Finite Group Databasebeta

← #20254389

Subgroups — #20254389

Order 6016.

400 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689677C211yesmaximal, characteristic, complemented
2#124×D47C211yesmaximal, characteristic
3#15689516C211yesmaximal, characteristic, complemented
4#15689514C211yesmaximal, characteristic, complemented
5#15689484C211yesmaximal, characteristic, complemented
6#15689481C211yesmaximal, characteristic, complemented
7#15689346C211yesmaximal, characteristic, complemented
8#15689345C211yesmaximal, characteristic, complemented
9#15689342C211yesmaximal, characteristic, complemented
10#15689280C211yesmaximal, characteristic, complemented
11#15689277C211yesmaximal, characteristic, complemented
12#15689275C211yesmaximal, characteristic
13#15689272C211yesmaximal, characteristic
14#15689179C211yesmaximal, characteristic, complemented
15C47×#464C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×Dic188C2211yescharacteristic, complemented
19C2×#10625337C2211yescharacteristic, complemented
20C2×#10625337C2211yescharacteristic, complemented
21C2×#10625325C2211yescharacteristic
22C2×#10625335C2211yescharacteristic
23C2×#10625336C2211yescharacteristic
24#13094023C2211yescharacteristic, complemented
25#13094022C2211yescharacteristic, complemented
26#13094014—21no—
27#13094013C2211yescharacteristic
28#13094012C2211yescharacteristic
29#13094011C2211yescharacteristic
30#13094010—21no—
31#13094010—21no—
32#13094004C2211yescharacteristic
33#13094002—21no—
34#13094000C2211yescharacteristic
35C4×Dic94—21no—
36C4×Dic94C2211yescharacteristic, complemented
37#13093981—21no—
38C22⋊C4×D47—21no—
39C22⋊C4×D47—21no—
40C42×D47C2211yescharacteristic
41C4⋊(C47⋊C8)C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093948C2211yescharacteristic, complemented
44#13093947C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093944C2211yescharacteristic
48(C2×D47)⋊C8C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50#13093934C2211yescharacteristic, complemented
51#13093934C2211yescharacteristic, complemented
52C2×Q16×C47C2211yescharacteristic, complemented
53C2×SD16×C47C2211yescharacteristic
54#124×C47C2211yescharacteristic
55C4×Q8×C47C2211yescharacteristic, complemented
56C4⋊C8×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64Q8×D47—41no—
65Q8×D47—41no—
66D4×D47—41no—
67D4×D47—41no—
68C2×D188C2311yescharacteristic
69C2×C4×D47—21no—
70C2×C4×D47D411yescharacteristic
71C2×C4×D47D411yescharacteristic
72C2×C4×D47C2311yescharacteristic
73C2×Dic94—21no—
74C2×Dic94—21no—
75C2×Dic94C2311yescharacteristic
76C2×Dic94C2311yescharacteristic
77Q16×C47—41no—
78SD16×C47—41no—
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C4⋊C4×C47—21no—
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C42×C47—21no—
86C42×C47C2311yescharacteristic
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89#10625337—41no—
90#10625337—41no—
91#10625336—41no—
92#10625335—41no—
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)⋊C4—21no—
99C4⋊Dic47—21no—
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106C4×Dic47—21no—
107C4×Dic47D411yescharacteristic
108C4×Dic47D411yescharacteristic
109C4×Dic47C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112Dic188—41no—
113#10625325—41no—
114C23×C47—21no—
115C22×D47—21no—
116C22×D47—42no—
117C22×D47—42no—
118C22×D47—42no—
119C22×D47C2×D411yescharacteristic
120Q8×C47—21no—
121Q8×C47—21no—
122Q8×C47—21no—
123Q8×C47—21no—
124D4×C47—21no—
125D4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2411yescharacteristic
132C22⋊D47—42no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138C2×Dic47C2×D411yescharacteristic
139D188—21no—
140D188—21no—
141C4×D47—22no—
142C4×D47—21no—
143C4×D47—21no—
144C4×D47—41no—
145C4×D47—42no—
146Dic94—21no—
147Dic94—21no—
148Dic94—21no—
149Dic94—21no—
150Dic94—42no—
151Dic94—42no—
152C8×C47—21no—
153C8×C47—21no—
154C47⋊C8—21no—
155C47⋊C8—21no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47C22×D411yescharacteristic
160C2×D47—21no—
161C2×D47—21no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—84no—
166C2×D47#13712yes—
167C4×C47—21no—
168C4×C47—21no—
169C4×C47—41no—
170C4×C47—41no—
171C4×C47—41no—
172C4×C47H(5,𝔽2)11yescharacteristic
173C4×C47H(5,𝔽2)11yescharacteristic
174Dic47—21no—
175Dic47—21no—
176Dic47—21no—
177Dic47—41no—
178Dic47—41no—
179Dic47—41no—
180#3215—471nomaximal, Sylow
181C2×C47—81no—
182C2×C47#53511yescharacteristic
