Finite Group Databasebeta

← #20253545

Subgroups — #20253545

Order 6016.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689675C211yesmaximal, characteristic, complemented
2#15689591C211yesmaximal, characteristic
3#15689464C211yesmaximal, characteristic, complemented
4#15689417C211yesmaximal, characteristic, complemented
5#15689412C211yesmaximal, characteristic, complemented
6#15689332C211yesmaximal, characteristic, complemented
7#15689327C211yesmaximal, characteristic, complemented
8#15689287C211yesmaximal, characteristic
9#15689283C211yesmaximal, characteristic
10#15689229C211yesmaximal, characteristic, complemented
11#15689227C211yesmaximal, characteristic, complemented
12#15689226C211yesmaximal, characteristic, complemented
13#15689222C211yesmaximal, characteristic, complemented
14#15689177C211yesmaximal, characteristic, complemented
15C47×#485C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×Dic188C2211yescharacteristic
18C2×#10625337C2211yescharacteristic
19C2×#10625325C2211yescharacteristic
20C2×#10625336C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094022C2211yescharacteristic
23#13094014—21no—
24#13094003C2211yescharacteristic
25#13094001—21no—
26Q8×Dic47C2211yescharacteristic
27#13093989—21no—
28#13093989C2211yescharacteristic
29#13093989C2211yescharacteristic
30#13093989C2211yescharacteristic
31#13093986C2211yescharacteristic
32#13093986C2211yescharacteristic
33(C22⋊D47)⋊C4—21no—
34(C22⋊D47)⋊C4—21no—
35#13093981—21no—
36#13093980—21no—
37C2×C4×Dic47C2211yescharacteristic
38C42×D47—21no—
39#13093957C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50#13093934C2211yescharacteristic
51#13093934C2211yescharacteristic
52C22⋊Q8×C47C2211yescharacteristic
53#117×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C2×C22⋊D47—21no—
62C22×Dic47D411yescharacteristic
63C22×Dic47D411yescharacteristic
64#10625350—22no—
65#10625350—22no—
66C2×D188C2311yescharacteristic
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×Dic94—21no—
71C2×Dic94C2311yescharacteristic
72C2×Dic94C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C4⋊C4×C47—21no—
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C42×C47—21no—
82C22⋊Dic47—21no—
83#10625337—22no—
84#10625336—22no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47C2311yescharacteristic
89Dic47⋊C4—21no—
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×Dic47—21no—
100C4×Dic47D411yescharacteristic
101C4×Dic47D411yescharacteristic
102C4×Dic47C2311yescharacteristic
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106Dic188—22no—
107#10625325—22no—
108C23×C47C2×D411yescharacteristic
109C22×D47—21no—
110Q8×C47—21no—
111Q8×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×C47C2×D411yescharacteristic
119C2×C4×C47C2411yescharacteristic
120C22⋊D47—24no—
121C2×Dic47—21no—
122C2×Dic47—22no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—41no—
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130D188—21no—
131D188#4112yes—
132C4×D47—24no—
133C4×D47—42no—
134C4×D47—42no—
135Dic94—21no—
136Dic94—21no—
137Dic94—21no—
138Dic94—42no—
139Dic94#4112yes—
140C8×C47—21no—
141C8×C47—21no—
142C47⋊C8—21no—
143C47⋊C8—21no—
144C22×C47—21no—
145C22×C47—21no—
146C22×C47—21no—
147C22×C47C22×D411yescharacteristic
148C2×D47—22no—
149C2×D47—41no—
150C2×D47—41no—
151C4×C47—21no—
152C4×C47—41no—
153C4×C47—41no—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47C2×#4111yescharacteristic
157C4×C47C2×#4111yescharacteristic
158Dic47—22no—
159Dic47—21no—
160Dic47—21no—
161Dic47—21no—
162Dic47—41no—
163Dic47—41no—
