Finite Group Databasebeta

← #20254699

Subgroups — #20254699

Order 6016.

392 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689675C211yesmaximal, characteristic, complemented
2#15689668C211yesmaximal, characteristic
3#15689412C211yesmaximal, characteristic, complemented
4#15689411C211yesmaximal, characteristic, complemented
5#15689407C211yesmaximal, characteristic, complemented
6#15689406C211yesmaximal, characteristic, complemented
7#15689354C211yesmaximal, characteristic, complemented
8#15689352C211yesmaximal, characteristic, complemented
9#15689350C211yesmaximal, characteristic, complemented
10#15689327C211yesmaximal, characteristic, complemented
11#15689326C211yesmaximal, characteristic, complemented
12#15689322C211yesmaximal, characteristic, complemented
13#15689321C211yesmaximal, characteristic, complemented
14C2×Dic47⋊C8C211yesmaximal, characteristic, complemented
15C47×#465C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17C2×#10625325C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20C22×C47⋊C8C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094023C2211yescharacteristic
23#13094022C2211yescharacteristic
24#13094020C2211yescharacteristic
25#13094014—21no—
26#13094010—21no—
27#13094003C2211yescharacteristic
28#13094001—21no—
29#13093998C2211yescharacteristic
30#13093996—21no—
31Q8×Dic47C2211yescharacteristic
32#13093989—21no—
33#13093989C2211yescharacteristic
34D4×Dic47C2211yescharacteristic
35#13093986C2211yescharacteristic
36(C22⋊D47)⋊C4—21no—
37#13093980—21no—
38C2×C4×Dic47C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41#13093955C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093948C2211yescharacteristic
48#13093947C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093945C2211yescharacteristic
51#13093944C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C22×C8×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#106×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⋊D47—21no—
65C2×C22⋊D47—21no—
66C22×Dic47—21no—
67C22×Dic47D411yescharacteristic
68C22×Dic47D411yescharacteristic
69#10625352—44no—
70C2×D188C2311yescharacteristic
71C2×C4×D47—21no—
72C2×Dic94—21no—
73C2×Dic94—21no—
74C2×Dic94C2311yescharacteristic
75SD16×C47—41no—
76C2×C8×C47—41no—
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C4⋊C4×C47—21no—
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C22⋊C4×C47—21no—
83C22⋊C4×C47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86#10625336—41no—
87#10625335—41no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90C4⋊Dic47—21no—
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47D411yescharacteristic
102C4×Dic47D411yescharacteristic
103C4×Dic47C2311yescharacteristic
104C4×Dic47C2311yescharacteristic
105C2×C47⋊C8—41no—
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108#10625325—41no—
109C23×C47—21no—
110C23×C47C2×D411yescharacteristic
111C22×D47—21no—
112Q8×C47—21no—
113Q8×C47—21no—
114D4×C47—21no—
115D4×C47—21no—
116D4×C47—42no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2411yescharacteristic
124C22⋊D47—42no—
125C22⋊D47—42no—
126C22⋊D47—42no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—41no—
131C2×Dic47—42no—
132C2×Dic47SD1614yescomplemented
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137D188—21no—
138D188—21no—
139C4×D47—42no—
140Dic94—21no—
141Dic94—21no—
142Dic94—42no—
143Dic94—42no—
144C8×C47—21no—
145C8×C47—21no—
146C47⋊C8—21no—
147C47⋊C8—21no—
148C22×C47—21no—
149C22×C47—21no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47C2×SD1612yes—
154C22×C47C22×D411yescharacteristic
155C2×D47—41no—
156C2×D47—41no—
157C2×D47—41no—
158C4×C47—21no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47H(5,𝔽2)11yescharacteristic
163C4×C472−1+411yescharacteristic
164Dic47—21no—
165Dic47—21no—
166Dic47—41no—
167Dic47—41no—
