Finite Group Databasebeta

← #20255493

Subgroups — #20255493

Order 6016.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689782C211yesmaximal, characteristic
2#15689485C211yesmaximal, characteristic, complemented
3#15689453C211yesmaximal, characteristic, complemented
4#15689441C211yesmaximal, characteristic, complemented
5#15689405C211yesmaximal, characteristic, complemented
6#15689379C211yesmaximal, characteristic, complemented
7#15689354C211yesmaximal, characteristic, complemented
8#15689345C211yesmaximal, characteristic, complemented
9#15689283C211yesmaximal, characteristic, complemented
10#15689278C211yesmaximal, characteristic, complemented
11#15689228C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689122C211yesmaximal, characteristic, complemented
14C2×#13093947C211yesmaximal, characteristic, complemented
15C47×#554C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18C2×#10625337C2211yescharacteristic
19C2×#10625337C2211yescharacteristic
20C2×#10625336C2211yescharacteristic
21C2×#10625329C2211yescharacteristic
22C22×C47⋊C8C2211yescharacteristic
23#13094012C2211yescharacteristic
24#13094010—21no—
25#13094003C2211yescharacteristic
26#13094002—21no—
27#13093998C2211yescharacteristic
28#13093996—21no—
29C4×Dic94C2211yescharacteristic
30(C22⋊D47)⋊C4—21no—
31#13093955C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35#13093948C2211yescharacteristic
36#13093947C2211yescharacteristic
37#13093947C2211yescharacteristic
38#13093947C2211yescharacteristic
39#13093947C2211yescharacteristic
40#13093947C2211yescharacteristic
41#13093947C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44#13093944C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47#13093935C2211yescharacteristic
48C4⋊Q8×C47C2211yescharacteristic
49#125×C47—21no—
50C22⋊Q8×C47—21no—
51C22⋊Q8×C47—21no—
52C22⋊Q8×C47C2211yescharacteristic
53C22⋊Q8×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55C4×D4×C47—21no—
56C4×D4×C47C2211yescharacteristic
57C2×C4⋊C4×C47C2211yescharacteristic
58C2×C4⋊C4×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47D411yescharacteristic
62C22×C4×C47—21no—
63C22×C4×C47—21no—
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C22×Dic47—21no—
69#10625350—22no—
70#10625350—41no—
71C2×D188C2311yescharacteristic
72C2×C4×D47—21no—
73C2×Dic94—22no—
74C2×Dic94—21no—
75C2×Dic94—41no—
76C2×Dic94C2311yescharacteristic
77C2×Dic94C2311yescharacteristic
78C4⋊C4×C47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47—21no—
82C4⋊C4×C47—21no—
83C4⋊C4×C47—21no—
84C4⋊C4×C47D411yescharacteristic
85C4⋊C4×C47C2311yescharacteristic
86C4⋊C4×C47C2311yescharacteristic
87C4⋊C4×C47C2311yescharacteristic
88C22⋊C4×C47—21no—
89C22⋊C4×C47—21no—
90C22⋊C4×C47D411yescharacteristic
91C22⋊C4×C47D411yescharacteristic
92C42×C47—21no—
93C42×C47C2311yescharacteristic
94C22⋊Dic47—21no—
95#10625337—22no—
96#10625337—41no—
97#10625336—41no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104C4×Dic47—21no—
105#10625329—41no—
106C2×C47⋊C8—41no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C23×C47C2×D411yescharacteristic
112C23×C47C2×D411yescharacteristic
113C22×D47—21no—
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47—81no—
117D4×C47—22no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—81no—
127C2×C4×C47—81no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2×D411yescharacteristic
132C2×C4×C47C2411yescharacteristic
133C22⋊D47—42no—
134C22⋊D47—42no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—42no—
139D188—21no—
140D188—21no—
141C4×D47—42no—
142Dic94—21no—
143Dic94—21no—
144Dic94—21no—
145Dic94—42no—
146Dic94#4112yes—
147C47⋊C8—21no—
148C47⋊C8—21no—
149C47⋊C8—21no—
150C47⋊C8—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47#13712yes—
157C22×C47C22×D411yescharacteristic
158C2×D47—41no—
159C2×D47—41no—
160C2×D47—41no—
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—21no—
165C4×C47—41no—
166C4×C47—41no—
