Finite Group Databasebeta

← #20247704

Subgroups — #20247704

Order 6016.

584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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×(C22⋊D47)⋊C4C211yesmaximal, characteristic
2C22×Dic47⋊C4C211yesmaximal, characteristic, complemented
3#15689064C212yesmaximal, complemented
4#15689058C212yesmaximal, complemented
5#15689018C212yesmaximal, complemented
6#15689002C211yesmaximal, characteristic
7#15689000C211yesmaximal, characteristic
8#15688995C211yesmaximal, characteristic, complemented
9#15688982C212yesmaximal, complemented
10#15688981C211yesmaximal, characteristic, complemented
11C47×#385C211yesmaximal, characteristic, complemented
12C22×C22⋊D47C2211yescharacteristic
13C23×Dic47C2211yescharacteristic
14C23×Dic47C2211yescharacteristic
15C22×C4×D47C2211yescharacteristic
16(C22⋊D47)⋊C4—24no—
17C2×Dic47⋊C4—24no—
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2212yes—
21C2×Dic47⋊C4C2211yescharacteristic
22C2×Dic47⋊C4C2212yes—
23C2×C22⋊Dic47C2211yescharacteristic
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2212yes—
27C2×C4×Dic47C2211yescharacteristic
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C23×C4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2212yes—
34C2×C22⋊C4×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2211yescharacteristic
36#95×C47C2212yes—
37C24×C47C2311yescharacteristic
38C23×D47C2311yescharacteristic
39C22×C4×C47—22no—
40C22×C4×C47—42no—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2312yes—
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2312yes—
45C2×C22⋊D47—22no—
46C2×C22⋊D47—22no—
47C2×C22⋊D47Q814yes—
48C22×Dic47—24no—
49C22×Dic47—22no—
50C22×Dic47—42no—
51C22×Dic47D414yes—
52C22×Dic47C2312yes—
53C22×Dic47C2312yes—
54C22×Dic47C2311yescharacteristic
55C22×Dic47C2311yescharacteristic
56C22×Dic47C2311yescharacteristic
57C2×C4×D47—22no—
58C2×C4×D47—24no—
59C4⋊C4×C47—42no—
60C22⋊C4×C47—22no—
61C22⋊C4×C47—22no—
62C22⋊Dic47—22no—
63(C2×D47)⋊C4—22no—
64(C2×D47)⋊C4—42no—
65(C2×D47)⋊C4—42no—
66Dic47⋊C4—24no—
67Dic47⋊C4—24no—
68Dic47⋊C4—22no—
69Dic47⋊C4—24no—
70Dic47⋊C4—42no—
71C4×Dic47—22no—
72C23×C47—22no—
73C23×C47—22no—
74C23×C47C2×D412yes—
75C23×C47C2×Q812yes—
76C23×C47#4112yes—
77C23×C47C2411yescharacteristic
78C22×D47—21no—
79C22×D47—22no—
80C22×D47—21no—
81C22×D47—22no—
82C22×D47C2×Q812yes—
83C2×C4×C47—21no—
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×C47—22no—
93C2×C4×C47—44no—
94C22⋊D47—28no—
95C2×Dic47—21no—
96C2×Dic47—22no—
97C2×Dic47—21no—
98C2×Dic47—28no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—44no—
106C2×Dic47C2×D412yes—
107C2×Dic47C2×D412yes—
108C2×Dic47C2×Q812yes—
109C2×Dic47#4114yes—
110C4×D47—44no—
111C22×C47—22no—
112C22×C47—22no—
113C22×C47—24no—
114C22×C47—24no—
115C22×C47C22⋊Q814yes—
116C22×C47C22×D411yescharacteristic
117C22×C47C22×Q811yescharacteristic
118C22×C47C2×#4112yes—
119C22×C47C2×#4111yescharacteristic
120C22×C47H(5,𝔽2)12yes—
121C2×D47—22no—
122C2×D47—24no—
123C2×D47—41no—
124C2×D47—41no—
125C2×D47—42no—
126C4×C47—41no—
127C4×C47—41no—
128C4×C47—42no—
129C4×C47—42no—
130Dic47—22no—
131Dic47—22no—
132Dic47—42no—
133Dic47—42no—
134Dic47#12314yes—
