Finite Group Databasebeta

← #20249283

Subgroups — #20249283

Order 6016.

562 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13094018C211yesmaximal, characteristic, complemented
2#15689061C211yesmaximal, characteristic, complemented
3#15689058C211yesmaximal, characteristic, complemented
4#15689046C212yesmaximal, complemented
5#15689039C212yesmaximal, complemented
6#15689037C211yesmaximal, characteristic, complemented
7#15689031C211yesmaximal, characteristic
8#15689002C212yesmaximal, complemented
9#15688996C212yesmaximal, complemented
10#15688989C211yesmaximal, characteristic, complemented
11C2×C4×D4×C47C211yesmaximal, characteristic, complemented
12C22×C22⋊D47C2212yes—
13#13094018—24no—
14C2×C4⋊Dic47C2212yes—
15C2×Dic47⋊C4C2211yescharacteristic
16C2×Dic47⋊C4C2211yescharacteristic
17C2×Dic47⋊C4C2211yescharacteristic
18C2×Dic47⋊C4C2212yes—
19C2×C22⋊Dic47C2212yes—
20C2×C22⋊Dic47C2212yes—
21C2×C22⋊Dic47C2212yes—
22C2×(C2×D47)⋊C4C2211yescharacteristic
23C2×(C2×D47)⋊C4C2211yescharacteristic
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2212yes—
26C47⋊#95C2212yes—
27C47⋊#95C2211yescharacteristic
28C47⋊#95C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C22×D4×C47C2211yescharacteristic
32C23×C4×C47C2212yes—
33C4×D4×C47—24no—
34C2×C4⋊C4×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2212yes—
36C2×C42×C47C2211yescharacteristic
37C24×C47C2312yes—
38C23×D47C2311yescharacteristic
39C2×D4×C47—24no—
40C2×D4×C47—22no—
41C22×C4×C47—24no—
42C22×C4×C47—42no—
43C22×C4×C47—42no—
44C22×C4×C47C2312yes—
45C22×C4×C47C2311yescharacteristic
46C22×C4×C47C2311yescharacteristic
47C22×C4×C47C2311yescharacteristic
48C2×C22⋊D47—24no—
49C2×C22⋊D47—42no—
50C2×C22⋊D47—42no—
51C22×Dic47C2312yes—
52C22×Dic47C2311yescharacteristic
53C22×Dic47C2311yescharacteristic
54C22×Dic47C2312yes—
55C22×Dic47C2311yescharacteristic
56C4⋊C4×C47—22no—
57C22⋊C4×C47—24no—
58C42×C47D414yescomplemented
59C22⋊Dic47—24no—
60C22⋊Dic47—42no—
61C22⋊Dic47—42no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—22no—
64(C2×D47)⋊C4—22no—
65(C2×D47)⋊C4—42no—
66C4⋊Dic47—42no—
67Dic47⋊C4—22no—
68Dic47⋊C4—22no—
69Dic47⋊C4—22no—
70Dic47⋊C4—42no—
71C23×C47—22no—
72C23×C47—22no—
73C23×C47—22no—
74C23×C47—22no—
75C23×C47—22no—
76C23×C47—22no—
77C23×C47#4114yes—
78C23×C47C2411yescharacteristic
79C22×D47—21no—
80C22×D47—22no—
81C22×D47—22no—
82C22×D47—21no—
83C22×D47—21no—
84D4×C47—28no—
85C2×C4×C47—22no—
86C2×C4×C47—21no—
87C2×C4×C47—22no—
88C2×C4×C47—21no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—48no—
93C2×C4×C47C2×D412yes—
94C2×C4×C47C2×D412yes—
95C2×C4×C47C2×D412yes—
96C22⋊D47—48no—
97C2×Dic47—21no—
98C2×Dic47—21no—
99C2×Dic47—21no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47—22no—
107C2×Dic47—21no—
108C2×Dic47—22no—
109C2×Dic47—21no—
110C22×C47—24no—
111C22×C47—24no—
112C22×C47—24no—
113C22×C47—42no—
114C22×C47—42no—
115C22×C47—42no—
116C22×C47—42no—
117C22×C47C22×D411yescharacteristic
118C22×C47C2×#4112yes—
119C22×C47H(5,𝔽2)12yes—
120C22×C47H(5,𝔽2)11yescharacteristic
121C22×C472−1+411yescharacteristic
122C2×D47—41no—
123C2×D47—41no—
124C2×D47—41no—
125C2×D47—42no—
126C2×D47—42no—
127C4×C47—22no—
128C4×C47—22no—
129C4×C47—22no—
130C4×C47—42no—
131Dic47—41no—
132Dic47—41no—
133Dic47—41no—
134Dic47—42no—
135Dic47—42no—
