Finite Group Databasebeta

← #20252924

Subgroups — #20252924

Order 6016.

504 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×#13094051C211yesmaximal, characteristic, complemented
2C2×#13094045C211yesmaximal, characteristic, complemented
3#15689686C211yesmaximal, characteristic, complemented
4#15689605C211yesmaximal, characteristic, complemented
5#15689345C211yesmaximal, characteristic, complemented
6#15689343C211yesmaximal, characteristic, complemented
7#15689339C211yesmaximal, characteristic, complemented
8#15689337C211yesmaximal, characteristic, complemented
9#15689321C211yesmaximal, characteristic, complemented
10#15689317C211yesmaximal, characteristic, complemented
11#15689315C211yesmaximal, characteristic, complemented
12#15689148C211yesmaximal, characteristic, complemented
13#15689121C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#460C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625352C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic
19#13094051—24no—
20#13094045—24no—
21C2×#10625337C2211yescharacteristic, complemented
22C2×#10625325C2211yescharacteristic, complemented
23C2×#10625336C2211yescharacteristic
24C2×D376C2211yescharacteristic
25C2×#10625334C2211yescharacteristic
26C2×#10625334C2211yescharacteristic, complemented
27C2×#10625324C2211yescharacteristic
28C2×C8×D47C2211yescharacteristic
29#13094020C2211yescharacteristic
30#13094012C2211yescharacteristic
31#13094011C2211yescharacteristic
32#13093996—21no—
33#13093996—21no—
34#13093992—21no—
35#13093992—21no—
36Q8×Dic47C2211yescharacteristic, complemented
37C4×D188—21no—
38C4×D188C2211yescharacteristic, complemented
39#13093986—21no—
40#13093986C2211yescharacteristic, complemented
41#13093981—21no—
42#13093981C2211yescharacteristic
43C4⋊C4×D47—21no—
44C4⋊C4×D47C2211yescharacteristic
45C4⋊(C47⋊C8)C2211yescharacteristic, complemented
46Dic47⋊C8C2211yescharacteristic, complemented
47Dic47⋊C8C2211yescharacteristic, complemented
48#13093949C2211yescharacteristic, complemented
49#13093947C2211yescharacteristic, complemented
50#13093946C2211yescharacteristic
51#13093945C2211yescharacteristic
52#13093945C2211yescharacteristic, complemented
53#13093944C2211yescharacteristic
54C2×SD16×C47C2211yescharacteristic
55C2×SD16×C47C2211yescharacteristic, complemented
56#127×C47C2211yescharacteristic
57C4×Q8×C47C2211yescharacteristic, complemented
58C4⋊C8×C47C2211yescharacteristic, complemented
59#102×C47C2211yescharacteristic
60#102×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47—21no—
65C2×D4×C47C2311yescharacteristic
66C2×D4×C47C2311yescharacteristic
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C22×Dic47—21no—
72#10625354—22no—
73#10625354D414yescomplemented
74#10625352—22no—
75#10625352—22no—
76D4×D47—22no—
77D4×D47—22no—
78C2×D188—21no—
79C2×D188C2311yescharacteristic
80C2×D188C2311yescharacteristic
81C2×C4×D47—21no—
82C2×C4×D47—21no—
83C2×C4×D47—21no—
84C2×C4×D47—21no—
85C2×C4×D47C2311yescharacteristic
86C2×Dic94C2311yescharacteristic
87SD16×C47—22no—
88SD16×C47—22no—
89C2×C8×C47C2311yescharacteristic
90C2×C8×C47C2311yescharacteristic
91C4⋊C4×C47—21no—
92C4⋊C4×C47C2311yescharacteristic
93C42×C47—21no—
94C42×C47C2311yescharacteristic
95C22⋊Dic47—21no—
96C22⋊Dic47—21no—
97#10625337—22no—
98#10625336—22no—
99#10625334—22no—
100#10625334—22no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104(C2×D47)⋊C4—21no—
105(C2×D47)⋊C4D411yescharacteristic
