Finite Group Databasebeta

← #20255920

Subgroups — #20255920

Order 6016.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689843C211yesmaximal, characteristic
2#15689813C211yesmaximal, characteristic
3#15689532C211yesmaximal, characteristic, complemented
4#15689465C211yesmaximal, characteristic, complemented
5#15689465C211yesmaximal, characteristic, complemented
6#15689465C211yesmaximal, characteristic, complemented
7#15689459C211yesmaximal, characteristic, complemented
8#15689431C211yesmaximal, characteristic, complemented
9#15689419C211yesmaximal, characteristic, complemented
10#15689381C211yesmaximal, characteristic, complemented
11#15689364C211yesmaximal, characteristic, complemented
12#15689231C211yesmaximal, characteristic, complemented
13#15689165C211yesmaximal, characteristic, complemented
14#15689161C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic
16C2×Dic188C2211yescharacteristic
17#13094024C2211yescharacteristic
18#13094017—21no—
19#13094017—21no—
20#13094017—21no—
21#13094016C2211yescharacteristic
22#13094014—21no—
23#13094011—21no—
24#13094005—21no—
25#13094003C2211yescharacteristic
26#13094003C2211yescharacteristic
27#13094003C2211yescharacteristic
28#13094003C2211yescharacteristic
29C4×Dic94C2211yescharacteristic
30C4×Dic94C2211yescharacteristic
31#13093989—21no—
32#13093983C2211yescharacteristic
33#13093983C2211yescharacteristic
34#13093983C2211yescharacteristic
35#13093980—21no—
36C2×C4⋊Dic47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093958C2211yescharacteristic
41#13093958C2211yescharacteristic
42#13093956C2211yescharacteristic
43#13093956C2211yescharacteristic
44#13093956C2211yescharacteristic
45#13093956C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093949C2211yescharacteristic
49#13093949C2211yescharacteristic
50#13093949C2211yescharacteristic
51#13093949C2211yescharacteristic
52C2×M16×C47C2211yescharacteristic
53C22×C8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55C4⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57C22⋊C8×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×D4×C47D411yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×Dic47—21no—
63C2×Dic94—21no—
64C2×Dic94C2311yescharacteristic
65C2×Dic94C2311yescharacteristic
66M16×C47—22no—
67C2×C8×C47—22no—
68C2×C8×C47C2311yescharacteristic
69C2×C8×C47C2311yescharacteristic
70C2×C8×C47C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C4⋊C4×C47D411yescharacteristic
73C22⋊C4×C47D411yescharacteristic
74C22⋊C4×C47D411yescharacteristic
75C42×C47C2311yescharacteristic
76C22⋊Dic47—21no—
77C22⋊Dic47—21no—
78C22⋊Dic47—21no—
79C22⋊Dic47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83C4⋊Dic47—21no—
84C4⋊Dic47—21no—
85C4⋊Dic47C2311yescharacteristic
86C4⋊Dic47C2311yescharacteristic
87C4⋊Dic47C2311yescharacteristic
88C4⋊Dic47C2311yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104Dic188—22no—
105C23×C47C2×D411yescharacteristic
106C23×C47C2×D411yescharacteristic
107D4×C47—41no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47C2×D411yescharacteristic
113C2×C4×C47C2×D411yescharacteristic
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2411yescharacteristic
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—42no—
126Dic94—21no—
127Dic94—21no—
128Dic94—21no—
129Dic94—21no—
130Dic94—42no—
131C8×C47—21no—
132C8×C47—21no—
133C8×C47—21no—
134C8×C47#4112yes—
135C22×C47—21no—
136C22×C47—21no—
137C22×C47—21no—
138C22×C47—21no—
139C22×C47—21no—
140C22×C47—21no—
141C22×C47C22×D411yescharacteristic
142C4×C47—21no—
143C4×C47—21no—
144C4×C47—21no—
145C4×C47—21no—
146C4×C47C2×#4111yescharacteristic
147C4×C472−1+411yescharacteristic
148Dic47—41no—
149Dic47—41no—
150Dic47—41no—
