Finite Group Databasebeta

← #20255320

Subgroups — #20255320

Order 6016.

396 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689844C211yesmaximal, characteristic, complemented
2#15689792C211yesmaximal, characteristic
3#15689468C211yesmaximal, characteristic, complemented
4#15689448C211yesmaximal, characteristic, complemented
5#15689445C211yesmaximal, characteristic, complemented
6#15689406C211yesmaximal, characteristic, complemented
7#15689354C211yesmaximal, characteristic, complemented
8#15689349C211yesmaximal, characteristic, complemented
9#15689321C211yesmaximal, characteristic, complemented
10#15689284C211yesmaximal, characteristic, complemented
11Q16×Dic47C211yesmaximal, characteristic, complemented
12(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
13#15689119C211yesmaximal, characteristic, complemented
14#15689118C211yesmaximal, characteristic, complemented
15C47×#452C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625336C2211yescharacteristic
18C22×C47⋊C8C2211yescharacteristic
19C2×C8×D47C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094020—21no—
22#13094020C2211yescharacteristic
23#13094019—21no—
24#13094017—21no—
25#13094010—21no—
26#13094000C2211yescharacteristic
27#13093998—21no—
28#13093998C2211yescharacteristic
29#13093995—21no—
30#13093995C2211yescharacteristic
31Q8×Dic47C2211yescharacteristic
32Q8×Dic47C2211yescharacteristic
33#13093989—21no—
34C4×C22⋊D47—21no—
35C4×C22⋊D47C2211yescharacteristic
36#13093983C2211yescharacteristic
37#13093982C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42#13093948C2211yescharacteristic
43#13093948C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093944C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×#41×C47C2211yescharacteristic
53C2×Q16×C47C2211yescharacteristic
54C2×SD16×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59#41×C47—22no—
60#41×C47—41no—
61C2×Q8×C47C2311yescharacteristic
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47D411yescharacteristic
72#10625354—22no—
73#10625354—41no—
74C2×D188—21no—
75C2×D188C2311yescharacteristic
76C2×C4×D47—21no—
77C2×C4×D47C2311yescharacteristic
78C2×Dic94—21no—
79Q16×C47—22no—
80SD16×C47—41no—
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C4⋊C4×C47—21no—
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88C22⋊Dic47D411yescharacteristic
89#10625336—41no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4D411yescharacteristic
94C4⋊Dic47—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4D411yescharacteristic
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47C2311yescharacteristic
107C2×C47⋊C8—41no—
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C8×D47—41no—
111C23×C47—21no—
112C23×C47C2×D411yescharacteristic
113C22×D47—21no—
114C22×D47C2×D411yescharacteristic
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—21no—
118Q8×C47#4112yes—
119D4×C47—21no—
120D4×C47—21no—
121D4×C47—42no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—42no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—22no—
131C22⋊D47—42no—
132C22⋊D47—81no—
133C22⋊D47—81no—
134C22⋊D47—81no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47C2×D411yescharacteristic
139C2×Dic47C2×D411yescharacteristic
140C2×Dic47C2×D411yescharacteristic
141D188—21no—
142D188—21no—
143D188—42no—
144C4×D47—21no—
145C4×D47—21no—
146C4×D47—42no—
147Dic94—42no—
148C8×C47—21no—
149C8×C47—21no—
150C47⋊C8—21no—
151C47⋊C8—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47C22×D411yescharacteristic
159C2×D47—21no—
160C2×D47—21no—
161C2×D47—21no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—41no—
165C4×C47—22no—
166C4×C47—21no—
167C4×C47—41no—
168C4×C47—41no—
169C4×C47C2×#4111yescharacteristic
170C4×C47H(5,𝔽2)11yescharacteristic
171Dic47—21no—
172Dic47—21no—
173Dic47—41no—
174Dic47—41no—
175Dic47—41no—
176Dic47#13512yes—
