Finite Group Databasebeta

← #20255471

Subgroups — #20255471

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#15689830C211yesmaximal, characteristic, complemented
2#15689769C211yesmaximal, characteristic
3#15689483C211yesmaximal, characteristic, complemented
4#15689459C211yesmaximal, characteristic, complemented
5#15689437C211yesmaximal, characteristic, complemented
6#15689404C211yesmaximal, characteristic, complemented
7#15689369C211yesmaximal, characteristic, complemented
8#15689364C211yesmaximal, characteristic, complemented
9#15689346C211yesmaximal, characteristic, complemented
10#15689287C211yesmaximal, characteristic, complemented
11#15689276C211yesmaximal, characteristic, complemented
12#15689225C211yesmaximal, characteristic, complemented
13#15689125C211yesmaximal, characteristic, complemented
14C2×#13093946C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C2×Dic188C2211yescharacteristic, complemented
19C2×#10625325C2211yescharacteristic
20C2×#10625325C2211yescharacteristic
21#13094024C2211yescharacteristic, complemented
22#13094015—21no—
23#13094012C2211yescharacteristic
24#13094009—21no—
25#13094003C2211yescharacteristic
26#13094003C2211yescharacteristic
27#13094003C2211yescharacteristic, complemented
28#13094001—21no—
29#13094001—21no—
30#13093998C2211yescharacteristic
31#13093997—21no—
32#13093992—21no—
33C4×Dic94C2211yescharacteristic, complemented
34C4×D188C2211yescharacteristic
35D4×Dic47—21no—
36C2×C4⋊Dic47C2211yescharacteristic
37C2×C4⋊Dic47C2211yescharacteristic, complemented
38C22⋊C4×D47—21no—
39#13093958C2211yescharacteristic, complemented
40#13093958C2211yescharacteristic, complemented
41#13093958C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093949C2211yescharacteristic, complemented
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52C2×M16×C47C2211yescharacteristic, complemented
53C22×C8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55C4⋊C8×C47C2211yescharacteristic, complemented
56C22⋊C8×C47C2211yescharacteristic
57C22⋊C8×C47C2211yescharacteristic, complemented
58#97×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×D4×C47D411yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C22×Dic47—21no—
66C22×Dic47—21no—
67#10625350—22no—
68#10625350—41no—
69C2×D188—22no—
70C2×D188—21no—
71C2×D188—41no—
72C2×D188C2311yescharacteristic
73C2×D188C2311yescharacteristic
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×Dic94—21no—
77C2×Dic94C2311yescharacteristic
78C2×Dic94C2311yescharacteristic
79M16×C47—41no—
80C2×C8×C47—41no—
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C2×C8×C47C2311yescharacteristic
84C2×C8×C47C2311yescharacteristic
85C4⋊C4×C47D411yescharacteristic
86C22⋊C4×C47D411yescharacteristic
87C22⋊C4×C47D411yescharacteristic
88C42×C47C2311yescharacteristic
89C22⋊Dic47—21no—
90C22⋊Dic47—21no—
91C22⋊Dic47—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47—21no—
98C4⋊Dic47—21no—
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102C4⋊Dic47C2311yescharacteristic
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106Dic47⋊C4—21no—
107C4×Dic47—21no—
108Dic188—41no—
109#10625325—22no—
110#10625325—41no—
111C23×C47C2×D411yescharacteristic
112C23×C47C2×D411yescharacteristic
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—42no—
116C22×D47—42no—
117C22×D47—81no—
118D4×C47—22no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2411yescharacteristic
128C22⋊D47—42no—
129C22⋊D47—81no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—81no—
137C2×Dic47—81no—
138D188—21no—
139D188—21no—
140D188—21no—
141D188—42no—
142D188#4112yes—
143C4×D47—42no—
144C4×D47—81no—
145Dic94—21no—
146Dic94—21no—
147Dic94—21no—
148Dic94—21no—
149Dic94—81no—
150C8×C47—21no—
151C8×C47—21no—
152C8×C47—21no—
153C8×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—21no—
159C22×C47#13712yes—
160C22×C47C22×D411yescharacteristic
161C2×D47—22no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—84no—
168C4×C47—21no—
169C4×C47—21no—
170C4×C47—21no—
171C4×C47—21no—
172C4×C47C2×#4111yescharacteristic
173C4×C47H(5,𝔽2)11yescharacteristic
174Dic47—41no—
175Dic47—41no—
176Dic47—41no—
177Dic47—41no—
178Dic47—41no—
179Dic47—41no—
