Finite Group Databasebeta

← #20246780

Subgroups — #20246780

Order 6016.

814 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13093992C211yesmaximal, characteristic
2C22×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D47C211yesmaximal, characteristic, complemented
4#15689049C212yesmaximal, complemented
5#15689039C212yesmaximal, complemented
6#15689003C211yesmaximal, characteristic, complemented
7#15688999C212yesmaximal, complemented
8#15688998C211yesmaximal, characteristic, complemented
9#15688986C211yesmaximal, characteristic, complemented
10#15688980C212yesmaximal, complemented
11C2×#123×C47C211yesmaximal, characteristic, complemented
12C24×D47C2211yescharacteristic
13C22×C22⋊D47C2211yescharacteristic
14C22×C22⋊D47C2211yescharacteristic
15C23×Dic47C2211yescharacteristic
16C22×C4×D47C2212yes—
17#13093992—24no—
18C2×C4⋊Dic47C2212yescomplemented
19C2×C22⋊Dic47C2211yescharacteristic
20C2×C22⋊Dic47C2211yescharacteristic
21C2×C22⋊Dic47C2212yescomplemented
22C2×(C2×D47)⋊C4—24no—
23C2×(C2×D47)⋊C4C2211yescharacteristic
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C22⋊C4×D47—24no—
29C47⋊#95C2212yescomplemented
30C47⋊#95C2212yescomplemented
31C47⋊#95C2212yescomplemented
32C47⋊#95C2212yescomplemented
33C22×D4×C47C2211yescharacteristic
34C23×C4×C47C2211yescharacteristic
35#123×C47—24no—
36C2×C4⋊C4×C47C2212yescomplemented
37C2×C22⋊C4×C47C2211yescharacteristic
38C2×C22⋊C4×C47C2212yescomplemented
39C24×C47C2311yescharacteristic
40C24×C47C2311yescharacteristic
41C23×D47—22no—
42C23×D47—22no—
43C23×D47—24no—
44C23×D47—42no—
45C23×D47D414yes—
46C23×D47C2311yescharacteristic
47C23×D47C2311yescharacteristic
48C2×D4×C47—22no—
49C2×D4×C47—22no—
50C2×D4×C47—22no—
51C22×C4×C47—22no—
52C22×C4×C47—22no—
53C22×C4×C47—22no—
54C22×C4×C47C2312yes—
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2312yes—
57C2×C22⋊D47—22no—
58C2×C22⋊D47—22no—
59C2×C22⋊D47—24no—
60C2×C22⋊D47—42no—
61C22×Dic47—22no—
62C22×Dic47—42no—
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2312yes—
65C22×Dic47C2312yes—
66C22×Dic47C2311yescharacteristic
67C2×C4×D47—24no—
68C2×C4×D47—24no—
69C2×C4×D47—42no—
70C4⋊C4×C47—24no—
71C22⋊C4×C47—24no—
72C22⋊C4×C47D414yescomplemented
73C22⋊Dic47—22no—
74C22⋊Dic47—22no—
75C22⋊Dic47—42no—
76(C2×D47)⋊C4—24no—
77(C2×D47)⋊C4—24no—
78(C2×D47)⋊C4—22no—
79(C2×D47)⋊C4—22no—
80(C2×D47)⋊C4—24no—
81C4⋊Dic47—42no—
82C23×C47—22no—
83C23×C47—22no—
84C23×C47—21no—
85C23×C47—21no—
86C23×C47—22no—
87C23×C47—21no—
88C23×C47—22no—
89C23×C47C2×D412yes—
90C23×C47C2×D412yes—
91C23×C47#4112yes—
92C23×C47C2411yescharacteristic
93C22×D47—21no—
94C22×D47—21no—
95C22×D47—22no—
96C22×D47—28no—
97C22×D47—21no—
98C22×D47—22no—
99C22×D47—21no—
100C22×D47—22no—
