Finite Group Databasebeta

← #20255912

Subgroups — #20255912

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#15689813C211yesmaximal, characteristic
2#15689529C211yesmaximal, characteristic, complemented
3#15689464C211yesmaximal, characteristic, complemented
4#15689464C211yesmaximal, characteristic, complemented
5#15689461C211yesmaximal, characteristic, complemented
6#15689456C211yesmaximal, characteristic, complemented
7#15689430C211yesmaximal, characteristic, complemented
8#15689415C211yesmaximal, characteristic, complemented
9#15689379C211yesmaximal, characteristic, complemented
10#15689362C211yesmaximal, characteristic, complemented
11#15689228C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic
13#15689166C211yesmaximal, characteristic, complemented
14#15689159C211yesmaximal, characteristic, complemented
15C47×#556C211yesmaximal, characteristic
16C2×#10625337C2211yescharacteristic
17C2×#10625329C2211yescharacteristic
18C22×C47⋊C8C2211yescharacteristic
19#13094017—21no—
20#13094016C2211yescharacteristic
21#13094014—21no—
22#13094005—21no—
23#13094003C2211yescharacteristic
24#13094003C2211yescharacteristic
25C4×Dic94C2211yescharacteristic
26#13093983C2211yescharacteristic
27#13093980—21no—
28C2×C4⋊Dic47C2211yescharacteristic
29#13093957C2211yescharacteristic
30#13093957C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093957C2211yescharacteristic
33#13093957C2211yescharacteristic
34#13093955C2211yescharacteristic
35#13093955C2211yescharacteristic
36#13093955C2211yescharacteristic
37#13093955C2211yescharacteristic
38C4⋊(C47⋊C8)C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093948C2211yescharacteristic
41#13093948C2211yescharacteristic
42#13093947C2211yescharacteristic
43#13093947C2211yescharacteristic
44#13093947C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47#13093935C2211yescharacteristic
48C4⋊Q8×C47C2211yescharacteristic
49#126×C47—21no—
50#126×C47—21no—
51#124×C47—21no—
52C22⋊Q8×C47C2211yescharacteristic
53C22⋊Q8×C47C2211yescharacteristic
54C4×Q8×C47—21no—
55C4×Q8×C47C2211yescharacteristic
56C4×D4×C47C2211yescharacteristic
57#117×C47C2211yescharacteristic
58#117×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47D411yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×Dic47—21no—
65C2×Dic94C2311yescharacteristic
66C4⋊C4×C47—21no—
67C4⋊C4×C47—21no—
68C4⋊C4×C47—21no—
69C4⋊C4×C47—21no—
70C4⋊C4×C47D411yescharacteristic
71C4⋊C4×C47C2311yescharacteristic
72C4⋊C4×C47C2311yescharacteristic
73C4⋊C4×C47C2311yescharacteristic
74C22⋊C4×C47—21no—
75C22⋊C4×C47—21no—
76C22⋊C4×C47—21no—
77C22⋊C4×C47—21no—
78C22⋊C4×C47D411yescharacteristic
79C22⋊C4×C47D411yescharacteristic
80C42×C47—21no—
81C42×C47—21no—
82C42×C47—21no—
83C42×C47C2311yescharacteristic
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87#10625337—22no—
88C4⋊Dic47—21no—
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99#10625329—22no—
100C2×C47⋊C8—22no—
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C23×C47C2×D411yescharacteristic
106C23×C47C2×D411yescharacteristic
107Q8×C47—21no—
108Q8×C47—21no—
109Q8×C47—42no—
110D4×C47—41no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
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×C47C2×D411yescharacteristic
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2411yescharacteristic
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—42no—
129Dic94—21no—
130Dic94—21no—
