Group #19134672 — subgroups

Subgroups — #19134672

Order 5504.

300 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 93 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	#14582762	C₂	1	2	yes	maximal
2	#14582666	C₂	1	4	yes	maximal
3	C₂×#117×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊Dic₄₃	C₂²	1	4	yes	—
5	C₄₃⋊#95	—	2	4	no	—
6	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
7	#117×C₄₃	—	2	4	no	—
8	C₂×C₄⋊C₄×C₄₃	C₄	1	2	yes	complemented
9	C₂×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
10	C₂×C₄²×C₄₃	C₄	1	2	yes	complemented
11	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
12	C₂²×C₄×C₄₃	—	2	4	no	—
13	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	C₂×C₄	1	4	yes	—
16	C₂²×C₄×C₄₃	D₄	1	4	yes	—
17	C₂²×Dic₄₃	—	2	4	no	—
18	C₄⋊C₄×C₄₃	—	2	4	no	—
19	C₂²⋊C₄×C₄₃	—	2	4	no	—
20	C₄²×C₄₃	—	2	4	no	—
21	C₂²⋊Dic₄₃	—	2	8	no	—
22	C₂³×C₄₃	—	4	2	no	—
23	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
24	C₂³×C₄₃	C₂×D₄	1	2	yes	—
25	C₂³×C₄₃	#41	1	4	yes	—
26	C₂×C₄×C₄₃	—	2	2	no	—
27	C₂×C₄×C₄₃	—	2	2	no	—
28	C₂×C₄×C₄₃	—	2	8	no	—
29	C₂×C₄×C₄₃	—	2	4	no	—
30	C₂×C₄×C₄₃	—	4	4	no	—
31	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
32	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
33	C₂×Dic₄₃	—	4	8	no	—
34	C₂×Dic₄₃	—	4	4	no	—
35	C₂²×C₄₃	—	2	2	no	—
36	C₂²×C₄₃	—	2	4	no	—
37	C₂²×C₄₃	—	4	4	no	—
38	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
39	C₂²×C₄₃	#117	1	2	yes	—
40	C₂²×C₄₃	#123	1	4	yes	—
41	C₄×C₄₃	—	2	2	no	—
42	C₄×C₄₃	—	2	2	no	—
43	C₄×C₄₃	—	4	4	no	—
44	Dic₄₃	—	8	4	no	—
45	#1820	—	43	1	no	maximal, Sylow
46	C₂×C₄₃	—	2	4	no	—
47	C₂×C₄₃	—	2	2	no	—
48	C₂×C₄₃	#381	1	1	yes	characteristic
49	C₂×C₄₃	#410	1	2	yes	—
50	C₂×#117	D₄₃	1	1	yes	characteristic
51	#381	—	43	2	no	—
52	#342	—	43	4	no	—
53	C₄₃	#1820	1	1	yes	characteristic, complemented, Sylow
54	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
55	#117	—	2	4	no	—
56	C₂×C₄⋊C₄	Dic₄₃	1	2	yes	complemented
57	C₂×C₂²⋊C₄	—	43	4	no	—
58	C₂×C₂²⋊C₄	C₂×D₄₃	1	2	yes	—
59	C₂×C₄²	Dic₄₃	1	2	yes	complemented
60	#95	—	86	4	no	—
61	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
62	C₂²×C₄	—	2	4	no	—
63	C₂²×C₄	—	86	4	no	—
64	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
65	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
66	C₂²×C₄	C₂×Dic₄₃	1	4	yes	—
67	C₂²×C₄	C₂²⋊D₄₃	1	4	yes	—
68	C₄⋊C₄	—	2	4	no	—
69	C₂²⋊C₄	—	2	4	no	—
70	C₂²⋊C₄	—	86	8	no	—
71	C₄²	—	2	4	no	—
72	C₂³	—	4	2	no	—
73	C₂³	#10621898	1	4	yes	—
74	C₂³	C₂²×Dic₄₃	1	1	yes	characteristic
75	C₂³	C₂×C₂²⋊D₄₃	1	2	yes	—
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	—	2	2	no	—
78	C₂×C₄	—	2	8	no	—
79	C₂×C₄	—	2	4	no	—
80	C₂×C₄	—	4	4	no	—
81	C₂×C₄	—	172	8	no	—
82	C₂×C₄	—	172	4	no	—
83	C₂×C₄	C₂²⋊Dic₄₃	1	2	yes	—
84	C₂×C₄	C₂²⋊Dic₄₃	1	2	yes	—
85	C₂²	—	2	2	no	—
86	C₂²	—	2	4	no	—
87	C₂²	—	4	4	no	—
88	C₂²	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
89	C₂²	#13063284	1	2	yes	—
90	C₂²	#13063308	1	4	yes	—
91	C₄	—	2	2	no	—
92	C₄	—	2	2	no	—
93	C₄	—	4	4	no	—
94	C₄	—	344	4	no	—
95	C₂	—	2	4	no	—
96	C₂	—	2	2	no	—
97	C₂	#14582762	1	1	yes	characteristic
98	C₂	#14582873	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14582762

