Finite Group Databasebeta

← #20256472

Subgroups — #20256472

Order 6016.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689858C211yesmaximal, characteristic, complemented
2#15689513C211yesmaximal, characteristic, complemented
3#15689510C211yesmaximal, characteristic, complemented
4#15689505C211yesmaximal, characteristic, complemented
5#15689345C211yesmaximal, characteristic, complemented
6#15689342C211yesmaximal, characteristic, complemented
7#15689338C211yesmaximal, characteristic, complemented
8#15689335C211yesmaximal, characteristic, complemented
9#15689318C211yesmaximal, characteristic, complemented
10#15689315C211yesmaximal, characteristic, complemented
11#15689254C211yesmaximal, characteristic, complemented
12#15689223C211yesmaximal, characteristic, complemented
13#15689221C211yesmaximal, characteristic, complemented
14C4×#10625334C211yesmaximal, characteristic, complemented
15C47×#559C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C2×#10625335C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20C2×#10625336C2211yescharacteristic
21C2×#10625334C2211yescharacteristic
22C2×#10625334C2211yescharacteristic
23C2×#10625334C2211yescharacteristic
24C2×#10625334C2211yescharacteristic
25#13094021C2211yescharacteristic
26#13094013—21no—
27#13094012C2211yescharacteristic
28#13094012C2211yescharacteristic
29#13094009—21no—
30#13094009—21no—
31C4×Dic94C2211yescharacteristic
32C4×D188C2211yescharacteristic
33C4×D188C2211yescharacteristic
34#13093986—21no—
35#13093957C2211yescharacteristic
36C4⋊(C47⋊C8)C2211yescharacteristic
37C4⋊(C47⋊C8)C2211yescharacteristic
38C4⋊(C47⋊C8)C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093947C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093945C2211yescharacteristic
43#13093944C2211yescharacteristic
44#13093944C2211yescharacteristic
45#13093935C2211yescharacteristic
46#13093935C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48#127×C47C2211yescharacteristic
49#124×C47—21no—
50#124×C47C2211yescharacteristic
51#124×C47C2211yescharacteristic
52#123×C47—21no—
53#123×C47—21no—
54C4×Q8×C47C2211yescharacteristic
55C4×Q8×C47C2211yescharacteristic
56C4×D4×C47—21no—
57C4×D4×C47C2211yescharacteristic
58C4×D4×C47C2211yescharacteristic
59C2×Q8×C47D411yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47—21no—
62C2×D4×C47—21no—
63C2×D4×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C2×D188—21no—
68C2×D188—21no—
69C2×D188C2311yescharacteristic
70C2×D188C2311yescharacteristic
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×Dic94C2311yescharacteristic
74C4⋊C4×C47—21no—
75C4⋊C4×C47D411yescharacteristic
76C4⋊C4×C47D411yescharacteristic
77C4⋊C4×C47D411yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C22⋊C4×C47—21no—
82C22⋊C4×C47—21no—
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C42×C47—21no—
86C42×C47C2311yescharacteristic
87C42×C47C2311yescharacteristic
88C42×C47C2311yescharacteristic
89#10625337—41no—
90#10625336—22no—
91#10625336—41no—
92#10625335—22no—
93#10625335—41no—
94#10625334—22no—
95#10625334—41no—
96#10625334—41no—
97#10625334—41no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104C4⋊Dic47C2311yescharacteristic
105Dic47⋊C4—21no—
106C4×Dic47—21no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C23×C47—21no—
112C23×C47—21no—
113C22×D47—21no—
114C22×D47—21no—
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—41no—
118D4×C47—21no—
119D4×C47—21no—
120D4×C47—21no—
121D4×C47—21no—
122D4×C47—42no—
123D4×C47—81no—
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×C47C2×D411yescharacteristic
133C2×C4×C47C2×D411yescharacteristic
134C2×C4×C47C2411yescharacteristic
135C2×Dic47—21no—
136C2×Dic47—21no—
137D188—21no—
138D188—21no—
139D188—21no—
140D188—21no—
141D188—42no—
142D188—81no—
143C4×D47—81no—
144C4×D47—81no—
145Dic94—21no—
146Dic94—21no—
147C47⋊C8—21no—
148C47⋊C8—21no—
149C47⋊C8—21no—
150C47⋊C8#4112yes—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47C22×D411yescharacteristic
158C2×D47—41no—
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—41no—
162C2×D47—41no—
163C2×D47—41no—
164C4×C47—21no—
