Group #19136821 — subgroups

Subgroups — #19136821

Order 5504.

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

normal subgroups only

This group has 140 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	#14583303	C₂	1	1	yes	maximal, characteristic
2	#14583277	C₂	1	1	yes	maximal, characteristic
3	#14582704	C₂	1	1	yes	maximal, characteristic
4	#14582703	C₂	1	1	yes	maximal, characteristic
5	#14582702	C₂	1	1	yes	maximal, characteristic
6	C₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#358	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×#10621885	—	2	1	no	—
10	#13063324	—	2	1	no	—
11	#13063323	—	2	1	no	—
12	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
13	#13063259	C₂²	1	1	yes	characteristic
14	#13063258	—	2	1	no	—
15	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
16	C₂×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
18	#107×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×Q₈×C₄₃	—	2	1	no	—
20	C₂×Dic₈₆	—	2	1	no	—
21	C₂×Dic₈₆	—	4	1	no	—
22	Q₁₆×C₄₃	—	2	1	no	—
23	Q₁₆×C₄₃	—	2	1	no	—
24	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
25	C₄⋊C₄×C₄₃	—	2	1	no	—
26	#10621885	—	4	2	no	—
27	C₄⋊Dic₄₃	—	2	1	no	—
28	Dic₄₃⋊C₄	—	4	1	no	—
29	Dic₄₃⋊C₄	—	4	1	no	—
30	Dic₄₃⋊C₄	—	4	1	no	—
31	C₄×Dic₄₃	D₄	1	1	yes	characteristic
32	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
33	Dic₁₇₂	—	2	1	no	—
34	Dic₁₇₂	—	2	1	no	—
35	C₁₆×C₄₃	—	2	1	no	—
36	C₄₃⋊C₁₆	—	2	1	no	—
37	Q₈×C₄₃	—	4	1	no	—
38	Q₈×C₄₃	—	4	1	no	—
39	C₂×C₄×C₄₃	—	4	1	no	—
40	C₂×C₄×C₄₃	—	4	1	no	—
41	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
42	C₂×Dic₄₃	—	4	1	no	—
43	C₂×Dic₄₃	—	4	1	no	—
44	C₂×Dic₄₃	D₈	1	1	yes	characteristic
45	C₂×Dic₄₃	D₈	1	1	yes	characteristic
46	Dic₈₆	—	4	1	no	—
47	Dic₈₆	—	4	1	no	—
48	Dic₈₆	—	8	2	no	—
49	C₈×C₄₃	#41	1	1	yes	characteristic
50	C₈×C₄₃	#41	1	1	yes	characteristic
51	C₄₃⋊C₈	SD₁₆	1	2	yes	—
52	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
53	C₄×C₄₃	—	8	1	no	—
54	C₄×C₄₃	—	8	1	no	—
55	C₄×C₄₃	#124	1	1	yes	characteristic
56	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
57	Dic₄₃	—	8	1	no	—
58	Dic₄₃	—	8	1	no	—
59	Dic₄₃	SD₃₂	1	2	yes	—
60	Dic₄₃	Q₃₂	1	2	yes	—
61	#2241	—	43	1	no	maximal, Sylow
62	C₂×C₄₃	#486	1	1	yes	characteristic
63	C₂×C₄₃	C₂×SD₃₂	1	1	yes	characteristic
64	C₂×C₄₃	C₂×Q₃₂	1	1	yes	characteristic
65	#500	—	43	1	no	—
66	#494	—	43	1	no	—
67	#358	—	43	1	no	—
68	#358	—	43	1	no	—
69	#358	—	43	1	no	—
70	#358	D₄₃	1	1	yes	characteristic
71	C₄×C₁₆	—	43	1	no	—
72	C₄₃	#2241	1	1	yes	characteristic, complemented, Sylow
73	C₂×Q₁₆	—	43	1	no	—
74	C₂×Q₁₆	—	86	1	no	—
75	C₂×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
76	C₄⋊Q₈	—	86	1	no	—
77	C₄⋊Q₈	—	86	1	no	—
78	C₂×C₁₆	—	43	1	no	—
79	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
80	#107	—	43	1	no	—
81	#107	—	86	1	no	—
82	#107	C₂×D₄₃	1	1	yes	characteristic
83	C₄×C₈	—	43	1	no	—
84	C₂×Q₈	—	2	1	no	—
85	C₂×Q₈	—	86	1	no	—
86	C₂×Q₈	—	172	1	no	—
87	Q₁₆	—	2	1	no	—
88	Q₁₆	—	2	1	no	—
89	Q₁₆	—	86	1	no	—
90	Q₁₆	—	86	1	no	—
91	Q₁₆	—	172	2	no	—
92	C₂×C₈	—	43	1	no	—
93	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
94	C₄⋊C₄	—	2	1	no	—
95	C₄⋊C₄	—	86	1	no	—
96	C₄⋊C₄	—	172	1	no	—
97	C₄⋊C₄	—	172	1	no	—
98	C₄⋊C₄	—	172	1	no	—
99	C₄²	—	43	1	no	—
100	C₁₆	—	2	1	no	—
101	C₁₆	—	86	1	no	—
102	Q₈	—	4	1	no	—
103	Q₈	—	4	1	no	—
104	Q₈	—	344	2	no	—
105	Q₈	—	172	1	no	—
106	Q₈	—	172	1	no	—
107	C₂×C₄	—	4	1	no	—
108	C₂×C₄	—	4	1	no	—
109	C₂×C₄	—	43	1	no	—
110	C₂×C₄	—	43	1	no	—
111	C₂×C₄	—	172	1	no	—
112	C₂×C₄	—	172	1	no	—
113	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
114	C₈	—	43	2	no	—
115	C₈	#10621898	1	1	yes	characteristic
116	C₈	#10621900	1	1	yes	characteristic
117	C₂²	D₈×D₄₃	1	1	yes	characteristic
118	C₄	—	8	1	no	—
119	C₄	—	8	1	no	—
120	C₄	—	43	2	no	—
121	C₄	—	43	2	no	—
122	C₄	—	344	1	no	—
123	C₄	—	344	1	no	—
124	C₄	#13063311	1	1	yes	characteristic
125	C₄	SD₁₆×D₄₃	1	1	yes	characteristic
126	C₂	#14583244	1	1	yes	characteristic
127	C₂	SD₃₂×D₄₃	1	1	yes	characteristic
128	C₂	Q₃₂×D₄₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583303

