Finite Group Databasebeta

← #20255379

Subgroups — #20255379

Order 6016.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689777C211yesmaximal, characteristic, complemented
2#15689482C211yesmaximal, characteristic, complemented
3#15689456C211yesmaximal, characteristic, complemented
4#15689434C211yesmaximal, characteristic, complemented
5#15689418C211yesmaximal, characteristic, complemented
6#15689371C211yesmaximal, characteristic, complemented
7#15689357C211yesmaximal, characteristic, complemented
8#15689335C211yesmaximal, characteristic, complemented
9#15689268C211yesmaximal, characteristic, complemented
10#15689262C211yesmaximal, characteristic, complemented
11#15689221C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689124C211yesmaximal, characteristic, complemented
14C2×#13093948C211yesmaximal, characteristic, complemented
15C47×#548C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17C2×#10625336C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20C2×#10625329C2211yescharacteristic
21C22×C47⋊C8C2211yescharacteristic
22#13094024C2211yescharacteristic
23#13094008—21no—
24#13094008—21no—
25#13094004—21no—
26#13093998C2211yescharacteristic
27#13093998C2211yescharacteristic
28C4×D188C2211yescharacteristic
29C2×C4⋊Dic47C2211yescharacteristic
30C2×C4⋊Dic47C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093957C2211yescharacteristic
33#13093957C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35#13093948C2211yescharacteristic
36#13093948C2211yescharacteristic
37#13093948C2211yescharacteristic
38#13093948C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093948C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093945C2211yescharacteristic
43#13093945C2211yescharacteristic
44#13093944C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47#13093935C2211yescharacteristic
48C2×#41×C47C2211yescharacteristic
49C22×Q8×C47C2211yescharacteristic
50#124×C47—21no—
51#124×C47C2211yescharacteristic
52C22⋊Q8×C47—21no—
53C22⋊Q8×C47C2211yescharacteristic
54#121×C47—21no—
55#121×C47C2211yescharacteristic
56C4×Q8×C47C2211yescharacteristic
57C4×D4×C47—21no—
58C4×D4×C47C2211yescharacteristic
59#41×C47—22no—
60#41×C47—41no—
61C2×Q8×C47—21no—
62C2×Q8×C47—22no—
63C2×Q8×C47—41no—
64C2×Q8×C47C2311yescharacteristic
65C2×Q8×C47C2311yescharacteristic
66C2×D4×C47—21no—
67C2×D4×C47—21no—
68C2×D4×C47D411yescharacteristic
69C2×D4×C47C2311yescharacteristic
70C22×C4×C47—21no—
71C22×C4×C47—21no—
72C22×C4×C47C2311yescharacteristic
73C22×C4×C47C2311yescharacteristic
74C2×C22⋊D47—21no—
75C2×C22⋊D47—21no—
76C22×Dic47—21no—
77C22×Dic47—21no—
78#10625352—44no—
79C2×D188C2311yescharacteristic
80C2×C4×D47—21no—
81C2×Dic94—21no—
82C4⋊C4×C47—21no—
83C4⋊C4×C47—21no—
84C4⋊C4×C47D411yescharacteristic
85C4⋊C4×C47C2311yescharacteristic
86C22⋊C4×C47—21no—
87C22⋊C4×C47—21no—
88C22⋊C4×C47—21no—
89C22⋊C4×C47—21no—
90C22⋊C4×C47D411yescharacteristic
91C22⋊C4×C47D411yescharacteristic
92C42×C47—21no—
93C42×C47C2311yescharacteristic
94#10625336—22no—
95#10625336—41no—
96#10625334—41no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100C4⋊Dic47—21no—
101C4⋊Dic47—21no—
102C4⋊Dic47—21no—
103C4⋊Dic47C2311yescharacteristic
104C4⋊Dic47C2311yescharacteristic
105C4⋊Dic47C2311yescharacteristic
106#10625329—41no—
107C2×C47⋊C8—41no—
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112C23×C47—21no—
113C23×C47C2×D411yescharacteristic
114C23×C47C2×D411yescharacteristic
115C22×D47—21no—
116Q8×C47—21no—
117Q8×C47—21no—
118Q8×C47—21no—
119Q8×C47—42no—
120Q8×C47#4112yescomplemented
121D4×C47—22no—
122D4×C47—21no—
123D4×C47—21no—
124D4×C47—42no—
125D4×C47—42no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—42no—
134C2×C4×C47—42no—
135C2×C4×C47C2×D411yescharacteristic
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2×D411yescharacteristic
138C2×C4×C47C2×D411yescharacteristic
139C2×C4×C47C2411yescharacteristic
140C22⋊D47—42no—
141C22⋊D47—42no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—42no—
146C2×Dic47—42no—
147D188—21no—
148D188—21no—
149C4×D47—42no—
150Dic94—42no—
151C47⋊C8—21no—
152C47⋊C8—21no—
153C47⋊C8—21no—
154C47⋊C8—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—21no—
159C22×C47—21no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47AGL(1,ℤ/8)12yes—
164C22×C47C22×D411yescharacteristic
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—41no—
