Finite Group Databasebeta

← #20255845

Subgroups — #20255845

Order 6016.

344 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689830C211yesmaximal, characteristic
2#15689813C211yesmaximal, characteristic
3#15689532C211yesmaximal, characteristic, complemented
4#15689465C211yesmaximal, characteristic, complemented
5#15689459C211yesmaximal, characteristic, complemented
6#15689454C211yesmaximal, characteristic, complemented
7#15689454C211yesmaximal, characteristic, complemented
8#15689431C211yesmaximal, characteristic, complemented
9#15689409C211yesmaximal, characteristic, complemented
10#15689381C211yesmaximal, characteristic, complemented
11#15689364C211yesmaximal, characteristic, complemented
12#15689231C211yesmaximal, characteristic, complemented
13#15689165C211yesmaximal, characteristic, complemented
14C2×#13093956C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic
16C2×Dic188C2211yescharacteristic
17#13094024C2211yescharacteristic
18#13094017—21no—
19#13094016C2211yescharacteristic
20#13094015—21no—
21#13094014—21no—
22#13094005—21no—
23#13094003C2211yescharacteristic
24#13094003C2211yescharacteristic
25#13094003C2211yescharacteristic
26#13094003C2211yescharacteristic
27#13094001—21no—
28#13094001—21no—
29C4×Dic94C2211yescharacteristic
30C4×Dic94C2211yescharacteristic
31D4×Dic47—21no—
32#13093983C2211yescharacteristic
33#13093980—21no—
34C2×C4⋊Dic47C2211yescharacteristic
35C2×C4⋊Dic47C2211yescharacteristic
36C2×C4⋊Dic47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093956C2211yescharacteristic
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—
63C22×Dic47—21no—
64C22×Dic47—21no—
65C2×Dic94—21no—
66C2×Dic94C2311yescharacteristic
67C2×Dic94C2311yescharacteristic
68M16×C47—22no—
69C2×C8×C47—22no—
70C2×C8×C47C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C4⋊C4×C47D411yescharacteristic
75C22⋊C4×C47D411yescharacteristic
76C22⋊C4×C47D411yescharacteristic
77C42×C47C2311yescharacteristic
78C22⋊Dic47—21no—
79C22⋊Dic47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83C4⋊Dic47—21no—
84C4⋊Dic47—21no—
85C4⋊Dic47—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47C2311yescharacteristic
88C4⋊Dic47C2311yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104Dic188—22no—
105C23×C47C2×D411yescharacteristic
106C23×C47C2×D411yescharacteristic
107D4×C47—22no—
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—
126C2×Dic47—81no—
127C2×Dic47—81no—
128Dic94—21no—
129Dic94—21no—
130Dic94—21no—
131Dic94—21no—
132Dic94—81no—
133C8×C47—21no—
134C8×C47—21no—
135C8×C47—21no—
136C8×C47#4112yes—
137C22×C47—21no—
138C22×C47—21no—
139C22×C47—21no—
140C22×C47—21no—
141C22×C47—21no—
142C22×C47#13712yes—
143C22×C47C22×D411yescharacteristic
144C4×C47—21no—
145C4×C47—21no—
146C4×C47—21no—
147C4×C47—21no—
148C4×C47C2×#4111yescharacteristic
149C4×C472−1+411yescharacteristic
150Dic47—41no—
151Dic47—41no—
152Dic47—41no—
153Dic47—41no—
154Dic47—41no—
155Dic47—41no—
156Dic47—41no—
157Dic47—41no—
158#3344—471nomaximal, Sylow
159C2×C47—22no—
160C2×C47—41no—
161C2×C47#54711yescharacteristic
162C2×C47C2×#13711yescharacteristic
163C2×C47#57711yescharacteristic
164#554—471no—
165#552—471no—
166#501—471no—
167#485—471no—
168#484—471no—
169#483—471no—
170#483—471no—
171#479—471no—
172#475—471no—
