Finite Group Databasebeta

← #20253174

Subgroups — #20253174

Order 6016.

388 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689676C211yesmaximal, characteristic, complemented
2#15689591C211yesmaximal, characteristic
3#15689433C211yesmaximal, characteristic, complemented
4#15689429C211yesmaximal, characteristic, complemented
5#15689426C211yesmaximal, characteristic, complemented
6#15689422C211yesmaximal, characteristic, complemented
7#15689417C211yesmaximal, characteristic, complemented
8#15689412C211yesmaximal, characteristic, complemented
9#15689407C211yesmaximal, characteristic, complemented
10#15689402C211yesmaximal, characteristic, complemented
11#15689159C211yesmaximal, characteristic, complemented
12C2×Dic47⋊C8C211yesmaximal, characteristic, complemented
13#15689120C211yesmaximal, characteristic
14#15689117C211yesmaximal, characteristic
15C47×#427C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×C47⋊C8C2211yescharacteristic
18#13094023C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094015C2211yescharacteristic
21#13094015C2211yescharacteristic
22#13094001—21no—
23#13094001—21no—
24C4×Dic94—21no—
25C4×Dic94—21no—
26#13093989C2211yescharacteristic
27#13093989C2211yescharacteristic
28#13093986C2211yescharacteristic
29#13093986C2211yescharacteristic
30(C22⋊D47)⋊C4—21no—
31(C22⋊D47)⋊C4—21no—
32#13093983C2211yescharacteristic
33#13093981—21no—
34C2×C4×Dic47C2211yescharacteristic
35C42×D47—21no—
36#13093957C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093955C2211yescharacteristic
39#13093955C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093944C2211yescharacteristic
51#13093944C2211yescharacteristic
52C22×C8×C47C2211yescharacteristic
53#117×C47C2211yescharacteristic
54#117×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic
57#106×C47C2211yescharacteristic
58#106×C47C2211yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C2×C22⋊D47—21no—
61C22×Dic47D411yescharacteristic
62C22×Dic47D411yescharacteristic
63#10625350—22no—
64#10625350Q814yescomplemented
65C2×D188C2311yescharacteristic
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×Dic94—21no—
70C2×Dic94—21no—
71C2×Dic94C2311yescharacteristic
72C2×C8×C47—22no—
73C2×C8×C47C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C42×C47—21no—
82C42×C47—21no—
83C22⋊Dic47—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47C2311yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90Dic47⋊C4—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96C4×Dic47—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47D411yescharacteristic
100C4×Dic47D411yescharacteristic
101C4×Dic47C2311yescharacteristic
102C4×Dic47C2311yescharacteristic
103C2×C47⋊C8—22no—
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C23×C47C2×D411yescharacteristic
107C22×D47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47C2×D411yescharacteristic
113C2×C4×C47C2×Q812yes—
114C2×C4×C47#4112yes—
115C2×C4×C47C2411yescharacteristic
116C22⋊D47—24no—
117C2×Dic47—21no—
118C2×Dic47—22no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—41no—
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124C2×Dic47C2×D411yescharacteristic
125C2×Dic47C2×D411yescharacteristic
126D188—21no—
127D188C2×Q812yes—
128C4×D47—24no—
129C4×D47—42no—
130C4×D47—42no—
131Dic94—21no—
132Dic94—42no—
133Dic94—42no—
134Dic94C2×Q812yes—
135C8×C47—21no—
136C8×C47—21no—
137C47⋊C8—21no—
138C47⋊C8—21no—
139C22×C47—21no—
140C22×C47—21no—
141C22×C47C22⋊Q812yes—
142C22×C47C22×D411yescharacteristic
143C2×D47—22no—
144C2×D47—41no—
145C2×D47—41no—
146C4×C47—41no—
147C4×C47—41no—
148C4×C47—41no—
149C4×C47—41no—
150C4×C47C22⋊Q812yes—
151C4×C47C22×Q811yescharacteristic
152C4×C47C2×#4111yescharacteristic
