Finite Group Databasebeta

← #20254576

Subgroups — #20254576

Order 6016.

368 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689670C211yesmaximal, characteristic
2#125×D47C211yesmaximal, characteristic, complemented
3#15689531C211yesmaximal, characteristic, complemented
4#15689530C211yesmaximal, characteristic, complemented
5#15689486C211yesmaximal, characteristic, complemented
6#15689486C211yesmaximal, characteristic, complemented
7#15689443C211yesmaximal, characteristic, complemented
8#15689440C211yesmaximal, characteristic, complemented
9#15689438C211yesmaximal, characteristic, complemented
10#15689435C211yesmaximal, characteristic, complemented
11#15689424C211yesmaximal, characteristic, complemented
12#15689423C211yesmaximal, characteristic, complemented
13#15689420C211yesmaximal, characteristic, complemented
14#15689179C211yesmaximal, characteristic, complemented
15C47×#478C211yesmaximal, characteristic, complemented
16C2×#10625350—21no—
17#13094023C2211yescharacteristic
18#13094020C2211yescharacteristic
19#13094016C2211yescharacteristic
20#13094015C2211yescharacteristic
21#13094015C2211yescharacteristic
22#13094014—21no—
23#13094014—21no—
24#13094010—21no—
25#13093999C2211yescharacteristic
26#13093997—21no—
27#13093995C2211yescharacteristic
28C4×D188C2211yescharacteristic
29C4×C22⋊D47—21no—
30C4⋊C4×D47—21no—
31C4⋊C4×D47—21no—
32C4⋊C4×D47C2211yescharacteristic
33C4⋊C4×D47C2211yescharacteristic
34C42×D47C2211yescharacteristic
35#13093958C2211yescharacteristic
36#13093957C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093956C2211yescharacteristic
39#13093955C2211yescharacteristic
40#13093955C2211yescharacteristic
41C4⋊(C47⋊C8)C2211yescharacteristic
42#13093946C2211yescharacteristic
43#13093946C2211yescharacteristic
44#13093945C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic
48(C2×D47)⋊C8C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50#13093934C2211yescharacteristic
51#13093934C2211yescharacteristic
52#125×C47C2211yescharacteristic
53C4×D4×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×D4×C47C2311yescharacteristic
60C22×C4×C47—21no—
61C2×C22⋊D47—21no—
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64#10625350—44no—
65C2×D188—21no—
66C2×D188C2311yescharacteristic
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47D411yescharacteristic
71C2×C4×D47D411yescharacteristic
72C2×C4×D47C2311yescharacteristic
73C2×Dic94—21no—
74C2×C8×C47C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C4⋊C4×C47—21no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C22⋊C4×C47—21no—
82C42×C47C2311yescharacteristic
83C22⋊Dic47—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47C2311yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98C4×Dic47D411yescharacteristic
99C4×Dic47D411yescharacteristic
100C4×Dic47C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C23×C47—21no—
104C22×D47—21no—
105C22×D47C2×D411yescharacteristic
106D4×C47—21no—
107D4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—42no—
112C2×C4×C47C2×D411yescharacteristic
113C2×C4×C47C2×D411yescharacteristic
114C2×C4×C47C2411yescharacteristic
115C22⋊D47—42no—
116C22⋊D47—42no—
117C22⋊D47—42no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47C2×D411yescharacteristic
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124D188—21no—
125D188—21no—
126D188—42no—
127C4×D47—22no—
128C4×D47—21no—
129C4×D47—21no—
130C4×D47—41no—
131C4×D47—42no—
132C4×D47—42no—
133C4×D47—42no—
134Dic94—42no—
135C8×C47—21no—
136C8×C47—21no—
137C47⋊C8—21no—
138C47⋊C8—21no—
139C22×C47—41no—
140C22×C47—41no—
141C22×C47—41no—
142C22×C47C22×D411yescharacteristic
143C2×D47—21no—
144C2×D47—21no—
145C2×D47—41no—
146C2×D47—41no—
147C2×D47—41no—
148C2×D47AGL(1,ℤ/8)12yes—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—41no—
152C4×C47—41no—
