Finite Group Databasebeta

← #20255373

Subgroups — #20255373

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#15689782C211yesmaximal, characteristic, complemented
2#15689485C211yesmaximal, characteristic, complemented
3#15689458C211yesmaximal, characteristic, complemented
4#15689436C211yesmaximal, characteristic, complemented
5#15689415C211yesmaximal, characteristic, complemented
6#15689367C211yesmaximal, characteristic, complemented
7#15689357C211yesmaximal, characteristic, complemented
8#15689338C211yesmaximal, characteristic, complemented
9#15689266C211yesmaximal, characteristic, complemented
10#15689261C211yesmaximal, characteristic, complemented
11#15689223C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689122C211yesmaximal, characteristic, complemented
14C2×#13093947C211yesmaximal, characteristic, complemented
15C47×#547C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20C2×#10625334C2211yescharacteristic
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#13093957C2211yescharacteristic
32#13093957C2211yescharacteristic
33#13093957C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35#13093947C2211yescharacteristic
36#13093947C2211yescharacteristic
37#13093947C2211yescharacteristic
38#13093947C2211yescharacteristic
39#13093947C2211yescharacteristic
40#13093947C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44#13093944C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47#13093935C2211yescharacteristic
48C2×#41×C47—21no—
49C4⋊Q8×C47C2211yescharacteristic
50#123×C47—21no—
51#123×C47—21no—
52C22⋊Q8×C47—21no—
53#121×C47C2211yescharacteristic
54#121×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic
56C4×D4×C47C2211yescharacteristic
57C2×C4⋊C4×C47C2211yescharacteristic
58C2×C4⋊C4×C47C2211yescharacteristic
59#41×C47—44no—
60C2×Q8×C47—21no—
61C2×D4×C47—21no—
62C2×D4×C47—21no—
63C2×D4×C47D411yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—21no—
68C22×C4×C47C2311yescharacteristic
69C22×C4×C47C2311yescharacteristic
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C22×Dic47—21no—
73#10625350—22no—
74#10625350—41no—
75C2×D188C2311yescharacteristic
76C2×C4×D47—21no—
77C2×Dic94—22no—
78C2×Dic94—21no—
79C2×Dic94—41no—
80C2×Dic94C2311yescharacteristic
81C2×Dic94C2311yescharacteristic
82C4⋊C4×C47—21no—
83C4⋊C4×C47—21no—
84C4⋊C4×C47—21no—
85C4⋊C4×C47D411yescharacteristic
86C4⋊C4×C47C2311yescharacteristic
87C4⋊C4×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C22⋊C4×C47—21no—
90C22⋊C4×C47—21no—
91C22⋊C4×C47—21no—
92C22⋊C4×C47D411yescharacteristic
93C22⋊C4×C47D411yescharacteristic
94C42×C47C2311yescharacteristic
95C22⋊Dic47—21no—
96#10625335—22no—
97#10625335—41no—
98#10625334—41no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102C4⋊Dic47C2311yescharacteristic
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105C4×Dic47—21no—
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—42no—
117D4×C47—22no—
118D4×C47—21no—
119D4×C47—21no—
120D4×C47—42no—
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—21no—
128C2×C4×C47—21no—
129C2×C4×C47—42no—
130C2×C4×C47—42no—
131C2×C4×C47—42no—
132C2×C4×C47C2×D411yescharacteristic
133C2×C4×C47C2×D411yescharacteristic
134C2×C4×C47C2×D411yescharacteristic
135C2×C4×C47C2×D411yescharacteristic
136C2×C4×C47C2411yescharacteristic
137C22⋊D47—42no—
138C22⋊D47—42no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47—42no—
143D188—21no—
144D188—21no—
145C4×D47—42no—
146Dic94—21no—
147Dic94—21no—
148Dic94—21no—
149Dic94—42no—
150Dic94#4112yescomplemented
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—21no—
171C4×C47—21no—
172C4×C47—41no—
173C4×C47—41no—
174C4×C47—41no—
175C4×C47C2×#4111yescharacteristic
176C4×C47H(5,𝔽2)11yescharacteristic
177Dic47—22no—
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#548—471no—
189#547D4711yescharacteristic, complemented
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—21no—
205C2×#41—471no—
206C22×Q8—471no—
207C2×SD16—471no—
208C2×SD16—471no—
209C2×D8—471no—
210C2×M16—471no—
211C22×C8—471no—
212C4⋊Q8C2×D4711yescharacteristic
213#124—471no—
214#124—941no—
215#123—21no—
216#123—21no—
217C22⋊Q8—21no—
218C22⋊Q8—471no—
219C22⋊Q8—941no—
220#121—471no—
221#121—941no—
222#121C2×D4711yescharacteristic
223#121C2×D4711yescharacteristic
224C4×Q8—471no—
225C4×D4—941no—
226C4×D4C2×D4711yescharacteristic
227C4×D4C2×D4711yescharacteristic
228C2×C4⋊C4C2×D4711yescharacteristic
229C2×C4⋊C4C2×D4711yescharacteristic
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—44no—
248#41—942no—
249#41—1881no—
250C2×Q8—21no—
251C2×Q8—471no—
252C2×Q8—471no—
253C2×Q8—942no—
254C2×Q8—941no—
255C2×Q8—1881no—
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—21no—
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—21no—
282C4⋊C4—471no—
283C4⋊C4—941no—
284C4⋊C4—941no—
285C4⋊C4C22⋊D4711yescharacteristic
286C4⋊C4C22×D4711yescharacteristic
287C4⋊C4C22×D4711yescharacteristic
288C4⋊C4C22×D4711yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4C22⋊D4711yescharacteristic
297C22⋊C4C22⋊D4711yescharacteristic
298C42—941no—
299C42C22×D4711yescharacteristic
300C23—21no—
301C23—941no—
302C23C2×C22⋊D4711yescharacteristic
303C23C2×C22⋊D4711yescharacteristic
304Q8—42no—
305Q8—472no—
306Q8—941no—
307Q8—941no—
308Q8—941no—
309Q8—1882no—
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—42no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—941no—
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#1309405012yes—
355C22C22×C22⋊D4711yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—942no—
364C4—1881no—
365C4—1881no—
366C4#41×D4711yescharacteristic
367C4#1309407011yescharacteristic
368C2—22no—
369C2—41no—
370C2—81no—
371C2—3761no—
372C2#1568976111yescharacteristic
373C2C2×#1309405011yescharacteristic
374C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#547C2
socleC22×C47C22×D4
hypercenter#547D47
hypocenterC47#3308
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #15689782C2semidirect
2. #15689485C2semidirect
3. #15689458C2semidirect
4. #15689436C2semidirect
5. #15689415C2semidirect
6. #15689367C2semidirect
7. #15689357C2semidirect
8. #15689338C2semidirect
9. #15689266C2semidirect
10. #15689261C2semidirect
11. #15689223C2semidirect
12. #15689195C2semidirect
13. #15689122C2semidirect
14. C2×#13093947C2semidirect
15. C47×#547C2semidirect
150. Dic94#41semidirect
189. #547D47semidirect
203. C47#3308semidirect