Finite Group Databasebeta

← #20254959

Subgroups — #20254959

Order 6016.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094055C211yesmaximal, characteristic, complemented
2C22×#10625337C211yesmaximal, characteristic, complemented
3#15689782C211yesmaximal, characteristic
4#15689515C211yesmaximal, characteristic, complemented
5#15689379C211yesmaximal, characteristic, complemented
6#15689354C211yesmaximal, characteristic, complemented
7#15689345C211yesmaximal, characteristic, complemented
8#15689330C211yesmaximal, characteristic, complemented
9#15689283C211yesmaximal, characteristic, complemented
10#15689279C211yesmaximal, characteristic, complemented
11#15689278C211yesmaximal, characteristic, complemented
12#15689262C211yesmaximal, characteristic, complemented
13#15689228C211yesmaximal, characteristic, complemented
14#15689195C211yesmaximal, characteristic, complemented
15D4×Q8×C47C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18#13094055—24no—
19C2×#10625337—24no—
20C2×#10625337C2211yescharacteristic
21C2×#10625337C2211yescharacteristic
22C2×#10625337C2211yescharacteristic
23C2×#10625337C2211yescharacteristic
24C2×#10625337C2211yescharacteristic
25C2×#10625337C2211yescharacteristic
26C2×#10625336C2211yescharacteristic
27C2×#10625336C2211yescharacteristic
28C2×#10625336C2211yescharacteristic
29C2×#10625329C2211yescharacteristic
30C22×C47⋊C8C2211yescharacteristic
31#13094012C2211yescharacteristic
32#13094010—21no—
33#13094003C2211yescharacteristic
34#13094002—21no—
35#13093998C2211yescharacteristic
36#13093996—21no—
37C4×Dic94C2211yescharacteristic
38(C22⋊D47)⋊C4—21no—
39#13093955C2211yescharacteristic
40C4⋊(C47⋊C8)C2211yescharacteristic
41#13093948C2211yescharacteristic
42#13093948C2211yescharacteristic
43#13093948C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093944C2211yescharacteristic
47C22⋊(C47⋊C8)C2211yescharacteristic
48C22⋊(C47⋊C8)C2211yescharacteristic
49#13093935C2211yescharacteristic
50C22×Q8×C47C2211yescharacteristic
51C22×Q8×C47C2211yescharacteristic
52C4⋊Q8×C47—21no—
53C4⋊Q8×C47C2211yescharacteristic
54C22⋊Q8×C47—21no—
55C22⋊Q8×C47—21no—
56C22⋊Q8×C47C2211yescharacteristic
57C22⋊Q8×C47C2211yescharacteristic
58C4×Q8×C47C2211yescharacteristic
59C4×D4×C47—21no—
60C4×D4×C47C2211yescharacteristic
61C2×Q8×C47—21no—
62C2×Q8×C47—21no—
63C2×Q8×C47—22no—
64C2×Q8×C47—22no—
65C2×Q8×C47—41no—
66C2×Q8×C47—41no—
67C2×Q8×C47C2311yescharacteristic
68C2×Q8×C47C2311yescharacteristic
69C2×Q8×C47C2311yescharacteristic
70C2×D4×C47D411yescharacteristic
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47C2311yescharacteristic
74C22×C4×C47C2311yescharacteristic
75C2×C22⋊D47—21no—
76C2×C22⋊D47—21no—
77C22×Dic47—21no—
78#10625350—22no—
79#10625350—41no—
80C2×D188C2311yescharacteristic
81C2×C4×D47—21no—
82C2×Dic94—22no—
83C2×Dic94—21no—
84C2×Dic94—41no—
85C2×Dic94C2311yescharacteristic
86C2×Dic94C2311yescharacteristic
87C4⋊C4×C47—21no—
88C4⋊C4×C47—21no—
89C4⋊C4×C47—21no—
90C4⋊C4×C47—21no—
91C4⋊C4×C47—21no—
92C4⋊C4×C47D411yescharacteristic
93C4⋊C4×C47C2311yescharacteristic
94C22⋊C4×C47—21no—
95C22⋊C4×C47—21no—
96C22⋊C4×C47D411yescharacteristic
