Finite Group Databasebeta

← #20256221

Subgroups — #20256221

Order 6016.

346 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689842C211yesmaximal, characteristic, complemented
2#15689829C211yesmaximal, characteristic, complemented
3#15689490C211yesmaximal, characteristic, complemented
4#15689481C211yesmaximal, characteristic, complemented
5#15689427C211yesmaximal, characteristic, complemented
6#15689425C211yesmaximal, characteristic, complemented
7#15689406C211yesmaximal, characteristic, complemented
8#15689337C211yesmaximal, characteristic
9#15689335C211yesmaximal, characteristic
10#15689327C211yesmaximal, characteristic, complemented
11#15689253C211yesmaximal, characteristic, complemented
12#15689232C211yesmaximal, characteristic
13#15689226C211yesmaximal, characteristic, complemented
14C4×#10625325C211yesmaximal, characteristic, complemented
15C47×#488C211yesmaximal, characteristic, complemented
16C2×#10625325C2211yescharacteristic
17C2×#10625336C2211yescharacteristic
18C2×#10625334C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094022C2211yescharacteristic
21#13094017—21no—
22#13094017—21no—
23#13094015C2211yescharacteristic
24#13094011C2211yescharacteristic
25#13094004—21no—
26#13094002—21no—
27#13094002—21no—
28#13094001—21no—
29Q8×Dic47C2211yescharacteristic
30C4×Dic94C2211yescharacteristic
31C4×Dic94C2211yescharacteristic
32C4×D188C2211yescharacteristic
33D4×Dic47C2211yescharacteristic
34#13093986C2211yescharacteristic
35#13093986C2211yescharacteristic
36#13093980—21no—
37C4⋊C4×D47—21no—
38#13093957C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41C4⋊(C47⋊C8)C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093945C2211yescharacteristic
50#13093934C2211yescharacteristic
51#13093934C2211yescharacteristic
52#125×C47C2211yescharacteristic
53#124×C47C2211yescharacteristic
54#103×C47C2211yescharacteristic
55#103×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47C2311yescharacteristic
61C22×Dic47—21no—
62C2×D188C2311yescharacteristic
63C2×C4×D47—21no—
64C2×C4×D47—21no—
65C2×C4×D47—21no—
66C2×Dic94—21no—
67C2×Dic94D411yescharacteristic
68C2×Dic94C2311yescharacteristic
69C2×C8×C47C2311yescharacteristic
70C2×C8×C47C2311yescharacteristic
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47C2311yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C22⋊C4×C47—21no—
76C22⋊C4×C47—21no—
77C42×C47C2311yescharacteristic
78C22⋊Dic47—21no—
79C22⋊Dic47—21no—
80C22⋊Dic47—21no—
81#10625336—22no—
82#10625334—22no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47D411yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4D411yescharacteristic
97Dic47⋊C4D411yescharacteristic
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47C2311yescharacteristic
101C4×Dic47C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104#10625325—22no—
105C23×C47—21no—
106C22×D47—21no—
107Q8×C47—21no—
108Q8×C47—21no—
109D4×C47—21no—
110D4×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×Dic47—42no—
121C2×Dic47C2×D411yescharacteristic
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124C2×Dic47C2×D411yescharacteristic
125D188—21no—
126D188#4112yes—
127C4×D47—42no—
128C4×D47—81no—
129C4×D47—81no—
130Dic94—21no—
131Dic94—21no—
132Dic94—41no—
133Dic94—81no—
134C8×C47—21no—
135C8×C47—21no—
136C47⋊C8—21no—
137C47⋊C8—21no—
138C22×C47—41no—
139C22×C47—41no—
140C22×C47—41no—
141C22×C47C22×D411yescharacteristic
142C2×D47—22no—
143C2×D47—41no—
144C2×D47—41no—
145C4×C47—21no—
146C4×C47—21no—
147C4×C47—41no—
148C4×C47—41no—
149C4×C47—41no—
150C4×C47C2×#4111yescharacteristic
151C4×C472−1+411yescharacteristic
