Finite Group Databasebeta

← #20255945

Subgroups — #20255945

Order 6016.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689826C211yesmaximal, characteristic
2#15689814C211yesmaximal, characteristic, complemented
3#15689522C211yesmaximal, characteristic, complemented
4#15689463C211yesmaximal, characteristic, complemented
5#15689452C211yesmaximal, characteristic, complemented
6#15689450C211yesmaximal, characteristic, complemented
7#15689443C211yesmaximal, characteristic, complemented
8#15689424C211yesmaximal, characteristic, complemented
9#15689372C211yesmaximal, characteristic, complemented
10#15689372C211yesmaximal, characteristic, complemented
11C4×#10625336C211yesmaximal, characteristic, complemented
12#15689200C211yesmaximal, characteristic, complemented
13#15689164C211yesmaximal, characteristic, complemented
14#15689162C211yesmaximal, characteristic, complemented
15C47×#479C211yesmaximal, characteristic, complemented
16C2×#10625336C2211yescharacteristic
17C2×#10625324C2211yescharacteristic
18C2×#10625324C2211yescharacteristic
19#13094019—21no—
20#13094018—21no—
21#13094016C2211yescharacteristic
22#13094014—21no—
23#13094009—21no—
24#13094009—21no—
25#13094000C2211yescharacteristic
26#13094000C2211yescharacteristic
27#13093999—21no—
28#13093999C2211yescharacteristic
29#13093999C2211yescharacteristic
30C4×D188C2211yescharacteristic
31C4×D188C2211yescharacteristic
32#13093986—21no—
33#13093982C2211yescharacteristic
34#13093982C2211yescharacteristic
35#13093981—21no—
36C4⋊C4×D47C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093955C2211yescharacteristic
43#13093955C2211yescharacteristic
44#13093955C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093944C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C4×C47⋊C8C2211yescharacteristic
52#125×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D188—21no—
61C2×D188—21no—
62C2×D188D411yescharacteristic
63C2×D188C2311yescharacteristic
64C2×C4×D47—21no—
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×C4×D47C2311yescharacteristic
68C2×C4×D47C2311yescharacteristic
69C2×C8×C47C2311yescharacteristic
70C2×C8×C47C2311yescharacteristic
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C42×C47—21no—
78C42×C47C2311yescharacteristic
79#10625336—22no—
80(C2×D47)⋊C4—21no—
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4D411yescharacteristic
88(C2×D47)⋊C4D411yescharacteristic
89C4⋊Dic47D411yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103#10625324—22no—
104#10625324—22no—
105C22×D47—21no—
106C22×D47C2×D411yescharacteristic
107C22×D47C2×D411yescharacteristic
108Q8×C47—21no—
109Q8×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2411yescharacteristic
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47C2×D411yescharacteristic
121C2×Dic47C2×D411yescharacteristic
122D188—21no—
123D188—21no—
124D188—41no—
125D188—42no—
126D188—81no—
127C4×D47—21no—
128C4×D47—21no—
129C4×D47—21no—
130C4×D47—21no—
131C4×D47—42no—
132C4×D47—81no—
133C4×D47—81no—
134C8×C47—21no—
135C8×C47—21no—
136C47⋊C8—21no—
137C47⋊C8#4112yes—
138C22×C47C22×D411yescharacteristic
139C2×D47—21no—
140C2×D47—21no—
141C2×D47—21no—
142C2×D47—21no—
143C2×D47—21no—
144C2×D47—21no—
145C2×D47—41no—
146C2×D47—41no—
147C2×D47—41no—
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47—41no—
153C4×C47—41no—
154C4×C47C2×#4111yescharacteristic
155C4×C472−1+411yescharacteristic
156Dic47—21no—
157Dic47—21no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161#3351—471nomaximal, Sylow
