Finite Group Databasebeta

← #20253401

Subgroups — #20253401

Order 6016.

396 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689654C211yesmaximal, characteristic, complemented
2#15689591C211yesmaximal, characteristic, complemented
3#15689464C211yesmaximal, characteristic, complemented
4#15689433C211yesmaximal, characteristic, complemented
5#15689426C211yesmaximal, characteristic, complemented
6#15689344C211yesmaximal, characteristic, complemented
7#15689337C211yesmaximal, characteristic, complemented
8#15689287C211yesmaximal, characteristic, complemented
9#15689266C211yesmaximal, characteristic
10#15689217C211yesmaximal, characteristic, complemented
11#15689214C211yesmaximal, characteristic, complemented
12#15689210C211yesmaximal, characteristic, complemented
13#15689203C211yesmaximal, characteristic, complemented
14#15689173C211yesmaximal, characteristic, complemented
15C47×#482C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×Dic188C2211yescharacteristic
18C2×#10625325C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20C2×#10625334C2211yescharacteristic
21#13094017—21no—
22#13094015C2211yescharacteristic
23#13094011C2211yescharacteristic
24#13094005—21no—
25#13094003C2211yescharacteristic
26#13093989C2211yescharacteristic
27#13093989C2211yescharacteristic
28#13093989C2211yescharacteristic
29D4×Dic47—21no—
30D4×Dic47C2211yescharacteristic
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
50C8×Dic47C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52#121×C47C2211yescharacteristic
53#117×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C22×Dic47—21no—
64C22×Dic47D411yescharacteristic
65C22×Dic47D411yescharacteristic
66#10625350—22no—
67#10625350—22no—
68C2×D188C2311yescharacteristic
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×Dic94C2311yescharacteristic
73C2×Dic94C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C42×C47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86#10625335—22no—
87#10625334—22no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90C4⋊Dic47—21no—
91C4⋊Dic47C2311yescharacteristic
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—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×C47—21no—
109C23×C47C2×D411yescharacteristic
110C22×D47—21no—
111D4×C47—21no—
112D4×C47—21no—
113D4×C47—42no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2411yescharacteristic
121C22⋊D47—24no—
122C2×Dic47—21no—
123C2×Dic47—22no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—41no—
127C2×Dic47—42no—
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132D188—21no—
133D188#4112yes—
134C4×D47—24no—
135C4×D47—42no—
136C4×D47—42no—
137Dic94—21no—
138Dic94—21no—
139Dic94—21no—
140Dic94#4112yes—
141C8×C47—21no—
142C8×C47—21no—
143C47⋊C8—21no—
144C47⋊C8—21no—
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—21no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47C22×D411yescharacteristic
152C2×D47—22no—
153C2×D47—41no—
154C2×D47—41no—
155C4×C47—21no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47—41no—
159C4×C47C2×#4111yescharacteristic
160C4×C47C2×#4111yescharacteristic
161Dic47—22no—
162Dic47—21no—
163Dic47—21no—
164Dic47—21no—
165Dic47—41no—
166Dic47—41no—
167Dic47#13512yes—
168#3102—471nomaximal, Sylow
169C2×C47—41no—
170C2×C47—81no—
171C2×C47#52511yescharacteristic
172C2×C47C2×#13511yescharacteristic
173C2×C47#57511yescharacteristic
174D47—42no—
175#529—471no—
176C4×#41—471no—