C₂

yes

maximal, characteristic

#14583277

C₂

yes

maximal, characteristic

#14582704

C₂

yes

maximal, characteristic

#14582703

C₂

yes

maximal, characteristic

#14582702

C₂

yes

maximal, characteristic

C₁₆×Dic₄₃

C₂

yes

maximal, characteristic

C₄₃×#358

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

C₂²

yes

—

—

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

#13063259

C₂²

yes

characteristic

#13063258

—

C₈×Dic₄₃

C₂²

yes

characteristic

C₂×Q₁₆×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

#107×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

#10621885

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

Dic₁₇₂

—

Dic₁₇₂

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

D₈

yes

characteristic

C₂×Dic₄₃

D₈

yes

characteristic

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

yes

C₈×C₄₃

yes

C₄₃⋊C₈

SD₁₆

yes

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#124

yes

characteristic

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

Dic₄₃

—

Dic₄₃

—

Dic₄₃

SD₃₂

yes

—

Dic₄₃

Q₃₂

yes

—

—

C₂×C₄₃

yes

C₂×C₄₃

C₂×SD₃₂

yes

characteristic

C₂×C₄₃

C₂×Q₃₂

yes

—

—

—

—

—

D₄₃

yes

characteristic

C₄×C₁₆

—

C₄₃

#2241

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₄₃

yes

characteristic

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

—

—

C₂×D₄₃

yes

characteristic

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

172

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

172

—

C₂×C₈

—

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄²

—

100

C₁₆

—

101

C₁₆

—

102

Q₈

—

103

Q₈

—

104

Q₈

—

344

—

105

Q₈

—

172

—

106

Q₈

—

172

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

172

—

112

C₂×C₄

—

172

—

113

C₂×C₄

D₄×D₄₃

yes

characteristic

114

C₈

—

115

C₈

#10621898

yes

characteristic

116

C₈

#10621900

yes

characteristic

117

C₂²

D₈×D₄₃

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

344

—

123

C₄

—

344

—

124

C₄

#13063311

yes

characteristic

125

C₄

SD₁₆×D₄₃

yes

characteristic

126

C₂

#14583244

yes

characteristic

127

C₂

SD₃₂×D₄₃

yes

characteristic

128

C₂

Q₃₂×D₄₃

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₃
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#358	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#358	D₄₃
hypocenter	C₄₃	#2241
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

subgroup

G/H

center

C₂²

D₈×D₄₃

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#358

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

N	H ≅ G/N	type
72. C₄₃	#2241	semidirect

H ≅ G/N

type

72. C₄₃

#2241

semidirect

Subgroups — #19136821

Conjugacy classes of subgroups

Complements