Finite Group Databasebeta

← #20256444

Subgroups — #20256444

Order 6016.

362 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689855C211yesmaximal, characteristic
2#15689851C211yesmaximal, characteristic, complemented
3#15689518C211yesmaximal, characteristic, complemented
4#15689516C211yesmaximal, characteristic, complemented
5#15689494C211yesmaximal, characteristic
6#15689348C211yesmaximal, characteristic, complemented
7#15689331C211yesmaximal, characteristic, complemented
8#15689329C211yesmaximal, characteristic, complemented
9#15689326C211yesmaximal, characteristic, complemented
10#15689322C211yesmaximal, characteristic
11#15689252C211yesmaximal, characteristic, complemented
12#15689221C211yesmaximal, characteristic, complemented
13#15689220C211yesmaximal, characteristic, complemented
14#15689215C211yesmaximal, characteristic, complemented
15C47×#464C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625325C2211yescharacteristic
19C2×#10625325C2211yescharacteristic
20C2×#10625335C2211yescharacteristic
21C2×#10625335C2211yescharacteristic
22C2×#10625336C2211yescharacteristic
23#13094024C2211yescharacteristic
24#13094022C2211yescharacteristic
25#13094022C2211yescharacteristic
26#13094020C2211yescharacteristic
27#13094016—21no—
28#13094014—21no—
29#13094014—21no—
30#13094013C2211yescharacteristic
31#13094010—21no—
32#13094008—21no—
33#13094006—21no—
34Q8×Dic47C2211yescharacteristic
35C4×Dic94—21no—
36C4×Dic94C2211yescharacteristic
37#13093989C2211yescharacteristic
38#13093989C2211yescharacteristic
39C4×D188C2211yescharacteristic
40D4×Dic47C2211yescharacteristic
41(C22⋊D47)⋊C4—21no—
42#13093957C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093948C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093935C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×Q16×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54#124×C47C2211yescharacteristic
55C4×Q8×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64C22×Dic47—21no—
65C2×D188C2311yescharacteristic
66C2×C4×D47—21no—
67C2×Dic94D411yescharacteristic
68C2×Dic94C2311yescharacteristic
69C2×Dic94C2311yescharacteristic
70Q16×C47—41no—
71SD16×C47—41no—
72C2×C8×C47C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C4⋊C4×C47—21no—
75C4⋊C4×C47C2311yescharacteristic
76C22⋊C4×C47—21no—
77C22⋊C4×C47—21no—
78C42×C47—21no—
79C42×C47C2311yescharacteristic
80C22⋊Dic47—21no—
81#10625337—22no—
82#10625337—41no—
83#10625336—22no—
84#10625335—22no—
85#10625335—41no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47—21no—
91C4⋊Dic47—21no—
92C4⋊Dic47D411yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4D411yescharacteristic
101Dic47⋊C4D411yescharacteristic
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105C4×Dic47C2311yescharacteristic
106C4×Dic47C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109#10625325—41no—
110#10625325—41no—
111C23×C47—21no—
112C22×D47—21no—
113Q8×C47—21no—
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47—21no—
117D4×C47—21no—
118D4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2411yescharacteristic
125C22⋊D47—42no—
126C22⋊D47—81no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—81no—
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135D188—21no—
136D188—21no—
137C4×D47—81no—
138Dic94—22no—
139Dic94—21no—
140Dic94—21no—
141Dic94—21no—
142Dic94—21no—
143C8×C47—21no—
144C8×C47—21no—
145C47⋊C8—21no—
146C47⋊C8#4112yes—
147C22×C47—41no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47C22×D411yescharacteristic
151C2×D47—41no—
152C2×D47—41no—
153C2×D47—41no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47—41no—
159C4×C47C2×#4111yescharacteristic
160C4×C47H(5,𝔽2)11yescharacteristic
