Finite Group Databasebeta

← #20255508

Subgroups — #20255508

Order 6016.

392 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#15689794C211yesmaximal, characteristic
2#15689489C211yesmaximal, characteristic, complemented
3#15689447C211yesmaximal, characteristic, complemented
4#15689441C211yesmaximal, characteristic, complemented
5#15689427C211yesmaximal, characteristic, complemented
6#15689371C211yesmaximal, characteristic, complemented
7#15689354C211yesmaximal, characteristic, complemented
8#15689323C211yesmaximal, characteristic, complemented
9#15689283C211yesmaximal, characteristic, complemented
10#15689283C211yesmaximal, characteristic, complemented
11#15689228C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689122C211yesmaximal, characteristic, complemented
14#15689117C211yesmaximal, characteristic, complemented
15C47×#552C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625350C2211yescharacteristic
18C2×#10625337C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20C2×#10625336C2211yescharacteristic
21C2×#10625329C2211yescharacteristic
22C22×C47⋊C8C2211yescharacteristic
23#13094021C2211yescharacteristic
24#13094020—21no—
25#13093998C2211yescharacteristic
26#13093998C2211yescharacteristic
27#13093997—21no—
28#13093997—21no—
29C4×Dic94C2211yescharacteristic
30#13093986—21no—
31#13093957C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35#13093948C2211yescharacteristic
36#13093947C2211yescharacteristic
37#13093947C2211yescharacteristic
38#13093947C2211yescharacteristic
39#13093944C2211yescharacteristic
40#13093944C2211yescharacteristic
41#13093944C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44#13093944C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47#13093935C2211yescharacteristic
48#126×C47—21no—
49#125×C47—21no—
50#125×C47C2211yescharacteristic
51#123×C47—21no—
52C22⋊Q8×C47C2211yescharacteristic
53C22⋊Q8×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic
56#117×C47—21no—
57#117×C47C2211yescharacteristic
58C2×C4⋊C4×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47D411yescharacteristic
61C22×C4×C47—21no—
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68#10625350—22no—
69#10625350—22no—
70#10625350—41no—
71#10625350—41no—
72C2×D188—21no—
73C2×D188—21no—
74C2×D188C2311yescharacteristic
75C2×D188C2311yescharacteristic
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×Dic94C2311yescharacteristic
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47—21no—
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×C47—21no—
95C42×C47—21no—
96C42×C47C2311yescharacteristic
97#10625337—22no—
98#10625336—41no—
99#10625336—41no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102C4⋊Dic47C2311yescharacteristic
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—
114C22×D47—21no—
115Q8×C47—21no—
116Q8×C47—21no—
117D4×C47—41no—
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—42no—
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2411yescharacteristic
132C22⋊D47—42no—
133C22⋊D47—42no—
134C22⋊D47—81no—
135C22⋊D47—81no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138D188—21no—
139D188—21no—
140D188—21no—
141D188—21no—
142D188—42no—
143D188—81no—
144C4×D47—42no—
145C4×D47—42no—
146Dic94—21no—
147Dic94#4112yes—
148C47⋊C8—21no—
149C47⋊C8—21no—
150C47⋊C8—21no—
151C47⋊C8—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47C22×D411yescharacteristic
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—41no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—41no—
165C4×C47—21no—
166C4×C47—21no—
167C4×C47—21no—
168C4×C47—21no—
169C4×C47—41no—
170C4×C47—41no—
171C4×C47—41no—
172C4×C47—41no—
173C4×C47C2×#4111yescharacteristic
174C4×C47H(5,𝔽2)11yescharacteristic
175Dic47—22no—
176Dic47—41no—
177#3317—471nomaximal, Sylow
178C2×C47—41no—
179C2×C47—41no—
