Group #24983194 — subgroups

Subgroups — #24983194

Order 11008.

304 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 107 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	#19134448	C₂	1	2	yes	maximal
2	C₄₃×#1831	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
4	C₂×#13063236	C₄	1	4	yes	—
5	#14582654	—	2	2	no	—
6	C₂×C₄⋊C₈×C₄₃	C₄	1	2	yes	—
7	C₄³×C₄₃	C₂²	1	1	yes	characteristic
8	C₄₃×#336	—	2	2	no	—
9	C₂²×C₄₃⋊C₈	—	2	4	no	—
10	C₄⋊(C₄₃⋊C₈)	—	2	8	no	—
11	#13063236	—	4	4	no	—
12	C₂²×C₈×C₄₃	—	2	2	no	—
13	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
14	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
16	C₂×C₄²×C₄₃	D₄	1	2	yes	—
17	C₂×C₄²×C₄₃	Q₈	1	1	yes	characteristic
18	C₄⋊C₈×C₄₃	—	4	2	no	—
19	C₂²×C₄×C₄₃	C₄²	1	1	yes	characteristic
20	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
21	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
23	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₈×C₄₃	—	4	2	no	—
25	C₂×C₈×C₄₃	—	4	4	no	—
26	C₄²×C₄₃	—	2	1	no	—
27	C₄²×C₄₃	—	2	2	no	—
28	C₄²×C₄₃	—	2	2	no	—
29	C₄²×C₄₃	—	2	1	no	—
30	C₄²×C₄₃	—	2	4	no	—
31	C₄²×C₄₃	—	2	2	no	—
32	C₄²×C₄₃	—	4	1	no	—
33	C₂×C₄₃⋊C₈	—	2	8	no	—
34	C₂×C₄₃⋊C₈	—	4	4	no	—
35	C₂×C₄₃⋊C₈	—	4	4	no	—
36	C₂³×C₄₃	#95	1	1	yes	characteristic
37	C₂×C₄×C₄₃	—	2	2	no	—
38	C₂×C₄×C₄₃	—	2	1	no	—
39	C₂×C₄×C₄₃	—	2	2	no	—
40	C₂×C₄×C₄₃	—	2	1	no	—
41	C₂×C₄×C₄₃	—	2	2	no	—
42	C₂×C₄×C₄₃	—	2	2	no	—
43	C₂×C₄×C₄₃	—	2	2	no	—
44	C₂×C₄×C₄₃	—	2	1	no	—
45	C₂×C₄×C₄₃	—	2	2	no	—
46	C₂×C₄×C₄₃	#100	1	2	yes	—
47	C₂×C₄×C₄₃	#100	1	1	yes	characteristic
48	C₂×C₄×C₄₃	#101	1	2	yes	—
49	C₂×C₄×C₄₃	#101	1	1	yes	characteristic
50	C₂×C₄×C₄₃	#104	1	4	yes	—
51	C₂×C₄×C₄₃	#108	1	2	yes	—
52	C₈×C₄₃	—	8	2	no	—
53	C₄₃⋊C₈	—	4	8	no	—
54	#7042	—	43	1	no	maximal, Sylow
55	C₂²×C₄₃	H(3,ℤ/4)	1	1	yes	characteristic
56	C₂²×C₄₃	#339	1	2	yes	—
57	C₂²×C₄₃	#341	1	1	yes	characteristic
58	C₂²×C₄₃	#343	1	2	yes	—
59	C₂²×C₄₃	#343	1	1	yes	characteristic
60	C₄×C₄₃	—	2	2	no	—
61	C₄×C₄₃	—	2	2	no	—
62	C₄×C₄₃	—	2	2	no	—
63	C₄×C₄₃	—	4	2	no	—
64	C₄×C₄₃	—	4	1	no	—
65	C₄×C₄₃	#329	1	2	yes	—
66	C₄×C₄₃	#330	1	2	yes	—
67	#1831	D₄₃	1	1	yes	characteristic
