Finite Group Databasebeta

← #20255899

Subgroups — #20255899

Order 6016.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689836C211yesmaximal, characteristic
2#15689812C211yesmaximal, characteristic, complemented
3#15689531C211yesmaximal, characteristic, complemented
4#15689467C211yesmaximal, characteristic, complemented
5#15689464C211yesmaximal, characteristic, complemented
6#15689447C211yesmaximal, characteristic, complemented
7#15689443C211yesmaximal, characteristic, complemented
8#15689422C211yesmaximal, characteristic, complemented
9#15689407C211yesmaximal, characteristic, complemented
10#15689370C211yesmaximal, characteristic, complemented
11#15689352C211yesmaximal, characteristic, complemented
12#15689222C211yesmaximal, characteristic, complemented
13#15689194C211yesmaximal, characteristic, complemented
14#15689164C211yesmaximal, characteristic, complemented
15C47×#427C211yesmaximal, characteristic, complemented
16C2×#10625325C2211yescharacteristic
17C2×#10625324C2211yescharacteristic
18#13094023C2211yescharacteristic
19#13094017—21no—
20#13094016—21no—
21#13094015C2211yescharacteristic
22#13094012—21no—
23#13094010—21no—
24#13094006—21no—
25#13094004C2211yescharacteristic
26#13094003C2211yescharacteristic
27#13093999C2211yescharacteristic
28#13093998C2211yescharacteristic
29#13093997—21no—
30#13093989C2211yescharacteristic
31#13093986C2211yescharacteristic
32C4×C22⋊D47C2211yescharacteristic
33#13093982C2211yescharacteristic
34#13093981—21no—
35#13093981—21no—
36C4⋊C4×D47C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41#13093955C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51#13093934C2211yescharacteristic
52C22×C8×C47C2211yescharacteristic
53#117×C47C2211yescharacteristic
54#117×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic
57#106×C47C2211yescharacteristic
58#106×C47C2211yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C2×C22⋊D47—21no—
61C2×C22⋊D47D411yescharacteristic
62C2×D188—21no—
63C2×D188C2311yescharacteristic
64C2×C4×D47—21no—
65C2×C4×D47—21no—
66C2×C4×D47C2311yescharacteristic
67C2×Dic94—21no—
68C2×Dic94C2311yescharacteristic
69C2×C8×C47—22no—
70C2×C8×C47C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C4⋊C4×C47C2311yescharacteristic
73C4⋊C4×C47C2311yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C22⋊C4×C47—21no—
77C22⋊C4×C47—21no—
78C42×C47—21no—
79C42×C47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47D411yescharacteristic
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4D411yescharacteristic
88C4⋊Dic47—21no—
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×C47C2×D411yescharacteristic
115C2×C4×C47C2411yescharacteristic
116C22⋊D47—41no—
117C22⋊D47—81no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47C2×D411yescharacteristic
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124D188—21no—
125D188—21no—
126D188—81no—
127C4×D47—21no—
128C4×D47—21no—
129C4×D47—42no—
130C4×D47—42no—
131Dic94—21no—
132Dic94—21no—
133Dic94—81no—
134C8×C47—21no—
135C8×C47#4112yes—
136C47⋊C8—21no—
137C47⋊C8—21no—
138C22×C47—21no—
139C22×C47—21no—
140C22×C47—21no—
141C22×C47C22×D411yescharacteristic
142C2×D47—21no—
143C2×D47—21no—
144C2×D47—21no—
145C2×D47—41no—
146C2×D47—41no—
147C2×D47—41no—
148C4×C47—21no—
149C4×C47—41no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47—41no—
153C4×C47C2×#4111yescharacteristic
154C4×C472−1+411yescharacteristic
155Dic47—21no—
156Dic47—21no—
157Dic47—21no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161#3348—471nomaximal, Sylow
