Group #19134664 — subgroups

Subgroups — #19134664

Order 5504.

292 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 101 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	C₂×C₂²⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#14582653	C₂	1	4	yes	maximal, complemented
4	C₂×C₂²⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
6	#13063284	—	2	2	no	—
7	#13063284	—	2	2	no	—
8	C₂×C₄⋊Dic₄₃	C₄	1	1	yes	characteristic
9	C₂×C₄⋊Dic₄₃	C₄	1	1	yes	characteristic
10	C₂×C₂²⋊Dic₄₃	C₄	1	2	yes	—
11	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
12	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
13	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
15	C₂²⋊C₈×C₄₃	—	2	2	no	—
16	C₂⁴×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄×C₄₃	—	2	4	no	—
18	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₄₃	D₄	1	2	yes	—
20	C₂²×C₄×C₄₃	D₄	1	2	yes	—
21	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
22	C₂²×Dic₄₃	C₂×C₄	1	2	yes	—
23	C₂²×Dic₄₃	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₄₃	—	2	2	no	—
25	C₂×C₈×C₄₃	—	2	4	no	—
26	C₂²⋊Dic₄₃	—	2	4	no	—
27	C₄⋊Dic₄₃	—	2	2	no	—
28	C₄⋊Dic₄₃	—	2	2	no	—
29	C₄×Dic₄₃	—	2	2	no	—
30	C₄×Dic₄₃	—	2	2	no	—
31	C₂×C₄₃⋊C₈	—	2	2	no	—
32	C₂×C₄₃⋊C₈	—	2	4	no	—
33	C₂³×C₄₃	—	2	2	no	—
34	C₂³×C₄₃	—	2	2	no	—
35	C₂³×C₄₃	—	2	2	no	—
36	C₂³×C₄₃	C₂²⋊C₄	1	2	yes	—
37	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₄₃	—	2	2	no	—
39	C₂×C₄×C₄₃	—	2	4	no	—
40	C₂×C₄×C₄₃	—	2	4	no	—
41	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
42	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₄₃	#41	1	4	yes	—
45	C₂×Dic₄₃	—	2	2	no	—
46	C₂×Dic₄₃	—	2	2	no	—
47	C₂×Dic₄₃	—	2	4	no	—
48	C₂×Dic₄₃	—	2	4	no	—
49	C₈×C₄₃	—	4	2	no	—
50	C₄₃⋊C₈	—	4	2	no	—
51	C₂²×C₄₃	—	2	2	no	—
52	C₂²×C₄₃	—	2	2	no	—
53	C₂²×C₄₃	—	2	2	no	—
54	C₂²×C₄₃	—	4	4	no	—
55	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄₃	#117	1	2	yes	—
57	C₂²×C₄₃	#131	1	2	yes	—
58	C₂²×C₄₃	#131	1	2	yes	—
59	C₄×C₄₃	—	2	2	no	—
60	C₄×C₄₃	#123	1	2	yes	—
61	C₄×C₄₃	#123	1	2	yes	—
62	Dic₄₃	—	4	2	no	—
63	Dic₄₃	—	4	2	no	—
64	#1818	—	43	1	no	maximal, Sylow
65	C₂×C₄₃	—	4	2	no	—
66	C₂×C₄₃	#381	1	1	yes	characteristic
67	C₂×C₄₃	#408	1	1	yes	characteristic
68	C₂×C₄₃	#408	1	1	yes	characteristic
69	C₂×C₄₃	#433	1	4	yes	—
70	C₂×#117	—	43	1	no	—
71	C₂×C₂²⋊C₈	—	43	1	no	—
72	C₂×C₂²⋊C₈	D₄₃	1	1	yes	characteristic
73	#336	—	43	4	no	—
74	C₄₃	#1818	1	1	yes	characteristic, complemented, Sylow
75	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
76	C₂²×C₈	—	43	2	no	—
77	C₂²×C₈	C₂×D₄₃	1	2	yes	—
78	#117	—	86	2	no	—
79	#117	—	86	2	no	—
80	C₂×C₄⋊C₄	—	43	1	no	—
81	C₂×C₄⋊C₄	—	43	1	no	—
82	C₂×C₂²⋊C₄	—	43	2	no	—
83	C₂×C₄²	—	43	2	no	—
84	C₂²⋊C₈	—	2	2	no	—
85	C₂²⋊C₈	—	86	2	no	—
86	C₂⁴	C₄×D₄₃	1	1	yes	characteristic
87	C₂²×C₄	—	2	4	no	—
88	C₂²×C₄	—	43	2	no	—
89	C₂²×C₄	—	43	2	no	—
90	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
91	C₂²×C₄	D₁₇₂	1	2	yes	—
92	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
93	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
94	C₂×C₈	—	2	4	no	—
95	C₂×C₈	—	2	2	no	—
96	C₂×C₈	—	86	2	no	—
97	C₂×C₈	—	86	4	no	—
98	C₄⋊C₄	—	86	2	no	—
99	C₄⋊C₄	—	86	2	no	—
100	C₂²⋊C₄	—	86	4	no	—
101	C₄²	—	86	2	no	—
102	C₄²	—	86	2	no	—
103	C₂³	—	2	2	no	—
104	C₂³	—	2	2	no	—
105	C₂³	—	2	2	no	—
106	C₂³	(C₂×D₄₃)⋊C₄	1	2	yes	—
107	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	—	2	4	no	—
110	C₂×C₄	—	2	4	no	—
111	C₂×C₄	—	86	2	no	—
112	C₂×C₄	—	86	2	no	—
113	C₂×C₄	—	86	4	no	—
114	C₂×C₄	—	86	4	no	—
115	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
116	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
117	C₂×C₄	#10621900	1	4	yes	—
118	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
119	C₈	—	4	2	no	—
120	C₈	—	172	2	no	—
121	C₂²	—	2	2	no	—
122	C₂²	—	2	2	no	—
123	C₂²	—	2	2	no	—
124	C₂²	—	4	4	no	—
125	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
126	C₂²	#13063281	1	2	yes	—
127	C₂²	#13063331	1	2	yes	—
128	C₂²	#13063333	1	2	yes	—
129	C₄	—	2	2	no	—
130	C₄	—	172	2	no	—
131	C₄	—	172	2	no	—
132	C₄	#13063306	1	2	yes	—
133	C₄	#13063309	1	2	yes	—
134	C₂	—	4	2	no	—
135	C₂	#14582760	1	1	yes	characteristic
136	C₂	#14582865	1	1	yes	characteristic
137	C₂	#14582867	1	1	yes	characteristic
138	C₂	#14582957	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063284

