Finite Group Databasebeta

← #20248556

Subgroups — #20248556

Order 6016.

564 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C2×#13094022C211yesmaximal, characteristic, complemented
2C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic
3#15689036C211yesmaximal, characteristic, complemented
4#15689035C211yesmaximal, characteristic, complemented
5#15689034C211yesmaximal, characteristic, complemented
6#15689023C212yesmaximal
7#15688987C212yesmaximal, complemented
8#15688982C212yesmaximal, complemented
9#15688981C212yesmaximal, complemented
10#15688974C211yesmaximal, characteristic, complemented
11C47×#393C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×C22⋊D47C2211yescharacteristic
14C23×Dic47C2211yescharacteristic
15C22×C4×D47C2211yescharacteristic
16#13094022—24no—
17(C22⋊D47)⋊C4—24no—
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2212yes—
22C2×C22⋊Dic47C2212yes—
23C2×(C2×D47)⋊C4C2211yescharacteristic
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2212yes—
26C2×C4×Dic47C2212yes—
27C2×C4×Dic47C2211yescharacteristic
28C47⋊#95C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×Q8×C47C2211yescharacteristic
33C2×C22⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2212yes—
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C24×C47C2311yescharacteristic
38C23×D47C2311yescharacteristic
39C2×Q8×C47—22no—
40C2×Q8×C47—42no—
41C22×C4×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2312yes—
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—22no—
46C2×C22⋊D47—22no—
47C2×C22⋊D47Q814yescomplemented
48C22×Dic47—22no—
49C22×Dic47—24no—
50C22×Dic47C2311yescharacteristic
51C22×Dic47C2312yes—
52C22×Dic47C2312yes—
53C22×Dic47C2311yescharacteristic
54C22×Dic47C2311yescharacteristic
55C2×C4×D47—22no—
56C2×C4×D47—24no—
57C2×Dic94—22no—
58C2×Dic94—42no—
59C22⋊C4×C47—22no—
60C22⋊C4×C47—42no—
61C22⋊Dic47—42no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—42no—
64(C2×D47)⋊C4—42no—
65Dic47⋊C4—22no—
66Dic47⋊C4—24no—
67Dic47⋊C4—24no—
68Dic47⋊C4—24no—
69C4×Dic47—24no—
70C4×Dic47D414yes—
71C23×C47—21no—
72C23×C47—22no—
73C23×C47—21no—
74C23×C47—22no—
75C23×C47C2×Q812yes—
76C23×C47C2411yescharacteristic
77C22×D47—21no—
78C22×D47—22no—
79C22×D47—21no—
80C22×D47—22no—
81C22×D47C2×Q812yes—
82Q8×C47—44no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—21no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47C2×D412yes—
93C22⋊D47—28no—
94C2×Dic47—22no—
95C2×Dic47—21no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—44no—
103C2×Dic47C2×D412yes—
104C2×Dic47C2×D412yes—
105C2×Dic47C2×Q812yes—
106C2×Dic47#4112yes—
107C2×Dic47#4114yes—
108C4×D47—44no—
109Dic94—44no—
110C22×C47—22no—
111C22×C47—24no—
112C22×C47—41no—
113C22×C47—41no—
114C22×C47—42no—
115C22×C47C22×D411yescharacteristic
116C22×C47C22×Q811yescharacteristic
117C22×C47C2×#4111yescharacteristic
118C22×C47C2×#4112yes—
119C22×C47H(5,𝔽2)12yes—
120C2×D47—22no—
121C2×D47—24no—
122C2×D47—41no—
123C2×D47—41no—
124C2×D47—42no—
125C4×C47—22no—
126C4×C47—41no—
127C4×C47—42no—
128C4×C47—42no—
129Dic47—41no—
130Dic47—42no—
131Dic47—42no—
132Dic47C22⋊Q814yes—
133Dic47#12414yes—
