Finite Group Databasebeta

← #20252928

Subgroups — #20252928

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×#13094048C211yesmaximal, characteristic, complemented
2C2×#13094045C211yesmaximal, characteristic, complemented
3#15689691C211yesmaximal, characteristic, complemented
4#15689602C211yesmaximal, characteristic, complemented
5#15689348C211yesmaximal, characteristic, complemented
6#15689342C211yesmaximal, characteristic, complemented
7#15689340C211yesmaximal, characteristic, complemented
8#15689324C211yesmaximal, characteristic, complemented
9#15689322C211yesmaximal, characteristic, complemented
10#15689318C211yesmaximal, characteristic, complemented
11#15689316C211yesmaximal, characteristic, complemented
12#15689148C211yesmaximal, characteristic, complemented
13#15689123C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#463C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625352C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic
19#13094048—24no—
20#13094045—24no—
21C2×#10625337C2211yescharacteristic, complemented
22C2×#10625325C2211yescharacteristic
23C2×#10625325C2211yescharacteristic, complemented
24C2×#10625335C2211yescharacteristic
25C2×#10625334C2211yescharacteristic
26C2×#10625334C2211yescharacteristic, complemented
27C2×#10625324C2211yescharacteristic
28C2×C8×D47C2211yescharacteristic
29#13094021C2211yescharacteristic
30#13094020C2211yescharacteristic
31#13094013C2211yescharacteristic
32#13093997—21no—
33#13093997—21no—
34#13093994—21no—
35#13093994—21no—
36C4×Dic94C2211yescharacteristic, complemented
37#13093989C2211yescharacteristic, complemented
38D4×Dic47C2211yescharacteristic, complemented
39C4×C22⋊D47—21no—
40(C22⋊D47)⋊C4—21no—
41#13093981C2211yescharacteristic
42#13093980—21no—
43C2×Dic47⋊C4—21no—
44C4⋊C4×D47C2211yescharacteristic
45C4⋊(C47⋊C8)C2211yescharacteristic, complemented
46Dic47⋊C8C2211yescharacteristic, complemented
47Dic47⋊C8C2211yescharacteristic, complemented
48#13093948C2211yescharacteristic, complemented
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic, complemented
51#13093945C2211yescharacteristic
52#13093944C2211yescharacteristic
53#13093944C2211yescharacteristic, complemented
54C2×SD16×C47C2211yescharacteristic, complemented
55C2×D8×C47C2211yescharacteristic
56#124×C47C2211yescharacteristic
57C4×D4×C47C2211yescharacteristic, complemented
58C4⋊C8×C47C2211yescharacteristic, complemented
59#103×C47C2211yescharacteristic, complemented
60#102×C47C2211yescharacteristic
61C23×D47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C22×Dic47—21no—
71C22×Dic47—21no—
72#10625354—22no—
73#10625354—22no—
74#10625352—22no—
75#10625352D414yescomplemented
76D4×D47—22no—
77D4×D47—22no—
78C2×D188—21no—
79C2×D188—21no—
80C2×D188—21no—
81C2×D188C2311yescharacteristic
82C2×D188C2311yescharacteristic
83C2×C4×D47—21no—
84C2×C4×D47—21no—
85C2×C4×D47C2311yescharacteristic
86C2×Dic94C2311yescharacteristic
87SD16×C47—22no—
88D8×C47—22no—
89C2×C8×C47C2311yescharacteristic
90C2×C8×C47C2311yescharacteristic
91C4⋊C4×C47C2311yescharacteristic
92C22⋊C4×C47—21no—
93C22⋊C4×C47—21no—
