Finite Group Databasebeta

← #20255976

Subgroups — #20255976

Order 6016.

386 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#15689837C211yesmaximal, characteristic, complemented
2#15689774C211yesmaximal, characteristic, complemented
3#15689520C211yesmaximal, characteristic, complemented
4#15689449C211yesmaximal, characteristic, complemented
5#15689448C211yesmaximal, characteristic, complemented
6#15689440C211yesmaximal, characteristic, complemented
7#15689412C211yesmaximal, characteristic, complemented
8#15689401C211yesmaximal, characteristic, complemented
9#15689375C211yesmaximal, characteristic, complemented
10#15689374C211yesmaximal, characteristic, complemented
11#15689203C211yesmaximal, characteristic, complemented
12#15689198C211yesmaximal, characteristic, complemented
13#15689163C211yesmaximal, characteristic, complemented
14#15689162C211yesmaximal, characteristic, complemented
15C47×#481C211yesmaximal, characteristic, complemented
16C2×#10625350—21no—
17C2×#10625334C2211yescharacteristic
18C2×#10625329C2211yescharacteristic
19C2×#10625324C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094011—21no—
23#13094010—21no—
24#13094009—21no—
25#13094007—21no—
26#13094002—21no—
27#13093999C2211yescharacteristic
28#13093998C2211yescharacteristic
29#13093996—21no—
30#13093995C2211yescharacteristic
31D4×Dic47C2211yescharacteristic
32#13093986C2211yescharacteristic
33C4×C22⋊D47C2211yescharacteristic
34#13093983C2211yescharacteristic
35#13093982C2211yescharacteristic
36#13093980—21no—
37C4⋊C4×D47C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093955C2211yescharacteristic
43#13093955C2211yescharacteristic
44#13093955C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093944C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52#121×C47C2211yescharacteristic
53C2×C4⋊C4×C47C2211yescharacteristic
54#106×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47D411yescharacteristic
66C22×Dic47—21no—
67#10625350—44no—
68C2×D188—21no—
69C2×D188C2311yescharacteristic
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47C2311yescharacteristic
73C2×Dic94—21no—
74C2×Dic94—21no—
75C2×C8×C47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C4⋊C4×C47—21no—
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C22⋊C4×C47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47D411yescharacteristic
86#10625334—22no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4D411yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4D411yescharacteristic
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102#10625329—22no—
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105#10625324—22no—
106C23×C47—21no—
107C23×C47C2×D411yescharacteristic
108C22×D47—21no—
109C22×D47C2×D411yescharacteristic
110D4×C47—21no—
111D4×C47—21no—
112D4×C47—81no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—42no—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2411yescharacteristic
121C22⋊D47—22no—
122C22⋊D47—42no—
123C22⋊D47—81no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—42no—
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131D188—21no—
132D188—21no—
133D188—42no—
134C4×D47—21no—
135C4×D47—21no—
136C4×D47—42no—
137C4×D47—42no—
138Dic94—42no—
139Dic94—81no—
140C8×C47—21no—
141C8×C47—21no—
142C47⋊C8—21no—
143C47⋊C8#4112yescomplemented
144C22×C47—21no—
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—41no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47C22×D411yescharacteristic
151C2×D47—21no—
152C2×D47—21no—
153C2×D47—21no—
154C2×D47—41no—
155C2×D47—41no—
156C2×D47—41no—
157C4×C47—21no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47C2×#4111yescharacteristic
162C4×C472−1+411yescharacteristic
163Dic47—21no—
164Dic47—21no—
165Dic47—41no—
