Finite Group Databasebeta

← #20253752

Subgroups — #20253752

Order 6016.

372 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#15689753C211yesmaximal, characteristic, complemented
2#15689693C211yesmaximal, characteristic
3#15689493C211yesmaximal, characteristic, complemented
4#15689490C211yesmaximal, characteristic, complemented
5#15689482C211yesmaximal, characteristic, complemented
6#15689481C211yesmaximal, characteristic, complemented
7#15689476C211yesmaximal, characteristic, complemented
8#15689474C211yesmaximal, characteristic, complemented
9#15689472C211yesmaximal, characteristic, complemented
10#15689130C211yesmaximal, characteristic, complemented
11#15689121C211yesmaximal, characteristic
12#15689116C211yesmaximal, characteristic
13#103×D47C211yesmaximal, characteristic, complemented
14#15689077C211yesmaximal, characteristic, complemented
15C47×#488C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18C2×#10625324C2211yescharacteristic
19C2×C8×D47C2211yescharacteristic
20#13094024C2211yescharacteristic
21#13094024C2211yescharacteristic
22#13094023—21no—
23#13094023C2211yescharacteristic
24#13094022C2211yescharacteristic
25#13094015C2211yescharacteristic
26#13094014—21no—
27#13094011C2211yescharacteristic
28#13094006—21no—
29#13094006—21no—
30#13094004—21no—
31#13094002—21no—
32#13094001—21no—
33#13094001—21no—
34#13093982C2211yescharacteristic
35#13093981C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic
37#13093949C2211yescharacteristic
38#13093949C2211yescharacteristic
39#13093949C2211yescharacteristic
40#13093949C2211yescharacteristic
41#13093948C2211yescharacteristic
42#13093948C2211yescharacteristic
43#13093947C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093935C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52#125×C47C2211yescharacteristic
53#124×C47C2211yescharacteristic
54#103×C47C2211yescharacteristic
55#103×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47C2311yescharacteristic
61C2×C22⋊D47—21no—
62C22×Dic47—21no—
63Q8×D47—22no—
64Q8×D47—22no—
65#10625352—22no—
66#10625352—22no—
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47C2311yescharacteristic
70C2×Dic94—21no—
71C2×Dic94—21no—
72C2×Dic94—21no—
73C2×Dic94C2311yescharacteristic
74C2×Dic94C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C4⋊C4×C47—21no—
78C4⋊C4×C47—21no—
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C22⋊C4×C47—21no—
82C22⋊C4×C47—21no—
83C42×C47C2311yescharacteristic
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4D411yescharacteristic
88(C2×D47)⋊C4D411yescharacteristic
89C4⋊Dic47—21no—
90C4⋊Dic47—21no—
91C4⋊Dic47—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4D411yescharacteristic
101Dic47⋊C4D411yescharacteristic
102C4×Dic47—21no—
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106#10625324—22no—
107C8×D47—22no—
108C23×C47—21no—
109C22×D47C2×D411yescharacteristic
110Q8×C47—21no—
111Q8×C47—21no—
112D4×C47—21no—
113D4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2411yescharacteristic
120C22⋊D47—42no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—42no—
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129C4×D47—42no—
130C4×D47—81no—
131C4×D47#4112yes—
132C4×D47#4112yes—
133Dic94—21no—
134Dic94—21no—
135Dic94—21no—
136Dic94—21no—
137Dic94—42no—
138Dic94—81no—
139Dic94—81no—
140C8×C47—21no—
141C8×C47—21no—
142C47⋊C8—21no—
143C47⋊C8—21no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47C22×D411yescharacteristic
148C2×D47—21no—
149C2×D47—21no—
150C2×D47#12412yes—
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—41no—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47C2×#4111yescharacteristic
157C4×C47C2×#4111yescharacteristic
