Group #19142956 — subgroups

Subgroups — #19142956

Order 5504.

472 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 197 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×#13063316	C₂	1	2	yes	maximal
2	#14582798	C₂	1	4	yes	maximal
3	#14582795	C₂	1	4	yes	maximal
4	#14582769	C₂	1	1	yes	maximal, characteristic
5	#14582764	C₂	1	2	yes	maximal
6	C₄²×Dic₄₃	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#384	C₂	1	1	yes	maximal, characteristic
8	#13063316	—	2	8	no	—
9	C₂×C₄⋊Dic₄₃	C₂²	1	4	yes	—
10	C₂×C₄⋊Dic₄₃	C₂²	1	4	yes	—
11	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
12	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
13	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
14	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
15	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
17	C₄₃⋊#95	C₂²	1	8	yes	—
18	C₂×C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
19	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
20	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
22	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
24	C₂²×Dic₄₃	C₂³	1	4	yes	—
25	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
26	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
27	C₂²×Dic₄₃	C₂³	1	2	yes	—
28	C₄⋊C₄×C₄₃	—	2	4	no	—
29	C₄⋊C₄×C₄₃	—	2	8	no	—
30	C₄²×C₄₃	Q₈	1	4	yes	—
31	C₄⋊Dic₄₃	—	2	4	no	—
32	C₄⋊Dic₄₃	—	2	8	no	—
33	C₄⋊Dic₄₃	—	2	8	no	—
34	Dic₄₃⋊C₄	—	2	8	no	—
35	C₄×Dic₄₃	—	2	4	no	—
36	C₄×Dic₄₃	—	2	4	no	—
37	C₄×Dic₄₃	D₄	1	4	yes	—
38	C₄×Dic₄₃	Q₈	1	4	yes	—
39	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
40	C₂×C₄×C₄₃	—	2	4	no	—
41	C₂×C₄×C₄₃	—	2	8	no	—
42	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₄₃	C₂×Q₈	1	4	yes	—
44	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
45	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
46	C₂×C₄×C₄₃	#41	1	4	yes	—
47	C₂×C₄×C₄₃	#41	1	4	yes	—
48	C₂×Dic₄₃	—	2	2	no	—
49	C₂×Dic₄₃	—	2	2	no	—
50	C₂×Dic₄₃	—	2	2	no	—
51	C₂×Dic₄₃	—	2	2	no	—
52	C₂×Dic₄₃	—	2	4	no	—
53	C₂×Dic₄₃	—	2	8	no	—
54	C₂×Dic₄₃	C₂×D₄	1	2	yes	—
55	C₂×Dic₄₃	C₂×D₄	1	2	yes	—
56	C₂×Dic₄₃	C₂×Q₈	1	4	yes	—
57	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
58	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
59	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
60	C₂²×C₄₃	C₂×#41	1	2	yes	—
61	C₂²×C₄₃	C₂×#41	1	2	yes	—
62	C₄×C₄₃	—	4	4	no	—
63	C₄×C₄₃	#125	1	8	yes	complemented
64	C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
65	Dic₄₃	—	2	2	no	—
66	Dic₄₃	—	2	2	no	—
67	Dic₄₃	—	2	4	no	—
68	Dic₄₃	—	4	4	no	—
69	#2859	—	43	1	no	maximal, Sylow
70	C₂×C₄₃	C₂×#125	1	2	yes	—
71	C₂×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
72	C₂×C₄₃	#532	1	1	yes	characteristic
73	C₂×C₄₃	#532	1	1	yes	characteristic
74	C₂×C₄₃	#533	1	2	yes	—
75	C₂×#125	—	43	2	no	—
76	#389	—	43	4	no	—
77	#389	—	43	4	no	—
78	#384	—	43	1	no	—
79	#384	D₄₃	1	1	yes	characteristic
80	#382	—	43	2	no	—
81	C₄³	—	43	1	no	—
82	C₄₃	#2859	1	1	yes	characteristic, complemented, Sylow
83	#125	—	86	8	no	—
84	C₂×C₄⋊C₄	—	43	4	no	—
85	C₂×C₄⋊C₄	—	43	2	no	—
86	C₂×C₄⋊C₄	—	43	4	no	—
87	C₂×C₄⋊C₄	—	43	4	no	—
88	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
89	C₂×C₄⋊C₄	C₂×D₄₃	1	4	yes	—
90	C₂×C₄²	—	43	1	no	—
91	C₂×C₄²	—	43	1	no	—
92	C₂×C₄²	—	43	2	no	—
93	C₂×C₄²	—	43	2	no	—
94	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
95	#95	—	43	8	no	—
96	C₂²×C₄	—	43	2	no	—
97	C₂²×C₄	—	43	1	no	—
98	C₂²×C₄	—	43	1	no	—
99	C₂²×C₄	—	43	4	no	—
100	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
101	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
102	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
103	C₄⋊C₄	—	2	4	no	—
104	C₄⋊C₄	—	2	8	no	—
105	C₄⋊C₄	—	86	8	no	—
106	C₄⋊C₄	—	86	8	no	—
107	C₄⋊C₄	—	86	4	no	—
108	C₄⋊C₄	—	86	8	no	—
109	C₄²	—	43	4	no	—
110	C₄²	—	43	4	no	—
111	C₄²	—	86	4	no	—
112	C₄²	—	86	4	no	—
113	C₄²	Dic₈₆	1	4	yes	—
114	C₂³	C₂³×D₄₃	1	1	yes	characteristic
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	2	8	no	—
117	C₂×C₄	—	43	2	no	—
118	C₂×C₄	—	43	2	no	—
119	C₂×C₄	—	43	4	no	—
120	C₂×C₄	—	86	2	no	—
121	C₂×C₄	—	86	2	no	—
122	C₂×C₄	—	86	2	no	—
123	C₂×C₄	—	86	2	no	—
124	C₂×C₄	—	86	4	no	—
125	C₂×C₄	—	86	8	no	—
126	C₂×C₄	C₂×Dic₈₆	1	4	yes	—
127	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
128	C₂×C₄	D₄×D₄₃	1	2	yes	—
129	C₂×C₄	#10621900	1	4	yes	—
130	C₂×C₄	Q₈×D₄₃	1	2	yes	—
131	C₂×C₄	#10621902	1	4	yes	—
132	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
133	C₂²	C₂×Q₈×D₄₃	1	1	yes	characteristic
134	C₂²	C₂²×Dic₈₆	1	1	yes	characteristic
135	C₂²	C₂×#10621900	1	2	yes	—
136	C₂²	C₂×#10621902	1	2	yes	—
137	C₄	—	4	4	no	—
138	C₄	—	86	2	no	—
139	C₄	—	86	2	no	—
140	C₄	—	86	4	no	—
141	C₄	—	172	4	no	—
142	C₄	#13063316	1	8	yes	complemented
143	C₄	#13063324	1	4	yes	—
144	C₂	C₂×#13063316	1	2	yes	—
145	C₂	C₂×#13063324	1	1	yes	characteristic
146	C₂	#14583447	1	1	yes	characteristic
147	C₂	#14583450	1	1	yes	characteristic
148	C₂	#14583454	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063316

