Group #19134174 — subgroups

Subgroups — #19134174

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	#14583191	C₂	1	1	yes	maximal, characteristic
2	#14583181	C₂	1	1	yes	maximal, characteristic
3	#14583029	C₂	1	1	yes	maximal, characteristic
4	#14582650	C₂	1	1	yes	maximal, characteristic
5	#14582648	C₂	1	1	yes	maximal, characteristic
6	#14582645	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#487	C₂	1	1	yes	maximal, characteristic
8	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
9	#13063258	—	2	1	no	—
10	#13063256	—	2	1	no	—
11	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
12	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
13	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
14	Dic₄₃⋊C₈	—	2	1	no	—
15	#13063248	—	2	1	no	—
16	#13063248	—	2	1	no	—
17	#13063235	—	2	1	no	—
18	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
20	#103×C₄₃	—	2	1	no	—
21	#103×C₄₃	—	2	1	no	—
22	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₄₃	—	2	1	no	—
24	C₂×Q₈×C₄₃	—	2	1	no	—
25	C₂×Dic₈₆	D₄	1	1	yes	characteristic
26	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
27	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
28	C₄⋊C₄×C₄₃	—	2	1	no	—
29	C₄⋊C₄×C₄₃	—	2	1	no	—
30	C₄⋊C₄×C₄₃	—	2	1	no	—
31	C₄⋊C₄×C₄₃	—	2	1	no	—
32	C₄²×C₄₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
38	C₂×C₄₃⋊C₈	—	2	1	no	—
39	Q₈×C₄₃	—	4	1	no	—
40	Q₈×C₄₃	—	4	1	no	—
41	Q₈×C₄₃	—	8	1	no	—
42	C₂×C₄×C₄₃	—	4	1	no	—
43	C₂×C₄×C₄₃	—	4	1	no	—
44	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
47	C₂×Dic₄₃	—	2	1	no	—
48	C₂×Dic₄₃	—	2	1	no	—
49	Dic₈₆	—	2	1	no	—
50	Dic₈₆	—	2	1	no	—
51	C₈×C₄₃	—	2	1	no	—
52	C₈×C₄₃	—	2	1	no	—
53	C₄₃⋊C₈	—	4	1	no	—
54	C₄₃⋊C₈	—	4	1	no	—
55	C₄₃⋊C₈	—	4	1	no	—
56	C₂²×C₄₃	#121	1	1	yes	characteristic
57	C₄×C₄₃	—	2	1	no	—
58	C₄×C₄₃	—	8	1	no	—
59	C₄×C₄₃	—	8	1	no	—
60	C₄×C₄₃	#135	1	1	yes	characteristic
61	C₄×C₄₃	#137	1	1	yes	characteristic
62	C₄×C₄₃	#137	1	1	yes	characteristic
63	C₄×C₄₃	#137	1	1	yes	characteristic
64	Dic₄₃	—	4	1	no	—
65	Dic₄₃	—	4	1	no	—
66	#1704	—	43	1	no	maximal, Sylow
67	C₂×C₄₃	#464	1	1	yes	characteristic
68	C₂×C₄₃	#470	1	1	yes	characteristic
69	C₂×C₄₃	#471	1	1	yes	characteristic
70	#487	D₄₃	1	1	yes	characteristic
71	#477	—	43	1	no	—
72	#475	—	43	1	no	—
73	#446	—	43	1	no	—
74	#334	—	43	1	no	—
75	#333	—	43	1	no	—
76	#332	—	43	1	no	—
77	C₄₃	#1704	1	1	yes	characteristic, complemented, Sylow
78	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
79	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
80	C₄×Q₈	—	43	1	no	—
81	#107	—	86	1	no	—
82	#106	—	86	1	no	—
83	C₄⋊C₈	—	43	1	no	—
84	C₄⋊C₈	—	43	1	no	—
85	C₄⋊C₈	—	43	1	no	—
86	C₄⋊C₈	—	86	1	no	—
87	#103	—	2	1	no	—
88	#103	—	2	1	no	—
89	#103	—	86	1	no	—
90	#103	—	86	1	no	—
91	#97	—	86	1	no	—
92	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
93	C₂×Q₈	—	2	1	no	—
94	C₂×Q₈	—	2	1	no	—
95	C₂×Q₈	—	43	1	no	—
96	C₂×C₈	—	86	1	no	—
97	C₂×C₈	—	86	1	no	—
98	C₂×C₈	—	86	1	no	—
99	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
100	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
101	C₄⋊C₄	—	2	1	no	—
102	C₄⋊C₄	—	2	1	no	—
103	C₄⋊C₄	—	2	1	no	—
104	C₄⋊C₄	—	2	1	no	—
105	C₄⋊C₄	—	43	1	no	—
106	C₄⋊C₄	—	86	1	no	—
107	C₄²	—	86	1	no	—
108	C₄²	C₂²×D₄₃	1	1	yes	characteristic
109	Q₈	—	4	1	no	—
110	Q₈	—	4	1	no	—
111	Q₈	—	8	1	no	—
112	Q₈	—	86	1	no	—
113	Q₈	—	86	1	no	—
114	C₂×C₄	—	4	1	no	—
115	C₂×C₄	—	4	1	no	—
116	C₂×C₄	—	86	1	no	—
117	C₂×C₄	—	86	1	no	—
118	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
119	C₂×C₄	#10621900	1	1	yes	characteristic
120	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
121	C₈	—	2	1	no	—
122	C₈	—	2	1	no	—
123	C₈	—	172	1	no	—
124	C₈	—	172	1	no	—
125	C₈	—	172	1	no	—
126	C₂²	#13063296	1	1	yes	characteristic
127	C₄	—	2	1	no	—
128	C₄	—	8	1	no	—
129	C₄	—	8	1	no	—
130	C₄	—	172	1	no	—
131	C₄	—	172	1	no	—
132	C₄	#13063345	1	1	yes	characteristic
133	C₄	#13063355	1	1	yes	characteristic
134	C₄	#13063357	1	1	yes	characteristic
135	C₄	#13063357	1	1	yes	characteristic
136	C₂	#14583118	1	1	yes	characteristic
137	C₂	#14583154	1	1	yes	characteristic
138	C₂	#14583159	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583191

