Finite Group Databasebeta

← #19133096

Subgroups — #19133096

Order 5504.

334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 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#14583409C211yesmaximal, characteristic
2#14582861C211yesmaximal, characteristic, complemented
3#95×D43C211yesmaximal, characteristic, complemented
4#14582637C211yesmaximal, characteristic, complemented
5#14582635C211yesmaximal, characteristic, complemented
6#14582633C211yesmaximal, characteristic, complemented
7C43×#327C211yesmaximal, characteristic, complemented
8C2×#10621900C411yescharacteristic, complemented
9C22×C4×D43—21no—
10C22×C4×D43C2211yescharacteristic
11C2×#10621872—21no—
12#13063307—21no—
13#13063305C411yescharacteristic, complemented
14#13063304C2211yescharacteristic
15#13063296C411yescharacteristic, complemented
16#13063293—21no—
17D4×Dic43—21no—
18(C22⋊D43)⋊C4—21no—
19#13063283C411yescharacteristic, complemented
20C22⋊(C43⋊C8)C2211yescharacteristic
21(C2×D43)⋊C8—21no—
22C43⋊#95—21no—
23C43⋊#95C2211yescharacteristic
24#121×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C23×D43D411yescharacteristic
28C2×D4×C43—21no—
29C2×D4×C43C2×C411yescharacteristic, complemented
30C22×C4×C43—21no—
31C22×C4×C43C2311yescharacteristic
32C2×C22⋊D43—21no—
33C2×C22⋊D43—21no—
34C22×Dic43—21no—
35C22×Dic43—21no—
36C22×Dic43D411yescharacteristic
37#10621900—42no—
38C2×C4×D43—24no—
39C2×C4×D43—42no—
40C2×C4×D43—42no—
41C2×C4×D43—42no—
42C2×C4×D43C2×C411yescharacteristic
43C2×C4×D43C2×C411yescharacteristic
44C2×C4×D43D411yescharacteristic
45C2×C4×D43D411yescharacteristic
46C2×Dic86C2×C411yescharacteristic, complemented
47C2×C8×C43—21no—
48C4⋊C4×C43C2×C411yescharacteristic, complemented
49C22⋊C4×C43—21no—
50C22⋊Dic43—21no—
51C22⋊Dic43—21no—
52(C2×D43)⋊C4—21no—
53(C2×D43)⋊C4—21no—
54C4⋊Dic43—21no—
55C4⋊Dic43C2×C411yescharacteristic, complemented
56Dic43⋊C4—21no—
57C4×Dic43—21no—
58C2×C43⋊C8—21no—
59#10621872—42no—
60C23×C43—21no—
61C23×C43C2×D411yescharacteristic
62C22×D43—21no—
63C22×D43—21no—
64C22×D43—22no—
65C22×D43—22no—
66C22×D43C22⋊C411yescharacteristic
67C22×D43C22⋊C411yescharacteristic
68D4×C43—41no—
69D4×C43—41no—
70D4×C43—41no—
71C2×C4×C43—22no—
72C2×C4×C43—21no—
73C2×C4×C43—41no—
74C2×C4×C43—41no—
75C2×C4×C43—41no—
76C2×C4×C43C22×C411yescharacteristic
77C2×C4×C43C2×D411yescharacteristic
78C22⋊D43—42no—
79C22⋊D43—42no—
80C2×Dic43—22no—
81C2×Dic43—21no—
82C2×Dic43—21no—
83C2×Dic43—41no—
84C2×Dic43—42no—
85C2×Dic43—41no—
86C2×Dic43—41no—
87C2×Dic43C22⋊C411yescharacteristic
88C2×Dic43C22⋊C411yescharacteristic
89C4×D43—22no—
90C4×D43—22no—
91C4×D43—41no—
92C4×D43—41no—
93C4×D43—48no—
94Dic86—41no—
95C8×C43—41no—
96C43⋊C8—41no—
97C22×C43—21no—
98C22×C43—21no—
99C22×C43—41no—
100C22×C43—41no—
101C22×C43—41no—
102C22×C43C2×C22⋊C411yescharacteristic
103C22×C43AGL(1,ℤ/8)11yescharacteristic
104C22×C43#13711yescharacteristic
105C2×D43—24no—
106C2×D43—24no—
107C2×D43—21no—
108C2×D43—21no—
109C2×D43—21no—
110C2×D43—21no—
111C2×D43#9912yes—
112C2×D43#10412yes—
113C4×C43—21no—
114C4×C43—21no—
115C4×C43—42no—
116C4×C43—41no—
117Dic43—21no—
118Dic43—21no—
119Dic43—42no—
120Dic43—41no—