152Dic47—21no—
153Dic47—21no—
154Dic47—21no—
155Dic47—21no—
156Dic47—41no—
157Dic47—41no—
158Dic47—41no—
159#3376—471nomaximal, Sylow
160C2×C47—81no—
161C2×C47#54811yescharacteristic
162C2×C47#57511yescharacteristic
163C2×C47#57711yescharacteristic
164D47—42no—
165#556—471no—
166#554—471no—
167#491—471no—
168#489—471no—
169#488D4711yescharacteristic, complemented
170#479—471no—
171#478—471no—
172#475—471no—
173#463—471no—
174#463—471no—
175#461—471no—
176#446—471no—
177#442—471no—
178#440—471no—
179C4×SD16—471no—
180C47#337611yescharacteristic, complemented, Sylow
181C2×SD16—471no—
182C2×SD16—471no—
183C2×D8—471no—
184C4⋊Q8—471no—
185C4⋊Q8—471no—
186#126—941no—
187#126—941no—
188#125—471no—
189#125C2×D4711yescharacteristic
190#124—471no—
191#124C2×D4711yescharacteristic
192C22⋊Q8—941no—
193C22⋊Q8—941no—
194C22⋊Q8—941no—
195C22⋊Q8—941no—
196C4×Q8—471no—
197C4×Q8—471no—
198C4×Q8—471no—
199C4×D4—471no—
200C4×D4—471no—
201C4×D4—471no—
202C4×D4—471no—
203#117—941no—
204C2×C4⋊C4—941no—
205#107—471no—
206#106—471no—
207#106—471no—
208C4⋊C8—471no—
209C4⋊C8—471no—
210C4⋊C8—471no—
211#103—471no—
212#103—471no—
213#103—471no—
214#103—471no—
215#103C2×D4711yescharacteristic
216#103C2×D4711yescharacteristic
217#102—471no—
218#102—471no—
219#102C2×D4711yescharacteristic
220#102C2×D4711yescharacteristic
221#97—471no—
222#97—471no—
223C4×C8C2×D4711yescharacteristic
224C2×Q8—471no—
225C2×Q8—471no—
226C2×Q8—941no—
227C2×Q8C22×D4711yescharacteristic
228C2×D4—471no—
229C2×D4C22×D4711yescharacteristic
230C22×C4—941no—
231C22×C4—941no—
232C22×C4—941no—
233C22×C4—941no—
234SD16—942no—
235SD16—942no—
236D8—942no—
237C2×C8—471no—
238C2×C8—471no—
239C2×C8C22×D4711yescharacteristic
240C2×C8C22×D4711yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—471no—
244C4⋊C4—471no—
245C4⋊C4—471no—
246C4⋊C4—471no—
247C4⋊C4—471no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4C22×D4711yescharacteristic
256C4⋊C4C22×D4711yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—941no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C42—471no—
266C42—471no—
267C42—941no—
268C42—941no—
269C42C22×D4711yescharacteristic
270C23—21no—
271C23—941no—
272Q8—21no—
273Q8—21no—
274Q8—941no—
275Q8—941no—
276Q8—3761no—
277Q8—1881no—
278D4—21no—
279D4—21no—
280D4—472no—
281D4—941no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—471no—
286C2×C4—471no—
287C2×C4—471no—
288C2×C4—471no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—3761no—
293C2×C4—3761no—
294C2×C4—1882no—
295C2×C4—1882no—
296C2×C4D4×D4711yescharacteristic
297C2×C4D4×D4711yescharacteristic
298C2×C4C23×D4711yescharacteristic
299C8—21no—
300C8—21no—
301C8—941no—
302C8—941no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—942no—
307C22—1881no—
308C22—1881no—
309C22C2×D4×D4711yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—941no—
316C4—941no—
317C4—941no—
318C4—941no—
319C4—1881no—
320C4—1881no—
321C4—1881no—
322C4#41×D4711yescharacteristic
323C4#1309407111yescharacteristic
324C2—81no—
325C2—1882no—
326C2#1568978111yescharacteristic
327C2#1568992011yescharacteristic
328C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#488C2
socleC22×C47C22×D4
hypercenter#488D47
hypocenterC47#3376
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #15689842C2semidirect
2. #15689829C2semidirect
3. #15689490C2semidirect
4. #15689481C2semidirect
5. #15689427C2semidirect
6. #15689425C2semidirect
7. #15689406C2semidirect
10. #15689327C2semidirect
11. #15689253C2semidirect
13. #15689226C2semidirect
14. C4×#10625325C2semidirect
15. C47×#488C2semidirect
169. #488D47semidirect
180. C47#3376semidirect