Finite Group Databasebeta

← #20255854

Subgroups — #20255854

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#15689821C211yesmaximal, characteristic, complemented
2#15689774C211yesmaximal, characteristic, complemented
3#15689530C211yesmaximal, characteristic, complemented
4#15689449C211yesmaximal, characteristic, complemented
5#15689443C211yesmaximal, characteristic, complemented
6#15689441C211yesmaximal, characteristic, complemented
7#15689436C211yesmaximal, characteristic, complemented
8#15689422C211yesmaximal, characteristic, complemented
9#15689412C211yesmaximal, characteristic, complemented
10#15689377C211yesmaximal, characteristic, complemented
11#15689359C211yesmaximal, characteristic, complemented
12#15689234C211yesmaximal, characteristic, complemented
13#15689194C211yesmaximal, characteristic, complemented
14#15689162C211yesmaximal, characteristic, complemented
15C2×#106×C47C211yesmaximal, characteristic, complemented
16C2×#10625350—21no—
17C2×D376C2211yescharacteristic
18C2×#10625324C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094019—21no—
21#13094015C2211yescharacteristic
22#13094009—21no—
23#13094009—21no—
24#13094007—21no—
25#13094002—21no—
26#13093999C2211yescharacteristic
27#13093999C2211yescharacteristic
28#13093998—21no—
29#13093998C2211yescharacteristic
30#13093998C2211yescharacteristic
31#13093986C2211yescharacteristic
32#13093986C2211yescharacteristic
33C4×C22⋊D47—21no—
34C4×C22⋊D47C2211yescharacteristic
35#13093982C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093955C2211yescharacteristic
41#13093955C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093944C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51#13093934C2211yescharacteristic
52C22×C8×C47C2211yescharacteristic
53C2×C4⋊C4×C47C2211yescharacteristic
54C2×C4⋊C4×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#106×C47C2211yescharacteristic
58#106×C47C2211yescharacteristic
59C22×C4×C47—21no—
60C22×C4×C47—21no—
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47D411yescharacteristic
65#10625350—44no—
66C2×D188—21no—
67C2×D188—21no—
68C2×D188C2311yescharacteristic
69C2×D188C2311yescharacteristic
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47C2311yescharacteristic
74C2×Dic94—21no—
75C2×C8×C47—22no—
76C2×C8×C47C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C4⋊C4×C47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C22⋊Dic47D411yescharacteristic
85(C2×D47)⋊C4—21no—
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—
92(C2×D47)⋊C4D411yescharacteristic
93C4⋊Dic47—21no—
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4D411yescharacteristic
100C4×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104D376—22no—
105#10625324—22no—
106C23×C47C2×D411yescharacteristic
107C22×D47—21no—
108C22×D47—21no—
109C22×D47C2×D411yescharacteristic
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—42no—
117C2×C4×C47—81no—
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2411yescharacteristic
120C22⋊D47—22no—
121C22⋊D47—42no—
122C22⋊D47—42no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128D188—21no—
129D188—21no—
130D188—21no—
131D188—21no—
132D188—42no—
133D188—81no—
134C4×D47—21no—
135C4×D47—21no—
136C4×D47—42no—
137C4×D47—42no—
138C4×D47—81no—
139Dic94—42no—
140C8×C47—21no—
141C8×C47#4112yescomplemented
142C47⋊C8—21no—
143C47⋊C8—21no—
144C22×C47—21no—
145C22×C47—21no—
146C22×C47AGL(1,ℤ/8)12yes—
147C22×C47C22×D411yescharacteristic
148C2×D47—21no—
149C2×D47—21no—
150C2×D47—21no—
151C2×D47—41no—
152C2×D47—41no—
153C2×D47—41no—
154C2×D47—41no—
155C2×D47—41no—
156C2×D47—41no—
157C4×C47—21no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47C2×#4111yescharacteristic
