Group #19132421 — subgroups

Subgroups — #19132421

Order 5504.

166 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 65 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	#14582654	C₂	1	2	yes	maximal
2	C₄₃×#391	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄₃⋊C₈	—	2	2	no	—
4	C₂²×Q₈×C₄₃	C₄	1	1	yes	characteristic
5	C₂×C₄⋊C₄×C₄₃	C₄	1	1	yes	characteristic
6	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
7	#95×C₄₃	—	2	2	no	—
8	C₂×Q₈×C₄₃	—	2	1	no	—
9	C₂×Q₈×C₄₃	—	4	1	no	—
10	C₂×Q₈×C₄₃	—	4	1	no	—
11	C₂×Q₈×C₄₃	C₈	1	2	yes	complemented
12	C₂²×C₄×C₄₃	—	2	1	no	—
13	C₂²×C₄×C₄₃	—	2	1	no	—
14	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	D₄	1	2	yes	—
16	C₄⋊C₄×C₄₃	—	4	1	no	—
17	C₄²×C₄₃	—	4	1	no	—
18	C₂×C₄₃⋊C₈	—	2	4	no	—
19	C₂×C₄₃⋊C₈	—	4	2	no	—
20	C₂×C₄₃⋊C₈	—	4	2	no	—
21	C₂³×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
22	Q₈×C₄₃	—	4	2	no	—
23	Q₈×C₄₃	—	4	2	no	—
24	C₂×C₄×C₄₃	—	2	2	no	—
25	C₂×C₄×C₄₃	—	2	1	no	—
26	C₂×C₄×C₄₃	—	2	1	no	—
27	C₂×C₄×C₄₃	—	2	2	no	—
28	C₂×C₄×C₄₃	—	2	2	no	—
29	C₂×C₄×C₄₃	—	4	1	no	—
30	C₂×C₄×C₄₃	—	4	1	no	—
31	C₂×C₄×C₄₃	—	4	1	no	—
32	C₂×C₄×C₄₃	—	4	2	no	—
33	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
34	C₂×C₄×C₄₃	M₁₆	1	1	yes	characteristic
35	C₂×C₄×C₄₃	SD₁₆	1	2	yes	—
36	C₂×C₄×C₄₃	Q₁₆	1	2	yes	—
37	C₄₃⋊C₈	—	4	4	no	—
38	C₂²×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
39	C₂²×C₄₃	#99	1	1	yes	characteristic
40	C₂²×C₄₃	#100	1	1	yes	characteristic
41	C₂²×C₄₃	#103	1	2	yes	—
42	C₂²×C₄₃	#104	1	2	yes	—
43	C₄×C₄₃	—	2	1	no	—
44	C₄×C₄₃	—	2	1	no	—
45	C₄×C₄₃	—	2	2	no	—
46	C₄×C₄₃	—	2	2	no	—
47	C₄×C₄₃	—	4	2	no	—
48	C₄×C₄₃	—	8	1	no	—
49	#1272	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	#323	1	1	yes	characteristic
51	C₂×C₄₃	Q₈⋊C₈	1	2	yes	—
52	C₂×C₄₃	#328	1	2	yes	—
53	C₂×C₄₃	#329	1	1	yes	characteristic
54	C₂×C₄₃	#333	1	1	yes	characteristic
55	#391	D₄₃	1	1	yes	characteristic
56	#336	—	43	2	no	—
57	C₄₃	#1272	1	1	yes	characteristic, complemented, Sylow
58	C₂²×Q₈	Dic₄₃	1	1	yes	characteristic
59	C₂²×C₈	—	86	2	no	—
60	C₂×C₄⋊C₄	Dic₄₃	1	1	yes	characteristic
61	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
62	#95	—	2	2	no	—
63	C₂×Q₈	—	2	1	no	—
64	C₂×Q₈	—	4	1	no	—
65	C₂×Q₈	—	4	1	no	—
66	C₂×Q₈	C₄₃⋊C₈	1	2	yes	complemented
67	C₂²×C₄	—	2	1	no	—
68	C₂²×C₄	—	2	1	no	—
69	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
70	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
71	C₂×C₈	—	86	4	no	—
72	C₂×C₈	—	172	2	no	—
73	C₂×C₈	—	172	2	no	—
74	C₄⋊C₄	—	4	1	no	—
75	C₄²	—	4	1	no	—
76	C₂³	C₂²⋊Dic₄₃	1	1	yes	characteristic
77	Q₈	—	4	2	no	—
78	Q₈	—	4	2	no	—
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	4	1	no	—
85	C₂×C₄	—	4	1	no	—
86	C₂×C₄	—	4	1	no	—
87	C₂×C₄	—	4	2	no	—
88	C₂×C₄	C₂×C₄₃⋊C₈	1	1	yes	characteristic
89	C₂×C₄	#10621877	1	1	yes	characteristic
90	C₂×C₄	#10621884	1	2	yes	—
91	C₂×C₄	#10621885	1	2	yes	—
92	C₈	—	172	4	no	—
93	C₂²	C₂²⋊(C₄₃⋊C₈)	1	1	yes	characteristic
94	C₂²	#13063240	1	1	yes	characteristic
95	C₂²	#13063242	1	1	yes	characteristic
96	C₂²	#13063249	1	2	yes	—
97	C₂²	#13063252	1	2	yes	—
98	C₄	—	2	1	no	—
99	C₄	—	2	1	no	—
100	C₄	—	2	2	no	—
101	C₄	—	2	2	no	—
102	C₄	—	4	2	no	—
103	C₄	—	8	1	no	—
104	C₂	#14582623	1	1	yes	characteristic
105	C₂	Q₈⋊(C₄₃⋊C₈)	1	2	yes	—
106	C₂	#14582636	1	2	yes	—
107	C₂	#14582639	1	1	yes	characteristic
108	C₂	#14582648	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582654

