Group #19134397 — subgroups

Subgroups — #19134397

Order 5504.

284 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 113 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×#13063332	C₂	1	1	yes	maximal, characteristic
2	#14582883	C₂	1	1	yes	maximal, characteristic
3	#14582855	C₂	1	2	yes	maximal, complemented
4	#14582669	C₂	1	2	yes	maximal, complemented
5	C₄₃×#410	C₂	1	1	yes	maximal, characteristic
6	#13063332	—	2	2	no	—
7	#13063332	—	2	2	no	—
8	C₂×#10621877	C₄	1	2	yes	complemented
9	C₂×#10621877	C₂²	1	2	yes	—
10	C₂×#10621877	C₂²	1	1	yes	characteristic
11	C₂²×C₄₃⋊C₈	C₄	1	2	yes	complemented
12	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
13	#13063244	C₄	1	2	yes	complemented
14	#13063242	C₄	1	2	yes	complemented
15	#13063236	—	2	2	no	—
16	C₄×C₄₃⋊C₈	—	2	2	no	—
17	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic
18	#117×C₄₃	C₂²	1	2	yes	—
19	#99×C₄₃	C₄	1	4	yes	—
20	#41×C₄₃	—	2	2	no	—
21	#41×C₄₃	—	2	2	no	—
22	C₂×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
23	C₂×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
24	C₂×D₄×C₄₃	C₂×C₄	1	2	yes	—
25	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
27	C₄⋊C₄×C₄₃	—	2	2	no	—
28	C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
29	C₄²×C₄₃	—	2	2	no	—
30	#10621877	—	2	2	no	—
31	#10621877	—	2	2	no	—
32	#10621877	—	2	4	no	—
33	#10621877	C₂×C₄	1	4	yes	—
34	C₂×C₄₃⋊C₈	—	2	2	no	—
35	C₂×C₄₃⋊C₈	—	2	2	no	—
36	C₂×C₄₃⋊C₈	—	2	2	no	—
37	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
38	C₂×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄₃⋊C₈	D₄	1	2	yes	—
41	C₂×C₄₃⋊C₈	D₄	1	2	yes	—
42	C₂³×C₄₃	C₄²	1	2	yes	—
43	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
44	Q₈×C₄₃	—	2	2	no	—
45	D₄×C₄₃	—	2	4	no	—
46	D₄×C₄₃	—	2	2	no	—
47	C₂×C₄×C₄₃	—	2	2	no	—
48	C₂×C₄×C₄₃	—	2	2	no	—
49	C₂×C₄×C₄₃	—	2	4	no	—
50	C₂×C₄×C₄₃	C₄²	1	2	yes	—
51	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₄₃	#41	1	2	yes	—
55	C₄₃⋊C₈	—	2	2	no	—
56	C₄₃⋊C₈	—	2	4	no	—
57	C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
58	C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
59	C₄₃⋊C₈	C₂²⋊C₄	1	2	yes	—
60	C₂²×C₄₃	—	2	2	no	—
61	C₂²×C₄₃	—	4	1	no	—
62	C₂²×C₄₃	—	4	2	no	—
63	C₂²×C₄₃	C₂×C₄²	1	1	yes	characteristic
64	C₂²×C₄₃	C₄×D₄	1	2	yes	—
65	C₄×C₄₃	—	2	2	no	—
66	C₄×C₄₃	—	4	4	no	—