164Dic47#13712yes—
165#3116—471nomaximal, Sylow
166C2×C47—41no—
167C2×C47#52511yescharacteristic
168C2×C47C2×#13711yescharacteristic
169C2×C47#57511yescharacteristic
170D47—42no—
171#533—471no—
172C4×#41—471no—
173#485—471no—
174#485D4711yescharacteristic, complemented
175#477—471no—
176#476—471no—
177#462—471no—
178#461—471no—
179#452—471no—
180#452—471no—
181#441—471no—
182#441—471no—
183#440—471no—
184#440—471no—
185#432—471no—
186C47#311611yescharacteristic, complemented, Sylow
187C2×#41—471no—
188C2×Q16—471no—
189C2×Q16—471no—
190C2×SD16—471no—
191C2×SD16—471no—
192C4⋊Q8—471no—
193C4⋊Q8—471no—
194#125—941no—
195C22⋊Q8—471no—
196C22⋊Q8—941no—
197C22⋊Q8C2×D4711yescharacteristic
198C4×Q8—471no—
199C4×Q8—471no—
200C4×Q8—471no—
201C4×Q8—471no—
202C4×Q8—941no—
203C4×D4—471no—
204C4×D4—471no—
205C4×D4—941no—
206C4×D4—941no—
207#117—941no—
208#117—941no—
209#117C2×D4711yescharacteristic
210C2×C42—471no—
211C2×C42—941no—
212#107—471no—
213#107C2×D4711yescharacteristic
214#106—471no—
215#106C2×D4711yescharacteristic
216C4⋊C8—471no—
217C4⋊C8—471no—
218#103—471no—
219#103—471no—
220#103—471no—
221#103—471no—
222#103C2×D4711yescharacteristic
223#103C2×D4711yescharacteristic
224#102—471no—
225#102—471no—
226C22⋊C8—471no—
227C22⋊C8C2×D4711yescharacteristic
228#97—471no—
229#97—471no—
230#41—942no—
231#41—942no—
232C2×Q8—471no—
233C2×Q8—471no—
234C2×Q8—941no—
235C2×Q8C22×D4711yescharacteristic
236C2×D4—471no—
237C2×D4—941no—
238C22×C4—471no—
239C22×C4—471no—
240C22×C4—941no—
241C22×C4—941no—
242C22×C4—941no—
243C22×C4C22×D4711yescharacteristic
244Q16—942no—
245Q16—942no—
246SD16—942no—
247SD16—942no—
248C2×C8—471no—
249C2×C8—471no—
250C2×C8C22×D4711yescharacteristic
251C2×C8C22×D4711yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—471no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4C22×D4711yescharacteristic
263C4⋊C4C22×D4711yescharacteristic
264C4⋊C4C22×D4711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C42—21no—
271C42—471no—
272C42—471no—
273C42—471no—
274C42—471no—
275C42—941no—
276C42—941no—
277C42—941no—
278C42—941no—
279C23—941no—
280C23D4×D4711yescharacteristic
281Q8—21no—
282Q8—21no—
283Q8—472no—
284Q8—941no—
285Q8—941no—
286Q8—941no—
287Q8—1882no—
288D4—472no—
289D4—944no—
290D4—941no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—471no—
298C2×C4—471no—
299C2×C4—471no—
300C2×C4—471no—
301C2×C4—944no—
302C2×C4—942no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—1882no—
307C2×C4—1882no—
308C2×C4—1881no—
309C2×C4D4×D4711yescharacteristic
310C2×C4C23×D4711yescharacteristic
311C8—21no—
312C8—21no—
313C8—941no—
314C8—941no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—942no—
319C22—1881no—
320C22—1881no—
321C22C2×D4×D4711yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—472no—
328C4—942no—
329C4—941no—
330C4—941no—
331C4—941no—
332C4—1881no—
333C4—1881no—
334C4#41×D4711yescharacteristic
335C4#41×D4711yescharacteristic
336C2—41no—
337C2—1882no—
338C2#1568963111yescharacteristic
339C2#137×D4711yescharacteristic
340C2#1568992011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#485C2
socleC22×C47C22×D4
hypercenter#485D47
hypocenterC47#3116
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #15689675C2semidirect
3. #15689464C2semidirect
4. #15689417C2semidirect
5. #15689412C2semidirect
6. #15689332C2semidirect
7. #15689327C2semidirect
10. #15689229C2semidirect
11. #15689227C2semidirect
12. #15689226C2semidirect
13. #15689222C2semidirect
14. #15689177C2semidirect
15. C47×#485C2semidirect
174. #485D47semidirect
186. C47#3116semidirect