Finite Group Databasebeta

← #20255741

Subgroups — #20255741

Order 6016.

388 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689828C211yesmaximal, characteristic, complemented
2#15689774C211yesmaximal, characteristic
3#15689520C211yesmaximal, characteristic, complemented
4#15689455C211yesmaximal, characteristic, complemented
5#15689453C211yesmaximal, characteristic, complemented
6#15689443C211yesmaximal, characteristic, complemented
7#15689441C211yesmaximal, characteristic, complemented
8#15689412C211yesmaximal, characteristic, complemented
9#15689407C211yesmaximal, characteristic, complemented
10#15689353C211yesmaximal, characteristic, complemented
11#15689352C211yesmaximal, characteristic, complemented
12#15689210C211yesmaximal, characteristic, complemented
13C8×C22⋊D47C211yesmaximal, characteristic, complemented
14#106×D47C211yesmaximal, characteristic, complemented
15C2×#106×C47C211yesmaximal, characteristic, complemented
16C2×#10625350—21no—
17C2×#10625325C2211yescharacteristic
18C2×C8×D47C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094014—21no—
22#13094009—21no—
23#13094007—21no—
24#13094004C2211yescharacteristic
25#13094003—21no—
26#13094003C2211yescharacteristic
27#13094002—21no—
28#13094002—21no—
29#13093999C2211yescharacteristic
30#13093998C2211yescharacteristic
31#13093989C2211yescharacteristic
32#13093986C2211yescharacteristic
33C4×C22⋊D47—21no—
34C4×C22⋊D47C2211yescharacteristic
35C4⋊C4×D47C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic
37#13093956C2211yescharacteristic
38#13093955C2211yescharacteristic
39#13093955C2211yescharacteristic
40#13093955C2211yescharacteristic
41#13093955C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C22×C8×C47C2211yescharacteristic
53C2×C4⋊C4×C47C2211yescharacteristic
54C2×C4⋊C4×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#106×C47C2211yescharacteristic
58#106×C47C2211yescharacteristic
59C22×C4×C47—21no—
60C22×C4×C47—21no—
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C2×C22⋊D47D411yescharacteristic
64#10625350—44no—
65C2×D188—21no—
66C2×D188C2311yescharacteristic
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47C2311yescharacteristic
71C2×Dic94—21no—
72C2×Dic94—21no—
73C2×Dic94C2311yescharacteristic
74C2×C8×C47—22no—
75C2×C8×C47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C4⋊C4×C47—21no—
78C4⋊C4×C47—21no—
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊Dic47—21no—
84C22⋊Dic47D411yescharacteristic
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4D411yescharacteristic
90C4⋊Dic47—21no—
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4D411yescharacteristic
100C4×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104#10625325—22no—
105C8×D47—22no—
106C23×C47C2×D411yescharacteristic
107C22×D47—21no—
108C22×D47C2×D411yescharacteristic
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—42no—
116C2×C4×C47—81no—
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2411yescharacteristic
119C22⋊D47—42no—
120C22⋊D47SD1614yescomplemented
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47C2×D411yescharacteristic
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127D188—21no—
128D188—21no—
129D188—42no—
130C4×D47—21no—
131C4×D47—21no—
132C4×D47—42no—
133C4×D47—42no—
134C4×D47—81no—
135Dic94—21no—
136Dic94—21no—
137Dic94—42no—
138Dic94—81no—
139C8×C47—21no—
140C8×C47#4112yescomplemented
141C47⋊C8—21no—
142C47⋊C8—21no—
143C22×C47—21no—
144C22×C47—21no—
145C22×C47C2×SD1612yes—
146C22×C47C22×D411yescharacteristic
147C2×D47—21no—
148C2×D47—21no—
149C2×D47—41no—
150C2×D47—41no—
151C2×D47—41no—
152C2×D47C2×SD1612yes—
153C4×C47—21no—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47C2×#4111yescharacteristic
159C4×C472−1+411yescharacteristic
160Dic47—21no—
161Dic47—21no—
162Dic47—41no—
163Dic47—41no—
164Dic47—41no—