C₂

yes

maximal

#14582798

C₂

yes

maximal

#14582795

C₂

yes

maximal

#14582769

C₂

yes

maximal, characteristic

#14582764

C₂

yes

maximal

C₄²×Dic₄₃

C₂

yes

maximal, characteristic

C₄₃×#384

C₂

yes

maximal, characteristic

#13063316

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

C₄₃⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

Q₈

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

D₄

yes

—

C₄×Dic₄₃

Q₈

yes

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

C₂×Q₈

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₂²×C₄₃

C₂×#41

yes

—

C₄×C₄₃

—

C₄×C₄₃

#125

yes

complemented

C₄×C₄₃

C₄⋊Q₈

yes

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#2859

—

maximal, Sylow

C₂×C₄₃

C₂×#125

yes

—

C₂×C₄₃

C₂×C₄⋊Q₈

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

—

—

—

D₄₃

yes

characteristic

#382

—

C₄³

—

C₄₃

#2859

yes

characteristic, complemented, Sylow

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

C₂²×D₄₃

yes

—

101

C₂²×C₄

C₂²×D₄₃

yes

characteristic

102

C₂²×C₄

C₂²×D₄₃

yes

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄²

—

110

C₄²

—

111

C₄²

—

112

C₄²

—

113

C₄²

Dic₈₆

yes

—

114

C₂³

C₂³×D₄₃

yes

characteristic

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

C₂×Dic₈₆

yes

—

127

C₂×C₄

C₂×Dic₈₆

yes

—

128

C₂×C₄

D₄×D₄₃

yes

—

129

C₂×C₄

#10621900

yes

—

130

C₂×C₄

Q₈×D₄₃

yes

—

131

C₂×C₄

#10621902

yes

—

132

C₂²

C₂×D₄×D₄₃

yes

characteristic

133

C₂²

C₂×Q₈×D₄₃

yes

characteristic

134

C₂²

C₂²×Dic₈₆

yes

characteristic

135

C₂²

C₂×#10621900

yes

—

136

C₂²

C₂×#10621902

yes

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

172

—

142

C₄

#13063316

yes

complemented

143

C₄

#13063324

yes

—

144

C₂

C₂×#13063316

yes

—

145

C₂

C₂×#13063324

yes

characteristic

146

C₂

#14583447

yes

characteristic

147

C₂

#14583450

yes

characteristic

148

C₂

#14583454

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#384	C₂
hypercenter	#384	D₄₃
hypocenter	C₄₃	#2859
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄₃×#384

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
63. C₄×C₄₃	#125	semidirect
82. C₄₃	#2859	semidirect
142. C₄	#13063316	semidirect

H ≅ G/N

type

63. C₄×C₄₃

#125

semidirect

82. C₄₃

#2859

semidirect

142. C₄

#13063316

semidirect

Subgroups — #19142956

Conjugacy classes of subgroups

Complements