135#2487—471nomaximal, Sylow
136C2×C47—24no—
137C2×C47C2×C22⋊Q811yescharacteristic
138C2×C47C2×#12311yescharacteristic
139C2×C47#53511yescharacteristic
140C2×C47#55312yes—
141C2×C47#55412yes—
142D47—42no—
143C2×C4×D4—471no—
144C22×C4⋊C4—471no—
145#400—472no—
146#399—472no—
147#389—472no—
148#386—471no—
149#386—471no—
150#385—471no—
151#385D4711yescharacteristic, complemented
152#380—471no—
153#380—472no—
154C47#248711yescharacteristic, complemented, Sylow
155C22×D4—471no—
156C23×C4—471no—
157C23×C4—471no—
158C23×C4—471no—
159C23×C4C2×D4711yescharacteristic
160C4×D4—944no—
161C2×C4⋊C4—472no—
162C2×C4⋊C4—472no—
163C2×C4⋊C4—471no—
164C2×C4⋊C4—472no—
165C2×C4⋊C4—472no—
166C2×C4⋊C4—944no—
167C2×C4⋊C4C2×D4712yes—
168C2×C22⋊C4—471no—
169C2×C22⋊C4—471no—
170C2×C22⋊C4—472no—
171C2×C22⋊C4—472no—
172C2×C22⋊C4C2×D4711yescharacteristic
173C2×C22⋊C4C2×D4711yescharacteristic
174C2×C42—471no—
175#95—472no—
176#95—472no—
177#95—472no—
178#95—472no—
179#95C2×D4712yes—
180C24—471no—
181C24C22×D4711yescharacteristic
182C2×D4—474no—
183C2×D4—942no—
184C2×D4—942no—
185C22×C4—22no—
186C22×C4—42no—
187C22×C4—471no—
188C22×C4—474no—
189C22×C4—471no—
190C22×C4—471no—
191C22×C4—472no—
192C22×C4—472no—
193C22×C4—942no—
194C22×C4—944no—
195C22×C4—944no—
196C22×C4—942no—
197C22×C4—1882no—
198C22×C4C22×D4711yescharacteristic
199C22×C4C22×D4712yes—
200C22×C4C22×D4712yes—
201C22×C4C22×D4711yescharacteristic
202C4⋊C4—42no—
203C4⋊C4—944no—
204C4⋊C4—944no—
205C4⋊C4—944no—
206C4⋊C4—942no—
207C4⋊C4—1882no—
208C22⋊C4—22no—
209C22⋊C4—22no—
210C22⋊C4—942no—
211C22⋊C4—942no—
212C22⋊C4—1882no—
213C22⋊C4—1882no—
214C42—942no—
215C23—22no—
216C23—22no—
217C23—472no—
218C23—941no—
219C23—942no—
220C23—941no—
221C23—942no—
222C23#1062535012yes—
223C23D4×D4712yes—
224C23Q8×D4712yes—
225C23C23×D4711yescharacteristic
226D4—948no—
227C2×C4—21no—
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—22no—
237C2×C4—44no—
238C2×C4—472no—
239C2×C4—474no—
240C2×C4—472no—
241C2×C4—472no—
242C2×C4—948no—
243C2×C4—941no—
244C2×C4—942no—
245C2×C4—941no—
246C2×C4—942no—
247C2×C4—942no—
248C2×C4—942no—
249C2×C4—942no—
250C2×C4—942no—
251C2×C4—942no—
252C2×C4—1884no—
253C2×C4—1884no—
254C22—24no—
255C22—24no—
256C22—22no—
257C22—22no—
258C22—944no—
259C22—942no—
260C22—1882no—
261C22—1881no—
262C22—1881no—
263C22#1309400214yes—
264C22C2×D4×D4711yescharacteristic
265C22C2×Q8×D4711yescharacteristic
266C22#41×D4712yes—
267C22C2×#1062535011yescharacteristic
268C22#1309406912yes—
269C4—42no—
270C4—41no—
271C4—42no—
272C4—41no—
273C4—474no—
274C4—942no—
275C4—942no—
276C4—1882no—
277C4—1882no—
278C2—24no—
279C2—1882no—
280C2C2×#1309400211yescharacteristic
281C2#123×D4711yescharacteristic
282C2#1568968811yescharacteristic
283C2#1568982212yes—
284C2#1568982712yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#385C2
hypercenter#385D47
hypocenterC47#2487
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C22×Dic47⋊C4C2semidirect
3. #15689064C2semidirect
4. #15689058C2semidirect
5. #15689018C2semidirect
8. #15688995C2semidirect
9. #15688982C2semidirect
10. #15688981C2semidirect
11. C47×#385C2semidirect
151. #385D47semidirect
154. C47#2487semidirect