101C22×D47—28no—
102C22×D47—44no—
103C22×D47—48no—
104C22×D47—48no—
105C22×D47C2×D412yes—
106C22×D47C2×D412yes—
107C22×D47#4114yes—
108D4×C47—44no—
109C2×C4×C47—22no—
110C2×C4×C47—22no—
111C2×C4×C47—22no—
112C2×C4×C47—21no—
113C2×C4×C47—22no—
114C2×C4×C47—21no—
115C2×C4×C47—22no—
116C2×C4×C47—21no—
117C2×C4×C47—44no—
118C2×C4×C47C2×D414yes—
119C22⋊D47—44no—
120C22⋊D47—44no—
121C2×Dic47—22no—
122C2×Dic47—22no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—22no—
126C2×Dic47—22no—
127C2×Dic47—22no—
128C2×Dic47—22no—
129C2×Dic47—22no—
130C2×Dic47—22no—
131C2×Dic47—44no—
132C4×D47—48no—
133C22×C47—22no—
134C22×C47—22no—
135C22×C47—24no—
136C22×C47—24no—
137C22×C47—41no—
138C22×C47—41no—
139C22×C47—41no—
140C22×C47—42no—
141C22×C47—42no—
142C22×C47#12114yes—
143C22×C47C22×D411yescharacteristic
144C22×C47C22×D411yescharacteristic
145C22×C47C2×#4112yes—
146C22×C47C2×#4111yescharacteristic
147C22×C47H(5,𝔽2)12yes—
148C2×D47—22no—
149C2×D47—22no—
150C2×D47—24no—
151C2×D47—24no—
152C2×D47—22no—
153C2×D47—22no—
154C2×D47—22no—
155C2×D47—416no—
156C2×D47—42no—
157C2×D47—42no—
158C2×D47#12314yescomplemented
159C4×C47—24no—
160C4×C47—42no—
161C4×C47—41no—
162Dic47—41no—
163Dic47—42no—
164Dic47—41no—
165Dic47—42no—
166#2412—471nomaximal, Sylow
167C2×C47—24no—
168C2×C47—81no—
169C2×C47C2×#12111yescharacteristic
170C2×C47C2×#12311yescharacteristic
171C2×C47#53411yescharacteristic
172C2×C47#54612yes—
173C2×C47#55112yes—
174D47—24no—
175D47—42no—
176C2×#123D4711yescharacteristic, complemented
177C2×#120—471no—
178C22×C22⋊C4—471no—
179C22×C22⋊C4—471no—
180#397—472no—
181#394—472no—
182#386—471no—
183#386—472no—
184#385—471no—
185#381—471no—
186#380—472no—
187C47#241211yescharacteristic, complemented, Sylow
188C25—471no—
189C22×D4—471no—
190C22×D4—471no—
191C22×D4C2×D4711yescharacteristic
192C23×C4—471no—
193C23×C4—472no—
194C23×C4C2×D4711yescharacteristic
195#123—24no—
196#120—944no—
197C2×C4⋊C4—472no—
198C2×C4⋊C4C2×D4712yescomplemented
199C2×C22⋊C4—471no—
200C2×C22⋊C4—471no—
201C2×C22⋊C4—472no—
202C2×C22⋊C4—472no—
203C2×C22⋊C4—472no—
204C2×C22⋊C4—471no—
205C2×C22⋊C4—471no—
206C2×C22⋊C4—472no—
207C2×C22⋊C4—944no—
208C2×C22⋊C4—944no—
209C2×C22⋊C4C2×D4711yescharacteristic
210C2×C22⋊C4C2×D4712yescomplemented
211#95—472no—
212#95—472no—
213#95—472no—
214#95—472no—
215C24—471no—
216C24—471no—
217C24—474no—
218C24—944no—
219C24—942no—
220C24—942no—
221C24—1882no—
222C24C22×D4711yescharacteristic
223C24C22×D4711yescharacteristic
224C2×D4—22no—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—942no—
228C2×D4—942no—
229C2×D4—944no—
230C2×D4—1882no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—471no—
235C22×C4—472no—
236C22×C4—472no—
237C22×C4—471no—
