Finite Group Databasebeta

← #20255852

Subgroups — #20255852

Order 6016.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689777C211yesmaximal, characteristic, complemented
2#15689533C211yesmaximal, characteristic, complemented
3#15689447C211yesmaximal, characteristic, complemented
4#15689441C211yesmaximal, characteristic, complemented
5#15689439C211yesmaximal, characteristic, complemented
6#15689434C211yesmaximal, characteristic, complemented
7#15689420C211yesmaximal, characteristic, complemented
8#15689413C211yesmaximal, characteristic, complemented
9#15689374C211yesmaximal, characteristic, complemented
10#15689357C211yesmaximal, characteristic, complemented
11#15689233C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689166C211yesmaximal, characteristic, complemented
14C2×#13093955C211yesmaximal, characteristic, complemented
15C47×#553C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17C2×#10625334C2211yescharacteristic
18C2×#10625329C2211yescharacteristic
19C22×C47⋊C8C2211yescharacteristic
20#13094024C2211yescharacteristic
21#13094008—21no—
22#13094008—21no—
23#13094004—21no—
24#13093998C2211yescharacteristic
25#13093998C2211yescharacteristic
26C4×D188C2211yescharacteristic
27C2×C4⋊Dic47C2211yescharacteristic
28C2×C4⋊Dic47C2211yescharacteristic
29#13093957C2211yescharacteristic
30#13093957C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34#13093955C2211yescharacteristic
35#13093955C2211yescharacteristic
36#13093955C2211yescharacteristic
37#13093955C2211yescharacteristic
38C4⋊(C47⋊C8)C2211yescharacteristic
39#13093945C2211yescharacteristic
40#13093945C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44#13093944C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47#13093935C2211yescharacteristic
48#126×C47—21no—
49#125×C47C2211yescharacteristic
50#123×C47—21no—
51#121×C47—21no—
52#121×C47C2211yescharacteristic
53#121×C47C2211yescharacteristic
54C4×D4×C47—21no—
55C4×D4×C47C2211yescharacteristic
56C4×D4×C47C2211yescharacteristic
57#117×C47C2211yescharacteristic
58C2×C4⋊C4×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47—21no—
61C2×D4×C47D411yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C22×Dic47—21no—
70C22×Dic47—21no—
71#10625352—44no—
72C2×D188C2311yescharacteristic
73C2×C4×D47—21no—
74C2×Dic94—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47D411yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C22⋊C4×C47—21no—
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C22⋊C4×C47—21no—
86C22⋊C4×C47D411yescharacteristic
87C22⋊C4×C47D411yescharacteristic
88C42×C47—21no—
89C42×C47C2311yescharacteristic
90#10625334—22no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94C4⋊Dic47—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100#10625329—22no—
101C2×C47⋊C8—22no—
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C23×C47—21no—
107C23×C47C2×D411yescharacteristic
108C23×C47C2×D411yescharacteristic
109C22×D47—21no—
110D4×C47—22no—
111D4×C47—21no—
112D4×C47—21no—
113D4×C47—42no—
114D4×C47—81no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—81no—
123C2×C4×C47—81no—
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2411yescharacteristic
129C22⋊D47—42no—
130C22⋊D47—42no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—42no—
135C2×Dic47—42no—
136D188—21no—
137D188—21no—
138C4×D47—42no—
139Dic94—42no—
140C47⋊C8—21no—
141C47⋊C8—21no—
142C47⋊C8—21no—
143C47⋊C8#4112yescomplemented
144C22×C47—21no—
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—21no—
148C22×C47—21no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47AGL(1,ℤ/8)12yes—
153C22×C47C22×D411yescharacteristic
154C2×D47—41no—
155C2×D47—41no—
156C2×D47—41no—
157C4×C47—21no—
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47—41no—
164C4×C47C2×#4111yescharacteristic
165C4×C472−1+411yescharacteristic
166Dic47—41no—
167Dic47—41no—
