Finite Group Databasebeta

← #20255970

Subgroups — #20255970

Order 6016.

374 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#15689841C211yesmaximal, characteristic, complemented
2#15689773C211yesmaximal, characteristic
3#15689527C211yesmaximal, characteristic, complemented
4#15689460C211yesmaximal, characteristic, complemented
5#15689459C211yesmaximal, characteristic, complemented
6#15689445C211yesmaximal, characteristic, complemented
7#15689407C211yesmaximal, characteristic, complemented
8#15689401C211yesmaximal, characteristic, complemented
9#15689368C211yesmaximal, characteristic, complemented
10#15689367C211yesmaximal, characteristic, complemented
11#15689214C211yesmaximal, characteristic, complemented
12#15689198C211yesmaximal, characteristic, complemented
13#15689166C211yesmaximal, characteristic, complemented
14#15689162C211yesmaximal, characteristic, complemented
15C47×#482C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17C2×#10625335C2211yescharacteristic
18C2×#10625329C2211yescharacteristic
19C2×#10625324C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094018—21no—
23#13094017—21no—
24#13094010—21no—
25#13094006—21no—
26#13094005—21no—
27#13094004C2211yescharacteristic
28#13094003C2211yescharacteristic
29#13094001—21no—
30#13093995C2211yescharacteristic
31C4×Dic94—21no—
32#13093989C2211yescharacteristic
33D4×Dic47C2211yescharacteristic
34C4×C22⋊D47C2211yescharacteristic
35#13093982C2211yescharacteristic
36C2×C4⋊Dic47C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093957C2211yescharacteristic
42#13093957C2211yescharacteristic
43#13093955C2211yescharacteristic
44#13093955C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093947C2211yescharacteristic
49#13093945C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52#121×C47C2211yescharacteristic
53#117×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C2×C22⋊D47D411yescharacteristic
64C22×Dic47—21no—
65C22×Dic47—21no—
66#10625352—44no—
67C2×C4×D47—21no—
68C2×C4×D47C2311yescharacteristic
69C2×Dic94—21no—
70C2×Dic94—21no—
71C2×Dic94C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C22⋊C4×C47—21no—
78C22⋊C4×C47—21no—
79C42×C47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47D411yescharacteristic
84#10625335—22no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4D411yescharacteristic
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4D411yescharacteristic
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102#10625329—22no—
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105#10625324—22no—
106C23×C47—21no—
107C23×C47C2×D411yescharacteristic
108C22×D47C2×D411yescharacteristic
109D4×C47—21no—
110D4×C47—21no—
111D4×C47—42no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2411yescharacteristic
119C22⋊D47—22no—
120C22⋊D47—42no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—42no—
126C2×Dic47—42no—
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130C4×D47—21no—
131C4×D47—21no—
132C4×D47—42no—
133Dic94—21no—
134Dic94—21no—
135Dic94—42no—
136Dic94—42no—
137C8×C47—21no—
138C8×C47—21no—
139C47⋊C8—21no—
140C47⋊C8#4112yescomplemented
141C22×C47—21no—
142C22×C47—21no—
143C22×C47—21no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47C22×D411yescharacteristic
148C2×D47—21no—
149C2×D47—21no—
150C2×D47—21no—
151C4×C47—21no—
152C4×C47—41no—
153C4×C47—41no—
154C4×C47—41no—
155C4×C47C2×#4111yescharacteristic
156C4×C472−1+411yescharacteristic
157Dic47—21no—
158Dic47—21no—
159Dic47—41no—
