Finite Group Databasebeta

← #20241946

Subgroups — #20241946

Order 6016.

264 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 69 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#15688987C211yesmaximal, 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×Dic47C2211yescharacteristic
19Dic47⋊C8—21no—
20C22⋊(C47⋊C8)C2211yescharacteristic
21C8×Dic47—21no—
22C47⋊#95—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—21no—
51Dic47⋊C4—42no—
52C4×Dic47C2×C411yescharacteristic
53C4×Dic47C2×C411yescharacteristic
54C4×Dic47D411yescharacteristic
55C4×Dic47D411yescharacteristic
56C2×C47⋊C8—21no—
57C23×C47—21no—
58C23×C47C2×D411yescharacteristic
59C22×D47—21no—
60D4×C47—41no—
61D4×C47—41no—
62D4×C47—41no—
63C2×C4×C47—21no—
64C2×C4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47C22×C411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C22⋊D47—42no—
71C22⋊D47—41no—
72C22⋊D47—41no—
73C22⋊D47—42no—
74C2×Dic47—21no—
75C2×Dic47—41no—
76C2×Dic47—42no—
77C2×Dic47—41no—
78C2×Dic47—41no—
79C2×Dic47—41no—
80C2×Dic47C22⋊C411yescharacteristic
81C2×Dic47C22⋊C411yescharacteristic
82C2×Dic47C22⋊C411yescharacteristic
83C2×Dic47C22⋊C411yescharacteristic
84C2×Dic47D812yes—
85C2×Dic47SD1612yes—
86D188—41no—
87C4×D47—42no—
88Dic94—42no—
89C8×C47—41no—
90C47⋊C8—41no—
91C22×C47—21no—
92C22×C47—21no—
93C22×C47—41no—
94C22×C47—41no—
95C22×C47—41no—
96C22×C47C2×C22⋊C411yescharacteristic
97C22×C47C2×D811yescharacteristic
98C22×C47C2×SD1611yescharacteristic
99C2×D47—41no—
100C2×D47—41no—
101C2×D47—41no—
102C4×C47—21no—
103C4×C47—21no—
104C4×C47—41no—
105C4×C47—81no—
106Dic47—21no—
107Dic47—21no—
108Dic47—41no—
109Dic47—81no—
110Dic47#10212yes—
111Dic47#10212yes—
112#1517—471nomaximal, Sylow
113C2×C47—21no—
114C2×C47—21no—
115C2×C47—81no—
116C2×C47#41011yescharacteristic
117C2×C47C2×#10211yescharacteristic
118C2×C47#42111yescharacteristic
119D47—81no—
120#532—471no—
121#431—471no—
122#382—471no—
123#327—471no—
124#327—471no—
125#327—471no—
126#327D4711yescharacteristic, complemented
127C47#151711yescharacteristic, complemented, Sylow
128C2×#41—941no—
129C4⋊Q8—471no—
130#127—471no—
131#124—941no—
132#121—471no—
133#121—941no—
134#121C2×D4711yescharacteristic
135C4×D4—471no—
136C4×D4—471no—
137C4×D4—941no—
138C2×C4⋊C4—941no—
139C2×C42—471no—
140C4⋊C8—941no—
141C22⋊C8—471no—
142C22⋊C8C2×D4711yescharacteristic
143C4×C8—941no—
144#95—471no—
145#95—941no—
146#95C2×D4711yescharacteristic
147#41—1882no—
148#41—1882no—
149C2×Q8—941no—
150C2×D4—21no—
151C2×D4—471no—
152C2×D4—941no—
153C2×D4—941no—
154C2×D4—941no—
155C2×D4C4×D4711yescharacteristic
156C22×C4—21no—
157C22×C4—471no—
158C22×C4—471no—
159C22×C4—941no—
160C22×C4—941no—
161C22×C4—941no—
162C22×C4C22×D4711yescharacteristic
163C2×C8—21no—
164C2×C8—941no—
165C4⋊C4—471no—
166C4⋊C4—941no—
167C4⋊C4—1882no—
168C4⋊C4C4×D4711yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—941no—
171C22⋊C4—941no—
172C22⋊C4—941no—
173C42—471no—
174C42—471no—
175C42—471no—
176C42—471no—
177C23—21no—
178C23—941no—
179C23D4×D4711yescharacteristic
180Q8—1882no—
181D4—41no—
182D4—41no—
183D4—41no—
184D4—1881no—
185D4—1882no—
186D4—1882no—
187D4—1881no—
188D4—1881no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—471no—
195C2×C4—471no—
196C2×C4—472no—
197C2×C4—472no—
198C2×C4—471no—
199C2×C4—471no—
200C2×C4—941no—
201C2×C4—1882no—
202C2×C4—1882no—
203C2×C4—1881no—
204C2×C4—1881no—
205C2×C4—1881no—
206C2×C4—1881no—
207C2×C4C2×C4×D4711yescharacteristic
208C2×C4D4×D4711yescharacteristic
209C8—41no—
210C8—1881no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—1881no—
217C22—1881no—
218C22—1881no—
219C22C22⋊C4×D4711yescharacteristic
220C22D8×D4711yescharacteristic
221C22SD16×D4711yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—81no—
226C4—472no—
227C4—472no—
228C4—941no—
229C4—941no—
230C4—3761no—
231C4—1881no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—3761no—
236C2#1568909511yescharacteristic
237C2#102×D4711yescharacteristic
238C2#1568913811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#327C2
socleC22×C47C2×C22⋊C4
hypercenter#327D47
hypocenterC47#1517
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. #15688987C2semidirect
4. #15688858C2semidirect
5. #15688857C2semidirect
6. #15688856C2semidirect
7. C47×#327C2semidirect
9. #13094023C4semidirect
10. #13094020C4semidirect
14. D4×Dic47C4semidirect
15. #13093986C4semidirect
126. #327D47semidirect
127. C47#1517semidirect