168C4×C47—21no—
169C4×C47—21no—
170C4×C47—22no—
171C4×C47—21no—
172C4×C47—21no—
173C4×C47—41no—
174C4×C47—41no—
175C4×C47C2×#4111yescharacteristic
176C4×C47H(5,𝔽2)11yescharacteristic
177Dic47—41no—
178Dic47—41no—
179Dic47—41no—
180#3308—471nomaximal, Sylow
181C2×C47—22no—
182C2×C47—41no—
183C2×C47—81no—
184C2×C47#54611yescharacteristic
185C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
186C2×C47#57811yescharacteristic
187D47—81no—
188#548D4711yescharacteristic, complemented
189#547—471no—
190#489—471no—
191#484—471no—
192#480—471no—
193#477—471no—
194#468—471no—
195#466—471no—
196#463—471no—
197#449—471no—
198#448—471no—
199#440—471no—
200#435—471no—
201#417—471no—
202C2×#103—471no—
203C47#330811yescharacteristic, complemented, Sylow
204C2×#41—941no—
205C2×#41C2×D4711yescharacteristic
206C22×Q8C2×D4711yescharacteristic
207C2×SD16—471no—
208C2×SD16—471no—
209C2×D8—471no—
210C2×M16—471no—
211C22×C8—471no—
212C4⋊Q8—471no—
213#124—21no—
214#124C2×D4711yescharacteristic
215#123—941no—
216#123—941no—
217C22⋊Q8—21no—
218C22⋊Q8—941no—
219C22⋊Q8C2×D4711yescharacteristic
220#121—21no—
221#121—471no—
222#121—471no—
223#121C2×D4711yescharacteristic
224C4×Q8C2×D4711yescharacteristic
225C4×D4—21no—
226C4×D4—471no—
227C4×D4C2×D4711yescharacteristic
228C2×C4⋊C4—471no—
229C2×C4⋊C4—471no—
230#107—471no—
231#107—471no—
232#107—471no—
233C4⋊C8—471no—
234#103—471no—
235#103—471no—
236#103—471no—
237#103—471no—
238#103—471no—
239#103—471no—
240#102—471no—
241#102—471no—
242#102—471no—
243#102—471no—
244C22⋊C8—471no—
245C22⋊C8—471no—
246#97—471no—
247#41—22no—
248#41—41no—
249#41—1884no—
250C2×Q8—21no—
251C2×Q8—22no—
252C2×Q8—41no—
253C2×Q8—941no—
254C2×Q8C22×D4711yescharacteristic
255C2×Q8C22×D4711yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—471no—
259C2×D4—941no—
260C2×D4—941no—
261C2×D4C22⋊D4711yescharacteristic
262C2×D4C22×D4711yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—941no—
266C22×C4—941no—
267C22×C4—941no—
268C22×C4C22×D4711yescharacteristic
269C22×C4C22×D4711yescharacteristic
270SD16—942no—
271SD16—1881no—
272D8—1881no—
273M16—1881no—
274C2×C8—471no—
275C2×C8—471no—
276C2×C8—471no—
277C2×C8—471no—
278C2×C8—1881no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—471no—
282C4⋊C4—471no—
283C4⋊C4—471no—
284C4⋊C4—941no—
285C4⋊C4—941no—
286C4⋊C4—941no—
287C4⋊C4C22⋊D4711yescharacteristic
288C4⋊C4C22×D4711yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4C22⋊D4711yescharacteristic
297C22⋊C4C22⋊D4711yescharacteristic
298C42—21no—
299C42C22×D4711yescharacteristic
300C23—21no—
301C23—941no—
302C23C2×C22⋊D4711yescharacteristic
303C23C2×C22⋊D4711yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—1882no—
309Q8#1062535212yescomplemented
310D4—22no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—42no—
315D4—941no—
316D4—941no—
317D4—1882no—
318D4—1882no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—1882no—
332C2×C4—1882no—
333C2×C4—1882no—
334C2×C4C2×C22⋊D4711yescharacteristic
335C2×C4C2×C22⋊D4711yescharacteristic
336C2×C4C2×C22⋊D4711yescharacteristic
337C2×C4C2×C22⋊D4711yescharacteristic
338C2×C4C23×D4711yescharacteristic
339C8—941no—
340C8—941no—
341C8—941no—
342C8—941no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—1881no—
352C22—1881no—
353C22—1881no—
354C22#1309404912yes—
355C22C22×C22⋊D4711yescharacteristic
356C4—21no—
357C4—21no—
358C4—22no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—1881no—
364C4—1881no—
365C4—1881no—
366C4C2×#1062535211yescharacteristic
367C4#1309406911yescharacteristic
368C2—22no—
369C2—41no—
370C2—81no—
371C2—3761no—
372C2#1568976711yescharacteristic
373C2C2×#1309404911yescharacteristic
374C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#548C2
socleC22×C47C22×D4
hypercenter#548D47
hypocenterC47#3308
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #15689777C2semidirect
2. #15689482C2semidirect
3. #15689456C2semidirect
4. #15689434C2semidirect
5. #15689418C2semidirect
6. #15689371C2semidirect
7. #15689357C2semidirect
8. #15689335C2semidirect
9. #15689268C2semidirect
10. #15689262C2semidirect
11. #15689221C2semidirect
12. #15689195C2semidirect
13. #15689124C2semidirect
14. C2×#13093948C2semidirect
15. C47×#548C2semidirect
120. Q8×C47#41semidirect
188. #548D47semidirect
203. C47#3308semidirect
309. Q8#10625352semidirect