151Dic47—41no—
152Dic47—41no—
153Dic47—41no—
154Dic47—41no—
155Dic47—41no—
156#3349—471nomaximal, Sylow
157C2×C47—41no—
158C2×C47—41no—
159C2×C47#54711yescharacteristic
160C2×C47#57511yescharacteristic
161C2×C47#57811yescharacteristic
162#556—471no—
163#552—471no—
164#501—471no—
165#485—471no—
166#485—471no—
167#485—471no—
168#484—471no—
169#479—471no—
170#477—471no—
171#470—471no—
172#467—471no—
173#441—471no—
174#435D4711yescharacteristic
175#428—471no—
176#427—471no—
177C47#334911yescharacteristic, complemented, Sylow
178C2×Q16—471no—
179C2×M16C2×D4711yescharacteristic
180C22×C8C2×D4711yescharacteristic
181C4⋊Q8—471no—
182#126—941no—
183#126—941no—
184#126—941no—
185#125—471no—
186#125—941no—
187#124—941no—
188#123—941no—
189C22⋊Q8—471no—
190C22⋊Q8—471no—
191C22⋊Q8—471no—
192C22⋊Q8—471no—
193C4×Q8—471no—
194C4×Q8—471no—
195C4×Q8—941no—
196C4×D4C2×D4711yescharacteristic
197#117—471no—
198#117—471no—
199#117—471no—
200#117—941no—
201C2×C4⋊C4—471no—
202#107—471no—
203#107—471no—
204#107—471no—
205#107—471no—
206#107—471no—
207#106—471no—
208#106—471no—
209#106—471no—
210#106—471no—
211C4⋊C8C2×D4711yescharacteristic
212#103—471no—
213#103—471no—
214#103—471no—
215#103—471no—
216#103—471no—
217#103—471no—
218C22⋊C8C2×D4711yescharacteristic
219C22⋊C8C2×D4711yescharacteristic
220#97C2×D4711yescharacteristic
221C2×Q8—471no—
222C2×Q8—471no—
223C2×Q8—941no—
224C2×D4D18811yescharacteristic
225C22×C4—941no—
226C22×C4C22×D4711yescharacteristic
227C22×C4C22×D4711yescharacteristic
228Q16—942no—
229M16—22no—
230C2×C8—22no—
231C2×C8C22×D4711yescharacteristic
232C2×C8C22×D4711yescharacteristic
233C2×C8C22×D4711yescharacteristic
234C2×C8C22×D4711yescharacteristic
235C4⋊C4—471no—
236C4⋊C4—471no—
237C4⋊C4—471no—
238C4⋊C4—471no—
239C4⋊C4—471no—
240C4⋊C4—471no—
241C4⋊C4—941no—
242C4⋊C4—941no—
243C4⋊C4—941no—
244C4⋊C4—941no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4D18811yescharacteristic
252C22⋊C4—941no—
253C22⋊C4—941no—
254C22⋊C4—941no—
255C22⋊C4—941no—
256C22⋊C4—941no—
257C22⋊C4—941no—
258C22⋊C4—941no—
259C22⋊C4D18811yescharacteristic
260C22⋊C4D18811yescharacteristic
261C42—941no—
262C42—941no—
263C42—941no—
264C42—941no—
265C42—941no—
266C42C22×D4711yescharacteristic
267C23C2×D18811yescharacteristic
268C23C2×D18811yescharacteristic
269Q8—941no—
270Q8—941no—
271Q8—941no—
272Q8—941no—
273Q8—1882no—
274D4—41no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—941no—
280C2×C4—941no—
281C2×C4—941no—
282C2×C4—941no—
283C2×C4—941no—
284C2×C4—941no—
285C2×C4—941no—
286C2×C4—941no—
287C2×C4—1882no—
288C2×C4C2×D18811yescharacteristic
289C2×C4C2×D18811yescharacteristic
290C2×C4C2×D18811yescharacteristic
291C2×C4C2×D18811yescharacteristic
292C2×C4C23×D4711yescharacteristic
293C8—21no—
294C8—21no—
295C8—21no—
296C8#1062535212yes—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22C22×D18811yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—1881no—
309C4—1881no—
310C4—1881no—
311C4—1881no—
312C4—1881no—
313C4—1881no—
314C4—1881no—
315C4—1881no—
316C4C2×#1062535211yescharacteristic
317C4#1309407111yescharacteristic
318C2—41no—
319C2—41no—
320C2#1568977711yescharacteristic
321C2#1568992311yescharacteristic
322C2#1568994011yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#435C2
socleC22×C47C22×D4
hypercenter#435D47
hypocenterC47#3349
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
3. #15689532C2semidirect
4. #15689465C2semidirect
5. #15689465C2semidirect
6. #15689465C2semidirect
7. #15689459C2semidirect
8. #15689431C2semidirect
9. #15689419C2semidirect
10. #15689381C2semidirect
11. #15689364C2semidirect
12. #15689231C2semidirect
13. #15689165C2semidirect
14. #15689161C2semidirect
177. C47#3349semidirect