Finite Group Databasebeta

← #20253669

Subgroups — #20253669

Order 6016.

384 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#15689738C211yesmaximal, characteristic, complemented
2#15689602C211yesmaximal, characteristic, complemented
3#15689455C211yesmaximal, characteristic, complemented
4#15689440C211yesmaximal, characteristic, complemented
5#15689411C211yesmaximal, characteristic, complemented
6#15689407C211yesmaximal, characteristic, complemented
7#15689344C211yesmaximal, characteristic, complemented
8#15689336C211yesmaximal, characteristic, complemented
9#15689286C211yesmaximal, characteristic, complemented
10#15689265C211yesmaximal, characteristic
11#15689231C211yesmaximal, characteristic, complemented
12C4×#10625335C211yesmaximal, characteristic, complemented
13C4×#10625335C211yesmaximal, characteristic, complemented
14#15689185C211yesmaximal, characteristic, complemented
15C47×#442C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×Dic188C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094017—21no—
22#13094011C2211yescharacteristic
23#13094010—21no—
24#13094007—21no—
25#13094004C2211yescharacteristic
26#13094003—21no—
27#13093995C2211yescharacteristic
28C4×Dic94C2211yescharacteristic
29C4×Dic94C2211yescharacteristic
30#13093989C2211yescharacteristic
31D4×Dic47C2211yescharacteristic
32C4×C22⋊D47—21no—
33(C22⋊D47)⋊C4—21no—
34#13093981C2211yescharacteristic
35#13093980—21no—
36C2×Dic47⋊C4—21no—
37C4⋊C4×D47C2211yescharacteristic
38#13093956C2211yescharacteristic
39#13093955C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C4×C47⋊C8C2211yescharacteristic
52C2×D8×C47C2211yescharacteristic
53C4×D4×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×D4×C47C2311yescharacteristic
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C22×C4×C47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C22×Dic47—21no—
66C22×Dic47—21no—
67#10625352—22no—
68#10625352—22no—
69C2×C4×D47—21no—
70C2×C4×D47C2311yescharacteristic
71C2×Dic94—21no—
72C2×Dic94C2311yescharacteristic
73C2×Dic94C2311yescharacteristic
74D8×C47—22no—
75C2×C8×C47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C42×C47C2311yescharacteristic
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86#10625335—22no—
87#10625335—22no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4D411yescharacteristic
90(C2×D47)⋊C4D411yescharacteristic
91C4⋊Dic47—21no—
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4D411yescharacteristic
100Dic47⋊C4D411yescharacteristic
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107Dic188—22no—
108C23×C47—21no—
109C23×C47—21no—
110C22×D47C2×D411yescharacteristic
111D4×C47—21no—
112D4×C47—21no—
113D4×C47—21no—
114D4×C47#4112yes—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—81no—
118C2×C4×C47—81no—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C22⋊D47—24no—
123C22⋊D47—81no—
124C2×Dic47—24no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—81no—
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133C4×D47—21no—
134C4×D47—21no—
135C4×D47—81no—
136Dic94—21no—
137Dic94—21no—
138Dic94—21no—
139Dic94—81no—
140Dic94#4112yes—
141C8×C47—21no—
142C8×C47—21no—
143C47⋊C8—21no—
144C47⋊C8—21no—
145C22×C47—22no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47C22×D411yescharacteristic
152C2×D47—21no—
153C2×D47—21no—
154C2×D47—21no—
155C4×C47—21no—
156C4×C47—21no—
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—41no—