158Dic47—21no—
159Dic47—21no—
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164Dic47#12412yes—
165#3137—471nomaximal, Sylow
166C2×C47—81no—
167C2×C47C2×#12411yescharacteristic
168C2×C47#57711yescharacteristic
169C2×C47#57811yescharacteristic
170D47—22no—
171#544—471no—
172#536—471no—
173#491—471no—
174#491—471no—
175#489—471no—
176#489—471no—
177#488—471no—
178#488D4711yescharacteristic, complemented
179#487—471no—
180#487—471no—
181#419—471no—
182#417—471no—
183#416—471no—
184C2×#103—471no—
185#405—471no—
186C47#313711yescharacteristic, complemented, Sylow
187C2×#41—471no—
188C22×Q8—471no—
189C2×M16—471no—
190C22×C8—471no—
191C4⋊Q8—471no—
192C4⋊Q8—471no—
193C4⋊Q8—471no—
194C4⋊Q8—471no—
195C4⋊Q8—941no—
196#125—471no—
197#125—941no—
198#125C2×D4711yescharacteristic
199#124—471no—
200#124C2×D4711yescharacteristic
201#123—941no—
202#123—941no—
203C22⋊Q8—941no—
204C22⋊Q8—941no—
205C22⋊Q8—941no—
206C22⋊Q8—941no—
207#117—471no—
208#117—471no—
209C2×C4⋊C4—471no—
210#103—471no—
211#103—471no—
212#103—471no—
213#103—471no—
214#103—471no—
215#103—471no—
216#103—471no—
217#103—471no—
218#103—471no—
219#103—471no—
220#103C2×D4711yescharacteristic
221#103C2×D4711yescharacteristic
222#102—471no—
223#102—471no—
224#102C2×D4711yescharacteristic
225#102C2×D4711yescharacteristic
226#97—471no—
227#97—471no—
228C4×C8—471no—
229C4×C8C2×D4711yescharacteristic
230#41—942no—
231#41—942no—
232C2×Q8—471no—
233C2×Q8—471no—
234C2×Q8—941no—
235C2×Q8—941no—
236C2×Q8—942no—
237C2×Q8—942no—
238C2×Q8—941no—
239C2×Q8C22×D4711yescharacteristic
240C2×D4—941no—
241C2×D4C22×D4711yescharacteristic
242C22×C4—471no—
243C22×C4—941no—
244C22×C4—941no—
245C22×C4—941no—
246M16—942no—
247C2×C8—471no—
248C2×C8—471no—
249C2×C8—942no—
250C2×C8C22×D4711yescharacteristic
251C2×C8C22×D4711yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—471no—
255C4⋊C4—471no—
256C4⋊C4—471no—
257C4⋊C4—471no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4C22×D4711yescharacteristic
268C4⋊C4C22×D4711yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—471no—
272C22⋊C4—471no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C42—471no—
277C42—941no—
278C42C22×D4711yescharacteristic
279C23—21no—
280C23—471no—
281Q8—21no—
282Q8—21no—
283Q8—941no—
284Q8—941no—
285Q8—941no—
286Q8—941no—
287Q8—3761no—
288Q8—3761no—
289Q8—1882no—
290D4—21no—
291D4—21no—
292D4—1882no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—471no—
297C2×C4—472no—
298C2×C4—472no—
299C2×C4—471no—
300C2×C4—471no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—3761no—
306C2×C4—1882no—
307C2×C4—1882no—
308C2×C4D4×D4711yescharacteristic
309C2×C4D4×D4711yescharacteristic
310C2×C4C23×D4711yescharacteristic
311C8—21no—
312C8—21no—
313C8—941no—
314C8—941no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—472no—
319C22—941no—
320C22—941no—
321C22C2×D4×D4711yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—472no—
328C4—941no—
329C4—941no—
330C4—1881no—
331C4—1881no—
332C4—1881no—
333C4—1881no—
334C4#41×D4711yescharacteristic
335C4#41×D4711yescharacteristic
336C2—81no—
337C2—942no—
338C2#124×D4711yescharacteristic
339C2#1568993011yescharacteristic
340C2#1568993711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#488C2
socleC22×C47C22×D4
hypercenter#488D47
hypocenterC47#3137
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #15689753C2semidirect
3. #15689493C2semidirect
4. #15689490C2semidirect
5. #15689482C2semidirect
6. #15689481C2semidirect
7. #15689476C2semidirect
8. #15689474C2semidirect
9. #15689472C2semidirect
10. #15689130C2semidirect
13. #103×D47C2semidirect
14. #15689077C2semidirect
15. C47×#488C2semidirect
178. #488D47semidirect
186. C47#3137semidirect