Group #19132445 — subgroups

Subgroups — #19132445

Order 5504.

160 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 81 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	#14582952	C₂	1	1	yes	maximal, characteristic
2	C₄×#10621877	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#10621877	C₄	1	2	yes	—
5	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
6	C₂²⋊(C₄₃⋊C₈)	C₄	1	2	yes	—
7	#13063236	—	2	1	no	—
8	C₄×C₄₃⋊C₈	—	2	1	no	—
9	C₄×C₄₃⋊C₈	—	2	1	no	—
10	C₂²×C₈×C₄₃	C₄	1	2	yes	—
11	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
12	C₄⋊C₈×C₄₃	—	2	1	no	—
13	C₄⋊C₈×C₄₃	—	2	1	no	—
14	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₄₃	—	2	2	no	—
18	C₂×C₈×C₄₃	—	4	2	no	—
19	C₄²×C₄₃	D₄	1	1	yes	characteristic
20	C₄²×C₄₃	D₄	1	1	yes	characteristic
21	C₄²×C₄₃	D₄	1	1	yes	characteristic
22	C₄²×C₄₃	Q₈	1	1	yes	characteristic
23	#10621877	—	2	2	no	—
24	#10621877	C₈	1	4	yes	complemented
25	C₂×C₄₃⋊C₈	—	2	2	no	—
26	C₂×C₄₃⋊C₈	—	2	2	no	—
27	C₂³×C₄₃	C₄²	1	1	yes	characteristic
28	C₂×C₄×C₄₃	—	2	1	no	—
29	C₂×C₄×C₄₃	—	2	1	no	—
30	C₂×C₄×C₄₃	—	4	1	no	—
31	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₄₃	C₂×C₈	1	2	yes	—
38	C₂×C₄×C₄₃	M₁₆	1	2	yes	—
39	C₈×C₄₃	—	4	2	no	—
40	C₄₃⋊C₈	—	2	4	no	—
41	C₄₃⋊C₈	—	4	2	no	—
42	C₂²×C₄₃	—	2	1	no	—
43	C₂²×C₄₃	—	2	1	no	—
44	C₂²×C₄₃	#95	1	1	yes	characteristic
45	C₂²×C₄₃	C₄×C₈	1	1	yes	characteristic
46	C₂²×C₄₃	#97	1	1	yes	characteristic
47	C₄×C₄₃	—	2	1	no	—
48	C₄×C₄₃	—	2	1	no	—
49	C₄×C₄₃	—	2	1	no	—
50	C₄×C₄₃	C₂²⋊C₈	1	2	yes	—
51	C₄×C₄₃	#100	1	1	yes	characteristic
52	C₄×C₄₃	#101	1	1	yes	characteristic
53	C₄×C₄₃	C₄⋊C₈	1	2	yes	—
54	#1283	—	43	1	no	maximal, Sylow
55	C₂×C₄₃	—	2	1	no	—
56	C₂×C₄₃	—	2	1	no	—
57	C₂×C₄₃	#336	1	1	yes	characteristic
58	C₂×C₄₃	#343	1	1	yes	characteristic
59	C₂×C₄₃	#344	1	1	yes	characteristic
60	#431	—	43	1	no	—
61	C₂×C₄⋊C₈	D₄₃	1	1	yes	characteristic
62	C₄×M₁₆	—	43	1	no	—
63	C₄₃	#1283	1	1	yes	characteristic, complemented, Sylow
64	C₂×M₁₆	—	43	2	no	—
65	C₂²×C₈	Dic₄₃	1	2	yes	—
66	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
67	C₄⋊C₈	—	2	1	no	—
68	C₄⋊C₈	—	2	1	no	—
69	C₄⋊C₈	—	86	1	no	—
70	C₂²⋊C₈	—	43	2	no	—
71	#97	—	86	1	no	—
72	C₄×C₈	—	86	1	no	—
73	C₄×C₈	—	86	1	no	—
74	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
75	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
76	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
77	M₁₆	—	43	4	no	—
78	M₁₆	—	86	2	no	—
79	C₂×C₈	—	2	2	no	—
80	C₂×C₈	—	4	2	no	—
81	C₂×C₈	—	86	2	no	—
82	C₂×C₈	—	86	2	no	—
83	C₄²	Dic₈₆	1	1	yes	characteristic
84	C₄²	D₁₇₂	1	1	yes	characteristic
85	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
86	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
87	C₂³	C₄×Dic₄₃	1	1	yes	characteristic
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	4	1	no	—
91	C₂×C₄	C₈×D₄₃	1	2	yes	—
92	C₂×C₄	#10621872	1	2	yes	—
93	C₂×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
94	C₂×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
95	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
96	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
97	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
98	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
99	C₈	—	4	2	no	—
100	C₈	—	86	4	no	—
101	C₈	—	172	2	no	—
102	C₂²	—	2	1	no	—
103	C₂²	—	2	1	no	—
104	C₂²	C₄₃⋊#95	1	1	yes	characteristic
105	C₂²	C₈×Dic₄₃	1	1	yes	characteristic
106	C₂²	#13063235	1	1	yes	characteristic
107	C₄	—	2	1	no	—
108	C₄	—	2	1	no	—
109	C₄	—	2	1	no	—
110	C₄	(C₂×D₄₃)⋊C₈	1	2	yes	—
111	C₄	#13063242	1	1	yes	characteristic
112	C₄	#13063244	1	1	yes	characteristic
113	C₄	Dic₄₃⋊C₈	1	2	yes	—
114	C₂	—	2	1	no	—
115	C₂	—	2	1	no	—
116	C₂	#14582653	1	1	yes	characteristic
117	C₂	#14582668	1	1	yes	characteristic
118	C₂	#14582670	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582952

