Finite Group Databasebeta

← #19133607

Subgroups — #19133607

Order 5504.

232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583487C211yesmaximal, characteristic
2#14583229C211yesmaximal, characteristic, complemented
3#14583212C211yesmaximal, characteristic, complemented
4#14582635C211yesmaximal, characteristic, complemented
5#14582632C211yesmaximal, characteristic, complemented
6#14582623C211yesmaximal, characteristic, complemented
7C43×#397C211yesmaximal, characteristic, complemented
8#13063318—21no—
9#13063311—21no—
10#13063307—21no—
11#13063304C2211yescharacteristic
12#13063299C2211yescharacteristic
13#13063298—21no—
14#13063294—21no—
15C4×C22⋊D43—21no—
16#13063258—21no—
17#13063256—21no—
18#13063248—21no—
19#13063245—21no—
20C22⋊(C43⋊C8)C2211yescharacteristic
21C22⋊(C43⋊C8)C2211yescharacteristic
22C2×C4⋊C4×C43C2211yescharacteristic
23C2×C22⋊C4×C43—21no—
24C2×C22⋊C4×C43C2211yescharacteristic
25#95×C43—21no—
26#95×C43C2211yescharacteristic
27C24×C43D411yescharacteristic
28C22×C4×C43—21no—
29C22×C4×C43—21no—
30C22×C4×C43D411yescharacteristic
31C22×C4×C43C2311yescharacteristic
32C2×C22⋊D43—21no—
33C2×C22⋊D43—21no—
34C2×C22⋊D43—21no—
35C2×D172D411yescharacteristic
36C2×C4×D43—21no—
37C2×Dic86D411yescharacteristic
38C4⋊C4×C43—21no—
39C4⋊C4×C43—21no—
40C22⋊C4×C43—21no—
41C22⋊C4×C43—21no—
42C22⋊C4×C43—42no—
43C22⋊Dic43—21no—
44C22⋊Dic43—21no—
45C22⋊Dic43—21no—
46(C2×D43)⋊C4—21no—
47(C2×D43)⋊C4—21no—
48C4⋊Dic43D411yescharacteristic
49C4⋊Dic43D411yescharacteristic
50Dic43⋊C4—21no—
51Dic43⋊C4—21no—
52C4×Dic43—21no—
53C2×C43⋊C8—21no—
54C2×C43⋊C8—21no—
55C23×C43—21no—
56C23×C43—21no—
57C23×C43—21no—
58C23×C43—41no—
59C23×C43—41no—
60C23×C43C2×D411yescharacteristic
61C22×D43—21no—
62C2×C4×C43—21no—
63C2×C4×C43—41no—
64C2×C4×C43—41no—
65C2×C4×C43—41no—
66C2×C4×C43—41no—
67C2×C4×C43—41no—
68C2×C4×C43—41no—
69C2×C4×C43—41no—
70C2×C4×C43—41no—
71C2×C4×C43C2×D411yescharacteristic
72C2×C4×C43C2×D411yescharacteristic
73C22⋊D43—41no—
74C22⋊D43—41no—
75C22⋊D43—81no—
76C22⋊D43—81no—
77C2×Dic43—21no—
78C2×Dic43—21no—
79C2×Dic43—21no—
80D172—41no—
81C4×D43—81no—
82Dic86—41no—
83C43⋊C8—41no—
84C43⋊C8—41no—
85C22×C43—21no—
86C22×C43—21no—
87C22×C43—42no—
88C22×C43—41no—
89C22×C43—41no—
90C22×C43—41no—
91C22×C43—81no—
92C22×C43#12011yescharacteristic
93C22×C43#13511yescharacteristic
94C22×C43AGL(1,ℤ/8)11yescharacteristic
95C2×D43—41no—
96C2×D43—41no—
97C2×D43—41no—
98C4×C43—21no—
99C4×C43—21no—
100C4×C43—41no—
101C4×C43—81no—
102C4×C43—81no—
103Dic43—41no—
104Dic43—41no—
105Dic43—41no—
106#1612—431nomaximal, Sylow
107C2×C43—21no—
108C2×C43—21no—
109C2×C43—81no—
110C2×C43#44911yescharacteristic
111C2×C43#45511yescharacteristic
112C2×C43#45811yescharacteristic
113D43—81no—
114#538—431no—
115#483—431no—
116#480—431no—
117#397D4311yescharacteristic, complemented
118#328—431no—
119#327—431no—
120#323—431no—
121C43#161211yescharacteristic, complemented, Sylow
122#126—861no—
123#124—861no—
124#123—861no—
125C22⋊Q8—431no—
126#121—431no—
127#121—861no—
128#120—861no—
129C4×D4—861no—
130C2×C4⋊C4C2×D4311yescharacteristic
131C2×C22⋊C4—21no—
132C2×C22⋊C4C2×D4311yescharacteristic
133#107—861no—
134#106—861no—
135#103—861no—
136#102—861no—
137C22⋊C8—431no—
138C22⋊C8—431no—
139#95—21no—
140#95C2×D4311yescharacteristic
141C24C22⋊D4311yescharacteristic
142C2×Q8—431no—
143C2×D4—431no—
144C2×D4—861no—
145C2×D4—861no—
146C2×D4—861no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—861no—
150C22×C4C22⋊D4311yescharacteristic
151C22×C4C22×D4311yescharacteristic
152C2×C8—861no—
153C2×C8—861no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—431no—
157C4⋊C4—431no—
158C4⋊C4—861no—
159C4⋊C4—861no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—42no—
163C22⋊C4—861no—
164C22⋊C4—861no—
165C22⋊C4—861no—
166C22⋊C4—861no—
167C22⋊C4—861no—
168C42—861no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—861no—
175C23C2×C22⋊D4311yescharacteristic
176Q8—1721no—
177D4—3441no—
178D4—3441no—
179D4—1721no—
180D4—1721no—
181D4—1721no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—861no—
192C2×C4—861no—
193C2×C4—861no—
194C2×C4—3441no—
195C2×C4D4×D4311yescharacteristic
196C2×C4D4×D4311yescharacteristic
197C8—1721no—
198C8—1721no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22—1721no—
207C22—1721no—
208C22—1721no—
209C22#1306329311yescharacteristic
210C22#1306334511yescharacteristic
211C22#1306335111yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—81no—
217C4—1721no—
218C4—1721no—
219C4—1721no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—3441no—
224C2#1458304211yescharacteristic
225C2#1458307611yescharacteristic
226C2#1458308811yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#397C2
socleC22×C43#120
hypercenter#397D43
hypocenterC43#1612
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #397

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14583229C2semidirect
3. #14583212C2semidirect
4. #14582635C2semidirect
5. #14582632C2semidirect
6. #14582623C2semidirect
7. C43×#397C2semidirect
117. #397D43semidirect
121. C43#1612semidirect