Finite Group Databasebeta

← #394×D47 #20246590

Subgroups — #394×D47 #20246590

Order 6016.

1252 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D47C211yesmaximal, characteristic
2C2×C4⋊C4×D47C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D47C212yesmaximal, complemented
4C2×C22⋊C4×D47C212yesmaximal, complemented
5#15689041C211yesmaximal, characteristic, complemented
6#15689040C211yesmaximal, characteristic, complemented
7#15689039C212yesmaximal, complemented
8#15689038C212yesmaximal, complemented
9#15689037C211yesmaximal, characteristic, complemented
10#95×D47C211yesmaximal, characteristic, complemented
11C47×#394C211yesmaximal, characteristic, complemented
12C24×D47C2212yes—
13C22×D188C2211yescharacteristic
14C22×C22⋊D47C2212yes—
15C2×D4×D47—28no—
16C2×D4×D47—24no—
17C22×C4×D47C2212yes—
18C22×C4×D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic, complemented
22C2×Dic47⋊C4C2211yescharacteristic, complemented
23C2×Dic47⋊C4C2211yescharacteristic, complemented
24C4⋊C4×D47—24no—
25C2×C22⋊Dic47C2212yescomplemented
26C2×C22⋊Dic47C2212yescomplemented
27C2×(C2×D47)⋊C4C2212yescomplemented
28C2×(C2×D47)⋊C4C2212yescomplemented
29C2×(C2×D47)⋊C4C2212yescomplemented
30C2×(C2×D47)⋊C4C2212yescomplemented
31C22⋊C4×D47—28no—
32C22⋊C4×D47—28no—
33C47⋊#95C2211yescharacteristic, complemented
34C47⋊#95C2212yescomplemented
35C22×D4×C47C2211yescharacteristic
36C2×C4⋊C4×C47C2211yescharacteristic, complemented
37C2×C22⋊C4×C47C2212yescomplemented
38C2×C22⋊C4×C47C2212yescomplemented
39#95×C47C2211yescharacteristic, complemented
40C24×C47C2312yes—
41C23×D47—24no—
42C23×D47—24no—
43C23×D47—24no—
44C23×D47—24no—
45C23×D47—24no—
46C23×D47—24no—
47C23×D47D418yes—
48C23×D47C2312yes—
49C23×D47C2311yescharacteristic
50C2×D4×C47—24no—
51C2×D4×C47—22no—
52C22×C4×C47C2311yescharacteristic
53C22×C4×C47C2312yes—
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C2×C22⋊D47—24no—
57C2×C22⋊D47—24no—
58C2×C22⋊D47—24no—
59C22×Dic47C2312yes—
60C22×Dic47C2311yescharacteristic
61C22×Dic47C2311yescharacteristic
62C22×Dic47C2311yescharacteristic
63D4×D47—232no—
64C2×D188—24no—
65C2×D188—22no—
66C2×C4×D47—22no—
67C2×C4×D47—24no—
68C2×C4×D47—22no—
69C2×C4×D47—24no—
70C2×C4×D47—24no—
71C2×C4×D47—24no—
72C2×C4×D47—22no—
73C2×C4×D47—24no—
74C2×C4×D47D414yes—
75C2×C4×D47D414yescomplemented
76C4⋊C4×C47—22no—
77C22⋊C4×C47—24no—
78C22⋊C4×C47—24no—
79C22⋊Dic47—24no—
80C22⋊Dic47—24no—
81(C2×D47)⋊C4—24no—
82(C2×D47)⋊C4—24no—
83(C2×D47)⋊C4—24no—
84(C2×D47)⋊C4—24no—
85C4⋊Dic47—22no—
86Dic47⋊C4—22no—
87Dic47⋊C4—22no—
88C23×C47—22no—
89C23×C47—22no—
90C23×C47—22no—
91C23×C47—22no—
92C23×C47—22no—
93C23×C47—22no—
94C23×C47C2×D414yes—
95C23×C47C2411yescharacteristic
96C22×D47—22no—
97C22×D47—22no—
98C22×D47—22no—
99C22×D47—22no—
100C22×D47—22no—
101C22×D47—22no—
102C22×D47—216no—
103C22×D47—216no—
104C22×D47—216no—
105C22×D47—48no—
106C22×D47—48no—
107C22×D47—48no—
108C22×D47—48no—
109C22×D47C2×D414yes—
