Finite Group Databasebeta

← #20248570

Subgroups — #20248570

Order 6016.

584 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 161 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×C4×C22⋊D47C211yesmaximal, characteristic
2#15689061C211yesmaximal, characteristic, complemented
3#15689058C211yesmaximal, characteristic, complemented
4#15689042C211yesmaximal, characteristic, complemented
5#15689034C211yesmaximal, characteristic, complemented
6#15689004C212yesmaximal, complemented
7#15689000C212yesmaximal
8#15688994C212yesmaximal, complemented
9#15688981C212yesmaximal, complemented
10C2×C47⋊#95C211yesmaximal, characteristic, complemented
11C2×C22⋊Q8×C47C211yesmaximal, characteristic, complemented
12C22×C22⋊D47C2211yescharacteristic
13C23×Dic47C2212yes—
14C22×C4×D47C2211yescharacteristic
15C4×C22⋊D47—24no—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2211yescharacteristic
18C2×Dic47⋊C4C2212yes—
19C2×C22⋊Dic47C2211yescharacteristic
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2211yescharacteristic
22C2×(C2×D47)⋊C4C2212yes—
23C2×C4×Dic47C2211yescharacteristic
24C47⋊#95C2212yes—
25C47⋊#95C2211yescharacteristic
26C47⋊#95C2211yescharacteristic
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C22×Q8×C47C2211yescharacteristic
32C23×C4×C47C2211yescharacteristic
33C22⋊Q8×C47—24no—
34C2×C4⋊C4×C47C2212yes—
35C2×C4⋊C4×C47C2211yescharacteristic
36C2×C22⋊C4×C47C2212yes—
37C24×C47C2311yescharacteristic
38C23×D47C2311yescharacteristic
39C2×Q8×C47—22no—
40C2×Q8×C47—42no—
41C22×C4×C47—42no—
42C22×C4×C47D414yes—
43C22×C4×C47C2312yes—
44C22×C4×C47C2312yes—
45C22×C4×C47C2311yescharacteristic
46C22×C4×C47C2311yescharacteristic
47C2×C22⋊D47—22no—
48C2×C22⋊D47—22no—
49C2×C22⋊D47Q814yescomplemented
50C22×Dic47—24no—
51C22×Dic47—24no—
52C22×Dic47—42no—
53C22×Dic47C2312yes—
54C22×Dic47C2311yescharacteristic
55C22×Dic47C2311yescharacteristic
56C22×Dic47C2311yescharacteristic
57C22×Dic47C2312yes—
58C2×C4×D47—22no—
59C2×C4×D47—42no—
60C4⋊C4×C47—22no—
61C4⋊C4×C47—24no—
62C22⋊C4×C47—24no—
63C22⋊Dic47—22no—
64(C2×D47)⋊C4—22no—
65(C2×D47)⋊C4—24no—
66(C2×D47)⋊C4—42no—
67Dic47⋊C4—22no—
68Dic47⋊C4—24no—
69Dic47⋊C4—42no—
70C4×Dic47—22no—
71C23×C47—22no—
72C23×C47—22no—
73C23×C47C2×D412yes—
74C23×C47C2×Q812yes—
75C23×C47#4112yes—
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—22no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—44no—
92C2×C4×C47C2×D412yes—
93C2×C4×C47C2×D412yes—
94C22⋊D47—28no—
95C2×Dic47—21no—
96C2×Dic47—22no—
97C2×Dic47—21no—
98C2×Dic47—22no—
99C2×Dic47—21no—
100C2×Dic47—21no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47—48no—
107C2×Dic47C2×Q812yes—
108C2×Dic47#4114yes—
109C4×D47—44no—
110C22×C47—22no—
111C22×C47—22no—
112C22×C47—24no—
113C22×C47—24no—
114C22×C47C22⋊Q814yes—
115C22×C47C22×D411yescharacteristic
116C22×C47C22×Q811yescharacteristic
117C22×C47C2×#4112yes—
118C22×C47C2×#4111yescharacteristic
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—22no—
127C4×C47—42no—
128C4×C47—42no—
129Dic47—22no—
130Dic47—24no—
131Dic47—41no—
132Dic47—41no—
133Dic47—42no—
134#2564—471nomaximal, Sylow
135C2×C47—24no—
136C2×C47C2×C22⋊Q811yescharacteristic
