Finite Group Databasebeta

← #20249116

Subgroups — #20249116

Order 6016.

816 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×#10625352C211yesmaximal, characteristic
2C2×#13094002C211yesmaximal, characteristic, complemented
3C2×#13094001C212yesmaximal, complemented
4#15689044C211yesmaximal, characteristic, complemented
5#15689043C211yesmaximal, characteristic, complemented
6#15689039C212yesmaximal, complemented
7#15689038C212yesmaximal, complemented
8#15689037C211yesmaximal, characteristic, complemented
9#15688982C211yesmaximal, characteristic, complemented
10#15688981C212yesmaximal, complemented
11C47×#394C211yesmaximal, characteristic, complemented
12C2×#10625352—28no—
13C2×#10625352—24no—
14C22×Dic94C2211yescharacteristic
15C22×Dic94C2211yescharacteristic
16C22×C22⋊D47C2212yes—
17C23×Dic47C2212yes—
18C22×C4×D47C2211yescharacteristic
19#13094002—24no—
20#13094001—28no—
21C2×C4⋊Dic47C2212yes—
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2212yes—
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2212yes—
26C2×C22⋊Dic47C2212yes—
27C2×C22⋊Dic47C2212yes—
28C2×(C2×D47)⋊C4C2211yescharacteristic
29C2×(C2×D47)⋊C4C2211yescharacteristic
30C2×(C2×D47)⋊C4C2212yes—
31C47⋊#95C2212yes—
32C47⋊#95C2212yes—
33C47⋊#95C2211yescharacteristic
34C22×D4×C47C2211yescharacteristic
35C2×C4⋊C4×C47C2211yescharacteristic
36C2×C22⋊C4×C47C2212yes—
37C2×C22⋊C4×C47C2212yes—
38#95×C47C2211yescharacteristic
39C24×C47C2312yes—
40C23×D47C2311yescharacteristic
41C2×D4×C47—24no—
42C2×D4×C47—22no—
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2311yescharacteristic
45C22×C4×C47C2312yes—
46C22×C4×C47C2311yescharacteristic
47C2×C22⋊D47—24no—
48C2×C22⋊D47—24no—
49C2×C22⋊D47—24no—
50C22×Dic47—24no—
51C22×Dic47—24no—
52C22×Dic47D418yes—
53C22×Dic47C2311yescharacteristic
54C22×Dic47C2312yes—
55C22×Dic47C2311yescharacteristic
56C22×Dic47C2312yes—
57C22×Dic47C2311yescharacteristic
58#10625352—232no—
59C2×C4×D47—24no—
60C2×C4×D47D414yes—
61C2×Dic94—22no—
62C2×Dic94—24no—
63C2×Dic94—24no—
64C2×Dic94—22no—
65C4⋊C4×C47—22no—
66C22⋊C4×C47—24no—
67C22⋊C4×C47—42no—
68C22⋊Dic47—24no—
69C22⋊Dic47—42no—
70(C2×D47)⋊C4—22no—
71(C2×D47)⋊C4—22no—
72(C2×D47)⋊C4—42no—
73C4⋊Dic47—24no—
74Dic47⋊C4—22no—
75Dic47⋊C4—24no—
76Dic47⋊C4—24no—
77Dic47⋊C4—22no—
78C23×C47—22no—
79C23×C47—22no—
80C23×C47—22no—
81C23×C47—22no—
82C23×C47—22no—
83C23×C47—22no—
84C23×C47C2×D414yes—
85C23×C47C2411yescharacteristic
86C22×D47—22no—
87C22×D47—21no—
88C22×D47—22no—
89C22×D47—21no—
90C22×D47C2×D412yes—
91D4×C47—28no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47—21no—
95C2×C4×C47—22no—
96C2×C4×C47—21no—
97C2×C4×C47—22no—
98C2×C4×C47—21no—
99C2×C4×C47—21no—
100C2×C4×C47—22no—
101C2×C4×C47C2×D412yes—
102C22⋊D47—216no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—216no—
106C2×Dic47—21no—
107C2×Dic47—22no—
108C2×Dic47—21no—
109C2×Dic47—22no—
110C2×Dic47—22no—
111C2×Dic47—21no—
112C2×Dic47—22no—
113C2×Dic47—21no—
114C2×Dic47C2×D414yes—
115C2×Dic47C2×D414yes—
116C2×Dic47C2×D412yes—
117C4×D47—28no—
118Dic94—28no—
119Dic94—44no—
120C22×C47—24no—
121C22×C47—24no—
122C22×C47—24no—
123C22×C47—42no—
124C22×C47—42no—
125C22×C47—42no—
126C22×C47—42no—
127C22×C47C22×D411yescharacteristic
128C22×C47C22×D412yes—
129C22×C47H(5,𝔽2)11yescharacteristic
130C22×C472−1+412yes—
131C22×C472−1+411yescharacteristic
132C2×D47—22no—
133C2×D47—22no—
134C2×D47—22no—
135C2×D47—42no—
136C2×D47—42no—