97C22⋊C4×C47D411yescharacteristic
98C42×C47—21no—
99C42×C47C2311yescharacteristic
100C22⋊Dic47—21no—
101#10625337—22no—
102#10625337—22no—
103#10625337—22no—
104#10625337—22no—
105#10625337—41no—
106#10625337D414yescomplemented
107#10625336—22no—
108#10625336—22no—
109#10625336—41no—
110(C2×D47)⋊C4—21no—
111(C2×D47)⋊C4—21no—
112(C2×D47)⋊C4—21no—
113C4⋊Dic47C2311yescharacteristic
114Dic47⋊C4—21no—
115Dic47⋊C4—21no—
116C4×Dic47—21no—
117#10625329—22no—
118C2×C47⋊C8—22no—
119C2×C47⋊C8C2311yescharacteristic
120C2×C47⋊C8C2311yescharacteristic
121C2×C47⋊C8C2311yescharacteristic
122C2×C47⋊C8C2311yescharacteristic
123C23×C47C2×D411yescharacteristic
124C23×C47C2×D411yescharacteristic
125C22×D47—21no—
126Q8×C47—21no—
127Q8×C47—21no—
128Q8×C47—21no—
129Q8×C47—21no—
130Q8×C47—21no—
131Q8×C47—42no—
132Q8×C47—42no—
133Q8×C47C2×D412yes—
134D4×C47—22no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—42no—
144C2×C4×C47—42no—
145C2×C4×C47C2×D411yescharacteristic
146C2×C4×C47C2×D411yescharacteristic
147C2×C4×C47C2×D411yescharacteristic
148C2×C4×C47C2×D411yescharacteristic
149C2×C4×C47C2411yescharacteristic
150C22⋊D47—42no—
151C22⋊D47—42no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—42no—
156D188—21no—
157D188—21no—
158C4×D47—42no—
159Dic94—21no—
160Dic94—21no—
161Dic94—21no—
162Dic94—42no—
163Dic94C2×D412yes—
164C47⋊C8—21no—
165C47⋊C8—21no—
166C47⋊C8—21no—
167C47⋊C8C2×D412yes—
168C22×C47—21no—
169C22×C47—21no—
170C22×C47—21no—
171C22×C47—21no—
172C22×C47—21no—
173C22×C47#13712yescomplemented
174C22×C47C22×D411yescharacteristic
175C2×D47—41no—
176C2×D47—41no—
177C2×D47—41no—
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—22no—
181C4×C47—21no—
182C4×C47—21no—
183C4×C47—41no—
184C4×C47—41no—
185C4×C47—41no—
186C4×C47C22×D411yescharacteristic
187C4×C47H(5,𝔽2)11yescharacteristic
188Dic47—22no—
189Dic47—41no—
190Dic47—41no—
191#3270—471nomaximal, Sylow
192C2×C47—22no—
193C2×C47—41no—
194C2×C47D4211yescharacteristic
195C2×C47C2×#13711yescharacteristic
196C2×C47#57811yescharacteristic
197D47—81no—
198C2×#137—471no—
199C22×Q16—471no—
200D4×Q8D4711yescharacteristic, complemented
201#548—471no—
202#497—471no—
203#470—471no—
204#465—471no—
205#464—471no—
206#462—471no—
207#452—471no—
208#451—471no—
209#451—471no—
210#448—471no—
211#441—471no—
212#435—471no—
213C47#327011yescharacteristic, complemented, Sylow
214C2×#41—471no—
215C22×Q8—471no—
216C22×Q8C2×D4711yescharacteristic
217C22×Q8C2×D4711yescharacteristic
218#137—944no—
219C2×Q16—471no—
220C2×Q16—471no—
221C2×Q16—471no—
222C2×Q16—471no—
223C2×Q16—471no—
224C2×Q16—471no—
225C2×Q16—944no—
226C2×SD16—471no—
227C2×SD16—471no—
228C2×SD16—471no—
229C2×M16—471no—
230C22×C8—471no—
231C4⋊Q8—21no—
232C4⋊Q8C2×D4711yescharacteristic
233#124—471no—
234#124—941no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C22⋊Q8—471no—
238C22⋊Q8—941no—
239C22⋊Q8C2×D4711yescharacteristic
240C22⋊Q8C2×D4711yescharacteristic
241#121—471no—
242#121—941no—
243C4×Q8—471no—
244C4×Q8C2×D4711yescharacteristic
245C4×D4—21no—
246C4×D4—941no—
247C4×D4C2×D4711yescharacteristic
248#106—471no—
249C4⋊C8—471no—