168Dic47—41no—
169#3345—471nomaximal, Sylow
170C2×C47—22no—
171C2×C47—41no—
172C2×C47—81no—
173C2×C47#54711yescharacteristic
174C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
175C2×C47#57711yescharacteristic
176D47—81no—
177#553D4711yescharacteristic, complemented
178#547—471no—
179#501—471no—
180#482—471no—
181#481—471no—
182#481—471no—
183#480—471no—
184#478—471no—
185#476—471no—
186#469—471no—
187#466—471no—
188#442—471no—
189#435—471no—
190#428—471no—
191C2×#106—471no—
192C47#334511yescharacteristic, complemented, Sylow
193C2×#41—941no—
194C2×D8—471no—
195C2×M16—471no—
196C22×C8—471no—
197C4⋊Q8—471no—
198#126—21no—
199#125C2×D4711yescharacteristic
200#123—21no—
201#123—941no—
202#123—941no—
203C22⋊Q8—941no—
204#121—21no—
205#121—471no—
206#121—471no—
207#121C2×D4711yescharacteristic
208#121C2×D4711yescharacteristic
209C4×D4—21no—
210C4×D4—471no—
211C4×D4C2×D4711yescharacteristic
212C4×D4C2×D4711yescharacteristic
213#117C2×D4711yescharacteristic
214C2×C4⋊C4—471no—
215C2×C4⋊C4—471no—
216C2×C4⋊C4C2×D4711yescharacteristic
217#107—471no—
218#107—471no—
219#107—471no—
220#106—471no—
221#106—471no—
222#106—471no—
223#106—471no—
224#106—471no—
225#106—471no—
226C4⋊C8—471no—
227#102—471no—
228#102—471no—
229#102—471no—
230#102—471no—
231#102—471no—
232#102—471no—
233C22⋊C8—471no—
234C22⋊C8—471no—
235#97—471no—
236#41—1884no—
237C2×Q8—941no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—471no—
241C2×D4—941no—
242C2×D4—941no—
243C2×D4C22⋊D4711yescharacteristic
244C2×D4C22×D4711yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—941no—
248C22×C4—941no—
249C22×C4—941no—
250C22×C4C22×D4711yescharacteristic
251C22×C4C22×D4711yescharacteristic
252D8—942no—
253M16—942no—
254C2×C8—471no—
255C2×C8—471no—
256C2×C8—471no—
257C2×C8—471no—
258C2×C8—942no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—471no—
263C4⋊C4—471no—
264C4⋊C4—471no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4C22⋊D4711yescharacteristic
269C4⋊C4C22×D4711yescharacteristic
270C4⋊C4C22×D4711yescharacteristic
271C4⋊C4C22×D4711yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4C22⋊D4711yescharacteristic
280C22⋊C4C22⋊D4711yescharacteristic
281C42—21no—
282C42C22×D4711yescharacteristic
283C23—21no—
284C23—941no—
285C23C2×C22⋊D4711yescharacteristic
286C23C2×C22⋊D4711yescharacteristic
287Q8—1882no—
288D4—22no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—81no—
293D4—941no—
294D4—941no—
295D4—1882no—
296D4—1882no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—1882no—
310C2×C4—1882no—
311C2×C4—1882no—
312C2×C4C2×C22⋊D4711yescharacteristic
313C2×C4C2×C22⋊D4711yescharacteristic
314C2×C4C2×C22⋊D4711yescharacteristic
315C2×C4C2×C22⋊D4711yescharacteristic
316C2×C4C23×D4711yescharacteristic
317C8—472no—
318C8—941no—
319C8—941no—
320C8—941no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—1881no—
330C22—1881no—
331C22—1881no—
332C22#1309404912yes—
333C22C22×C22⋊D4711yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—1881no—
342C4—1881no—
343C4—1881no—
344C4#41×D4711yescharacteristic
345C4#1309407111yescharacteristic
346C2—22no—
347C2—41no—
348C2—81no—
349C2—3761no—
350C2#1568977211yescharacteristic
351C2C2×#1309404911yescharacteristic
352C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#553C2
socleC22×C47C22×D4
hypercenter#553D47
hypocenterC47#3345
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #15689777C2semidirect
2. #15689533C2semidirect
3. #15689447C2semidirect
4. #15689441C2semidirect
5. #15689439C2semidirect
6. #15689434C2semidirect
7. #15689420C2semidirect
8. #15689413C2semidirect
9. #15689374C2semidirect
10. #15689357C2semidirect
11. #15689233C2semidirect
12. #15689195C2semidirect
13. #15689166C2semidirect
14. C2×#13093955C2semidirect
15. C47×#553C2semidirect
143. C47⋊C8#41semidirect
177. #553D47semidirect
192. C47#3345semidirect