Finite Group Databasebeta

← #20255475

Subgroups — #20255475

Order 6016.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689831C211yesmaximal, characteristic, complemented
2#15689764C211yesmaximal, characteristic
3#15689484C211yesmaximal, characteristic, complemented
4#15689456C211yesmaximal, characteristic, complemented
5#15689438C211yesmaximal, characteristic, complemented
6#15689402C211yesmaximal, characteristic, complemented
7#15689372C211yesmaximal, characteristic, complemented
8#15689347C211yesmaximal, characteristic, complemented
9#15689284C211yesmaximal, characteristic, complemented
10#15689273C211yesmaximal, characteristic, complemented
11#15689226C211yesmaximal, characteristic, complemented
12#15689194C211yesmaximal, characteristic, complemented
13#15689123C211yesmaximal, characteristic, complemented
14C2×#13093946C211yesmaximal, characteristic, complemented
15C47×#467C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20C2×#10625324C2211yescharacteristic, complemented
21#13094023C2211yescharacteristic, complemented
22#13094014—21no—
23#13094013C2211yescharacteristic
24#13094009—21no—
25#13094004—21no—
26#13094001—21no—
27#13094000C2211yescharacteristic, complemented
28#13093999—21no—
29#13093999C2211yescharacteristic
30#13093994—21no—
31Q8×Dic47C2211yescharacteristic, complemented
32#13093986C2211yescharacteristic
33C4×C22⋊D47C2211yescharacteristic
34(C22⋊D47)⋊C4—21no—
35C2×C4⋊Dic47C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic, complemented
37C22⋊C4×D47—21no—
38#13093957C2211yescharacteristic, complemented
39#13093957C2211yescharacteristic, complemented
40Dic47⋊C8C2211yescharacteristic, complemented
41#13093948C2211yescharacteristic, complemented
42#13093948C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51#13093934C2211yescharacteristic, complemented
52C2×Q16×C47C2211yescharacteristic, complemented
53C22×C8×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58#103×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47D411yescharacteristic
64C22×Dic47—21no—
65#10625354—22no—
66#10625354—41no—
67C2×D188—22no—
68C2×D188—21no—
69C2×D188—21no—
70C2×D188—21no—
71C2×D188—41no—
72C2×D188C2311yescharacteristic
73C2×D188C2311yescharacteristic
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×C4×D47—21no—
77C2×C4×D47C2311yescharacteristic
78C2×Dic94—21no—
79Q16×C47—41no—
80C2×C8×C47—41no—
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C4⋊C4×C47—21no—
84C4⋊C4×C47—21no—
85C4⋊C4×C47C2311yescharacteristic
86C4⋊C4×C47C2311yescharacteristic
87C22⋊C4×C47—21no—
88C22⋊C4×C47—21no—
89C22⋊Dic47D411yescharacteristic
90#10625336—22no—
91#10625336—41no—
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)⋊C4D411yescharacteristic
98C4⋊Dic47—21no—
99C4⋊Dic47—21no—
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4D411yescharacteristic
106C4×Dic47—21no—
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110#10625324—41no—
111C23×C47C2×D411yescharacteristic
112C22×D47—21no—
113C22×D47—21no—
114C22×D47—42no—
115C22×D47—42no—
116C22×D47—81no—
117C22×D47C2×D411yescharacteristic
118Q8×C47—21no—
119Q8×C47—21no—
120Q8×C47—21no—
121Q8×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—21no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—22no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—81no—
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137D188—21no—
138D188—21no—
139D188—21no—
140D188—42no—
141D188—42no—
142D188—81no—
143D188#4112yes—
144C4×D47—21no—
145C4×D47—21no—
146C4×D47—42no—
147C4×D47—81no—
148C4×D47—81no—
149Dic94—81no—
150C8×C47—21no—
151C8×C47—21no—
152C47⋊C8—21no—
153C47⋊C8—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47#13712yes—
157C22×C47C22×D411yescharacteristic
158C2×D47—21no—
159C2×D47—22no—
160C2×D47—21no—
161C2×D47—21no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—84no—
168C4×C47—21no—
169C4×C47—41no—
170C4×C47—41no—
171C4×C47—41no—
172C4×C47—41no—
173C4×C47C2×#4111yescharacteristic
174C4×C47H(5,𝔽2)11yescharacteristic
175Dic47—21no—
176Dic47—21no—
177Dic47—21no—
178Dic47—41no—
179Dic47—41no—
180#3314—471nomaximal, Sylow
181C2×C47—22no—
182C2×C47#54611yescharacteristic
183C2×C47C2×#13711yescharacteristic
184C2×C47#57611yescharacteristic
185D47—41no—
186D47—42no—
187D47—81no—
188#554—471no—
189#546—471no—
190#489—471no—
191#484—471no—
192#480—471no—
