Finite Group Databasebeta

← #20254897

Subgroups — #20254897

Order 6016.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094056C211yesmaximal, characteristic, complemented
2C2×SD16×D47C211yesmaximal, characteristic, complemented
3#15689788C211yesmaximal, characteristic, complemented
4#15689766C211yesmaximal, characteristic
5#15689366C211yesmaximal, characteristic, complemented
6#15689361C211yesmaximal, characteristic, complemented
7#15689342C211yesmaximal, characteristic, complemented
8#15689325C211yesmaximal, characteristic, complemented
9#15689284C211yesmaximal, characteristic, complemented
10#15689277C211yesmaximal, characteristic, complemented
11#15689272C211yesmaximal, characteristic, complemented
12#15689260C211yesmaximal, characteristic, complemented
13#15689225C211yesmaximal, characteristic, complemented
14#15689196C211yesmaximal, characteristic, complemented
15C47×#497C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18C2×Q8×D47C2211yescharacteristic, complemented
19C2×D4×D47C2211yescharacteristic
20#13094056—24no—
21C2×#10625337C2211yescharacteristic, complemented
22C2×#10625325C2211yescharacteristic
23C2×#10625335C2211yescharacteristic
24C2×#10625336C2211yescharacteristic
25C2×#10625336C2211yescharacteristic
26SD16×D47—24no—
27C2×#10625324C2211yescharacteristic, complemented
28C2×C8×D47C2211yescharacteristic
29#13094023—21no—
30#13094006—21no—
31#13094002—21no—
32#13094002—21no—
33#13094000C2211yescharacteristic
34#13094000C2211yescharacteristic
35#13094000C2211yescharacteristic, complemented
36#13093997—21no—
37#13093995C2211yescharacteristic
38#13093994—21no—
39C4×Dic94C2211yescharacteristic, complemented
40C4×D188C2211yescharacteristic
41C4×D188C2211yescharacteristic
42#13093986—21no—
43C22⋊C4×D47—21no—
44#13093958C2211yescharacteristic, complemented
45C4⋊(C47⋊C8)C2211yescharacteristic, complemented
46#13093949C2211yescharacteristic, complemented
47#13093948C2211yescharacteristic, complemented
48#13093948C2211yescharacteristic, complemented
49#13093948C2211yescharacteristic, complemented
50#13093946C2211yescharacteristic
51#13093945C2211yescharacteristic
52(C2×D47)⋊C8C2211yescharacteristic
53(C2×D47)⋊C8C2211yescharacteristic, complemented
54C2×Q16×C47C2211yescharacteristic, complemented
55C2×Q16×C47C2211yescharacteristic, complemented
56C2×SD16×C47C2211yescharacteristic
57C2×SD16×C47C2211yescharacteristic
58C4⋊Q8×C47C2211yescharacteristic, complemented
59#124×C47C2211yescharacteristic
60#97×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×Q8×C47C2311yescharacteristic
64C2×Q8×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68#10625354—22no—
69#10625354—41no—
70Q8×D47—22no—
71Q8×D47—22no—
72Q8×D47—41no—
73Q8×D47—41no—
74D4×D47—22no—
75D4×D47—41no—
76C2×D188—21no—
77C2×D188D411yescharacteristic
78C2×D188C2311yescharacteristic
79C2×C4×D47—21no—
80C2×C4×D47—21no—
81C2×C4×D47—21no—
82C2×C4×D47—21no—
83C2×C4×D47C2311yescharacteristic
84C2×C4×D47C2311yescharacteristic
85C2×Dic94—21no—
86C2×Dic94—21no—
87C2×Dic94C2311yescharacteristic
88Q16×C47—22no—
89Q16×C47—41no—
90SD16×C47—22no—
91SD16×C47—41no—
92C2×C8×C47C2311yescharacteristic
93C2×C8×C47C2311yescharacteristic
94C4⋊C4×C47—21no—
95C4⋊C4×C47—21no—
96C22⋊C4×C47—21no—
97C22⋊C4×C47—21no—
98C42×C47C2311yescharacteristic
99C22⋊Dic47—21no—
100#10625337—22no—
101#10625336—22no—
102#10625336—22no—
103#10625335—22no—
104(C2×D47)⋊C4—21no—
105(C2×D47)⋊C4—21no—
