Group #19134676 — subgroups

Subgroups — #19134676

Order 5504.

272 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₂×#13063284	C₂	1	1	yes	maximal, characteristic
2	#14582863	C₂	1	1	yes	maximal, characteristic
3	#14582667	C₂	1	4	yes	maximal, complemented
4	C₄₃×#407	C₂	1	1	yes	maximal, characteristic
5	C₂×#10621877	C₂²	1	2	yes	—
6	#13063284	—	2	2	no	—
7	#13063284	—	2	2	no	—
8	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
9	C₂×C₂²⋊Dic₄₃	C₄	1	2	yes	—
10	C₂×C₄×Dic₄₃	C₄	1	2	yes	—
11	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
12	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂²⋊C₈×C₄₃	—	2	2	no	—
15	C₂⁴×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₄₃	—	2	4	no	—
17	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₄₃	D₄	1	2	yes	—
19	C₂²×C₄×C₄₃	D₄	1	2	yes	—
20	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
21	C₂²×Dic₄₃	C₂×C₄	1	4	yes	—
22	M₁₆×C₄₃	—	2	4	no	—
23	C₂×C₈×C₄₃	—	2	2	no	—
24	C₂²⋊Dic₄₃	—	2	4	no	—
25	C₄⋊Dic₄₃	—	2	2	no	—
26	C₄⋊Dic₄₃	—	2	2	no	—
27	C₄×Dic₄₃	—	2	4	no	—
28	#10621877	—	2	4	no	—
29	C₂×C₄₃⋊C₈	—	2	2	no	—
30	C₂³×C₄₃	—	2	2	no	—
31	C₂³×C₄₃	—	4	2	no	—
32	C₂³×C₄₃	C₂²⋊C₄	1	2	yes	—
33	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₄₃	—	2	2	no	—
35	C₂×C₄×C₄₃	—	2	4	no	—
36	C₂×C₄×C₄₃	—	2	4	no	—
37	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
38	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₄₃	#41	1	4	yes	—
41	C₂×Dic₄₃	—	2	4	no	—
42	C₂×Dic₄₃	—	4	4	no	—
43	C₈×C₄₃	—	4	2	no	—
44	C₄₃⋊C₈	—	4	2	no	—
45	C₂²×C₄₃	—	2	2	no	—
46	C₂²×C₄₃	—	2	2	no	—
47	C₂²×C₄₃	—	2	4	no	—
48	C₂²×C₄₃	—	4	4	no	—
49	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₄₃	#117	1	2	yes	—
51	C₄×C₄₃	—	2	2	no	—
52	C₄×C₄₃	#123	1	2	yes	—
53	C₄×C₄₃	#123	1	2	yes	—
54	Dic₄₃	—	4	4	no	—
55	#1822	—	43	1	no	maximal, Sylow
56	C₂×C₄₃	—	2	2	no	—
57	C₂×C₄₃	—	4	2	no	—
58	C₂×C₄₃	#381	1	1	yes	characteristic
59	C₂×C₄₃	#413	1	2	yes	—
60	C₂×#117	—	43	1	no	—
61	#407	—	43	1	no	—
62	#407	D₄₃	1	1	yes	characteristic
63	#343	—	43	4	no	—
64	C₄₃	#1822	1	1	yes	characteristic, complemented, Sylow
65	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
66	C₂×M₁₆	—	43	2	no	—
67	C₂×M₁₆	C₂×D₄₃	1	2	yes	—
68	#117	—	86	2	no	—
69	#117	—	86	2	no	—
70	C₂×C₄⋊C₄	—	43	2	no	—
71	C₂×C₂²⋊C₄	—	43	2	no	—
72	C₂×C₄²	—	43	2	no	—
73	C₂²⋊C₈	—	2	2	no	—
74	C₂²⋊C₈	—	86	2	no	—
75	C₂⁴	C₄×D₄₃	1	1	yes	characteristic
76	C₂²×C₄	—	2	4	no	—
77	C₂²×C₄	—	43	4	no	—
78	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
79	C₂²×C₄	D₁₇₂	1	2	yes	—
80	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
81	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
82	M₁₆	—	2	4	no	—
83	M₁₆	—	86	4	no	—
84	C₂×C₈	—	2	2	no	—
85	C₂×C₈	—	86	2	no	—
86	C₄⋊C₄	—	86	2	no	—
87	C₄⋊C₄	—	86	2	no	—
88	C₂²⋊C₄	—	86	4	no	—
89	C₄²	—	86	4	no	—
90	C₂³	—	2	2	no	—
91	C₂³	—	4	2	no	—
92	C₂³	(C₂×D₄₃)⋊C₄	1	2	yes	—
93	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	86	4	no	—
98	C₂×C₄	—	172	4	no	—
99	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
100	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
101	C₂×C₄	#10621900	1	4	yes	—
102	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
103	C₈	—	4	2	no	—
104	C₈	—	172	2	no	—
105	C₂²	—	2	2	no	—
106	C₂²	—	2	4	no	—
107	C₂²	—	2	2	no	—
108	C₂²	—	4	4	no	—
109	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
110	C₂²	#13063281	1	2	yes	—
111	C₄	—	2	2	no	—
112	C₄	—	172	4	no	—
113	C₄	#13063306	1	2	yes	—
114	C₄	#13063309	1	2	yes	—
115	C₂	—	2	2	no	—
116	C₂	—	4	2	no	—
117	C₂	#14582760	1	1	yes	characteristic
118	C₂	#14582881	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063284

