Finite Group Databasebeta

← #20255834

Subgroups — #20255834

Order 6016.

376 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#15689815C211yesmaximal, characteristic, complemented
2#15689773C211yesmaximal, characteristic
3#15689530C211yesmaximal, characteristic, complemented
4#15689457C211yesmaximal, characteristic, complemented
5#15689451C211yesmaximal, characteristic, complemented
6#15689445C211yesmaximal, characteristic, complemented
7#15689434C211yesmaximal, characteristic, complemented
8#15689421C211yesmaximal, characteristic, complemented
9#15689416C211yesmaximal, characteristic, complemented
10#15689366C211yesmaximal, characteristic, complemented
11#15689224C211yesmaximal, characteristic, complemented
12#15689194C211yesmaximal, characteristic, complemented
13#15689162C211yesmaximal, characteristic, complemented
14C2×#13093958C211yesmaximal, characteristic, complemented
15C47×#465C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17C2×#10625324C2211yescharacteristic
18#13094023C2211yescharacteristic
19#13094019—21no—
20#13094015—21no—
21#13094015C2211yescharacteristic
22#13094008—21no—
23#13094006—21no—
24#13094005—21no—
25#13094001—21no—
26#13094000C2211yescharacteristic
27#13093995C2211yescharacteristic
28Q8×Dic47C2211yescharacteristic
29D4×Dic47C2211yescharacteristic
30C4×C22⋊D47C2211yescharacteristic
31#13093982C2211yescharacteristic
32#13093980—21no—
33C2×C4⋊Dic47C2211yescharacteristic
34C2×C4⋊Dic47C2211yescharacteristic
35C4⋊C4×D47C2211yescharacteristic
36#13093958C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093957C2211yescharacteristic
42#13093955C2211yescharacteristic
43#13093955C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51#13093934C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C22×C8×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47D411yescharacteristic
65C22×Dic47—21no—
66C22×Dic47—21no—
67C22×Dic47—21no—
68#10625352—44no—
69C2×C4×D47—21no—
70C2×C4×D47C2311yescharacteristic
71C2×Dic94—21no—
72SD16×C47—22no—
73C2×C8×C47—22no—
74C2×C8×C47C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C4⋊C4×C47—21no—
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47D411yescharacteristic
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4D411yescharacteristic
87C4⋊Dic47—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47—21no—
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4D411yescharacteristic
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105#10625324—22no—
106C23×C47—21no—
107C23×C47C2×D411yescharacteristic
108C22×D47C2×D411yescharacteristic
109Q8×C47—21no—
110Q8×C47—21no—
111D4×C47—21no—
112D4×C47—21no—
113D4×C47—42no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2411yescharacteristic
121C22⋊D47—22no—
122C22⋊D47—42no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—42no—
128C2×Dic47—42no—
129C2×Dic47—42no—
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133C4×D47—21no—
134C4×D47—21no—
135C4×D47—42no—
136Dic94—42no—
137C8×C47—21no—
138C8×C47#4112yescomplemented
139C47⋊C8—21no—
140C47⋊C8—21no—
141C22×C47—21no—
142C22×C47—21no—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47AGL(1,ℤ/8)12yes—
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—21no—
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164#3343—471nomaximal, Sylow
165C2×C47—22no—
166C2×C47—81no—
167C2×C47#54711yescharacteristic
168C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
169C2×C47#57811yescharacteristic
170D47—41no—
