Finite Group Databasebeta

← #20241881

Subgroups — #20241881

Order 6016.

284 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 71 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#15689668C211yesmaximal, characteristic
2#15689173C211yesmaximal, characteristic, complemented
3#15688974C211yesmaximal, characteristic, complemented
4#15688858C211yesmaximal, characteristic, complemented
5#15688857C211yesmaximal, characteristic, complemented
6#15688856C211yesmaximal, characteristic, complemented
7C47×#327C211yesmaximal, characteristic, complemented
8C2×#10625352—21no—
9#13094023C411yescharacteristic, complemented
10#13094020C411yescharacteristic, complemented
11#13094010—21no—
12#13093998C2211yescharacteristic
13#13093996—21no—
14D4×Dic47C411yescharacteristic, complemented
15#13093986C411yescharacteristic, complemented
16(C22⋊D47)⋊C4—21no—
17C2×Dic47⋊C4—21no—
18C2×C4×Dic47—21no—
19C2×C4×Dic47C2211yescharacteristic
20Dic47⋊C8—21no—
21C22⋊(C47⋊C8)C2211yescharacteristic
22C8×Dic47—21no—
23C47⋊#95C2211yescharacteristic
24#121×C47C2211yescharacteristic
25C22⋊C8×C47C2211yescharacteristic
26#95×C47C2211yescharacteristic
27C2×D4×C47—21no—
28C2×D4×C47C2×C411yescharacteristic
29C22×C4×C47—21no—
30C22×C4×C47C2311yescharacteristic
31C2×C22⋊D47—21no—
32C2×C22⋊D47—21no—
33C2×C22⋊D47—21no—
34C22×Dic47—21no—
35C22×Dic47—21no—
36C22×Dic47D411yescharacteristic
37C22×Dic47D411yescharacteristic
38#10625352—42no—
39#10625352—42no—
40C2×D188C2×C411yescharacteristic
41C2×C4×D47—21no—
42C2×Dic94—21no—
43C2×C8×C47—21no—
44C4⋊C4×C47C2×C411yescharacteristic
45C22⋊C4×C47—21no—
46C22⋊Dic47—21no—
47(C2×D47)⋊C4—21no—
48(C2×D47)⋊C4—21no—
49C4⋊Dic47C2×C411yescharacteristic
50Dic47⋊C4—24no—
51Dic47⋊C4—21no—
52C4×Dic47—42no—
53C4×Dic47C2×C411yescharacteristic
54C4×Dic47C2×C411yescharacteristic
55C4×Dic47D411yescharacteristic
56C4×Dic47D411yescharacteristic
57C2×C47⋊C8—21no—
58C23×C47—21no—
59C23×C47C2×D411yescharacteristic
60C22×D47—21no—
61D4×C47—41no—
62D4×C47—41no—
63D4×C47—41no—
64C2×C4×C47—22no—
65C2×C4×C47—21no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47C22×C411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C22⋊D47—41no—
72C22⋊D47—41no—
73C22⋊D47—42no—
74C22⋊D47—42no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—21no—
78C2×Dic47—41no—
79C2×Dic47—41no—
80C2×Dic47—42no—
81C2×Dic47C22⋊C411yescharacteristic
82C2×Dic47C22⋊C411yescharacteristic
83C2×Dic47C22⋊C411yescharacteristic
84C2×Dic47C22⋊C411yescharacteristic
85C2×Dic47D812yes—
86C2×Dic47SD1612yes—
87D188—41no—
88C4×D47—42no—
89Dic94—42no—
90C8×C47—41no—
91C47⋊C8—41no—
92C22×C47—21no—
93C22×C47—21no—
94C22×C47—41no—
95C22×C47—41no—
96C22×C47—41no—
97C22×C47C2×C22⋊C411yescharacteristic
98C22×C47C2×D811yescharacteristic
99C22×C47C2×SD1611yescharacteristic
100C2×D47—41no—
101C2×D47—41no—
102C2×D47—41no—
103C4×C47—21no—
104C4×C47—21no—
105C4×C47—42no—
106C4×C47—41no—