173#470—471no—
174#467—471no—
175#441—471no—
176#435D4711yescharacteristic
177#428—471no—
178C2×#106—471no—
179C47#334411yescharacteristic, complemented, Sylow
180C2×Q16—471no—
181C2×M16C2×D4711yescharacteristic
182C22×C8C2×D4711yescharacteristic
183C4⋊Q8—471no—
184#126—941no—
185#125—471no—
186#125—941no—
187#125—941no—
188#123—941no—
189C22⋊Q8—471no—
190C22⋊Q8—471no—
191C22⋊Q8—471no—
192C22⋊Q8—471no—
193C22⋊Q8—941no—
194C22⋊Q8—941no—
195C4×Q8—471no—
196C4×Q8—471no—
197C4×D4—941no—
198C4×D4C2×D4711yescharacteristic
199#117—471no—
200#117—941no—
201C2×C4⋊C4—471no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4—471no—
204#107—471no—
205#107—471no—
206#107—471no—
207#106—471no—
208#106—471no—
209#106—471no—
210#106—471no—
211#106—471no—
212#106—471no—
213C4⋊C8C2×D4711yescharacteristic
214#103—471no—
215#103—471no—
216#103—471no—
217#103—471no—
218#103—471no—
219#103—471no—
220C22⋊C8C2×D4711yescharacteristic
221C22⋊C8C2×D4711yescharacteristic
222#97C2×D4711yescharacteristic
223C2×Q8—471no—
224C2×Q8—471no—
225C2×Q8—941no—
226C2×D4D18811yescharacteristic
227C22×C4—941no—
228C22×C4—941no—
229C22×C4—941no—
230C22×C4C22×D4711yescharacteristic
231C22×C4C22×D4711yescharacteristic
232Q16—942no—
233M16—22no—
234C2×C8—22no—
235C2×C8C22×D4711yescharacteristic
236C2×C8C22×D4711yescharacteristic
237C2×C8C22×D4711yescharacteristic
238C2×C8C22×D4711yescharacteristic
239C4⋊C4—471no—
240C4⋊C4—471no—
241C4⋊C4—471no—
242C4⋊C4—471no—
243C4⋊C4—471no—
244C4⋊C4—471no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4D18811yescharacteristic
258C22⋊C4—941no—
259C22⋊C4—941no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C22⋊C4D18811yescharacteristic
264C22⋊C4D18811yescharacteristic
265C42—941no—
266C42—941no—
267C42—941no—
268C42C22×D4711yescharacteristic
269C23C2×D18811yescharacteristic
270C23C2×D18811yescharacteristic
271Q8—941no—
272Q8—941no—
273Q8—941no—
274Q8—941no—
275Q8—3761no—
276D4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—941no—
282C2×C4—941no—
283C2×C4—941no—
284C2×C4—941no—
285C2×C4—941no—
286C2×C4—941no—
287C2×C4—941no—
288C2×C4—941no—
289C2×C4—3761no—
290C2×C4—3761no—
291C2×C4—1882no—
292C2×C4C2×D18811yescharacteristic
293C2×C4C2×D18811yescharacteristic
294C2×C4C2×D18811yescharacteristic
295C2×C4C2×D18811yescharacteristic
296C2×C4C23×D4711yescharacteristic
297C8—21no—
298C8—21no—
299C8—21no—
300C8#1062535212yes—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22#1309405712yes—
307C22C22×D18811yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—1881no—
313C4—1881no—
314C4—1881no—
315C4—1881no—
316C4—1881no—
317C4—1881no—
318C4—1881no—
319C4—1881no—
320C4C2×#1062535211yescharacteristic
321C4#1309407111yescharacteristic
322C2—22no—
323C2—41no—
324C2#1568977711yescharacteristic
325C2C2×#1309405711yescharacteristic
326C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#435C2
socleC22×C47C22×D4
hypercenter#435D47
hypocenterC47#3344
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. #15689459C2semidirect
6. #15689454C2semidirect
7. #15689454C2semidirect
8. #15689431C2semidirect
9. #15689409C2semidirect
10. #15689381C2semidirect
11. #15689364C2semidirect
12. #15689231C2semidirect
13. #15689165C2semidirect
14. C2×#13093956C2semidirect
179. C47#3344semidirect