106(C2×D47)⋊C4D411yescharacteristic
107C4⋊Dic47—21no—
108C4⋊Dic47C2311yescharacteristic
109Dic47⋊C4—21no—
110Dic47⋊C4D411yescharacteristic
111Dic47⋊C4D411yescharacteristic
112C4×Dic47—21no—
113C4×Dic47C2311yescharacteristic
114C2×C47⋊C8C2311yescharacteristic
115C2×C47⋊C8C2311yescharacteristic
116D376—22no—
117#10625325—22no—
118#10625324—22no—
119C8×D47—22no—
120C23×C47—21no—
121C23×C47—21no—
122C22×D47—21no—
123C22×D47—21no—
124C22×D47—42no—
125C22×D47—81no—
126C22×D47—81no—
127C22×D47C2×D411yescharacteristic
128Q8×C47—21no—
129Q8×C47C2×D412yes—
130D4×C47—21no—
131D4×C47—21no—
132D4×C47—21no—
133D4×C47—21no—
134D4×C47—81no—
135D4×C47—81no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47C2×D411yescharacteristic
139C2×C4×C47C2×D411yescharacteristic
140C2×C4×C47C2411yescharacteristic
141C22⋊D47—42no—
142C22⋊D47—42no—
143C22⋊D47—81no—
144C22⋊D47—81no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—42no—
148C2×Dic47C2×D411yescharacteristic
149C2×Dic47C2×D411yescharacteristic
150C2×Dic47C2×D411yescharacteristic
151D188—24no—
152D188—21no—
153D188—21no—
154D188—21no—
155D188C2×D412yes—
156C4×D47—24no—
157C4×D47—81no—
158C4×D47—81no—
159C4×D47—81no—
160C4×D47C2×D412yes—
161C4×D47#4112yes—
162Dic94—21no—
163Dic94—21no—
164C8×C47—21no—
165C8×C47—21no—
166C47⋊C8—21no—
167C47⋊C8—21no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—41no—
173C22×C47—41no—
174C22×C47C22×D411yescharacteristic
175C2×D47—21no—
176C2×D47—21no—
177C2×D47—22no—
178C2×D47—41no—
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—41no—
183C2×D47—84no—
184C2×D47#12112yes—
185C4×C47—22no—
186C4×C47—21no—
187C4×C47—21no—
188C4×C47—41no—
189C4×C47C22×D411yescharacteristic
190C4×C47C2×#4111yescharacteristic
191Dic47—21no—
192Dic47—21no—
193Dic47—41no—
194Dic47—41no—
195Dic47#12112yes—
196#3045—471nomaximal, Sylow
197C2×C47—81no—
198C2×C47—81no—
199C2×C47C2×#12111yescharacteristic
200C2×C47#57611yescharacteristic
201C2×C47#57711yescharacteristic
202D47—22no—
203D47—42no—
204D47—81no—
205C2×AGL(1,ℤ/8)—471no—
206C2×#135—471no—
207#535—471no—
208#520—471no—
209#464—471no—
210#464—471no—
211#463—471no—
212#463—471no—
213#460—471no—
214#460D4711yescharacteristic, complemented
215#459—471no—
216#459—471no—
217#424—471no—
218#417—471no—
219C2×#102—471no—
220C47#304511yescharacteristic, complemented, Sylow
221C2×#41—471no—
222C2×#41—471no—
223C22×D4—471no—
224AGL(1,ℤ/8)—944no—
225#135—944no—
226C2×Q16—471no—
227C2×SD16—471no—
228C2×SD16—471no—
229C2×SD16C2×D4711yescharacteristic
230C2×SD16C2×D4711yescharacteristic, complemented
231C2×D8—471no—
232C2×D8—471no—
233C2×D8—471no—
234C2×M16—471no—
235C22×C8—471no—
236#127—471no—
237#127C2×D4711yescharacteristic
238#124—471no—
239#124—471no—
240#121—941no—
241#121—941no—
242#120—941no—
243#120—941no—
244C4×Q8—471no—
245C4×Q8C2×D4711yescharacteristic, complemented
246C4×D4—471no—
247C4×D4—471no—
248C4×D4—941no—
249C4×D4—941no—
250#117—471no—
251#117—941no—
252C2×C4⋊C4—471no—
253C2×C4⋊C4—941no—
254C4⋊C8—471no—
255C4⋊C8—471no—
256C4⋊C8—471no—
257C4⋊C8C2×D4711yescharacteristic, complemented
258#103—471no—
259#103—471no—
260#102—471no—
261#102—471no—
262#102—471no—
263#102—471no—
264#102C2×D4711yescharacteristic
265#102C2×D4711yescharacteristic, complemented
266C24—941no—
267#41—474no—
268#41—942no—
269#41—942no—
270#41—942no—
271C2×Q8—471no—
272C2×Q8C22×D4711yescharacteristic