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₄₃⋊C₈)

C₂

yes

maximal, characteristic

#14582653

C₂

yes

maximal, complemented

C₂×C₂²⋊C₈×C₄₃

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

—

#13063284

—

#13063284

—

C₂×C₄⋊Dic₄₃

C₄

yes

characteristic

C₂×C₄⋊Dic₄₃

C₄

yes

characteristic

C₂×C₂²⋊Dic₄₃

C₄

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₂²⋊(C₄₃⋊C₈)

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂²×C₈×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

—

C₂²×Dic₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

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

—

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

—

C₂²×C₄₃

#131

yes

—

C₂²×C₄₃

#131

yes

—

C₄×C₄₃

—

C₄×C₄₃

#123

yes

—

C₄×C₄₃

#123

yes

—

Dic₄₃

—

Dic₄₃

—

#1818

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×#117

—

C₂×C₂²⋊C₈

—

C₂×C₂²⋊C₈

D₄₃

yes

characteristic

#336

—

C₄₃

#1818

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₄₃

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₂×D₄₃

yes

—

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂⁴

C₄×D₄₃

yes

characteristic

C₂²×C₄

—

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

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₂²⋊C₄

—

101

C₄²

—

102

C₄²

—

103

C₂³

—

104

C₂³

—

105

C₂³

—

106

C₂³

(C₂×D₄₃)⋊C₄

yes

—

107

C₂³

C₂×C₄×D₄₃

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

116

C₂×C₄

C₂×D₁₇₂

yes

characteristic

117

C₂×C₄

#10621900

yes

—

118

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

119

C₈

—

120

C₈

—

172

—

121

C₂²

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

126

C₂²

#13063281

yes

—

127

C₂²

#13063331

yes

—

128

C₂²

#13063333

yes

—

129

C₄

—

130

C₄

—

172

—

131

C₄

—

172

—

132

C₄

#13063306

yes

—

133

C₄

#13063309

yes

—

134

C₂

—

135

C₂

#14582760

yes

characteristic

136

C₂

#14582865

yes

characteristic

137

C₂

#14582867

yes

characteristic

138

C₂

#14582957

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₄₃
commutator, socle	C₂³×C₄₃	C₂²×C₄
Fitting	C₂×C₂²⋊C₈×C₄₃	C₂
hypercenter	C₂×C₂²⋊C₈	D₄₃
hypocenter	C₄₃	#1818
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₄₃

commutator, socle

C₂³×C₄₃

C₂²×C₄

Fitting

C₂×C₂²⋊C₈×C₄₃

C₂

hypercenter

C₂×C₂²⋊C₈

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈

N	H ≅ G/N	type
3. #14582653	C₂	semidirect
74. C₄₃	#1818	semidirect

H ≅ G/N

type

3. #14582653

C₂

semidirect

74. C₄₃

#1818

semidirect

Subgroups — #19134664

Conjugacy classes of subgroups

Complements