C₂

yes

maximal

C₄₃×#391

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

—

C₂²×Q₈×C₄₃

C₄

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₄

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#95×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

C₈

yes

complemented

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂²⋊C₄

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

M₁₆

yes

characteristic

C₂×C₄×C₄₃

SD₁₆

yes

—

C₂×C₄×C₄₃

Q₁₆

yes

—

C₄₃⋊C₈

—

C₂²×C₄₃

C₂²⋊C₈

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂²×C₄₃

#104

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

Q₈⋊C₈

yes

—

C₂×C₄₃

#328

yes

—

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

yes

characteristic

#336

—

C₄₃

#1272

yes

characteristic, complemented, Sylow

C₂²×Q₈

Dic₄₃

yes

characteristic

C₂²×C₈

—

C₂×C₄⋊C₄

Dic₄₃

yes

characteristic

C₂×C₄²

C₂×D₄₃

yes

characteristic

#95

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₄₃⋊C₈

yes

complemented

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

C₂²×C₄

C₂²⋊D₄₃

yes

—

C₂×C₈

—

C₂×C₈

—

172

—

C₂×C₈

—

172

—

C₄⋊C₄

—

C₄²

—

C₂³

C₂²⋊Dic₄₃

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄₃⋊C₈

yes

C₂×C₄

yes

C₂×C₄

yes

—

C₂×C₄

#10621885

yes

—

C₈

—

172

—

C₂²

C₂²⋊(C₄₃⋊C₈)

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

#13063252

yes

—

C₄

—

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

—

104

C₂

#14582623

yes

characteristic

105

C₂

Q₈⋊(C₄₃⋊C₈)

yes

—

106

C₂

#14582636

yes

—

107

C₂

#14582639

yes

characteristic

108

C₂

#14582648

yes

characteristic

	subgroup	G/H
center	C₂³	C₂²⋊Dic₄₃
commutator	C₂×C₄×C₄₃	C₂×C₈
Frattini	C₂×C₄²	C₂×D₄₃
Fitting	C₄₃×#391	C₂
socle	C₂³×C₄₃	C₂²⋊C₄
hypercenter	#391	D₄₃
hypocenter	C₄₃	#1272
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

subgroup

G/H

center

C₂³

C₂²⋊Dic₄₃

commutator

C₂×C₄×C₄₃

C₂×C₈

Frattini

C₂×C₄²

C₂×D₄₃

Fitting

C₄₃×#391

C₂

socle

C₂³×C₄₃

C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

N	H ≅ G/N	type
11. C₂×Q₈×C₄₃	C₈	semidirect
57. C₄₃	#1272	semidirect
66. C₂×Q₈	C₄₃⋊C₈	semidirect

H ≅ G/N

type

11. C₂×Q₈×C₄₃

C₈

semidirect

57. C₄₃

#1272

semidirect

66. C₂×Q₈

C₄₃⋊C₈

semidirect

Subgroups — #19132421

Conjugacy classes of subgroups

Complements