137C4×C47—22no—
138C4×C47—41no—
139C4×C47—42no—
140C4×C47—41no—
141Dic47—24no—
142Dic47—41no—
143Dic47—42no—
144Dic47—41no—
145Dic47#12014yes—
146#2616—471nomaximal, Sylow
147C2×C47—44no—
148C2×C47C2×#12011yescharacteristic
149C2×C47#53611yescharacteristic
150C2×C47#53612yes—
151C2×C47#53712yes—
152C2×C47#53711yescharacteristic
153D47—42no—
154C22×#41—471no—
155C2×C22⋊Q8—471no—
156C2×C22⋊Q8—472no—
157#395—471no—
158#395—471no—
159#394—471no—
160#394—472no—
161#394—472no—
162#394D4711yescharacteristic, complemented
163#380—472no—
164#380—471no—
165C47#261611yescharacteristic, complemented, Sylow
166C2×#41—948no—
167C2×#41—944no—
168C22×Q8—471no—
169C22×Q8—471no—
170C22×D4—472no—
171C22×D4C2×D4711yescharacteristic
172C23×C4—472no—
173C23×C4—471no—
174C22⋊Q8—948no—
175C22⋊Q8—944no—
176C2×C4⋊C4—471no—
177C2×C4⋊C4—472no—
178C2×C4⋊C4—472no—
179C2×C4⋊C4—471no—
180C2×C4⋊C4—472no—
181C2×C4⋊C4C2×D4711yescharacteristic
182C2×C22⋊C4—472no—
183C2×C22⋊C4—471no—
184C2×C22⋊C4—471no—
185C2×C22⋊C4—472no—
186C2×C22⋊C4—472no—
187C2×C22⋊C4C2×D4712yes—
188C2×C22⋊C4C2×D4712yes—
189#95—472no—
190#95—472no—
191#95—471no—
192#95C2×D4711yescharacteristic
193C24—471no—
194C24C22×D4712yes—
195#41—9432no—
196C2×Q8—944no—
197C2×Q8—944no—
198C2×Q8—942no—
199C2×Q8—942no—
200C2×D4—24no—
201C2×D4—22no—
202C2×D4—944no—
203C2×D4—944no—
204C2×D4—944no—
205C22×C4—471no—
206C22×C4—478no—
207C22×C4—472no—
208C22×C4—474no—
209C22×C4—472no—
210C22×C4—471no—
211C22×C4—471no—
212C22×C4—944no—
213C22×C4—944no—
214C22×C4—944no—
215C22×C4C22×D4711yescharacteristic
216C22×C4C22×D4712yes—
217C22×C4C22×D4711yescharacteristic
218C22×C4C22×D4711yescharacteristic
219C4⋊C4—22no—
220C4⋊C4—944no—
221C4⋊C4—944no—
222C4⋊C4—942no—
223C4⋊C4—944no—
224C4⋊C4—942no—
225C22⋊C4—24no—
226C22⋊C4—42no—
227C22⋊C4—942no—
228C22⋊C4—942no—
229C22⋊C4—944no—
230C22⋊C4—1882no—
231C22⋊C4—1882no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—472no—
239C23—942no—
240C23—941no—
241C23—942no—
242C23—941no—
243C23D4×D4714yes—
244C23C23×D4711yescharacteristic
245Q8—948no—
246Q8—1884no—
247D4—28no—
248D4—9416no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—472no—
259C2×C4—474no—
260C2×C4—474no—
261C2×C4—948no—
262C2×C4—9416no—
263C2×C4—942no—
264C2×C4—942no—
265C2×C4—942no—
266C2×C4—941no—
267C2×C4—941no—
268C2×C4—942no—
269C2×C4—942no—
270C2×C4—941no—
271C2×C4—942no—
272C2×C4—941no—
273C2×C4D4×D4712yes—
274C22—24no—
275C22—24no—
276C22—24no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—942no—
282C22—942no—
283C22—942no—
284C22—1882no—
285C22—1882no—
286C22C2×D4×D4711yescharacteristic
287C22C2×D4×D4712yes—
288C22#1309406911yescharacteristic
289C22#1309407112yes—
290C22#1309407111yescharacteristic
291C4—22no—
292C4—41no—
293C4—42no—
294C4—41no—
295C4—474no—
296C4—944no—
297C4—1881no—
298C4—1882no—
299C4—1881no—
300C2—44no—
301C2—1882no—
302C2#120×D4711yescharacteristic
303C2#1568969311yescharacteristic
304C2#1568969512yes—
305C2#1568970012yes—
306C2#1568970211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#394C2
hypercenter#394D47
hypocenterC47#2616
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#13094002C2semidirect
3. C2×#13094001C2semidirect
4. #15689044C2semidirect
5. #15689043C2semidirect
6. #15689039C2semidirect
7. #15689038C2semidirect
8. #15689037C2semidirect
9. #15688982C2semidirect
10. #15688981C2semidirect
11. C47×#394C2semidirect
162. #394D47semidirect
165. C47#2616semidirect