94C22⋊C4×C47—21no—
95C42×C47C2311yescharacteristic
96C22⋊Dic47—21no—
97#10625337—22no—
98#10625335—22no—
99#10625334—22no—
100#10625334—22no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4D411yescharacteristic
104(C2×D47)⋊C4D411yescharacteristic
105C4⋊Dic47C2311yescharacteristic
106Dic47⋊C4—21no—
107Dic47⋊C4—21no—
108Dic47⋊C4—21no—
109Dic47⋊C4D411yescharacteristic
110Dic47⋊C4D411yescharacteristic
111C4×Dic47—21no—
112C4×Dic47—21no—
113C4×Dic47C2311yescharacteristic
114C2×C47⋊C8C2311yescharacteristic
115C2×C47⋊C8C2311yescharacteristic
116#10625325—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×C47—21no—
130D4×C47—21no—
131D4×C47—21no—
132D4×C47—21no—
133D4×C47C2×D412yes—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—81no—
137C2×C4×C47C2×D411yescharacteristic
138C2×C4×C47C2×D411yescharacteristic
139C2×C4×C47C2411yescharacteristic
140C22⋊D47—24no—
141C22⋊D47—42no—
142C22⋊D47—81no—
143C22⋊D47—81no—
144C2×Dic47—21no—
145C2×Dic47—24no—
146C2×Dic47—21no—
147C2×Dic47—81no—
148C2×Dic47C2×D411yescharacteristic
149C2×Dic47C2×D411yescharacteristic
150C2×Dic47C2×D411yescharacteristic
151D188—21no—
152D188—21no—
153D188—21no—
154D188—21no—
155D188—42no—
156D188—81no—
157D188—81no—
158C4×D47—42no—
159C4×D47—81no—
160C4×D47C2×D412yes—
161C4×D47#4112yes—
162Dic94—21no—
163Dic94C2×D412yes—
164C8×C47—21no—
165C8×C47—21no—
166C47⋊C8—21no—
167C47⋊C8—21no—
168C22×C47—22no—
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—41no—
178C2×D47—41no—
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—41no—
183C2×D47—84no—
184C2×D47#12112yes—
185C4×C47—21no—
186C4×C47—21no—
187C4×C47—41no—
188C4×C47—41no—
189C4×C47C22×D411yescharacteristic
190C4×C47C2×#4111yescharacteristic
191Dic47—22no—
192Dic47—21no—
193Dic47—21no—
194Dic47—41no—
195Dic47#12112yes—
196#3045—471nomaximal, Sylow
197C2×C47—42no—
198C2×C47—81no—
199C2×C47C2×#12111yescharacteristic
200C2×C47#57611yescharacteristic
201C2×C47#57711yescharacteristic
202D47—22no—
203D47—81no—
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#463D4711yescharacteristic, complemented
213#460—471no—
214#460—471no—
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×SD16—471no—
230C2×SD16C2×D4711yescharacteristic, complemented
231C2×D8—471no—
232C2×D8—471no—
233C2×D8C2×D4711yescharacteristic
234C2×M16—471no—
235C22×C8—471no—
236#127—471no—
237#127—471no—
238#124—471no—
239#124C2×D4711yescharacteristic
240#121—941no—
241#121—941no—
242#120—941no—
243#120—941no—
244C4×Q8—471no—
245C4×Q8—471no—
246C4×D4—471no—
247C4×D4—941no—
248C4×D4—941no—
249C4×D4C2×D4711yescharacteristic, complemented
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#103C2×D4711yescharacteristic, complemented
260#102—471no—
261#102—471no—
262#102—471no—
263#102—471no—
264#102—471no—
265#102C2×D4711yescharacteristic
266C24—941no—
267#41—474no—
268#41—942no—
269#41—942no—
270#41—942no—
271C2×Q8—471no—
272C2×Q8C22×D4711yescharacteristic
273C2×D4—471no—
274C2×D4—471no—
275C2×D4—941no—
276C2×D4—942no—
277C2×D4—942no—
278C2×D4—941no—
279C2×D4—941no—
280C2×D4—941no—
281C2×D4—941no—
282C2×D4—941no—
