Group #19143464 — subgroups

Subgroups — #19143464

Order 5504.

456 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 189 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	C₂²×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic
2	#14583376	C₂	1	2	yes	maximal
3	#14583007	C₂	1	4	yes	maximal, complemented
4	C₄×Dic₁₇₂	C₂	1	4	yes	maximal, complemented
5	#14582937	C₂	1	1	yes	maximal, characteristic
6	#14582909	C₂	1	2	yes	maximal
7	C₄₃×#405	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₈₆	C₂²	1	2	yes	—
9	C₂×Dic₁₇₂	C₄	1	8	yes	complemented
10	C₂×Dic₁₇₂	C₂²	1	2	yes	—
11	C₂×Dic₁₇₂	C₂²	1	2	yes	—
12	C₄×Dic₈₆	C₂²	1	8	yes	—
13	#13063290	—	2	4	no	—
14	#13063284	C₂²	1	2	yes	—
15	#13063281	—	2	4	no	—
16	#13063259	C₂²	1	2	yes	—
17	#13063257	C₂²	1	2	yes	—
18	#13063250	C₂²	1	8	yes	—
19	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
21	#117×C₄₃	C₂²	1	1	yes	characteristic
22	#97×C₄₃	C₂²	1	2	yes	—
23	C₄×C₈×C₄₃	C₂²	1	2	yes	—
24	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
25	C₂²×Dic₄₃	—	2	2	no	—
26	C₂×Dic₈₆	—	2	2	no	—
27	C₂×Dic₈₆	—	2	4	no	—
28	C₂×Dic₈₆	C₂×C₄	1	8	yes	—
29	C₂×Dic₈₆	C₂³	1	4	yes	—
30	M₁₆×C₄₃	—	2	2	no	—
31	C₂×C₈×C₄₃	C₂×C₄	1	4	yes	—
32	C₂×C₈×C₄₃	C₂³	1	2	yes	—
33	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
34	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
35	C₄⋊C₄×C₄₃	D₄	1	2	yes	—
36	C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
37	C₄²×C₄₃	C₂³	1	2	yes	—
38	C₂²⋊Dic₄₃	—	2	2	no	—
39	C₄⋊Dic₄₃	C₂³	1	4	yes	—
40	Dic₄₃⋊C₄	—	2	8	no	—
41	C₄×Dic₄₃	—	2	8	no	—
42	C₄×Dic₄₃	—	2	2	no	—
43	Dic₁₇₂	C₂×C₄	1	8	yes	—
44	Dic₁₇₂	C₂×C₄	1	8	yes	—
45	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
47	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
48	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₄₃	#41	1	2	yes	—
50	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
51	C₂×Dic₄₃	—	2	8	no	—
52	C₂×Dic₄₃	—	2	4	no	—
53	C₂×Dic₄₃	—	2	4	no	—
54	Dic₈₆	—	2	8	no	—
55	Dic₈₆	—	2	4	no	—
56	Dic₈₆	C₂²×C₄	1	8	yes	—
57	C₈×C₄₃	—	2	2	no	—
58	C₈×C₄₃	C₂²×C₄	1	2	yes	—
59	C₈×C₄₃	C₂²×C₄	1	2	yes	—
60	C₂²×C₄₃	—	2	2	no	—
61	C₂²×C₄₃	C₄×D₄	1	2	yes	—
62	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
63	C₄×C₄₃	—	2	4	no	—
64	C₄×C₄₃	C₄×D₄	1	2	yes	—
65	C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
66	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
