Finite Group Databasebeta

← #20241928

Subgroups — #20241928

Order 6016.

286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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#15689633C211yesmaximal, characteristic
2#15689085C211yesmaximal, characteristic, complemented
3#15688982C211yesmaximal, characteristic, complemented
4#15688861C211yesmaximal, characteristic, complemented
5#15688859C211yesmaximal, characteristic, complemented
6#15688857C211yesmaximal, characteristic, complemented
7C47×#327C211yesmaximal, characteristic, complemented
8C2×#10625352C411yescharacteristic, complemented
9C22×C4×D47C2211yescharacteristic
10C2×#10625324—21no—
11#13094006—21no—
12#13094004C411yescharacteristic, complemented
13#13094003C2211yescharacteristic
14#13093995C411yescharacteristic, complemented
15#13093992—21no—
16D4×Dic47—21no—
17(C22⋊D47)⋊C4—21no—
18#13093982C411yescharacteristic, complemented
19C2×Dic47⋊C4—21no—
20C2×(C2×D47)⋊C4—21no—
21C22⋊(C47⋊C8)C2211yescharacteristic
22(C2×D47)⋊C8—21no—
23C47⋊#95C2211yescharacteristic
24#121×C47C2211yescharacteristic
25C22⋊C8×C47C2211yescharacteristic
26#95×C47C2211yescharacteristic
27C23×D47D411yescharacteristic
28C2×D4×C47—21no—
29C2×D4×C47C2×C411yescharacteristic
30C22×C4×C47—21no—
31C22×C4×C47C2311yescharacteristic
32C2×C22⋊D47—21no—
33C2×C22⋊D47—21no—
34C22×Dic47—21no—
35C22×Dic47—21no—
36C22×Dic47D411yescharacteristic
37#10625352—42no—
38C2×C4×D47—42no—
39C2×C4×D47C2×C411yescharacteristic
40C2×C4×D47C2×C411yescharacteristic
41C2×C4×D47D411yescharacteristic
42C2×C4×D47D411yescharacteristic
43C2×Dic94C2×C411yescharacteristic
44C2×C8×C47—21no—
45C4⋊C4×C47C2×C411yescharacteristic
46C22⋊C4×C47—21no—
47C22⋊Dic47—21no—
48C22⋊Dic47—21no—
49(C2×D47)⋊C4—21no—
50(C2×D47)⋊C4—21no—
51(C2×D47)⋊C4—42no—
52C4⋊Dic47—21no—
53C4⋊Dic47C2×C411yescharacteristic
54Dic47⋊C4—21no—
55Dic47⋊C4—42no—
56C4×Dic47—21no—
57C2×C47⋊C8—21no—
58#10625324—42no—
59C23×C47—21no—
60C23×C47C2×D411yescharacteristic
61C22×D47—21no—
62C22×D47—21no—
63C22×D47—41no—
64C22×D47—41no—
65C22×D47C22⋊C411yescharacteristic
66C22×D47C22⋊C411yescharacteristic
67D4×C47—41no—
68D4×C47—41no—
69D4×C47—41no—
70C2×C4×C47—21no—
71C2×C4×C47—41no—
72C2×C4×C47—41no—
73C2×C4×C47—41no—
74C2×C4×C47—41no—
75C2×C4×C47C22×C411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C22⋊D47—42no—
78C22⋊D47—42no—
79C2×Dic47—22no—
80C2×Dic47—21no—
81C2×Dic47—21no—
82C2×Dic47—42no—
83C2×Dic47—41no—
84C2×Dic47—41no—
85C2×Dic47—41no—
86C2×Dic47C22⋊C411yescharacteristic
87C2×Dic47C22⋊C411yescharacteristic
88C4×D47—22no—
89C4×D47—22no—
90C4×D47—41no—
91C4×D47—41no—
92Dic94—41no—
93C8×C47—41no—
94C47⋊C8—41no—
95C22×C47—21no—
96C22×C47—21no—
97C22×C47—41no—
98C22×C47—41no—
99C22×C47—41no—
100C22×C47C2×C22⋊C411yescharacteristic
101C22×C47AGL(1,ℤ/8)11yescharacteristic
102C22×C47#13711yescharacteristic
103C2×D47—21no—
104C2×D47—21no—
105C2×D47—21no—
106C2×D47—21no—
107C2×D47—21no—
108C2×D47—21no—
109C2×D47—42no—
110C2×D47—42no—
111C4×C47—21no—
112C4×C47—21no—
113C4×C47—41no—