134#2563—471nomaximal, Sylow
135C2×C47—42no—
136C2×C47C2×C22⋊Q811yescharacteristic
137C2×C47C2×#12411yescharacteristic
138C2×C47#53511yescharacteristic
139C2×C47#55412yes—
140C2×C47#55512yes—
141D47—42no—
142C2×C4⋊Q8—471no—
143C2×C4×D4—471no—
144#393—471no—
145#393—471no—
146#393—471no—
147#393D4711yescharacteristic, complemented
148#390—472no—
149#382—472no—
150#380—472no—
151#380—472no—
152C4×C4⋊C4—471no—
153C47#256311yescharacteristic, complemented, Sylow
154C22×Q8—471no—
155C22×Q8C2×D4711yescharacteristic
156C22×D4—471no—
157C23×C4—471no—
158C23×C4—471no—
159C4⋊Q8—944no—
160C4×D4—944no—
161C2×C4⋊C4—471no—
162C2×C4⋊C4—472no—
163C2×C4⋊C4—472no—
164C2×C4⋊C4—472no—
165C2×C22⋊C4—471no—
166C2×C22⋊C4—472no—
167C2×C22⋊C4—472no—
168C2×C22⋊C4—472no—
169C2×C22⋊C4C2×D4711yescharacteristic
170C2×C22⋊C4C2×D4712yes—
171C2×C42—471no—
172C2×C42—472no—
173#95—471no—
174#95—472no—
175#95—472no—
176#95—472no—
177#95C2×D4711yescharacteristic
178#95C2×D4712yes—
179C24—471no—
180C24C22×D4711yescharacteristic
181C2×Q8—22no—
182C2×Q8—42no—
183C2×Q8—942no—
184C2×Q8—1882no—
185C2×D4—474no—
186C2×D4—942no—
187C2×D4—942no—
188C22×C4—471no—
189C22×C4—471no—
190C22×C4—471no—
191C22×C4—472no—
192C22×C4—472no—
193C22×C4—942no—
194C22×C4—944no—
195C22×C4—942no—
196C22×C4—944no—
197C22×C4C22×D4711yescharacteristic
198C22×C4C22×D4712yes—
199C22×C4C22×D4712yes—
200C22×C4C22×D4711yescharacteristic
201C4⋊C4—944no—
202C4⋊C4—942no—
203C4⋊C4—944no—
204C4⋊C4—944no—
205C22⋊C4—22no—
206C22⋊C4—42no—
207C22⋊C4—942no—
208C22⋊C4—1882no—
209C22⋊C4—1882no—
210C22⋊C4—1882no—
211C42—474no—
212C42—944no—
213C23—21no—
214C23—22no—
215C23—21no—
216C23—22no—
217C23—472no—
218C23—941no—
219C23—942no—
220C23—941no—
221C23—942no—
222C23Q8×D4712yes—
223C23C23×D4711yescharacteristic
224Q8—44no—
225Q8—1884no—
226D4—948no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—472no—
237C2×C4—472no—
238C2×C4—472no—
239C2×C4—472no—
240C2×C4—474no—
241C2×C4—941no—
242C2×C4—942no—
243C2×C4—942no—
244C2×C4—942no—
245C2×C4—942no—
246C2×C4—942no—
247C2×C4—942no—
248C2×C4—942no—
249C2×C4—1884no—
250C2×C4—1884no—
251C2×C4D4×D4712yes—
252C22—24no—
253C22—22no—
254C22—42no—
255C22—41no—
256C22—41no—
257C22—944no—
258C22—942no—
259C22—1882no—
260C22—1881no—
261C22—1881no—
262C22C2×D4×D4711yescharacteristic
263C22C2×Q8×D4711yescharacteristic
264C22#41×D4712yes—
265C22#41×D4711yescharacteristic
266C22#1309406912yes—
267C4—22no—
268C4—42no—
269C4—41no—
270C4—42no—
271C4—474no—
272C4—474no—
273C4—1882no—
274C4—1881no—
275C4—1882no—
276C2—42no—
277C2—1882no—
278C2C22⋊Q8×D4711yescharacteristic
279C2#124×D4711yescharacteristic
280C2#1568968811yescharacteristic
281C2#1568982712yes—
282C2#1568983512yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#393C2
hypercenter#393D47
hypocenterC47#2563
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#13094022C2semidirect
3. #15689036C2semidirect
4. #15689035C2semidirect
5. #15689034C2semidirect
7. #15688987C2semidirect
8. #15688982C2semidirect
9. #15688981C2semidirect
10. #15688974C2semidirect
11. C47×#393C2semidirect
47. C2×C22⋊D47Q8semidirect
147. #393D47semidirect
153. C47#2563semidirect