Finite Group Databasebeta

← #20256327

Subgroups — #20256327

Order 6016.

334 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689833C211yesmaximal, characteristic
2#15689533C211yesmaximal, characteristic, complemented
3#15689529C211yesmaximal, characteristic, complemented
4#15689522C211yesmaximal, characteristic, complemented
5#15689430C211yesmaximal, characteristic, complemented
6#15689430C211yesmaximal, characteristic, complemented
7#15689420C211yesmaximal, characteristic
8#15689420C211yesmaximal, characteristic
9#15689410C211yesmaximal, characteristic
10#15689408C211yesmaximal, characteristic, complemented
11#15689254C211yesmaximal, characteristic, complemented
12#15689221C211yesmaximal, characteristic
13#15689221C211yesmaximal, characteristic
14C4×#10625336C211yesmaximal, characteristic
15C47×#557C211yesmaximal, characteristic, complemented
16C2×#10625336C2211yescharacteristic
17#13094024C2211yescharacteristic
18#13094016C2211yescharacteristic
19#13094016C2211yescharacteristic
20#13094002—21no—
21#13094002—21no—
22#13094000—21no—
23C4×D188C2211yescharacteristic
24C4×D188C2211yescharacteristic
25C4×D188C2211yescharacteristic
26C4⋊C4×D47—21no—
27#13093957C2211yescharacteristic
28#13093957C2211yescharacteristic
29#13093957C2211yescharacteristic
30#13093957C2211yescharacteristic
31#13093955C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34#13093955C2211yescharacteristic
35#13093955C2211yescharacteristic
36C4⋊(C47⋊C8)C2211yescharacteristic
37C4⋊(C47⋊C8)C2211yescharacteristic
38C4⋊(C47⋊C8)C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093948C2211yescharacteristic
41#13093948C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44#13093944C2211yescharacteristic
45#13093935C2211yescharacteristic
46#13093935C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48C4⋊Q8×C47—21no—
49C4⋊Q8×C47C2211yescharacteristic
50#125×C47—21no—
51#125×C47—21no—
52#125×C47C2211yescharacteristic
53#125×C47C2211yescharacteristic
54C4×Q8×C47—21no—
55C4×Q8×C47C2211yescharacteristic
56C4×Q8×C47C2211yescharacteristic
57C4×Q8×C47C2211yescharacteristic
58C4×Q8×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47D411yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C2×D188C2311yescharacteristic
63C2×C4×D47—21no—
64C2×C4×D47—21no—
65C2×C4×D47—21no—
66C2×Dic94—21no—
67C4⋊C4×C47—21no—
68C4⋊C4×C47—21no—
69C4⋊C4×C47—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47D411yescharacteristic
76C4⋊C4×C47D411yescharacteristic
77C4⋊C4×C47D411yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C42×C47—21no—
82C42×C47—21no—
83C42×C47—21no—
84C42×C47C2311yescharacteristic
85C42×C47C2311yescharacteristic
86C42×C47C2311yescharacteristic
87#10625336Q814yescomplemented
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91C4⋊Dic47—21no—
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99C2×C47⋊C8C2311yescharacteristic
100C2×C47⋊C8C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C22×D47—21no—
104Q8×C47—21no—
105Q8×C47—41no—
106Q8×C47—42no—
107Q8×C47C2×Q812yes—
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×C47C2×D411yescharacteristic
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2411yescharacteristic
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122D188—21no—
123D188C2×Q812yes—
124C4×D47—42no—
125C4×D47—81no—
126C4×D47—81no—
127Dic94—81no—
128C47⋊C8—21no—
129C47⋊C8—21no—
130C47⋊C8—21no—
131C47⋊C8C2×Q812yes—
132C22×C47C22×D411yescharacteristic
133C2×D47—22no—
134C2×D47—41no—
135C2×D47—41no—
136C4×C47—22no—
137C4×C47—21no—
138C4×C47—21no—
139C4×C47—21no—
140C4×C47—21no—
141C4×C47—21no—
142C4×C47—21no—
143C4×C47—41no—
