Finite Group Databasebeta

← #20255028

Subgroups — #20255028

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×#13094053C211yesmaximal, characteristic, complemented
2Q8×C22⋊D47C211yesmaximal, characteristic, complemented
3#15689772C211yesmaximal, characteristic
4#15689501C211yesmaximal, characteristic, complemented
5#15689381C211yesmaximal, characteristic, complemented
6#15689378C211yesmaximal, characteristic, complemented
7#15689331C211yesmaximal, characteristic, complemented
8#15689326C211yesmaximal, characteristic, complemented
9#15689285C211yesmaximal, characteristic, complemented
10#15689282C211yesmaximal, characteristic, complemented
11#15689279C211yesmaximal, characteristic, complemented
12#15689277C211yesmaximal, characteristic, complemented
13SD16×Dic47C211yesmaximal, characteristic, complemented
14#15689199C211yesmaximal, characteristic, complemented
15C2×#137×C47C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18#13094053—24no—
19C2×Dic188C2211yescharacteristic
20C2×#10625337C2211yescharacteristic
21C2×#10625337C2211yescharacteristic
22C2×#10625337C2211yescharacteristic
23C2×#10625335C2211yescharacteristic
24C2×#10625324C2211yescharacteristic
25#13094022—21no—
26#13094022C2211yescharacteristic
27#13094022C2211yescharacteristic
28#13094007—21no—
29#13094005—21no—
30#13094003—21no—
31#13094003C2211yescharacteristic
32#13094003C2211yescharacteristic
33#13094000—21no—
34#13094000C2211yescharacteristic
35#13094000C2211yescharacteristic
36#13093996—21no—
37Q8×Dic47C2211yescharacteristic
38D4×Dic47C2211yescharacteristic
39C4×C22⋊D47—21no—
40C4×C22⋊D47C2211yescharacteristic
41C2×Dic47⋊C4—21no—
42#13093956C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093948C2211yescharacteristic
48#13093948C2211yescharacteristic
49#13093945C2211yescharacteristic
50C22⋊(C47⋊C8)C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic
52C8×Dic47C2211yescharacteristic
53C2×#41×C47C2211yescharacteristic
54C22×Q8×C47C2211yescharacteristic
55#137×C47—24no—
56C2×Q16×C47C2211yescharacteristic
57C2×Q16×C47C2211yescharacteristic
58C2×SD16×C47C2211yescharacteristic
59C2×SD16×C47C2211yescharacteristic
60C2×M16×C47C2211yescharacteristic
61#41×C47—22no—
62#41×C47—41no—
63C2×Q8×C47—21no—
64C2×Q8×C47—22no—
65C2×Q8×C47—41no—
66C2×Q8×C47C2311yescharacteristic
67C2×Q8×C47C2311yescharacteristic
68C2×Q8×C47C2311yescharacteristic
69C2×D4×C47—21no—
70C2×D4×C47C2311yescharacteristic
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47C2311yescharacteristic
74C2×C22⋊D47—21no—
75C2×C22⋊D47D411yescharacteristic
76C22×Dic47—21no—
77C22×Dic47—21no—
78Q8×D47—22no—
79Q8×D47—41no—
80#10625352—22no—
81#10625352—41no—
82C2×C4×D47—21no—
83C2×C4×D47C2311yescharacteristic
84C2×Dic94—21no—
85C2×Dic94C2311yescharacteristic
86C2×Dic94C2311yescharacteristic
87Q16×C47—22no—
88Q16×C47—22no—
89SD16×C47—22no—
90SD16×C47D414yescomplemented
91M16×C47—22no—
92C2×C8×C47C2311yescharacteristic
93C2×C8×C47C2311yescharacteristic
