Finite Group Databasebeta

← #20253602

Subgroups — #20253602

Order 6016.

372 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#15689735C211yesmaximal, characteristic, complemented
2#15689458C211yesmaximal, characteristic, complemented
3#15689453C211yesmaximal, characteristic, complemented
4#15689430C211yesmaximal, characteristic, complemented
5#15689423C211yesmaximal, characteristic, complemented
6#15689333C211yesmaximal, characteristic, complemented
7#15689328C211yesmaximal, characteristic, complemented
8#15689285C211yesmaximal, characteristic
9#15689285C211yesmaximal, characteristic
10#15689228C211yesmaximal, characteristic, complemented
11#15689223C211yesmaximal, characteristic, complemented
12C4×#10625337C211yesmaximal, characteristic, complemented
13C4×#10625335C211yesmaximal, characteristic, complemented
14#15689184C211yesmaximal, characteristic, complemented
15C47×#520C211yesmaximal, characteristic
16C2×#10625337C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20#13094024C2211yescharacteristic
21#13094017—21no—
22#13094017—21no—
23#13094016C2211yescharacteristic
24#13094014—21no—
25#13094014—21no—
26#13094003C2211yescharacteristic
27#13094003C2211yescharacteristic
28C4×Dic94C2211yescharacteristic
29C4×Dic94C2211yescharacteristic
30#13093957C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35C4⋊(C47⋊C8)C2211yescharacteristic
36#13093948C2211yescharacteristic
37#13093948C2211yescharacteristic
38#13093947C2211yescharacteristic
39#13093947C2211yescharacteristic
40#13093947C2211yescharacteristic
41#13093947C2211yescharacteristic
42#13093945C2211yescharacteristic
43#13093945C2211yescharacteristic
44C22⋊(C47⋊C8)C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46#13093935C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48C2×#41×C47C2211yescharacteristic
49C4×Q8×C47C2211yescharacteristic
50C4×Q8×C47C2211yescharacteristic
51C4×D4×C47—21no—
52C4×D4×C47—21no—
53C4×D4×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55#117×C47—21no—
56#117×C47C2211yescharacteristic
57C2×C4⋊C4×C47—21no—
58C2×C4⋊C4×C47C2211yescharacteristic
59#41×C47—22no—
60#41×C47—22no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47—21no—
63C2×D4×C47C2311yescharacteristic
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—21no—
68C22×C4×C47C2311yescharacteristic
69C2×Dic94C2311yescharacteristic
70C2×Dic94C2311yescharacteristic
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47D411yescharacteristic
75C4⋊C4×C47D411yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C22⋊C4×C47—21no—
79C22⋊C4×C47—21no—
80C22⋊C4×C47D411yescharacteristic
81C22⋊C4×C47D411yescharacteristic
82C42×C47—21no—
83C42×C47—21no—
84C42×C47C2311yescharacteristic
85C42×C47C2311yescharacteristic
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88#10625337—22no—
89#10625337—22no—
90#10625335—22no—
91#10625335—22no—
92C4⋊Dic47—21no—
93C4⋊Dic47—21no—
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47—21no—
109C23×C47C2×D411yescharacteristic
110Q8×C47—21no—
111Q8×C47#4112yes—
112D4×C47—24no—
113D4×C47—21no—
114D4×C47#4112yes—
115C2×C4×C47—24no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—81no—
122C2×C4×C47—81no—
123C2×C4×C47—81no—
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134Dic94—21no—
135Dic94—21no—
136Dic94—21no—
137Dic94—21no—
138C47⋊C8—21no—
139C47⋊C8—21no—
140C47⋊C8—21no—
141C47⋊C8—21no—
142C22×C47—21no—
143C22×C47—22no—
144C22×C47—21no—
145C22×C47—21no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47C22×D411yescharacteristic
149C4×C47—21no—
150C4×C47—22no—