161Dic47—21no—
162Dic47—21no—
163Dic47—21no—
164Dic47—41no—
165Dic47—41no—
166Dic47—41no—
167Dic47#13712yes—
168#3400—471nomaximal, Sylow
169C2×C47—81no—
170C2×C47#55011yescharacteristic
171C2×C47C2×#13711yescharacteristic
172C2×C47#57711yescharacteristic
173D47—81no—
174#559—471no—
175#557—471no—
176#497—471no—
177#497—471no—
178#492—471no—
179#464—471no—
180#464D4711yescharacteristic, complemented
181#462—471no—
182#461—471no—
183#461—471no—
184#460—471no—
185#446—471no—
186#440—471no—
187#440—471no—
188C4×Q16—471no—
189C47#340011yescharacteristic, complemented, Sylow
190C2×Q16—471no—
191C2×Q16—471no—
192C2×Q16C2×D4711yescharacteristic
193C2×SD16—471no—
194C2×SD16—471no—
195C2×SD16—471no—
196C2×SD16—471no—
197C2×SD16—471no—
198C2×SD16C2×D4711yescharacteristic
199C4⋊Q8—471no—
200C4⋊Q8—471no—
201C4⋊Q8—471no—
202#127—471no—
203#125—941no—
204#125—941no—
205#125—941no—
206#124—471no—
207#124—941no—
208#124C2×D4711yescharacteristic
209#123—941no—
210#123—941no—
211C4×Q8—471no—
212C4×Q8—471no—
213C4×Q8—471no—
214C4×Q8—471no—
215C4×Q8—941no—
216C4×Q8C2×D4711yescharacteristic
217C4×D4—471no—
218C4×D4—471no—
219C4×D4—941no—
220#107—471no—
221C4⋊C8—471no—
222C4⋊C8—471no—
223C4⋊C8C2×D4711yescharacteristic
224#103—471no—
225#103—471no—
226#103—471no—
227#103C2×D4711yescharacteristic
228#102—471no—
229#102C2×D4711yescharacteristic
230#97—471no—
231#97—471no—
232C4×C8—471no—
233C2×Q8—471no—
234C2×Q8—471no—
235C2×Q8—471no—
236C2×Q8C22×D4711yescharacteristic
237C2×Q8C22×D4711yescharacteristic
238C2×D4—471no—
239C2×D4—941no—
240C2×D4—941no—
241C2×D4C22×D4711yescharacteristic
242C22×C4—941no—
243C22×C4—941no—
244Q16—41no—
245Q16—942no—
246Q16—1881no—
247SD16—41no—
248SD16—942no—
249SD16—942no—
250SD16—1881no—
251SD16—1881no—
252SD16—1881no—
253C2×C8—471no—
254C2×C8—471no—
255C2×C8C22×D4711yescharacteristic
256C2×C8C22×D4711yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—471no—
259C4⋊C4—471no—
260C4⋊C4—471no—
261C4⋊C4—471no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4C22×D4711yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C42—21no—
279C42—471no—
280C42—471no—
281C42—941no—
282C42—941no—
283C42—941no—
284C42C22×D4711yescharacteristic
285C23—21no—
286C23—941no—
287Q8—21no—
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—942no—
292Q8—941no—
293Q8—941no—
294Q8—941no—
295Q8—941no—
296D4—21no—
297D4—21no—
298D4—941no—
299D4—941no—
300D4—3761no—
301D4—1882no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—471no—
306C2×C4—471no—
307C2×C4—471no—
308C2×C4—471no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—3761no—
313C2×C4—3761no—
314C2×C4D4×D4711yescharacteristic
315C2×C4D4×D4711yescharacteristic
316C2×C4C23×D4711yescharacteristic
317C8—21no—
318C8—21no—
319C8—472no—
320C8—941no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—1881no—
325C22—1881no—
326C22—1881no—
327C22C2×D4×D4711yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—472no—
334C4—941no—
335C4—941no—
336C4—941no—
337C4—1881no—
338C4—1881no—
339C4—1881no—
340C4#41×D4711yescharacteristic
341C4#1309406911yescharacteristic
342C2—81no—
343C2—3761no—
344C2#1568979111yescharacteristic
345C2#137×D4711yescharacteristic
346C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#464C2
socleC22×C47C22×D4
hypercenter#464D47
hypocenterC47#3400
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. #15689851C2semidirect
3. #15689518C2semidirect
4. #15689516C2semidirect
6. #15689348C2semidirect
7. #15689331C2semidirect
8. #15689329C2semidirect
9. #15689326C2semidirect
11. #15689252C2semidirect
12. #15689221C2semidirect
13. #15689220C2semidirect
14. #15689215C2semidirect
15. C47×#464C2semidirect
180. #464D47semidirect
189. C47#3400semidirect