Group #19132438 — subgroups

Subgroups — #19132438

Order 5504.

264 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 97 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×C₂²⋊(C₄₃⋊C₈)	C₂	1	2	yes	maximal
2	C₂×#95×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄₃⋊C₈	—	2	2	no	—
4	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
5	C₂²⋊(C₄₃⋊C₈)	C₄	1	4	yes	complemented
6	C₂³×C₄×C₄₃	C₄	1	2	yes	—
7	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
8	#95×C₄₃	—	2	2	no	—
9	C₂⁴×C₄₃	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄×C₄₃	—	2	2	no	—
11	C₂²×C₄×C₄₃	—	2	2	no	—
12	C₂²×C₄×C₄₃	—	4	2	no	—
13	C₂²×C₄×C₄₃	—	4	2	no	—
14	C₂²×C₄×C₄₃	—	4	2	no	—
15	C₂²×C₄×C₄₃	C₈	1	4	yes	complemented
16	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₄₃	D₄	1	2	yes	—
18	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₄₃	Q₈	1	1	yes	characteristic
20	C₂×C₄₃⋊C₈	—	2	4	no	—
21	C₂×C₄₃⋊C₈	—	4	4	no	—
22	C₂³×C₄₃	—	2	2	no	—
23	C₂³×C₄₃	—	2	1	no	—
24	C₂³×C₄₃	—	2	1	no	—
25	C₂³×C₄₃	C₄²	1	1	yes	characteristic
26	C₂³×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂³×C₄₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂³×C₄₃	C₂×C₈	1	2	yes	—
29	C₂³×C₄₃	M₁₆	1	2	yes	—
30	C₂×C₄×C₄₃	—	2	4	no	—
31	C₂×C₄×C₄₃	—	2	4	no	—
32	C₂×C₄×C₄₃	—	4	2	no	—
33	C₂×C₄×C₄₃	—	4	1	no	—
34	C₂×C₄×C₄₃	—	4	1	no	—
35	C₂×C₄×C₄₃	—	4	4	no	—
36	C₂×C₄×C₄₃	—	4	2	no	—
37	C₂×C₄×C₄₃	—	4	2	no	—
38	C₂×C₄×C₄₃	—	4	4	no	—
39	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
40	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
41	C₄₃⋊C₈	—	4	4	no	—
42	C₂²×C₄₃	—	2	2	no	—
43	C₂²×C₄₃	—	2	2	no	—
44	C₂²×C₄₃	—	2	2	no	—
45	C₂²×C₄₃	—	2	2	no	—
46	C₂²×C₄₃	—	2	1	no	—
47	C₂²×C₄₃	—	2	1	no	—
48	C₂²×C₄₃	—	2	1	no	—
49	C₂²×C₄₃	—	2	1	no	—
50	C₂²×C₄₃	#95	1	1	yes	characteristic
51	C₂²×C₄₃	C₄×C₈	1	1	yes	characteristic
52	C₂²×C₄₃	#97	1	1	yes	characteristic
53	C₂²×C₄₃	C₂²⋊C₈	1	2	yes	—
54	C₂²×C₄₃	#99	1	2	yes	—
55	C₂²×C₄₃	#100	1	1	yes	characteristic
56	C₂²×C₄₃	#101	1	1	yes	characteristic
57	C₂²×C₄₃	C₄⋊C₈	1	2	yes	—
58	C₄×C₄₃	—	2	2	no	—
59	C₄×C₄₃	—	2	2	no	—
60	C₄×C₄₃	—	4	4	no	—
61	#1280	—	43	1	no	maximal, Sylow
62	C₂×C₄₃	—	2	1	no	—
63	C₂×C₄₃	—	2	1	no	—
64	C₂×C₄₃	—	2	2	no	—