162C2×C47—41no—
163C2×C47#54711yescharacteristic
164C2×C47#57511yescharacteristic
165C2×C47#57711yescharacteristic
166D47—41no—
167D47—81no—
168#555—471no—
169#552—471no—
170#501—471no—
171#485—471no—
172#485—471no—
173#482—471no—
174#481—471no—
175#478—471no—
176#475—471no—
177#468—471no—
178#465—471no—
179#440—471no—
180#435—471no—
181#428—471no—
182#427D4711yescharacteristic, complemented
183C47#334811yescharacteristic, complemented, Sylow
184C2×SD16—471no—
185C2×M16—471no—
186C22×C8C2×D4711yescharacteristic
187C4⋊Q8—471no—
188#126—941no—
189#125—471no—
190#125—941no—
191#124—941no—
192#124—941no—
193#123—941no—
194C22⋊Q8—471no—
195C22⋊Q8—471no—
196#121—471no—
197#121—471no—
198#121—941no—
199C4×Q8—471no—
200C4×D4—471no—
201C4×D4—471no—
202#117—471no—
203#117—941no—
204#117—941no—
205#117C2×D4711yescharacteristic
206#117C2×D4711yescharacteristic
207C2×C4⋊C4—471no—
208#107—471no—
209#107—471no—
210#107C2×D4711yescharacteristic
211#107C2×D4711yescharacteristic
212#106—471no—
213#106—471no—
214#106—471no—
215#106C2×D4711yescharacteristic
216#106C2×D4711yescharacteristic
217C4⋊C8—471no—
218#103—471no—
219#103—471no—
220#103—471no—
221#102—471no—
222#102—471no—
223#102—471no—
224C22⋊C8—471no—
225C22⋊C8—471no—
226#97—471no—
227C2×Q8—471no—
228C2×Q8—941no—
229C2×D4—471no—
230C2×D4—471no—
231C2×D4—941no—
232C2×D4—941no—
233C22×C4—471no—
234C22×C4—941no—
235C22×C4—941no—
236C22×C4C22×D4711yescharacteristic
237SD16—942no—
238M16—942no—
239C2×C8—22no—
240C2×C8—471no—
241C2×C8—471no—
242C2×C8C22×D4711yescharacteristic
243C2×C8C22×D4711yescharacteristic
244C4⋊C4—471no—
245C4⋊C4—471no—
246C4⋊C4—471no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4C22×D4711yescharacteristic
255C4⋊C4C22×D4711yescharacteristic
256C4⋊C4C22×D4711yescharacteristic
257C4⋊C4C22×D4711yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—471no—
261C22⋊C4—471no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C42—21no—
269C42—21no—
270C42—471no—
271C42—941no—
272C42—941no—
273C23—471no—
274C23—941no—
275C23D4×D4711yescharacteristic
276Q8—941no—
277Q8—941no—
278Q8—3761no—
279D4—941no—
280D4—941no—
281D4—3761no—
282D4—3761no—
283D4—1881no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—471no—
291C2×C4—471no—
292C2×C4—471no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—1882no—
299C2×C4—1882no—
300C2×C4D4×D4711yescharacteristic
301C2×C4C23×D4711yescharacteristic
302C8—21no—
303C8—941no—
304C8—941no—
305C8#1062535012yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—941no—
310C22—941no—
311C22—941no—
312C22—1881no—
313C22—1881no—
314C22—1881no—
315C22C2×D4×D4711yescharacteristic
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—941no—
322C4—941no—
323C4—941no—
324C4—1881no—
325C4—1881no—
326C4—1881no—
327C4C2×#1062535011yescharacteristic
328C4#1309407211yescharacteristic
329C2—41no—
330C2—3761no—
331C2—1881no—
332C2#1568977411yescharacteristic
333C2#1568992011yescharacteristic
334C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#427C2
socleC22×C47C22×D4
hypercenter#427D47
hypocenterC47#3348
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
2. #15689812C2semidirect
3. #15689531C2semidirect
4. #15689467C2semidirect
5. #15689464C2semidirect
6. #15689447C2semidirect
7. #15689443C2semidirect
8. #15689422C2semidirect
9. #15689407C2semidirect
10. #15689370C2semidirect
11. #15689352C2semidirect
12. #15689222C2semidirect
13. #15689194C2semidirect
14. #15689164C2semidirect
15. C47×#427C2semidirect
182. #427D47semidirect
183. C47#3348semidirect