131C47⋊C8—21no—
132C47⋊C8—21no—
133C47⋊C8—21no—
134C47⋊C8#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×C47—41no—
147C4×C47—41no—
148C4×C47—41no—
149C4×C47—41no—
150C4×C47C2×#4111yescharacteristic
151C4×C472−1+411yescharacteristic
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#556D4711yescharacteristic
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#435—471no—
175#428—471no—
176#427—471no—
177C47#334911yescharacteristic, complemented, Sylow
178C2×Q16—471no—
179C2×M16—471no—
180C22×C8—471no—
181C4⋊Q8C2×D4711yescharacteristic
182#126—21no—
183#126—21no—
184#126—941no—
185#125—471no—
186#125—941no—
187#124—21no—
188#123—941no—
189C22⋊Q8—471no—
190C22⋊Q8—471no—
191C22⋊Q8C2×D4711yescharacteristic
192C22⋊Q8C2×D4711yescharacteristic
193C4×Q8—21no—
194C4×Q8—471no—
195C4×Q8C2×D4711yescharacteristic
196C4×D4C2×D4711yescharacteristic
197#117—471no—
198#117—941no—
199#117C2×D4711yescharacteristic
200#117C2×D4711yescharacteristic
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⋊C8—471no—
212#103—471no—
213#103—471no—
214#103—471no—
215#103—471no—
216#103—471no—
217#103—471no—
218C22⋊C8—471no—
219C22⋊C8—471no—
220#97—471no—
221C2×Q8—21no—
222C2×Q8—471no—
223C2×Q8C22×D4711yescharacteristic
224C2×D4C22⋊D4711yescharacteristic
225C22×C4—941no—
226C22×C4C22×D4711yescharacteristic
227C22×C4C22×D4711yescharacteristic
228Q16—942no—
229M16—942no—
230C2×C8—471no—
231C2×C8—471no—
232C2×C8—471no—
233C2×C8—471no—
234C2×C8—942no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—471no—
240C4⋊C4—471no—
241C4⋊C4—471no—
242C4⋊C4—941no—
243C4⋊C4—941no—
244C4⋊C4—941no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4C22⋊D4711yescharacteristic
249C4⋊C4C22×D4711yescharacteristic
250C4⋊C4C22×D4711yescharacteristic
251C4⋊C4C22×D4711yescharacteristic
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—21no—
256C22⋊C4—941no—
257C22⋊C4—941no—
258C22⋊C4—941no—
259C22⋊C4C22⋊D4711yescharacteristic
260C22⋊C4C22⋊D4711yescharacteristic
261C42—21no—
262C42—21no—
263C42—21no—
264C42—941no—
265C42—941no—
266C42C22×D4711yescharacteristic
267C23C2×C22⋊D4711yescharacteristic
268C23C2×C22⋊D4711yescharacteristic
269Q8—21no—
270Q8—21no—
271Q8—42no—
272Q8—941no—
273Q8—941no—
274D4—41no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—941no—
284C2×C4—941no—
285C2×C4—941no—
286C2×C4—941no—
287C2×C4—1882no—
288C2×C4C2×C22⋊D4711yescharacteristic
289C2×C4C2×C22⋊D4711yescharacteristic
290C2×C4C2×C22⋊D4711yescharacteristic
291C2×C4C2×C22⋊D4711yescharacteristic
292C2×C4C23×D4711yescharacteristic
293C8—472no—
294C8—941no—
295C8—941no—
296C8—941no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22C22×C22⋊D4711yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—1881no—
313C4—1881no—
314C4—1881no—
315C4—1881no—
316C4#41×D4711yescharacteristic
317C4#1309407111yescharacteristic
318C2—41no—
319C2—41no—
320C2#1568977211yescharacteristic
321C2#1568992111yescharacteristic
322C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#556C2
socleC22×C47C22×D4
hypercenter#556D47
hypocenterC47#3349
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
2. #15689529C2semidirect
3. #15689464C2semidirect
4. #15689464C2semidirect
5. #15689461C2semidirect
6. #15689456C2semidirect
7. #15689430C2semidirect
8. #15689415C2semidirect
9. #15689379C2semidirect
10. #15689362C2semidirect
11. #15689228C2semidirect
13. #15689166C2semidirect
14. #15689159C2semidirect
177. C47#3349semidirect