Finite Group Databasebeta

← #20255677

Subgroups — #20255677

Order 6016.

386 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689837C211yesmaximal, characteristic
2#15689786C211yesmaximal, characteristic, complemented
3#15689472C211yesmaximal, characteristic, complemented
4#15689466C211yesmaximal, characteristic, complemented
5#15689461C211yesmaximal, characteristic, complemented
6#15689417C211yesmaximal, characteristic, complemented
7#15689368C211yesmaximal, characteristic, complemented
8#15689326C211yesmaximal, characteristic, complemented
9#15689261C211yesmaximal, characteristic, complemented
10#15689260C211yesmaximal, characteristic, complemented
11#15689214C211yesmaximal, characteristic, complemented
12#15689199C211yesmaximal, characteristic, complemented
13#15689133C211yesmaximal, characteristic, complemented
14#15689130C211yesmaximal, characteristic, complemented
15C47×#468C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20C2×#10625324C2211yescharacteristic
21#13094023—21no—
22#13094023C2211yescharacteristic
23#13094022C2211yescharacteristic
24#13094011—21no—
25#13094010—21no—
26#13094004C2211yescharacteristic
27#13094002—21no—
28#13094001—21no—
29#13093996—21no—
30#13093995C2211yescharacteristic
31#13093989C2211yescharacteristic
32D4×Dic47C2211yescharacteristic
33C4×C22⋊D47C2211yescharacteristic
34(C22⋊D47)⋊C4—21no—
35#13093983C2211yescharacteristic
36#13093982C2211yescharacteristic
37#13093980—21no—
38#13093957C2211yescharacteristic
39#13093955C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41#13093949C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093947C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47D411yescharacteristic
65C22×Dic47—21no—
66C22×Dic47—21no—
67Q8×D47—22no—
68Q8×D47—41no—
69C2×C4×D47—21no—
70C2×C4×D47C2311yescharacteristic
71C2×Dic94—22no—
72C2×Dic94—21no—
73C2×Dic94—21no—
74C2×Dic94—21no—
75C2×Dic94—41no—
76C2×Dic94C2311yescharacteristic
77C2×Dic94C2311yescharacteristic
78SD16×C47—41no—
79M16×C47—41no—
80C2×C8×C47C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C4⋊C4×C47—21no—
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90C22⋊Dic47D411yescharacteristic
91#10625335—22no—
92#10625335—41no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4D411yescharacteristic
96C4⋊Dic47—21no—
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4D411yescharacteristic
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47—21no—
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110#10625324—41no—
111C23×C47—21no—
112C23×C47C2×D411yescharacteristic
113C22×D47C2×D411yescharacteristic
114Q8×C47—21no—
115Q8×C47—21no—
116D4×C47—21no—
117D4×C47—21no—
118D4×C47—81no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2411yescharacteristic
126C22⋊D47—22no—
127C22⋊D47—81no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—42no—
133C2×Dic47—42no—
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137C4×D47—21no—
138C4×D47—21no—
139C4×D47—42no—
140Dic94—21no—
141Dic94—21no—
142Dic94—21no—
143Dic94—42no—
144Dic94—42no—
145Dic94—81no—
146Dic94#4112yes—
147C8×C47—21no—
148C8×C47—21no—
149C47⋊C8—21no—
150C47⋊C8—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—41no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47C22×D411yescharacteristic
158C2×D47—21no—
159C2×D47—21no—
160C2×D47—21no—
161C4×C47—21no—
162C4×C47—41no—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47C2×#4111yescharacteristic
166C4×C47H(5,𝔽2)11yescharacteristic
167Dic47—22no—
168Dic47—21no—
169Dic47—21no—
170Dic47—41no—
171Dic47—41no—
172Dic47—41no—
173Dic47#13712yes—
174#3329—471nomaximal, Sylow
175C2×C47—41no—
176C2×C47—81no—
177C2×C47#54611yescharacteristic
178C2×C47C2×#13711yescharacteristic