180#3314—471nomaximal, Sylow
181C2×C47—22no—
182C2×C47—41no—
183C2×C47#54611yescharacteristic
184C2×C47C2×#13711yescharacteristic
185C2×C47#57611yescharacteristic
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#467—471no—
196#464—471no—
197#452—471no—
198#450—471no—
199#440—471no—
200#435D4711yescharacteristic, complemented
201#417—471no—
202C2×#102—471no—
203C47#331411yescharacteristic, complemented, Sylow
204C2×#41—471no—
205C22×D4—471no—
206C2×Q16—471no—
207C2×SD16—471no—
208C2×SD16—471no—
209C2×M16C2×D4711yescharacteristic, complemented
210C22×C8C2×D4711yescharacteristic
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—941no—
226C4×D4C2×D4711yescharacteristic
227C2×C4⋊C4—471no—
228C2×C4⋊C4—471no—
229C2×C22⋊C4—941no—
230#107—471no—
231#107—471no—
232#107—471no—
233C4⋊C8C2×D4711yescharacteristic, complemented
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#102—471no—
243#102—471no—
244C22⋊C8C2×D4711yescharacteristic
245C22⋊C8C2×D4711yescharacteristic, complemented
246#97C2×D4711yescharacteristic, complemented
247C24—941no—
248#41—942no—
249#41—1881no—
250C2×Q8—471no—
251C2×Q8—471no—
252C2×Q8—941no—
253C2×D4—471no—
254C2×D4—471no—
255C2×D4—942no—
256C2×D4—941no—
257C2×D4—941no—
258C2×D4—941no—
259C2×D4—1881no—
260C2×D4D18811yescharacteristic
261C22×C4—941no—
262C22×C4—941no—
263C22×C4—941no—
264C22×C4—941no—
265C22×C4C22×D4711yescharacteristic
266C22×C4C22×D4711yescharacteristic
267Q16—1881no—
268SD16—942no—
269SD16—1881no—
270M16—41no—
271C2×C8—41no—
272C2×C8C22×D4711yescharacteristic
273C2×C8C22×D4711yescharacteristic
274C2×C8C22×D4711yescharacteristic
275C2×C8C22×D4711yescharacteristic
276C4⋊C4—471no—
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⋊C4—941no—
287C4⋊C4D18811yescharacteristic
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4D18811yescharacteristic
296C22⋊C4D18811yescharacteristic
297C42—941no—
298C42C22×D4711yescharacteristic
299C23—941no—
300C23—941no—
301C23—3761no—
302C23—1882no—
303C23—1882no—
304C23C2×D18811yescharacteristic
305C23C2×D18811yescharacteristic
306Q8—941no—
307Q8—941no—
308Q8—941no—
309Q8—941no—
310Q8—3761no—
311D4—22no—
312D4—472no—
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—941no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—3761no—
330C2×C4—3761no—
331C2×C4—3761no—
332C2×C4—1882no—
333C2×C4C2×D18811yescharacteristic
334C2×C4C2×D18811yescharacteristic
335C2×C4C2×D18811yescharacteristic
336C2×C4C2×D18811yescharacteristic
337C2×C4C23×D4711yescharacteristic
338C8—21no—
339C8—21no—
340C8—21no—
341C8—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—942no—
348C22—3764no—
349C22—1881no—
350C22—1881no—
351C22—1881no—
352C22—1881no—
353C22—1881no—
354C22#1309405712yes—
355C22C22×D18811yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—1881no—
361C4—1881no—
362C4—1881no—
363C4—1881no—
364C4—1881no—
365C4—1881no—
366C4#41×D4711yescharacteristic
367C4#1309406911yescharacteristic
368C2—22no—
369C2—41no—
370C2—3761no—
371C2—1882no—
372C2#1568976811yescharacteristic
373C2C2×#1309405711yescharacteristic
374C2#1568992811yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#435C2
socleC22×C47C22×D4
hypercenter#435D47
hypocenterC47#3314
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #15689830C2semidirect
3. #15689483C2semidirect
4. #15689459C2semidirect
5. #15689437C2semidirect
6. #15689404C2semidirect
7. #15689369C2semidirect
8. #15689364C2semidirect
9. #15689346C2semidirect
10. #15689287C2semidirect
11. #15689276C2semidirect
12. #15689225C2semidirect
13. #15689125C2semidirect
14. C2×#13093946C2semidirect
15. C47×#435C2semidirect
18. C2×Dic188C22semidirect
21. #13094024C22semidirect
27. #13094003C22semidirect
33. C4×Dic94C22semidirect
37. C2×C4⋊Dic47C22semidirect
39. #13093958C22semidirect
40. #13093958C22semidirect
41. #13093958C22semidirect
42. #13093949C22semidirect
43. #13093949C22semidirect
44. #13093949C22semidirect
45. #13093949C22semidirect
52. C2×M16×C47C22semidirect
55. C4⋊C8×C47C22semidirect
57. C22⋊C8×C47C22semidirect
58. #97×C47C22semidirect
200. #435D47semidirect
203. C47#3314semidirect
209. C2×M16C2×D47semidirect
233. C4⋊C8C2×D47semidirect
245. C22⋊C8C2×D47semidirect
246. #97C2×D47semidirect