C₂

yes

maximal, characteristic

#14582863

C₂

yes

maximal, characteristic

#14582667

C₂

yes

maximal, complemented

C₄₃×#407

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

—

#13063284

—

#13063284

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₄

yes

—

C₂×C₄×Dic₄₃

C₄

yes

—

C₂²⋊(C₄₃⋊C₈)

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂×M₁₆×C₄₃

C₂²

yes

—

C₂²⋊C₈×C₄₃

—

C₂⁴×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂²⋊C₄

yes

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₃

#117

yes

—

C₄×C₄₃

—

C₄×C₄₃

#123

yes

—

C₄×C₄₃

#123

yes

—

Dic₄₃

—

#1822

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#381

yes

characteristic

C₂×C₄₃

#413

yes

—

C₂×#117

—

#407

—

#407

D₄₃

yes

characteristic

#343

—

C₄₃

#1822

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₄₃

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

—

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂⁴

C₄×D₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

D₁₇₂

yes

—

C₂²×C₄

C₂²⋊D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

—

C₂³

—

C₂³

(C₂×D₄₃)⋊C₄

yes

—

C₂³

C₂×C₄×D₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

100

C₂×C₄

C₂×D₁₇₂

yes

characteristic

101

C₂×C₄

#10621900

yes

—

102

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

103

C₈

—

104

C₈

—

172

—

105

C₂²

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

110

C₂²

#13063281

yes

—

111

C₄

—

112

C₄

—

172

—

113

C₄

#13063306

yes

—

114

C₄

#13063309

yes

—

115

C₂

—

116

C₂

—

117

C₂

#14582760

yes

characteristic

118

C₂

#14582881

yes

—

	subgroup	G/H
center	C₂²	C₂×(C₂×D₄₃)⋊C₄
commutator	C₂³×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#407	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₄
hypercenter	#407	D₄₃
hypocenter	C₄₃	#1822
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #407

subgroup

G/H

center

C₂²

C₂×(C₂×D₄₃)⋊C₄

commutator

C₂³×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#407

C₂

socle

C₂²×C₄₃

C₂×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #407

N	H ≅ G/N	type
3. #14582667	C₂	semidirect
64. C₄₃	#1822	semidirect

H ≅ G/N

type

3. #14582667

C₂

semidirect

64. C₄₃

#1822

semidirect

Subgroups — #19134676

Conjugacy classes of subgroups

Complements