68	#1767	—	43	2	no	—
69	C₂×C₄₃	#1285	1	2	yes	—
70	C₂×C₄₃	#1290	1	1	yes	characteristic
71	C₂×C₄₃	#1295	1	1	yes	characteristic
72	C₂×C₄₃	#1299	1	2	yes	—
73	C₂×C₄₃	#1309	1	1	yes	characteristic
74	C₂×C₄⋊C₈	—	86	2	no	—
75	C₂×C₄⋊C₈	Dic₄₃	1	2	yes	—
76	C₂×#97	—	43	4	no	—
77	C₄³	C₂×D₄₃	1	1	yes	characteristic
78	#336	—	2	2	no	—
79	#336	—	86	2	no	—
80	C₄₃	#7042	1	1	yes	characteristic, complemented, Sylow
81	C₂²×C₈	—	2	2	no	—
82	C₂²×C₈	—	86	4	no	—
83	C₂×C₄²	Dic₈₆	1	1	yes	characteristic
84	C₂×C₄²	C₄×D₄₃	1	2	yes	—
85	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
86	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
87	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
88	C₄⋊C₈	—	4	2	no	—
89	C₄⋊C₈	—	86	8	no	—
90	#97	—	172	4	no	—
91	C₂²×C₄	C₄×Dic₄₃	1	1	yes	characteristic
92	C₂²×C₄	Dic₄₃⋊C₄	1	2	yes	—
93	C₂²×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
94	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
95	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
96	C₂×C₈	—	4	2	no	—
97	C₂×C₈	—	4	4	no	—
98	C₂×C₈	—	86	8	no	—
99	C₂×C₈	—	172	4	no	—
100	C₂×C₈	—	172	4	no	—
101	C₄²	—	2	2	no	—
102	C₄²	—	2	1	no	—
103	C₄²	—	2	2	no	—
104	C₄²	—	2	1	no	—
105	C₄²	—	2	4	no	—
106	C₄²	—	2	2	no	—
107	C₄²	—	4	1	no	—
108	C₂³	C₄₃⋊#95	1	1	yes	characteristic
109	C₂×C₄	—	2	2	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	#13063241	1	2	yes	—
119	C₂×C₄	#13063242	1	1	yes	characteristic
120	C₂×C₄	#13063243	1	2	yes	—
121	C₂×C₄	#13063244	1	1	yes	characteristic
122	C₂×C₄	#13063252	1	4	yes	—
123	C₂×C₄	#13063261	1	2	yes	—
124	C₈	—	8	2	no	—
125	C₈	—	172	8	no	—
126	C₂²	#14582656	1	1	yes	characteristic
127	C₂²	#14582658	1	2	yes	—
128	C₂²	#14582664	1	1	yes	characteristic
129	C₂²	#14582667	1	2	yes	—
130	C₂²	#14582668	1	1	yes	characteristic
131	C₄	—	2	2	no	—
132	C₄	—	2	2	no	—
133	C₄	—	2	2	no	—
134	C₄	—	4	2	no	—
135	C₄	—	4	1	no	—
136	C₄	#14582639	1	2	yes	—
137	C₄	#14582641	1	2	yes	—
138	C₂	#19132452	1	2	yes	—
139	C₂	#19132465	1	1	yes	characteristic
140	C₂	#19132476	1	1	yes	characteristic
141	C₂	#19132486	1	2	yes	—
142	C₂	C₄₃⋊#1309	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19134448

