Finite Group Databasebeta

← #20253441

Subgroups — #20253441

Order 6016.

434 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#15689668C211yesmaximal, characteristic, complemented
2#41×Dic47C211yesmaximal, characteristic, complemented
3#15689448C211yesmaximal, characteristic, complemented
4#15689444C211yesmaximal, characteristic, complemented
5#15689416C211yesmaximal, characteristic, complemented
6#15689411C211yesmaximal, characteristic, complemented
7#15689321C211yesmaximal, characteristic, complemented
8#15689316C211yesmaximal, characteristic, complemented
9#15689268C211yesmaximal, characteristic, complemented
10SD16×Dic47C211yesmaximal, characteristic, complemented
11#15689208C211yesmaximal, characteristic, complemented
12D8×Dic47C211yesmaximal, characteristic, complemented
13#15689203C211yesmaximal, characteristic, complemented
14#15689173C211yesmaximal, characteristic, complemented
15C47×#449C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17C2×#10625336C2211yescharacteristic
18C2×#10625334C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094020C2211yescharacteristic
21#13094010—21no—
22#13093998C2211yescharacteristic
23#13093996—21no—
24Q8×Dic47C2211yescharacteristic
25Q8×Dic47C2211yescharacteristic
26D4×Dic47—21no—
27D4×Dic47—21no—
28D4×Dic47C2211yescharacteristic
29D4×Dic47C2211yescharacteristic
30D4×Dic47C2211yescharacteristic
31#13093986C2211yescharacteristic
32(C22⋊D47)⋊C4—21no—
33#13093983—21no—
34#13093983C2211yescharacteristic
35C2×C4×Dic47—21no—
36C2×C4×Dic47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093948C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50C8×Dic47C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×#41×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54C2×D8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59#41×C47—22no—
60#41×C47—22no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47—21no—
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47—21no—
67C22×C4×C47C2311yescharacteristic
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C22×Dic47—21no—
72C22×Dic47—21no—
73C22×Dic47—21no—
74C22×Dic47D411yescharacteristic
75C22×Dic47D411yescharacteristic
76#10625352—44no—
77C2×D188C2311yescharacteristic
78C2×C4×D47—21no—
79C2×Dic94—21no—
80SD16×C47—22no—
81D8×C47—22no—
82C2×C8×C47C2311yescharacteristic
83C2×C8×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90#10625336—22no—
91#10625334—22no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94C4⋊Dic47—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47D411yescharacteristic
104C4×Dic47D411yescharacteristic
105C4×Dic47C2311yescharacteristic
106C4×Dic47C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C23×C47—21no—
110C23×C47—21no—
111C23×C47C2×D411yescharacteristic
112C22×D47—21no—
113Q8×C47—21no—
114Q8×C47#4112yescomplemented
115D4×C47—24no—
116D4×C47—21no—
117D4×C47—21no—
118D4×C47—21no—
119D4×C47—42no—
120D4×C47#4112yescomplemented
121C2×C4×C47—24no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2411yescharacteristic
128C22⋊D47—42no—
129C22⋊D47—42no—
130C22⋊D47—42no—
131C2×Dic47—22no—
132C2×Dic47—22no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—42no—
137C2×Dic47—42no—
138C2×Dic47—42no—
139C2×Dic47C2×D411yescharacteristic
140C2×Dic47C2×D411yescharacteristic
141C2×Dic47C2×D411yescharacteristic
142C2×Dic47C2×D411yescharacteristic
143D188—21no—
144D188—21no—
145C4×D47—42no—
146Dic94—42no—
147C8×C47—21no—
148C8×C47—21no—
149C47⋊C8—21no—
150C47⋊C8—21no—
151C22×C47—21no—
152C22×C47—22no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47C22×D411yescharacteristic
161C2×D47—41no—
162C2×D47—41no—
163C2×D47—41no—
164C4×C47—21no—
165C4×C47—22no—
166C4×C47—41no—
167C4×C47C2×#4111yescharacteristic
168C4×C47C2×#4111yescharacteristic
169Dic47—21no—
170Dic47—21no—
171Dic47—41no—
172Dic47—41no—
173Dic47—41no—
174Dic47#13512yes—
175Dic47AGL(1,ℤ/8)12yes—
176#3106—471nomaximal, Sylow
177C2×C47—41no—
178C2×C47—42no—
179C2×C47—81no—
180C2×C47#52511yescharacteristic
