Finite Group Databasebeta

← #19133523

Subgroups — #19133523

Order 5504.

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

normal subgroups only

This group has 272 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#14583498C211yesmaximal, characteristic, complemented
2#14583033C211yesmaximal, characteristic
3#14582813C211yesmaximal, characteristic, complemented
4#14582636C211yesmaximal, characteristic, complemented
5#14582634C211yesmaximal, characteristic, complemented
6#14582624C211yesmaximal, characteristic, complemented
7C43×#450C211yesmaximal, characteristic, complemented
8C2×#10621882—21no—
9#13063320—21no—
10#13063316—21no—
11#13063310—21no—
12#13063309—21no—
13#13063301—21no—
14#13063299C2211yescharacteristic
15(C22⋊D43)⋊C4—21no—
16C2×Dic43⋊C4C2211yescharacteristic
17C2×C22⋊Dic43—21no—
18C2×C22⋊Dic43—21no—
19#13063246—21no—
20C22⋊(C43⋊C8)C2211yescharacteristic
21C43⋊#95C2211yescharacteristic
22C22×D4×C43C2211yescharacteristic
23C2×SD16×C43—21no—
24C22⋊Q8×C43C2211yescharacteristic
25#102×C43—21no—
26C22⋊C8×C43C2211yescharacteristic
27C24×C43—21no—
28C2×Q8×C43D411yescharacteristic
29C2×D4×C43—21no—
30C2×D4×C43—21no—
31C2×D4×C43—42no—
32C22×C4×C43C2311yescharacteristic
33C2×C22⋊D43—21no—
34C22×Dic43—21no—
35C22×Dic43D411yescharacteristic
36C22×Dic43D411yescharacteristic
37C2×D172D411yescharacteristic
38C2×C4×D43—21no—
39SD16×C43—42no—
40C2×C8×C43—21no—
41C4⋊C4×C43—21no—
42C4⋊C4×C43D411yescharacteristic
43C22⋊C4×C43—21no—
44C22⋊Dic43—42no—
45C22⋊Dic43—42no—
46#10621882—42no—
47(C2×D43)⋊C4—21no—
48(C2×D43)⋊C4—21no—
49(C2×D43)⋊C4—21no—
50(C2×D43)⋊C4—21no—
51C4⋊Dic43—21no—
52C4⋊Dic43—21no—
53C4⋊Dic43D411yescharacteristic
54Dic43⋊C4—21no—
55Dic43⋊C4—21no—
56Dic43⋊C4—21no—
57C4×Dic43—21no—
58C2×C43⋊C8—21no—
59C23×C43—22no—
60C23×C43—41no—
61C23×C43—41no—
62C23×C43—41no—
63C23×C43—41no—
64C23×C43—41no—
65C23×C43—41no—
66C23×C43C2×D411yescharacteristic
67C22×D43—21no—
68Q8×C43—41no—
69D4×C43—22no—
70D4×C43—22no—
71D4×C43—41no—
72D4×C43—41no—
73C2×C4×C43—21no—
74C2×C4×C43—21no—
75C2×C4×C43—41no—
76C2×C4×C43C2×D411yescharacteristic
77C2×C4×C43C2×D411yescharacteristic
78C22⋊D43—41no—
79C22⋊D43—41no—
80C2×Dic43—21no—
81C2×Dic43—21no—
82C2×Dic43—21no—
83C2×Dic43—21no—
84C2×Dic43—21no—
85C2×Dic43—41no—
86C2×Dic43—41no—
87C2×Dic43—41no—
88C2×Dic43—41no—
89D172—41no—
90C4×D43—81no—
91C8×C43—41no—
92C43⋊C8—41no—
93C22×C43—21no—
94C22×C43—21no—
95C22×C43—42no—
96C22×C43—42no—
97C22×C43—42no—
98C22×C43—81no—
99C22×C43—81no—
100C22×C43—81no—
101C22×C43—81no—
102C22×C43#12011yescharacteristic
103C22×C43#13511yescharacteristic
104C22×C43AGL(1,ℤ/8)11yescharacteristic
105C2×D43—41no—
106C2×D43—41no—
107C2×D43—41no—
108C4×C43—21no—
109C4×C43—21no—
110C4×C43—41no—
111C4×C43—41no—
112Dic43—41no—
113Dic43—41no—
114Dic43—41no—
