Finite Group Databasebeta

← #19133100

Subgroups — #19133100

Order 5504.

334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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#14583410C211yesmaximal, characteristic
2C2×C43⋊#95C211yesmaximal, characteristic, complemented
3#14582637C212yesmaximal, complemented
4#14582634C212yesmaximal, complemented
5C43×#407C211yesmaximal, characteristic, complemented
6C2×#10621898C411yescharacteristic, complemented
7C23×Dic43—21no—
8#13063308—21no—
9#13063304C411yescharacteristic, complemented
10#13063304C2211yescharacteristic
11#13063299C411yescharacteristic, complemented
12#13063299C2211yescharacteristic
13#13063294—21no—
14C4×C22⋊D43—21no—
15C4×C22⋊D43—21no—
16#13063284C411yescharacteristic, complemented
17C43⋊#95—21no—
18C43⋊#95C2212yes—
19C23×C4×C43C2211yescharacteristic
20C2×M16×C43—21no—
21C22⋊C8×C43—21no—
22C22⋊C8×C43C2212yes—
23C24×C43D411yescharacteristic
24C22×C4×C43—42no—
25C22×C4×C43C2×C411yescharacteristic
26C22×C4×C43C2×C411yescharacteristic
27C22×C4×C43D411yescharacteristic
28C22×C4×C43D411yescharacteristic
29C22×C4×C43D411yescharacteristic
30C22×C4×C43C2311yescharacteristic
31C2×C22⋊D43—21no—
32C2×C22⋊D43—21no—
33C2×C22⋊D43—21no—
34C22×Dic43—24no—
35C22×Dic43—22no—
36C22×Dic43—42no—
37C22×Dic43—42no—
38#10621898—42no—
39C2×D172C2×C411yescharacteristic, complemented
40C2×C4×D43—21no—
41C2×Dic86C2×C411yescharacteristic, complemented
42M16×C43—42no—
43C2×C8×C43—22no—
44C22⋊Dic43—21no—
45C22⋊Dic43—21no—
46C22⋊Dic43—21no—
47(C2×D43)⋊C4—21no—
48(C2×D43)⋊C4—21no—
49C4⋊Dic43C2×C411yescharacteristic, complemented
50C4⋊Dic43C2×C411yescharacteristic, complemented
51Dic43⋊C4—21no—
52Dic43⋊C4—21no—
53C4×Dic43—21no—
54C23×C43—22no—
55C23×C43—22no—
56C23×C43—21no—
57C23×C43—21no—
58C23×C43C22⋊C411yescharacteristic
59C23×C43C22⋊C411yescharacteristic
60C23×C43C2×D411yescharacteristic
61C22×D43—21no—
62C2×C4×C43—22no—
63C2×C4×C43—22no—
64C2×C4×C43—41no—
65C2×C4×C43—41no—
66C2×C4×C43—41no—
67C2×C4×C43—41no—
68C2×C4×C43C22⋊C411yescharacteristic
69C2×C4×C43C22⋊C411yescharacteristic
70C2×C4×C43C22×C411yescharacteristic
71C2×C4×C43C2×D411yescharacteristic
72C22⋊D43—42no—
73C22⋊D43—42no—
74C22⋊D43—41no—
75C22⋊D43—41no—
76C2×Dic43—24no—
77C2×Dic43—21no—
78C2×Dic43—21no—
79C2×Dic43—21no—
80C2×Dic43—48no—
81C2×Dic43—42no—
82C2×Dic43—42no—
83D172—41no—
84C4×D43—42no—
85Dic86—41no—
86C8×C43—42no—
87C22×C43—24no—
88C22×C43—24no—
89C22×C43—21no—
90C22×C43—21no—
91C22×C43—21no—
92C22×C43—21no—
93C22×C43—21no—
94C22×C43—21no—
95C22×C43#9912yes—
96C22×C43#10412yes—
97C22×C43C2×C22⋊C411yescharacteristic
98C22×C43AGL(1,ℤ/8)11yescharacteristic
99C22×C43#13711yescharacteristic
100C2×D43—41no—
101C2×D43—41no—
102C2×D43—41no—
103C4×C43—21no—
104C4×C43—21no—
105C4×C43—21no—
106C4×C43—21no—
107Dic43—44no—
108Dic43—41no—
109Dic43—41no—
110Dic43—41no—
111#1504—431nomaximal, Sylow
112C2×C43—21no—
113C2×C43—22no—
114C2×C43—22no—
115C2×C43—21no—
