Finite Group Databasebeta

← #20253017

Subgroups — #20253017

Order 6016.

496 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094056C211yesmaximal, characteristic, complemented
2C2×M16×D47C211yesmaximal, characteristic, complemented
3#15689636C211yesmaximal, characteristic
4C22⋊Q8×D47C211yesmaximal, characteristic, complemented
5#15689379C211yesmaximal, characteristic, complemented
6#15689371C211yesmaximal, characteristic, complemented
7#15689369C211yesmaximal, characteristic, complemented
8#15689363C211yesmaximal, characteristic, complemented
9#15689361C211yesmaximal, characteristic, complemented
10#15689355C211yesmaximal, characteristic, complemented
11#15689353C211yesmaximal, characteristic, complemented
12#15689162C211yesmaximal, characteristic, complemented
13#15689130C211yesmaximal, characteristic, complemented
14#15689123C211yesmaximal, characteristic, complemented
15C47×#470C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19#13094056—24no—
20C2×#10625337C2211yescharacteristic, complemented
21C2×#10625325C2211yescharacteristic, complemented
22C2×#10625336C2211yescharacteristic, complemented
23C2×#10625329C2211yescharacteristic
24C2×#10625324C2211yescharacteristic
25C2×#10625324C2211yescharacteristic
26M16×D47—24no—
27C2×C8×D47C2211yescharacteristic
28C2×C8×D47C2211yescharacteristic
29#13094009—21no—
30#13094004C2211yescharacteristic
31#13094003C2211yescharacteristic
32#13094002—21no—
33#13094001—21no—
34#13094000C2211yescharacteristic
35#13094000C2211yescharacteristic
36#13093999C2211yescharacteristic
37#13093998C2211yescharacteristic
38#13093994—21no—
39#13093986—21no—
40(C22⋊D47)⋊C4—21no—
41#13093982C2211yescharacteristic
42C4⋊C4×D47—21no—
43C4⋊C4×D47C2211yescharacteristic
44C22⋊C4×D47—21no—
45#13093958C2211yescharacteristic, complemented
46#13093957C2211yescharacteristic, complemented
47#13093955C2211yescharacteristic, complemented
48#13093949C2211yescharacteristic, complemented
49#13093948C2211yescharacteristic, complemented
50#13093948C2211yescharacteristic, complemented
51#13093947C2211yescharacteristic, complemented
52#13093946C2211yescharacteristic, complemented
53#13093944C2211yescharacteristic, complemented
54C2×Q16×C47C2211yescharacteristic, complemented
55C2×M16×C47C2211yescharacteristic
56C22⋊Q8×C47C2211yescharacteristic
57C22⋊Q8×C47C2211yescharacteristic
58#106×C47C2211yescharacteristic, complemented
59#103×C47C2211yescharacteristic, complemented
60#103×C47C2211yescharacteristic, complemented
61C23×D47D411yescharacteristic
62C2×Q8×C47C2311yescharacteristic
63C2×Q8×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C2×C22⋊D47—21no—
66C22×Dic47D411yescharacteristic
67#10625354—22no—
68#10625354—22no—
69Q8×D47—22no—
70Q8×D47—22no—
71C2×D188—21no—
72C2×D188—21no—
73C2×D188C2311yescharacteristic
74C2×C4×D47—22no—
75C2×C4×D47—22no—
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×C4×D47—21no—
79C2×C4×D47D411yescharacteristic
80C2×C4×D47D411yescharacteristic
81C2×C4×D47C2311yescharacteristic
82C2×C4×D47C2311yescharacteristic
83C2×Dic94—21no—
84C2×Dic94C2311yescharacteristic
85Q16×C47—22no—
86M16×C47—22no—
87C2×C8×C47C2311yescharacteristic
88C2×C8×C47C2311yescharacteristic
89C4⋊C4×C47—21no—
90C4⋊C4×C47—21no—
91C4⋊C4×C47C2311yescharacteristic