168#3125—471nomaximal, Sylow
169C2×C47—42no—
170C2×C47—81no—
171C2×C47#52511yescharacteristic
172C2×C47#57711yescharacteristic
173C2×C47#57711yescharacteristic
174D47—41no—
175#542—471no—
176#520—471no—
177#483—471no—
178#481—471no—
179#476—471no—
180#475—471no—
181#464—471no—
182#463—471no—
183#452—471no—
184#449—471no—
185#442D4711yescharacteristic, complemented
186#441—471no—
187C4×SD16—471no—
188C4×SD16—471no—
189#433—471no—
190C47#312511yescharacteristic, complemented, Sylow
191C2×#41—471no—
192C2×Q16—471no—
193C2×SD16—471no—
194C2×SD16—471no—
195C2×D8C2×D4711yescharacteristic
196C4⋊Q8—471no—
197#126—941no—
198#124—471no—
199#124—941no—
200#123—941no—
201C22⋊Q8—471no—
202C22⋊Q8—941no—
203#121—471no—
204C4×Q8—471no—
205C4×Q8—471no—
206C4×Q8—471no—
207C4×D4—471no—
208C4×D4—941no—
209C4×D4—941no—
210C4×D4C2×D4711yescharacteristic
211C4×D4C2×D4711yescharacteristic
212#117—471no—
213#117—941no—
214C2×C4⋊C4—471no—
215C2×C4⋊C4—941no—
216#106—471no—
217#106—471no—
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⋊C8—471no—
232#97C2×D4711yescharacteristic
233C4×C8—471no—
234#41—942no—
235#41—942no—
236C2×Q8—471no—
237C2×Q8—471no—
238C2×Q8—941no—
239C2×D4—941no—
240C2×D4—941no—
241C2×D4C22×D4711yescharacteristic
242C2×D4C22×D4711yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—471no—
246C22×C4—941no—
247C22×C4—941no—
248C22×C4—941no—
249Q16—942no—
250SD16—942no—
251SD16—942no—
252D8—22no—
253C2×C8—471no—
254C2×C8—471no—
255C2×C8C22×D4711yescharacteristic
256C2×C8C22×D4711yescharacteristic
257C4⋊C4—471no—
258C4⋊C4—471no—
259C4⋊C4—471no—
260C4⋊C4—471no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4C22×D4711yescharacteristic
268C4⋊C4C22×D4711yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—471no—
272C22⋊C4—471no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C42—471no—
279C42—941no—
280C42—941no—
281C42—941no—
282C42C22×D4711yescharacteristic
283C23—21no—
284C23—21no—
285C23—471no—
286Q8—472no—
287Q8—941no—
288Q8—941no—
289Q8—941no—
290Q8—3761no—
291D4—21no—
292D4—21no—
293D4—21no—
294D4—944no—
295D4—3761no—
296D4#1062535012yes—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—471no—
302C2×C4—471no—
303C2×C4—471no—
304C2×C4—944no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—3761no—
312C2×C4—3761no—
313C2×C4D4×D4711yescharacteristic
314C2×C4D4×D4711yescharacteristic
315C2×C4C23×D4711yescharacteristic
316C8—21no—
317C8—21no—
318C8—941no—
319C8—941no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—941no—
327C22—941no—
328C22—941no—
329C22C2×D4×D4711yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—941no—
335C4—942no—
336C4—941no—
337C4—941no—
338C4—1881no—
339C4—1881no—
340C4—1881no—
341C4#41×D4711yescharacteristic
342C4C2×#1062535011yescharacteristic
343C2—42no—
344C2—81no—
345C2—1881no—
346C2#1568963211yescharacteristic
347C2#1568993311yescharacteristic
348C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#442C2
socleC22×C47C22×D4
hypercenter#442D47
hypocenterC47#3125
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #15689738C2semidirect
2. #15689602C2semidirect
3. #15689455C2semidirect
4. #15689440C2semidirect
5. #15689411C2semidirect
6. #15689407C2semidirect
7. #15689344C2semidirect
8. #15689336C2semidirect
9. #15689286C2semidirect
11. #15689231C2semidirect
12. C4×#10625335C2semidirect
13. C4×#10625335C2semidirect
14. #15689185C2semidirect
15. C47×#442C2semidirect
185. #442D47semidirect
190. C47#3125semidirect