67	Dic₄₃	—	2	8	no	—
68	Dic₄₃	—	4	4	no	—
69	#2950	—	43	1	no	maximal, Sylow
70	C₂×C₄₃	—	2	2	no	—
71	C₂×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
72	C₂×C₄₃	#578	1	2	yes	—
73	C₂²×Q₁₆	—	43	1	no	—
74	#519	—	43	2	no	—
75	#441	—	43	4	no	—
76	C₄×Q₁₆	—	43	4	no	—
77	#427	—	43	1	no	—
78	#419	—	43	2	no	—
79	#405	D₄₃	1	1	yes	characteristic
80	C₄₃	#2950	1	1	yes	characteristic, complemented, Sylow
81	C₂²×Q₈	—	43	2	no	—
82	C₂×Q₁₆	—	43	2	no	—
83	C₂×Q₁₆	—	43	2	no	—
84	C₂×Q₁₆	—	43	8	no	—
85	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
86	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
87	C₄×Q₈	—	43	8	no	—
88	C₄×Q₈	—	86	4	no	—
89	#117	—	43	2	no	—
90	#117	—	86	4	no	—
91	#117	C₂×D₄₃	1	1	yes	characteristic
92	#107	—	43	2	no	—
93	#106	—	43	2	no	—
94	#103	—	43	8	no	—
95	#97	C₂×D₄₃	1	2	yes	—
96	C₄×C₈	C₂×D₄₃	1	2	yes	—
97	C₂×Q₈	—	43	8	no	—
98	C₂×Q₈	—	43	4	no	—
99	C₂×Q₈	—	86	2	no	—
100	C₂×Q₈	—	86	4	no	—
101	C₂²×C₄	—	86	2	no	—
102	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
103	Q₁₆	—	43	8	no	—
104	Q₁₆	—	43	8	no	—
105	M₁₆	—	2	2	no	—
106	C₂×C₈	C₄×D₄₃	1	4	yes	—
107	C₂×C₈	C₂²×D₄₃	1	2	yes	—
108	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
109	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
110	C₄⋊C₄	—	43	4	no	—
111	C₄⋊C₄	—	86	8	no	—
112	C₄⋊C₄	D₁₇₂	1	2	yes	—
113	C₂²⋊C₄	—	86	2	no	—
114	C₂²⋊C₄	D₁₇₂	1	2	yes	—
115	C₄²	—	86	2	no	—
116	C₄²	—	86	8	no	—
117	C₄²	C₂²×D₄₃	1	2	yes	—
118	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
119	Q₈	—	43	8	no	—
120	Q₈	—	86	8	no	—
121	Q₈	—	86	4	no	—
122	C₂×C₄	—	86	8	no	—
123	C₂×C₄	—	86	4	no	—
124	C₂×C₄	—	86	4	no	—
125	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
126	C₂×C₄	C₂×D₁₇₂	1	4	yes	—
127	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
128	C₂×C₄	#10621898	1	2	yes	—
129	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
130	C₈	—	2	2	no	—
131	C₈	C₂×C₄×D₄₃	1	2	yes	—
132	C₈	C₂×C₄×D₄₃	1	2	yes	—
133	C₂²	—	2	2	no	—
134	C₂²	C₄×D₁₇₂	1	2	yes	—
135	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
136	C₄	—	2	4	no	—
137	C₄	—	86	8	no	—
138	C₄	—	172	4	no	—
139	C₄	C₄×D₁₇₂	1	2	yes	—
140	C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
141	C₄	C₂×#10621898	1	1	yes	characteristic
142	C₂	—	2	2	no	—
143	C₂	C₂×C₄×D₁₇₂	1	1	yes	characteristic
144	C₂	#14583716	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₁₇₂