92C4⋊C4×C47C2311yescharacteristic
93C22⋊C4×C47—21no—
94C22⋊C4×C47—21no—
95C22⋊Dic47—21no—
96#10625337—22no—
97#10625336—22no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104C4⋊Dic47—21no—
105C4⋊Dic47C2311yescharacteristic
106C4⋊Dic47C2311yescharacteristic
107Dic47⋊C4—21no—
108Dic47⋊C4—21no—
109Dic47⋊C4—21no—
110Dic47⋊C4—21no—
111C4×Dic47—21no—
112#10625329—22no—
113C2×C47⋊C8C2311yescharacteristic
114C2×C47⋊C8C2311yescharacteristic
115#10625325—22no—
116#10625324—22no—
117#10625324D414yescomplemented
118C8×D47—22no—
119C8×D47—22no—
120C23×C47C2×D411yescharacteristic
121C22×D47—22no—
122C22×D47—22no—
123C22×D47—21no—
124C22×D47—41no—
125C22×D47C2×D411yescharacteristic
126C22×D47C2×D411yescharacteristic
127Q8×C47—21no—
128Q8×C47—21no—
129Q8×C47—21no—
130Q8×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47C2×D411yescharacteristic
138C2×C4×C47C2411yescharacteristic
139C22⋊D47—42no—
140C2×Dic47—22no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47C2×D411yescharacteristic
145C2×Dic47C2×D411yescharacteristic
146D188—21no—
147D188—21no—
148D188—42no—
149D188—42no—
150C4×D47—22no—
151C4×D47—21no—
152C4×D47—21no—
153C4×D47—22no—
154C4×D47—42no—
155C4×D47—42no—
156C4×D47—42no—
157C4×D47C2×D412yes—
158C4×D47#4112yes—
159Dic94—21no—
160Dic94—21no—
161Dic94—42no—
162C8×C47—21no—
163C8×C47C2×D412yes—
164C47⋊C8—21no—
165C47⋊C8C2×D412yes—
166C22×C47—21no—
167C22×C47—21no—
168C22×C47—21no—
169C22×C47C22×D411yescharacteristic
170C2×D47—21no—
171C2×D47—21no—
172C2×D47—21no—
173C2×D47—21no—
174C2×D47—44no—
175C2×D47—41no—
176C2×D47—41no—
177C2×D47—41no—
178C2×D47#12112yes—
179C2×D47#13712yescomplemented
180C4×C47—21no—
181C4×C47—41no—
182C4×C47—41no—
183C4×C47—41no—
184C4×C47—41no—
185C4×C47C22×D411yescharacteristic
186C4×C47C2×#4111yescharacteristic
187Dic47—21no—
188Dic47—41no—
189Dic47—41no—
190Dic47—41no—
191Dic47#12112yes—
192#3056—471nomaximal, Sylow
193C2×C47—41no—
194C2×C47C2×#12111yescharacteristic
195C2×C47C2×#13711yescharacteristic
196C2×C47#57511yescharacteristic
197D47—22no—
198D47—22no—
199D47—81no—
200C2×#137—471no—
201C22×M16—471no—
202#525—471no—
203C2×C22⋊Q8—471no—
204#470—471no—
205#470D4711yescharacteristic, complemented
206#468—471no—
207#468—471no—
208#467—471no—
209#467—471no—
210#465—471no—
211#465—471no—
212#428—471no—
213#419—471no—
214#417—471no—
215C47#305611yescharacteristic, complemented, Sylow
216C2×#41—471no—
217C22×Q8—471no—
218C23×C4—471no—
219#137—944no—
220C2×Q16—471no—
221C2×Q16C2×D4711yescharacteristic, complemented
222C2×SD16—471no—
223C2×SD16—471no—
224C2×M16—471no—
225C2×M16—471no—
226C2×M16—471no—
227C2×M16—944no—
228C2×M16C2×D4711yescharacteristic
229C22×C8—471no—
230C22×C8—471no—
231#123—941no—
232C22⋊Q8—471no—
233C22⋊Q8—471no—
234C22⋊Q8—471no—
235C22⋊Q8—471no—
236C22⋊Q8—941no—
237C22⋊Q8—941no—
238C22⋊Q8C2×D4711yescharacteristic
239C22⋊Q8C2×D4711yescharacteristic
240#121—471no—
241#121—471no—
242#120—941no—
243C4×D4—941no—
244C4×D4—941no—
245#117—471no—
246C2×C4⋊C4—471no—
247C2×C4⋊C4—941no—
248C2×C22⋊C4—941no—
249#107—471no—
250#107—471no—
251#106—471no—
252#106C2×D4711yescharacteristic, complemented
253#103—471no—
254#103—471no—
255#103—471no—
256#103—471no—
257#103C2×D4711yescharacteristic, complemented