153Dic47—22no—
154Dic47—21no—
155Dic47—21no—
156Dic47—21no—
157Dic47—41no—
158Dic47—41no—
159Dic47#13512yes—
160#3076—471nomaximal, Sylow
161C2×C47—22no—
162C2×C47C2×C22⋊Q811yescharacteristic
163C2×C47C2×#13511yescharacteristic
164C2×C47#57511yescharacteristic
165D47—42no—
166#533—471no—
167C4×#41—471no—
168#479—471no—
169#479—471no—
170#478—471no—
171#478—471no—
172#477—471no—
173#476—471no—
174#475—471no—
175#474—471no—
176#427—471no—
177#427D4711yescharacteristic, complemented
178C2×C4⋊C8—471no—
179#416—471no—
180#416—471no—
181C47#307611yescharacteristic, complemented, Sylow
182C2×#41—471no—
183C22×C8—471no—
184C22×C8C2×D4711yescharacteristic
185C4⋊Q8—471no—
186C4⋊Q8—471no—
187#125—471no—
188#125—471no—
189C22⋊Q8—941no—
190C22⋊Q8—941no—
191C4×Q8—471no—
192C4×Q8—471no—
193C4×Q8—941no—
194C4×Q8—941no—
195C4×D4—471no—
196C4×D4—471no—
197C4×D4—941no—
198C4×D4—941no—
199#117—471no—
200#117—941no—
201#117C2×D4711yescharacteristic
202#117C2×D4711yescharacteristic
203C2×C42—471no—
204C2×C42—941no—
205#107—471no—
206#107—471no—
207#107C2×D4711yescharacteristic
208#107C2×D4711yescharacteristic
209#106—471no—
210#106—471no—
211#106C2×D4711yescharacteristic
212#106C2×D4711yescharacteristic
213C4⋊C8—471no—
214C4⋊C8—471no—
215C4⋊C8—471no—
216C4⋊C8—471no—
217#103—471no—
218#103—471no—
219#103—471no—
220#103—471no—
221#102—471no—
222#102—471no—
223#102—471no—
224#102—471no—
225#41—474no—
226#41—942no—
227C2×Q8—471no—
228C2×Q8—941no—
229C2×Q8—941no—
230C2×D4—471no—
231C2×D4—941no—
232C22×C4—471no—
233C22×C4—471no—
234C22×C4—941no—
235C22×C4—941no—
236C22×C4—941no—
237C22×C4C22×D4711yescharacteristic
238C2×C8—22no—
239C2×C8—471no—
240C2×C8—471no—
241C2×C8—942no—
242C2×C8C22×D4711yescharacteristic
243C2×C8C22×D4711yescharacteristic
244C4⋊C4—471no—
245C4⋊C4—471no—
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⋊C4C22×D4711yescharacteristic
255C4⋊C4C22×D4711yescharacteristic
256C4⋊C4C22×D4711yescharacteristic
257C4⋊C4C22×D4711yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C42—21no—
264C42—21no—
265C42—471no—
266C42—471no—
267C42—471no—
268C42—471no—
269C42—941no—
270C42—941no—
271C42—941no—
272C23—941no—
273C23D4×D4711yescharacteristic
274Q8—472no—
275Q8—941no—
276Q8—1882no—
277Q8—1882no—
278D4—472no—
279D4—944no—
280D4—941no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—471no—
286C2×C4—471no—
287C2×C4—471no—
288C2×C4—471no—
289C2×C4—942no—
290C2×C4—941no—
291C2×C4—944no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—1882no—
295C2×C4—1882no—
296C2×C4—1881no—
297C2×C4#1062535012yes—
298C2×C4D4×D4711yescharacteristic
299C2×C4Q8×D4712yes—
300C2×C4C23×D4711yescharacteristic
301C8—21no—
302C8—21no—
303C8—941no—
304C8—941no—
305C22—21no—
306C22—21no—
307C22—942no—
308C22—1881no—
309C22—1881no—
310C22#1309400212yes—
311C22C2×D4×D4711yescharacteristic
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—472no—
317C4—942no—
318C4—941no—
319C4—941no—
320C4—941no—
321C4—1881no—
322C4—1881no—
323C4#1309400212yes—
324C4C2×Q8×D4711yescharacteristic
325C4C2×#1062535011yescharacteristic
326C2—22no—
327C2—1882no—
328C2C2×#1309400211yescharacteristic
329C2#135×D4711yescharacteristic
330C2#1568992011yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#427C2
socleC22×C47C22×D4
hypercenter#427D47
hypocenterC47#3076
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
1. #15689676C2semidirect
3. #15689433C2semidirect
4. #15689429C2semidirect
5. #15689426C2semidirect
6. #15689422C2semidirect
7. #15689417C2semidirect
8. #15689412C2semidirect
9. #15689407C2semidirect
10. #15689402C2semidirect
11. #15689159C2semidirect
12. C2×Dic47⋊C8C2semidirect
15. C47×#427C2semidirect
64. #10625350Q8semidirect
177. #427D47semidirect
181. C47#3076semidirect