137C2×C47#53211yescharacteristic
138C2×C47#53411yescharacteristic
139C2×C47#55112yes—
140C2×C47#55412yes—
141D47—42no—
142C2×C22⋊Q8D4711yescharacteristic, complemented
143C2×C4×D4—471no—
144#400—471no—
145#399—471no—
146#395—471no—
147#393—471no—
148#387—472no—
149#386—472no—
150#385—472no—
151#380—472no—
152C2×#95—471no—
153C47#256411yescharacteristic, complemented, Sylow
154C22×Q8C2×D4711yescharacteristic
155C22×D4—471no—
156C23×C4—472no—
157C23×C4—471no—
158C23×C4C2×D4711yescharacteristic
159C22⋊Q8—24no—
160C4×D4—944no—
161C2×C4⋊C4—471no—
162C2×C4⋊C4—472no—
163C2×C4⋊C4—472no—
164C2×C4⋊C4C2×D4712yes—
165C2×C4⋊C4C2×D4711yescharacteristic
166C2×C22⋊C4—471no—
167C2×C22⋊C4—471no—
168C2×C22⋊C4—472no—
169C2×C22⋊C4—472no—
170C2×C22⋊C4C2×D4712yes—
171C2×C42—471no—
172#95—472no—
173#95—471no—
174#95—471no—
175#95—472no—
176#95—472no—
177#95—472no—
178#95—472no—
179C24—471no—
180C24C22×D4711yescharacteristic
181C2×Q8—22no—
182C2×Q8—42no—
183C2×D4—474no—
184C2×D4—942no—
185C2×D4—942no—
186C22×C4—42no—
187C22×C4—471no—
188C22×C4—472no—
189C22×C4—472no—
190C22×C4—471no—
191C22×C4—471no—
192C22×C4—944no—
193C22×C4—944no—
194C22×C4—942no—
195C22×C4—1882no—
196C22×C4—1882no—
197C22×C4C22⋊D4714yes—
198C22×C4C22×D4712yes—
199C22×C4C22×D4712yes—
200C22×C4C22×D4711yescharacteristic
201C22×C4C22×D4711yescharacteristic
202C4⋊C4—22no—
203C4⋊C4—24no—
204C4⋊C4—944no—
205C4⋊C4—942no—
206C4⋊C4—1882no—
207C22⋊C4—24no—
208C22⋊C4—944no—
209C22⋊C4—942no—
210C22⋊C4—942no—
211C22⋊C4—1882no—
212C42—942no—
213C23—22no—
214C23—22no—
215C23—472no—
216C23—941no—
217C23—942no—
218C23—941no—
219C23—942no—
220C23Q8×D4712yes—
221C23#1062535412yes—
222C23C2×C22⋊D4712yes—
223C23C23×D4711yescharacteristic
224Q8—44no—
225D4—948no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—44no—
235C2×C4—472no—
236C2×C4—474no—
237C2×C4—941no—
238C2×C4—942no—
239C2×C4—941no—
240C2×C4—942no—
241C2×C4—941no—
242C2×C4—941no—
243C2×C4—942no—
244C2×C4—942no—
245C2×C4—942no—
246C2×C4—942no—
247C2×C4—942no—
248C2×C4—1884no—
249C2×C4—1888no—
250C2×C4C2×C22⋊D4712yes—
251C2×C4C2×C22⋊D4712yes—
252C22—24no—
253C22—24no—
254C22—22no—
255C22—22no—
256C22—944no—
257C22—942no—
258C22—1882no—
259C22—1881no—
260C22—1881no—
261C22#1309400014yes—
262C22C22×C22⋊D4711yescharacteristic
263C22C2×Q8×D4711yescharacteristic
264C22#41×D4712yes—
265C22C2×#1062535411yescharacteristic
266C22#1309406912yes—
267C4—22no—
268C4—22no—
269C4—42no—
270C4—42no—
271C4—944no—
272C4—942no—
273C4—1882no—
274C4—1881no—
275C4—1881no—
276C2—24no—
277C2—1882no—
278C2C2×#1309400011yescharacteristic
279C2#1568966911yescharacteristic
280C2#1568968211yescharacteristic
281C2#1568980012yes—
282C2#1568982712yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C22⋊Q8×C47C2
hypercenterC2×C22⋊Q8D47
hypocenterC47#2564
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #15689061C2semidirect
3. #15689058C2semidirect
4. #15689042C2semidirect
5. #15689034C2semidirect
6. #15689004C2semidirect
8. #15688994C2semidirect
9. #15688981C2semidirect
10. C2×C47⋊#95C2semidirect
11. C2×C22⋊Q8×C47C2semidirect
49. C2×C22⋊D47Q8semidirect
142. C2×C22⋊Q8D47semidirect
153. C47#2564semidirect