Finite Group Databasebeta

← #20253976

Subgroups — #20253976

Order 6016.

408 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689668C211yesmaximal, characteristic, complemented
2#15689659C211yesmaximal, characteristic, complemented
3#15689531C211yesmaximal, characteristic, complemented
4#15689509C211yesmaximal, characteristic, complemented
5#15689486C211yesmaximal, characteristic, complemented
6#15689484C211yesmaximal, characteristic, complemented
7#15689376C211yesmaximal, characteristic, complemented
8#15689374C211yesmaximal, characteristic, complemented
9#15689371C211yesmaximal, characteristic, complemented
10SD16×Dic47C211yesmaximal, characteristic, complemented
11#15689208C211yesmaximal, characteristic, complemented
12#15689205C211yesmaximal, characteristic, complemented
13#15689203C211yesmaximal, characteristic, complemented
14M16×Dic47C211yesmaximal, characteristic, complemented
15C47×#468C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17C2×#10625336C2211yescharacteristic
18C2×D376C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20C2×#10625329C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094020C2211yescharacteristic
23#13094019—21no—
24#13094015C2211yescharacteristic
25#13094013C2211yescharacteristic
26#13094010—21no—
27#13094008—21no—
28#13093998C2211yescharacteristic
29#13093998C2211yescharacteristic
30#13093996—21no—
31Q8×Dic47C2211yescharacteristic
32D4×Dic47C2211yescharacteristic
33#13093986C2211yescharacteristic
34#13093986C2211yescharacteristic
35(C22⋊D47)⋊C4—21no—
36(C22⋊D47)⋊C4—21no—
37#13093982—21no—
38C2×C4×Dic47C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093955C2211yescharacteristic
42#13093948C2211yescharacteristic
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093934C2211yescharacteristic
49#13093934C2211yescharacteristic
50C8×Dic47C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C22×Dic47—21no—
68C22×Dic47D411yescharacteristic
69C22×Dic47D411yescharacteristic
70#10625352—44no—
71C2×D188C2311yescharacteristic
72C2×D188C2311yescharacteristic
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×Dic94—21no—
76SD16×C47—22no—
77M16×C47—22no—
78C2×C8×C47C2311yescharacteristic
79C2×C8×C47C2311yescharacteristic
80C4⋊C4×C47—21no—
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C22⋊Dic47—21no—
86#10625336—22no—
87#10625334—22no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94C4⋊Dic47—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100C4×Dic47—21no—
101C4×Dic47D411yescharacteristic
102C4×Dic47D411yescharacteristic
103C4×Dic47C2311yescharacteristic
104C4×Dic47C2311yescharacteristic
105#10625329—22no—
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108D376—22no—
109C23×C47—21no—
110C23×C47C2×D411yescharacteristic
111C22×D47—21no—
112C22×D47—21no—
113Q8×C47—21no—
114Q8×C47—21no—
115D4×C47—21no—
116D4×C47—21no—
117D4×C47—42no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2411yescharacteristic
125C22⋊D47—42no—
126C22⋊D47—42no—
127C22⋊D47—42no—
128C22⋊D47—42no—
129C2×Dic47—22no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—41no—
133C2×Dic47—42no—
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138D188—21no—
139D188—21no—
140D188—21no—
141D188—21no—
142C4×D47—42no—
143C4×D47—42no—
144Dic94—42no—
145C8×C47—21no—
146C8×C47#4112yescomplemented
147C47⋊C8—21no—
148C47⋊C8#4112yescomplemented
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—21no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47C22×D411yescharacteristic
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—41no—
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—41no—
162C4×C47—21no—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47C2×#4111yescharacteristic
167C4×C47C2×#4111yescharacteristic
168Dic47—21no—
169Dic47—21no—
170Dic47—21no—
171Dic47—41no—
172Dic47—41no—
173Dic47AGL(1,ℤ/8)12yes—
174#3171—471nomaximal, Sylow