144C4×C47—41no—
145C4×C47—41no—
146C4×C47C22×Q811yescharacteristic
147C4×C472−1+411yescharacteristic
148Dic47—41no—
149Dic47—41no—
150Dic47—41no—
151#3388—471nomaximal, Sylow
152C2×C47D4×Q811yescharacteristic
153C2×C47#57511yescharacteristic
154C2×C47#57711yescharacteristic
155D47—42no—
156#557D4711yescharacteristic, complemented
157#554—471no—
158#501—471no—
159#501—471no—
160#499—471no—
161#479—471no—
162#479—471no—
163#478—471no—
164#478—471no—
165#476—471no—
166#475—471no—
167#446—471no—
168#440—471no—
169#440—471no—
170C4×SD16—471no—
171C47#338811yescharacteristic, complemented, Sylow
172C2×SD16—471no—
173C4⋊Q8—21no—
174C4⋊Q8—471no—
175C4⋊Q8C2×D4711yescharacteristic
176#125—21no—
177#125—21no—
178#125—471no—
179#125—471no—
180#125C2×D4711yescharacteristic
181#125C2×D4711yescharacteristic
182C22⋊Q8—941no—
183C22⋊Q8—941no—
184C22⋊Q8—941no—
185C4×Q8—21no—
186C4×Q8C2×D4711yescharacteristic
187C4×Q8C2×D4711yescharacteristic
188C4×Q8C2×D4711yescharacteristic
189C4×Q8C2×D4711yescharacteristic
190C4×D4—471no—
191C4×D4—471no—
192C4×D4—471no—
193C2×C4⋊C4—941no—
194#107—471no—
195#107—471no—
196#107—471no—
197#107—471no—
198#106—471no—
199#106—471no—
200#106—471no—
201#106—471no—
202#106—471no—
203C4⋊C8—471no—
204C4⋊C8—471no—
205C4⋊C8—471no—
206#103—471no—
207#103—471no—
208#103—471no—
209#102—471no—
210#102—471no—
211#102—471no—
212#97—471no—
213#97—471no—
214C4×C8—471no—
215C2×Q8—21no—
216C2×Q8—941no—
217C2×Q8C22⋊D4711yescharacteristic
218C2×Q8C22×D4711yescharacteristic
219C2×D4—471no—
220C22×C4—941no—
221C22×C4—941no—
222C22×C4—941no—
223SD16—474no—
224C2×C8—471no—
225C2×C8—471no—
226C2×C8—471no—
227C2×C8—471no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—471no—
237C4⋊C4—471no—
238C4⋊C4—471no—
239C4⋊C4—941no—
240C4⋊C4—941no—
241C4⋊C4—941no—
242C4⋊C4—941no—
243C4⋊C4—941no—
244C4⋊C4C22⋊D4711yescharacteristic
245C4⋊C4C22⋊D4711yescharacteristic
246C4⋊C4C22⋊D4711yescharacteristic
247C4⋊C4C22×D4711yescharacteristic
248C4⋊C4C22×D4711yescharacteristic
249C4⋊C4C22×D4711yescharacteristic
250C22⋊C4—941no—
251C22⋊C4—941no—
252C22⋊C4—941no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42C22×D4711yescharacteristic
257C42C22×D4711yescharacteristic
258C42C22×D4711yescharacteristic
259C23—941no—
260Q8—21no—
261Q8—41no—
262Q8—42no—
263Q8—3761no—
264Q8Q8×D4712yes—
265D4—472no—
266D4—941no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—941no—
272C2×C4—941no—
273C2×C4—941no—
274C2×C4—3761no—
275C2×C4—3761no—
276C2×C4—1882no—
277C2×C4C2×C22⋊D4711yescharacteristic
278C2×C4C2×C22⋊D4711yescharacteristic
279C2×C4C2×C22⋊D4711yescharacteristic
280C2×C4C2×C22⋊D4711yescharacteristic
281C2×C4C2×C22⋊D4711yescharacteristic
282C2×C4C2×C22⋊D4711yescharacteristic
283C2×C4C23×D4711yescharacteristic
284C8—472no—
285C8—941no—
286C8—941no—
287C8—941no—
288C22—942no—
289C22—1881no—
290C22—1881no—
291C22C22×C22⋊D4711yescharacteristic
292C4—22no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—41no—
300C4—41no—
301C4—41no—
302C4—1881no—
303C4—1881no—
304C4—1881no—
305C4C2×Q8×D4711yescharacteristic
306C4#1309407211yescharacteristic
307C2—1882no—
308C2Q8×C22⋊D4711yescharacteristic
309C2#1568992111yescharacteristic
310C2#1568993111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#557C2
socleC22×C47C22×D4
hypercenter#557D47
hypocenterC47#3388
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
2. #15689533C2semidirect
3. #15689529C2semidirect
4. #15689522C2semidirect
5. #15689430C2semidirect
6. #15689430C2semidirect
10. #15689408C2semidirect
11. #15689254C2semidirect
15. C47×#557C2semidirect
87. #10625336Q8semidirect
156. #557D47semidirect
171. C47#3388semidirect