94C22⋊Dic47—21no—
95C22⋊Dic47—21no—
96C22⋊Dic47—21no—
97C22⋊Dic47D411yescharacteristic
98#10625337—22no—
99#10625337—41no—
100#10625337—41no—
101#10625335—22no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104(C2×D47)⋊C4D411yescharacteristic
105C4⋊Dic47—21no—
106C4⋊Dic47C2311yescharacteristic
107C4⋊Dic47C2311yescharacteristic
108Dic47⋊C4—21no—
109Dic47⋊C4—21no—
110Dic47⋊C4—21no—
111Dic47⋊C4—21no—
112Dic47⋊C4—21no—
113Dic47⋊C4—21no—
114Dic47⋊C4—21no—
115Dic47⋊C4—21no—
116Dic47⋊C4D411yescharacteristic
117C4×Dic47—21no—
118C4×Dic47C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120C2×C47⋊C8C2311yescharacteristic
121Dic188—22no—
122#10625324—22no—
123C23×C47—21no—
124C23×C47C2×D411yescharacteristic
125C22×D47C2×D411yescharacteristic
126Q8×C47—21no—
127Q8×C47—21no—
128Q8×C47—21no—
129Q8×C47—21no—
130Q8×C47—21no—
131Q8×C47—42no—
132Q8×C47C2×D412yes—
133D4×C47—21no—
134D4×C47—42no—
135D4×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—42no—
142C2×C4×C47—42no—
143C2×C4×C47C2×D411yescharacteristic
144C2×C4×C47C2411yescharacteristic
145C22⋊D47—22no—
146C22⋊D47—42no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—42no—
152C2×Dic47—42no—
153C2×Dic47C2×D411yescharacteristic
154C2×Dic47C2×D411yescharacteristic
155C2×Dic47C2×D411yescharacteristic
156C4×D47—21no—
157C4×D47—21no—
158C4×D47—42no—
159Dic94—21no—
160Dic94—21no—
161Dic94—21no—
162Dic94—21no—
163Dic94—42no—
164C8×C47—21no—
165C8×C47C2×D412yes—
166C47⋊C8—21no—
167C47⋊C8—21no—
168C22×C47—22no—
169C22×C47—21no—
170C22×C47—21no—
171C22×C47—21no—
172C22×C47—41no—
173C22×C47—41no—
174C22×C47C22×D411yescharacteristic
175C2×D47—21no—
176C2×D47—21no—
177C2×D47—21no—
178C4×C47—22no—
179C4×C47—21no—
180C4×C47—41no—
181C4×C47—41no—
182C4×C47C22×D411yescharacteristic
183C4×C47H(5,𝔽2)11yescharacteristic
184Dic47—21no—
185Dic47—21no—
186Dic47—41no—
187Dic47—41no—
188Dic47—41no—
189Dic47—41no—
190Dic47#13712yescomplemented
191#3276—471nomaximal, Sylow
192C2×C47—41no—
193C2×C47—42no—
194C2×C47D4211yescharacteristic
195C2×C47C2×#13711yescharacteristic
196C2×C47#57811yescharacteristic
197D47—41no—
198C2×#137—471no—
199C2×#137D4711yescharacteristic, complemented
200D4×Q8—471no—
201#547—471no—
202#494—471no—
203#470—471no—
204#470—471no—
205#462—471no—
206#461—471no—
207#452—471no—
208#452—471no—
209#451—471no—
210#451—471no—
211C4×SD16—471no—
212#436—471no—
213C47#327611yescharacteristic, complemented, Sylow
214C2×#41—471no—
215C2×#41C2×D4711yescharacteristic
216C22×Q8—471no—
217C22×Q8C2×D4711yescharacteristic
218#137—24no—
219#137—944no—
220C2×Q16—471no—
221C2×Q16—471no—
222C2×Q16—471no—
223C2×Q16—471no—
224C2×Q16C2×D4711yescharacteristic
225C2×Q16C2×D4711yescharacteristic
226C2×SD16—471no—
227C2×SD16C2×D4711yescharacteristic
228C2×SD16C2×D4711yescharacteristic
229C2×M16—471no—
230C2×M16C2×D4711yescharacteristic
231C4⋊Q8—471no—
232C4⋊Q8—471no—
233C4⋊Q8—941no—
234#123—941no—
235#123—941no—
236C22⋊Q8—471no—
237C22⋊Q8—471no—
238C22⋊Q8—471no—
