Finite Group Databasebeta

← #20256175

Subgroups — #20256175

Order 6016.

384 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689855C211yesmaximal, characteristic, complemented
2D4×Dic94C211yesmaximal, characteristic, complemented
3#15689484C211yesmaximal, characteristic, complemented
4#15689482C211yesmaximal, characteristic, complemented
5#15689468C211yesmaximal, characteristic, complemented
6#15689414C211yesmaximal, characteristic, complemented
7#15689411C211yesmaximal, characteristic, complemented
8#15689406C211yesmaximal, characteristic, complemented
9#15689340C211yesmaximal, characteristic, complemented
10#15689316C211yesmaximal, characteristic
11#15689252C211yesmaximal, characteristic, complemented
12#15689235C211yesmaximal, characteristic, complemented
13#15689233C211yesmaximal, characteristic, complemented
14SD16×Dic47C211yesmaximal, characteristic, complemented
15C47×#463C211yesmaximal, characteristic, complemented
16C22×Dic94—21no—
17C2×#10625334C2211yescharacteristic
18#13094024C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094020C2211yescharacteristic
22#13094013C2211yescharacteristic
23#13094010—21no—
24#13094008—21no—
25#13094006—21no—
26#13094003—21no—
27#13094001—21no—
28#13094001—21no—
29Q8×Dic47C2211yescharacteristic
30C4×Dic94C2211yescharacteristic
31C4×D188C2211yescharacteristic
32D4×Dic47C2211yescharacteristic
33D4×Dic47C2211yescharacteristic
34D4×Dic47C2211yescharacteristic
35(C22⋊D47)⋊C4—21no—
36#13093956C2211yescharacteristic
37#13093956C2211yescharacteristic
38#13093955C2211yescharacteristic
39Dic47⋊C8C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41#13093948C2211yescharacteristic
42#13093948C2211yescharacteristic
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093935C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C2×D8×C47C2211yescharacteristic
54#124×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C22×Dic47—21no—
66C22×Dic47—21no—
67C22×Dic47—21no—
68C2×D188C2311yescharacteristic
69C2×C4×D47—21no—
70C2×Dic94—21no—
71C2×Dic94—21no—
72C2×Dic94—21no—
73C2×Dic94—44no—
74C2×Dic94D411yescharacteristic
75SD16×C47—22no—
76D8×C47—22no—
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C22⋊C4×C47—21no—
81C22⋊C4×C47—21no—
82C22⋊C4×C47—21no—
83C42×C47C2311yescharacteristic
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87#10625334—22no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91C4⋊Dic47—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47D411yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4D411yescharacteristic
100Dic47⋊C4D411yescharacteristic
101C4×Dic47—21no—
102C4×Dic47C2311yescharacteristic
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C23×C47—21no—
107C23×C47—21no—
108C22×D47—21no—
109Q8×C47—21no—
110Q8×C47—21no—
111D4×C47—21no—
112D4×C47—21no—
113D4×C47—21no—
114D4×C47#4112yes—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—42no—
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2411yescharacteristic
121C22⋊D47—42no—
122C22⋊D47—81no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—42no—
127C2×Dic47—42no—
128C2×Dic47—81no—
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133D188—21no—
134D188—21no—
135C4×D47—81no—
136Dic94—22no—
137Dic94—42no—
138Dic94—42no—
139Dic94—42no—
140C8×C47—21no—
141C8×C47—21no—
142C47⋊C8—21no—
143C47⋊C8—21no—
144C22×C47—22no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47C22×D411yescharacteristic
151C2×D47—41no—
152C2×D47—41no—
153C2×D47—41no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47C2×#4111yescharacteristic
159C4×C472−1+411yescharacteristic
160Dic47—21no—
161Dic47—21no—
162Dic47—21no—
163Dic47—41no—
164Dic47—41no—
165Dic47—41no—
166Dic47AGL(1,ℤ/8)12yes—