283C2×D4—941no—
284C2×D4C22×D4711yescharacteristic
285C2×D4C22×D4711yescharacteristic
286C22×C4—21no—
287C22×C4—471no—
288C22×C4—941no—
289C22×C4—941no—
290C22×C4—941no—
291C22×C4—941no—
292Q16—942no—
293SD16—22no—
294SD16—942no—
295SD16—942no—
296SD16—942no—
297D8—22no—
298D8—942no—
299D8—942no—
300M16—942no—
301C2×C8—471no—
302C2×C8—471no—
303C2×C8—942no—
304C2×C8C22×D4711yescharacteristic
305C2×C8C22×D4711yescharacteristic
306C4⋊C4—471no—
307C4⋊C4—471no—
308C4⋊C4—471no—
309C4⋊C4—941no—
310C4⋊C4—941no—
311C4⋊C4—941no—
312C4⋊C4C22×D4711yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—471no—
317C22⋊C4—471no—
318C22⋊C4—941no—
319C22⋊C4—941no—
320C22⋊C4—941no—
321C42—471no—
322C42—941no—
323C42—941no—
324C42C22×D4711yescharacteristic
325C23—21no—
326C23—21no—
327C23—471no—
328C23—941no—
329C23—941no—
330C23—3761no—
331C23—3761no—
332C23—1882no—
333Q8—21no—
334Q8—21no—
335Q8—472no—
336Q8—941no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—944no—
341D4—941no—
342D4—941no—
343D4—941no—
344D4—941no—
345D4—3761no—
346D4—3761no—
347D4—3761no—
348D4—3761no—
349D4—1882no—
350D4—1882no—
351D4D4×D4712yes—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—81no—
355C2×C4—471no—
356C2×C4—472no—
357C2×C4—472no—
358C2×C4—471no—
359C2×C4—471no—
360C2×C4—944no—
361C2×C4—941no—
362C2×C4—941no—
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—22no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—472no—
380C22—941no—
381C22—941no—
382C22—3764no—
383C22—1881no—
384C22—1881no—
385C22—1881no—
386C22—1881no—
387C22—1881no—
388C22—1881no—
389C22C2×D4×D4711yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—472no—
395C4—942no—
396C4—941no—
397C4—941no—
398C4—1881no—
399C4C2×D4×D4711yescharacteristic
400C4#41×D4711yescharacteristic
401C2—42no—
402C2—81no—
403C2—942no—
404C2—3761no—
405C2—3761no—
406C2#121×D4711yescharacteristic
407C2#1568992711yescharacteristic
408C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#463C2
socleC22×C47C22×D4
hypercenter#463D47
hypocenterC47#3045
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#13094048C2semidirect
2. C2×#13094045C2semidirect
3. #15689691C2semidirect
4. #15689602C2semidirect
5. #15689348C2semidirect
6. #15689342C2semidirect
7. #15689340C2semidirect
8. #15689324C2semidirect
9. #15689322C2semidirect
10. #15689318C2semidirect
11. #15689316C2semidirect
12. #15689148C2semidirect
13. #15689123C2semidirect
14. #102×D47C2semidirect
15. C47×#463C2semidirect
21. C2×#10625337C22semidirect
23. C2×#10625325C22semidirect
26. C2×#10625334C22semidirect
36. C4×Dic94C22semidirect
37. #13093989C22semidirect
38. D4×Dic47C22semidirect
45. C4⋊(C47⋊C8)C22semidirect
46. Dic47⋊C8C22semidirect
47. Dic47⋊C8C22semidirect
48. #13093948C22semidirect
50. #13093946C22semidirect
53. #13093944C22semidirect
54. C2×SD16×C47C22semidirect
57. C4×D4×C47C22semidirect
58. C4⋊C8×C47C22semidirect
59. #103×C47C22semidirect
75. #10625352D4semidirect
212. #463D47semidirect
220. C47#3045semidirect
230. C2×SD16C2×D47semidirect
249. C4×D4C2×D47semidirect
257. C4⋊C8C2×D47semidirect
259. #103C2×D47semidirect