121Dic43—41no—
122#1504—431nomaximal, Sylow
123C2×C43—21no—
124C2×C43—21no—
125C2×C43—81no—
126C2×C43C2×#9911yescharacteristic
127C2×C43#41711yescharacteristic
128C2×C43C2×#10411yescharacteristic
129D43—22no—
130D43—22no—
131#525—431no—
132#407—431no—
133C2×#95—431no—
134#328—431no—
135#328—431no—
136#327—431no—
137#327D4311yescharacteristic, complemented
138C43#150411yescharacteristic, complemented, Sylow
139C2×#41—431no—
140C23×C4—431no—
141C23×C4—861no—
142C2×M16—861no—
143#123—861no—
144C22⋊Q8—431no—
145C22⋊Q8—431no—
146#121—431no—
147#121C2×D4311yescharacteristic
148#120—861no—
149C4×D4—861no—
150C4×D4—861no—
151#117—431no—
152C22⋊C8—431no—
153C22⋊C8—861no—
154C22⋊C8C2×D4311yescharacteristic
155#95—431no—
156#95—861no—
157#95C2×D4311yescharacteristic
158C24—431no—
159#41—1722no—
160C2×Q8—431no—
161C2×D4—21no—
162C2×D4—861no—
163C2×D4—861no—
164C2×D4C4×D4311yescharacteristic, complemented
165C22×C4—21no—
166C22×C4—431no—
167C22×C4—431no—
168C22×C4—431no—
169C22×C4—431no—
170C22×C4—431no—
171C22×C4—864no—
172C22×C4—861no—
173C22×C4—861no—
174C22×C4—1722no—
175C22×C4—1722no—
176C22×C4—1722no—
177C22×C4C22×D4311yescharacteristic
178M16—1722no—
179C2×C8—21no—
180C2×C8—861no—
181C4⋊C4—431no—
182C4⋊C4—861no—
183C4⋊C4—861no—
184C4⋊C4C4×D4311yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—861no—
187C22⋊C4—861no—
188C22⋊C4—861no—
189C22⋊C4—861no—
190C42—861no—
191C23—21no—
192C23—431no—
193C23—431no—
194C23—862no—
195C23—862no—
196C23—861no—
197C23—861no—
198C23D4×D4311yescharacteristic
199Q8—1721no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—1722no—
204D4—1722no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—431no—
211C2×C4—431no—
212C2×C4—862no—
213C2×C4—862no—
214C2×C4—862no—
215C2×C4—861no—
216C2×C4—861no—
217C2×C4—1721no—
218C2×C4—1721no—
219C2×C4—1728no—
220C2×C4—1721no—
221C2×C4—1722no—
222C2×C4—1721no—
223C2×C4—1721no—
224C2×C4C2×C4×D4311yescharacteristic
225C2×C4D4×D4311yescharacteristic
226C8—41no—
227C8—1721no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—432no—
234C22—432no—
235C22—864no—
236C22—864no—
237C22—861no—
238C22—861no—
239C22—861no—
240C22—861no—
241C22C22⋊C4×D4311yescharacteristic
242C22#1306334911yescharacteristic
243C22#1306335411yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—41no—
248C4—861no—
249C4—861no—
250C4—1722no—
251C4—1721no—
252C4—1721no—
253C2—21no—
254C2—21no—
255C2—81no—
256C2—862no—
257C2—862no—
258C2#99×D4311yescharacteristic
259C2#1458289711yescharacteristic
260C2#104×D4311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#327C2
socleC22×C43C2×C22⋊C4
hypercenter#327D43
hypocenterC43#1504
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14582861C2semidirect
3. #95×D43C2semidirect
4. #14582637C2semidirect
5. #14582635C2semidirect
6. #14582633C2semidirect
7. C43×#327C2semidirect
8. C2×#10621900C4semidirect
13. #13063305C4semidirect
15. #13063296C4semidirect
19. #13063283C4semidirect
29. C2×D4×C43C2×C4semidirect
46. C2×Dic86C2×C4semidirect
48. C4⋊C4×C43C2×C4semidirect
55. C4⋊Dic43C2×C4semidirect
137. #327D43semidirect
138. C43#1504semidirect
164. C2×D4C4×D43semidirect
184. C4⋊C4C4×D43semidirect