167#3373—471nomaximal, Sylow
168C2×C47—42no—
169C2×C47—81no—
170C2×C47#54811yescharacteristic
171C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
172C2×C47#57711yescharacteristic
173D47—81no—
174#559—471no—
175D4×Q8—471no—
176#489—471no—
177#489—471no—
178#486—471no—
179#476—471no—
180#476—471no—
181#475—471no—
182#463—471no—
183#463D4711yescharacteristic, complemented
184#459—471no—
185#446—471no—
186#442—471no—
187#442—471no—
188C4×SD16—471no—
189C47#337311yescharacteristic, complemented, Sylow
190C22×Q8—941no—
191C2×SD16C2×D4711yescharacteristic
192C2×D8—471no—
193C2×D8C2×D4711yescharacteristic
194C4⋊Q8—471no—
195C4⋊Q8—471no—
196C4⋊Q8—471no—
197#127—471no—
198#124—471no—
199#124—941no—
200#124C2×D4711yescharacteristic
201#123—941no—
202#123—941no—
203C22⋊Q8—941no—
204C22⋊Q8—941no—
205C22⋊Q8—941no—
206C4×Q8—471no—
207C4×Q8—471no—
208C4×D4—471no—
209C4×D4—471no—
210C4×D4—471no—
211C4×D4—471no—
212C4×D4—941no—
213C4×D4C2×D4711yescharacteristic
214#106—471no—
215#106—471no—
216#106—471no—
217C4⋊C8—471no—
218C4⋊C8—471no—
219C4⋊C8C2×D4711yescharacteristic
220#103—471no—
221#103—471no—
222#103C2×D4711yescharacteristic
223#102—471no—
224#102—471no—
225#102—471no—
226#102—471no—
227#102—471no—
228#102—471no—
229#102C2×D4711yescharacteristic
230#97—471no—
231#97—471no—
232C4×C8—471no—
233C2×Q8—471no—
234C2×Q8—941no—
235C2×Q8—941no—
236C2×Q8—941no—
237C2×Q8—1884no—
238C2×Q8C22×D4711yescharacteristic
239C2×D4—471no—
240C2×D4—941no—
241C2×D4—941no—
242C2×D4C22×D4711yescharacteristic
243C2×D4C22×D4711yescharacteristic
244C22×C4—21no—
245C22×C4—941no—
246C22×C4—941no—
247C22×C4—941no—
248C22×C4—941no—
249SD16—22no—
250D8—22no—
251D8—942no—
252C2×C8—471no—
253C2×C8—471no—
254C2×C8C22×D4711yescharacteristic
255C2×C8C22×D4711yescharacteristic
256C4⋊C4—471no—
257C4⋊C4—471no—
258C4⋊C4—471no—
259C4⋊C4—471no—
260C4⋊C4—471no—
261C4⋊C4—471no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4C22×D4711yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C42—471no—
277C42—471no—
278C42—941no—
279C42C22×D4711yescharacteristic
280C23—21no—
281C23—21no—
282C23—941no—
283Q8—21no—
284Q8—21no—
285Q8—942no—
286Q8—1882no—
287Q8—1882no—
288Q8—1882no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—941no—
293D4—941no—
294D4—3761no—
295D4—1882no—
296D4#1062535212yes—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—471no—
301C2×C4—471no—
302C2×C4—471no—
303C2×C4—471no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—3761no—
308C2×C4—3761no—
309C2×C4—1882no—
310C2×C4—1882no—
311C2×C4D4×D4711yescharacteristic
312C2×C4D4×D4711yescharacteristic
313C2×C4C23×D4711yescharacteristic
314C8—21no—
315C8—21no—
316C8—941no—
317C8—941no—
318C22—22no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—1881no—
325C22—1881no—
326C22—1881no—
327C22C2×D4×D4711yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—472no—
333C4—941no—
334C4—941no—
335C4—941no—
336C4—1881no—
337C4—1881no—
338C4—1881no—
339C4C2×#1062535211yescharacteristic
340C4#1309407111yescharacteristic
341C2—42no—
342C2—81no—
343C2—3761no—
344C2#1568977911yescharacteristic
345C2AGL(1,ℤ/8)×D4711yescharacteristic
346C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#463C2
socleC22×C47C22×D4
hypercenter#463D47
hypocenterC47#3373
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #15689855C2semidirect
2. D4×Dic94C2semidirect
3. #15689484C2semidirect
4. #15689482C2semidirect
5. #15689468C2semidirect
6. #15689414C2semidirect
7. #15689411C2semidirect
8. #15689406C2semidirect
9. #15689340C2semidirect
11. #15689252C2semidirect
12. #15689235C2semidirect
13. #15689233C2semidirect
14. SD16×Dic47C2semidirect
15. C47×#463C2semidirect
183. #463D47semidirect
189. C47#3373semidirect