Finite Group Databasebeta

← #20253443

Subgroups — #20253443

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#15689591C211yesmaximal, characteristic, complemented
3#15689447C211yesmaximal, characteristic, complemented
4#15689417C211yesmaximal, characteristic, complemented
5#15689412C211yesmaximal, characteristic, complemented
6#15689322C211yesmaximal, characteristic, complemented
7#15689317C211yesmaximal, characteristic, complemented
8#15689270C211yesmaximal, characteristic, complemented
9#15689266C211yesmaximal, characteristic, complemented
10#15689214C211yesmaximal, characteristic, complemented
11#15689210C211yesmaximal, characteristic, complemented
12#15689205C211yesmaximal, characteristic, complemented
13#15689203C211yesmaximal, characteristic, complemented
14#15689173C211yesmaximal, characteristic, complemented
15C47×#482C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625352—21no—
18C2×#10625325C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20C2×D376C2211yescharacteristic
21C2×#10625334C2211yescharacteristic
22#13094023C2211yescharacteristic
23#13094020C2211yescharacteristic
24#13094010—21no—
25#13093998C2211yescharacteristic
26#13093996—21no—
27#13093989C2211yescharacteristic
28#13093989C2211yescharacteristic
29D4×Dic47C2211yescharacteristic
30#13093986C2211yescharacteristic
31#13093986C2211yescharacteristic
32#13093986C2211yescharacteristic
33(C22⋊D47)⋊C4—21no—
34(C22⋊D47)⋊C4—21no—
35(C22⋊D47)⋊C4—21no—
36#13093981—21no—
37C2×C4×Dic47C2211yescharacteristic
38C42×D47—21no—
39#13093957C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50C8×Dic47C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52#121×C47C2211yescharacteristic
53#117×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C22×Dic47—21no—
67C22×Dic47D411yescharacteristic
68C22×Dic47D411yescharacteristic
69#10625352—44no—
70#10625350—22no—
71#10625350—22no—
72C2×D188C2311yescharacteristic
73C2×D188C2311yescharacteristic
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×Dic94—21no—
79C2×Dic94C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C42×C47—21no—
88C22⋊Dic47—21no—
89#10625335—22no—
90#10625334—22no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95C4⋊Dic47C2311yescharacteristic
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47D411yescharacteristic
102C4×Dic47D411yescharacteristic
103C4×Dic47C2311yescharacteristic
104C4×Dic47C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107D376—22no—
108#10625325—22no—
109C23×C47—21no—
110C23×C47C2×D411yescharacteristic
111C22×D47—21no—
112C22×D47—21no—
113D4×C47—21no—
114D4×C47—21no—
115D4×C47—42no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2411yescharacteristic
123C22⋊D47—24no—
124C22⋊D47—42no—
125C22⋊D47—42no—
126C22⋊D47—42no—
127C2×Dic47—21no—
128C2×Dic47—22no—
129C2×Dic47—22no—
130C2×Dic47—21no—
131C2×Dic47—42no—
132C2×Dic47C2×D411yescharacteristic
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136D188—21no—
137D188—21no—
138D188—21no—
139D188#4112yescomplemented
140C4×D47—24no—
141C4×D47—42no—
142C4×D47—42no—
143C4×D47—42no—
144Dic94—21no—
145Dic94—42no—
146Dic94#4112yescomplemented
147C8×C47—21no—
148C8×C47—21no—
149C47⋊C8—21no—
150C47⋊C8—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—41no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47C22×D411yescharacteristic
158C2×D47—22no—
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—41no—
162C2×D47—41no—
163C2×D47—41no—
164C4×C47—21no—
165C4×C47—41no—
166C4×C47—41no—
167C4×C47—41no—
168C4×C47C2×#4111yescharacteristic
169C4×C47C2×#4111yescharacteristic
170Dic47—22no—
171Dic47—21no—
172Dic47—21no—
