Finite Group Databasebeta

← #20254583

Subgroups — #20254583

Order 6016.

366 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689676C211yesmaximal, characteristic, complemented
2#15689668C211yesmaximal, characteristic
3#15689531C211yesmaximal, characteristic, complemented
4#15689530C211yesmaximal, characteristic, complemented
5#15689486C211yesmaximal, characteristic, complemented
6#15689486C211yesmaximal, characteristic, complemented
7#15689448C211yesmaximal, characteristic, complemented
8#15689447C211yesmaximal, characteristic, complemented
9#15689444C211yesmaximal, characteristic, complemented
10#15689412C211yesmaximal, characteristic, complemented
11#15689411C211yesmaximal, characteristic, complemented
12#15689402C211yesmaximal, characteristic, complemented
13#15689401C211yesmaximal, characteristic, complemented
14#15689177C211yesmaximal, characteristic, complemented
15C47×#482C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17#13094023C2211yescharacteristic
18#13094023C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094020C2211yescharacteristic
21#13094015C2211yescharacteristic
22#13094015C2211yescharacteristic
23#13094010—21no—
24#13094001—21no—
25#13094001—21no—
26#13093998C2211yescharacteristic
27#13093996—21no—
28C4×Dic94—21no—
29C4×Dic94—21no—
30D4×Dic47C2211yescharacteristic
31#13093986C2211yescharacteristic
32(C22⋊D47)⋊C4—21no—
33#13093983C2211yescharacteristic
34C2×C4×Dic47C2211yescharacteristic
35#13093958C2211yescharacteristic
36#13093957C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093956C2211yescharacteristic
39#13093955C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50#13093934C2211yescharacteristic
51#13093934C2211yescharacteristic
52#121×C47C2211yescharacteristic
53#117×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C22×Dic47—21no—
66C22×Dic47D411yescharacteristic
67C22×Dic47D411yescharacteristic
68#10625352—44no—
69C2×D188C2311yescharacteristic
70C2×C4×D47—21no—
71C2×Dic94—21no—
72C2×Dic94—21no—
73C2×Dic94—21no—
74C2×C8×C47C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C42×C47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47C2311yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96C4×Dic47—21no—
97C4×Dic47D411yescharacteristic
98C4×Dic47D411yescharacteristic
99C4×Dic47C2311yescharacteristic
100C4×Dic47C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C23×C47—21no—
104C23×C47C2×D411yescharacteristic
105C22×D47—21no—
106D4×C47—21no—
107D4×C47—21no—
108D4×C47—42no—
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—42no—
117C22⋊D47—42no—
118C22⋊D47—42no—
119C2×Dic47—22no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—41no—
124C2×Dic47—42no—
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129D188—21no—
130D188—21no—
131C4×D47—42no—
132Dic94—42no—
133Dic94—42no—
134Dic94—42no—
135C8×C47—21no—
136C8×C47—21no—
137C47⋊C8—21no—
138C47⋊C8—21no—
139C22×C47—21no—
140C22×C47—21no—
141C22×C47—21no—
142C22×C47—41no—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47C22×D411yescharacteristic
146C2×D47—41no—
147C2×D47—41no—
148C2×D47—41no—
149C4×C47—21no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47—41no—
153C4×C472−1+411yescharacteristic
154C4×C472−1+411yescharacteristic
155Dic47—21no—
156Dic47—21no—
157Dic47—21no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161Dic47AGL(1,ℤ/8)12yes—
162#3235—471nomaximal, Sylow
163C2×C47—41no—
164C2×C47—81no—
165C2×C47#53611yescharacteristic
