Finite Group Databasebeta

← #20249330

Subgroups — #20249330

Order 6016.

584 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13094020C211yesmaximal, characteristic
2C2×#13094014C211yesmaximal, characteristic, complemented
3#15689041C211yesmaximal, characteristic, complemented
4#15689040C211yesmaximal, characteristic, complemented
5#15689039C212yesmaximal, complemented
6#15689038C212yesmaximal, complemented
7#15689037C211yesmaximal, characteristic, complemented
8#15689023C212yesmaximal, complemented
9#15689023C212yesmaximal, complemented
10#15688968C211yesmaximal, characteristic, complemented
11C47×#394C211yesmaximal, characteristic, complemented
12C22×D188C2211yescharacteristic
13C22×C22⋊D47C2212yes—
14C22×C22⋊D47C2212yes—
15#13094020—24no—
16#13094014—24no—
17C2×C4⋊Dic47C2211yescharacteristic
18C2×Dic47⋊C4C2211yescharacteristic
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×C22⋊Dic47C2212yes—
23C2×C22⋊Dic47C2212yes—
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2212yes—
28C2×C4×Dic47C2212yes—
29C2×C4×Dic47C2211yescharacteristic
30C47⋊#95C2211yescharacteristic
31C47⋊#95C2212yes—
32C22×D4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2212yes—
35C2×C22⋊C4×C47C2212yes—
36#95×C47C2211yescharacteristic
37C24×C47C2312yes—
38C23×D47C2312yes—
39C2×D4×C47—22no—
40C2×D4×C47—42no—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2312yes—
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—24no—
46C2×C22⋊D47—24no—
47C2×C22⋊D47—24no—
48C2×C22⋊D47—24no—
49C2×C22⋊D47—42no—
50C2×C22⋊D47—42no—
51C22×Dic47C2312yes—
52C22×Dic47C2311yescharacteristic
53C22×Dic47C2311yescharacteristic
54C22×Dic47C2311yescharacteristic
55C22×Dic47C2311yescharacteristic
56C2×D188—22no—
57C2×D188—42no—
58C4⋊C4×C47—22no—
59C22⋊C4×C47—42no—
60C22⋊C4×C47—42no—
61C22⋊Dic47—42no—
62C22⋊Dic47—42no—
63(C2×D47)⋊C4—42no—
64(C2×D47)⋊C4—42no—
65(C2×D47)⋊C4—42no—
66(C2×D47)⋊C4—42no—
67C4⋊Dic47—22no—
68Dic47⋊C4—22no—
69Dic47⋊C4—22no—
70Dic47⋊C4—22no—
71Dic47⋊C4—22no—
72C4×Dic47—24no—
73C4×Dic47D414yes—
74C23×C47—22no—
75C23×C47—22no—
76C23×C47—22no—
77C23×C47—22no—
78C23×C47—22no—
79C23×C47—22no—
80C23×C47—22no—
81C23×C47C2411yescharacteristic
82C22×D47—22no—
83C22×D47—22no—
84C22×D47—22no—
85C22×D47—22no—
86C22×D47—22no—
87C22×D47—22no—
88C22×D47—22no—
89D4×C47—44no—
90C2×C4×C47—22no—
91C2×C4×C47—21no—
92C2×C4×C47—21no—
93C2×C4×C47—22no—
94C2×C4×C47—21no—
95C2×C4×C47—22no—
96C2×C4×C47—22no—
97C2×C4×C47—22no—
98C2×C4×C47—21no—
99C2×C4×C47C2×D412yes—
100C22⋊D47—48no—
101C22⋊D47—48no—
102C2×Dic47—21no—
103C2×Dic47—21no—
104C2×Dic47—21no—
105C2×Dic47—21no—
106C2×Dic47—22no—
107C2×Dic47—21no—
108C2×Dic47—22no—
109C2×Dic47—22no—
110C2×Dic47—22no—
111C2×Dic47—21no—
112C2×Dic47C2×D412yes—
113C2×Dic47C2×D412yes—
114C2×Dic47#4114yes—
115D188—44no—
116C22×C47—42no—
117C22×C47—42no—
118C22×C47—42no—
119C22×C47—42no—
120C22×C47—42no—
121C22×C47—42no—
122C22×C47—42no—
123C22×C47C22×D411yescharacteristic
124C22×C47C2×#4112yes—
125C22×C47H(5,𝔽2)12yes—
126C22×C47H(5,𝔽2)11yescharacteristic
127C22×C47H(5,𝔽2)11yescharacteristic
128C2×D47—42no—
129C2×D47—42no—
130C2×D47—42no—
131C2×D47—42no—
132C2×D47—42no—
133C2×D47—42no—
134C2×D47—42no—
135C4×C47—22no—
136C4×C47—41no—
137C4×C47—41no—
138C4×C47—42no—
139Dic47—22no—
140Dic47—41no—
141Dic47—41no—
