Finite Group Databasebeta

← #20254958

Subgroups — #20254958

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×#13094056C211yesmaximal, characteristic, complemented
2Q8×C22⋊D47C211yesmaximal, characteristic, complemented
3#15689784C211yesmaximal, characteristic
4#15689516C211yesmaximal, characteristic, complemented
5#15689378C211yesmaximal, characteristic, complemented
6#15689352C211yesmaximal, characteristic, complemented
7#15689347C211yesmaximal, characteristic, complemented
8#15689331C211yesmaximal, characteristic, complemented
9#15689284C211yesmaximal, characteristic, complemented
10#15689279C211yesmaximal, characteristic, complemented
11#15689277C211yesmaximal, characteristic, complemented
12#15689262C211yesmaximal, characteristic, complemented
13#15689230C211yesmaximal, characteristic, complemented
14#15689194C211yesmaximal, characteristic, complemented
15C22×Q16×C47C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18#13094056—24no—
19C2×#10625337C2211yescharacteristic
20C2×#10625337C2211yescharacteristic
21C2×#10625325C2211yescharacteristic
22C2×#10625336C2211yescharacteristic
23C2×#10625336C2211yescharacteristic
24C2×#10625324C2211yescharacteristic
25#13094022—21no—
26#13094022C2211yescharacteristic
27#13094013—21no—
28#13094013C2211yescharacteristic
29#13094003—21no—
30#13094003C2211yescharacteristic
31#13094000—21no—
32#13094000—21no—
33#13094000C2211yescharacteristic
34#13094000C2211yescharacteristic
35#13093998—21no—
36#13093998C2211yescharacteristic
37Q8×Dic47C2211yescharacteristic
38Q8×Dic47C2211yescharacteristic
39C4×C22⋊D47—21no—
40C4×C22⋊D47—21no—
41C4×C22⋊D47C2211yescharacteristic
42#13093956C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093948C2211yescharacteristic
48#13093948C2211yescharacteristic
49#13093946C2211yescharacteristic
50C22⋊(C47⋊C8)C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic
52#13093934C2211yescharacteristic
53C22×Q8×C47C2211yescharacteristic
54C22×Q8×C47C2211yescharacteristic
55C2×Q16×C47—24no—
56C2×Q16×C47C2211yescharacteristic
57C2×Q16×C47C2211yescharacteristic
58C2×Q16×C47C2211yescharacteristic
59C2×Q16×C47C2211yescharacteristic
60C22×C8×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×Q8×C47C2311yescharacteristic
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47C2311yescharacteristic
74C2×C22⋊D47—21no—
75C2×C22⋊D47D411yescharacteristic
76#10625354—22no—
77#10625354—41no—
78Q8×D47—22no—
79Q8×D47—41no—
80C2×D188—21no—
81C2×D188C2311yescharacteristic
82C2×C4×D47—21no—
83C2×C4×D47—21no—
84C2×C4×D47C2311yescharacteristic
85C2×Dic94—21no—
86C2×Dic94C2311yescharacteristic
87Q16×C47—22no—
88Q16×C47—22no—
89Q16×C47—22no—
90Q16×C47D414yescomplemented
91C2×C8×C47—22no—
92C2×C8×C47C2311yescharacteristic
93C2×C8×C47C2311yescharacteristic
94C22⋊Dic47—21no—
95C22⋊Dic47D411yescharacteristic
96#10625337—22no—
97#10625337—41no—
98#10625336—22no—
99#10625336—41no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104(C2×D47)⋊C4—21no—
105(C2×D47)⋊C4D411yescharacteristic
106C4⋊Dic47—21no—
107C4⋊Dic47—21no—
108C4⋊Dic47C2311yescharacteristic
109C4⋊Dic47C2311yescharacteristic
110Dic47⋊C4—21no—
111Dic47⋊C4—21no—
112Dic47⋊C4—21no—
113Dic47⋊C4—21no—
114Dic47⋊C4—21no—
115Dic47⋊C4D411yescharacteristic
116C4×Dic47—21no—
117C4×Dic47—21no—
118C4×Dic47C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120C2×C47⋊C8C2311yescharacteristic
121#10625325—22no—
122#10625324—22no—
123C23×C47C2×D411yescharacteristic
124C22×D47—21no—
125C22×D47C2×D411yescharacteristic
126Q8×C47—21no—
127Q8×C47—21no—
128Q8×C47—21no—
129Q8×C47—21no—
130Q8×C47—21no—
131Q8×C47—21no—
132Q8×C47—42no—
133Q8×C47—42no—
134Q8×C47C2×D412yes—
135Q8×C47C2×D412yes—
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—42no—
143C2×C4×C47—42no—
144C2×C4×C47C2×D411yescharacteristic
145C2×C4×C47C2411yescharacteristic
146C22⋊D47—22no—
147C22⋊D47—42no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47C2×D411yescharacteristic
152C2×Dic47C2×D411yescharacteristic
153C2×Dic47C2×D411yescharacteristic
154D188—21no—
155D188—21no—
156D188—42no—
157C4×D47—21no—
158C4×D47—21no—
159C4×D47—42no—
160C4×D47—42no—
161Dic94—21no—
162Dic94—21no—
163Dic94—42no—
164C8×C47—21no—
165C8×C47C2×D412yes—