175C2×C47—41no—
176C2×C47—81no—
177C2×C47#53211yescharacteristic
178C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
179C2×C47#57511yescharacteristic
180D47—81no—
181D47—81no—
182#532—471no—
183#529—471no—
184#501—471no—
185#496—471no—
186#490—471no—
187#489—471no—
188#469—471no—
189#469—471no—
190#468—471no—
191#468D4711yescharacteristic, complemented
192C4×SD16—471no—
193C4×SD16—471no—
194C4×D8—471no—
195C4×D8—471no—
196C4×M16—471no—
197C47#317111yescharacteristic, complemented, Sylow
198C2×#41—941no—
199C2×SD16—471no—
200C2×SD16C2×D4711yescharacteristic
201C2×D8—471no—
202C2×D8—471no—
203C2×M16—471no—
204C2×M16C2×D4711yescharacteristic
205C4⋊Q8—471no—
206#127—471no—
207#126—941no—
208#125—471no—
209#124—471no—
210#124—941no—
211#123—941no—
212C22⋊Q8C2×D4711yescharacteristic
213#121—471no—
214#121—471no—
215#121—941no—
216#121C2×D4711yescharacteristic
217C4×Q8—471no—
218C4×D4—471no—
219C4×D4—471no—
220C4×D4—471no—
221C4×D4—941no—
222C4×D4—941no—
223#117—941no—
224C2×C42—471no—
225#107—471no—
226#107C2×D4711yescharacteristic
227#106—471no—
228#106—471no—
229#103—471no—
230#103C2×D4711yescharacteristic
231#102—471no—
232#102—471no—
233#102—471no—
234#102—471no—
235#102—471no—
236#102C2×D4711yescharacteristic
237#97—471no—
238#97—471no—
239C4×C8—471no—
240C4×C8—471no—
241#41—1884no—
242C2×Q8—941no—
243C2×Q8C22×D4711yescharacteristic
244C2×D4—21no—
245C2×D4—471no—
246C2×D4—471no—
247C2×D4—941no—
248C2×D4—941no—
249C2×D4—941no—
250C2×D4—941no—
251C2×D4C22×D4711yescharacteristic
252C22×C4—471no—
253C22×C4—471no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4C22×D4711yescharacteristic
258SD16—22no—
259SD16—942no—
260D8—942no—
261D8—942no—
262M16—22no—
263M16—942no—
264C2×C8—471no—
265C2×C8—471no—
266C2×C8C22×D4711yescharacteristic
267C2×C8C22×D4711yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—471no—
270C4⋊C4—471no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4C22×D4711yescharacteristic
276C4⋊C4C22×D4711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—941no—
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—
291C23—21no—
292C23—941no—
293C23—941no—
294C23D4×D4711yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—1882no—
298D4—21no—
299D4—21no—
300D4—42no—
301D4—941no—
302D4—941no—
303D4—941no—
304D4—941no—
305D4—1882no—
306D4—1882no—
307D4—1882no—
308D4—1882no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—471no—
315C2×C4—471no—
316C2×C4—471no—
317C2×C4—471no—
318C2×C4—942no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—1882no—
322C2×C4—1882no—
323C2×C4—1882no—
324C2×C4—1881no—
325C2×C4D4×D4711yescharacteristic
326C2×C4C23×D4711yescharacteristic
327C8—21no—
328C8—472no—
329C8—941no—
330C8#1062535212yescomplemented
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—1881no—
338C22—1881no—
339C22—1881no—
340C22—1881no—
341C22—1881no—
342C22—1881no—
343C22C2×D4×D4711yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—472no—
349C4—941no—
350C4—941no—
351C4—941no—
352C4—1881no—
353C4—1881no—
354C4#41×D4711yescharacteristic
355C4C2×#1062535211yescharacteristic
356C2—41no—
357C2—81no—
358C2—3761no—
359C2—3761no—
360C2#1568966811yescharacteristic
361C2AGL(1,ℤ/8)×D4711yescharacteristic
362C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#468C2
socleC22×C47C22×D4
hypercenter#468D47
hypocenterC47#3171
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #15689668C2semidirect
2. #15689659C2semidirect
3. #15689531C2semidirect
4. #15689509C2semidirect
5. #15689486C2semidirect
6. #15689484C2semidirect
7. #15689376C2semidirect
8. #15689374C2semidirect
9. #15689371C2semidirect
10. SD16×Dic47C2semidirect
11. #15689208C2semidirect
12. #15689205C2semidirect
13. #15689203C2semidirect
14. M16×Dic47C2semidirect
15. C47×#468C2semidirect
146. C8×C47#41semidirect
148. C47⋊C8#41semidirect
191. #468D47semidirect
197. C47#3171semidirect
330. C8#10625352semidirect