107Dic47—21no—
108Dic47—42no—
109Dic47—41no—
110Dic47#10212yes—
111Dic47#10212yes—
112Dic47#10412yes—
113#1502—471nomaximal, Sylow
114C2×C47—21no—
115C2×C47—21no—
116C2×C47—81no—
117C2×C47#41011yescharacteristic
118C2×C47C2×#10211yescharacteristic
119C2×C47C2×#10411yescharacteristic
120D47—81no—
121#532—471no—
122#431—471no—
123C4×C4⋊C4—471no—
124#327—471no—
125#327—471no—
126#327—471no—
127#327D4711yescharacteristic, complemented
128C47#150211yescharacteristic, complemented, Sylow
129C2×#41—941no—
130C4⋊Q8—471no—
131#127—471no—
132#124—941no—
133#121—471no—
134#121—941no—
135#121C2×D4711yescharacteristic
136C4×D4—471no—
137C4×D4—471no—
138C4×D4—941no—
139C2×C4⋊C4—941no—
140C2×C42—471no—
141C2×C42—941no—
142C4⋊C8—941no—
143C22⋊C8—471no—
144C22⋊C8C2×D4711yescharacteristic
145C4×C8—941no—
146#95—471no—
147#95C2×D4711yescharacteristic
148#41—1882no—
149#41—1882no—
150C2×Q8—941no—
151C2×D4—21no—
152C2×D4—471no—
153C2×D4—941no—
154C2×D4—941no—
155C2×D4—941no—
156C2×D4C4×D4711yescharacteristic
157C22×C4—21no—
158C22×C4—471no—
159C22×C4—471no—
160C22×C4—941no—
161C22×C4—941no—
162C22×C4—941no—
163C22×C4C22×D4711yescharacteristic
164C2×C8—21no—
165C2×C8—941no—
166C4⋊C4—471no—
167C4⋊C4—941no—
168C4⋊C4—944no—
169C4⋊C4C4×D4711yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—941no—
172C22⋊C4—941no—
173C22⋊C4—941no—
174C42—471no—
175C42—471no—
176C42—471no—
177C42—471no—
178C42—1882no—
179C23—21no—
180C23—941no—
181C23D4×D4711yescharacteristic
182Q8—1882no—
183D4—41no—
184D4—41no—
185D4—41no—
186D4—1881no—
187D4—1882no—
188D4—1882no—
189D4—1881no—
190D4—1881no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—471no—
197C2×C4—471no—
198C2×C4—471no—
199C2×C4—472no—
200C2×C4—472no—
201C2×C4—471no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—941no—
205C2×C4—1882no—
206C2×C4—1882no—
207C2×C4—1881no—
208C2×C4—1881no—
209C2×C4C2×C4×D4711yescharacteristic
210C2×C4D4×D4711yescharacteristic
211C8—41no—
212C8—1881no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—1881no—
219C22—1881no—
220C22—1881no—
221C22C22⋊C4×D4711yescharacteristic
222C22D8×D4711yescharacteristic
223C22SD16×D4711yescharacteristic
224C4—21no—
225C4—21no—
226C4—42no—
227C4—41no—
228C4—472no—
229C4—472no—
230C4—472no—
231C4—941no—
232C4—1882no—
233C4—1881no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—3761no—
238C2#1568909511yescharacteristic
239C2#102×D4711yescharacteristic
240C2#104×D4711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#327C2
socleC22×C47C2×C22⋊C4
hypercenter#327D47
hypocenterC47#1502
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #15689173C2semidirect
3. #15688974C2semidirect
4. #15688858C2semidirect
5. #15688857C2semidirect
6. #15688856C2semidirect
7. C47×#327C2semidirect
9. #13094023C4semidirect
10. #13094020C4semidirect
14. D4×Dic47C4semidirect
15. #13093986C4semidirect
127. #327D47semidirect
128. C47#1502semidirect