183C2×C47C2×#13711yescharacteristic
184C2×C47#57511yescharacteristic
185D47—22no—
186D47—81no—
187#533—471no—
188C2×#124—471no—
189#497—471no—
190#497—471no—
191#489—471no—
192#489—471no—
193#464—471no—
194#464—471no—
195#464—471no—
196#464D4711yescharacteristic, complemented
197#451—471no—
198#451—471no—
199#450—471no—
200#450—471no—
201#432—471no—
202C47#321511yescharacteristic, complemented, Sylow
203C22×Q8—471no—
204C22×D4—471no—
205C2×Q16—471no—
206C2×Q16—471no—
207C2×Q16—471no—
208C2×Q16C2×D4711yescharacteristic, complemented
209C2×SD16—471no—
210C2×SD16—471no—
211C2×SD16—471no—
212C2×SD16C2×D4711yescharacteristic
213C4⋊Q8—471no—
214C4⋊Q8—471no—
215#125—941no—
216#124—471no—
217#124—471no—
218#124—471no—
219#124—941no—
220#124—941no—
221#124C2×D4711yescharacteristic
222C22⋊Q8—471no—
223C22⋊Q8—471no—
224C22⋊Q8—941no—
225C4×Q8—471no—
226C4×Q8—941no—
227C4×Q8C2×D4711yescharacteristic, complemented
228#117—941no—
229C2×C22⋊C4—941no—
230C2×C22⋊C4—941no—
231C2×C42—471no—
232C4⋊C8—471no—
233C4⋊C8C2×D4711yescharacteristic, complemented
234#103—471no—
235#103—471no—
236#103—471no—
237#103C2×D4711yescharacteristic, complemented
238#102—471no—
239#102—471no—
240#102—471no—
241#102C2×D4711yescharacteristic
242C22⋊C8—471no—
243C22⋊C8—471no—
244#97—471no—
245#97—471no—
246C24—941no—
247C2×Q8—471no—
248C2×Q8—471no—
249C2×Q8—941no—
250C2×Q8—941no—
251C2×Q8—1881no—
252C2×Q8—1881no—
253C2×Q8C22×D4711yescharacteristic
254C2×Q8C22×D4711yescharacteristic
255C2×D4—471no—
256C2×D4—941no—
257C2×D4—1881no—
258C2×D4—1881no—
259C2×D4C22×D4711yescharacteristic
260C22×C4—471no—
261C22×C4—471no—
262C22×C4—471no—
263C22×C4—941no—
264Q16—41no—
265Q16—1881no—
266Q16—1881no—
267Q16—1881no—
268SD16—41no—
269SD16—1881no—
270SD16—1881no—
271SD16—1881no—
272C2×C8—471no—
273C2×C8—471no—
274C2×C8C22×D4711yescharacteristic
275C2×C8C22×D4711yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—471no—
278C4⋊C4—941no—
279C4⋊C4—941no—
280C4⋊C4—941no—
281C4⋊C4—941no—
282C4⋊C4—941no—
283C4⋊C4—941no—
284C4⋊C4C22×D4711yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C42—21no—
296C42—471no—
297C42—471no—
298C42—471no—
299C42—941no—
300C42C22×D4711yescharacteristic
301C23—21no—
302C23—471no—
303C23—941no—
304C23—1882no—
305C23—1882no—
306C23—1882no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—941no—
312Q8—941no—
313Q8—941no—
314Q8—941no—
315Q8—1882no—
316Q8—1882no—
317D4—21no—
318D4—21no—
319D4—941no—
320D4—941no—
321D4—1882no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—471no—
326C2×C4—471no—
327C2×C4—471no—
328C2×C4—942no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—941no—
332C2×C4—941no—
333C2×C4—941no—
334C2×C4—1881no—
335C2×C4—1882no—
336C2×C4D4×D4711yescharacteristic
337C2×C4D4×D4711yescharacteristic
338C2×C4C23×D4711yescharacteristic
339C8—21no—
340C8—21no—
341C8—941no—
342C8—941no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—472no—
347C22—941no—
348C22—941no—
349C22—3764no—
350C22—1881no—
351C22—1881no—
352C22—1881no—
353C22C2×D4×D4711yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—941no—
360C4—941no—
361C4—941no—
362C4—1881no—
363C4—1881no—
364C4—1881no—
365C4#1309406911yescharacteristic
366C4#1309407011yescharacteristic
367C2—81no—
368C2—942no—
369C2—3761no—
370C2#1568968911yescharacteristic
371C2#137×D4711yescharacteristic
372C2#1568992011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#464C2
socleC22×C47C22×D4
hypercenter#464D47
hypocenterC47#3215
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #15689677C2semidirect
3. #15689516C2semidirect
4. #15689514C2semidirect
5. #15689484C2semidirect
6. #15689481C2semidirect
7. #15689346C2semidirect
8. #15689345C2semidirect
9. #15689342C2semidirect
10. #15689280C2semidirect
11. #15689277C2semidirect
14. #15689179C2semidirect
15. C47×#464C2semidirect
18. C2×Dic188C22semidirect
19. C2×#10625337C22semidirect
20. C2×#10625337C22semidirect
24. #13094023C22semidirect
25. #13094022C22semidirect
36. C4×Dic94C22semidirect
41. C4⋊(C47⋊C8)C22semidirect
42. #13093949C22semidirect
43. #13093948C22semidirect
44. #13093947C22semidirect
50. #13093934C22semidirect
51. #13093934C22semidirect
52. C2×Q16×C47C22semidirect
55. C4×Q8×C47C22semidirect
56. C4⋊C8×C47C22semidirect
57. #103×C47C22semidirect
196. #464D47semidirect
202. C47#3215semidirect
208. C2×Q16C2×D47semidirect
227. C4×Q8C2×D47semidirect
233. C4⋊C8C2×D47semidirect
237. #103C2×D47semidirect