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163Dic47AGL(1,ℤ/8)12yes—
164#3353—471nomaximal, Sylow
165C2×C47—41no—
166C2×C47—81no—
167C2×C47#54711yescharacteristic
168C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
169C2×C47#57811yescharacteristic
170D47—41no—
171#556—471no—
172#547—471no—
173#500—471no—
174#484—471no—
175#484—471no—
176#482—471no—
177#482D4711yescharacteristic, complemented
178#475—471no—
179#474—471no—
180#468—471no—
181#468—471no—
182C4×SD16—471no—
183#436—471no—
184#428—471no—
185#428—471no—
186C47#335311yescharacteristic, complemented, Sylow
187C2×#41—941no—
188C2×SD16—471no—
189C2×M16—471no—
190C2×M16—471no—
191C4⋊Q8—471no—
192C4⋊Q8—471no—
193#126—941no—
194#126—941no—
195#124—941no—
196#123—941no—
197#123—941no—
198C22⋊Q8—471no—
199C22⋊Q8—471no—
200C22⋊Q8—941no—
201#121—471no—
202#121C2×D4711yescharacteristic
203C4×Q8—471no—
204C4×Q8—941no—
205C4×D4—471no—
206C4×D4—471no—
207#117—471no—
208#117C2×D4711yescharacteristic
209C2×C4⋊C4—471no—
210C2×C4⋊C4—471no—
211#107—471no—
212#107—471no—
213#107—471no—
214#107—471no—
215#107—471no—
216#107C2×D4711yescharacteristic
217#106—471no—
218#106—471no—
219#106C2×D4711yescharacteristic
220C4⋊C8—471no—
221#103—471no—
222#103—471no—
223#103—471no—
224#102—471no—
225#102C2×D4711yescharacteristic
226#102C2×D4711yescharacteristic
227C22⋊C8—471no—
228C22⋊C8C2×D4711yescharacteristic
229C4×C8—471no—
230#41—1884no—
231C2×Q8—471no—
232C2×Q8—941no—
233C2×Q8—941no—
234C2×D4—21no—
235C2×D4—471no—
236C2×D4—941no—
237C2×D4C22×D4711yescharacteristic
238C22×C4—471no—
239C22×C4—941no—
240C22×C4—941no—
241C22×C4—941no—
242C22×C4C22×D4711yescharacteristic
243SD16—942no—
244M16—942no—
245M16—942no—
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—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—21no—
266C22⋊C4—471no—
267C22⋊C4—471no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C42—21no—
274C42—471no—
275C42—941no—
276C42—941no—
277C23—21no—
278C23—471no—
279C23D4×D4711yescharacteristic
280Q8—941no—
281Q8—941no—
282Q8—1882no—
283Q8—1882no—
284D4—21no—
285D4—21no—
286D4—42no—
287D4—942no—
288D4—1882no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—471no—
295C2×C4—471no—
296C2×C4—471no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—1882no—
304C2×C4—1882no—
305C2×C4—1882no—
306C2×C4D4×D4711yescharacteristic
307C2×C4C23×D4711yescharacteristic
308C8—21no—
309C8—21no—
310C8—472no—
311C8—941no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—941no—
319C22—941no—
320C22—941no—
321C22C2×D4×D4711yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—472no—
327C4—941no—
328C4—941no—
329C4—1881no—
330C4—1881no—
331C4—1881no—
332C4—1881no—
333C4#41×D4711yescharacteristic
334C4#1309407111yescharacteristic
335C2—41no—
336C2—81no—
337C2—1881no—
338C2#1568977111yescharacteristic
339C2AGL(1,ℤ/8)×D4711yescharacteristic
340C2#1568993711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#482C2
socleC22×C47C22×D4
hypercenter#482D47
hypocenterC47#3353
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #15689841C2semidirect
3. #15689527C2semidirect
4. #15689460C2semidirect
5. #15689459C2semidirect
6. #15689445C2semidirect
7. #15689407C2semidirect
8. #15689401C2semidirect
9. #15689368C2semidirect
10. #15689367C2semidirect
11. #15689214C2semidirect
12. #15689198C2semidirect
13. #15689166C2semidirect
14. #15689162C2semidirect
15. C47×#482C2semidirect
140. C47⋊C8#41semidirect
177. #482D47semidirect
186. C47#3353semidirect