168Dic47—41no—
169Dic47C2×SD1612yes—
170Dic47C2×SD1612yes—
171#3246—471nomaximal, Sylow
172C2×C47—22no—
173C2×C47—81no—
174C2×C47#53711yescharacteristic
175C2×C47C22×SD1611yescharacteristic
176C2×C47#57511yescharacteristic
177D47—81no—
178#533—471no—
179#532—471no—
180#476—471no—
181#476—471no—
182#475—471no—
183#475—471no—
184#465—471no—
185#465—471no—
186#465—471no—
187#465D4711yescharacteristic, complemented
188#461—471no—
189#461—471no—
190#460—471no—
191#460—471no—
192C2×C4⋊C8—471no—
193C47#324611yescharacteristic, complemented, Sylow
194C2×#41—941no—
195C2×SD16—471no—
196C2×SD16—471no—
197C2×SD16—471no—
198C2×SD16C2×D4711yescharacteristic
199C22×C8—471no—
200C22×C8C2×D4711yescharacteristic
201C4⋊Q8—471no—
202C4⋊Q8—471no—
203C4⋊Q8—471no—
204#127—471no—
205#125—941no—
206#124—941no—
207C22⋊Q8—471no—
208C22⋊Q8—941no—
209C22⋊Q8C2×D4711yescharacteristic
210#121—471no—
211#121—941no—
212#121C2×D4711yescharacteristic
213C4×Q8—471no—
214C4×Q8—471no—
215C4×Q8—941no—
216C4×D4—471no—
217C4×D4—471no—
218C4×D4—941no—
219#117—941no—
220C2×C42—471no—
221#106—471no—
222#106—471no—
223#106—471no—
224#106C2×D4711yescharacteristic
225C4⋊C8—471no—
226C4⋊C8—471no—
227C4⋊C8—471no—
228C4⋊C8—471no—
229#103—471no—
230#103—471no—
231#103—471no—
232#103C2×D4711yescharacteristic
233#102—471no—
234#102—471no—
235#102—471no—
236#102C2×D4711yescharacteristic
237#41—1884no—
238C2×Q8—471no—
239C2×Q8—941no—
240C2×Q8—941no—
241C2×Q8C22×D4711yescharacteristic
242C2×D4—21no—
243C2×D4—471no—
244C2×D4—941no—
245C2×D4—941no—
246C2×D4—941no—
247C2×D4C22×D4711yescharacteristic
248C22×C4—471no—
249C22×C4—471no—
250C22×C4—941no—
251C22×C4—941no—
252C22×C4C22×D4711yescharacteristic
253SD16—41no—
254SD16—1881no—
255SD16—1881no—
256SD16—1881no—
257C2×C8—41no—
258C2×C8—471no—
259C2×C8—471no—
260C2×C8—1881no—
261C2×C8C22×D4711yescharacteristic
262C2×C8C22×D4711yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—471no—
265C4⋊C4—471no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4C22×D4711yescharacteristic
274C4⋊C4C22×D4711yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C42—471no—
282C42—471no—
283C42—471no—
284C42—471no—
285C42—941no—
286C42—941no—
287C23—21no—
288C23—941no—
289C23D4×D4711yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—941no—
293Q8—941no—
294Q8—1882no—
295Q8—1882no—
296D4—21no—
297D4—21no—
298D4—42no—
299D4—941no—
300D4—941no—
301D4—1882no—
302D4—1882no—
303D4—1882no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—474no—
310C2×C4—471no—
311C2×C4—471no—
312C2×C4—471no—
313C2×C4—471no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—1882no—
318C2×C4—1882no—
319C2×C4—1881no—
320C2×C4D4×D4711yescharacteristic
321C2×C4C23×D4711yescharacteristic
322C8—21no—
323C8—21no—
324C8—941no—
325C8—941no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—1881no—
332C22—1881no—
333C22—1881no—
334C22SD16×D4712yes—
335C22C2×D4×D4711yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—472no—
341C4—472no—
342C4—941no—
343C4—941no—
344C4—1881no—
345C4—1881no—
346C4—1881no—
347C4#1309406911yescharacteristic
348C4#1309407111yescharacteristic
349C2—22no—
350C2—81no—
351C2—3761no—
352C2#1568970011yescharacteristic
353C2C2×SD16×D4711yescharacteristic
354C2#1568992011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#465C2
socleC22×C47C22×D4
hypercenter#465D47
hypocenterC47#3246
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #15689675C2semidirect
3. #15689412C2semidirect
4. #15689411C2semidirect
5. #15689407C2semidirect
6. #15689406C2semidirect
7. #15689354C2semidirect
8. #15689352C2semidirect
9. #15689350C2semidirect
10. #15689327C2semidirect
11. #15689326C2semidirect
12. #15689322C2semidirect
13. #15689321C2semidirect
14. C2×Dic47⋊C8C2semidirect
15. C47×#465C2semidirect
132. C2×Dic47SD16semidirect
187. #465D47semidirect
193. C47#3246semidirect