193#474—471no—
194#468—471no—
195#467D4711yescharacteristic, complemented
196#464—471no—
197#452—471no—
198#450—471no—
199#440—471no—
200#435—471no—
201#417—471no—
202C2×#102—471no—
203C47#331411yescharacteristic, complemented, Sylow
204C2×#41—471no—
205C22×D4—471no—
206C2×Q16C2×D4711yescharacteristic, complemented
207C2×SD16—471no—
208C2×SD16—471no—
209C2×M16—471no—
210C22×C8C2×D4711yescharacteristic
211C4⋊Q8—471no—
212#125—941no—
213#124—471no—
214#123—941no—
215C22⋊Q8—471no—
216C22⋊Q8—941no—
217C22⋊Q8—941no—
218C22⋊Q8C2×D4711yescharacteristic
219C22⋊Q8C2×D4711yescharacteristic
220#121—471no—
221#121—941no—
222#120—941no—
223C4×Q8—471no—
224C4×D4—471no—
225C4×D4—471no—
226C4×D4—941no—
227C2×C4⋊C4—471no—
228C2×C4⋊C4—471no—
229C2×C22⋊C4—941no—
230#107—471no—
231#107—471no—
232#107C2×D4711yescharacteristic, complemented
233C4⋊C8—471no—
234#103—471no—
235#103—471no—
236#103C2×D4711yescharacteristic, complemented
237#103C2×D4711yescharacteristic, complemented
238#102—471no—
239#102—471no—
240#102—471no—
241#102—471no—
242#102—471no—
243#102—471no—
244C22⋊C8—471no—
245C22⋊C8—471no—
246#97—471no—
247C24—941no—
248#41—942no—
249#41—1881no—
250C2×Q8—941no—
251C2×Q8C22×D4711yescharacteristic
252C2×Q8C22×D4711yescharacteristic
253C2×D4—471no—
254C2×D4—471no—
255C2×D4—471no—
256C2×D4—942no—
257C2×D4—941no—
258C2×D4—941no—
259C2×D4—941no—
260C2×D4—1881no—
261C22×C4—471no—
262C22×C4—941no—
263C22×C4—941no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4C22×D4711yescharacteristic
267Q16—41no—
268SD16—942no—
269SD16—1881no—
270M16—1881no—
271C2×C8—41no—
272C2×C8—471no—
273C2×C8—471no—
274C2×C8C22×D4711yescharacteristic
275C2×C8C22×D4711yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—471no—
279C4⋊C4—471no—
280C4⋊C4—471no—
281C4⋊C4—941no—
282C4⋊C4—941no—
283C4⋊C4—941no—
284C4⋊C4—941no—
285C4⋊C4—941no—
286C4⋊C4C22×D4711yescharacteristic
287C4⋊C4C22×D4711yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—471no—
291C22⋊C4—471no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C42—471no—
298C42—941no—
299C23—471no—
300C23—941no—
301C23—941no—
302C23—3761no—
303C23—1882no—
304C23—1882no—
305C23D4×D4711yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—3761no—
311D4—472no—
312D4—942no—
313D4—941no—
314D4—941no—
315D4—941no—
316D4—3761no—
317D4—1882no—
318D4—1882no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—471no—
326C2×C4—471no—
327C2×C4—471no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—941no—
332C2×C4—3761no—
333C2×C4—3761no—
334C2×C4—3761no—
335C2×C4—1882no—
336C2×C4D4×D4711yescharacteristic
337C2×C4C23×D4711yescharacteristic
338C8—21no—
339C8—21no—
340C8—941no—
341C8—941no—
342C22—21no—
343C22—21no—
344C22—941no—
345C22—942no—
346C22—941no—
347C22—941no—
348C22—3764no—
349C22—1881no—
350C22—1881no—
351C22—1881no—
352C22—1881no—
353C22—1881no—
354C22#1309405612yes—
355C22C2×D4×D4711yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—941no—
362C4—941no—
363C4—941no—
364C4—1881no—
365C4—1881no—
366C4#41×D4711yescharacteristic
367C4#1309406911yescharacteristic
368C2—22no—
369C2—3761no—
370C2—1881no—
371C2—1882no—
372C2#1568976211yescharacteristic
373C2C2×#1309405611yescharacteristic
374C2#1568992511yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#467C2
socleC22×C47C22×D4
hypercenter#467D47
hypocenterC47#3314
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #15689831C2semidirect
3. #15689484C2semidirect
4. #15689456C2semidirect
5. #15689438C2semidirect
6. #15689402C2semidirect
7. #15689372C2semidirect
8. #15689347C2semidirect
9. #15689284C2semidirect
10. #15689273C2semidirect
11. #15689226C2semidirect
12. #15689194C2semidirect
13. #15689123C2semidirect
14. C2×#13093946C2semidirect
15. C47×#467C2semidirect
20. C2×#10625324C22semidirect
21. #13094023C22semidirect
27. #13094000C22semidirect
31. Q8×Dic47C22semidirect
36. C4⋊C4×D47C22semidirect
38. #13093957C22semidirect
39. #13093957C22semidirect
40. Dic47⋊C8C22semidirect
41. #13093948C22semidirect
42. #13093948C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. #13093934C22semidirect
52. C2×Q16×C47C22semidirect
56. #107×C47C22semidirect
57. #103×C47C22semidirect
58. #103×C47C22semidirect
195. #467D47semidirect
203. C47#3314semidirect
206. C2×Q16C2×D47semidirect
232. #107C2×D47semidirect
236. #103C2×D47semidirect
237. #103C2×D47semidirect