Finite Group Databasebeta

← #20255309

Subgroups — #20255309

Order 6016.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689837C211yesmaximal, characteristic, complemented
2#15689772C211yesmaximal, characteristic, complemented
3#15689472C211yesmaximal, characteristic, complemented
4#15689465C211yesmaximal, characteristic, complemented
5#15689463C211yesmaximal, characteristic, complemented
6#15689411C211yesmaximal, characteristic, complemented
7#15689350C211yesmaximal, characteristic, complemented
8#15689349C211yesmaximal, characteristic, complemented
9#15689326C211yesmaximal, characteristic, complemented
10#15689265C211yesmaximal, characteristic, complemented
11D8×Dic47C211yesmaximal, characteristic, complemented
12(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
13#15689119C211yesmaximal, characteristic, complemented
14#15689116C211yesmaximal, characteristic, complemented
15C47×#449C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×#10625335C2211yescharacteristic
18C22×C47⋊C8C2211yescharacteristic
19C2×C8×D47C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094022C2211yescharacteristic
22#13094011—21no—
23#13094010—21no—
24#13094007—21no—
25#13094005—21no—
26#13094003C2211yescharacteristic
27#13094000C2211yescharacteristic
28#13093996—21no—
29#13093996—21no—
30#13093995C2211yescharacteristic
31D4×Dic47C2211yescharacteristic
32D4×Dic47C2211yescharacteristic
33C4×C22⋊D47C2211yescharacteristic
34#13093983C2211yescharacteristic
35#13093982C2211yescharacteristic
36#13093980—21no—
37C2×Dic47⋊C4—21no—
38#13093958C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093945C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×#41×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54C2×D8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59#41×C47—22no—
60#41×C47—41no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47—21no—
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47—21no—
67C22×C4×C47C2311yescharacteristic
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47D411yescharacteristic
71C22×Dic47—21no—
72C22×Dic47—21no—
73C22×Dic47—21no—
74#10625352—22no—
75#10625352—41no—
76C2×C4×D47C2311yescharacteristic
77C2×Dic94—21no—
78C2×Dic94C2311yescharacteristic
79SD16×C47—41no—
80D8×C47—22no—
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C22⋊C4×C47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90C22⋊Dic47D411yescharacteristic
91#10625335—41no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4D411yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4D411yescharacteristic
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47C2311yescharacteristic
107C2×C47⋊C8—41no—
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C8×D47—41no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47C2×D411yescharacteristic
114C22×D47C2×D411yescharacteristic
115Q8×C47—21no—
116Q8×C47—21no—
117D4×C47—21no—
118D4×C47—21no—
119D4×C47—21no—
120D4×C47—42no—
121D4×C47—81no—
122D4×C47#4112yes—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—42no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—22no—
131C22⋊D47—42no—
132C22⋊D47—81no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—42no—
138C2×Dic47—42no—
139C2×Dic47—42no—
140C2×Dic47C2×D411yescharacteristic
141C2×Dic47C2×D411yescharacteristic
142C2×Dic47C2×D411yescharacteristic
143C4×D47—21no—
144C4×D47—21no—
145Dic94—21no—
146Dic94—21no—
147Dic94—81no—
148C8×C47—21no—
149C8×C47—21no—
150C47⋊C8—21no—
151C47⋊C8—21no—
152C22×C47—22no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47C22×D411yescharacteristic
162C2×D47—21no—
163C2×D47—21no—
164C2×D47—21no—
165C4×C47—21no—
166C4×C47—41no—
167C4×C47—41no—
168C4×C47C2×#4111yescharacteristic
169C4×C47H(5,𝔽2)11yescharacteristic
170Dic47—21no—
171Dic47—21no—
172Dic47—41no—
173Dic47—41no—
174Dic47—41no—
175Dic47—41no—
176Dic47#13512yes—