258#103C2×D4711yescharacteristic, complemented
259#102—471no—
260#102—471no—
261C24—471no—
262#41—942no—
263#41—942no—
264C2×Q8—471no—
265C2×Q8—941no—
266C2×Q8—942no—
267C2×Q8—942no—
268C2×Q8C22×D4711yescharacteristic
269C2×Q8C22×D4711yescharacteristic
270C2×D4—471no—
271C2×D4—941no—
272C2×D4—941no—
273C2×D4—941no—
274C22×C4—471no—
275C22×C4—471no—
276C22×C4—471no—
277C22×C4—471no—
278C22×C4—471no—
279C22×C4—942no—
280C22×C4—942no—
281C22×C4—941no—
282C22×C4—941no—
283C22×C4—941no—
284C22×C4C22×D4711yescharacteristic
285Q16—22no—
286Q16—942no—
287SD16—942no—
288SD16—942no—
289M16—22no—
290M16—474no—
291M16—942no—
292M16—942no—
293C2×C8—471no—
294C2×C8—471no—
295C2×C8—942no—
296C2×C8—942no—
297C2×C8C22×D4711yescharacteristic
298C2×C8C22×D4711yescharacteristic
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—471no—
302C4⋊C4—471no—
303C4⋊C4—941no—
304C4⋊C4—941no—
305C4⋊C4—941no—
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⋊C4—941no—
317C22⋊C4—941no—
318C22⋊C4—941no—
319C42—941no—
320C23—471no—
321C23—471no—
322C23—942no—
323C23—942no—
324C23—941no—
325C23—1881no—
326C23D4×D4711yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—21no—
330Q8—21no—
331Q8—941no—
332Q8—941no—
333Q8—1882no—
334D4—941no—
335D4—941no—
336D4—1882no—
337D4—1882no—
338D4—1882no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—471no—
346C2×C4—472no—
347C2×C4—472no—
348C2×C4—471no—
349C2×C4—942no—
350C2×C4—942no—
351C2×C4—942no—
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—472no—
364C8—941no—
365C8D4×D4712yes—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—472no—
370C22—472no—
371C22—941no—
372C22—941no—
373C22—941no—
374C22—941no—
375C22—1884no—
376C22—1881no—
377C22—1881no—
378C22—1881no—
379C22C2×D4×D4711yescharacteristic
380C4—21no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—472no—
386C4—941no—
387C4—1881no—
388C4—1881no—
389C4—1881no—
390C4C2×D4×D4711yescharacteristic
391C4#41×D4711yescharacteristic
392C2—41no—
393C2—942no—
394C2—942no—
395C2—3761no—
396C2#121×D4711yescharacteristic
397C2#137×D4711yescharacteristic
398C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#470C2
socleC22×C47C22×D4
hypercenter#470D47
hypocenterC47#3056
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. C2×#13094056C2semidirect
2. C2×M16×D47C2semidirect
4. C22⋊Q8×D47C2semidirect
5. #15689379C2semidirect
6. #15689371C2semidirect
7. #15689369C2semidirect
8. #15689363C2semidirect
9. #15689361C2semidirect
10. #15689355C2semidirect
11. #15689353C2semidirect
12. #15689162C2semidirect
13. #15689130C2semidirect
14. #15689123C2semidirect
15. C47×#470C2semidirect
20. C2×#10625337C22semidirect
21. C2×#10625325C22semidirect
22. C2×#10625336C22semidirect
45. #13093958C22semidirect
46. #13093957C22semidirect
47. #13093955C22semidirect
48. #13093949C22semidirect
49. #13093948C22semidirect
50. #13093948C22semidirect
51. #13093947C22semidirect
52. #13093946C22semidirect
53. #13093944C22semidirect
54. C2×Q16×C47C22semidirect
58. #106×C47C22semidirect
59. #103×C47C22semidirect
60. #103×C47C22semidirect
117. #10625324D4semidirect
179. C2×D47#137semidirect
205. #470D47semidirect
215. C47#3056semidirect
221. C2×Q16C2×D47semidirect
252. #106C2×D47semidirect
257. #103C2×D47semidirect
258. #103C2×D47semidirect