167C4×C47—41no—
168C4×C47—41no—
169C4×C47C2×#4111yescharacteristic
170C4×C47H(5,𝔽2)11yescharacteristic
171Dic47—22no—
172Dic47—41no—
173Dic47—41no—
174#3316—471nomaximal, Sylow
175C2×C47—22no—
176C2×C47—41no—
177C2×C47#54611yescharacteristic
178C2×C47C2×#13711yescharacteristic
179C2×C47#57711yescharacteristic
180D47—81no—
181#554D4711yescharacteristic, complemented
182#548—471no—
183#489—471no—
184#483—471no—
185#481—471no—
186#475—471no—
187#470—471no—
188#465—471no—
189#464—471no—
190#452—471no—
191#451—471no—
192#441—471no—
193#435—471no—
194#417—471no—
195C2×#103—471no—
196C47#331611yescharacteristic, complemented, Sylow
197C2×#41—471no—
198C22×Q8—471no—
199C2×Q16—471no—
200C2×Q16—471no—
201C2×SD16—471no—
202C2×M16—471no—
203C22×C8—471no—
204C4⋊Q8C2×D4711yescharacteristic
205#125—21no—
206#124—471no—
207#124—941no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—471no—
211C22⋊Q8—941no—
212C22⋊Q8C2×D4711yescharacteristic
213C22⋊Q8C2×D4711yescharacteristic
214#121—471no—
215#121—941no—
216C4×Q8—471no—
217C4×Q8C2×D4711yescharacteristic
218C4×D4—21no—
219C4×D4—941no—
220C4×D4C2×D4711yescharacteristic
221C2×C4⋊C4C2×D4711yescharacteristic
222C2×C4⋊C4C2×D4711yescharacteristic
223#106—471no—
224#106—471no—
225#106—471no—
226C4⋊C8—471no—
227#103—471no—
228#103—471no—
229#103—471no—
230#103—471no—
231#103—471no—
232#103—471no—
233#103—471no—
234#102—471no—
235#102—471no—
236#102—471no—
237C22⋊C8—471no—
238C22⋊C8—471no—
239#97—471no—
240#41—942no—
241#41—1881no—
242C2×Q8—21no—
243C2×Q8—471no—
244C2×Q8—471no—
245C2×Q8—942no—
246C2×Q8—941no—
247C2×Q8—1881no—
248C2×Q8C22×D4711yescharacteristic
249C2×D4—471no—
250C2×D4—941no—
251C2×D4—941no—
252C2×D4C22⋊D4711yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4C22×D4711yescharacteristic
258C22×C4C22×D4711yescharacteristic
259Q16—942no—
260Q16—1881no—
261SD16—1881no—
262M16—1881no—
263C2×C8—471no—
264C2×C8—471no—
265C2×C8—471no—
266C2×C8—471no—
267C2×C8—1881no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—471no—
275C4⋊C4—941no—
276C4⋊C4—941no—
277C4⋊C4C22⋊D4711yescharacteristic
278C4⋊C4C22×D4711yescharacteristic
279C4⋊C4C22×D4711yescharacteristic
280C4⋊C4C22×D4711yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4C22⋊D4711yescharacteristic
288C22⋊C4C22⋊D4711yescharacteristic
289C42—21no—
290C42—941no—
291C42C22×D4711yescharacteristic
292C23—941no—
293C23C2×C22⋊D4711yescharacteristic
294C23C2×C22⋊D4711yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—81no—
298Q8—472no—
299Q8—941no—
300Q8—941no—
301Q8—941no—
302Q8—1882no—
303D4—22no—
304D4—941no—
305D4—941no—
306D4—1882no—
307D4—1882no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—1882no—
322C2×C4—1882no—
323C2×C4C2×C22⋊D4711yescharacteristic
324C2×C4C2×C22⋊D4711yescharacteristic
325C2×C4C2×C22⋊D4711yescharacteristic
326C2×C4C2×C22⋊D4711yescharacteristic
327C2×C4C23×D4711yescharacteristic
328C8—941no—
329C8—941no—
330C8—941no—
331C8—941no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—1881no—
338C22—1881no—
339C22—1881no—
340C22#1309405512yes—
341C22C22×C22⋊D4711yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—942no—
351C4—1881no—
352C4—1881no—
353C4#41×D4711yescharacteristic
354C4#1309407011yescharacteristic
355C2—22no—
356C2—41no—
357C2—3761no—
358C2#1568976111yescharacteristic
359C2C2×#1309405511yescharacteristic
360C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#554C2
socleC22×C47C22×D4
hypercenter#554D47
hypocenterC47#3316
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #15689485C2semidirect
3. #15689453C2semidirect
4. #15689441C2semidirect
5. #15689405C2semidirect
6. #15689379C2semidirect
7. #15689354C2semidirect
8. #15689345C2semidirect
9. #15689283C2semidirect
10. #15689278C2semidirect
11. #15689228C2semidirect
12. #15689195C2semidirect
13. #15689122C2semidirect
14. C2×#13093947C2semidirect
15. C47×#554C2semidirect
181. #554D47semidirect
196. C47#3316semidirect