67	C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
68	C₄×C₄₃	#117	1	1	yes	characteristic
69	C₄×C₄₃	C₄×D₄	1	2	yes	—
70	#1757	—	43	1	no	maximal, Sylow
71	C₂×C₄₃	—	2	2	no	—
72	C₂×C₄₃	—	2	1	no	—
73	C₂×C₄₃	—	4	2	no	—
74	C₂×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
75	C₂×#131	—	43	1	no	—
76	#413	—	43	1	no	—
77	#410	D₄₃	1	1	yes	characteristic
78	#405	—	43	2	no	—
79	#344	—	43	2	no	—
80	C₄₃	#1757	1	1	yes	characteristic, complemented, Sylow
81	C₂×#41	C₂×D₄₃	1	1	yes	characteristic
82	#131	—	86	2	no	—
83	#131	—	86	2	no	—
84	C₂×M₁₆	—	43	1	no	—
85	C₂×M₁₆	—	43	2	no	—
86	C₂×M₁₆	—	43	2	no	—
87	C₂²×C₈	—	43	1	no	—
88	C₂²×C₈	—	43	2	no	—
89	#117	C₂×D₄₃	1	2	yes	—
90	#101	—	43	2	no	—
91	#100	—	43	2	no	—
92	#99	Dic₄₃	1	4	yes	—
93	#97	—	86	2	no	—
94	C₄×C₈	—	86	2	no	—
95	#41	—	2	2	no	—
96	#41	—	2	2	no	—
97	C₂×Q₈	C₄×D₄₃	1	1	yes	characteristic
98	C₂×D₄	C₄×D₄₃	1	1	yes	characteristic
99	C₂×D₄	C₂×Dic₄₃	1	2	yes	—
100	C₂²×C₄	C₄×D₄₃	1	2	yes	—
101	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
102	M₁₆	—	43	4	no	—
103	M₁₆	—	86	4	no	—
104	M₁₆	—	86	2	no	—
105	M₁₆	—	86	2	no	—
106	C₂×C₈	—	43	1	no	—
107	C₂×C₈	—	43	1	no	—
108	C₂×C₈	—	43	2	no	—
109	C₂×C₈	—	43	2	no	—
110	C₂×C₈	—	43	2	no	—
111	C₂×C₈	—	86	2	no	—
112	C₂×C₈	—	86	2	no	—
113	C₂×C₈	—	86	2	no	—
114	C₄⋊C₄	—	2	2	no	—
115	C₂²⋊C₄	C₂×Dic₄₃	1	4	yes	—
116	C₄²	—	2	2	no	—
117	C₂³	C₄×Dic₄₃	1	2	yes	—
118	C₂³	C₂²×Dic₄₃	1	1	yes	characteristic
119	Q₈	—	2	2	no	—
120	D₄	—	2	4	no	—
121	D₄	—	2	2	no	—
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	2	4	no	—
125	C₂×C₄	C₄×Dic₄₃	1	2	yes	—
126	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
127	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
128	C₂×C₄	D₄×D₄₃	1	2	yes	—
129	C₂×C₄	#10621900	1	2	yes	—
130	C₈	—	43	1	no	—
131	C₈	—	43	1	no	—
132	C₈	—	43	2	no	—
133	C₈	—	86	2	no	—
134	C₈	—	86	4	no	—
135	C₂²	—	2	2	no	—
136	C₂²	—	4	1	no	—
137	C₂²	—	4	2	no	—
138	C₂²	C₂×C₄×Dic₄₃	1	1	yes	characteristic
139	C₂²	D₄×Dic₄₃	1	2	yes	—
140	C₄	—	2	2	no	—
141	C₄	—	4	4	no	—
142	C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
143	C₄	#13063281	1	1	yes	characteristic
144	C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
145	C₂	—	2	2	no	—
146	C₂	—	2	1	no	—
147	C₂	—	4	2	no	—
148	C₂	C₂²⋊C₄×Dic₄₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063332

