Group #19133998 — subgroups

Subgroups — #19133998

Order 5504.

144 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 53 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	#14583302	C₂	1	1	yes	maximal, characteristic
2	#14583195	C₂	1	1	yes	maximal, characteristic
3	#14583191	C₂	1	1	yes	maximal, characteristic
4	#14583023	C₂	1	1	yes	maximal, characteristic
5	#14582651	C₂	1	1	yes	maximal, characteristic
6	#14582647	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#333	C₂	1	1	yes	maximal, characteristic
8	#13063325	C₂²	1	1	yes	characteristic
9	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
10	#13063259	—	2	1	no	—
11	#13063258	—	2	1	no	—
12	#13063258	—	2	1	no	—
13	#13063258	—	2	1	no	—
14	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
15	Dic₄₃⋊C₈	—	2	1	no	—
16	#13063250	—	2	1	no	—
17	#13063248	—	2	1	no	—
18	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₈×Dic₄₃	—	2	1	no	—
20	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₄₃	—	2	1	no	—
24	C₂×Dic₈₆	—	2	1	no	—
25	C₂×Dic₈₆	D₄	1	1	yes	characteristic
26	C₂×C₈×C₄₃	—	2	1	no	—
27	C₂×C₈×C₄₃	—	2	1	no	—
28	C₄⋊C₄×C₄₃	—	2	1	no	—
29	C₄⋊C₄×C₄₃	—	2	1	no	—
30	C₄²×C₄₃	C₂³	1	1	yes	characteristic
31	C₄⋊Dic₄₃	—	2	1	no	—
32	C₄⋊Dic₄₃	—	2	1	no	—
33	C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
34	Dic₄₃⋊C₄	—	2	1	no	—
35	C₄×Dic₄₃	—	2	1	no	—
36	C₂×C₄₃⋊C₈	—	2	1	no	—
37	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
38	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
39	Q₈×C₄₃	—	8	1	no	—
40	C₂×C₄×C₄₃	—	4	1	no	—
41	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
44	C₂×Dic₄₃	—	2	1	no	—
45	C₂×Dic₄₃	—	2	1	no	—
46	C₂×Dic₄₃	—	4	1	no	—
47	Dic₈₆	—	2	1	no	—
48	Dic₈₆	—	8	1	no	—
49	Dic₈₆	Q₁₆	1	2	yes	—
50	C₈×C₄₃	—	4	1	no	—
51	C₈×C₄₃	—	4	1	no	—
52	C₄₃⋊C₈	—	2	1	no	—
53	C₄₃⋊C₈	—	4	1	no	—
54	C₄₃⋊C₈	Q₁₆	1	2	yes	—
55	C₂²×C₄₃	#121	1	1	yes	characteristic
56	C₄×C₄₃	—	2	1	no	—
57	C₄×C₄₃	—	8	1	no	—
58	C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
59	C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
60	C₄×C₄₃	#135	1	1	yes	characteristic
61	C₄×C₄₃	#137	1	1	yes	characteristic
62	Dic₄₃	—	2	2	no	—
63	Dic₄₃	—	4	1	no	—
64	Dic₄₃	—	8	1	no	—
65	#1676	—	43	1	no	maximal, Sylow
66	C₂×C₄₃	#462	1	1	yes	characteristic
67	C₂×C₄₃	#467	1	1	yes	characteristic
68	C₂×C₄₃	#472	1	1	yes	characteristic
69	#500	—	43	1	no	—
70	#477	—	43	1	no	—
71	#477	—	43	1	no	—
72	C₈×Q₈	—	43	1	no	—
73	#335	—	43	1	no	—
74	#333	—	43	1	no	—
75	#333	D₄₃	1	1	yes	characteristic
76	C₄₃	#1676	1	1	yes	characteristic, complemented, Sylow
77	C₄⋊Q₈	—	43	1	no	—
78	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
79	C₄×Q₈	—	43	1	no	—
80	#107	—	86	1	no	—
81	#107	—	86	1	no	—
82	#107	—	86	1	no	—
83	#107	—	86	1	no	—
84	C₄⋊C₈	—	43	1	no	—
85	C₄⋊C₈	—	86	1	no	—
86	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
87	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
88	#103	—	86	1	no	—
89	#103	—	86	1	no	—
90	C₄×C₈	—	43	1	no	—
91	C₄×C₈	—	86	1	no	—
92	C₂×Q₈	—	2	1	no	—
93	C₂×Q₈	—	43	1	no	—
94	C₂×Q₈	—	86	1	no	—
95	C₂×C₈	—	2	1	no	—
96	C₂×C₈	—	2	1	no	—
97	C₂×C₈	—	43	1	no	—
98	C₂×C₈	—	43	1	no	—
99	C₂×C₈	—	86	1	no	—
100	C₄⋊C₄	—	2	1	no	—
101	C₄⋊C₄	—	2	1	no	—
102	C₄⋊C₄	—	43	1	no	—
103	C₄⋊C₄	—	86	1	no	—
104	C₄⋊C₄	—	86	1	no	—
105	C₄⋊C₄	—	86	1	no	—
106	C₄²	—	86	1	no	—
107	C₄²	C₂²×D₄₃	1	1	yes	characteristic
108	Q₈	—	8	1	no	—
109	Q₈	—	43	2	no	—
110	Q₈	—	86	1	no	—
111	Q₈	—	344	1	no	—
112	C₂×C₄	—	4	1	no	—
113	C₂×C₄	—	86	1	no	—
114	C₂×C₄	—	86	1	no	—
115	C₂×C₄	—	172	1	no	—
116	C₂×C₄	#10621898	1	1	yes	characteristic
117	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
118	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
119	C₈	—	4	1	no	—
120	C₈	—	4	1	no	—
121	C₈	—	43	2	no	—
122	C₈	—	86	1	no	—
123	C₈	—	172	1	no	—
124	C₂²	#13063298	1	1	yes	characteristic
125	C₄	—	2	1	no	—
126	C₄	—	8	1	no	—
127	C₄	—	86	2	no	—
128	C₄	—	344	1	no	—
129	C₄	—	172	1	no	—
130	C₄	Q₁₆×D₄₃	1	1	yes	characteristic
131	C₄	Q₁₆×D₄₃	1	1	yes	characteristic
132	C₄	#13063346	1	1	yes	characteristic
133	C₄	#13063354	1	1	yes	characteristic
134	C₂	#14583108	1	1	yes	characteristic
135	C₂	#14583139	1	1	yes	characteristic
136	C₂	#14583168	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583302