238C22×C4—944no—
239C22×C4—942no—
240C22×C4—944no—
241C22×C4—1882no—
242C22×C4—1882no—
243C22×C4C22×D4712yes—
244C22×C4C22×D4711yescharacteristic
245C22×C4C22×D4712yes—
246C4⋊C4—24no—
247C4⋊C4—1882no—
248C22⋊C4—24no—
249C22⋊C4—944no—
250C22⋊C4—944no—
251C22⋊C4—942no—
252C22⋊C4—942no—
253C22⋊C4—942no—
254C22⋊C4—942no—
255C22⋊C4—944no—
256C22⋊C4—1882no—
257C22⋊C4C22⋊D4714yescomplemented
258C23—22no—
259C23—22no—
260C23—21no—
261C23—21no—
262C23—22no—
263C23—21no—
264C23—22no—
265C23—472no—
266C23—474no—
267C23—472no—
268C23—948no—
269C23—941no—
270C23—941no—
271C23—942no—
272C23—948no—
273C23—941no—
274C23—942no—
275C23—941no—
276C23—942no—
277C23—1884no—
278C23—1888no—
279C23—1888no—
280C23D4×D4712yes—
281C23#1062535212yes—
282C23C2×C22⋊D4712yes—
283C23C23×D4711yescharacteristic
284D4—44no—
285D4—1884no—
286D4—1884no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—44no—
296C2×C4—942no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—942no—
300C2×C4—942no—
301C2×C4—942no—
302C2×C4—942no—
303C2×C4—942no—
304C2×C4—942no—
305C2×C4—942no—
306C2×C4—1888no—
307C2×C4—1884no—
308C2×C4C2×C22⋊D4714yes—
309C22—24no—
310C22—24no—
311C22—22no—
312C22—22no—
313C22—42no—
314C22—42no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—474no—
319C22—944no—
320C22—944no—
321C22—942no—
322C22—942no—
323C22—942no—
324C22—942no—
325C22—942no—
326C22—18816no—
327C22—1882no—
328C22—1882no—
329C22#1309399514yes—
330C22C2×D4×D4711yescharacteristic
331C22C22×C22⋊D4711yescharacteristic
332C22#41×D4712yes—
333C22C2×#1062535211yescharacteristic
334C22#1309407012yes—
335C4—24no—
336C4—42no—
337C4—41no—
338C4—1882no—
339C4—1881no—
340C4—1882no—
341C4—1881no—
342C2—24no—
343C2—81no—
344C2—944no—
345C2—1882no—
346C2C2×#1309399511yescharacteristic
347C2#123×D4711yescharacteristic
348C2#1568968411yescharacteristic
349C2#1568976112yes—
350C2#1568979612yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#123×C47C2
hypercenterC2×#123D47
hypocenterC47#2412
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C22×(C2×D47)⋊C4C2semidirect
3. C2×C22⋊C4×D47C2semidirect
4. #15689049C2semidirect
5. #15689039C2semidirect
6. #15689003C2semidirect
7. #15688999C2semidirect
8. #15688998C2semidirect
9. #15688986C2semidirect
10. #15688980C2semidirect
11. C2×#123×C47C2semidirect
18. C2×C4⋊Dic47C22semidirect
21. C2×C22⋊Dic47C22semidirect
29. C47⋊#95C22semidirect
30. C47⋊#95C22semidirect
31. C47⋊#95C22semidirect
32. C47⋊#95C22semidirect
36. C2×C4⋊C4×C47C22semidirect
38. C2×C22⋊C4×C47C22semidirect
72. C22⋊C4×C47D4semidirect
158. C2×D47#123semidirect
176. C2×#123D47semidirect
187. C47#2412semidirect
198. C2×C4⋊C4C2×D47semidirect
210. C2×C22⋊C4C2×D47semidirect
257. C22⋊C4C22⋊D47semidirect