Finite Group Databasebeta

← #20253990

Subgroups — #20253990

Order 6016.

364 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#15689677C211yesmaximal, characteristic, complemented
2#15689655C211yesmaximal, characteristic
3#15689530C211yesmaximal, characteristic, complemented
4#15689514C211yesmaximal, characteristic, complemented
5#15689490C211yesmaximal, characteristic, complemented
6#15689481C211yesmaximal, characteristic, complemented
7#15689382C211yesmaximal, characteristic, complemented
8#15689380C211yesmaximal, characteristic, complemented
9#15689368C211yesmaximal, characteristic
10#15689366C211yesmaximal, characteristic
11C4×Dic188C211yesmaximal, characteristic, complemented
12C4×#10625337C211yesmaximal, characteristic, complemented
13C4×#10625335C211yesmaximal, characteristic, complemented
14C4×#10625324C211yesmaximal, characteristic, complemented
15C4×SD16×C47C211yesmaximal, characteristic, complemented
16C2×Dic188C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625324C2211yescharacteristic
20C2×#10625324C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094022C2211yescharacteristic
23#13094017—21no—
24#13094015C2211yescharacteristic
25#13094014—21no—
26#13094011C2211yescharacteristic
27#13094006—21no—
28#13094004C2211yescharacteristic
29#13094004C2211yescharacteristic
30#13094002—21no—
31#13094000C2211yescharacteristic
32#13093995C2211yescharacteristic
33C4×Dic94—21no—
34C4×Dic94C2211yescharacteristic
35C4×Dic94C2211yescharacteristic
36C4×C22⋊D47—21no—
37#13093983—21no—
38#13093981—21no—
39C42×D47C2211yescharacteristic
40#13093958C2211yescharacteristic
41#13093957C2211yescharacteristic
42#13093955C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093934C2211yescharacteristic
50#13093934C2211yescharacteristic
51C4×C47⋊C8C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C2×C22⋊D47—21no—
63C2×C4×D47D411yescharacteristic
64C2×C4×D47D411yescharacteristic
65C2×C4×D47C2311yescharacteristic
66C2×Dic94—21no—
67C2×Dic94C2311yescharacteristic
68C2×Dic94C2311yescharacteristic
69SD16×C47—22no—
70C2×C8×C47C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C4⋊C4×C47—21no—
73C4⋊C4×C47C2311yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C22⋊C4×C47—21no—
76C42×C47—21no—
77C42×C47C2311yescharacteristic
78C22⋊Dic47—21no—
79C22⋊Dic47—21no—
80C22⋊Dic47—21no—
81#10625337—22no—
82#10625335—22no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47—21no—
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×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47D411yescharacteristic
101C4×Dic47D411yescharacteristic
102C4×Dic47C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105Dic188—22no—
106#10625324—22no—
107#10625324—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×C47—42no—
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2411yescharacteristic
121C22⋊D47—42no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129C4×D47—22no—
130C4×D47—21no—
131C4×D47—21no—
132C4×D47—41no—
133Dic94—21no—
134Dic94—21no—
135Dic94—21no—
136Dic94—21no—
137Dic94—42no—
138C8×C47—21no—
139C8×C47#4112yes—
140C47⋊C8—21no—
141C47⋊C8#4112yes—
142C22×C47—41no—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47C22×D411yescharacteristic
146C2×D47—21no—
147C2×D47—21no—
148C2×D47—21no—
149C4×C47—21no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47—41no—
153C4×C47#13712yes—
154C4×C47C2×#4111yescharacteristic
155C4×C47C2×#4111yescharacteristic
156Dic47—21no—
157Dic47—21no—
158Dic47—21no—
159Dic47—41no—