180C2×C47#54611yescharacteristic
181C2×C47#57511yescharacteristic
182C2×C47#57711yescharacteristic
183D47—81no—
184D47—81no—
185#552D4711yescharacteristic, complemented
186#550—471no—
187#490—471no—
188#482—471no—
189#481—471no—
190#479—471no—
191#468—471no—
192#465—471no—
193#460—471no—
194#452—471no—
195#452—471no—
196#441—471no—
197#435—471no—
198#417—471no—
199#416—471no—
200C47#331711yescharacteristic, complemented, Sylow
201C2×#41—471no—
202C2×#41—471no—
203C2×Q16—471no—
204C2×SD16—471no—
205C2×SD16—471no—
206C2×M16—471no—
207C22×C8—471no—
208#127—471no—
209#127—941no—
210#126—21no—
211#125—21no—
212#125C2×D4711yescharacteristic
213#123—21no—
214C22⋊Q8C2×D4711yescharacteristic
215C22⋊Q8C2×D4711yescharacteristic
216#121—471no—
217#121—471no—
218#121—941no—
219#121—941no—
220C4×Q8—471no—
221C4×Q8C2×D4711yescharacteristic
222C4×D4—941no—
223C4×D4C2×D4711yescharacteristic
224#117—21no—
225#117C2×D4711yescharacteristic
226C2×C4⋊C4C2×D4711yescharacteristic
227#107—471no—
228#106—471no—
229#106—471no—
230C4⋊C8—471no—
231#103—471no—
232#103—471no—
233#103—471no—
234#103—471no—
235#102—471no—
236#102—471no—
237#102—471no—
238#102—471no—
239#102—471no—
240#102—471no—
241C22⋊C8—471no—
242C22⋊C8—471no—
243#97—471no—
244#41—942no—
245#41—942no—
246#41—1881no—
247#41—1881no—
248C2×Q8—471no—
249C2×Q8C22×D4711yescharacteristic
250C2×D4—471no—
251C2×D4—471no—
252C2×D4—941no—
253C2×D4—941no—
254C2×D4—941no—
255C2×D4—941no—
256C2×D4—941no—
257C2×D4—941no—
258C2×D4C22⋊D4711yescharacteristic
259C22×C4—21no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4C22×D4711yescharacteristic
263C22×C4C22×D4711yescharacteristic
264Q16—942no—
265SD16—1881no—
266SD16—1881no—
267M16—1881no—
268C2×C8—471no—
269C2×C8—471no—
270C2×C8—471no—
271C2×C8—471no—
272C2×C8—1881no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—471no—
280C4⋊C4—941no—
281C4⋊C4C22⋊D4711yescharacteristic
282C4⋊C4C22×D4711yescharacteristic
283C4⋊C4C22×D4711yescharacteristic
284C4⋊C4C22×D4711yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4C22⋊D4711yescharacteristic
291C22⋊C4C22⋊D4711yescharacteristic
292C42—21no—
293C42—21no—
294C42—941no—
295C42C22×D4711yescharacteristic
296C23—941no—
297C23—941no—
298C23C2×C22⋊D4711yescharacteristic
299C23C2×C22⋊D4711yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—472no—
303Q8—941no—
304D4—41no—
305D4—941no—
306D4—941no—
307D4—941no—
308D4—941no—
309D4—3761no—
310D4—3761no—
311D4—3761no—
312D4—1882no—
313D4—1882no—
314D4—1882no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—1882no—
327C2×C4—1882no—
328C2×C4C2×C22⋊D4711yescharacteristic
329C2×C4C2×C22⋊D4711yescharacteristic
330C2×C4C2×C22⋊D4711yescharacteristic
331C2×C4C2×C22⋊D4711yescharacteristic
332C2×C4C23×D4711yescharacteristic
333C8—941no—
334C8—941no—
335C8—941no—
336C8—941no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—1881no—
344C22—1881no—
345C22—1881no—
346C22—1881no—
347C22—1881no—
348C22—1881no—
349C22C22×C22⋊D4711yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—942no—
359C4—1881no—
360C4#41×D4711yescharacteristic
361C4#1309407011yescharacteristic
362C2—41no—
363C2—41no—
364C2—3761no—
365C2—3761no—
366C2#1568976111yescharacteristic
367C2#1568992111yescharacteristic
368C2#1568993111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#552C2
socleC22×C47C22×D4
hypercenter#552D47
hypocenterC47#3317
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #15689489C2semidirect
3. #15689447C2semidirect
4. #15689441C2semidirect
5. #15689427C2semidirect
6. #15689371C2semidirect
7. #15689354C2semidirect
8. #15689323C2semidirect
9. #15689283C2semidirect
10. #15689283C2semidirect
11. #15689228C2semidirect
12. #15689195C2semidirect
13. #15689122C2semidirect
14. #15689117C2semidirect
15. C47×#552C2semidirect
185. #552D47semidirect
200. C47#3317semidirect