110C22×D47C2×D414yes—
111C22×D47C2×D412yes—
112C22×D47C2×D412yes—
113C22×D47#4112yes—
114C22×D47#4114yes—
115D4×C47—28no—
116C2×C4×C47—21no—
117C2×C4×C47—22no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—22no—
121C2×C4×C47—22no—
122C2×C4×C47—22no—
123C2×C4×C47—22no—
124C2×C4×C47C2×D412yes—
125C2×C4×C47C2×D412yescomplemented
126C22⋊D47—216no—
127C2×Dic47—21no—
128C2×Dic47—22no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—22no—
132C2×Dic47—22no—
133C2×Dic47—22no—
134C2×Dic47—22no—
135C2×Dic47C2×D412yes—
136C2×Dic47C2×D412yescomplemented
137D188—28no—
138C4×D47—28no—
139C4×D47—28no—
140C4×D47—44no—
141C4×D47—48no—
142C22×C47—24no—
143C22×C47—24no—
144C22×C47—24no—
145C22×C47—42no—
146C22×C47—42no—
147C22×C47—42no—
148C22×C47—42no—
149C22×C47C22×D412yes—
150C22×C47C22×D411yescharacteristic
151C22×C47C22×D411yescharacteristic
152C22×C47C2×#4111yescharacteristic
153C22×C47C2×#4112yes—
154C2×D47—24no—
155C2×D47—24no—
156C2×D47—24no—
157C2×D47—42no—
158C2×D47—42no—
159C2×D47—42no—
160C2×D47—42no—
161C2×D47—432no—
162C2×D47#12014yes—
163C2×D47#12114yes—
164C2×D47#12118yes—
165C2×D47#12318yes—
166C2×D47#12414yes—
167C4×C47—22no—
168C4×C47—22no—
169C4×C47—41no—
170C4×C47—42no—
171Dic47—22no—
172Dic47—22no—
173Dic47—41no—
174Dic47—42no—
175C2×#394—471nomaximal, Sylow
176C2×C47—44no—
177C2×C47C2×#12011yescharacteristic
178C2×C47C2×#12111yescharacteristic
179C2×C47C2×#12112yes—
180C2×C47C2×#12312yes—
181C2×C47C2×#12411yescharacteristic
182D47—44no—
183D47#39418yesdirect product factor
184C23×D4—471no—
185C22×C4⋊C4—471no—
186C22×C22⋊C4—472no—
187C22×C22⋊C4—472no—
188#394—471no—
189#394—471no—
190#394—472no—
191#394—472no—
192#394—471no—
193#394D4711yescharacteristic, direct product factor
194C2×#95—471no—
195C47C2×#39411yescharacteristic, complemented, Sylow
196C25—472no—
197C22×D4—472no—
198C22×D4—471no—
199C22×D4—944no—
200C22×D4—948no—
201C22×D4C2×D4711yescharacteristic
202C23×C4—471no—
203C23×C4—471no—
204C23×C4—471no—
205C23×C4—472no—
206C2×C4⋊C4—471no—
207C2×C4⋊C4—471no—
208C2×C4⋊C4—471no—
209C2×C4⋊C4—944no—
210C2×C4⋊C4C2×D4711yescharacteristic, complemented
211C2×C22⋊C4—472no—
212C2×C22⋊C4—472no—
213C2×C22⋊C4—472no—
214C2×C22⋊C4—472no—
215C2×C22⋊C4—472no—
216C2×C22⋊C4—472no—
217C2×C22⋊C4—948no—
218C2×C22⋊C4—948no—
219C2×C22⋊C4C2×D4712yescomplemented
220C2×C22⋊C4C2×D4712yescomplemented
221#95—472no—
222#95—471no—
223#95C2×D4711yescharacteristic, complemented
224C24—471no—
225C24—478no—
226C24—472no—
227C24—944no—
228C24—944no—
229C24—944no—
230C24—944no—
231C24—944no—
232C24—944no—
233C24C22×D4712yes—
234C2×D4—24no—
235C2×D4—22no—
236C2×D4—944no—
237C2×D4—944no—
238C2×D4—9432no—
239C2×D4—944no—
240C2×D4—944no—
241C2×D4—942no—
242C22×C4—471no—
243C22×C4—471no—
244C22×C4—474no—
245C22×C4—474no—
246C22×C4—472no—
247C22×C4—471no—
248C22×C4—942no—
249C22×C4—942no—
250C22×C4—944no—
251C22×C4—944no—
252C22×C4—944no—
253C22×C4—944no—
254C22×C4—942no—
255C22×C4—944no—
256C22×C4C22×D4712yes—
