Finite Group Databasebeta

← #20255473

Subgroups — #20255473

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#15689767C211yesmaximal, characteristic
3#15689481C211yesmaximal, characteristic, complemented
4#15689459C211yesmaximal, characteristic, complemented
5#15689435C211yesmaximal, characteristic, complemented
6#15689401C211yesmaximal, characteristic, complemented
7#15689366C211yesmaximal, characteristic, complemented
8#15689362C211yesmaximal, characteristic, complemented
9#15689343C211yesmaximal, characteristic, complemented
10#15689282C211yesmaximal, characteristic, complemented
11#15689224C211yesmaximal, characteristic, complemented
12#15689191C211yesmaximal, characteristic, complemented
13#15689121C211yesmaximal, characteristic, complemented
14C2×#13093945C211yesmaximal, characteristic, complemented
15C47×#450C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×#10625337C2211yescharacteristic, complemented
18C2×#10625324C2211yescharacteristic, complemented
19C22×C47⋊C8C2211yescharacteristic
20#13094023C2211yescharacteristic, complemented
21#13094014—21no—
22#13094011C2211yescharacteristic
23#13094005—21no—
24#13094004—21no—
25#13094003C2211yescharacteristic
26#13094001—21no—
27#13094000C2211yescharacteristic, complemented
28#13093996—21no—
29#13093995C2211yescharacteristic
30#13093993—21no—
31Q8×Dic47C2211yescharacteristic, complemented
32D4×Dic47C2211yescharacteristic
33C4×C22⋊D47C2211yescharacteristic
34(C22⋊D47)⋊C4—21no—
35C2×C4⋊Dic47C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic, complemented
37C2×C22⋊Dic47—21no—
38#13093958C2211yescharacteristic, complemented
39#13093958C2211yescharacteristic, complemented
40#13093957C2211yescharacteristic, complemented
41Dic47⋊C8C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093948C2211yescharacteristic, complemented
45#13093947C2211yescharacteristic, complemented
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093945C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51#13093934C2211yescharacteristic, complemented
52C22×D4×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54C2×SD16×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C24×C47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47—22no—
62C2×D4×C47—21no—
63C2×D4×C47—41no—
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47D411yescharacteristic
70C22×Dic47—21no—
71C22×Dic47—21no—
72C22×Dic47—21no—
73#10625352—22no—
74#10625352—41no—
75C2×C4×D47—21no—
76C2×C4×D47C2311yescharacteristic
77C2×Dic94—21no—
78C2×Dic94C2311yescharacteristic
79SD16×C47—22no—
80SD16×C47—41no—
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C4⋊C4×C47—21no—
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90C22⋊Dic47—21no—
91C22⋊Dic47D411yescharacteristic
92#10625337—41no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4D411yescharacteristic
95C4⋊Dic47—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4D411yescharacteristic
105C4×Dic47—21no—
106C4×Dic47C2311yescharacteristic
107C2×C47⋊C8—41no—
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110#10625324—41no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—42no—
114C23×C47—42no—
115C23×C47—81no—
116C23×C47C2×D411yescharacteristic
117C22×D47C2×D411yescharacteristic
118Q8×C47—21no—
119Q8×C47—21no—
120D4×C47—21no—
121D4×C47—21no—
122D4×C47—21no—
123D4×C47—42no—
124D4×C47#4112yes—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2411yescharacteristic
131C22⋊D47—22no—
132C22⋊D47—42no—
133C22⋊D47—81no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—42no—
139C2×Dic47—81no—
140C2×Dic47—81no—
141C2×Dic47C2×D411yescharacteristic
142C2×Dic47C2×D411yescharacteristic
143C2×Dic47C2×D411yescharacteristic
144C4×D47—21no—
145C4×D47—21no—
146C4×D47—81no—
147Dic94—21no—
148Dic94—21no—
149Dic94—81no—
150C8×C47—21no—
151C8×C47—21no—
152C47⋊C8—21no—
153C47⋊C8—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—22no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—84no—
163C22×C47#13712yes—
164C22×C47C22×D411yescharacteristic
165C2×D47—21no—
166C2×D47—21no—
167C2×D47—21no—
168C4×C47—21no—
169C4×C47—41no—
170C4×C47—41no—
171C4×C47C2×#4111yescharacteristic
