Finite Group Databasebeta

← #20256010

Subgroups — #20256010

Order 6016.

354 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689836C211yesmaximal, characteristic
2#15689828C211yesmaximal, characteristic, complemented
3#15689527C211yesmaximal, characteristic, complemented
4#15689467C211yesmaximal, characteristic, complemented
5#15689464C211yesmaximal, characteristic, complemented
6#15689438C211yesmaximal, characteristic, complemented
7#15689436C211yesmaximal, characteristic, complemented
8#15689417C211yesmaximal, characteristic, complemented
9#15689412C211yesmaximal, characteristic, complemented
10#15689370C211yesmaximal, characteristic, complemented
11#15689369C211yesmaximal, characteristic, complemented
12#15689210C211yesmaximal, characteristic, complemented
13#15689199C211yesmaximal, characteristic, complemented
14#15689162C211yesmaximal, characteristic, complemented
15C47×#428C211yesmaximal, characteristic, complemented
16C2×#10625325C2211yescharacteristic
17C2×#10625324C2211yescharacteristic
18#13094023C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094014—21no—
21#13094012—21no—
22#13094010—21no—
23#13094004C2211yescharacteristic
24#13094003—21no—
25#13094003C2211yescharacteristic
26#13094002—21no—
27#13093999C2211yescharacteristic
28#13093998C2211yescharacteristic
29#13093997—21no—
30#13093989C2211yescharacteristic
31#13093986C2211yescharacteristic
32C4×C22⋊D47—21no—
33C4×C22⋊D47C2211yescharacteristic
34#13093982C2211yescharacteristic
35#13093981—21no—
36C4⋊C4×D47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093955C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×M16×C47C2211yescharacteristic
53#117×C47C2211yescharacteristic
54C2×C4⋊C4×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic
57#106×C47C2211yescharacteristic
58#106×C47C2211yescharacteristic
59C22×C4×C47—21no—
60C22×C4×C47C2311yescharacteristic
61C2×C22⋊D47—21no—
62C2×C22⋊D47D411yescharacteristic
63C2×D188—21no—
64C2×D188C2311yescharacteristic
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×C4×D47C2311yescharacteristic
68C2×Dic94—21no—
69C2×Dic94—21no—
70C2×Dic94C2311yescharacteristic
71M16×C47—22no—
72C2×C8×C47C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C4⋊C4×C47—21no—
75C4⋊C4×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C42×C47—21no—
81C22⋊Dic47—21no—
82C22⋊Dic47D411yescharacteristic
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4D411yescharacteristic
89C4⋊Dic47—21no—
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4D411yescharacteristic
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103#10625325—22no—
104#10625324—22no—
105C23×C47C2×D411yescharacteristic
106C22×D47—21no—
107C22×D47C2×D411yescharacteristic
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—81no—
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2411yescharacteristic
117C22⋊D47—22no—
118C22⋊D47—81no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124C2×Dic47C2×D411yescharacteristic
125D188—21no—
126D188—21no—
127D188—81no—
128C4×D47—21no—
129C4×D47—21no—
130C4×D47—42no—
131C4×D47—81no—
132Dic94—21no—
133Dic94—21no—
134Dic94—81no—
135Dic94—81no—
136C8×C47—21no—
137C8×C47#4112yes—
138C47⋊C8—21no—
139C47⋊C8—21no—
140C22×C47—21no—
141C22×C47—21no—
142C22×C47—21no—
143C22×C47C22×D411yescharacteristic
144C2×D47—21no—
145C2×D47—21no—
146C2×D47—21no—
147C2×D47—41no—
148C2×D47—41no—
149C2×D47—41no—
150C4×C47—21no—
151C4×C47—41no—
152C4×C47—41no—
153C4×C47—41no—
154C4×C47—41no—
155C4×C47C2×#4111yescharacteristic
156C4×C472−1+411yescharacteristic
157Dic47—21no—
158Dic47—21no—
159Dic47—41no—
160Dic47—41no—
161Dic47—41no—
162Dic47#13712yes—