163C4×C472−1+411yescharacteristic
164Dic47—21no—
165Dic47—21no—
166Dic47—21no—
167Dic47—41no—
168Dic47—41no—
169#3345—471nomaximal, Sylow
170C2×C47—22no—
171C2×C47#54711yescharacteristic
172C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C47#57711yescharacteristic
174D47—41no—
175D47—81no—
176D47—81no—
177#553—471no—
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×#106D4711yescharacteristic, complemented
192C47#334511yescharacteristic, complemented, Sylow
193C2×#41—941no—
194C2×D8—471no—
195C2×M16—471no—
196C22×C8C2×D4711yescharacteristic
197C4⋊Q8—471no—
198#126—941no—
199#125—471no—
200#123—941no—
201#123—941no—
202#123—941no—
203C22⋊Q8—941no—
204#121—471no—
205#121—471no—
206#121—471no—
207#121—471no—
208#121—941no—
209C4×D4—471no—
210C4×D4—471no—
211C4×D4—471no—
212C4×D4—941no—
213#117—471no—
214C2×C4⋊C4—471no—
215C2×C4⋊C4C2×D4711yescharacteristic
216C2×C4⋊C4C2×D4711yescharacteristic
217#107—471no—
218#107—471no—
219#107—471no—
220#106—471no—
221#106—471no—
222#106C2×D4711yescharacteristic
223#106C2×D4711yescharacteristic
224#106C2×D4711yescharacteristic
225#106C2×D4711yescharacteristic
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—471no—
239C2×D4—471no—
240C2×D4—471no—
241C2×D4—941no—
242C2×D4—941no—
243C2×D4—941no—
244C2×D4—941no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—471no—
248C22×C4—941no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4C22×D4711yescharacteristic
252D8—942no—
253M16—942no—
254C2×C8—22no—
255C2×C8—471no—
256C2×C8—471no—
257C2×C8C22×D4711yescharacteristic
258C2×C8C22×D4711yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—471no—
262C4⋊C4—471no—
263C4⋊C4—471no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4C22×D4711yescharacteristic
269C4⋊C4C22×D4711yescharacteristic
270C4⋊C4C22×D4711yescharacteristic
271C4⋊C4C22×D4711yescharacteristic
272C22⋊C4—471no—
273C22⋊C4—471no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C42—471no—
282C42—941no—
283C23—471no—
284C23—941no—
285C23—941no—
286C23D4×D4711yescharacteristic
287Q8—1882no—
288D4—942no—
289D4—941no—
290D4—941no—
291D4—941no—
292D4—941no—
293D4—3761no—
294D4—1882no—
295D4—1882no—
296D4—1882no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—42no—
304C2×C4—81no—
305C2×C4—471no—
306C2×C4—471no—
307C2×C4—471no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—3761no—
313C2×C4—1882no—
314C2×C4—1882no—
315C2×C4D4×D4711yescharacteristic
316C2×C4C23×D4711yescharacteristic
317C8—21no—
318C8—941no—
319C8—941no—
320C8#1062535012yescomplemented
321C22—21no—
322C22—21no—
323C22—941no—
324C22—941no—
325C22—941no—
326C22—1881no—
327C22—1881no—
328C22—1881no—
329C22—1881no—
330C22—1881no—
331C22—1881no—
332C22#1309405112yes—
333C22C2×D4×D4711yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—941no—
340C4—941no—
341C4—941no—
342C4—1881no—
343C4—1881no—
344C4C2×#1062535011yescharacteristic
345C4#1309407211yescharacteristic
346C2—22no—
347C2—3761no—
348C2—3761no—
349C2—1881no—
350C2#1568977411yescharacteristic
351C2C2×#1309405111yescharacteristic
352C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#106×C47C2
socleC22×C47C22×D4
hypercenterC2×#106D47
hypocenterC47#3345
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
1. #15689821C2semidirect
2. #15689774C2semidirect
3. #15689530C2semidirect
4. #15689449C2semidirect
5. #15689443C2semidirect
6. #15689441C2semidirect
7. #15689436C2semidirect
8. #15689422C2semidirect
9. #15689412C2semidirect
10. #15689377C2semidirect
11. #15689359C2semidirect
12. #15689234C2semidirect
13. #15689194C2semidirect
14. #15689162C2semidirect
15. C2×#106×C47C2semidirect
141. C8×C47#41semidirect
191. C2×#106D47semidirect
192. C47#3345semidirect
320. C8#10625350semidirect