Finite Group Databasebeta

← #20255957

Subgroups — #20255957

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#15689522C211yesmaximal, characteristic, complemented
3#15689464C211yesmaximal, characteristic, complemented
4#15689461C211yesmaximal, characteristic, complemented
5#15689458C211yesmaximal, characteristic, complemented
6#15689456C211yesmaximal, characteristic, complemented
7#15689430C211yesmaximal, characteristic, complemented
8#15689427C211yesmaximal, characteristic, complemented
9#15689379C211yesmaximal, characteristic, complemented
10#15689379C211yesmaximal, characteristic, complemented
11C4×#10625337C211yesmaximal, characteristic, complemented
12#15689201C211yesmaximal, characteristic
13#15689166C211yesmaximal, characteristic, complemented
14#15689163C211yesmaximal, characteristic, complemented
15C47×#552C211yesmaximal, characteristic
16C2×#10625337C2211yescharacteristic
17C2×#10625329C2211yescharacteristic
18C2×#10625329C2211yescharacteristic
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
47C4×C47⋊C8C2211yescharacteristic
48#126×C47—21no—
49#125×C47—21no—
50#125×C47C2211yescharacteristic
51#123×C47—21no—
52C22⋊Q8×C47C2211yescharacteristic
53C22⋊Q8×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic
56#117×C47—21no—
57#117×C47C2211yescharacteristic
58C2×C4⋊C4×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47D411yescharacteristic
61C22×C4×C47—21no—
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×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47D411yescharacteristic
73C4⋊C4×C47C2311yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C22⋊C4×C47—21no—
77C22⋊C4×C47—21no—
78C22⋊C4×C47—21no—
79C22⋊C4×C47D411yescharacteristic
80C22⋊C4×C47D411yescharacteristic
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—
100#10625329—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—
109D4×C47—41no—
110C2×C4×C47—21no—
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—42no—
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#3352—471nomaximal, Sylow
157C2×C47—41no—
158C2×C47—41no—
159C2×C47#54711yescharacteristic
160C2×C47#57511yescharacteristic
161C2×C47#57811yescharacteristic
162#552—471no—
163#552D4711yescharacteristic
164#499—471no—
165#485—471no—
166#485—471no—
167#484—471no—
168#484—471no—
169#479—471no—
170#479—471no—
171#470—471no—
172#470—471no—
173C4×Q16—471no—
174#436—471no—
175#428—471no—
176#428—471no—
177C47#335211yescharacteristic, complemented, Sylow
178C2×Q16—471no—
179C2×M16—471no—
180C2×M16—471no—
181#126—21no—
182#126—941no—
183#125—21no—
184#125—471no—
185#125—941no—
186#125C2×D4711yescharacteristic
187#123—21no—
188#123—941no—
189C22⋊Q8—471no—
190C22⋊Q8—471no—
191C22⋊Q8C2×D4711yescharacteristic
192C22⋊Q8C2×D4711yescharacteristic
193C4×Q8—471no—
194C4×Q8C2×D4711yescharacteristic
195C4×D4C2×D4711yescharacteristic
196#117—21no—
197#117—471no—
198#117—941no—
199#117C2×D4711yescharacteristic
200C2×C4⋊C4—471no—
201C2×C4⋊C4C2×D4711yescharacteristic
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—
220C4×C8—471no—
221C2×Q8—471no—
222C2×Q8C22×D4711yescharacteristic
223C2×D4C22⋊D4711yescharacteristic
224C22×C4—21no—
225C22×C4—941no—
226C22×C4C22×D4711yescharacteristic
227C22×C4C22×D4711yescharacteristic
228Q16—942no—
229M16—942no—
230M16—942no—
231C2×C8—471no—
232C2×C8—471no—
233C2×C8—471no—
234C2×C8—471no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—471no—
242C4⋊C4—471no—
243C4⋊C4—471no—
244C4⋊C4—941no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4C22⋊D4711yescharacteristic
251C4⋊C4C22×D4711yescharacteristic
252C4⋊C4C22×D4711yescharacteristic
253C4⋊C4C22×D4711yescharacteristic
254C22⋊C4—21no—
255C22⋊C4—21no—
256C22⋊C4—21no—
257C22⋊C4—941no—
258C22⋊C4—941no—
259C22⋊C4—941no—
260C22⋊C4C22⋊D4711yescharacteristic
261C22⋊C4C22⋊D4711yescharacteristic
262C42—21no—
263C42—21no—
264C42—941no—
265C42—941no—
266C42C22×D4711yescharacteristic
267C23C2×C22⋊D4711yescharacteristic
268C23C2×C22⋊D4711yescharacteristic
269Q8—21no—
270Q8—21no—
271Q8—941no—
272Q8—941no—
273D4—41no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
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×#552C2
socleC22×C47C22×D4
hypercenter#552D47
hypocenterC47#3352
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #15689522C2semidirect
3. #15689464C2semidirect
4. #15689461C2semidirect
5. #15689458C2semidirect
6. #15689456C2semidirect
7. #15689430C2semidirect
8. #15689427C2semidirect
9. #15689379C2semidirect
10. #15689379C2semidirect
11. C4×#10625337C2semidirect
13. #15689166C2semidirect
14. #15689163C2semidirect
177. C47#3352semidirect