114C4×C47—81no—
115Dic47—21no—
116Dic47—41no—
117Dic47—41no—
118Dic47—81no—
119Dic47#9912yes—
120#1513—471nomaximal, Sylow
121C2×C47—21no—
122C2×C47—21no—
123C2×C47—81no—
124C2×C47C2×#9911yescharacteristic
125C2×C47#41711yescharacteristic
126C2×C47#42111yescharacteristic
127D47—41no—
128D47—41no—
129#525—471no—
130#407—471no—
131#380—471no—
132#328—471no—
133#328—471no—
134#327—471no—
135#327D4711yescharacteristic, complemented
136C47#151311yescharacteristic, complemented, Sylow
137C2×#41—471no—
138C23×C4—471no—
139C2×M16—941no—
140#123—941no—
141C22⋊Q8—471no—
142C22⋊Q8—471no—
143#121—471no—
144#121C2×D4711yescharacteristic
145#120—941no—
146C4×D4—941no—
147C4×D4—941no—
148#117—471no—
149C2×C4⋊C4—941no—
150C2×C22⋊C4—941no—
151C22⋊C8—471no—
152C22⋊C8—941no—
153C22⋊C8C2×D4711yescharacteristic
154#95—471no—
155#95C2×D4711yescharacteristic
156C24—471no—
157#41—1882no—
158C2×Q8—471no—
159C2×D4—21no—
160C2×D4—941no—
161C2×D4—941no—
162C2×D4C4×D4711yescharacteristic
163C22×C4—21no—
164C22×C4—471no—
165C22×C4—471no—
166C22×C4—471no—
167C22×C4—471no—
168C22×C4—471no—
169C22×C4—941no—
170C22×C4—941no—
171C22×C4—1882no—
172C22×C4C22×D4711yescharacteristic
173M16—1882no—
174C2×C8—21no—
175C2×C8—941no—
176C4⋊C4—471no—
177C4⋊C4—941no—
178C4⋊C4—941no—
179C4⋊C4—1882no—
180C4⋊C4C4×D4711yescharacteristic
181C22⋊C4—21no—
182C22⋊C4—941no—
183C22⋊C4—941no—
184C22⋊C4—941no—
185C22⋊C4—941no—
186C22⋊C4—1882no—
187C42—941no—
188C23—21no—
189C23—471no—
190C23—471no—
191C23—941no—
192C23—941no—
193C23—1881no—
194C23—1881no—
195C23D4×D4711yescharacteristic
196Q8—1881no—
197D4—41no—
198D4—41no—
199D4—41no—
200D4—1882no—
201D4—1882no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—471no—
208C2×C4—471no—
209C2×C4—942no—
210C2×C4—942no—
211C2×C4—942no—
212C2×C4—941no—
213C2×C4—941no—
214C2×C4—1881no—
215C2×C4—1881no—
216C2×C4—1882no—
217C2×C4—1881no—
218C2×C4—1881no—
219C2×C4—1881no—
220C2×C4C2×C4×D4711yescharacteristic
221C2×C4D4×D4711yescharacteristic
222C8—41no—
223C8—1881no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—941no—
230C22—941no—
231C22—941no—
232C22—941no—
233C22—941no—
234C22—941no—
235C22—1882no—
236C22—1882no—
237C22C22⋊C4×D4711yescharacteristic
238C22#1309404811yescharacteristic
239C22#1309405311yescharacteristic
240C4—21no—
241C4—21no—
242C4—41no—
243C4—81no—
244C4—472no—
245C4—941no—
246C4—3761no—
247C4—1881no—
248C4—1881no—
249C2—21no—
250C2—21no—
251C2—81no—
252C2—1881no—
253C2—1881no—
254C2#99×D4711yescharacteristic
255C2#1568912111yescharacteristic
256C2#1568913811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#327C2
socleC22×C47C2×C22⋊C4
hypercenter#327D47
hypocenterC47#1513
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. #15689085C2semidirect
3. #15688982C2semidirect
4. #15688861C2semidirect
5. #15688859C2semidirect
6. #15688857C2semidirect
7. C47×#327C2semidirect
8. C2×#10625352C4semidirect
12. #13094004C4semidirect
14. #13093995C4semidirect
18. #13093982C4semidirect
135. #327D47semidirect
136. C47#1513semidirect