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4—21no—
108(C2×D47)⋊C4D411yescharacteristic
109(C2×D47)⋊C4D411yescharacteristic
110C4⋊Dic47D411yescharacteristic
111C4⋊Dic47C2311yescharacteristic
112C4⋊Dic47C2311yescharacteristic
113Dic47⋊C4—21no—
114Dic47⋊C4—21no—
115Dic47⋊C4—21no—
116Dic47⋊C4—21no—
117C4×Dic47—21no—
118C2×C47⋊C8C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120#10625325D414yescomplemented
121#10625324—22no—
122C8×D47—22no—
123C23×C47—21no—
124C22×D47—21no—
125C22×D47—42no—
126C22×D47—42no—
127C22×D47—81no—
128C22×D47C2×D411yescharacteristic
129C22×D47C2×D411yescharacteristic
130Q8×C47—21no—
131Q8×C47—21no—
132Q8×C47—21no—
133Q8×C47—21no—
134Q8×C47—21no—
135Q8×C47—21no—
136D4×C47—21no—
137D4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47C2×D411yescharacteristic
142C2×C4×C47C2×D411yescharacteristic
143C2×C4×C47C2411yescharacteristic
144C22⋊D47—42no—
145C22⋊D47—81no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47C2×D411yescharacteristic
150C2×Dic47C2×D411yescharacteristic
151D188—22no—
152D188—21no—
153D188—42no—
154D188C2×D412yes—
155C4×D47—21no—
156C4×D47—21no—
157C4×D47—21no—
158C4×D47—21no—
159C4×D47—42no—
160C4×D47—42no—
161C4×D47—42no—
162C4×D47—81no—
163Dic94—21no—
164Dic94—42no—
165Dic94—42no—
166Dic94C2×D412yes—
167C8×C47—21no—
168C8×C47C2×D412yes—
169C47⋊C8—21no—
170C47⋊C8—21no—
171C22×C47—41no—
172C22×C47—41no—
173C22×C47—41no—
174C22×C47C22×D411yescharacteristic
175C2×D47—21no—
176C2×D47—21no—
177C2×D47—21no—
178C2×D47—22no—
179C2×D47—21no—
180C2×D47—21no—
181C2×D47—41no—
182C2×D47—41no—
183C2×D47—84no—
184C2×D47#13712yescomplemented
185C4×C47—21no—
186C4×C47—21no—
187C4×C47—41no—
188C4×C47—41no—
189C4×C47—41no—
190C4×C47C22×D411yescharacteristic
191C4×C47H(5,𝔽2)11yescharacteristic
192Dic47—22no—
193Dic47—21no—
194Dic47—21no—
195Dic47—41no—
196Dic47—41no—
197#3266—471nomaximal, Sylow
198C2×C47—81no—
199C2×C47D4211yescharacteristic
200C2×C47C2×#13711yescharacteristic
201C2×C47#57711yescharacteristic
202D47—22no—
203D47—41no—
204D47—42no—
205C2×#137—471no—
206C22×SD16—471no—
207D4×Q8—471no—
208#546—471no—
209#497D4711yescharacteristic, complemented
210#468—471no—
211#467—471no—
212#464—471no—
213#461—471no—
214#452—471no—
215#451—471no—
216#450—471no—
217#448—471no—
218#440—471no—
219#435—471no—
220C47#326611yescharacteristic, complemented, Sylow
221C2×#41—471no—
222C22×Q8—471no—
223C22×Q8—471no—
224C22×D4—471no—
225#137—944no—
226C2×Q16—471no—
227C2×Q16C2×D4711yescharacteristic, complemented
228C2×Q16C2×D4711yescharacteristic, complemented
229C2×SD16—471no—
230C2×SD16—471no—
231C2×SD16—471no—
232C2×SD16—471no—
233C2×SD16—944no—
234C2×SD16C2×D4711yescharacteristic
235C2×SD16C2×D4711yescharacteristic
236C2×M16—471no—
237C22×C8—471no—
238C4⋊Q8—941no—
239C4⋊Q8C2×D4711yescharacteristic, complemented
240#124C2×D4711yescharacteristic
241#123—941no—
242C22⋊Q8—471no—
243C22⋊Q8—471no—
244C22⋊Q8—471no—
245C22⋊Q8—941no—
246C22⋊Q8—941no—
247#121—471no—
248#121—941no—
249#120—941no—
250C4×Q8—471no—
251C4×D4—471no—
252C4×D4—471no—
253C4×D4—941no—
254C2×C22⋊C4—941no—
255#107—471no—
256C4⋊C8—471no—
257#103—471no—
258#103—471no—
259#103—471no—
260#103—471no—
261#102—471no—
262#102—471no—
263C22⋊C8—471no—
264C22⋊C8—471no—
265#97C2×D4711yescharacteristic, complemented
266C24—941no—
267#41—942no—
268#41—1881no—
269C2×Q8—471no—
270C2×Q8—941no—
271C2×Q8—941no—
272C2×Q8—942no—
273C2×Q8—942no—
274C2×Q8—1881no—