163#3357—471nomaximal, Sylow
164C2×C47—41no—
165C2×C47#54711yescharacteristic
166C2×C47C2×#13711yescharacteristic
167C2×C47#57611yescharacteristic
168D47—41no—
169D47—81no—
170#555—471no—
171#554—471no—
172#500—471no—
173#485—471no—
174#485—471no—
175#480—471no—
176#480—471no—
177#477—471no—
178#476—471no—
179#468—471no—
180#468—471no—
181C4×SD16—471no—
182#436—471no—
183#428—471no—
184#428D4711yescharacteristic, complemented
185C47#335711yescharacteristic, complemented, Sylow
186C2×SD16—471no—
187C2×M16—471no—
188C2×M16C2×D4711yescharacteristic
189C4⋊Q8—471no—
190C4⋊Q8—471no—
191#125—941no—
192#124—941no—
193#124—941no—
194C22⋊Q8—471no—
195C22⋊Q8—471no—
196C22⋊Q8—941no—
197C22⋊Q8—941no—
198#121—471no—
199#121—471no—
200#121—941no—
201C4×Q8—471no—
202C4×D4—471no—
203C4×D4—471no—
204C4×D4—941no—
205#117—471no—
206#117—941no—
207#117C2×D4711yescharacteristic
208C2×C4⋊C4—471no—
209C2×C4⋊C4C2×D4711yescharacteristic
210#107—471no—
211#107—471no—
212#107—471no—
213#107—471no—
214#107C2×D4711yescharacteristic
215#107C2×D4711yescharacteristic
216#106—471no—
217#106C2×D4711yescharacteristic
218#106C2×D4711yescharacteristic
219C4⋊C8—471no—
220#103—471no—
221#103—471no—
222#103—471no—
223#102—471no—
224#102—471no—
225#102—471no—
226C22⋊C8—471no—
227C22⋊C8—471no—
228C4×C8—471no—
229C2×Q8—471no—
230C2×Q8—941no—
231C2×Q8—941no—
232C2×D4—471no—
233C2×D4—471no—
234C2×D4—941no—
235C2×D4—941no—
236C22×C4—21no—
237C22×C4—471no—
238C22×C4—941no—
239C22×C4—941no—
240C22×C4C22×D4711yescharacteristic
241SD16—942no—
242M16—22no—
243M16—942no—
244C2×C8—471no—
245C2×C8—471no—
246C2×C8C22×D4711yescharacteristic
247C2×C8C22×D4711yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—471no—
250C4⋊C4—471no—
251C4⋊C4—471no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4C22×D4711yescharacteristic
259C4⋊C4C22×D4711yescharacteristic
260C4⋊C4C22×D4711yescharacteristic
261C4⋊C4C22×D4711yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—471no—
264C22⋊C4—471no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C42—21no—
272C42—471no—
273C42—941no—
274C42—941no—
275C23—471no—
276C23—941no—
277C23D4×D4711yescharacteristic
278Q8—941no—
279Q8—941no—
280Q8—3761no—
281Q8—3761no—
282D4—942no—
283D4—941no—
284D4—941no—
285D4—3761no—
286D4—3761no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—81no—
294C2×C4—471no—
295C2×C4—471no—
296C2×C4—471no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—3761no—
303C2×C4—1882no—
304C2×C4D4×D4711yescharacteristic
305C2×C4C23×D4711yescharacteristic
306C8—21no—
307C8—941no—
308C8—941no—
309C8#1062535012yes—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—941no—
314C22—941no—
315C22—941no—
316C22—1881no—
317C22—1881no—
318C22—1881no—
319C22C2×D4×D4711yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—472no—
326C4—941no—
327C4—941no—
328C4—1881no—
329C4—1881no—
330C4—1881no—
331C4C2×#1062535011yescharacteristic
332C4#1309407211yescharacteristic
333C2—41no—
334C2—3761no—
335C2—1881no—
336C2#1568977411yescharacteristic
337C2#137×D4711yescharacteristic
338C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#428C2
socleC22×C47C22×D4
hypercenter#428D47
hypocenterC47#3357
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #15689828C2semidirect
3. #15689527C2semidirect
4. #15689467C2semidirect
5. #15689464C2semidirect
6. #15689438C2semidirect
7. #15689436C2semidirect
8. #15689417C2semidirect
9. #15689412C2semidirect
10. #15689370C2semidirect
11. #15689369C2semidirect
12. #15689210C2semidirect
13. #15689199C2semidirect
14. #15689162C2semidirect
15. C47×#428C2semidirect
184. #428D47semidirect
185. C47#3357semidirect