162C2×C47#54711yescharacteristic
163C2×C47#57511yescharacteristic
164C2×C47#57711yescharacteristic
165D47—41no—
166D47—41no—
167D47—81no—
168#553—471no—
169#552—471no—
170#499—471no—
171#485—471no—
172#483—471no—
173#482—471no—
174#481—471no—
175#479D4711yescharacteristic, complemented
176#478—471no—
177#468—471no—
178#468—471no—
179C4×SD16—471no—
180#436—471no—
181#428—471no—
182#428—471no—
183C47#335111yescharacteristic, complemented, Sylow
184C2×SD16—471no—
185C2×M16—471no—
186C2×M16—471no—
187#126—941no—
188#126—941no—
189#125—471no—
190#125—941no—
191#125C2×D4711yescharacteristic
192#123—941no—
193#123—941no—
194C22⋊Q8—471no—
195C22⋊Q8—471no—
196#121—471no—
197#121—471no—
198#121—941no—
199C4×Q8C2×D4711yescharacteristic
200C4×D4—471no—
201C4×D4—471no—
202C4×D4—941no—
203#117—471no—
204#117—471no—
205#117—941no—
206C2×C4⋊C4—471no—
207C2×C4⋊C4—471no—
208#107—471no—
209#107—471no—
210#107—471no—
211#107C2×D4711yescharacteristic
212#106—471no—
213#106—471no—
214#106—471no—
215#106—471no—
216#106C2×D4711yescharacteristic
217C4⋊C8C2×D4711yescharacteristic
218#103—471no—
219#103C2×D4711yescharacteristic
220#103C2×D4711yescharacteristic
221#102—471no—
222#102—471no—
223#102—471no—
224C22⋊C8—471no—
225C22⋊C8—471no—
226C4×C8—471no—
227C2×Q8C22×D4711yescharacteristic
228C2×D4—471no—
229C2×D4—471no—
230C2×D4—941no—
231C2×D4—941no—
232C22×C4—471no—
233C22×C4—471no—
234C22×C4—941no—
235C22×C4—941no—
236C22×C4—941no—
237SD16—942no—
238M16—942no—
239M16—942no—
240C2×C8—471no—
241C2×C8—471no—
242C2×C8C22×D4711yescharacteristic
243C2×C8C22×D4711yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—471no—
248C4⋊C4—471no—
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⋊C4C22×D4711yescharacteristic
258C4⋊C4C22×D4711yescharacteristic
259C4⋊C4C22×D4711yescharacteristic
260C22⋊C4—471no—
261C22⋊C4—471no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C42—21no—
270C42—941no—
271C42—941no—
272C42C22×D4711yescharacteristic
273C23—471no—
274C23—471no—
275C23—941no—
276Q8—21no—
277Q8—21no—
278D4—941no—
279D4—941no—
280D4—3761no—
281D4—1881no—
282D4—1882no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—471no—
288C2×C4—471no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—3761no—
297C2×C4—3761no—
298C2×C4—1882no—
299C2×C4D4×D4711yescharacteristic
300C2×C4D4×D4711yescharacteristic
301C2×C4C23×D4711yescharacteristic
302C8—21no—
303C8—21no—
304C8—472no—
305C8—941no—
306C22—941no—
307C22—941no—
308C22—941no—
309C22—941no—
310C22—941no—
311C22—941no—
312C22—1881no—
313C22—1881no—
314C22—1881no—
315C22C2×D4×D4711yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—941no—
323C4—941no—
324C4—1881no—
325C4—1881no—
326C4—1881no—
327C4#41×D4711yescharacteristic
328C4#1309407211yescharacteristic
329C2—3761no—
330C2—1881no—
331C2—1881no—
332C2#1568977511yescharacteristic
333C2#1568992011yescharacteristic
334C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#479C2
socleC22×C47C22×D4
hypercenter#479D47
hypocenterC47#3351
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. #15689814C2semidirect
3. #15689522C2semidirect
4. #15689463C2semidirect
5. #15689452C2semidirect
6. #15689450C2semidirect
7. #15689443C2semidirect
8. #15689424C2semidirect
9. #15689372C2semidirect
10. #15689372C2semidirect
11. C4×#10625336C2semidirect
12. #15689200C2semidirect
13. #15689164C2semidirect
14. #15689162C2semidirect
15. C47×#479C2semidirect
175. #479D47semidirect
183. C47#3351semidirect