173Dic47—41no—
174Dic47#13512yes—
175Dic47AGL(1,ℤ/8)12yes—
176#3106—471nomaximal, Sylow
177C2×C47—41no—
178C2×C47—81no—
179C2×C47#52511yescharacteristic
180C2×C47C2×#13511yescharacteristic
181C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
182D47—42no—
183D47—81no—
184#532—471no—
185C4×#41—471no—
186#482—471no—
187#482D4711yescharacteristic, complemented
188#477—471no—
189#476—471no—
190#460—471no—
191#459—471no—
192#449—471no—
193#449—471no—
194C4×SD16—471no—
195C4×SD16—471no—
196C4×D8—471no—
197C4×D8—471no—
198#431—471no—
199C47#310611yescharacteristic, complemented, Sylow
200C2×#41—471no—
201C2×#41—941no—
202C2×SD16—471no—
203C2×SD16—471no—
204C2×D8—471no—
205C2×D8—471no—
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—941no—
222#117C2×D4711yescharacteristic
223C2×C42—471no—
224C2×C42—941no—
225#107—471no—
226#107C2×D4711yescharacteristic
227#106—471no—
228#106C2×D4711yescharacteristic
229C4⋊C8—471no—
230C4⋊C8—471no—
231#103—471no—
232#103—471no—
233#102—471no—
234#102—471no—
235#102—471no—
236#102—471no—
237#102C2×D4711yescharacteristic
238#102C2×D4711yescharacteristic
239C22⋊C8—471no—
240C22⋊C8C2×D4711yescharacteristic
241C4×C8—471no—
242C4×C8—471no—
243#41—942no—
244#41—942no—
245#41—1884no—
246C2×Q8—471no—
247C2×Q8—941no—
248C2×D4—21no—
249C2×D4—471no—
250C2×D4—471no—
251C2×D4—941no—
252C2×D4—941no—
253C2×D4—941no—
254C2×D4—941no—
255C2×D4C22×D4711yescharacteristic
256C22×C4—471no—
257C22×C4—471no—
258C22×C4—941no—
259C22×C4—941no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4—941no—
263C22×C4C22×D4711yescharacteristic
264SD16—942no—
265SD16—942no—
266D8—942no—
267D8—942no—
268C2×C8—471no—
269C2×C8—471no—
270C2×C8C22×D4711yescharacteristic
271C2×C8C22×D4711yescharacteristic
272C4⋊C4—471no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4—941no—
276C4⋊C4C22×D4711yescharacteristic
277C4⋊C4C22×D4711yescharacteristic
278C4⋊C4C22×D4711yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C42—21no—
287C42—471no—
288C42—471no—
289C42—471no—
290C42—471no—
291C42—941no—
292C42—941no—
293C23—21no—
294C23—941no—
295C23—941no—
296C23D4×D4711yescharacteristic
297Q8—472no—
298Q8—941no—
299Q8—1882no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—472no—
304D4—944no—
305D4—941no—
306D4—941no—
307D4—941no—
308D4—1882no—
309D4—1882no—
310D4—1882no—
311C2×C4—21no—
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—944no—
321C2×C4—942no—
322C2×C4—942no—
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—21no—
337C22—21no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—942no—
342C22—1881no—
343C22—1881no—
344C22—1881no—
345C22—1881no—
346C22—1881no—
347C22C2×D4×D4711yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—472no—
353C4—472no—
354C4—942no—
355C4—941no—
356C4—941no—
357C4—1881no—
358C4#41×D4711yescharacteristic
359C4#41×D4711yescharacteristic
360C2—41no—
361C2—81no—
362C2—3761no—
363C2—1882no—
364C2#1568963111yescharacteristic
365C2#135×D4711yescharacteristic
366C2AGL(1,ℤ/8)×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#482C2
socleC22×C47C22×D4
hypercenter#482D47
hypocenterC47#3106
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #15689668C2semidirect
2. #15689591C2semidirect
3. #15689447C2semidirect
4. #15689417C2semidirect
5. #15689412C2semidirect
6. #15689322C2semidirect
7. #15689317C2semidirect
8. #15689270C2semidirect
9. #15689266C2semidirect
10. #15689214C2semidirect
11. #15689210C2semidirect
12. #15689205C2semidirect
13. #15689203C2semidirect
14. #15689173C2semidirect
15. C47×#482C2semidirect
139. D188#41semidirect
146. Dic94#41semidirect
187. #482D47semidirect
199. C47#3106semidirect