115Dic43—81no—
116#1597—431nomaximal, Sylow
117C2×C43—21no—
118C2×C43—21no—
119C2×C43—82no—
120C2×C43#44911yescharacteristic
121C2×C43#45411yescharacteristic
122C2×C43B(4,𝔽2)11yescharacteristic
123D43—81no—
124#539—431no—
125#450D4311yescharacteristic, complemented
126#447—431no—
127#394—431no—
128#328—431no—
129#327—431no—
130#324—431no—
131C43#159711yescharacteristic, complemented, Sylow
132C22×D4C2×D4311yescharacteristic
133C2×SD16—21no—
134C2×D8—861no—
135#126—861no—
136#125—861no—
137#123—861no—
138#123—861no—
139C22⋊Q8—861no—
140C22⋊Q8C2×D4311yescharacteristic
141#121—431no—
142C4×D4—861no—
143C2×C4⋊C4—431no—
144C2×C22⋊C4—861no—
145C2×C22⋊C4—861no—
146#102—21no—
147#102—861no—
148C22⋊C8—431no—
149C22⋊C8C2×D4311yescharacteristic
150#95—431no—
151C24—21no—
152C2×Q8C22⋊D4311yescharacteristic
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—42no—
156C2×D4—431no—
157C2×D4—861no—
158C22×C4—431no—
159C22×C4—431no—
160C22×C4—861no—
161C22×C4—861no—
162C22×C4C22×D4311yescharacteristic
163SD16—42no—
164D8—1722no—
165C2×C8—21no—
166C2×C8—861no—
167C4⋊C4—21no—
168C4⋊C4—431no—
169C4⋊C4—861no—
170C4⋊C4—861no—
171C4⋊C4—861no—
172C4⋊C4—861no—
173C4⋊C4—861no—
174C4⋊C4C22⋊D4311yescharacteristic
175C22⋊C4—21no—
176C22⋊C4—861no—
177C22⋊C4—861no—
178C22⋊C4—861no—
179C22⋊C4—861no—
180C22⋊C4—1722no—
181C22⋊C4—1722no—
182C42—861no—
183C23—22no—
184C23—41no—
185C23—41no—
186C23—41no—
187C23—41no—
188C23—41no—
189C23—41no—
190C23—861no—
191C23D4×D4311yescharacteristic
192Q8—41no—
193D4—22no—
194D4—22no—
195D4—41no—
196D4—41no—
197D4—1721no—
198D4—1721no—
199D4—1721no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—861no—
204C2×C4—861no—
205C2×C4—861no—
206C2×C4—861no—
207C2×C4—861no—
208C2×C4—3441no—
209C2×C4—1721no—
210C2×C4—1721no—
211C2×C4—1721no—
212C2×C4—1721no—
213C2×C4D4×D4311yescharacteristic
214C2×C4C2×C22⋊D4311yescharacteristic
215C8—41no—
216C8—1721no—
217C22—21no—
218C22—21no—
219C22—42no—
220C22—42no—
221C22—42no—
222C22—81no—
223C22—81no—
224C22—81no—
225C22—81no—
226C22—1721no—
227C22—1721no—
228C22—1721no—
229C22#1306329311yescharacteristic
230C22#1306334611yescharacteristic
231C22#1306335211yescharacteristic
232C4—21no—
233C4—21no—
234C4—41no—
235C4—41no—
236C4—3441no—
237C4—1721no—
238C4—1721no—
239C4—1721no—
240C2—21no—
241C2—21no—
242C2—82no—
243C2—3441no—
244C2#1458304311yescharacteristic
245C2#1458307011yescharacteristic
246C2#1458308511yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#450C2
socleC22×C43#120
hypercenter#450D43
hypocenterC43#1597
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #14583498C2semidirect
3. #14582813C2semidirect
4. #14582636C2semidirect
5. #14582634C2semidirect
6. #14582624C2semidirect
7. C43×#450C2semidirect
125. #450D43semidirect
131. C43#1597semidirect