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—471no—
276C2×D4—471no—
277C2×D4—941no—
278C2×D4—942no—
279C2×D4—942no—
280C2×D4—941no—
281C2×D4—941no—
282C2×D4—941no—
283C2×D4—941no—
284C2×D4C22×D4711yescharacteristic
285C2×D4C22×D4711yescharacteristic
286C22×C4—471no—
287C22×C4—941no—
288C22×C4—941no—
289C22×C4—941no—
290C22×C4—941no—
291C22×C4—941no—
292Q16—942no—
293SD16—22no—
294SD16—22no—
295SD16—942no—
296SD16—942no—
297D8—942no—
298D8—942no—
299D8—942no—
300M16—942no—
301C2×C8—471no—
302C2×C8—471no—
303C2×C8—942no—
304C2×C8C22×D4711yescharacteristic
305C2×C8C22×D4711yescharacteristic
306C4⋊C4—21no—
307C4⋊C4—471no—
308C4⋊C4—471no—
309C4⋊C4—471no—
310C4⋊C4—941no—
311C4⋊C4—941no—
312C4⋊C4C22×D4711yescharacteristic
313C22⋊C4—471no—
314C22⋊C4—471no—
315C22⋊C4—941no—
316C22⋊C4—941no—
317C22⋊C4—941no—
318C22⋊C4—941no—
319C22⋊C4—941no—
320C22⋊C4—941no—
321C42—21no—
322C42—471no—
323C42—941no—
324C42C22×D4711yescharacteristic
325C23—21no—
326C23—21no—
327C23—471no—
328C23—941no—
329C23—941no—
330C23—3761no—
331C23—3761no—
332C23—1882no—
333Q8—21no—
334Q8—941no—
335Q8—941no—
336Q8D4×D4712yes—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—81no—
342D4—81no—
343D4—472no—
344D4—944no—
345D4—941no—
346D4—941no—
347D4—941no—
348D4—3761no—
349D4—3761no—
350D4—1882no—
351D4—1882no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—471no—
355C2×C4—472no—
356C2×C4—472no—
357C2×C4—471no—
358C2×C4—471no—
359C2×C4—944no—
360C2×C4—941no—
361C2×C4—941no—
362C2×C4—3761no—
363C2×C4—3761no—
364C2×C4—3761no—
365C2×C4—1882no—
366C2×C4D4×D4711yescharacteristic
367C2×C4D4×D4711yescharacteristic
368C2×C4C23×D4711yescharacteristic
369C8—21no—
370C8—21no—
371C8—941no—
372C8—941no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—472no—
380C22—941no—
381C22—941no—
382C22—942no—
383C22—3764no—
384C22—1881no—
385C22—1881no—
386C22—1881no—
387C22—1881no—
388C22—1881no—
389C22C2×D4×D4711yescharacteristic
390C4—22no—
391C4—21no—
392C4—21no—
393C4—41no—
394C4—472no—
395C4—941no—
396C4—941no—
397C4—1881no—
398C4—1881no—
399C4C2×D4×D4711yescharacteristic
400C4#41×D4711yescharacteristic
401C2—81no—
402C2—81no—
403C2—942no—
404C2—3761no—
405C2—1882no—
406C2#121×D4711yescharacteristic
407C2#1568992711yescharacteristic
408C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#460C2
socleC22×C47C22×D4
hypercenter#460D47
hypocenterC47#3045
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#13094051C2semidirect
2. C2×#13094045C2semidirect
3. #15689686C2semidirect
4. #15689605C2semidirect
5. #15689345C2semidirect
6. #15689343C2semidirect
7. #15689339C2semidirect
8. #15689337C2semidirect
9. #15689321C2semidirect
10. #15689317C2semidirect
11. #15689315C2semidirect
12. #15689148C2semidirect
13. #15689121C2semidirect
14. #102×D47C2semidirect
15. C47×#460C2semidirect
21. C2×#10625337C22semidirect
22. C2×#10625325C22semidirect
26. C2×#10625334C22semidirect
36. Q8×Dic47C22semidirect
38. C4×D188C22semidirect
40. #13093986C22semidirect
45. C4⋊(C47⋊C8)C22semidirect
46. Dic47⋊C8C22semidirect
47. Dic47⋊C8C22semidirect
48. #13093949C22semidirect
49. #13093947C22semidirect
52. #13093945C22semidirect
55. C2×SD16×C47C22semidirect
57. C4×Q8×C47C22semidirect
58. C4⋊C8×C47C22semidirect
60. #102×C47C22semidirect
73. #10625354D4semidirect
214. #460D47semidirect
220. C47#3045semidirect
230. C2×SD16C2×D47semidirect
245. C4×Q8C2×D47semidirect
257. C4⋊C8C2×D47semidirect
265. #102C2×D47semidirect