177#485—471no—
178#482D4711yescharacteristic, complemented
179#479—471no—
180#478—471no—
181#464—471no—
182#463—471no—
183#452—471no—
184#449—471no—
185C4×Q16—471no—
186C4×SD16—471no—
187C4×SD16—471no—
188C4×D8—471no—
189#431—471no—
190C47#310211yescharacteristic, complemented, Sylow
191C2×#41—471no—
192C2×Q16—471no—
193C2×SD16—471no—
194C2×SD16—471no—
195C2×D8—471no—
196#126—941no—
197#125—471no—
198#124—471no—
199#123—941no—
200C22⋊Q8—471no—
201#121C2×D4711yescharacteristic
202C4×Q8—471no—
203C4×Q8—471no—
204C4×Q8—471no—
205C4×D4—471no—
206C4×D4—471no—
207C4×D4—471no—
208C4×D4—941no—
209C4×D4—941no—
210C4×D4—941no—
211#117—941no—
212#117—941no—
213#117C2×D4711yescharacteristic
214C2×C42—471no—
215C2×C42—941no—
216#107—471no—
217#107C2×D4711yescharacteristic
218#106—471no—
219#106C2×D4711yescharacteristic
220C4⋊C8—471no—
221C4⋊C8—471no—
222#103—471no—
223#103—471no—
224#103—471no—
225#103—471no—
226#102—471no—
227#102—471no—
228#102C2×D4711yescharacteristic
229#102C2×D4711yescharacteristic
230C22⋊C8—471no—
231C22⋊C8C2×D4711yescharacteristic
232C4×C8—471no—
233C4×C8—471no—
234#41—942no—
235#41—942no—
236C2×Q8—471no—
237C2×Q8—471no—
238C2×D4—21no—
239C2×D4—471no—
240C2×D4—941no—
241C2×D4C22×D4711yescharacteristic
242C22×C4—471no—
243C22×C4—471no—
244C22×C4—941no—
245C22×C4—941no—
246C22×C4—941no—
247C22×C4—941no—
248C22×C4C22×D4711yescharacteristic
249Q16—942no—
250SD16—942no—
251SD16—942no—
252D8—942no—
253C2×C8—471no—
254C2×C8—471no—
255C2×C8C22×D4711yescharacteristic
256C2×C8C22×D4711yescharacteristic
257C4⋊C4—471no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4C22×D4711yescharacteristic
265C4⋊C4C22×D4711yescharacteristic
266C4⋊C4C22×D4711yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C42—21no—
276C42—471no—
277C42—471no—
278C42—471no—
279C42—471no—
280C42—941no—
281C42—941no—
282C42—941no—
283C23—21no—
284C23—941no—
285C23D4×D4711yescharacteristic
286Q8—472no—
287Q8—941no—
288Q8—941no—
289Q8—941no—
290D4—21no—
291D4—21no—
292D4—42no—
293D4—472no—
294D4—944no—
295D4—941no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—471no—
302C2×C4—471no—
303C2×C4—471no—
304C2×C4—471no—
305C2×C4—944no—
306C2×C4—942no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—1882no—
311C2×C4—1882no—
312C2×C4—1882no—
313C2×C4—1881no—
314C2×C4D4×D4711yescharacteristic
315C2×C4C23×D4711yescharacteristic
316C8—21no—
317C8—21no—
318C8—941no—
319C8—941no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—942no—
327C22—1881no—
328C22—1881no—
329C22C2×D4×D4711yescharacteristic
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—472no—
335C4—942no—
336C4—941no—
337C4—941no—
338C4—941no—
339C4—1881no—
340C4—1881no—
341C4#41×D4711yescharacteristic
342C4#41×D4711yescharacteristic
343C2—41no—
344C2—81no—
345C2—1882no—
346C2#1568963111yescharacteristic
347C2#135×D4711yescharacteristic
348C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#482C2
socleC22×C47C22×D4
hypercenter#482D47
hypocenterC47#3102
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #15689654C2semidirect
2. #15689591C2semidirect
3. #15689464C2semidirect
4. #15689433C2semidirect
5. #15689426C2semidirect
6. #15689344C2semidirect
7. #15689337C2semidirect
8. #15689287C2semidirect
10. #15689217C2semidirect
11. #15689214C2semidirect
12. #15689210C2semidirect
13. #15689203C2semidirect
14. #15689173C2semidirect
15. C47×#482C2semidirect
178. #482D47semidirect
190. C47#3102semidirect