116C2×C43C2×#9911yescharacteristic
117C2×C43#41711yescharacteristic
118C2×C43C2×#10411yescharacteristic
119D43—81no—
120#525—431no—
121#407D4311yescharacteristic, complemented
122C2×#95—431no—
123#328—432no—
124#327—432no—
125C43#150411yescharacteristic, complemented, Sylow
126C2×#41—431no—
127C23×C4—861no—
128C23×C4C2×D4311yescharacteristic
129C2×M16—21no—
130#123—861no—
131C22⋊Q8—431no—
132C22⋊Q8—431no—
133#121—431no—
134#121—431no—
135#120—861no—
136C4×D4—861no—
137C4×D4—861no—
138#117—431no—
139C22⋊C8—21no—
140C22⋊C8C2×D4312yes—
141#95—432no—
142#95—861no—
143C24D17211yescharacteristic
144#41—1722no—
145C2×Q8—431no—
146C2×D4—431no—
147C2×D4—861no—
148C2×D4—861no—
149C2×D4—861no—
150C22×C4—42no—
151C22×C4—864no—
152C22×C4—862no—
153C22×C4—861no—
154C22×C4—1722no—
155C22×C4—1722no—
156C22×C4C4×D4311yescharacteristic
157C22×C4C4×D4311yescharacteristic
158C22×C4D17211yescharacteristic
159C22×C4C22⋊D4311yescharacteristic
160C22×C4C22⋊D4311yescharacteristic
161C22×C4C22×D4311yescharacteristic
162M16—42no—
163C2×C8—22no—
164C4⋊C4—431no—
165C4⋊C4—431no—
166C4⋊C4—861no—
167C4⋊C4—861no—
168C22⋊C4—861no—
169C22⋊C4—861no—
170C22⋊C4—861no—
171C22⋊C4—861no—
172C22⋊C4—861no—
173C42—861no—
174C23—22no—
175C23—22no—
176C23—21no—
177C23—21no—
178C23—861no—
179C23(C2×D43)⋊C411yescharacteristic
180C23(C2×D43)⋊C411yescharacteristic
181C23C2×D17211yescharacteristic
182Q8—1721no—
183D4—1721no—
184D4—1722no—
185D4—1722no—
186D4—1721no—
187D4—1721no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—864no—
195C2×C4—861no—
196C2×C4—861no—
197C2×C4—861no—
198C2×C4—1722no—
199C2×C4—1728no—
200C2×C4—1722no—
201C2×C4—1722no—
202C2×C4(C2×D43)⋊C411yescharacteristic
203C2×C4(C2×D43)⋊C411yescharacteristic
204C2×C4C2×C4×D4311yescharacteristic
205C2×C4C2×C22⋊D4311yescharacteristic
206C8—42no—
207C22—24no—
208C22—24no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—1721no—
216C22—1721no—
217C22—1721no—
218C22#1306323912yes—
219C22#1306325112yes—
220C22C2×(C2×D43)⋊C411yescharacteristic
221C22#1306335311yescharacteristic
222C22#1306335811yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—21no—
227C4—1724no—
228C4—1721no—
229C4—1721no—
230C4—1721no—
231C2—21no—
232C2—22no—
233C2—22no—
234C2—21no—
235C2—3441no—
236C2C2×#1306323911yescharacteristic
237C2#1458290111yescharacteristic
238C2C2×#1306325111yescharacteristic
subgroupG/H
centerC22C2×(C2×D43)⋊C4
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#407C2
socleC22×C43C2×C22⋊C4
hypercenter#407D43
hypocenterC43#1504
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×C43⋊#95C2semidirect
3. #14582637C2semidirect
4. #14582634C2semidirect
5. C43×#407C2semidirect
6. C2×#10621898C4semidirect
9. #13063304C4semidirect
11. #13063299C4semidirect
16. #13063284C4semidirect
39. C2×D172C2×C4semidirect
41. C2×Dic86C2×C4semidirect
49. C4⋊Dic43C2×C4semidirect
50. C4⋊Dic43C2×C4semidirect
121. #407D43semidirect
125. C43#1504semidirect