₉	—	4	1	no	—
18	C₂×D₄×C₁₉	—	4	1	no	—
19	C₂×D₄×C₁₉	—	4	2	no	—
20	Q₁₆×C₁₉	—	8	2	no	—
21	D₈×C₁₉	—	8	2	no	—
22	C₂×C₈×C₁₉	—	2	1	no	—
23	C₂×C₈×C₁₉	D₈	1	2	yes	—
24	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
25	C₄⋊C₄×C₁₉	—	4	2	no	—
26	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₁₉⋊C₁₆	—	8	2	no	—
28	#7092	—	19	1	no	maximal, Sylow
29	C₂³×C₁₉	—	8	1	no	—
30	Q₈×C₁₉	—	8	2	no	—
31	D₄×C₁₉	—	8	2	no	—
32	D₄×C₁₉	—	8	2	no	—
33	D₄×C₁₉	—	8	2	no	—
34	C₂×C₄×C₁₉	—	8	1	no	—
35	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
36	C₂×C₄×C₁₉	#102	1	2	yes	—
37	C₈×C₁₉	—	2	2	no	—
38	C₈×C₁₉	—	2	2	no	—
39	C₈×C₁₉	—	2	2	no	—
40	#1709	D₁₉	1	1	yes	characteristic
41	#1367	—	19	2	no	—
42	C₂²×C₁₉	—	16	1	no	—
43	C₂²×C₁₉	—	16	2	no	—
44	C₂²×C₁₉	#331	1	1	yes	characteristic
45	C₄×C₁₉	—	2	1	no	—
46	C₄×C₁₉	—	16	1	no	—
47	C₄×C₁₉	#359	1	2	yes	—
48	C₄×C₁₉	#360	1	2	yes	—
49	#494	Dic₁₉	1	1	yes	characteristic
50	#493	Dic₁₉	1	1	yes	characteristic
51	#486	—	2	2	no	—
52	C₄⋊C₁₆	—	38	2	no	—
53	C₈²	C₂×D₁₉	1	1	yes	characteristic
54	C₂×C₁₉	—	32	1	no	—
55	C₂×C₁₉	#1357	1	1	yes	characteristic
56	C₂×C₁₉	#1360	1	2	yes	—
57	C₂×Q₁₆	—	4	1	no	—
58	C₂×D₈	—	4	1	no	—
59	C₄⋊Q₈	—	2	1	no	—
60	#127	—	2	1	no	—
61	C₂×C₁₆	—	76	2	no	—
62	#102	—	4	2	no	—
63	#102	—	4	2	no	—
64	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
65	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
66	C₁₉	#7092	1	1	yes	characteristic, complemented, Sylow
67	C₂×Q₈	—	4	1	no	—
68	C₂×D₄	—	4	2	no	—
69	C₂×D₄	—	4	1	no	—
70	Q₁₆	—	8	2	no	—
71	D₈	—	8	2	no	—
72	C₂×C₈	—	2	1	no	—
73	C₂×C₈	#64525	1	2	yes	—
74	C₂×C₈	#64526	1	2	yes	—
75	C₄⋊C₄	—	4	2	no	—
76	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
77	C₁₆	—	152	2	no	—
78	C₂³	—	8	1	no	—
79	Q₈	—	8	2	no	—
80	D₄	—	8	2	no	—
81	D₄	—	8	2	no	—
82	D₄	—	8	2	no	—
83	C₂×C₄	—	8	1	no	—
84	C₂×C₄	#10597289	1	2	yes	—
85	C₂×C₄	#10597290	1	1	yes	characteristic
86	C₈	—	2	2	no	—
87	C₈	—	2	2	no	—
88	C₈	—	2	2	no	—
89	C₂²	—	16	1	no	—
90	C₂²	—	16	2	no	—
91	C₂²	#11926288	1	1	yes	characteristic
92	C₄	—	2	1	no	—
93	C₄	—	16	1	no	—
94	C₄	#11926351	1	2	yes	—
95	C₄	#11926354	1	2	yes	—
96	C₂	—	32	1	no	—
97	C₂	#14561672	1	1	yes	characteristic
98	C₂	#14561678	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14561699

C₂

yes

maximal, complemented

C₁₉×#1709

C₂

yes

maximal, characteristic

C₄⋊(C₁₉⋊C₁₆)

—

C₁₉×#494

C₄

yes

characteristic

C₁₉×#493

C₄

yes

characteristic

C₁₉×#486

—

C₈²×C₁₉

C₂²

yes

characteristic

C₂×Q₁₆×C₁₉

—

C₂×D₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×#127

—

C₁₉×#102

—

C₁₉×#102

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

—

C₂×C₁₉⋊C₁₆

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

Q₁₆×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₁₉⋊C₁₆

—

#7092

—

maximal, Sylow

C₂³×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#100

yes

characteristic

C₂×C₄×C₁₉

#102

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#1709

D₁₉

yes

characteristic

#1367

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#331

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#359

yes

—

C₄×C₁₉

#360

yes

—

#494

Dic₁₉

yes

characteristic

#493

Dic₁₉

yes

characteristic

#486

—

C₄⋊C₁₆

—

C₈²

C₂×D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

#1357

yes

characteristic

C₂×C₁₉

#1360

yes

—

C₂×Q₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

#127

—

C₂×C₁₆

—

#102

—

#102

—

C₄×C₈

C₂×Dic₁₉

yes

characteristic

C₄×C₈

C₂²⋊D₁₉

yes

—

C₁₉

#7092

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

D₈

—

C₂×C₈

—

C₂×C₈

#64525

yes

—

C₂×C₈

#64526

yes

—

C₄⋊C₄

—

C₄²

C₂²⋊Dic₁₉

yes

characteristic

C₁₆

—

152

—

C₂³

—

Q₈

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

#10597289

yes

—

C₂×C₄

#10597290

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

#11926288

yes

characteristic

C₄

—

C₄

—

C₄

#11926351

yes

—

C₄

#11926354

yes

—

C₂

—

C₂

#14561672

yes

characteristic

C₂

#14561678

yes

—

	subgroup	G/H
center	C₂²	#11926288
commutator	C₄×C₈×C₁₉	C₂×C₄
Frattini	C₈²	C₂×D₁₉
Fitting	C₁₉×#1709	C₂
socle	C₂²×C₁₉	#331
prime radical	C₁₉×#493	C₄
cosocle	C₈²×C₁₉	C₂²
hypercenter	#1709	D₁₉
hypocenter	C₁₉	#7092
LCS	G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1709

subgroup

G/H

center

C₂²

#11926288

commutator

C₄×C₈×C₁₉

C₂×C₄

Frattini

C₈²

C₂×D₁₉

Fitting

C₁₉×#1709

C₂

socle

C₂²×C₁₉

#331

prime radical

C₁₉×#493

C₄

cosocle

C₈²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1709

N	H ≅ G/N	type
1. #14561699	C₂	semidirect
66. C₁₉	#7092	semidirect

H ≅ G/N

type

1. #14561699

C₂

semidirect

66. C₁₉

#7092

semidirect

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

subgroup	index
#14561699	2
C₁₉×#1709	2
#7092	19

subgroup

index

#14561699

C₁₉×#1709

#7092

Subgroups — #18069260

Conjugacy classes of subgroups

Complements

Maximal subgroups