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163#3172—471nomaximal, Sylow
164C2×C47—81no—
165C2×C47#53211yescharacteristic
166C2×C47C2×#13711yescharacteristic
167C2×C47#57511yescharacteristic
168D47—41no—
169#533—471no—
170#529—471no—
171#501—471no—
172#497—471no—
173#491—471no—
174#489—471no—
175#470—471no—
176#470—471no—
177#468—471no—
178#468—471no—
179C4×Q16—471no—
180C4×Q16—471no—
181C4×SD16—471no—
182C4×SD16D4711yescharacteristic, complemented
183C4×M16—471no—
184C47#317211yescharacteristic, complemented, Sylow
185C2×Q16—471no—
186C2×Q16—471no—
187C2×SD16—471no—
188C2×SD16C2×D4711yescharacteristic
189C2×M16—471no—
190C2×M16—471no—
191C4⋊Q8—471no—
192C4⋊Q8—471no—
193#126—941no—
194#125—471no—
195#125—941no—
196#124—471no—
197#123—941no—
198C22⋊Q8—471no—
199C22⋊Q8—471no—
200C22⋊Q8—471no—
201C22⋊Q8—941no—
202#121—471no—
203C4×Q8—471no—
204C4×Q8—471no—
205C4×Q8—941no—
206C4×Q8C2×D4711yescharacteristic
207C4×D4—941no—
208C4×D4C2×D4711yescharacteristic
209#117—941no—
210#117—941no—
211C2×C42—471no—
212#107—471no—
213#107—471no—
214#106—471no—
215#106C2×D4711yescharacteristic
216#103—471no—
217#103—471no—
218#103—471no—
219#103—471no—
220#103—471no—
221#103C2×D4711yescharacteristic
222#102—471no—
223#102C2×D4711yescharacteristic
224#97—471no—
225#97—471no—
226C4×C8—471no—
227C4×C8C2×D4711yescharacteristic
228C2×Q8—471no—
229C2×Q8—471no—
230C2×Q8—941no—
231C2×Q8C22×D4711yescharacteristic
232C2×D4—941no—
233C2×D4C22×D4711yescharacteristic
234C22×C4—21no—
235C22×C4—471no—
236C22×C4—471no—
237C22×C4—471no—
238Q16—942no—
239Q16—942no—
240SD16—22no—
241SD16—942no—
242M16—942no—
243M16—942no—
244C2×C8—471no—
245C2×C8—471no—
246C2×C8C22×D4711yescharacteristic
247C2×C8C22×D4711yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—471no—
250C4⋊C4—471no—
251C4⋊C4—941no—
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
263C22⋊C4—21no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C42—21no—
271C42—471no—
272C42—471no—
273C42—471no—
274C42—941no—
275C42—941no—
276C42C22×D4711yescharacteristic
277C23—21no—
278C23—471no—
279Q8—21no—
280Q8—21no—
281Q8—941no—
282Q8—941no—
283Q8—941no—
284Q8—941no—
285Q8—1882no—
286D4—21no—
287D4—21no—
288D4—1882no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—42no—
293C2×C4—471no—
294C2×C4—471no—
295C2×C4—471no—
296C2×C4—942no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—1881no—
304C2×C4D4×D4711yescharacteristic
305C2×C4D4×D4711yescharacteristic
306C2×C4C23×D4711yescharacteristic
307C8—21no—
308C8—472no—
309C8—941no—
310C8#1062535012yes—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—941no—
315C22—941no—
316C22—941no—
317C22C2×D4×D4711yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—941no—
323C4—941no—
324C4—941no—
325C4—1881no—
326C4—1881no—
327C4—1881no—
328C4—1881no—
329C4#1309405312yes—
330C4#41×D4711yescharacteristic
331C4C2×#1062535011yescharacteristic
332C2—81no—
333C2—1881no—
334C2#1568967011yescharacteristic
335C2C2×#1309405311yescharacteristic
336C2#1568992011yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×SD16×C47C2
socleC22×C47C22×D4
hypercenterC4×SD16D47
hypocenterC47#3172
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #15689677C2semidirect
3. #15689530C2semidirect
4. #15689514C2semidirect
5. #15689490C2semidirect
6. #15689481C2semidirect
7. #15689382C2semidirect
8. #15689380C2semidirect
11. C4×Dic188C2semidirect
12. C4×#10625337C2semidirect
13. C4×#10625335C2semidirect
14. C4×#10625324C2semidirect
15. C4×SD16×C47C2semidirect
182. C4×SD16D47semidirect
184. C47#3172semidirect