165Dic47C2×SD1612yes—
166#3335—471nomaximal, Sylow
167C2×C47—22no—
168C2×C47#54711yescharacteristic
169C2×C47C22×SD1611yescharacteristic
170C2×C47#57711yescharacteristic
171D47—22no—
172D47—81no—
173#554—471no—
174#547—471no—
175#498—471no—
176#483—471no—
177#483—471no—
178#481—471no—
179#481—471no—
180#476—471no—
181#475—471no—
182#465—471no—
183#465—471no—
184C4×SD16—471no—
185C8×D4—471no—
186C2×#106—471no—
187C2×#106D4711yescharacteristic, complemented
188C47#333511yescharacteristic, complemented, Sylow
189C2×#41—941no—
190C2×SD16—471no—
191C22×C8—471no—
192C22×C8C2×D4711yescharacteristic
193C4⋊Q8—471no—
194C4⋊Q8—471no—
195#125—941no—
196#123—941no—
197#123—941no—
198C22⋊Q8—471no—
199C22⋊Q8—471no—
200C22⋊Q8—941no—
201C22⋊Q8—941no—
202C22⋊Q8—941no—
203#121—471no—
204#121—471no—
205C4×Q8—471no—
206C4×D4—471no—
207C4×D4—471no—
208C4×D4—941no—
209C2×C4⋊C4—471no—
210C2×C4⋊C4—471no—
211C2×C4⋊C4C2×D4711yescharacteristic
212C2×C4⋊C4C2×D4711yescharacteristic
213#106—471no—
214#106—471no—
215#106—471no—
216#106—471no—
217#106—471no—
218#106C2×D4711yescharacteristic
219#106C2×D4711yescharacteristic
220#106C2×D4711yescharacteristic
221#106C2×D4711yescharacteristic
222C4⋊C8—471no—
223#103—471no—
224#103—471no—
225#103—471no—
226#102—471no—
227#102—471no—
228#102—471no—
229C22⋊C8—471no—
230C22⋊C8—471no—
231C4×C8—471no—
232#41—1884no—
233C2×Q8—471no—
234C2×Q8—941no—
235C2×Q8—941no—
236C2×D4—471no—
237C2×D4—471no—
238C2×D4—941no—
239C2×D4—941no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—471no—
243C22×C4—941no—
244C22×C4—941no—
245C22×C4—941no—
246C22×C4C22×D4711yescharacteristic
247SD16—942no—
248C2×C8—22no—
249C2×C8—471no—
250C2×C8—471no—
251C2×C8—942no—
252C2×C8C22×D4711yescharacteristic
253C2×C8C22×D4711yescharacteristic
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—471no—
257C4⋊C4—471no—
258C4⋊C4—471no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4C22×D4711yescharacteristic
267C4⋊C4C22×D4711yescharacteristic
268C4⋊C4C22×D4711yescharacteristic
269C4⋊C4C22×D4711yescharacteristic
270C22⋊C4—471no—
271C22⋊C4—471no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
277C42—471no—
278C42—941no—
279C23—471no—
280C23—941no—
281C23D4×D4711yescharacteristic
282Q8—941no—
283Q8—941no—
284Q8—3761no—
285Q8—1882no—
286D4—474no—
287D4—941no—
288D4—941no—
289D4—1882no—
290D4—1882no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—81no—
299C2×C4—471no—
300C2×C4—471no—
301C2×C4—471no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—3761no—
308C2×C4—1882no—
309C2×C4—1882no—
310C2×C4D4×D4711yescharacteristic
311C2×C4C23×D4711yescharacteristic
312C8—21no—
313C8—941no—
314C8—941no—
315C8#1062535012yescomplemented
316C22—21no—
317C22—21no—
318C22—472no—
319C22—941no—
320C22—941no—
321C22—1881no—
322C22—1881no—
323C22—1881no—
324C22SD16×D4712yes—
325C22C2×D4×D4711yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—472no—
332C4—941no—
333C4—941no—
334C4—1881no—
335C4—1881no—
336C4—1881no—
337C4C2×#1062535011yescharacteristic
338C4#1309407211yescharacteristic
339C2—22no—
340C2—942no—
341C2—3761no—
342C2#1568977411yescharacteristic
343C2C2×SD16×D4711yescharacteristic
344C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#106×C47C2
socleC22×C47C22×D4
hypercenterC2×#106D47
hypocenterC47#3335
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
1. #15689828C2semidirect
3. #15689520C2semidirect
4. #15689455C2semidirect
5. #15689453C2semidirect
6. #15689443C2semidirect
7. #15689441C2semidirect
8. #15689412C2semidirect
9. #15689407C2semidirect
10. #15689353C2semidirect
11. #15689352C2semidirect
12. #15689210C2semidirect
13. C8×C22⋊D47C2semidirect
14. #106×D47C2semidirect
15. C2×#106×C47C2semidirect
120. C22⋊D47SD16semidirect
140. C8×C47#41semidirect
187. C2×#106D47semidirect
188. C47#3335semidirect
315. C8#10625350semidirect