250#103—471no—
251#103—471no—
252#103—471no—
253#103—471no—
254#103—471no—
255#102—471no—
256C22⋊C8—471no—
257C22⋊C8—471no—
258#97—471no—
259#41—942no—
260#41—1881no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—22no—
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—471no—
268C2×Q8—471no—
269C2×Q8—942no—
270C2×Q8—941no—
271C2×Q8—1881no—
272C2×Q8C22×D4711yescharacteristic
273C2×Q8C22×D4711yescharacteristic
274C2×Q8C22×D4711yescharacteristic
275C2×D4—471no—
276C2×D4—941no—
277C2×D4—941no—
278C2×D4C22⋊D4711yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—941no—
282C22×C4—941no—
283C22×C4C22×D4711yescharacteristic
284C22×C4C22×D4711yescharacteristic
285Q16—474no—
286Q16—942no—
287Q16—942no—
288Q16—942no—
289Q16—942no—
290Q16—1881no—
291SD16—942no—
292SD16—942no—
293SD16—1881no—
294M16—942no—
295C2×C8—471no—
296C2×C8—471no—
297C2×C8—471no—
298C2×C8—471no—
299C2×C8—942no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—471no—
306C4⋊C4—941no—
307C4⋊C4—941no—
308C4⋊C4C22⋊D4711yescharacteristic
309C4⋊C4C22×D4711yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—941no—
313C22⋊C4—941no—
314C22⋊C4—941no—
315C22⋊C4—941no—
316C22⋊C4C22⋊D4711yescharacteristic
317C22⋊C4C22⋊D4711yescharacteristic
318C42—21no—
319C42—941no—
320C42C22×D4711yescharacteristic
321C23—941no—
322C23C2×C22⋊D4711yescharacteristic
323C23C2×C22⋊D4711yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—42no—
330Q8—42no—
331Q8—472no—
332Q8—941no—
333Q8—941no—
334Q8—941no—
335Q8—1882no—
336Q8D4×D4712yes—
337D4—22no—
338D4—941no—
339D4—941no—
340D4—1882no—
341D4—1882no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—941no—
353C2×C4—941no—
354C2×C4—941no—
355C2×C4—1882no—
356C2×C4—1882no—
357C2×C4C2×C22⋊D4711yescharacteristic
358C2×C4C2×C22⋊D4711yescharacteristic
359C2×C4C2×C22⋊D4711yescharacteristic
360C2×C4C2×C22⋊D4711yescharacteristic
361C2×C4C23×D4711yescharacteristic
362C8—472no—
363C8—941no—
364C8—941no—
365C8—941no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—1881no—
372C22—1881no—
373C22—1881no—
374C22#1309405512yescomplemented
375C22C22×C22⋊D4711yescharacteristic
376C4—21no—
377C4—21no—
378C4—22no—
379C4—21no—
380C4—21no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—942no—
385C4—1881no—
386C4—1881no—
387C4C2×D4×D4711yescharacteristic
388C4#1309406911yescharacteristic
389C2—22no—
390C2—41no—
391C2—3761no—
392C2D4×C22⋊D4711yescharacteristic
393C2C2×#1309405511yescharacteristic
394C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingD4×Q8×C47C2
socleC22×C47C22×D4
hypercenterD4×Q8D47
hypocenterC47#3270
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#13094055C2semidirect
2. C22×#10625337C2semidirect
4. #15689515C2semidirect
5. #15689379C2semidirect
6. #15689354C2semidirect
7. #15689345C2semidirect
8. #15689330C2semidirect
9. #15689283C2semidirect
10. #15689279C2semidirect
11. #15689278C2semidirect
12. #15689262C2semidirect
13. #15689228C2semidirect
14. #15689195C2semidirect
15. D4×Q8×C47C2semidirect
106. #10625337D4semidirect
173. C22×C47#137semidirect
200. D4×Q8D47semidirect
213. C47#3270semidirect
374. C22#13094055semidirect