Finite Group Databasebeta

← #20256118

Subgroups — #20256118

Order 6016.

382 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#15689849C211yesmaximal, characteristic, complemented
2#15689794C211yesmaximal, characteristic
3#15689488C211yesmaximal, characteristic, complemented
4#15689486C211yesmaximal, characteristic, complemented
5#15689468C211yesmaximal, characteristic, complemented
6#15689426C211yesmaximal, characteristic, complemented
7#15689423C211yesmaximal, characteristic, complemented
8#15689402C211yesmaximal, characteristic, complemented
9#15689323C211yesmaximal, characteristic, complemented
10#15689321C211yesmaximal, characteristic, complemented
11#15689321C211yesmaximal, characteristic, complemented
12#15689251C211yesmaximal, characteristic, complemented
13#15689226C211yesmaximal, characteristic, complemented
14#15689208C211yesmaximal, characteristic, complemented
15C47×#440C211yesmaximal, characteristic, complemented
16C2×#10625350—21no—
17C2×#10625336C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19#13094023—21no—
20#13094023C2211yescharacteristic
21#13094021C2211yescharacteristic
22#13094020C2211yescharacteristic
23#13094020C2211yescharacteristic
24#13094016—21no—
25#13094016C2211yescharacteristic
26#13094015—21no—
27#13094015C2211yescharacteristic
28#13093998—21no—
29#13093997—21no—
30#13093997—21no—
31Q8×Dic47C2211yescharacteristic
32Q8×Dic47C2211yescharacteristic
33C4×Dic94—21no—
34C4×Dic94C2211yescharacteristic
35#13093986C2211yescharacteristic
36#13093986C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093955C2211yescharacteristic
39C4⋊(C47⋊C8)C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42#13093946C2211yescharacteristic
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093944C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66#10625350—44no—
67C2×D188—21no—
68C2×D188—21no—
69C2×D188C2311yescharacteristic
70C2×D188C2311yescharacteristic
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×Dic94—21no—
74C2×Dic94D411yescharacteristic
75SD16×C47—22no—
76C2×C8×C47C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C4⋊C4×C47—21no—
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C22⋊C4×C47—21no—
82C42×C47—21no—
83C42×C47C2311yescharacteristic
84#10625336—22no—
85#10625336—22no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47—21no—
91C4⋊Dic47D411yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4D411yescharacteristic
99Dic47⋊C4D411yescharacteristic
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47C2311yescharacteristic
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C23×C47—21no—
107C22×D47—21no—
108C22×D47—21no—
109Q8×C47—21no—
110Q8×C47#4112yescomplemented
111D4×C47—21no—
112D4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—42no—
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2411yescharacteristic
120C22⋊D47—42no—
121C22⋊D47—42no—
122C22⋊D47—81no—
123C22⋊D47—81no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130D188—21no—
131D188—21no—
132D188—21no—
133D188—21no—
134D188—42no—
135D188—81no—
136C4×D47—42no—
137C4×D47—42no—
138Dic94—22no—
139Dic94—42no—
140C8×C47—21no—
141C8×C47—21no—
142C47⋊C8—21no—
143C47⋊C8—21no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47C22×D411yescharacteristic
148C2×D47—41no—
149C2×D47—41no—
150C2×D47—41no—
151C2×D47—41no—
152C2×D47—41no—
153C2×D47—41no—
154C4×C47—22no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—41no—
158C4×C47—41no—
159C4×C47C2×#4111yescharacteristic
160C4×C472−1+411yescharacteristic
161Dic47—21no—
162Dic47—21no—
163Dic47—21no—
164Dic47—41no—
165Dic47—41no—
166Dic47AGL(1,ℤ/8)12yes—
167#3368—471nomaximal, Sylow
168C2×C47—81no—
