Finite Group Databasebeta

← #20256258

Subgroups — #20256258

Order 6016.

338 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#15689850C211yesmaximal, characteristic, complemented
2#15689832C211yesmaximal, characteristic
3#15689524C211yesmaximal, characteristic, complemented
4#15689522C211yesmaximal, characteristic, complemented
5#15689520C211yesmaximal, characteristic, complemented
6#15689433C211yesmaximal, characteristic, complemented
7#15689431C211yesmaximal, characteristic, complemented
8#15689425C211yesmaximal, characteristic
9#15689417C211yesmaximal, characteristic, complemented
10#15689401C211yesmaximal, characteristic
11#15689247C211yesmaximal, characteristic, complemented
12#15689214C211yesmaximal, characteristic
13#15689214C211yesmaximal, characteristic
14C4×#10625335C211yesmaximal, characteristic
15C47×#478C211yesmaximal, characteristic
16C2×#10625335C2211yescharacteristic
17#13094023—21no—
18#13094023C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094016C2211yescharacteristic
21#13094015C2211yescharacteristic
22#13094015C2211yescharacteristic
23#13094014—21no—
24#13094014—21no—
25#13094003—21no—
26#13094001—21no—
27#13094001—21no—
28C4×Dic94C2211yescharacteristic
29C4×Dic94C2211yescharacteristic
30#13093989—21no—
31#13093989C2211yescharacteristic
32#13093989C2211yescharacteristic
33D4×Dic47C2211yescharacteristic
34D4×Dic47C2211yescharacteristic
35C2×Dic47⋊C4—21no—
36#13093958C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41#13093955C2211yescharacteristic
42#13093955C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093945C2211yescharacteristic
49C4×C47⋊C8C2211yescharacteristic
50C8×Dic47C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52#125×C47C2211yescharacteristic
53C4×D4×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×D4×C47C2311yescharacteristic
60C22×C4×C47—21no—
61C22×Dic47—21no—
62C22×Dic47—21no—
63C2×Dic94—21no—
64C2×Dic94—21no—
65C2×Dic94D411yescharacteristic
66C2×Dic94C2311yescharacteristic
67C2×C8×C47C2311yescharacteristic
68C2×C8×C47C2311yescharacteristic
69C4⋊C4×C47—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47C2311yescharacteristic
72C4⋊C4×C47C2311yescharacteristic
73C4⋊C4×C47C2311yescharacteristic
74C22⋊C4×C47—21no—
75C42×C47C2311yescharacteristic
76C22⋊Dic47—21no—
77C22⋊Dic47—21no—
78#10625335Q814yescomplemented
79C4⋊Dic47—21no—
80C4⋊Dic47—21no—
81C4⋊Dic47D411yescharacteristic
82C4⋊Dic47C2311yescharacteristic
83C4⋊Dic47C2311yescharacteristic
84C4⋊Dic47C2311yescharacteristic
85Dic47⋊C4—21no—
86Dic47⋊C4—21no—
87Dic47⋊C4—21no—
88Dic47⋊C4—21no—
89Dic47⋊C4—21no—
90Dic47⋊C4—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4D411yescharacteristic
95Dic47⋊C4D411yescharacteristic
96C4×Dic47—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47C2311yescharacteristic
100C4×Dic47C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C23×C47—21no—
104D4×C47—21no—
105D4×C47C2×Q812yes—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—81no—
110C2×C4×C47C2×D411yescharacteristic
111C2×C4×C47C2×D411yescharacteristic
112C2×C4×C47C2411yescharacteristic
113C2×Dic47—21no—
114C2×Dic47—21no—
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—42no—
118C2×Dic47—81no—
119C2×Dic47C2×D411yescharacteristic
120C2×Dic47C2×D411yescharacteristic
121C2×Dic47C2×D411yescharacteristic
122C2×Dic47C2×D411yescharacteristic
123Dic94—21no—
124Dic94—22no—
125Dic94—42no—
126Dic94—81no—
127Dic94C2×Q812yes—
128C8×C47—21no—
129C8×C47—21no—
130C47⋊C8—21no—
131C47⋊C8C2×Q812yes—
132C22×C47—22no—
133C22×C47—41no—
134C22×C47—41no—
135C22×C47C22×D411yescharacteristic
136C4×C47—21no—
137C4×C47—21no—
138C4×C47—41no—
139C4×C47—41no—