239C22⋊Q8—471no—
240C22⋊Q8—941no—
241C22⋊Q8—941no—
242#121—941no—
243C4×Q8—471no—
244C4×D4—471no—
245C4×D4—471no—
246C4×D4—941no—
247C2×C4⋊C4—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—
258C4×C8—471no—
259#41—22no—
260#41—41no—
261#41—942no—
262#41—1881no—
263C2×Q8—21no—
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—471no—
267C2×Q8—471no—
268C2×Q8—941no—
269C2×Q8—942no—
270C2×Q8—1881no—
271C2×Q8C22×D4711yescharacteristic
272C2×Q8C22×D4711yescharacteristic
273C2×Q8C22×D4711yescharacteristic
274C2×D4—21no—
275C2×D4—471no—
276C2×D4—941no—
277C2×D4C22×D4711yescharacteristic
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—471no—
281C22×C4—941no—
282C22×C4—941no—
283C22×C4—941no—
284C22×C4C22×D4711yescharacteristic
285Q16—22no—
286Q16—22no—
287Q16—942no—
288Q16—942no—
289Q16—1881no—
290Q16—1881no—
291SD16—22no—
292SD16—942no—
293SD16C22⋊D4714yescomplemented
294M16—22no—
295M16—942no—
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—
310C4⋊C4—941no—
311C4⋊C4—941no—
312C22⋊C4—471no—
313C22⋊C4—471no—
314C22⋊C4—941no—
315C22⋊C4—941no—
316C22⋊C4—941no—
317C22⋊C4—941no—
318C22⋊C4—941no—
319C42—471no—
320C42—941no—
321C23—21no—
322C23—471no—
323C23D4×D4711yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—42no—
330Q8—941no—
331Q8—941no—
332Q8—941no—
333Q8—941no—
334Q8—1882no—
335Q8C2×C22⋊D4712yes—
336D4—21no—
337D4—42no—
338D4—942no—
339D4—1882no—
340D4C2×C22⋊D4712yes—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—471no—
349C2×C4—471no—
350C2×C4—471no—
351C2×C4—941no—
352C2×C4—941no—
353C2×C4—941no—
354C2×C4—941no—
355C2×C4—941no—
356C2×C4—941no—
357C2×C4—1882no—
358C2×C4—1882no—
359C2×C4—1882no—
360C2×C4D4×D4711yescharacteristic
361C2×C4C23×D4711yescharacteristic
362C8—21no—
363C8—941no—
364C8—941no—
365C8C2×C22⋊D4712yes—
366C22—21no—
367C22—22no—
368C22—21no—
369C22—21no—
370C22—41no—
371C22—41no—
372C22—941no—
373C22—941no—
374C22—941no—
375C22C2×D4×D4711yescharacteristic
376C4—21no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—472no—
381C4—941no—
382C4—941no—
383C4—1881no—
384C4—1881no—
385C4—1881no—
386C4—1881no—
387C4C22×C22⋊D4711yescharacteristic
388C4#1309406911yescharacteristic
389C2—41no—
390C2—42no—
391C2—1881no—
392C2D4×C22⋊D4711yescharacteristic
393C2#137×D4711yescharacteristic
394C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#137×C47C2
socleC22×C47C22×D4
hypercenterC2×#137D47
hypocenterC47#3276
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#13094053C2semidirect
2. Q8×C22⋊D47C2semidirect
4. #15689501C2semidirect
5. #15689381C2semidirect
6. #15689378C2semidirect
7. #15689331C2semidirect
8. #15689326C2semidirect
9. #15689285C2semidirect
10. #15689282C2semidirect
11. #15689279C2semidirect
12. #15689277C2semidirect
13. SD16×Dic47C2semidirect
14. #15689199C2semidirect
15. C2×#137×C47C2semidirect
90. SD16×C47D4semidirect
190. Dic47#137semidirect
199. C2×#137D47semidirect
213. C47#3276semidirect
293. SD16C22⋊D47semidirect