65	C₂×C₄₃	#323	1	2	yes	—
66	C₂×C₄₃	#324	1	2	yes	—
67	C₂×C₄₃	#336	1	1	yes	characteristic
68	C₂×C₄₃	#342	1	1	yes	characteristic
69	C₂×C₄₃	#343	1	1	yes	characteristic
70	C₂×C₂²⋊C₈	—	43	2	no	—
71	C₂×#95	D₄₃	1	1	yes	characteristic
72	C₄₃	#1280	1	1	yes	characteristic, complemented, Sylow
73	C₂³×C₄	Dic₄₃	1	2	yes	—
74	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
75	C₂²×C₈	—	86	2	no	—
76	C₂²⋊C₈	—	43	4	no	—
77	C₂²⋊C₈	—	86	2	no	—
78	#95	—	2	2	no	—
79	C₂⁴	C₂×Dic₄₃	1	1	yes	characteristic
80	C₂²×C₄	—	2	2	no	—
81	C₂²×C₄	—	2	2	no	—
82	C₂²×C₄	—	4	2	no	—
83	C₂²×C₄	—	4	2	no	—
84	C₂²×C₄	—	4	2	no	—
85	C₂²×C₄	C₄₃⋊C₈	1	4	yes	complemented
86	C₂²×C₄	Dic₈₆	1	1	yes	characteristic
87	C₂²×C₄	C₄×D₄₃	1	2	yes	—
88	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
89	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
90	C₂×C₈	—	86	4	no	—
91	C₂×C₈	—	172	4	no	—
92	C₂³	—	2	2	no	—
93	C₂³	—	2	1	no	—
94	C₂³	—	2	1	no	—
95	C₂³	C₂×C₄₃⋊C₈	1	2	yes	—
96	C₂³	#10621877	1	2	yes	—
97	C₂³	C₄×Dic₄₃	1	1	yes	characteristic
98	C₂³	C₄⋊Dic₄₃	1	1	yes	characteristic
99	C₂³	C₂²⋊Dic₄₃	1	1	yes	characteristic
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	—	4	1	no	—
103	C₂×C₄	—	4	2	no	—
104	C₂×C₄	—	4	1	no	—
105	C₂×C₄	—	4	4	no	—
106	C₂×C₄	—	4	2	no	—
107	C₂×C₄	—	4	2	no	—
108	C₂×C₄	—	4	4	no	—
109	C₂×C₄	Dic₄₃⋊C₄	1	2	yes	—
110	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
111	C₈	—	172	4	no	—
112	C₂²	—	2	2	no	—
113	C₂²	—	2	2	no	—
114	C₂²	—	2	2	no	—
115	C₂²	—	2	2	no	—
116	C₂²	—	2	1	no	—
117	C₂²	—	2	1	no	—
118	C₂²	—	2	1	no	—
119	C₂²	—	2	1	no	—
120	C₂²	C₄₃⋊#95	1	1	yes	characteristic
121	C₂²	C₄×C₄₃⋊C₈	1	1	yes	characteristic
122	C₂²	#13063236	1	1	yes	characteristic
123	C₂²	C₂²⋊(C₄₃⋊C₈)	1	2	yes	—
124	C₂²	#13063240	1	2	yes	—
125	C₂²	#13063242	1	1	yes	characteristic
126	C₂²	#13063244	1	1	yes	characteristic
127	C₂²	C₄⋊(C₄₃⋊C₈)	1	2	yes	—
128	C₄	—	2	2	no	—
129	C₄	—	2	2	no	—
130	C₄	—	4	4	no	—
131	C₂	—	2	1	no	—
132	C₂	—	2	1	no	—
133	C₂	—	2	2	no	—
134	C₂	#14582623	1	2	yes	—
135	C₂	#14582625	1	2	yes	—
136	C₂	#14582654	1	1	yes	characteristic
137	C₂	#14582666	1	1	yes	characteristic
138	C₂	#14582668	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₂²⋊(C₄₃⋊C₈)

