Finite Group Databasebeta

← #20256134

Subgroups — #20256134

Order 6016.

358 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689859C211yesmaximal, characteristic, complemented
2#15689832C211yesmaximal, characteristic, complemented
3#15689487C211yesmaximal, characteristic, complemented
4#15689481C211yesmaximal, characteristic, complemented
5#15689476C211yesmaximal, characteristic, complemented
6#15689431C211yesmaximal, characteristic, complemented
7#15689425C211yesmaximal, characteristic, complemented
8#15689401C211yesmaximal, characteristic, complemented
9#15689336C211yesmaximal, characteristic, complemented
10#15689336C211yesmaximal, characteristic, complemented
11#15689252C211yesmaximal, characteristic, complemented
12#15689235C211yesmaximal, characteristic, complemented
13#15689223C211yesmaximal, characteristic, complemented
14D8×Dic47C211yesmaximal, characteristic, complemented
15C47×#459C211yesmaximal, characteristic
16C2×#10625335C2211yescharacteristic
17#13094023C2211yescharacteristic
18#13094016C2211yescharacteristic
19#13094015C2211yescharacteristic
20#13094011—21no—
21#13094011C2211yescharacteristic
22#13094011C2211yescharacteristic
23#13094005—21no—
24#13094005—21no—
25#13094003—21no—
26#13094001—21no—
27#13094001—21no—
28C4×Dic94C2211yescharacteristic
29C4×Dic94C2211yescharacteristic
30D4×Dic47—21no—
31D4×Dic47C2211yescharacteristic
32D4×Dic47C2211yescharacteristic
33D4×Dic47C2211yescharacteristic
34D4×Dic47C2211yescharacteristic
35C2×Dic47⋊C4—21no—
36#13093958C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093956C2211yescharacteristic
39Dic47⋊C8C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41#13093949C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093947C2211yescharacteristic
44#13093945C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093935C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×D8×C47C2211yescharacteristic
53C2×D8×C47C2211yescharacteristic
54#127×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C2×D4×C47C2311yescharacteristic
64C22×C4×C47—21no—
65C22×Dic47—21no—
66C22×Dic47—21no—
67C22×Dic47—21no—
68C22×Dic47—21no—
69C2×Dic94—21no—
70C2×Dic94D411yescharacteristic
71C2×Dic94C2311yescharacteristic
72D8×C47—22no—
73D8×C47—22no—
74C2×C8×C47C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C22⋊C4×C47—21no—
78C42×C47C2311yescharacteristic
79C22⋊Dic47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87#10625335—22no—
88C4⋊Dic47—21no—
89C4⋊Dic47D411yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4D411yescharacteristic
99Dic47⋊C4D411yescharacteristic
100C4×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102C4×Dic47C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C23×C47—21no—
106C23×C47—21no—
107C23×C47—21no—
108D4×C47—21no—
109D4×C47—21no—
110D4×C47—21no—
111D4×C47—21no—
112D4×C47—21no—
113D4×C47—42no—
114D4×C47—81no—
115D4×C47#4112yes—
116C2×C4×C47—21no—
117C2×C4×C47—81no—
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2411yescharacteristic
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—42no—
126C2×Dic47—81no—
127C2×Dic47—81no—
128C2×Dic47—81no—
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133Dic94—21no—
134Dic94—21no—
135Dic94—41no—
136Dic94—81no—
137C8×C47—21no—
138C8×C47—21no—
139C47⋊C8—21no—
140C47⋊C8—21no—
141C22×C47—22no—
142C22×C47—41no—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47C22×D411yescharacteristic
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—41no—
154C4×C47C2×#4111yescharacteristic
155C4×C472−1+411yescharacteristic
156Dic47—21no—
157Dic47—21no—
158Dic47—21no—