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47C2×#4111yescharacteristic
158C4×C47C2×#4111yescharacteristic
159Dic47—41no—
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163#3120—471nomaximal, Sylow
164C2×C47—41no—
165C2×C47—42no—
166C2×C47#52511yescharacteristic
167C2×C47#57711yescharacteristic
168C2×C47#57811yescharacteristic
169#541—471no—
170#520D4711yescharacteristic
171#484—471no—
172#483—471no—
173#479—471no—
174#478—471no—
175#462—471no—
176#461—471no—
177#452—471no—
178#452—471no—
179#441—471no—
180#440—471no—
181C4×Q16—471no—
182C4×SD16—471no—
183#433—471no—
184C47#312011yescharacteristic, complemented, Sylow
185C2×#41C2×D4711yescharacteristic
186C2×Q16—471no—
187C2×Q16—471no—
188C2×SD16—471no—
189C2×SD16—471no—
190C4⋊Q8—471no—
191#126—941no—
192#126—941no—
193#125—471no—
194#125—941no—
195#125—941no—
196C22⋊Q8—471no—
197C22⋊Q8—471no—
198C4×Q8—471no—
199C4×Q8—471no—
200C4×Q8C2×D4711yescharacteristic
201C4×Q8C2×D4711yescharacteristic
202C4×D4—21no—
203C4×D4—21no—
204C4×D4C2×D4711yescharacteristic
205C4×D4C2×D4711yescharacteristic
206#117—21no—
207#117C2×D4711yescharacteristic
208C2×C4⋊C4—21no—
209C2×C4⋊C4C2×D4711yescharacteristic
210#107—471no—
211#107—471no—
212#106—471no—
213#106—471no—
214C4⋊C8—471no—
215C4⋊C8—471no—
216#103—471no—
217#103—471no—
218#103—471no—
219#103—471no—
220#103—471no—
221#103—471no—
222#102—471no—
223#102—471no—
224C22⋊C8—471no—
225C22⋊C8—471no—
226#97—471no—
227C4×C8—471no—
228#41—22no—
229#41—22no—
230C2×Q8—471no—
231C2×Q8—471no—
232C2×Q8C22×D4711yescharacteristic
233C2×D4—21no—
234C2×D4C22×D4711yescharacteristic
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4C22×D4711yescharacteristic
240Q16—942no—
241Q16—942no—
242SD16—942no—
243SD16—942no—
244C2×C8—471no—
245C2×C8—471no—
246C2×C8—471no—
247C2×C8—471no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—471no—
252C4⋊C4—471no—
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
264C4⋊C4C22×D4711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4C22⋊D4711yescharacteristic
270C22⋊C4C22⋊D4711yescharacteristic
271C42—21no—
272C42—21no—
273C42—941no—
274C42—941no—
275C42C22×D4711yescharacteristic
276C42C22×D4711yescharacteristic
277C23—21no—
278C23C2×C22⋊D4711yescharacteristic
279Q8—21no—
280Q8—941no—
281Q8—941no—
282Q8—941no—
283Q8—941no—
284Q8#1062535012yes—
285D4—24no—
286D4—21no—
287D4#1062535012yes—
288C2×C4—24no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4C2×C22⋊D4711yescharacteristic
302C2×C4C2×C22⋊D4711yescharacteristic
303C2×C4C2×C22⋊D4711yescharacteristic
304C2×C4C2×C22⋊D4711yescharacteristic
305C2×C4C2×C22⋊D4711yescharacteristic
306C2×C4C23×D4711yescharacteristic
307C8—941no—
308C8—941no—
309C8—941no—
310C8—941no—
311C22—21no—
312C22—22no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22C22×C22⋊D4711yescharacteristic
318C4—21no—
319C4—22no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—1881no—
327C4—1881no—
328C4—1881no—
329C4—1881no—
330C4C2×#1062535011yescharacteristic
331C4C2×#1062535011yescharacteristic
332C2—41no—
333C2—42no—
334C2#1568963411yescharacteristic
335C2#1568993411yescharacteristic
336C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#520C2
socleC22×C47C22×D4
hypercenter#520D47
hypocenterC47#3120
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #15689735C2semidirect
2. #15689458C2semidirect
3. #15689453C2semidirect
4. #15689430C2semidirect
5. #15689423C2semidirect
6. #15689333C2semidirect
7. #15689328C2semidirect
10. #15689228C2semidirect
11. #15689223C2semidirect
12. C4×#10625337C2semidirect
13. C4×#10625335C2semidirect
14. #15689184C2semidirect
184. C47#3120semidirect