Finite Group Databasebeta

← #20247878

Subgroups — #20247878

Order 6016.

596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13093996C211yesmaximal, characteristic
2C22×Dic47⋊C4C211yesmaximal, characteristic, complemented
3#15689052C212yesmaximal, complemented
4#15689051C212yesmaximal, complemented
5#15689023C212yesmaximal, complemented
6#15689003C211yesmaximal, characteristic, complemented
7#15689002C211yesmaximal, characteristic, complemented
8#15689000C211yesmaximal, characteristic, complemented
9#15688987C212yesmaximal, complemented
10C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
11C47×#386C211yesmaximal, characteristic, complemented
12C22×C22⋊D47C2211yescharacteristic
13C22×C22⋊D47C2211yescharacteristic
14C23×Dic47C2211yescharacteristic
15C23×Dic47C2211yescharacteristic
16#13093996—24no—
17C2×Dic47⋊C4—24no—
18C2×Dic47⋊C4C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2212yes—
21C2×C22⋊Dic47C2211yescharacteristic
22C2×C22⋊Dic47C2211yescharacteristic
23C2×C22⋊Dic47C2212yes—
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2212yes—
27C2×C4×Dic47C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×D4×C47C2211yescharacteristic
33C23×C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2212yes—
36#95×C47C2212yes—
37C24×C47C2311yescharacteristic
38C24×C47C2311yescharacteristic
39C23×D47C2311yescharacteristic
40C2×D4×C47—22no—
41C2×D4×C47—22no—
42C2×D4×C47—22no—
43C22×C4×C47—22no—
44C22×C4×C47—42no—
45C22×C4×C47C2312yes—
46C22×C4×C47C2312yes—
47C22×C4×C47C2311yescharacteristic
48C2×C22⋊D47—22no—
49C2×C22⋊D47—22no—
50C2×C22⋊D47—22no—
51C2×C22⋊D47—22no—
52C2×C22⋊D47—24no—
53C22×Dic47—24no—
54C22×Dic47—22no—
55C22×Dic47—42no—
56C22×Dic47D414yes—
57C22×Dic47C2311yescharacteristic
58C22×Dic47C2312yes—
59C22×Dic47C2312yes—
60C22×Dic47C2311yescharacteristic
61C22×Dic47C2311yescharacteristic
62C22⋊C4×C47—22no—
63C22⋊C4×C47—42no—
64C22⋊Dic47—22no—
65C22⋊Dic47—22no—
66C22⋊Dic47—42no—
67(C2×D47)⋊C4—22no—
68(C2×D47)⋊C4—42no—
69(C2×D47)⋊C4—42no—
70Dic47⋊C4—24no—
71Dic47⋊C4—24no—
72Dic47⋊C4—22no—
73C4×Dic47—24no—
74C23×C47—22no—
75C23×C47—22no—
76C23×C47—21no—
77C23×C47—22no—
78C23×C47—21no—
79C23×C47—21no—
80C23×C47—22no—
81C23×C47C2×D412yes—
82C23×C47#4112yes—
83C23×C47#4112yes—
84C23×C47C2411yescharacteristic
85C22×D47—21no—
86C22×D47—22no—
87C22×D47—21no—
88C22×D47—21no—
89C22×D47—22no—
90D4×C47—44no—
91C2×C4×C47—22no—
92C2×C4×C47—21no—
93C2×C4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—22no—
98C2×C4×C47—22no—
99C2×C4×C47—22no—
100C2×C4×C47—44no—
101C22⋊D47—44no—
102C22⋊D47—44no—
103C2×Dic47—22no—
104C2×Dic47—28no—
105C2×Dic47—22no—
106C2×Dic47—21no—
107C2×Dic47—22no—
108C2×Dic47—22no—
109C2×Dic47—21no—
110C2×Dic47—21no—
111C2×Dic47—22no—
112C2×Dic47—22no—
113C2×Dic47—22no—
114C2×Dic47—44no—
115C2×Dic47C2×D412yes—
116C2×Dic47C2×D412yes—
117C2×Dic47#4114yes—
118C22×C47—22no—
119C22×C47—22no—
120C22×C47—24no—
121C22×C47—24no—
122C22×C47—41no—
123C22×C47—41no—
124C22×C47—41no—
125C22×C47—42no—
126C22×C47—42no—
127C22×C47#12414yes—
128C22×C47C22×D411yescharacteristic
129C22×C47C2×#4112yes—
130C22×C47C2×#4111yescharacteristic
131C22×C47C2×#4111yescharacteristic
132C22×C47H(5,𝔽2)12yes—
133C2×D47—41no—
134C2×D47—41no—
135C2×D47—41no—
136C2×D47—42no—
137C2×D47—42no—
138C4×C47—41no—
139C4×C47—42no—
140C4×C47—42no—
141Dic47—22no—
142Dic47—41no—
143Dic47—42no—
144Dic47—42no—
145Dic47#12314yes—
