Finite Group Databasebeta

← #20255470

Subgroups — #20255470

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#15689828C211yesmaximal, characteristic, complemented
2#15689761C211yesmaximal, characteristic
3#15689484C211yesmaximal, characteristic, complemented
4#15689457C211yesmaximal, characteristic, complemented
5#15689436C211yesmaximal, characteristic, complemented
6#15689401C211yesmaximal, characteristic, complemented
7#15689369C211yesmaximal, characteristic, complemented
8#15689363C211yesmaximal, characteristic, complemented
9#15689348C211yesmaximal, characteristic, complemented
10#15689285C211yesmaximal, characteristic, complemented
11#15689275C211yesmaximal, characteristic, complemented
12#15689220C211yesmaximal, characteristic, complemented
13#15689192C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#417C211yesmaximal, characteristic, complemented
16C2×D4×D47C2211yescharacteristic
17C2×#10625337C2211yescharacteristic, complemented
18C2×#10625325C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20C2×C8×D47C2211yescharacteristic
21#13094023C2211yescharacteristic, complemented
22#13094014—21no—
23#13094013C2211yescharacteristic
24#13094007—21no—
25#13094004C2211yescharacteristic
26#13094003—21no—
27#13094003C2211yescharacteristic, complemented
28#13094002—21no—
29#13094000C2211yescharacteristic
30#13093998C2211yescharacteristic
31#13093996—21no—
32#13093992—21no—
33#13093989C2211yescharacteristic, complemented
34D4×Dic47C2211yescharacteristic
35C4×C22⋊D47—21no—
36C4×C22⋊D47C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic
38C2×(C2×D47)⋊C4—21no—
39#13093958C2211yescharacteristic, complemented
40#13093957C2211yescharacteristic, complemented
41#13093957C2211yescharacteristic, complemented
42Dic47⋊C8C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093948C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic
51#13093934C2211yescharacteristic, complemented
52C2×#41×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic, complemented
54C2×C4⋊C4×C47C2211yescharacteristic, complemented
55#103×C47C2211yescharacteristic, complemented
56#103×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C23×D47—21no—
60#41×C47—22no—
61#41×C47—41no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47C2311yescharacteristic
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47D411yescharacteristic
71C22×Dic47—21no—
72D4×D47—22no—
73D4×D47—41no—
74C2×D188C2311yescharacteristic
75C2×C4×D47—21no—
76C2×C4×D47C2311yescharacteristic
77C2×Dic94—21no—
78C2×Dic94C2311yescharacteristic
79M16×C47—41no—
80C2×C8×C47C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C4⋊C4×C47—21no—
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47D411yescharacteristic
88#10625337—41no—
89#10625335—22no—
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)⋊C4D411yescharacteristic
96C4⋊Dic47—21no—
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4D411yescharacteristic
105C4×Dic47—21no—
106C4×Dic47C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109#10625325—41no—
110C8×D47—41no—
111C23×C47—21no—
112C23×C47C2×D411yescharacteristic
113C22×D47—21no—
114C22×D47—42no—
115C22×D47—42no—
116C22×D47—81no—
117C22×D47C2×D411yescharacteristic
118Q8×C47—21no—
119Q8×C47—21no—
120D4×C47—21no—
121D4×C47—42no—
122D4×C47#4112yes—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—42no—
129C2×C4×C47—81no—
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2411yescharacteristic
132C22⋊D47—22no—
133C22⋊D47—42no—
134C22⋊D47—81no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—81no—
139C2×Dic47C2×D411yescharacteristic
140C2×Dic47C2×D411yescharacteristic
141C2×Dic47C2×D411yescharacteristic
142D188—21no—
143D188—21no—
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—22no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47C22×D411yescharacteristic
161C2×D47—21no—
162C2×D47—21no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—84no—
167C2×D47#13712yes—
168C4×C47—21no—
169C4×C47—41no—
170C4×C47—41no—
171C4×C47—41no—
172C4×C47C2×#4111yescharacteristic
173C4×C47H(5,𝔽2)11yescharacteristic
174Dic47—21no—
175Dic47—21no—
176Dic47—21no—