257C22×C4C22×D4711yescharacteristic
258C22×C4C22×D4711yescharacteristic
259C22×C4C22×D4711yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—942no—
262C4⋊C4—942no—
263C4⋊C4—942no—
264C22⋊C4—24no—
265C22⋊C4—24no—
266C22⋊C4—944no—
267C22⋊C4—944no—
268C22⋊C4—944no—
269C22⋊C4—944no—
270C22⋊C4—944no—
271C22⋊C4—944no—
272C23—22no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—22no—
278C23—472no—
279C23—472no—
280C23—474no—
281C23—472no—
282C23—474no—
283C23—474no—
284C23—9416no—
285C23—9416no—
286C23—9416no—
287C23—942no—
288C23—942no—
289C23—942no—
290C23—942no—
291C23—942no—
292C23—942no—
293C23—1888no—
294C23—1888no—
295C23—1888no—
296C23—1888no—
297C23D4×D4714yes—
298C23C23×D4711yescharacteristic
299D4—28no—
300D4—948no—
301D4—9416no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—472no—
311C2×C4—472no—
312C2×C4—948no—
313C2×C4—948no—
314C2×C4—941no—
315C2×C4—942no—
316C2×C4—941no—
317C2×C4—942no—
318C2×C4—942no—
319C2×C4—942no—
320C2×C4—941no—
321C2×C4—942no—
322C2×C4—1884no—
323C2×C4—1888no—
324C2×C4D4×D4712yes—
325C2×C4D4×D4712yescomplemented
326C22—24no—
327C22—24no—
328C22—24no—
329C22—42no—
330C22—42no—
331C22—42no—
332C22—42no—
333C22—474no—
334C22—474no—
335C22—478no—
336C22—478no—
337C22—474no—
338C22—944no—
339C22—944no—
340C22—944no—
341C22—18832no—
342C22—1882no—
343C22—1882no—
344C22—1882no—
345C22—1882no—
346C22C2×D4×D4712yes—
347C22C2×D4×D4711yescharacteristic
348C22C2×D4×D4711yescharacteristic
349C22#41×D4711yescharacteristic
350C22#41×D4712yes—
351C4—22no—
352C4—22no—
353C4—41no—
354C4—42no—
355C4—942no—
356C4—942no—
357C4—1881no—
358C4—1882no—
359C2—44no—
360C2—478no—
361C2—1884no—
362C2#120×D4711yescharacteristic
363C2#121×D4711yescharacteristic
364C2#121×D4712yes—
365C2#123×D4712yes—
366C2#124×D4711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#394C2
hypercenter#394D47
hypocenterC47C2×#394
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D47C2semidirect
3. C2×C22⋊C4×D47C2semidirect
4. C2×C22⋊C4×D47C2semidirect
5. #15689041C2semidirect
6. #15689040C2semidirect
7. #15689039C2semidirect
8. #15689038C2semidirect
9. #15689037C2semidirect
10. #95×D47C2semidirect
11. C47×#394C2semidirect
21. C2×C4⋊Dic47C22semidirect
22. C2×Dic47⋊C4C22semidirect
23. C2×Dic47⋊C4C22semidirect
25. C2×C22⋊Dic47C22semidirect
26. C2×C22⋊Dic47C22semidirect
27. C2×(C2×D47)⋊C4C22semidirect
28. C2×(C2×D47)⋊C4C22semidirect
29. C2×(C2×D47)⋊C4C22semidirect
30. C2×(C2×D47)⋊C4C22semidirect
33. C47⋊#95C22semidirect
34. C47⋊#95C22semidirect
36. C2×C4⋊C4×C47C22semidirect
37. C2×C22⋊C4×C47C22semidirect
38. C2×C22⋊C4×C47C22semidirect
39. #95×C47C22semidirect
75. C2×C4×D47D4semidirect
125. C2×C4×C47C2×D4semidirect
136. C2×Dic47C2×D4semidirect
183. D47#394direct (N × H)
193. #394D47direct (N × H)
195. C47C2×#394semidirect
210. C2×C4⋊C4C2×D47semidirect
219. C2×C22⋊C4C2×D47semidirect
220. C2×C22⋊C4C2×D47semidirect
223. #95C2×D47semidirect
325. C2×C4D4×D47semidirect