140C4×C47—41no—
141C4×C47C22×Q811yescharacteristic
142C4×C472−1+411yescharacteristic
143Dic47—22no—
144Dic47—21no—
145Dic47—21no—
146Dic47—21no—
147Dic47—41no—
148Dic47—41no—
149Dic47—41no—
150Dic47#13512yes—
151#3381—471nomaximal, Sylow
152C2×C47—42no—
153C2×C47D4×Q811yescharacteristic
154C2×C47C2×#13511yescharacteristic
155C2×C47#57711yescharacteristic
156#557—471no—
157#554—471no—
158#499—471no—
159#499—471no—
160#498—471no—
161#479—471no—
162#479—471no—
163#478—471no—
164#478D4711yescharacteristic
165#477—471no—
166#474—471no—
167C8×Q8—471no—
168C4×SD16—471no—
169C4×SD16—471no—
170C4×SD16—471no—
171C47#338111yescharacteristic, complemented, Sylow
172C2×SD16—471no—
173C4⋊Q8—471no—
174C4⋊Q8—471no—
175C4⋊Q8—941no—
176#125—471no—
177#125—471no—
178#125—471no—
179#125—941no—
180#125—941no—
181#125C2×D4711yescharacteristic
182C22⋊Q8—941no—
183C22⋊Q8—941no—
184C22⋊Q8—941no—
185C4×Q8—471no—
186C4×Q8—471no—
187C4×Q8—471no—
188C4×Q8—471no—
189C4×Q8—941no—
190C4×D4—471no—
191C4×D4—471no—
192C4×D4C2×D4711yescharacteristic
193C2×C4⋊C4—941no—
194#107—471no—
195#107—471no—
196#107—471no—
197#107C2×D4711yescharacteristic
198#106—471no—
199#106—471no—
200#106—471no—
201#106—471no—
202#106C2×D4711yescharacteristic
203C4⋊C8—471no—
204C4⋊C8—471no—
205C4⋊C8C2×D4711yescharacteristic
206#103—471no—
207#103—471no—
208#103—471no—
209#102—471no—
210#102C2×D4711yescharacteristic
211#102C2×D4711yescharacteristic
212C4×C8—471no—
213C4×C8—471no—
214C4×C8—471no—
215C2×Q8—471no—
216C2×Q8—471no—
217C2×Q8—941no—
218C2×Q8—941no—
219C2×D4C22×D4711yescharacteristic
220C22×C4—21no—
221C22×C4—941no—
222C22×C4—941no—
223SD16—474no—
224C2×C8—471no—
225C2×C8—471no—
226C2×C8C22×D4711yescharacteristic
227C2×C8C22×D4711yescharacteristic
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—471no—
231C4⋊C4—471no—
232C4⋊C4—471no—
233C4⋊C4—471no—
234C4⋊C4—471no—
235C4⋊C4—471no—
236C4⋊C4—941no—
237C4⋊C4—941no—
238C4⋊C4—941no—
239C4⋊C4—941no—
240C4⋊C4—941no—
241C4⋊C4—941no—
242C4⋊C4—941no—
243C4⋊C4—941no—
244C4⋊C4—941no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4C22×D4711yescharacteristic
248C4⋊C4C22×D4711yescharacteristic
249C4⋊C4C22×D4711yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—941no—
252C22⋊C4—941no—
253C42—471no—
254C42—471no—
255C42—941no—
256C42—941no—
257C42—941no—
258C42C22×D4711yescharacteristic
259C23—21no—
260Q8—472no—
261Q8—942no—
262Q8—941no—
263Q8—3761no—
264Q8—1882no—
265D4—21no—
266D4Q8×D4712yes—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—81no—
271C2×C4—471no—
272C2×C4—471no—
273C2×C4—471no—
274C2×C4—471no—
275C2×C4—941no—
276C2×C4—941no—
277C2×C4—941no—
278C2×C4—941no—
279C2×C4—3761no—
280C2×C4—1882no—
281C2×C4D4×D4711yescharacteristic
282C2×C4D4×D4711yescharacteristic
283C2×C4C23×D4711yescharacteristic
284C8—21no—
285C8—21no—
286C8—472no—
287C8—941no—
288C22—22no—
289C22—41no—
290C22—41no—
291C22C2×D4×D4711yescharacteristic
292C4—21no—
293C4—21no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—472no—
298C4—942no—
299C4—941no—
300C4—941no—
301C4—941no—
302C4—1881no—
303C4—1881no—
304C4—1881no—
305C4C2×Q8×D4711yescharacteristic
306C4#1309407111yescharacteristic
307C2—42no—
308C2#1568978611yescharacteristic
309C2#135×D4711yescharacteristic
310C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#478C2
socleC22×C47C22×D4
hypercenter#478D47
hypocenterC47#3381
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #15689850C2semidirect
3. #15689524C2semidirect
4. #15689522C2semidirect
5. #15689520C2semidirect
6. #15689433C2semidirect
7. #15689431C2semidirect
9. #15689417C2semidirect
11. #15689247C2semidirect
78. #10625335Q8semidirect
171. C47#3381semidirect