177#3303—471nomaximal, Sylow
178C2×C47—41no—
179C2×C47—42no—
180C2×C47—81no—
181C2×C47#54611yescharacteristic
182C2×C47C2×#13511yescharacteristic
183C2×C47#57711yescharacteristic
184D47—41no—
185#555—471no—
186#547—471no—
187#487—471no—
188#485—471no—
189#485—471no—
190#476—471no—
191#465—471no—
192#465—471no—
193#461—471no—
194#449—471no—
195#449D4711yescharacteristic, complemented
196C4×D8—471no—
197C8×D4—471no—
198#416—471no—
199#416—471no—
200C47#330311yescharacteristic, complemented, Sylow
201C2×#41—471no—
202C2×#41C2×D4711yescharacteristic
203C2×SD16—471no—
204C2×SD16C2×D4711yescharacteristic
205C2×D8C2×D4711yescharacteristic
206C22×C8—471no—
207C22×C8—471no—
208C4⋊Q8—471no—
209C4⋊Q8—471no—
210#124—941no—
211#124—941no—
212#123—941no—
213#123—941no—
214C22⋊Q8—471no—
215C22⋊Q8—471no—
216#121—471no—
217#121—941no—
218#121—941no—
219#121C2×D4711yescharacteristic
220C4×D4—471no—
221C4×D4—471no—
222C4×D4—471no—
223#117—471no—
224#117—471no—
225#117—941no—
226C2×C4⋊C4—941no—
227#107—471no—
228#106—471no—
229#106—471no—
230C4⋊C8—471no—
231#103—471no—
232#103—471no—
233#103—471no—
234#103—471no—
235#103—471no—
236#103C2×D4711yescharacteristic
237#102—471no—
238#102—471no—
239#102—471no—
240#102C2×D4711yescharacteristic
241C22⋊C8—471no—
242C22⋊C8C2×D4711yescharacteristic
243C4×C8—471no—
244#41—22no—
245#41—41no—
246#41—942no—
247#41—1881no—
248C2×Q8—471no—
249C2×Q8—941no—
250C2×Q8C22×D4711yescharacteristic
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—471no—
254C2×D4—941no—
255C2×D4—941no—
256C2×D4C22×D4711yescharacteristic
257C2×D4C22×D4711yescharacteristic
258C22×C4—21no—
259C22×C4—471no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4—941no—
263C22×C4C22×D4711yescharacteristic
264SD16—41no—
265SD16—1881no—
266D8—22no—
267C2×C8—471no—
268C2×C8—471no—
269C2×C8—1881no—
270C2×C8—1881no—
271C2×C8C22×D4711yescharacteristic
272C2×C8C22×D4711yescharacteristic
273C4⋊C4—471no—
274C4⋊C4—471no—
275C4⋊C4—471no—
276C4⋊C4—471no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4—941no—
280C4⋊C4—941no—
281C4⋊C4—941no—
282C4⋊C4C22×D4711yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—471no—
285C22⋊C4—471no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C42—471no—
294C42—941no—
295C42—941no—
296C23—21no—
297C23—21no—
298C23—471no—
299C23D4×D4711yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—941no—
303Q8—941no—
304Q8—3761no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—942no—
311D4—3761no—
312D4—1882no—
313D4#1062535212yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—471no—
320C2×C4—471no—
321C2×C4—471no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—1882no—
329C2×C4—1882no—
330C2×C4—1882no—
331C2×C4D4×D4711yescharacteristic
332C2×C4C23×D4711yescharacteristic
333C8—21no—
334C8—21no—
335C8—941no—
336C8—941no—
337C22—21no—
338C22—22no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—941no—
347C22—941no—
348C22—941no—
349C22C2×D4×D4711yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—472no—
354C4—941no—
355C4—941no—
356C4—1881no—
357C4—1881no—
358C4—1881no—
359C4—1881no—
360C4C2×#1062535211yescharacteristic
361C4#1309406911yescharacteristic
362C2—41no—
363C2—42no—
364C2—81no—
365C2—1881no—
366C2#1568976011yescharacteristic
367C2#135×D4711yescharacteristic
368C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#449C2
socleC22×C47C22×D4
hypercenter#449D47
hypocenterC47#3303
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #15689837C2semidirect
2. #15689772C2semidirect
3. #15689472C2semidirect
4. #15689465C2semidirect
5. #15689463C2semidirect
6. #15689411C2semidirect
7. #15689350C2semidirect
8. #15689349C2semidirect
9. #15689326C2semidirect
10. #15689265C2semidirect
11. D8×Dic47C2semidirect
12. (C22⋊D47)⋊C8C2semidirect
13. #15689119C2semidirect
14. #15689116C2semidirect
15. C47×#449C2semidirect
195. #449D47semidirect
200. C47#3303semidirect