171#552—471no—
172#547—471no—
173#501—471no—
174#484—471no—
175#483—471no—
176#482—471no—
177#480—471no—
178#478—471no—
179#477—471no—
180#468—471no—
181#465D4711yescharacteristic, complemented
182#440—471no—
183#435—471no—
184#428—471no—
185C2×#107—471no—
186C47#334311yescharacteristic, complemented, Sylow
187C2×#41—941no—
188C2×SD16C2×D4711yescharacteristic
189C2×M16—471no—
190C22×C8C2×D4711yescharacteristic
191C4⋊Q8—471no—
192#126—941no—
193#125—471no—
194#125—941no—
195#123—941no—
196#123—941no—
197#123—941no—
198C22⋊Q8—471no—
199C22⋊Q8—941no—
200C22⋊Q8C2×D4711yescharacteristic
201#121—471no—
202#121C2×D4711yescharacteristic
203C4×Q8—471no—
204C4×D4—471no—
205C4×D4—471no—
206#117—471no—
207#117—941no—
208C2×C4⋊C4—471no—
209C2×C4⋊C4—471no—
210C2×C4⋊C4—471no—
211#107—471no—
212#107—471no—
213#107—471no—
214#107—471no—
215#107—471no—
216#107—471no—
217#106—471no—
218#106—471no—
219#106C2×D4711yescharacteristic
220C4⋊C8—471no—
221#103—471no—
222#103—471no—
223#103C2×D4711yescharacteristic
224#102—471no—
225#102—471no—
226#102C2×D4711yescharacteristic
227C22⋊C8—471no—
228C22⋊C8—471no—
229#97—471no—
230#41—1884no—
231C2×Q8—941no—
232C2×Q8C22×D4711yescharacteristic
233C2×D4—21no—
234C2×D4—471no—
235C2×D4—941no—
236C2×D4C22×D4711yescharacteristic
237C22×C4—471no—
238C22×C4—941no—
239C22×C4—941no—
240C22×C4—941no—
241C22×C4—941no—
242C22×C4C22×D4711yescharacteristic
243SD16—22no—
244M16—942no—
245C2×C8—22no—
246C2×C8—471no—
247C2×C8—471no—
248C2×C8C22×D4711yescharacteristic
249C2×C8C22×D4711yescharacteristic
250C4⋊C4—21no—
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⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4C22×D4711yescharacteristic
265C4⋊C4C22×D4711yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—471no—
269C22⋊C4—471no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C42—471no—
275C42—941no—
276C42—941no—
277C23—21no—
278C23—471no—
279C23D4×D4711yescharacteristic
280Q8—21no—
281Q8—21no—
282Q8—1882no—
283D4—21no—
284D4—21no—
285D4—42no—
286D4—942no—
287D4—1882no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—471no—
294C2×C4—471no—
295C2×C4—471no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—1882no—
303C2×C4—1882no—
304C2×C4—1882no—
305C2×C4—1882no—
306C2×C4D4×D4711yescharacteristic
307C2×C4C23×D4711yescharacteristic
308C8—21no—
309C8—941no—
310C8—941no—
311C8#1062535212yescomplemented
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—941no—
318C22—941no—
319C22—941no—
320C22#1309405112yes—
321C22C2×D4×D4711yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—941no—
327C4—941no—
328C4—941no—
329C4—1881no—
330C4—1881no—
331C4—1881no—
332C4—1881no—
333C4C2×#1062535211yescharacteristic
334C4#1309407111yescharacteristic
335C2—22no—
336C2—81no—
337C2—1881no—
338C2#1568977311yescharacteristic
339C2C2×#1309405111yescharacteristic
340C2#1568993711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#465C2
socleC22×C47C22×D4
hypercenter#465D47
hypocenterC47#3343
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #15689815C2semidirect
3. #15689530C2semidirect
4. #15689457C2semidirect
5. #15689451C2semidirect
6. #15689445C2semidirect
7. #15689434C2semidirect
8. #15689421C2semidirect
9. #15689416C2semidirect
10. #15689366C2semidirect
11. #15689224C2semidirect
12. #15689194C2semidirect
13. #15689162C2semidirect
14. C2×#13093958C2semidirect
15. C47×#465C2semidirect
138. C8×C47#41semidirect
181. #465D47semidirect
186. C47#3343semidirect
311. C8#10625352semidirect