C₂

yes

maximal, characteristic

#14582883

C₂

yes

maximal, characteristic

#14582855

C₂

yes

maximal, complemented

#14582669

C₂

yes

maximal, complemented

C₄₃×#410

C₂

yes

maximal, characteristic

#13063332

—

#13063332

—

C₂×#10621877

C₄

yes

complemented

C₂×#10621877

C₂²

yes

—

C₂×#10621877

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

C₄

yes

complemented

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

#13063244

C₄

yes

complemented

#13063242

C₄

yes

complemented

#13063236

—

C₄×C₄₃⋊C₈

—

C₂×#41×C₄₃

C₂²

yes

characteristic

#117×C₄₃

C₂²

yes

—

#99×C₄₃

C₄

yes

—

#41×C₄₃

—

#41×C₄₃

—

C₂×Q₈×C₄₃

C₂×C₄

yes

characteristic

C₂×D₄×C₄₃

C₂×C₄

yes

characteristic

C₂×D₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

—

—

—

—

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

—

C₂×C₄₃⋊C₈

D₄

yes

—

C₂³×C₄₃

C₄²

yes

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄²

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

C₂²⋊C₄

yes

characteristic

C₄₃⋊C₈

C₂²⋊C₄

yes

characteristic

C₄₃⋊C₈

C₂²⋊C₄

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₄²

yes

characteristic

C₂²×C₄₃

C₄×D₄

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₃

#117

yes

characteristic

C₄×C₄₃

C₄×D₄

yes

—

#1757

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

C₄×C₂²⋊C₄

yes

—

—

D₄₃

yes

characteristic

#405

—

#344

—

C₄₃

#1757

yes

characteristic, complemented, Sylow

C₂×#41

C₂×D₄₃

yes

characteristic

#131

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

#117

C₂×D₄₃

yes

—

#101

—

#100

—

#99

Dic₄₃

yes

—

#97

—

C₄×C₈

—

#41

—

#41

—

C₂×Q₈

C₄×D₄₃

yes

characteristic

C₂×D₄

C₄×D₄₃

yes

characteristic

C₂×D₄

C₂×Dic₄₃

yes

—

100

C₂²×C₄

C₄×D₄₃

yes

—

101

C₂²×C₄

C₂²×D₄₃

yes

characteristic

102

M₁₆

—

103

M₁₆

—

104

M₁₆

—

105

M₁₆

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₄⋊C₄

—

115

C₂²⋊C₄

C₂×Dic₄₃

yes

—

116

C₄²

—

117

C₂³

C₄×Dic₄₃

yes

—

118

C₂³

C₂²×Dic₄₃

yes

characteristic

119

Q₈

—

120

D₄

—

121

D₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

C₄×Dic₄₃

yes

—

126

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

127

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

128

C₂×C₄

D₄×D₄₃

yes

—

129

C₂×C₄

#10621900

yes

—

130

C₈

—

131

C₈

—

132

C₈

—

133

C₈

—

134

C₈

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

C₂×C₄×Dic₄₃

yes

characteristic

139

C₂²

D₄×Dic₄₃

yes

—

140

C₄

—

141

C₄

—

142

C₄

C₂²⋊C₄×D₄₃

yes

characteristic

143

C₄

#13063281

yes

characteristic

144

C₄

(C₂²⋊D₄₃)⋊C₄

yes

—

145

C₂

—

146

C₂

—

147

C₂

—

148

C₂

C₂²⋊C₄×Dic₄₃

yes

characteristic

	subgroup	G/H
center	C₄	C₂²⋊C₄×D₄₃
commutator	C₂²×C₄₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#410	C₂
socle	C₂×C₄₃	C₄×C₂²⋊C₄
hypercenter	#410	D₄₃
hypocenter	C₄₃	#1757
LCS	G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #410

subgroup

G/H

center

C₄

C₂²⋊C₄×D₄₃

commutator

C₂²×C₄₃

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#410

C₂

socle

C₂×C₄₃

C₄×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #410

N	H ≅ G/N	type
3. #14582855	C₂	semidirect
4. #14582669	C₂	semidirect
8. C₂×#10621877	C₄	semidirect
11. C₂²×C₄₃⋊C₈	C₄	semidirect
13. #13063244	C₄	semidirect
14. #13063242	C₄	semidirect
80. C₄₃	#1757	semidirect

H ≅ G/N

type

3. #14582855

C₂

semidirect

4. #14582669

C₂

semidirect

8. C₂×#10621877

C₄

semidirect

11. C₂²×C₄₃⋊C₈

C₄

semidirect

13. #13063244

C₄

semidirect

14. #13063242

C₄

semidirect

80. C₄₃

#1757

semidirect

Subgroups — #19134397

Conjugacy classes of subgroups

Complements