181C2×C47C2×#13511yescharacteristic
182C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
183D47—81no—
184#532—471no—
185C4×#41—471no—
186#482—471no—
187#482—471no—
188#477—471no—
189#476—471no—
190#460—471no—
191#459—471no—
192#449—471no—
193#449D4711yescharacteristic, complemented
194C4×SD16—471no—
195C4×SD16—471no—
196C4×D8—471no—
197C4×D8—471no—
198#431—471no—
199C47#310611yescharacteristic, complemented, Sylow
200C2×#41—941no—
201C2×#41C2×D4711yescharacteristic
202C2×SD16—471no—
203C2×SD16C2×D4711yescharacteristic
204C2×D8—471no—
205C2×D8C2×D4711yescharacteristic
206C4⋊Q8—471no—
207#127—471no—
208#124—941no—
209#121—471no—
210#121—941no—
211#121C2×D4711yescharacteristic
212C4×Q8—471no—
213C4×Q8—471no—
214C4×D4—471no—
215C4×D4—471no—
216C4×D4—471no—
217C4×D4—471no—
218C4×D4—941no—
219C4×D4—941no—
220C4×D4—941no—
221#117—471no—
222#117—941no—
223C2×C42—471no—
224C2×C42—941no—
225#107—471no—
226#107—471no—
227#106—471no—
228#106—471no—
229C4⋊C8—471no—
230C4⋊C8—471no—
231#103—471no—
232#103C2×D4711yescharacteristic
233#102—471no—
234#102—471no—
235#102—471no—
236#102—471no—
237#102—471no—
238#102C2×D4711yescharacteristic
239C22⋊C8—471no—
240C22⋊C8C2×D4711yescharacteristic
241C4×C8—471no—
242C4×C8—471no—
243#41—22no—
244#41—22no—
245#41—1884no—
246C2×Q8—941no—
247C2×Q8C22×D4711yescharacteristic
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—471no—
251C2×D4—941no—
252C2×D4—941no—
253C2×D4—941no—
254C2×D4C22×D4711yescharacteristic
255C2×D4C22×D4711yescharacteristic
256C22×C4—21no—
257C22×C4—471no—
258C22×C4—471no—
259C22×C4—941no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4—941no—
263C22×C4C22×D4711yescharacteristic
264SD16—22no—
265SD16—942no—
266D8—22no—
267D8—942no—
268C2×C8—471no—
269C2×C8—471no—
270C2×C8C22×D4711yescharacteristic
271C2×C8C22×D4711yescharacteristic
272C4⋊C4—471no—
273C4⋊C4—471no—
274C4⋊C4—471no—
275C4⋊C4—941no—
276C4⋊C4—941no—
277C4⋊C4—941no—
278C4⋊C4C22×D4711yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C42—471no—
287C42—471no—
288C42—471no—
289C42—471no—
290C42—941no—
291C42—941no—
292C42—941no—
293C23—21no—
294C23—21no—
295C23—941no—
296C23D4×D4711yescharacteristic
297Q8—21no—
298Q8—1882no—
299Q8#1062535212yescomplemented
300D4—24no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—42no—
305D4—941no—
306D4—941no—
307D4—1882no—
308D4—1882no—
309D4—1882no—
310D4#1062535212yescomplemented
311C2×C4—24no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—471no—
317C2×C4—471no—
318C2×C4—471no—
319C2×C4—471no—
320C2×C4—942no—
321C2×C4—942no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—1882no—
326C2×C4—1882no—
327C2×C4—1882no—
328C2×C4—1882no—
329C2×C4D4×D4711yescharacteristic
330C2×C4C23×D4711yescharacteristic
331C8—21no—
332C8—21no—
333C8—941no—
334C8—941no—
335C22—21no—
336C22—22no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—1881no—
345C22—1881no—
346C22—1881no—
347C22C2×D4×D4711yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—472no—
352C4—472no—
353C4—941no—
354C4—941no—
355C4—1881no—
356C4—1881no—
357C4—1881no—
358C4C2×#1062535211yescharacteristic
359C4C2×#1062535211yescharacteristic
360C2—41no—
361C2—42no—
362C2—81no—
363C2—3761no—
364C2#1568962911yescharacteristic
365C2#135×D4711yescharacteristic
366C2AGL(1,ℤ/8)×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#449C2
socleC22×C47C22×D4
hypercenter#449D47
hypocenterC47#3106
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #15689668C2semidirect
2. #41×Dic47C2semidirect
3. #15689448C2semidirect
4. #15689444C2semidirect
5. #15689416C2semidirect
6. #15689411C2semidirect
7. #15689321C2semidirect
8. #15689316C2semidirect
9. #15689268C2semidirect
10. SD16×Dic47C2semidirect
11. #15689208C2semidirect
12. D8×Dic47C2semidirect
13. #15689203C2semidirect
14. #15689173C2semidirect
15. C47×#449C2semidirect
114. Q8×C47#41semidirect
120. D4×C47#41semidirect
193. #449D47semidirect
199. C47#3106semidirect
299. Q8#10625352semidirect
310. D4#10625352semidirect