177Dic47—41no—
178Dic47—41no—
179Dic47—41no—
180#3314—471nomaximal, Sylow
181C2×C47—42no—
182C2×C47—41no—
183C2×C47#54611yescharacteristic
184C2×C47C2×#13711yescharacteristic
185C2×C47#57611yescharacteristic
186D47—22no—
187D47—81no—
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#450—471no—
199#440—471no—
200#435—471no—
201#417D4711yescharacteristic, complemented
202C2×#102—471no—
203C47#331411yescharacteristic, complemented, Sylow
204C2×#41C2×D4711yescharacteristic
205C22×D4—471no—
206C2×Q16—471no—
207C2×SD16—471no—
208C2×SD16—471no—
209C2×M16C2×D4711yescharacteristic, complemented
210C22×C8—471no—
211C4⋊Q8—471no—
212#125—941no—
213#124—471no—
214#123—941no—
215C22⋊Q8—471no—
216C22⋊Q8—471no—
217C22⋊Q8—471no—
218C22⋊Q8—941no—
219C22⋊Q8—941no—
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⋊C4C2×D4711yescharacteristic, complemented
229C2×C22⋊C4—941no—
230#107—471no—
231#107—471no—
232#107—471no—
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#102C2×D4711yescharacteristic
243#102C2×D4711yescharacteristic
244C22⋊C8—471no—
245C22⋊C8—471no—
246#97—471no—
247C24—941no—
248#41—22no—
249#41—41no—
250C2×Q8—471no—
251C2×Q8—941no—
252C2×Q8C22×D4711yescharacteristic
253C2×D4—21no—
254C2×D4—471no—
255C2×D4—471no—
256C2×D4—941no—
257C2×D4—942no—
258C2×D4—941no—
259C2×D4—1881no—
260C2×D4C22×D4711yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—471no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4C22×D4711yescharacteristic
267Q16—1881no—
268SD16—942no—
269SD16—1881no—
270M16—41no—
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—941no—
281C4⋊C4—941no—
282C4⋊C4—941no—
283C4⋊C4—941no—
284C4⋊C4—941no—
285C4⋊C4—941no—
286C4⋊C4C22×D4711yescharacteristic
287C4⋊C4C22×D4711yescharacteristic
288C22⋊C4—471no—
289C22⋊C4—471no—
290C22⋊C4—941no—
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—471no—
301C23—941no—
302C23—3761no—
303C23—1882no—
304C23—1882no—
305C23D4×D4711yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—941no—
309Q8—941no—
310Q8—3761no—
311D4—21no—
312D4—42no—
313D4—942no—
314D4—941no—
315D4—941no—
316D4—3761no—
317D4—1882no—
318D4#1062535012yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—81no—
326C2×C4—471no—
327C2×C4—471no—
328C2×C4—471no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—941no—
332C2×C4—941no—
333C2×C4—941no—
334C2×C4—3761no—
335C2×C4—3761no—
336C2×C4D4×D4711yescharacteristic
337C2×C4C23×D4711yescharacteristic
338C8—21no—
339C8—21no—
340C8—941no—
341C8—941no—
342C22—21no—
343C22—22no—
344C22—21no—
345C22—21no—
346C22—41no—
347C22—41no—
348C22—472no—
349C22—941no—
350C22—941no—
351C22—3764no—
352C22—1881no—
353C22—1881no—
354C22—1881no—
355C22C2×D4×D4711yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—941no—
361C4—941no—
362C4—941no—
363C4—1881no—
364C4—1881no—
365C4—1881no—
366C4C2×#1062535011yescharacteristic
367C4#1309406911yescharacteristic
368C2—41no—
369C2—42no—
370C2—942no—
371C2—3761no—
372C2#1568976311yescharacteristic
373C2#137×D4711yescharacteristic
374C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#417C2
socleC22×C47C22×D4
hypercenter#417D47
hypocenterC47#3314
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #15689828C2semidirect
3. #15689484C2semidirect
4. #15689457C2semidirect
5. #15689436C2semidirect
6. #15689401C2semidirect
7. #15689369C2semidirect
8. #15689363C2semidirect
9. #15689348C2semidirect
10. #15689285C2semidirect
11. #15689275C2semidirect
12. #15689220C2semidirect
13. #15689192C2semidirect
14. #102×D47C2semidirect
15. C47×#417C2semidirect
17. C2×#10625337C22semidirect
21. #13094023C22semidirect
27. #13094003C22semidirect
33. #13093989C22semidirect
39. #13093958C22semidirect
40. #13093957C22semidirect
41. #13093957C22semidirect
42. Dic47⋊C8C22semidirect
43. #13093949C22semidirect
44. #13093948C22semidirect
49. C22⋊(C47⋊C8)C22semidirect
51. #13093934C22semidirect
53. C2×M16×C47C22semidirect
54. C2×C4⋊C4×C47C22semidirect
55. #103×C47C22semidirect
56. #103×C47C22semidirect
201. #417D47semidirect
203. C47#3314semidirect
209. C2×M16C2×D47semidirect
228. C2×C4⋊C4C2×D47semidirect
236. #103C2×D47semidirect
237. #103C2×D47semidirect