C₂

yes

maximal, characteristic

#14583376

C₂

yes

maximal

#14583007

C₂

yes

maximal, complemented

C₄×Dic₁₇₂

C₂

yes

maximal, complemented

#14582937

C₂

yes

maximal, characteristic

#14582909

C₂

yes

maximal

C₄₃×#405

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

—

C₂×Dic₁₇₂

C₄

yes

complemented

C₂×Dic₁₇₂

C₂²

yes

—

C₂×Dic₁₇₂

C₂²

yes

—

C₄×Dic₈₆

C₂²

yes

—

#13063290

—

#13063284

C₂²

yes

—

#13063281

—

#13063259

C₂²

yes

—

#13063257

C₂²

yes

—

#13063250

C₂²

yes

—

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

characteristic

#117×C₄₃

C₂²

yes

characteristic

#97×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

C₂×C₄

yes

—

C₂×Dic₈₆

C₂³

yes

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

C₂³

yes

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

D₄

yes

—

C₂²⋊C₄×C₄₃

D₄

yes

—

C₄²×C₄₃

C₂³

yes

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂³

yes

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

Dic₁₇₂

C₂×C₄

yes

—

Dic₁₇₂

C₂×C₄

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

C₂²×C₄

yes

—

C₈×C₄₃

—

C₈×C₄₃

C₂²×C₄

yes

—

C₈×C₄₃

C₂²×C₄

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

C₄×D₄

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

—

C₄×C₄₃

C₂³×C₄

yes

characteristic

C₄×C₄₃

C₂×#41

yes

characteristic

Dic₄₃

—

Dic₄₃

—

#2950

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×C₄×D₄

yes

characteristic

C₂×C₄₃

#578

yes

—

C₂²×Q₁₆

—

#519

—

#441

—

C₄×Q₁₆

—

#427

—

#419

—

#405

D₄₃

yes

characteristic

C₄₃

#2950

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

characteristic

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

#117

—

#117

—

#117

C₂×D₄₃

yes

—

—

—

C₂×D₄₃

yes

—

C₄×C₈

C₂×D₄₃

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

100

C₂×Q₈

—

101

C₂²×C₄

—

102

C₂²×C₄

C₂²×D₄₃

yes

characteristic

103

Q₁₆

—

104

Q₁₆

—

105

M₁₆

—

106

C₂×C₈

C₄×D₄₃

yes

—

107

C₂×C₈

C₂²×D₄₃

yes

—

108

C₂×C₈

C₂²×D₄₃

yes

characteristic

109

C₂×C₈

C₂²×D₄₃

yes

characteristic

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

D₁₇₂

yes

—

113

C₂²⋊C₄

—

114

C₂²⋊C₄

D₁₇₂

yes

—

115

C₄²

—

116

C₄²

—

117

C₄²

C₂²×D₄₃

yes

—

118

C₂³

C₂×D₁₇₂

yes

characteristic

119

Q₈

—

120

Q₈

—

121

Q₈

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

C₂×C₄×D₄₃

yes

—

126

C₂×C₄

C₂×D₁₇₂

yes

—

127

C₂×C₄

C₂×D₁₇₂

yes

characteristic

128

C₂×C₄

#10621898

yes

—

129

C₂×C₄

C₂³×D₄₃

yes

characteristic

130

C₈

—

131

C₈

C₂×C₄×D₄₃

yes

—

132

C₈

C₂×C₄×D₄₃

yes

—

133

C₂²

—

134

C₂²

C₄×D₁₇₂

yes

—

135

C₂²

C₂²×D₁₇₂

yes

characteristic

136

C₄

—

137

C₄

—

138

C₄

—

172

—

139

C₄

C₄×D₁₇₂

yes

—

140

C₄

C₂²×C₄×D₄₃

yes

characteristic

141

C₄

C₂×#10621898

yes

characteristic

142

C₂

—

143

C₂

C₂×C₄×D₁₇₂

yes

characteristic

144

C₂

#14583716

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₁₇₂
commutator	C₄×C₄₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#405	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#405	D₄₃
hypocenter	C₄₃	#2950
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

subgroup

G/H

center

C₂²

C₂²×D₁₇₂

commutator

C₄×C₄₃

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₄₃×#405

C₂

socle

C₂²×C₄₃

C₂²×D₄

D₄₃

C₄₃

G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ #117 ◁ #405

N	H ≅ G/N	type
3. #14583007	C₂	semidirect
4. C₄×Dic₁₇₂	C₂	semidirect
9. C₂×Dic₁₇₂	C₄	semidirect
80. C₄₃	#2950	semidirect

H ≅ G/N

type

3. #14583007

C₂

semidirect

4. C₄×Dic₁₇₂

C₂

semidirect

9. C₂×Dic₁₇₂

C₄

semidirect

80. C₄₃

#2950

semidirect

Subgroups — #19143464

Conjugacy classes of subgroups

Complements