166C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
167C2×C47#57511yescharacteristic
168D47—81no—
169#533—471no—
170#532—471no—
171#501—471no—
172#501—471no—
173#490—471no—
174#490—471no—
175#482—471no—
176#482—471no—
177#482—471no—
178#482D4711yescharacteristic, complemented
179#476—471no—
180#476—471no—
181#474—471no—
182#474—471no—
183#432—471no—
184C47#323511yescharacteristic, complemented, Sylow
185C2×#41—941no—
186C4⋊Q8—471no—
187C4⋊Q8—471no—
188C4⋊Q8—471no—
189#127—471no—
190#125—471no—
191#125—471no—
192#124—941no—
193C22⋊Q8—941no—
194C22⋊Q8—941no—
195#121—471no—
196#121—941no—
197#121C2×D4711yescharacteristic
198C4×Q8—941no—
199C4×Q8—941no—
200C4×D4—471no—
201C4×D4—471no—
202C4×D4—941no—
203#117—471no—
204#117C2×D4711yescharacteristic
205C2×C42—471no—
206#107—471no—
207#107—471no—
208#107—471no—
209#107C2×D4711yescharacteristic
210#106—471no—
211#106—471no—
212#106—471no—
213#106C2×D4711yescharacteristic
214C4⋊C8—471no—
215C4⋊C8—471no—
216#102—471no—
217#102—471no—
218#102—471no—
219#102—471no—
220#102—471no—
221#102—471no—
222#102C2×D4711yescharacteristic
223#102C2×D4711yescharacteristic
224C22⋊C8—471no—
225C22⋊C8C2×D4711yescharacteristic
226#97—471no—
227#97—471no—
228#41—1884no—
229C2×Q8—941no—
230C2×Q8—941no—
231C2×Q8—941no—
232C2×D4—21no—
233C2×D4—471no—
234C2×D4—941no—
235C2×D4—941no—
236C2×D4—941no—
237C2×D4C22×D4711yescharacteristic
238C22×C4—471no—
239C22×C4—471no—
240C22×C4—941no—
241C22×C4—941no—
242C22×C4C22×D4711yescharacteristic
243C2×C8—471no—
244C2×C8—471no—
245C2×C8C22×D4711yescharacteristic
246C2×C8C22×D4711yescharacteristic
247C4⋊C4—471no—
248C4⋊C4—471no—
249C4⋊C4—471no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4C22×D4711yescharacteristic
258C4⋊C4C22×D4711yescharacteristic
259C4⋊C4C22×D4711yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C42—21no—
267C42—471no—
268C42—471no—
269C42—471no—
270C42—471no—
271C42—941no—
272C23—21no—
273C23—941no—
274C23D4×D4711yescharacteristic
275Q8—1882no—
276Q8—1882no—
277Q8—1882no—
278D4—21no—
279D4—21no—
280D4—42no—
281D4—941no—
282D4—941no—
283D4—1882no—
284D4—1882no—
285D4—1882no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—471no—
292C2×C4—471no—
293C2×C4—471no—
294C2×C4—471no—
295C2×C4—942no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—1882no—
300C2×C4—1882no—
301C2×C4—1881no—
302C2×C4D4×D4711yescharacteristic
303C2×C4C23×D4711yescharacteristic
304C8—21no—
305C8—21no—
306C8—941no—
307C8—941no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—1881no—
315C22—1881no—
316C22—1881no—
317C22C2×D4×D4711yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—472no—
323C4—941no—
324C4—941no—
325C4—941no—
326C4—1881no—
327C4—1881no—
328C4—1881no—
329C4#1309407111yescharacteristic
330C4#1309407111yescharacteristic
331C2—41no—
332C2—81no—
333C2—3761no—
334C2#1568969511yescharacteristic
335C2AGL(1,ℤ/8)×D4711yescharacteristic
336C2#1568992011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#482C2
socleC22×C47C22×D4
hypercenter#482D47
hypocenterC47#3235
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #15689676C2semidirect
3. #15689531C2semidirect
4. #15689530C2semidirect
5. #15689486C2semidirect
6. #15689486C2semidirect
7. #15689448C2semidirect
8. #15689447C2semidirect
9. #15689444C2semidirect
10. #15689412C2semidirect
11. #15689411C2semidirect
12. #15689402C2semidirect
13. #15689401C2semidirect
14. #15689177C2semidirect
15. C47×#482C2semidirect
178. #482D47semidirect
184. C47#3235semidirect