Finite Group Databasebeta

← #20255236

Subgroups — #20255236

Order 6016.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689821C211yesmaximal, characteristic, complemented
2#15689764C211yesmaximal, characteristic, complemented
3#15689479C211yesmaximal, characteristic, complemented
4#15689450C211yesmaximal, characteristic, complemented
5#15689426C211yesmaximal, characteristic, complemented
6#15689360C211yesmaximal, characteristic, complemented
7#15689354C211yesmaximal, characteristic, complemented
8#15689341C211yesmaximal, characteristic, complemented
9#15689271C211yesmaximal, characteristic, complemented
10#15689259C211yesmaximal, characteristic, complemented
11#15689205C211yesmaximal, characteristic, complemented
12(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
13#15689118C211yesmaximal, characteristic, complemented
14C2×#13093944C211yesmaximal, characteristic, complemented
15C47×#484C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C2×#10625336C2211yescharacteristic, complemented
19C2×D376C2211yescharacteristic
20C2×D376C2211yescharacteristic
21C22×C47⋊C8C2211yescharacteristic
22C2×C8×D47C2211yescharacteristic, complemented
23#13094019—21no—
24#13094015C2211yescharacteristic, complemented
25#13094013C2211yescharacteristic
26#13094009—21no—
27#13094009—21no—
28#13093999—21no—
29#13093999C2211yescharacteristic
30#13093999C2211yescharacteristic, complemented
31#13093998—21no—
32#13093998C2211yescharacteristic
33#13093994—21no—
34#13093986C2211yescharacteristic
35#13093986C2211yescharacteristic, complemented
36C4×C22⋊D47—21no—
37C4×C22⋊D47C2211yescharacteristic
38#13093982C2211yescharacteristic, complemented
39C22⋊C4×D47—21no—
40#13093955C2211yescharacteristic, complemented
41Dic47⋊C8C2211yescharacteristic, complemented
42#13093948C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093944C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093944C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C22⋊Q8×C47C2211yescharacteristic
53C2×C4⋊C4×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic, complemented
55#107×C47C2211yescharacteristic, complemented
56#103×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47D411yescharacteristic
65#10625354—22no—
66#10625354—41no—
67C2×D188—22no—
68C2×D188—21no—
69C2×D188—21no—
70C2×D188—21no—
71C2×D188—21no—
72C2×D188—41no—
73C2×D188C2311yescharacteristic
74C2×D188C2311yescharacteristic
75C2×D188C2311yescharacteristic
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×C4×D47—21no—
79C2×C4×D47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C4⋊C4×C47—21no—
83C4⋊C4×C47—21no—
84C4⋊C4×C47C2311yescharacteristic
85C4⋊C4×C47C2311yescharacteristic
86C4⋊C4×C47C2311yescharacteristic
87C22⋊C4×C47—21no—
88C22⋊Dic47D411yescharacteristic
89#10625336—41no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4D411yescharacteristic
99C4⋊Dic47—21no—
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
102Dic47⋊C4D411yescharacteristic
103C4×Dic47—21no—
104C4×Dic47C2311yescharacteristic
105C2×C47⋊C8—41no—
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108D376—22no—
109D376—41no—
110C8×D47—41no—
111C23×C47C2×D411yescharacteristic
112C22×D47—21no—
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—42no—
116C22×D47—42no—
117C22×D47—81no—
118C22×D47C2×D411yescharacteristic
119Q8×C47—21no—
120Q8×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—81no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—22no—
131C22⋊D47—42no—
132C2×Dic47—21no—
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136D188—21no—
137D188—21no—
138D188—21no—
139D188—21no—
140D188—21no—
141D188—42no—
142D188—42no—
143D188—81no—
144D188—81no—
145D188#4112yes—
146C4×D47—21no—
147C4×D47—21no—
148C4×D47—42no—
149C4×D47—81no—
150C4×D47—81no—
151C8×C47—21no—
152C8×C47—21no—
153C47⋊C8—21no—
154C47⋊C8—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47#13512yes—
158C22×C47C22×D411yescharacteristic
159C2×D47—21no—
160C2×D47—22no—
161C2×D47—21no—
162C2×D47—21no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—84no—
172C4×C47—21no—
173C4×C47—41no—
174C4×C47—41no—
175C4×C47—41no—
176C4×C47—41no—
177C4×C47C2×#4111yescharacteristic
178C4×C47H(5,𝔽2)11yescharacteristic
179Dic47—21no—
180Dic47—21no—
181Dic47—21no—
182Dic47—41no—
183#3297—471nomaximal, Sylow
184C2×C47—22no—
185C2×C47#54611yescharacteristic
186C2×C47C2×#13511yescharacteristic
187C2×C47#57611yescharacteristic
188D47—41no—
189D47—42no—
190D47—81no—
191D47—81no—
192#553—471no—
193#546—471no—