C₂

yes

maximal, characteristic

#14583195

C₂

yes

maximal, characteristic

#14583191

C₂

yes

maximal, characteristic

#14583023

C₂

yes

maximal, characteristic

#14582651

C₂

yes

maximal, characteristic

#14582647

C₂

yes

maximal, characteristic

C₄₃×#333

C₂

yes

maximal, characteristic

#13063325

C₂²

yes

characteristic

C₄×Dic₈₆

C₂²

yes

—

—

—

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

Dic₄₃⋊C₈

—

#13063250

—

#13063248

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₈×Dic₄₃

—

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

D₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

characteristic

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

Q₁₆

yes

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

Q₁₆

yes

—

C₂²×C₄₃

#121

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×Q₁₆

yes

characteristic

C₄×C₄₃

C₂×Q₁₆

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

—

C₈×Q₈

—

#335

—

#333

—

#333

D₄₃

yes

characteristic

C₄₃

#1676

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

C₄×Q₈

—

—

—

—

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₃

yes

characteristic

C₄⋊C₈

C₂×D₄₃

yes

characteristic

#103

—

#103

—

C₄×C₈

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄²

—

107

C₄²

C₂²×D₄₃

yes

characteristic

108

Q₈

—

109

Q₈

—

110

Q₈

—

111

Q₈

—

344

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

172

—

116

C₂×C₄

#10621898

yes

characteristic

117

C₂×C₄

D₄×D₄₃

yes

characteristic

118

C₂×C₄

D₄×D₄₃

yes

characteristic

119

C₈

—

120

C₈

—

121

C₈

—

122

C₈

—

123

C₈

—

172

—

124

C₂²

#13063298

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

—

344

—

129

C₄

—

172

—

130

C₄

Q₁₆×D₄₃

yes

characteristic

131

C₄

Q₁₆×D₄₃

yes

characteristic

132

C₄

#13063346

yes

characteristic

133

C₄

#13063354

yes

characteristic

134

C₂

#14583108

yes

characteristic

135

C₂

#14583139

yes

characteristic

136

C₂

#14583168

yes

characteristic

	subgroup	G/H
center	C₂²	#13063298
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#333	C₂
socle	C₂²×C₄₃	#121
hypercenter	#333	D₄₃
hypocenter	C₄₃	#1676
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

subgroup

G/H

center

C₂²

#13063298

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#333

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #333

N	H ≅ G/N	type
76. C₄₃	#1676	semidirect

H ≅ G/N

type

76. C₄₃

#1676

semidirect

Subgroups — #19133998

Conjugacy classes of subgroups

Complements