153C4×C47—41no—
154C4×C472−1+411yescharacteristic
155C4×C472−1+411yescharacteristic
156Dic47—21no—
157Dic47—21no—
158Dic47—21no—
159Dic47—41no—
160Dic47—41no—
161Dic47—41no—
162#3234—471nomaximal, Sylow
163C2×C47—81no—
164C2×C47#53611yescharacteristic
165C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
166C2×C47#57511yescharacteristic
167D47—22no—
168D47—81no—
169#532—471no—
170C2×#125—471no—
171#501—471no—
172#501—471no—
173#490—471no—
174#490—471no—
175#481—471no—
176#481—471no—
177#480—471no—
178#480—471no—
179#478—471no—
180#478—471no—
181#478—471no—
182#478D4711yescharacteristic, complemented
183#432—471no—
184C47#323411yescharacteristic, complemented, Sylow
185C2×#41—941no—
186C4⋊Q8—471no—
187#127—471no—
188#125—471no—
189#125—471no—
190#125—471no—
191#125—941no—
192#125—941no—
193#125C2×D4711yescharacteristic
194#124—941no—
195#121—471no—
196#121—471no—
197#121—941no—
198C4×D4—471no—
199C4×D4—941no—
200C4×D4C2×D4711yescharacteristic
201C2×C4⋊C4—471no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4—941no—
204C2×C4⋊C4—941no—
205C2×C42—471no—
206#107—471no—
207#107—471no—
208#107—471no—
209#107C2×D4711yescharacteristic
210#106—471no—
211#106—471no—
212#106—471no—
213#106C2×D4711yescharacteristic
214C4⋊C8—471no—
215C4⋊C8C2×D4711yescharacteristic
216#102—471no—
217#102—471no—
218#102—471no—
219#102—471no—
220#102—471no—
221#102—471no—
222#102C2×D4711yescharacteristic
223#102C2×D4711yescharacteristic
224C22⋊C8—471no—
225C22⋊C8—471no—
226#97—471no—
227#97—471no—
228#41—1884no—
229C2×Q8—941no—
230C2×D4—471no—
231C2×D4—941no—
232C2×D4—941no—
233C2×D4—941no—
234C2×D4—941no—
235C2×D4C22×D4711yescharacteristic
236C22×C4—21no—
237C22×C4—471no—
238C22×C4—471no—
239C22×C4—471no—
240C22×C4—941no—
241C22×C4—941no—
242C22×C4—941no—
243C2×C8—471no—
244C2×C8—471no—
245C2×C8C22×D4711yescharacteristic
246C2×C8C22×D4711yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—471no—
250C4⋊C4—471no—
251C4⋊C4—471no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4C22×D4711yescharacteristic
262C4⋊C4C22×D4711yescharacteristic
263C4⋊C4C22×D4711yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C42—471no—
269C42—471no—
270C42—471no—
271C42C22×D4711yescharacteristic
272C23—21no—
273C23—471no—
274C23—941no—
275Q8—1882no—
276D4—21no—
277D4—21no—
278D4—941no—
279D4—941no—
280D4—1882no—
281D4—1882no—
282D4—1882no—
283D4—1882no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—42no—
288C2×C4—471no—
289C2×C4—471no—
290C2×C4—471no—
291C2×C4—942no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—1881no—
298C2×C4—1882no—
299C2×C4—1882no—
300C2×C4—1882no—
301C2×C4D4×D4711yescharacteristic
302C2×C4D4×D4711yescharacteristic
303C2×C4C23×D4711yescharacteristic
304C8—21no—
305C8—21no—
306C8—941no—
307C8—941no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22—472no—
312C22—941no—
313C22—941no—
314C22—1881no—
315C22—1881no—
316C22—1881no—
317C22C2×D4×D4711yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—941no—
324C4—941no—
325C4—941no—
326C4—1881no—
327C4—1881no—
328C4—1881no—
329C4#1309407111yescharacteristic
330C4#1309407211yescharacteristic
331C2—81no—
332C2—942no—
333C2—3761no—
334C2#1568969611yescharacteristic
335C2AGL(1,ℤ/8)×D4711yescharacteristic
336C2#1568992011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#478C2
socleC22×C47C22×D4
hypercenter#478D47
hypocenterC47#3234
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
2. #125×D47C2semidirect
3. #15689531C2semidirect
4. #15689530C2semidirect
5. #15689486C2semidirect
6. #15689486C2semidirect
7. #15689443C2semidirect
8. #15689440C2semidirect
9. #15689438C2semidirect
10. #15689435C2semidirect
11. #15689424C2semidirect
12. #15689423C2semidirect
13. #15689420C2semidirect
14. #15689179C2semidirect
15. C47×#478C2semidirect
182. #478D47semidirect
184. C47#3234semidirect