136#2636—471nomaximal, Sylow
137C2×C47—44no—
138C2×C47#52511yescharacteristic
139C2×C47#53511yescharacteristic
140C2×C47#53711yescharacteristic
141C2×C47#53812yes—
142C2×C47#53912yes—
143D47—81no—
144C2×#126—471no—
145C2×C4×D4D4711yescharacteristic, complemented
146#400—471no—
147#399—471no—
148#396—472no—
149#394—471no—
150#394—472no—
151#392—471no—
152#386—472no—
153#385—472no—
154#382—471no—
155C47#263611yescharacteristic, complemented, Sylow
156C22×D4—472no—
157C22×D4C2×D4711yescharacteristic
158C23×C4C2×D4712yes—
159#126—944no—
160C4×D4—24no—
161C2×C4⋊C4—471no—
162C2×C4⋊C4—471no—
163C2×C4⋊C4—471no—
164C2×C4⋊C4—472no—
165C2×C4⋊C4—472no—
166C2×C4⋊C4C2×D4711yescharacteristic
167C2×C22⋊C4—472no—
168C2×C22⋊C4—471no—
169C2×C22⋊C4—471no—
170C2×C22⋊C4—471no—
171C2×C22⋊C4—472no—
172C2×C22⋊C4—472no—
173C2×C22⋊C4—472no—
174C2×C22⋊C4C2×D4712yes—
175C2×C42C2×D4711yescharacteristic
176#95—472no—
177#95—471no—
178#95—471no—
179#95—472no—
180#95—472no—
181C24—471no—
182C24C22×D4712yes—
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—944no—
186C2×D4—1882no—
187C2×D4—1882no—
188C22×C4—24no—
189C22×C4—42no—
190C22×C4—42no—
191C22×C4—472no—
192C22×C4—471no—
193C22×C4—471no—
194C22×C4—472no—
195C22×C4—471no—
196C22×C4C22×D4712yes—
197C22×C4C22×D4711yescharacteristic
198C22×C4C22×D4711yescharacteristic
199C22×C4C22×D4711yescharacteristic
200C4⋊C4—22no—
201C4⋊C4—942no—
202C4⋊C4—942no—
203C4⋊C4—942no—
204C4⋊C4—1882no—
205C4⋊C4—1882no—
206C22⋊C4—24no—
207C22⋊C4—944no—
208C22⋊C4—942no—
209C22⋊C4—942no—
210C22⋊C4—942no—
211C22⋊C4—1882no—
212C22⋊C4—1882no—
213C22⋊C4—1882no—
214C42C22⋊D4714yescomplemented
215C23—22no—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—941no—
222C23—942no—
223C23—942no—
224C23—941no—
225C23—941no—
226C23#1062535014yes—
227C23C23×D4711yescharacteristic
228D4—28no—
229D4—1888no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—48no—
238C2×C4—941no—
239C2×C4—941no—
240C2×C4—941no—
241C2×C4—942no—
242C2×C4—942no—
243C2×C4—942no—
244C2×C4—942no—
245C2×C4—942no—
246C2×C4—942no—
247C2×C4—941no—
248C2×C4—942no—
249C2×C4—942no—
250C2×C4—941no—
251C2×C4C2×C22⋊D4712yes—
252C2×C4C2×C22⋊D4712yes—
253C2×C4C2×C22⋊D4712yes—
254C22—24no—
255C22—24no—
256C22—24no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—1881no—
262C22—1881no—
263C22—1881no—
264C22—1882no—
265C22—1882no—
266C22C22×C22⋊D4711yescharacteristic
267C22C2×#1062535012yes—
268C22#1309406912yes—
269C22#1309407011yescharacteristic
270C22#1309407111yescharacteristic
271C4—22no—
272C4—22no—
273C4—22no—
274C4—42no—
275C4—1881no—
276C4—1881no—
277C4—1881no—
278C4—1882no—
279C4—1882no—
280C2—44no—
281C2—3761no—
282C2#1568963411yescharacteristic
283C2#1568969011yescharacteristic
284C2#1568970111yescharacteristic
285C2#1568970612yes—
286C2#1568971512yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C4×D4×C47C2
hypercenterC2×C4×D4D47
hypocenterC47#2636
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#13094018C2semidirect
2. #15689061C2semidirect
3. #15689058C2semidirect
4. #15689046C2semidirect
5. #15689039C2semidirect
6. #15689037C2semidirect
8. #15689002C2semidirect
9. #15688996C2semidirect
10. #15688989C2semidirect
11. C2×C4×D4×C47C2semidirect
58. C42×C47D4semidirect
145. C2×C4×D4D47semidirect
155. C47#2636semidirect
214. C42C22⋊D47semidirect