166C47⋊C8—21no—
167C47⋊C8—21no—
168C22×C47—21no—
169C22×C47—21no—
170C22×C47#13712yescomplemented
171C22×C47C22×D411yescharacteristic
172C2×D47—21no—
173C2×D47—21no—
174C2×D47—21no—
175C2×D47—41no—
176C2×D47—41no—
177C2×D47—41no—
178C4×C47—22no—
179C4×C47—22no—
180C4×C47—21no—
181C4×C47—41no—
182C4×C47—41no—
183C4×C47C22×D411yescharacteristic
184C4×C47H(5,𝔽2)11yescharacteristic
185Dic47—21no—
186Dic47—21no—
187Dic47—21no—
188Dic47—41no—
189Dic47—41no—
190Dic47—41no—
191#3270—471nomaximal, Sylow
192C2×C47—22no—
193C2×C47D4211yescharacteristic
194C2×C47C2×#13711yescharacteristic
195C2×C47#57811yescharacteristic
196D47—41no—
197D47—81no—
198C2×#137—471no—
199C22×Q16D4711yescharacteristic, complemented
200D4×Q8—471no—
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—24no—
220C2×Q16—471no—
221C2×Q16—471no—
222C2×Q16C2×D4711yescharacteristic
223C2×Q16C2×D4711yescharacteristic
224C2×Q16C2×D4711yescharacteristic
225C2×Q16C2×D4711yescharacteristic
226C2×SD16—471no—
227C2×SD16—471no—
228C2×SD16—471no—
229C2×M16—471no—
230C22×C8C2×D4711yescharacteristic
231C4⋊Q8—471no—
232C4⋊Q8—941no—
233#124—471no—
234#124—941no—
235C22⋊Q8—471no—
236C22⋊Q8—471no—
237C22⋊Q8—471no—
238C22⋊Q8—941no—
239C22⋊Q8—941no—
240C22⋊Q8—941no—
241#121—471no—
242#121—941no—
243C4×Q8—471no—
244C4×Q8—471no—
245C4×D4—471no—
246C4×D4—941no—
247C4×D4—941no—
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—941no—
269C2×Q8—942no—
270C2×Q8—1881no—
271C2×Q8C22×D4711yescharacteristic
272C2×Q8C22×D4711yescharacteristic
273C2×Q8C22×D4711yescharacteristic
274C2×Q8C22×D4711yescharacteristic
275C2×D4—471no—
276C2×D4—471no—
277C2×D4—941no—
278C2×D4—941no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—471no—
282C22×C4—941no—
283C22×C4—941no—
284C22×C4C22×D4711yescharacteristic
285Q16—22no—
286Q16—22no—
287Q16—22no—
288Q16—942no—
289Q16—1881no—
290Q16C22⋊D4714yescomplemented
291SD16—942no—
292SD16—942no—
293SD16—1881no—
294M16—942no—
295C2×C8—22no—
296C2×C8—471no—
297C2×C8—471no—
298C2×C8C22×D4711yescharacteristic
299C2×C8C22×D4711yescharacteristic
300C4⋊C4—471no—
301C4⋊C4—471no—
302C4⋊C4—471no—
303C4⋊C4—941no—
304C4⋊C4—941no—
305C4⋊C4—941no—
306C4⋊C4—941no—
307C4⋊C4—941no—
308C4⋊C4—941no—
309C4⋊C4—941no—
310C22⋊C4—471no—
311C22⋊C4—471no—
312C22⋊C4—941no—
313C22⋊C4—941no—
314C22⋊C4—941no—
315C22⋊C4—941no—
316C22⋊C4—941no—
317C22⋊C4—941no—
318C42—471no—
319C42—941no—
320C42—941no—
321C23—471no—
322C23—941no—
323C23D4×D4711yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—21no—
330Q8—42no—
331Q8—42no—
332Q8—941no—
333Q8—941no—
334Q8—1882no—
335Q8C2×C22⋊D4712yes—
336Q8C2×C22⋊D4712yes—
337D4—942no—
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—42no—
349C2×C4—42no—
350C2×C4—471no—
351C2×C4—471no—
352C2×C4—471no—
353C2×C4—941no—
354C2×C4—941no—
355C2×C4—941no—
356C2×C4—941no—
357C2×C4—941no—
358C2×C4—1882no—
359C2×C4—1882no—
360C2×C4D4×D4711yescharacteristic
361C2×C4C23×D4711yescharacteristic
362C8—21no—
363C8—941no—
364C8—941no—
365C8C2×C22⋊D4712yes—
366C22—21no—
367C22—21no—
368C22—941no—
369C22—941no—
370C22—941no—
371C22—1881no—
372C22—1881no—
373C22—1881no—
374C22#1309405612yescomplemented
375C22C2×D4×D4711yescharacteristic
376C4—21no—
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—941no—
382C4—941no—
383C4—941no—
384C4—1881no—
385C4—1881no—
386C4—1881no—
387C4C22×C22⋊D4711yescharacteristic
388C4#1309406911yescharacteristic
389C2—22no—
390C2—3761no—
391C2—1881no—
392C2D4×C22⋊D4711yescharacteristic
393C2C2×#1309405611yescharacteristic
394C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC22×Q16×C47C2
socleC22×C47C22×D4
hypercenterC22×Q16D47
hypocenterC47#3270
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#13094056C2semidirect
2. Q8×C22⋊D47C2semidirect
4. #15689516C2semidirect
5. #15689378C2semidirect
6. #15689352C2semidirect
7. #15689347C2semidirect
8. #15689331C2semidirect
9. #15689284C2semidirect
10. #15689279C2semidirect
11. #15689277C2semidirect
12. #15689262C2semidirect
13. #15689230C2semidirect
14. #15689194C2semidirect
15. C22×Q16×C47C2semidirect
90. Q16×C47D4semidirect
170. C22×C47#137semidirect
199. C22×Q16D47semidirect
213. C47#3270semidirect
290. Q16C22⋊D47semidirect
374. C22#13094056semidirect