169C2×C47#54811yescharacteristic
170C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
171C2×C47#57711yescharacteristic
172D47—81no—
173D47—81no—
174#557—471no—
175#550—471no—
176#490—471no—
177#490—471no—
178#486—471no—
179#478—471no—
180#478—471no—
181#474—471no—
182#460—471no—
183#460—471no—
184#460—471no—
185#446—471no—
186#440—471no—
187#440D4711yescharacteristic, complemented
188C4×SD16—471no—
189C47#336811yescharacteristic, complemented, Sylow
190C2×#41—941no—
191C2×SD16—471no—
192C2×SD16—471no—
193C2×SD16C2×D4711yescharacteristic
194C4⋊Q8—471no—
195C4⋊Q8—941no—
196#127—471no—
197#127—471no—
198#127—471no—
199#125—471no—
200#125—471no—
201#125—941no—
202#125—941no—
203#121—941no—
204#121—941no—
205#121—941no—
206C4×Q8—471no—
207C4×Q8—471no—
208C4×Q8—471no—
209C4×Q8—941no—
210C4×Q8C2×D4711yescharacteristic
211C4×D4—471no—
212C4×D4—471no—
213C4×D4C2×D4711yescharacteristic
214#107—471no—
215#107C2×D4711yescharacteristic
216#106—471no—
217C4⋊C8—471no—
218C4⋊C8—471no—
219C4⋊C8—471no—
220#103C2×D4711yescharacteristic
221#102—471no—
222#102—471no—
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#97C2×D4711yescharacteristic
232C4×C8—471no—
233#41—1884no—
234C2×Q8—471no—
235C2×Q8—941no—
236C2×Q8C22×D4711yescharacteristic
237C2×D4—471no—
238C2×D4—471no—
239C2×D4—941no—
240C2×D4—941no—
241C2×D4—941no—
242C2×D4—941no—
243C2×D4—941no—
244C2×D4—941no—
245C2×D4C22×D4711yescharacteristic
246C22×C4—21no—
247C22×C4—941no—
248C22×C4—941no—
249SD16—22no—
250SD16—942no—
251SD16—942no—
252C2×C8—471no—
253C2×C8—471no—
254C2×C8C22×D4711yescharacteristic
255C2×C8C22×D4711yescharacteristic
256C4⋊C4—21no—
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⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4C22×D4711yescharacteristic
270C4⋊C4C22×D4711yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C42—21no—
275C42—471no—
276C42—471no—
277C42—941no—
278C42—941no—
279C42C22×D4711yescharacteristic
280C23—21no—
281C23—941no—
282C23—941no—
283Q8—21no—
284Q8—942no—
285Q8—1882no—
286Q8#1062535012yescomplemented
287D4—21no—
288D4—21no—
289D4—941no—
290D4—941no—
291D4—941no—
292D4—941no—
293D4—3761no—
294D4—3761no—
295D4—3761no—
296D4—1882no—
297D4—1882no—
298D4—1882no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—471no—
304C2×C4—471no—
305C2×C4—471no—
306C2×C4—471no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—1882no—
310C2×C4—1882no—
311C2×C4D4×D4711yescharacteristic
312C2×C4D4×D4711yescharacteristic
313C2×C4C23×D4711yescharacteristic
314C8—21no—
315C8—21no—
316C8—941no—
317C8—941no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—1881no—
322C22—1881no—
323C22—1881no—
324C22—1881no—
325C22—1881no—
326C22—1881no—
327C22C2×D4×D4711yescharacteristic
328C4—22no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—472no—
334C4—941no—
335C4—941no—
336C4—941no—
337C4—1881no—
338C4—1881no—
339C4C2×#1062535011yescharacteristic
340C4#1309407111yescharacteristic
341C2—81no—
342C2—3761no—
343C2—3761no—
344C2#1568978211yescharacteristic
345C2AGL(1,ℤ/8)×D4711yescharacteristic
346C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#440C2
socleC22×C47C22×D4
hypercenter#440D47
hypocenterC47#3368
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #15689849C2semidirect
3. #15689488C2semidirect
4. #15689486C2semidirect
5. #15689468C2semidirect
6. #15689426C2semidirect
7. #15689423C2semidirect
8. #15689402C2semidirect
9. #15689323C2semidirect
10. #15689321C2semidirect
11. #15689321C2semidirect
12. #15689251C2semidirect
13. #15689226C2semidirect
14. #15689208C2semidirect
15. C47×#440C2semidirect
110. Q8×C47#41semidirect
187. #440D47semidirect
189. C47#3368semidirect
286. Q8#10625350semidirect