275C2×Q8—1881no—
276C2×Q8C22×D4711yescharacteristic
277C2×Q8C22×D4711yescharacteristic
278C2×Q8C22×D4711yescharacteristic
279C2×D4—471no—
280C2×D4—471no—
281C2×D4—941no—
282C2×D4—941no—
283C2×D4—942no—
284C2×D4—941no—
285C2×D4—1881no—
286C2×D4C22×D4711yescharacteristic
287C22×C4—471no—
288C22×C4—471no—
289C22×C4—941no—
290C22×C4—941no—
291C22×C4—941no—
292C22×C4—941no—
293Q16—22no—
294Q16—41no—
295Q16—942no—
296SD16—22no—
297SD16—41no—
298SD16—474no—
299SD16—942no—
300SD16—942no—
301SD16—942no—
302M16—942no—
303C2×C8—471no—
304C2×C8—471no—
305C2×C8—942no—
306C2×C8C22×D4711yescharacteristic
307C2×C8C22×D4711yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—471no—
311C4⋊C4—471no—
312C4⋊C4—471no—
313C4⋊C4—941no—
314C4⋊C4—941no—
315C4⋊C4—941no—
316C4⋊C4—941no—
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—471no—
320C22⋊C4—471no—
321C22⋊C4—941no—
322C22⋊C4—941no—
323C22⋊C4—941no—
324C22⋊C4—941no—
325C22⋊C4—941no—
326C42—941no—
327C42C22×D4711yescharacteristic
328C23—21no—
329C23—471no—
330C23—471no—
331C23—941no—
332C23—3761no—
333C23—1882no—
334C23—1882no—
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—21no—
341Q8—472no—
342Q8—941no—
343Q8—1882no—
344Q8—1882no—
345D4—21no—
346D4—21no—
347D4—472no—
348D4—942no—
349D4—941no—
350D4—3761no—
351D4—1882no—
352D4—1882no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—471no—
357C2×C4—471no—
358C2×C4—941no—
359C2×C4—941no—
360C2×C4—941no—
361C2×C4—941no—
362C2×C4—941no—
363C2×C4—941no—
364C2×C4—941no—
365C2×C4—3761no—
366C2×C4—1882no—
367C2×C4—1882no—
368C2×C4—1882no—
369C2×C4D4×D4711yescharacteristic
370C2×C4D4×D4711yescharacteristic
371C2×C4C23×D4711yescharacteristic
372C8—21no—
373C8—941no—
374C8—941no—
375C8D4×D4712yes—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—472no—
380C22—941no—
381C22—941no—
382C22—941no—
383C22—942no—
384C22—941no—
385C22—941no—
386C22—3764no—
387C22—1881no—
388C22—1881no—
389C22C2×D4×D4711yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—941no—
396C4—941no—
397C4—942no—
398C4—1881no—
399C4—1881no—
400C4C2×D4×D4711yescharacteristic
401C4#1309406911yescharacteristic
402C2—81no—
403C2—942no—
404C2—1881no—
405C2—1882no—
406C2#1568975811yescharacteristic
407C2#137×D4711yescharacteristic
408C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#497C2
socleC22×C47C22×D4
hypercenter#497D47
hypocenterC47#3266
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×#13094056C2semidirect
2. C2×SD16×D47C2semidirect
3. #15689788C2semidirect
5. #15689366C2semidirect
6. #15689361C2semidirect
7. #15689342C2semidirect
8. #15689325C2semidirect
9. #15689284C2semidirect
10. #15689277C2semidirect
11. #15689272C2semidirect
12. #15689260C2semidirect
13. #15689225C2semidirect
14. #15689196C2semidirect
15. C47×#497C2semidirect
18. C2×Q8×D47C22semidirect
21. C2×#10625337C22semidirect
27. C2×#10625324C22semidirect
35. #13094000C22semidirect
39. C4×Dic94C22semidirect
44. #13093958C22semidirect
45. C4⋊(C47⋊C8)C22semidirect
46. #13093949C22semidirect
47. #13093948C22semidirect
48. #13093948C22semidirect
49. #13093948C22semidirect
53. (C2×D47)⋊C8C22semidirect
54. C2×Q16×C47C22semidirect
55. C2×Q16×C47C22semidirect
58. C4⋊Q8×C47C22semidirect
60. #97×C47C22semidirect
120. #10625325D4semidirect
184. C2×D47#137semidirect
209. #497D47semidirect
220. C47#3266semidirect
227. C2×Q16C2×D47semidirect
228. C2×Q16C2×D47semidirect
239. C4⋊Q8C2×D47semidirect
265. #97C2×D47semidirect