166Dic47—41no—
167Dic47—41no—
168Dic47AGL(1,ℤ/8)12yes—
169#3354—471nomaximal, Sylow
170C2×C47—41no—
171C2×C47—81no—
172C2×C47#54711yescharacteristic
173C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
174C2×C47#57711yescharacteristic
175D47—41no—
176D47—81no—
177#555—471no—
178#547—471no—
179#498—471no—
180#482—471no—
181#482—471no—
182#481—471no—
183#481D4711yescharacteristic, complemented
184#476—471no—
185#474—471no—
186#469—471no—
187#469—471no—
188C4×D8—471no—
189#436—471no—
190#428—471no—
191#428—471no—
192C47#335411yescharacteristic, complemented, Sylow
193C2×#41—941no—
194C2×D8—471no—
195C2×M16—471no—
196C2×M16—471no—
197C4⋊Q8—471no—
198C4⋊Q8—471no—
199#124—941no—
200#124—941no—
201#123—941no—
202#123—941no—
203C22⋊Q8—941no—
204#121—471no—
205#121—471no—
206#121—471no—
207#121—941no—
208#121C2×D4711yescharacteristic
209C4×D4—471no—
210C4×D4—471no—
211C4×D4—471no—
212#117—471no—
213#117—471no—
214#117—941no—
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#106C2×D4711yescharacteristic
225#106C2×D4711yescharacteristic
226C4⋊C8—471no—
227#102—471no—
228#102—471no—
229#102—471no—
230#102—471no—
231#102C2×D4711yescharacteristic
232#102C2×D4711yescharacteristic
233C22⋊C8—471no—
234C22⋊C8C2×D4711yescharacteristic
235C4×C8—471no—
236#41—1884no—
237C2×Q8—941no—
238C2×Q8—941no—
239C2×D4—21no—
240C2×D4—471no—
241C2×D4—471no—
242C2×D4—941no—
243C2×D4—941no—
244C2×D4—941no—
245C2×D4C22×D4711yescharacteristic
246C22×C4—21no—
247C22×C4—471no—
248C22×C4—941no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4C22×D4711yescharacteristic
252D8—942no—
253M16—942no—
254M16—942no—
255C2×C8—471no—
256C2×C8—471no—
257C2×C8C22×D4711yescharacteristic
258C2×C8C22×D4711yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—471no—
261C4⋊C4—471no—
262C4⋊C4—471no—
263C4⋊C4—471no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4C22×D4711yescharacteristic
268C4⋊C4C22×D4711yescharacteristic
269C4⋊C4C22×D4711yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—471no—
272C22⋊C4—471no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C42—471no—
281C42—941no—
282C42—941no—
283C23—21no—
284C23—471no—
285C23—941no—
286C23D4×D4711yescharacteristic
287Q8—3761no—
288Q8—1882no—
289D4—21no—
290D4—21no—
291D4—81no—
292D4—942no—
293D4—941no—
294D4—941no—
295D4—3761no—
296D4—1882no—
297D4—1882no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—42no—
304C2×C4—471no—
305C2×C4—471no—
306C2×C4—471no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—1882no—
313C2×C4—1882no—
314C2×C4—1882no—
315C2×C4D4×D4711yescharacteristic
316C2×C4C23×D4711yescharacteristic
317C8—21no—
318C8—21no—
319C8—472no—
320C8—941no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—941no—
328C22—941no—
329C22—941no—
330C22—1881no—
331C22—1881no—
332C22—1881no—
333C22C2×D4×D4711yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—472no—
339C4—941no—
340C4—941no—
341C4—1881no—
342C4—1881no—
343C4—1881no—
344C4#41×D4711yescharacteristic
345C4#1309407111yescharacteristic
346C2—41no—
347C2—81no—
348C2—3761no—
349C2—1881no—
350C2#1568977111yescharacteristic
351C2AGL(1,ℤ/8)×D4711yescharacteristic
352C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#481C2
socleC22×C47C22×D4
hypercenter#481D47
hypocenterC47#3354
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #15689837C2semidirect
2. #15689774C2semidirect
3. #15689520C2semidirect
4. #15689449C2semidirect
5. #15689448C2semidirect
6. #15689440C2semidirect
7. #15689412C2semidirect
8. #15689401C2semidirect
9. #15689375C2semidirect
10. #15689374C2semidirect
11. #15689203C2semidirect
12. #15689198C2semidirect
13. #15689163C2semidirect
14. #15689162C2semidirect
15. C47×#481C2semidirect
143. C47⋊C8#41semidirect
183. #481D47semidirect
192. C47#3354semidirect