C₂

yes

maximal, characteristic

#14583181

C₂

yes

maximal, characteristic

#14583029

C₂

yes

maximal, characteristic

#14582650

C₂

yes

maximal, characteristic

#14582648

C₂

yes

maximal, characteristic

#14582645

C₂

yes

maximal, characteristic

C₄₃×#487

C₂

yes

maximal, characteristic

C₄×Dic₈₆

C₂²

yes

characteristic

#13063258

—

#13063256

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

Dic₄₃⋊C₈

—

#13063248

—

#13063248

—

#13063235

—

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

#103×C₄₃

—

#103×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Dic₈₆

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

D₄

yes

characteristic

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×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

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

#121

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

yes

—

—

—

—

—

—

C₄₃

#1704

yes

characteristic, complemented, Sylow

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

C₄×Q₈

—

#107

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

—

—

—

—

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

100

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄²

—

108

C₄²

C₂²×D₄₃

yes

characteristic

109

Q₈

—

110

Q₈

—

111

Q₈

—

112

Q₈

—

113

Q₈

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

D₄×D₄₃

yes

characteristic

119

C₂×C₄

#10621900

yes

characteristic

120

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

121

C₈

—

122

C₈

—

123

C₈

—

172

—

124

C₈

—

172

—

125

C₈

—

172

—

126

C₂²

#13063296

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

172

—

131

C₄

—

172

—

132

C₄

#13063345

yes

characteristic

133

C₄

#13063355

yes

characteristic

134

C₄

#13063357

yes

characteristic

135

C₄

#13063357

yes

characteristic

136

C₂

#14583118

yes

characteristic

137

C₂

#14583154

yes

characteristic

138

C₂

#14583159

yes

characteristic

	subgroup	G/H
center	C₂²	#13063296
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#487	C₂
socle	C₂²×C₄₃	#121
hypercenter	#487	D₄₃
hypocenter	C₄₃	#1704
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #487

subgroup

G/H

center

C₂²

#13063296

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#487

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #487

N	H ≅ G/N	type
77. C₄₃	#1704	semidirect

H ≅ G/N

type

77. C₄₃

#1704

semidirect

Subgroups — #19134174

Conjugacy classes of subgroups

Complements