165C4×C47—21no—
166C4×C47—21no—
167C4×C47—21no—
168C4×C47—21no—
169C4×C47—21no—
170C4×C47—41no—
171C4×C47—41no—
172C4×C47C2×#4111yescharacteristic
173C4×C47H(5,𝔽2)11yescharacteristic
174Dic47—41no—
175Dic47—41no—
176#3403—471nomaximal, Sylow
177C2×C47—81no—
178C2×C47—81no—
179C2×C47#55011yescharacteristic
180C2×C47#57511yescharacteristic
181C2×C47#57611yescharacteristic
182D47—81no—
183D47—81no—
184#559—471no—
185#559D4711yescharacteristic, complemented
186#496—471no—
187#496—471no—
188#495—471no—
189#464—471no—
190#464—471no—
191#463—471no—
192#463—471no—
193#459—471no—
194#459—471no—
195#446—471no—
196#440—471no—
197#440—471no—
198C4×D8—471no—
199C47#340311yescharacteristic, complemented, Sylow
200C2×Q16—471no—
201C2×SD16—471no—
202C2×SD16—471no—
203C2×SD16—471no—
204C2×SD16—471no—
205C2×D8—471no—
206C2×D8—471no—
207C2×D8—471no—
208C2×D8—471no—
209#127—471no—
210#127C2×D4711yescharacteristic
211#124—21no—
212#124—471no—
213#124—471no—
214#124—941no—
215#124C2×D4711yescharacteristic
216#124C2×D4711yescharacteristic
217#123—21no—
218#123—21no—
219#123—941no—
220#123—941no—
221C4×Q8—471no—
222C4×Q8C2×D4711yescharacteristic
223C4×Q8C2×D4711yescharacteristic
224C4×D4—21no—
225C4×D4—471no—
226C4×D4—471no—
227C4×D4—941no—
228C4×D4C2×D4711yescharacteristic
229C4×D4C2×D4711yescharacteristic
230#107—471no—
231C4⋊C8—471no—
232C4⋊C8—471no—
233C4⋊C8—471no—
234#103—471no—
235#103—471no—
236#102—471no—
237#102—471no—
238#102—471no—
239#102—471no—
240#97—471no—
241#97—471no—
242C4×C8—471no—
243C2×Q8—471no—
244C2×Q8C22⋊D4711yescharacteristic
245C2×Q8C22×D4711yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—471no—
249C2×D4—471no—
250C2×D4—941no—
251C2×D4—941no—
252C2×D4C22×D4711yescharacteristic
253C2×D4C22×D4711yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—941no—
257C22×C4—941no—
258Q16—1881no—
259SD16—942no—
260SD16—942no—
261SD16—1881no—
262SD16—1881no—
263D8—942no—
264D8—1881no—
265D8—1881no—
266D8—1881no—
267C2×C8—471no—
268C2×C8—471no—
269C2×C8—471no—
270C2×C8—471no—
271C4⋊C4—21no—
272C4⋊C4—471no—
273C4⋊C4—941no—
274C4⋊C4C22⋊D4711yescharacteristic
275C4⋊C4C22⋊D4711yescharacteristic
276C4⋊C4C22⋊D4711yescharacteristic
277C4⋊C4C22×D4711yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C42—21no—
291C42—941no—
292C42C22×D4711yescharacteristic
293C42C22×D4711yescharacteristic
294C42C22×D4711yescharacteristic
295C23—21no—
296C23—21no—
297C23—941no—
298C23—941no—
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—941no—
303Q8—941no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—941no—
311D4—941no—
312D4—941no—
313D4—941no—
314D4—3761no—
315D4—1882no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—941no—
321C2×C4—941no—
322C2×C4—3761no—
323C2×C4—3761no—
324C2×C4C2×C22⋊D4711yescharacteristic
325C2×C4C2×C22⋊D4711yescharacteristic
326C2×C4C2×C22⋊D4711yescharacteristic
327C2×C4C2×C22⋊D4711yescharacteristic
328C2×C4C2×C22⋊D4711yescharacteristic
329C2×C4C2×C22⋊D4711yescharacteristic
330C2×C4C23×D4711yescharacteristic
331C8—472no—
332C8—941no—
333C8—941no—
334C8—941no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—1881no—
342C22—1881no—
343C22—1881no—
344C22—1881no—
345C22—1881no—
346C22—1881no—
347C22C22×C22⋊D4711yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—1881no—
357C4—1881no—
358C4#41×D4711yescharacteristic
359C4#1309407011yescharacteristic
360C2—81no—
361C2—81no—
362C2—3761no—
363C2—3761no—
364C2#1568979211yescharacteristic
365C2#1568992111yescharacteristic
366C2#1568992611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#559C2
socleC22×C47C22×D4
hypercenter#559D47
hypocenterC47#3403
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #15689858C2semidirect
2. #15689513C2semidirect
3. #15689510C2semidirect
4. #15689505C2semidirect
5. #15689345C2semidirect
6. #15689342C2semidirect
7. #15689338C2semidirect
8. #15689335C2semidirect
9. #15689318C2semidirect
10. #15689315C2semidirect
11. #15689254C2semidirect
12. #15689223C2semidirect
13. #15689221C2semidirect
14. C4×#10625334C2semidirect
15. C47×#559C2semidirect
185. #559D47semidirect
199. C47#3403semidirect