C₂

yes

maximal

C₄₃×#1831

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₄₃⋊C₈)

—

C₂×#13063236

C₄

yes

—

#14582654

—

C₂×C₄⋊C₈×C₄₃

C₄

yes

—

C₄³×C₄₃

C₂²

yes

characteristic

C₄₃×#336

—

C₂²×C₄₃⋊C₈

—

C₄⋊(C₄₃⋊C₈)

—

#13063236

—

C₂²×C₈×C₄₃

—

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

Q₈

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²×C₄×C₄₃

C₄²

yes

characteristic

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

C₄⋊C₄

yes

—

C₂²×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#95

yes

characteristic

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

#100

yes

—

C₂×C₄×C₄₃

#100

yes

characteristic

C₂×C₄×C₄₃

#101

yes

—

C₂×C₄×C₄₃

#101

yes

characteristic

C₂×C₄×C₄₃

#104

yes

—

C₂×C₄×C₄₃

#108

yes

—

C₈×C₄₃

—

C₄₃⋊C₈

—

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂²×C₄₃

#341

yes

characteristic

C₂²×C₄₃

#343

yes

—

C₂²×C₄₃

#343

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#329

yes

—

C₄×C₄₃

#330

yes

—

#1831

D₄₃

yes

characteristic

#1767

—

C₂×C₄₃

#1285

yes

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#1309

yes

characteristic

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

Dic₄₃

yes

—

C₂×#97

—

C₄³

C₂×D₄₃

yes

characteristic

#336

—

#336

—

C₄₃

#7042

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

Dic₈₆

yes

characteristic

C₂×C₄²

C₄×D₄₃

yes

—

C₂×C₄²

D₁₇₂

yes

characteristic

C₂×C₄²

C₂×Dic₄₃

yes

characteristic

C₂×C₄²

C₂²⋊D₄₃

yes

—

C₄⋊C₈

—

C₄⋊C₈

—

#97

—

172

—

C₂²×C₄

C₄×Dic₄₃

yes

characteristic

C₂²×C₄

Dic₄₃⋊C₄

yes

—

C₂²×C₄

C₄⋊Dic₄₃

yes

characteristic

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

C₂²×C₄

C₂²⋊Dic₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

172

—

100

C₂×C₈

—

172

—

101

C₄²

—

102

C₄²

—

103

C₄²

—

104

C₄²

—

105

C₄²

—

106

C₄²

—

107

C₄²

—

108

C₂³

C₄₃⋊#95

yes

characteristic

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

#13063241

yes

—

119

C₂×C₄

#13063242

yes

characteristic

120

C₂×C₄

#13063243

yes

—

121

C₂×C₄

#13063244

yes

characteristic

122

C₂×C₄

#13063252

yes

—

123

C₂×C₄

#13063261

yes

—

124

C₈

—

125

C₈

—

172

—

126

C₂²

#14582656

yes

characteristic

127

C₂²

#14582658

yes

—

128

C₂²

#14582664

yes

characteristic

129

C₂²

#14582667

yes

—

130

C₂²

#14582668

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

#14582639

yes

—

137

C₄

#14582641

yes

—

138

C₂

#19132452

yes

—

139

C₂

#19132465

yes

characteristic

140

C₂

#19132476

yes

characteristic

141

C₂

#19132486

yes

—

142

C₂

C₄₃⋊#1309

yes

characteristic

	subgroup	G/H
center	C₂³	C₄₃⋊#95
commutator	C₂²×C₄×C₄₃	C₄²
Frattini	C₄³	C₂×D₄₃
Fitting	C₄₃×#1831	C₂
socle, prime radical	C₂³×C₄₃	#95
cosocle	C₄³×C₄₃	C₂²
hypercenter	#1831	D₄₃
hypocenter	C₄₃	#7042
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

subgroup

G/H

center

C₂³

C₄₃⋊#95

commutator

C₂²×C₄×C₄₃

C₄²

Frattini

C₄³

C₂×D₄₃

Fitting

C₄₃×#1831

C₂

socle, prime radical

C₂³×C₄₃

#95

cosocle

C₄³×C₄₃

C₂²

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

N	H ≅ G/N	type
80. C₄₃	#7042	semidirect

H ≅ G/N

type

80. C₄₃

#7042

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#19134448	2
C₄₃×#1831	2
#7042	43

subgroup

index

#19134448

C₄₃×#1831

#7042

Subgroups — #24983194

Conjugacy classes of subgroups

Complements

Maximal subgroups