C₂

yes

maximal

C₂×#95×C₄₃

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

—

C₂²⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

C₄

yes

complemented

C₂³×C₄×C₄₃

C₄

yes

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

#95×C₄₃

—

C₂⁴×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₈

yes

complemented

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

Q₈

yes

characteristic

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₄²

yes

characteristic

C₂³×C₄₃

C₂²⋊C₄

yes

characteristic

C₂³×C₄₃

C₄⋊C₄

yes

characteristic

C₂³×C₄₃

C₂×C₈

yes

—

C₂³×C₄₃

M₁₆

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#95

yes

characteristic

C₂²×C₄₃

C₄×C₈

yes

characteristic

C₂²×C₄₃

#97

yes

characteristic

C₂²×C₄₃

C₂²⋊C₈

yes

—

C₂²×C₄₃

#99

yes

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

C₄⋊C₈

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

#1280

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#323

yes

—

C₂×C₄₃

#324

yes

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₂²⋊C₈

—

C₂×#95

D₄₃

yes

characteristic

C₄₃

#1280

yes

characteristic, complemented, Sylow

C₂³×C₄

Dic₄₃

yes

—

C₂³×C₄

C₂×D₄₃

yes

characteristic

C₂²×C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#95

—

C₂⁴

C₂×Dic₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄₃⋊C₈

yes

complemented

C₂²×C₄

Dic₈₆

yes

characteristic

C₂²×C₄

C₄×D₄₃

yes

—

C₂²×C₄

D₁₇₂

yes

characteristic

C₂²×C₄

C₂²⋊D₄₃

yes

—

C₂×C₈

—

C₂×C₈

—

172

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂×C₄₃⋊C₈

yes

—

C₂³

#10621877

yes

—

C₂³

C₄×Dic₄₃

yes

characteristic

C₂³

C₄⋊Dic₄₃

yes

characteristic

C₂³

C₂²⋊Dic₄₃

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

Dic₄₃⋊C₄

yes

—

110

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

111

C₈

—

172

—

112

C₂²

—

113

C₂²

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

C₄₃⋊#95

yes

characteristic

121

C₂²

C₄×C₄₃⋊C₈

yes

characteristic

122

C₂²

#13063236

yes

characteristic

123

C₂²

C₂²⋊(C₄₃⋊C₈)

yes

—

124

C₂²

#13063240

yes

—

125

C₂²

#13063242

yes

characteristic

126

C₂²

#13063244

yes

characteristic

127

C₂²

C₄⋊(C₄₃⋊C₈)

yes

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₂

—

132

C₂

—

133

C₂

—

134

C₂

#14582623

yes

—

135

C₂

#14582625

yes

—

136

C₂

#14582654

yes

characteristic

137

C₂

#14582666

yes

characteristic

138

C₂

#14582668

yes

characteristic

	subgroup	G/H
center	C₂³	C₂²⋊Dic₄₃
commutator	C₂²×C₄₃	C₄×C₈
Frattini	C₂³×C₄	C₂×D₄₃
Fitting	C₂×#95×C₄₃	C₂
socle	C₂³×C₄₃	C₂²⋊C₄
hypercenter	C₂×#95	D₄₃
hypocenter	C₄₃	#1280
LCS	G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#95

subgroup

G/H

center

C₂³

C₂²⋊Dic₄₃

commutator

C₂²×C₄₃

C₄×C₈

Frattini

C₂³×C₄

C₂×D₄₃

Fitting

C₂×#95×C₄₃

C₂

socle

C₂³×C₄₃

C₂²⋊C₄

hypercenter

C₂×#95

D₄₃

hypocenter

C₄₃

#1280

LCS

G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#95

N	H ≅ G/N	type
5. C₂²⋊(C₄₃⋊C₈)	C₄	semidirect
15. C₂²×C₄×C₄₃	C₈	semidirect
72. C₄₃	#1280	semidirect
85. C₂²×C₄	C₄₃⋊C₈	semidirect

H ≅ G/N

type

5. C₂²⋊(C₄₃⋊C₈)

C₄

semidirect

15. C₂²×C₄×C₄₃

C₈

semidirect

72. C₄₃

#1280

semidirect

85. C₂²×C₄

C₄₃⋊C₈

semidirect

Subgroups — #19132438

Conjugacy classes of subgroups

Complements