159Dic47—21no—
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164#3370—471nomaximal, Sylow
165C2×C47—42no—
166C2×C47—81no—
167C2×C47—81no—
168C2×C47#54811yescharacteristic
169C2×C47#57511yescharacteristic
170C2×C47#57611yescharacteristic
171#559—471no—
172#554—471no—
173#490—471no—
174#489—471no—
175#488—471no—
176#479—471no—
177#478—471no—
178#474—471no—
179#463—471no—
180#463—471no—
181#459D4711yescharacteristic
182#446—471no—
183#442—471no—
184#440—471no—
185C4×D8—471no—
186C47#337011yescharacteristic, complemented, Sylow
187C2×SD16—471no—
188C2×D8C2×D4711yescharacteristic
189C2×D8C2×D4711yescharacteristic
190C4⋊Q8—471no—
191#127C2×D4711yescharacteristic
192#125—471no—
193#125—471no—
194#124—471no—
195#124—471no—
196#124—941no—
197#123—941no—
198#123—941no—
199C22⋊Q8—941no—
200C22⋊Q8—941no—
201C22⋊Q8—941no—
202C4×Q8—471no—
203C4×Q8—471no—
204C4×D4—471no—
205C4×D4—471no—
206C4×D4—471no—
207C4×D4—471no—
208C4×D4—941no—
209C4×D4C2×D4711yescharacteristic
210C2×C4⋊C4—941no—
211#107—471no—
212#107—471no—
213#106—471no—
214C4⋊C8—471no—
215C4⋊C8—471no—
216C4⋊C8C2×D4711yescharacteristic
217#103—471no—
218#103—471no—
219#103—471no—
220#102—471no—
221#102—471no—
222#102—471no—
223#102—471no—
224#102—471no—
225#102C2×D4711yescharacteristic
226#102C2×D4711yescharacteristic
227#97—471no—
228#97—471no—
229C4×C8—471no—
230C2×Q8—471no—
231C2×Q8—471no—
232C2×Q8—941no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4C22×D4711yescharacteristic
236C2×D4C22×D4711yescharacteristic
237C2×D4C22×D4711yescharacteristic
238C22×C4—21no—
239C22×C4—941no—
240C22×C4—941no—
241C22×C4—941no—
242C22×C4—941no—
243SD16—942no—
244D8—22no—
245D8—22no—
246C2×C8—471no—
247C2×C8—471no—
248C2×C8C22×D4711yescharacteristic
249C2×C8C22×D4711yescharacteristic
250C4⋊C4—471no—
251C4⋊C4—471no—
252C4⋊C4—471no—
253C4⋊C4—471no—
254C4⋊C4—471no—
255C4⋊C4—471no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4C22×D4711yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C42—471no—
273C42—471no—
274C42—941no—
275C42C22×D4711yescharacteristic
276C23—21no—
277C23—21no—
278C23—21no—
279Q8—941no—
280Q8—941no—
281Q8—3761no—
282Q8—1881no—
283D4—21no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—21no—
288D4—42no—
289D4—81no—
290D4#1062535212yes—
291C2×C4—21no—
292C2×C4—81no—
293C2×C4—471no—
294C2×C4—471no—
295C2×C4—471no—
296C2×C4—471no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—3761no—
302C2×C4—3761no—
303C2×C4—3761no—
304C2×C4—1882no—
305C2×C4D4×D4711yescharacteristic
306C2×C4D4×D4711yescharacteristic
307C2×C4C23×D4711yescharacteristic
308C8—21no—
309C8—21no—
310C8—941no—
311C8—941no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22C2×D4×D4711yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—941no—
326C4—941no—
327C4—941no—
328C4—941no—
329C4—1881no—
330C4—1881no—
331C4—1881no—
332C4—1881no—
333C4C2×#1062535211yescharacteristic
334C4#1309407111yescharacteristic
335C2—42no—
336C2—81no—
337C2—81no—
338C2#1568977911yescharacteristic
339C2#1568991911yescharacteristic
340C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#459C2
socleC22×C47C22×D4
hypercenter#459D47
hypocenterC47#3370
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #15689859C2semidirect
2. #15689832C2semidirect
3. #15689487C2semidirect
4. #15689481C2semidirect
5. #15689476C2semidirect
6. #15689431C2semidirect
7. #15689425C2semidirect
8. #15689401C2semidirect
9. #15689336C2semidirect
10. #15689336C2semidirect
11. #15689252C2semidirect
12. #15689235C2semidirect
13. #15689223C2semidirect
14. D8×Dic47C2semidirect
186. C47#3370semidirect