C₂

yes

maximal, characteristic

C₄×#10621877

C₂

yes

maximal, characteristic

C₂×C₄⋊C₈×C₄₃

C₂

yes

maximal, characteristic

C₂×#10621877

C₄

yes

—

C₄⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

C₄

yes

—

#13063236

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

C₂²×C₈×C₄₃

C₄

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

Q₈

yes

characteristic

#10621877

—

#10621877

C₈

yes

complemented

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₄²

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×C₈

yes

—

C₂×C₄×C₄₃

M₁₆

yes

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#95

yes

characteristic

C₂²×C₄₃

C₄×C₈

yes

characteristic

C₂²×C₄₃

#97

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊C₈

yes

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

C₄⋊C₈

yes

—

#1283

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄⋊C₈

D₄₃

yes

characteristic

C₄×M₁₆

—

C₄₃

#1283

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

Dic₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

Dic₈₆

yes

characteristic

C₄²

D₁₇₂

yes

characteristic

C₄²

C₂²⋊D₄₃

yes

characteristic

C₄²

C₂²⋊D₄₃

yes

characteristic

C₂³

C₄×Dic₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₄₃

yes

—

C₂×C₄

#10621872

yes

—

C₂×C₄

Dic₄₃⋊C₄

yes

characteristic

C₂×C₄

Dic₄₃⋊C₄

yes

characteristic

C₂×C₄

C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₂×C₄

C₂²⋊Dic₄₃

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

172

—

102

C₂²

—

103

C₂²

—

104

C₂²

C₄₃⋊#95

yes

characteristic

105

C₂²

C₈×Dic₄₃

yes

characteristic

106

C₂²

#13063235

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

(C₂×D₄₃)⋊C₈

yes

—

111

C₄

#13063242

yes

characteristic

112

C₄

#13063244

yes

characteristic

113

C₄

Dic₄₃⋊C₈

yes

—

114

C₂

—

115

C₂

—

116

C₂

#14582653

yes

characteristic

117

C₂

#14582668

yes

characteristic

118

C₂

#14582670

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₄₃
commutator	C₂²×C₄₃	C₄×C₈
Frattini	C₂×C₄²	C₂×D₄₃
Fitting	C₂×C₄⋊C₈×C₄₃	C₂
socle	C₂²×C₄₃	#95
hypercenter	C₂×C₄⋊C₈	D₄₃
hypocenter	C₄₃	#1283
LCS	G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

subgroup

G/H

center

C₂×C₄

C₂²⋊Dic₄₃

commutator

C₂²×C₄₃

C₄×C₈

Frattini

C₂×C₄²

C₂×D₄₃

Fitting

C₂×C₄⋊C₈×C₄₃

C₂

socle

C₂²×C₄₃

#95

hypercenter

C₂×C₄⋊C₈

D₄₃

hypocenter

C₄₃

#1283

LCS

G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
24. #10621877	C₈	semidirect
63. C₄₃	#1283	semidirect

H ≅ G/N

type

24. #10621877

C₈

semidirect

63. C₄₃

#1283

semidirect

Subgroups — #19132445

Conjugacy classes of subgroups

Complements