142Dic47—42no—
143Dic47#12414yes—
144#2641—471nomaximal, Sylow
145C2×C47—82no—
146C2×C47C2×#12411yescharacteristic
147C2×C47#53511yescharacteristic
148C2×C47#53511yescharacteristic
149C2×C47#54012yes—
150C2×C47#54012yes—
151D47—82no—
152C2×#127—471no—
153C2×#125—471no—
154#394—471no—
155#394—471no—
156#394—472no—
157#394—472no—
158#394—471no—
159#394D4711yescharacteristic, complemented
160#390—472no—
161#390—472no—
162#376—471no—
163C47#264111yescharacteristic, complemented, Sylow
164C22×D4—472no—
165C22×D4—472no—
166C22×D4—471no—
167C22×D4C2×D4711yescharacteristic
168#127—944no—
169#125—944no—
170C2×C4⋊C4—471no—
171C2×C4⋊C4—471no—
172C2×C4⋊C4—471no—
173C2×C4⋊C4—471no—
174C2×C4⋊C4—471no—
175C2×C4⋊C4C2×D4711yescharacteristic
176C2×C22⋊C4—472no—
177C2×C22⋊C4—472no—
178C2×C22⋊C4—472no—
179C2×C22⋊C4—472no—
180C2×C22⋊C4—472no—
181C2×C22⋊C4—472no—
182C2×C22⋊C4C2×D4712yes—
183C2×C22⋊C4C2×D4712yes—
184C2×C42—471no—
185C2×C42—472no—
186#95—472no—
187#95—471no—
188#95C2×D4711yescharacteristic
189C24—472no—
190C24C22×D4712yes—
191C2×D4—22no—
192C2×D4—42no—
193C2×D4—944no—
194C2×D4—944no—
195C2×D4—944no—
196C2×D4—944no—
197C2×D4—942no—
198C2×D4—1882no—
199C2×D4—1882no—
200C2×D4—1882no—
201C22×C4—471no—
202C22×C4—471no—
203C22×C4—472no—
204C22×C4—471no—
205C22×C4—471no—
206C22×C4C22×D4712yes—
207C22×C4C22×D4711yescharacteristic
208C22×C4C22×D4711yescharacteristic
209C22×C4C22×D4711yescharacteristic
210C4⋊C4—22no—
211C4⋊C4—942no—
212C4⋊C4—942no—
213C4⋊C4—942no—
214C4⋊C4—942no—
215C4⋊C4—942no—
216C22⋊C4—42no—
217C22⋊C4—42no—
218C22⋊C4—1882no—
219C22⋊C4—1882no—
220C22⋊C4—1882no—
221C22⋊C4—1882no—
222C22⋊C4—1882no—
223C22⋊C4—1882no—
224C42—474no—
225C42—944no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—942no—
234C23—942no—
235C23—942no—
236C23—942no—
237C23—942no—
238C23—942no—
239C23—942no—
240C23C23×D4711yescharacteristic
241D4—44no—
242D4—1884no—
243D4—1888no—
244D4—1888no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—472no—
255C2×C4—474no—
256C2×C4—472no—
257C2×C4—941no—
258C2×C4—941no—
259C2×C4—941no—
260C2×C4—941no—
261C2×C4—942no—
262C2×C4—942no—
263C2×C4—941no—
264C2×C4—942no—
265C2×C4—941no—
266C2×C4—942no—
267C2×C4D4×D4712yes—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—42no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—1882no—
276C22—1882no—
277C22—1882no—
278C22—1882no—
279C22—1882no—
280C22—1882no—
281C22—1882no—
282C22C2×D4×D4711yescharacteristic
283C22#41×D4712yes—
284C22#1309406912yes—
285C22#1309406911yescharacteristic
286C22#1309407011yescharacteristic
287C4—22no—
288C4—41no—
289C4—41no—
290C4—42no—
291C4—474no—
292C4—942no—
293C4—1881no—
294C4—1881no—
295C4—1882no—
296C2—82no—
297C2—3762no—
298C2#124×D4711yescharacteristic
299C2#1568968811yescharacteristic
300C2#1568968911yescharacteristic
301C2#1568972312yes—
302C2#1568972512yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#394C2
hypercenter#394D47
hypocenterC47#2641
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#13094014C2semidirect
3. #15689041C2semidirect
4. #15689040C2semidirect
5. #15689039C2semidirect
6. #15689038C2semidirect
7. #15689037C2semidirect
8. #15689023C2semidirect
9. #15689023C2semidirect
10. #15688968C2semidirect
11. C47×#394C2semidirect
159. #394D47semidirect
163. C47#2641semidirect