172C4×C47H(5,𝔽2)11yescharacteristic
173Dic47—21no—
174Dic47—21no—
175Dic47—21no—
176Dic47—41no—
177Dic47—41no—
178Dic47—41no—
179Dic47—41no—
180#3314—471nomaximal, Sylow
181C2×C47—22no—
182C2×C47—42no—
183C2×C47—81no—
184C2×C47#54611yescharacteristic
185C2×C47C2×#13711yescharacteristic
186C2×C47#57611yescharacteristic
187D47—41no—
188#554—471no—
189#546—471no—
190#489—471no—
191#484—471no—
192#480—471no—
193#474—471no—
194#468—471no—
195#467—471no—
196#464—471no—
197#452—471no—
198#450D4711yescharacteristic, complemented
199#440—471no—
200#435—471no—
201#417—471no—
202C2×#102—471no—
203C47#331411yescharacteristic, complemented, Sylow
204C2×#41—471no—
205C22×D4C2×D4711yescharacteristic
206C2×Q16—471no—
207C2×SD16C2×D4711yescharacteristic
208C2×SD16C2×D4711yescharacteristic
209C2×M16—471no—
210C22×C8—471no—
211C4⋊Q8—471no—
212#125—941no—
213#124—471no—
214#123—941no—
215C22⋊Q8—471no—
216C22⋊Q8—471no—
217C22⋊Q8—941no—
218C22⋊Q8—941no—
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#107—471no—
233C4⋊C8—471no—
234#103—471no—
235#103—471no—
236#103—471no—
237#103—471no—
238#102—471no—
239#102—471no—
240#102—471no—
241#102—471no—
242#102C2×D4711yescharacteristic
243#102C2×D4711yescharacteristic
244C22⋊C8—471no—
245C22⋊C8C2×D4711yescharacteristic
246#97—471no—
247C24—21no—
248#41—942no—
249#41—1881no—
250C2×Q8—471no—
251C2×Q8—941no—
252C2×Q8C22×D4711yescharacteristic
253C2×D4—22no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4—471no—
257C2×D4—941no—
258C2×D4—941no—
259C2×D4C22×D4711yescharacteristic
260C2×D4C22×D4711yescharacteristic
261C22×C4—471no—
262C22×C4—941no—
263C22×C4—941no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4C22×D4711yescharacteristic
267Q16—1881no—
268SD16—22no—
269SD16—41no—
270M16—1881no—
271C2×C8—471no—
272C2×C8—471no—
273C2×C8—1881no—
274C2×C8C22×D4711yescharacteristic
275C2×C8C22×D4711yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—471no—
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⋊C4—941no—
287C4⋊C4C22×D4711yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—471no—
290C22⋊C4—471no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C42—471no—
298C42—941no—
299C23—21no—
300C23—21no—
301C23—42no—
302C23—42no—
303C23—81no—
304C23—471no—
305C23D4×D4711yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—941no—
309Q8—941no—
310Q8—3761no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—942no—
316D4—3761no—
317D4—1882no—
318D4#1062535212yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—471no—
324C2×C4—471no—
325C2×C4—471no—
326C2×C4—941no—
327C2×C4—941no—
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—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—84no—
351C22—941no—
352C22—941no—
353C22—941no—
354C22#1309405312yes—
355C22C2×D4×D4711yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—941no—
360C4—941no—
361C4—941no—
362C4—1881no—
363C4—1881no—
364C4—1881no—
365C4—1881no—
366C4C2×#1062535211yescharacteristic
367C4#1309406911yescharacteristic
368C2—22no—
369C2—42no—
370C2—81no—
371C2—1881no—
372C2#1568976011yescharacteristic
373C2C2×#1309405311yescharacteristic
374C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#450C2
socleC22×C47C22×D4
hypercenter#450D47
hypocenterC47#3314
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #15689831C2semidirect
3. #15689481C2semidirect
4. #15689459C2semidirect
5. #15689435C2semidirect
6. #15689401C2semidirect
7. #15689366C2semidirect
8. #15689362C2semidirect
9. #15689343C2semidirect
10. #15689282C2semidirect
11. #15689224C2semidirect
12. #15689191C2semidirect
13. #15689121C2semidirect
14. C2×#13093945C2semidirect
15. C47×#450C2semidirect
17. C2×#10625337C22semidirect
18. C2×#10625324C22semidirect
20. #13094023C22semidirect
27. #13094000C22semidirect
31. Q8×Dic47C22semidirect
36. C4⋊C4×D47C22semidirect
38. #13093958C22semidirect
39. #13093958C22semidirect
40. #13093957C22semidirect
41. Dic47⋊C8C22semidirect
42. #13093949C22semidirect
43. #13093949C22semidirect
44. #13093948C22semidirect
45. #13093947C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. #13093934C22semidirect
198. #450D47semidirect
203. C47#3314semidirect