194#488—471no—
195#484D4711yescharacteristic, complemented
196#482—471no—
197#478—471no—
198#466—471no—
199#465—471no—
200#463—471no—
201#449—471no—
202#447—471no—
203C4×D8—471no—
204C8×D4—471no—
205#416—471no—
206C2×#102—471no—
207C47#329711yescharacteristic, complemented, Sylow
208C2×#41—471no—
209C22×D4—471no—
210C2×SD16—471no—
211C2×D8—471no—
212C2×D8—471no—
213C22×C8—471no—
214C22×C8—471no—
215#126—941no—
216#125—471no—
217#124—471no—
218#123—941no—
219#123—941no—
220C22⋊Q8C2×D4711yescharacteristic
221#121—471no—
222#121—471no—
223#121—471no—
224#121—941no—
225#121—941no—
226#120—941no—
227C4×D4—471no—
228C4×D4—471no—
229C4×D4—471no—
230C4×D4—941no—
231#117—471no—
232C2×C4⋊C4C2×D4711yescharacteristic
233C2×C22⋊C4—941no—
234#107C2×D4711yescharacteristic, complemented
235#107C2×D4711yescharacteristic, complemented
236#106—471no—
237C4⋊C8—471no—
238#103—471no—
239#103C2×D4711yescharacteristic, complemented
240#103C2×D4711yescharacteristic, complemented
241#102—471no—
242#102—471no—
243#102—471no—
244#102—471no—
245#102—471no—
246#102—471no—
247#102—471no—
248C22⋊C8—471no—
249C22⋊C8C2×D4711yescharacteristic
250C4×C8—471no—
251C24—941no—
252#41—942no—
253#41—1881no—
254C2×Q8C22×D4711yescharacteristic
255C2×D4—471no—
256C2×D4—471no—
257C2×D4—471no—
258C2×D4—471no—
259C2×D4—942no—
260C2×D4—941no—
261C2×D4—941no—
262C2×D4—941no—
263C2×D4—941no—
264C2×D4—941no—
265C2×D4—1881no—
266C22×C4—21no—
267C22×C4—471no—
268C22×C4—941no—
269C22×C4—941no—
270C22×C4—941no—
271C22×C4C22×D4711yescharacteristic
272SD16—1881no—
273D8—942no—
274D8—1881no—
275C2×C8—471no—
276C2×C8—471no—
277C2×C8—1881no—
278C2×C8—1881no—
279C2×C8C22×D4711yescharacteristic
280C2×C8C22×D4711yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—471no—
284C4⋊C4—471no—
285C4⋊C4—941no—
286C4⋊C4—941no—
287C4⋊C4C22×D4711yescharacteristic
288C4⋊C4C22×D4711yescharacteristic
289C4⋊C4C22×D4711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—471no—
292C22⋊C4—471no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C22⋊C4—941no—
298C22⋊C4—941no—
299C22⋊C4—941no—
300C22⋊C4—941no—
301C42—471no—
302C42—941no—
303C23—471no—
304C23—941no—
305C23—941no—
306C23—941no—
307C23—3761no—
308C23—1882no—
309C23—1882no—
310C23D4×D4711yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—472no—
314D4—942no—
315D4—941no—
316D4—941no—
317D4—941no—
318D4—941no—
319D4—941no—
320D4—3761no—
321D4—3761no—
322D4—1882no—
323D4—1882no—
324D4—1882no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—81no—
332C2×C4—471no—
333C2×C4—471no—
334C2×C4—471no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—941no—
338C2×C4—3761no—
339C2×C4—3761no—
340C2×C4—1882no—
341C2×C4D4×D4711yescharacteristic
342C2×C4C23×D4711yescharacteristic
343C8—21no—
344C8—21no—
345C8—941no—
346C8—941no—
347C22—21no—
348C22—21no—
349C22—941no—
350C22—942no—
351C22—941no—
352C22—941no—
353C22—3764no—
354C22—1881no—
355C22—1881no—
356C22—1881no—
357C22—1881no—
358C22—1881no—
359C22—1881no—
360C22—1881no—
361C22—1881no—
362C22#1309404712yes—
363C22C2×D4×D4711yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—941no—
370C4—941no—
371C4—941no—
372C4—1881no—
373C4#41×D4711yescharacteristic
374C4#1309407011yescharacteristic
375C2—22no—
376C2—3761no—
377C2—3761no—
378C2—1881no—
379C2—1882no—
380C2#1568976511yescharacteristic
381C2C2×#1309404711yescharacteristic
382C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#484C2
socleC22×C47C22×D4
hypercenter#484D47
hypocenterC47#3297
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #15689821C2semidirect
2. #15689764C2semidirect
3. #15689479C2semidirect
4. #15689450C2semidirect
5. #15689426C2semidirect
6. #15689360C2semidirect
7. #15689354C2semidirect
8. #15689341C2semidirect
9. #15689271C2semidirect
10. #15689259C2semidirect
11. #15689205C2semidirect
12. (C22⋊D47)⋊C8C2semidirect
13. #15689118C2semidirect
14. C2×#13093944C2semidirect
15. C47×#484C2semidirect
18. C2×#10625336C22semidirect
22. C2×C8×D47C22semidirect
24. #13094015C22semidirect
30. #13093999C22semidirect
35. #13093986C22semidirect
38. #13093982C22semidirect
40. #13093955C22semidirect
41. Dic47⋊C8C22semidirect
42. #13093948C22semidirect
49. #13093944C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. C8×Dic47C22semidirect
54. #107×C47C22semidirect
55. #107×C47C22semidirect
56. #103×C47C22semidirect
57. #103×C47C22semidirect
195. #484D47semidirect
207. C47#3297semidirect
234. #107C2×D47semidirect
235. #107C2×D47semidirect
239. #103C2×D47semidirect
240. #103C2×D47semidirect