179C2×C47#57711yescharacteristic
180D47—41no—
181#555—471no—
182D4×Q8—471no—
183#487—471no—
184#485—471no—
185#485—471no—
186#477—471no—
187#468—471no—
188#468D4711yescharacteristic, complemented
189#461—471no—
190#448—471no—
191#448—471no—
192C4×SD16—471no—
193#436—471no—
194#419—471no—
195#419—471no—
196C47#332911yescharacteristic, complemented, Sylow
197C22×Q8—471no—
198C22×Q8—471no—
199C2×SD16—471no—
200C2×SD16—471no—
201C2×SD16C2×D4711yescharacteristic
202C2×M16—471no—
203C2×M16C2×D4711yescharacteristic
204C4⋊Q8—471no—
205C4⋊Q8—471no—
206C4⋊Q8—941no—
207#124—941no—
208#124—941no—
209C22⋊Q8—471no—
210C22⋊Q8—941no—
211C22⋊Q8—941no—
212C22⋊Q8C2×D4711yescharacteristic
213#121—471no—
214#121—941no—
215#121C2×D4711yescharacteristic
216C4×Q8—471no—
217C4×D4—471no—
218C4×D4—471no—
219C4×D4—941no—
220#117—471no—
221#117—471no—
222#117—941no—
223#107—471no—
224#107C2×D4711yescharacteristic
225#106—471no—
226C4⋊C8—471no—
227#103—471no—
228#103—471no—
229#103—471no—
230#103—471no—
231#103—471no—
232#103—471no—
233#103—471no—
234#103—471no—
235#103C2×D4711yescharacteristic
236#102C2×D4711yescharacteristic
237C22⋊C8—471no—
238C22⋊C8—471no—
239C4×C8—471no—
240C2×Q8—471no—
241C2×Q8—471no—
242C2×Q8—941no—
243C2×Q8—941no—
244C2×Q8—942no—
245C2×Q8—941no—
246C2×Q8—942no—
247C2×Q8—1881no—
248C2×Q8—1881no—
249C2×Q8C22×D4711yescharacteristic
250C2×D4—21no—
251C2×D4—471no—
252C2×D4—941no—
253C2×D4C22×D4711yescharacteristic
254C22×C4—471no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4—941no—
258C22×C4C22×D4711yescharacteristic
259SD16—41no—
260SD16—942no—
261SD16—1881no—
262M16—41no—
263M16—1881no—
264C2×C8—471no—
265C2×C8—471no—
266C2×C8C22×D4711yescharacteristic
267C2×C8C22×D4711yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—471no—
270C4⋊C4—471no—
271C4⋊C4—471no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4—941no—
276C4⋊C4—941no—
277C4⋊C4C22×D4711yescharacteristic
278C4⋊C4C22×D4711yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—471no—
282C22⋊C4—471no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C42—471no—
289C42—941no—
290C42—941no—
291C42—941no—
292C23—21no—
293C23—471no—
294C23D4×D4711yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—472no—
298Q8—941no—
299Q8—941no—
300Q8—941no—
301Q8—3761no—
302Q8—1882no—
303Q8—1882no—
304D4—21no—
305D4—21no—
306D4—81no—
307D4—942no—
308D4—3761no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—471no—
315C2×C4—471no—
316C2×C4—471no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—941no—
322C2×C4—941no—
323C2×C4—1882no—
324C2×C4—1882no—
325C2×C4—1882no—
326C2×C4D4×D4711yescharacteristic
327C2×C4C23×D4711yescharacteristic
328C8—21no—
329C8—21no—
330C8—941no—
331C8—941no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—941no—
339C22—941no—
340C22—941no—
341C22C2×D4×D4711yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—472no—
347C4—941no—
348C4—942no—
349C4—941no—
350C4—1881no—
351C4—1881no—
352C4—1881no—
353C4#41×D4711yescharacteristic
354C4#1309406911yescharacteristic
355C2—41no—
356C2—81no—
357C2—1881no—
358C2#1568976211yescharacteristic
359C2#137×D4711yescharacteristic
360C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#468C2
socleC22×C47C22×D4
hypercenter#468D47
hypocenterC47#3329
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
2. #15689786C2semidirect
3. #15689472C2semidirect
4. #15689466C2semidirect
5. #15689461C2semidirect
6. #15689417C2semidirect
7. #15689368C2semidirect
8. #15689326C2semidirect
9. #15689261C2semidirect
10. #15689260C2semidirect
11. #15689214C2semidirect
12. #15689199C2semidirect
13. #15689133C2semidirect
14. #15689130C2semidirect
15. C47×#468C2semidirect
188. #468D47semidirect
196. C47#3329semidirect