Finite Group Databasebeta

← #20256183

Subgroups — #20256183

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#15689856C211yesmaximal, characteristic, complemented
2#15689788C211yesmaximal, characteristic, complemented
3#15689485C211yesmaximal, characteristic, complemented
4#15689481C211yesmaximal, characteristic, complemented
5#15689468C211yesmaximal, characteristic, complemented
6#15689412C211yesmaximal, characteristic, complemented
7#15689407C211yesmaximal, characteristic, complemented
8#15689339C211yesmaximal, characteristic, complemented
9#15689337C211yesmaximal, characteristic, complemented
10#15689317C211yesmaximal, characteristic
11#15689252C211yesmaximal, characteristic, complemented
12#15689234C211yesmaximal, characteristic, complemented
13#15689233C211yesmaximal, characteristic, complemented
14#15689210C211yesmaximal, characteristic, complemented
15C47×#476C211yesmaximal, characteristic, complemented
16C2×Q8×D47—21no—
17C2×#10625325C2211yescharacteristic
18C2×D376C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094020C2211yescharacteristic
23#13094012C2211yescharacteristic
24#13094011C2211yescharacteristic
25#13094010—21no—
26#13094007—21no—
27#13094006—21no—
28#13094002—21no—
29#13094002—21no—
30#13094000—21no—
31C4×Dic94C2211yescharacteristic
32#13093989C2211yescharacteristic
33C4×D188C2211yescharacteristic
34#13093986C2211yescharacteristic
35#13093986C2211yescharacteristic
36#13093986C2211yescharacteristic
37C4×C22⋊D47—21no—
38#13093955C2211yescharacteristic
39Dic47⋊C8C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41#13093949C2211yescharacteristic
42#13093947C2211yescharacteristic
43#13093947C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093935C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic
53C4×D4×C47C2211yescharacteristic
54#106×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64Q8×D47—44no—
65C2×D188C2311yescharacteristic
66C2×D188C2311yescharacteristic
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×Dic94—21no—
72C2×Dic94—21no—
73C2×Dic94D411yescharacteristic
74C2×Dic94C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C4⋊C4×C47—21no—
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C22⋊C4×C47—21no—
82C42×C47C2311yescharacteristic
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85#10625334—22no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92C4⋊Dic47D411yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4D411yescharacteristic
98Dic47⋊C4D411yescharacteristic
99C4×Dic47—21no—
100C4×Dic47C2311yescharacteristic
101C4×Dic47C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104D376—22no—
105#10625325—22no—
106C23×C47—21no—
107C22×D47—21no—
108C22×D47—21no—
109Q8×C47—42no—
110D4×C47—21no—
111D4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—81no—
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2411yescharacteristic
119C22⋊D47—42no—
120C22⋊D47—81no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47C2×D411yescharacteristic
124C2×Dic47C2×D411yescharacteristic
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127D188—21no—
128D188—21no—
129D188—21no—
130D188#4112yes—
131C4×D47—42no—
132C4×D47—42no—
133C4×D47—42no—
134C4×D47—81no—
135Dic94—22no—
136Dic94—21no—
137Dic94—21no—
138Dic94—42no—
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—22no—
149C2×D47—41no—
150C2×D47—41no—
151C2×D47—41no—
152C2×D47—41no—
153C2×D47—41no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—41no—
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#3373—471nomaximal, Sylow
168C2×C47—81no—
169C2×C47#54811yescharacteristic
170C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
171C2×C47#57711yescharacteristic
172D47—42no—
173D47—81no—
174#559—471no—
175D4×Q8—471no—
176#489—471no—
177#489—471no—
178#486—471no—
179#476—471no—
180#476D4711yescharacteristic, complemented
181#475—471no—
182#463—471no—
183#463—471no—
184#459—471no—
185#446—471no—
186#442—471no—
187#442—471no—
188C4×SD16—471no—
189C47#337311yescharacteristic, complemented, Sylow
190C22×Q8—941no—
191C2×SD16—471no—
192C2×D8—471no—
193C2×D8—471no—
194C4⋊Q8—471no—
195C4⋊Q8—471no—
196C4⋊Q8C2×D4711yescharacteristic
197#127—471no—
198#124—471no—
199#124—471no—
200#124—941no—
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#106C2×D4711yescharacteristic
216#106C2×D4711yescharacteristic
217C4⋊C8—471no—
218C4⋊C8—471no—
219C4⋊C8C2×D4711yescharacteristic
220#103—471no—
221#103—471no—
222#103—471no—
223#102—471no—
224#102—471no—
225#102—471no—
226#102—471no—
227#102—471no—
228#102C2×D4711yescharacteristic
229#102C2×D4711yescharacteristic
230#97—471no—
231#97—471no—
232C4×C8—471no—
233C2×Q8—21no—
234C2×Q8—471no—
235C2×Q8—471no—
236C2×Q8—941no—
237C2×Q8—941no—
238C2×Q8—1884no—
239C2×D4—471no—
240C2×D4—471no—
241C2×D4—941no—
242C2×D4—941no—
243C2×D4C22×D4711yescharacteristic
244C22×C4—21no—
245C22×C4—941no—
246C22×C4—941no—
247C22×C4—941no—
248C22×C4—941no—
249SD16—942no—
250D8—942no—
251D8—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—941no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4C22×D4711yescharacteristic
265C4⋊C4C22×D4711yescharacteristic
266C4⋊C4C22×D4711yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—941no—
269C22⋊C4—941no—
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—941no—
282C23—941no—
283Q8—42no—
284Q8—942no—
285Q8—941no—
286Q8—941no—
287Q8—1882no—
288Q8—1882no—
289D4—21no—
290D4—21no—
291D4—472no—
292D4—941no—
293D4—941no—
294D4—941no—
295D4—3761no—
296D4—1882no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—81no—
301C2×C4—471no—
302C2×C4—471no—
303C2×C4—471no—
304C2×C4—471no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—3761no—
308C2×C4—1882no—
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—942no—
322C22—1881no—
323C22—1881no—
324C22—1881no—
325C22—1881no—
326C22—1881no—
327C22C2×D4×D4711yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—472no—
334C4—941no—
335C4—941no—
336C4—941no—
337C4—1881no—
338C4—1881no—
339C4#41×D4711yescharacteristic
340C4#1309407211yescharacteristic
341C2—81no—
342C2—3761no—
343C2—1882no—
344C2#1568978311yescharacteristic
345C2AGL(1,ℤ/8)×D4711yescharacteristic
346C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#476C2
socleC22×C47C22×D4
hypercenter#476D47
hypocenterC47#3373
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #15689856C2semidirect
2. #15689788C2semidirect
3. #15689485C2semidirect
4. #15689481C2semidirect
5. #15689468C2semidirect
6. #15689412C2semidirect
7. #15689407C2semidirect
8. #15689339C2semidirect
9. #15689337C2semidirect
11. #15689252C2semidirect
12. #15689234C2semidirect
13. #15689233C2semidirect
14. #15689210C2semidirect
15. C47×#476C2semidirect
180. #476D47semidirect
189. C47#3373semidirect