177#3304—471nomaximal, Sylow
178C2×C47—41no—
179C2×C47—81no—
180C2×C47#54611yescharacteristic
181C2×C47C2×#13511yescharacteristic
182C2×C47#57711yescharacteristic
183D47—41no—
184D47—81no—
185#556—471no—
186#550—471no—
187#486—471no—
188#482—471no—
189#482—471no—
190#475—471no—
191#465—471no—
192#465—471no—
193#460—471no—
194#452—471no—
195#452D4711yescharacteristic, complemented
196C4×Q16—471no—
197C8×D4—471no—
198#416—471no—
199#416—471no—
200C47#330411yescharacteristic, complemented, Sylow
201C2×#41—471no—
202C2×#41C2×D4711yescharacteristic
203C2×Q16C2×D4711yescharacteristic
204C2×SD16—471no—
205C2×SD16C2×D4711yescharacteristic
206C22×C8—471no—
207C22×C8—471no—
208C4⋊Q8—471no—
209#127—471no—
210#127—941no—
211#126—941no—
212#126—941no—
213#124—941no—
214C22⋊Q8—471no—
215C22⋊Q8C2×D4711yescharacteristic
216#121—471no—
217#121—471no—
218#121—941no—
219#121—941no—
220C4×Q8—471no—
221C4×Q8—471no—
222C4×Q8—941no—
223C4×D4—471no—
224C4×D4—941no—
225#117—471no—
226#117—471no—
227#107—471no—
228#106—471no—
229#106—471no—
230C4⋊C8—471no—
231#103—471no—
232#103—471no—
233#103—471no—
234#103C2×D4711yescharacteristic
235#102—471no—
236#102—471no—
237#102—471no—
238#102—471no—
239#102—471no—
240#102C2×D4711yescharacteristic
241C22⋊C8—471no—
242C22⋊C8C2×D4711yescharacteristic
243C4×C8—471no—
244#41—22no—
245#41—41no—
246#41—942no—
247#41—1881no—
248C2×Q8—941no—
249C2×Q8C22×D4711yescharacteristic
250C2×Q8C22×D4711yescharacteristic
251C2×D4—21no—
252C2×D4—471no—
253C2×D4—471no—
254C2×D4—941no—
255C2×D4—941no—
256C2×D4—941no—
257C2×D4—941no—
258C2×D4—941no—
259C2×D4C22×D4711yescharacteristic
260C22×C4—21no—
261C22×C4—471no—
262C22×C4—941no—
263C22×C4C22×D4711yescharacteristic
264Q16—22no—
265SD16—41no—
266SD16—1881no—
267C2×C8—471no—
268C2×C8—471no—
269C2×C8—1881no—
270C2×C8—1881no—
271C2×C8C22×D4711yescharacteristic
272C2×C8C22×D4711yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—471no—
275C4⋊C4—471no—
276C4⋊C4—471no—
277C4⋊C4—471no—
278C4⋊C4—941no—
279C4⋊C4—941no—
280C4⋊C4—941no—
281C4⋊C4—941no—
282C4⋊C4C22×D4711yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—471no—
285C22⋊C4—471no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C42—471no—
292C42—941no—
293C42—941no—
294C42—941no—
295C42—941no—
296C23—21no—
297C23—471no—
298C23—941no—
299C23D4×D4711yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—1882no—
304Q8#1062535212yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—942no—
309D4—941no—
310D4—941no—
311D4—3761no—
312D4—3761no—
313D4—3761no—
314D4—1882no—
315D4—1882no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—471no—
323C2×C4—471no—
324C2×C4—471no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—1882no—
331C2×C4D4×D4711yescharacteristic
332C2×C4C23×D4711yescharacteristic
333C8—21no—
334C8—21no—
335C8—941no—
336C8—941no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—941no—
344C22—941no—
345C22—941no—
346C22—1881no—
347C22—1881no—
348C22—1881no—
349C22C2×D4×D4711yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—472no—
355C4—941no—
356C4—941no—
357C4—1881no—
358C4—1881no—
359C4—1881no—
360C4C2×#1062535211yescharacteristic
361C4#1309406911yescharacteristic
362C2—41no—
363C2—81no—
364C2—3761no—
365C2—1881no—
366C2#1568976011yescharacteristic
367C2#135×D4711yescharacteristic
368C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#452C2
socleC22×C47C22×D4
hypercenter#452D47
hypocenterC47#3304
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #15689844C2semidirect
3. #15689468C2semidirect
4. #15689448C2semidirect
5. #15689445C2semidirect
6. #15689406C2semidirect
7. #15689354C2semidirect
8. #15689349C2semidirect
9. #15689321C2semidirect
10. #15689284C2semidirect
11. Q16×Dic47C2semidirect
12. (C22⋊D47)⋊C8C2semidirect
13. #15689119C2semidirect
14. #15689118C2semidirect
15. C47×#452C2semidirect
195. #452D47semidirect
200. C47#3304semidirect