146#2504—471nomaximal, Sylow
147C2×C47—24no—
148C2×C47—81no—
149C2×C47C2×#12311yescharacteristic
150C2×C47C2×#12411yescharacteristic
151C2×C47#53511yescharacteristic
152C2×C47#55312yes—
153C2×C47#55312yes—
154D47—81no—
155C2×#121—471no—
156C22×C4⋊C4—471no—
157#397—472no—
158#397—472no—
159#390—472no—
160#386—471no—
161#386—471no—
162#386—471no—
163#386D4711yescharacteristic, complemented
164#382—472no—
165C4×C22⋊C4—471no—
166C47#250411yescharacteristic, complemented, Sylow
167C22×D4—471no—
168C22×D4—471no—
169C22×D4C2×D4711yescharacteristic
170C23×C4—471no—
171C23×C4—471no—
172C23×C4C2×D4711yescharacteristic
173#121—944no—
174C2×C4⋊C4—472no—
175C2×C4⋊C4—472no—
176C2×C4⋊C4—471no—
177C2×C4⋊C4—944no—
178C2×C22⋊C4—471no—
179C2×C22⋊C4—471no—
180C2×C22⋊C4—471no—
181C2×C22⋊C4—472no—
182C2×C22⋊C4—472no—
183C2×C22⋊C4—472no—
184C2×C22⋊C4C2×D4711yescharacteristic
185C2×C22⋊C4C2×D4712yes—
186C2×C42—472no—
187#95—472no—
188#95—472no—
189#95—472no—
190#95—472no—
191#95C2×D4712yes—
192C24—471no—
193C24C22×D4711yescharacteristic
194C24C22×D4711yescharacteristic
195C2×D4—22no—
196C2×D4—22no—
197C2×D4—22no—
198C2×D4—942no—
199C2×D4—944no—
200C2×D4—942no—
201C2×D4—942no—
202C2×D4—942no—
203C22×C4—22no—
204C22×C4—42no—
205C22×C4—471no—
206C22×C4—474no—
207C22×C4—471no—
208C22×C4—471no—
209C22×C4—472no—
210C22×C4—472no—
211C22×C4—944no—
212C22×C4—942no—
213C22×C4—1882no—
214C22×C4C22×D4711yescharacteristic
215C22×C4C22×D4712yes—
216C22×C4C22×D4712yes—
217C4⋊C4—944no—
218C4⋊C4—944no—
219C4⋊C4—942no—
220C22⋊C4—22no—
221C22⋊C4—42no—
222C22⋊C4—942no—
223C22⋊C4—942no—
224C22⋊C4—942no—
225C22⋊C4—1882no—
226C22⋊C4—1882no—
227C22⋊C4—1882no—
228C42—944no—
229C23—22no—
230C23—22no—
231C23—21no—
232C23—22no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—941no—
237C23—942no—
238C23—941no—
239C23—941no—
240C23—942no—
241C23#1062535012yes—
242C23D4×D4712yes—
243C23#1062535212yes—
244C23C23×D4711yescharacteristic
245D4—44no—
246D4—1884no—
247D4—1884no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—44no—
258C2×C4—472no—
259C2×C4—474no—
260C2×C4—472no—
261C2×C4—948no—
262C2×C4—942no—
263C2×C4—941no—
264C2×C4—942no—
265C2×C4—942no—
266C2×C4—941no—
267C2×C4—942no—
268C2×C4—941no—
269C2×C4—942no—
270C2×C4—942no—
271C2×C4—942no—
272C2×C4—1884no—
273C22—24no—
274C22—24no—
275C22—22no—
276C22—22no—
277C22—42no—
278C22—42no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—1882no—
283C22—1882no—
284C22—1881no—
285C22—1881no—
286C22—1881no—
287C22#1309401014yes—
288C22C2×D4×D4711yescharacteristic
289C22#41×D4712yes—
290C22C2×#1062535211yescharacteristic
291C22C2×#1062535011yescharacteristic
292C22#1309406912yes—
293C4—42no—
294C4—41no—
295C4—42no—
296C4—474no—
297C4—942no—
298C4—1882no—
299C4—1881no—
300C4—1882no—
301C2—24no—
302C2—81no—
303C2—3761no—
304C2#123×D4711yescharacteristic
305C2C2×#1309401011yescharacteristic
306C2#1568968811yescharacteristic
307C2#1568981612yes—
308C2#1568982212yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#386C2
hypercenter#386D47
hypocenterC47#2504
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C22×Dic47⋊C4C2semidirect
3. #15689052C2semidirect
4. #15689051C2semidirect
5. #15689023C2semidirect
6. #15689003C2semidirect
7. #15689002C2semidirect
8. #15689000C2semidirect
9. #15688987C2semidirect
10. C22⋊C4×Dic47C2semidirect
11. C47×#386C2semidirect
163. #386D47semidirect
166. C47#2504semidirect