C₂

yes

maximal

#14582666

C₂

yes

maximal

C₂×#117×C₄₃

C₂

yes

maximal, characteristic

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₄₃⋊#95

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

#117×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₄

yes

complemented

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₄

yes

complemented

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×Dic₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₂²⋊Dic₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂³×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

#41

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₃

#117

yes

—

C₂²×C₄₃

#123

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

#1820

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#381

yes

characteristic

C₂×C₄₃

#410

yes

—

C₂×#117

D₄₃

yes

characteristic

#381

—

#342

—

C₄₃

#1820

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₄₃

yes

characteristic

#117

—

C₂×C₄⋊C₄

Dic₄₃

yes

complemented

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

Dic₄₃

yes

complemented

#95

—

C₂⁴

C₂²×D₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

C₂²×C₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂²⋊D₄₃

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

—

C₂³

#10621898

yes

—

C₂³

C₂²×Dic₄₃

yes

characteristic

C₂³

C₂×C₂²⋊D₄₃

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

C₂²⋊Dic₄₃

yes

—

C₂×C₄

C₂²⋊Dic₄₃

yes

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₂×C₂²⋊Dic₄₃

yes

characteristic

C₂²

#13063284

yes

—

C₂²

#13063308

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

344

—

C₂

—

C₂

—

C₂

#14582762

yes

characteristic

C₂

#14582873

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₄₃
commutator	C₂³×C₄₃	C₂²×C₄
Frattini	C₂⁴	C₂²×D₄₃
Fitting	C₂×#117×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₄
hypercenter	C₂×#117	D₄₃
hypocenter	C₄₃	#1820
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#117

subgroup

G/H

center

C₂²

C₂×C₂²⋊Dic₄₃

commutator

C₂³×C₄₃

C₂²×C₄

Frattini

C₂⁴

C₂²×D₄₃

Fitting

C₂×#117×C₄₃

C₂

socle

C₂²×C₄₃

C₂×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#117

N	H ≅ G/N	type
8. C₂×C₄⋊C₄×C₄₃	C₄	semidirect
10. C₂×C₄²×C₄₃	C₄	semidirect
53. C₄₃	#1820	semidirect
56. C₂×C₄⋊C₄	Dic₄₃	semidirect
59. C₂×C₄²	Dic₄₃	semidirect

H ≅ G/N

type

8. C₂×C₄⋊C₄×C₄₃

C₄

semidirect

10. C₂×C₄²×C₄₃

C₄

semidirect

53. C₄₃

#1820

semidirect

56. C₂×C₄⋊C₄

Dic₄₃

semidirect

59. C₂×C₄²

Dic₄₃

semidirect

Subgroups — #19134672

Conjugacy classes of subgroups

Complements