Finite Group Databasebeta

← #20255649

Subgroups — #20255649

Order 6016.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689815C211yesmaximal, characteristic, complemented
2#15689780C211yesmaximal, characteristic
3#15689476C211yesmaximal, characteristic, complemented
4#15689459C211yesmaximal, characteristic, complemented
5#15689445C211yesmaximal, characteristic, complemented
6#15689432C211yesmaximal, characteristic, complemented
7#15689379C211yesmaximal, characteristic, complemented
8#15689366C211yesmaximal, characteristic, complemented
9#15689343C211yesmaximal, characteristic, complemented
10#15689277C211yesmaximal, characteristic, complemented
11Q16×Dic47C211yesmaximal, characteristic, complemented
12#15689198C211yesmaximal, characteristic, complemented
13#15689130C211yesmaximal, characteristic, complemented
14#15689124C211yesmaximal, characteristic, complemented
15C47×#452C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625329C2211yescharacteristic
19C2×#10625324C2211yescharacteristic
20#13094019—21no—
21#13094015—21no—
22#13094015C2211yescharacteristic
23#13094011—21no—
24#13094011C2211yescharacteristic
25#13094008—21no—
26#13094003—21no—
27#13094003C2211yescharacteristic
28#13094000C2211yescharacteristic
29#13093995—21no—
30#13093995C2211yescharacteristic
31Q8×Dic47C2211yescharacteristic
32Q8×Dic47C2211yescharacteristic
33C4×C22⋊D47—21no—
34C4×C22⋊D47C2211yescharacteristic
35#13093982C2211yescharacteristic
36#13093980—21no—
37C2×C4⋊Dic47C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093945C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×#41×C47C2211yescharacteristic
53C2×Q16×C47C2211yescharacteristic
54C2×SD16×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59#41×C47—22no—
60#41×C47—41no—
61C2×Q8×C47C2311yescharacteristic
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—21no—
68C2×C22⋊D47D411yescharacteristic
69C22×Dic47—21no—
70Q8×D47—22no—
71Q8×D47—41no—
72C2×C4×D47—21no—
73C2×C4×D47C2311yescharacteristic
74C2×Dic94—21no—
75C2×Dic94C2311yescharacteristic
76Q16×C47—22no—
77SD16×C47—41no—
78C2×C8×C47C2311yescharacteristic
79C2×C8×C47C2311yescharacteristic
80C4⋊C4×C47—21no—
81C4⋊C4×C47C2311yescharacteristic
82C22⋊C4×C47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47D411yescharacteristic
88#10625337—41no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4D411yescharacteristic
92C4⋊Dic47—21no—
93C4⋊Dic47—21no—
94C4⋊Dic47—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4D411yescharacteristic
103C4×Dic47—21no—
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47C2311yescharacteristic
107#10625329—41no—
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110#10625324—41no—
111C23×C47—21no—
112C23×C47C2×D411yescharacteristic
113C22×D47C2×D411yescharacteristic
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47#4112yes—
118D4×C47—21no—
119D4×C47—21no—
120D4×C47—42no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—42no—
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2411yescharacteristic
129C22⋊D47—41no—
130C22⋊D47—42no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—42no—
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138C2×Dic47C2×D411yescharacteristic
139C4×D47—21no—
140C4×D47—21no—
141C4×D47—42no—
142Dic94—21no—
143Dic94—21no—
144Dic94—42no—
145C8×C47—21no—
146C8×C47—21no—
147C47⋊C8—21no—
148C47⋊C8—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—21no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47C22×D411yescharacteristic
156C2×D47—21no—
157C2×D47—21no—
158C2×D47—21no—
159C4×C47—22no—
160C4×C47—21no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47C2×#4111yescharacteristic
164C4×C47H(5,𝔽2)11yescharacteristic
165Dic47—21no—
166Dic47—21no—
167Dic47—21no—
168Dic47—41no—
169Dic47—41no—
170Dic47—41no—
171Dic47—41no—
172#3327—471nomaximal, Sylow
173C2×C47—41no—
174C2×C47—81no—
175C2×C47#54611yescharacteristic
176C2×C47#57511yescharacteristic
177C2×C47#57811yescharacteristic
178D47—41no—
179#552—471no—
180#548—471no—
181#488—471no—
182#484—471no—
183#482—471no—
184#479—471no—
185#470—471no—
186#468—471no—
187#464—471no—
188#452D4711yescharacteristic, complemented
189#451—471no—
190C4×Q16—471no—
191#436—471no—
192#419—471no—
193#417—471no—
194C47#332711yescharacteristic, complemented, Sylow
195C2×#41C2×D4711yescharacteristic
196C22×Q8—471no—
197C2×Q16—471no—
198C2×Q16C2×D4711yescharacteristic
199C2×SD16C2×D4711yescharacteristic
200C2×M16—471no—
201C2×M16—471no—
202#126—941no—
203#125—471no—
204#125—941no—
205#124—471no—
206#124—941no—
207#123—941no—
208C22⋊Q8—471no—
209C22⋊Q8—471no—
210C22⋊Q8—941no—
211C22⋊Q8C2×D4711yescharacteristic
212#121—471no—
213#121—941no—
214C4×Q8—471no—
215C4×Q8—471no—
216C4×D4—471no—
217C4×D4—941no—
218#117—471no—
219#117—941no—
220C2×C4⋊C4—471no—
221#107—471no—
222#107—471no—
223#106—471no—
224C4⋊C8—471no—
225#103—471no—
226#103—471no—
227#103—471no—
228#103—471no—
229#103—471no—
230#103—471no—
231#103C2×D4711yescharacteristic
232#102—471no—
233#102—471no—
234#102C2×D4711yescharacteristic
235C22⋊C8—471no—
236C22⋊C8C2×D4711yescharacteristic
237C4×C8—471no—
238#41—22no—
239#41—41no—
240C2×Q8—471no—
241C2×Q8—941no—
242C2×Q8—942no—
243C2×Q8—1881no—
244C2×Q8C22×D4711yescharacteristic
245C2×Q8C22×D4711yescharacteristic
246C2×D4—21no—
247C2×D4—471no—
248C2×D4—941no—
249C2×D4C22×D4711yescharacteristic
250C22×C4—21no—
251C22×C4—471no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4C22×D4711yescharacteristic
255Q16—22no—
256Q16—1881no—
257SD16—41no—
258M16—1881no—
259M16—1881no—
260C2×C8—471no—
261C2×C8—471no—
262C2×C8C22×D4711yescharacteristic
263C2×C8C22×D4711yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—471no—
266C4⋊C4—471no—
267C4⋊C4—471no—
268C4⋊C4—471no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4—941no—
276C4⋊C4C22×D4711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—471no—
279C22⋊C4—471no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C42—471no—
287C42—941no—
288C42—941no—
289C42—941no—
290C23—21no—
291C23—471no—
292C23D4×D4711yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—941no—
297Q8—941no—
298Q8—1882no—
299Q8#1062535212yes—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—1881no—
304D4—1882no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—471no—
312C2×C4—471no—
313C2×C4—471no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—1882no—
321C2×C4—1882no—
322C2×C4D4×D4711yescharacteristic
323C2×C4C23×D4711yescharacteristic
324C8—21no—
325C8—21no—
326C8—941no—
327C8—941no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—941no—
335C22—941no—
336C22—941no—
337C22C2×D4×D4711yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—941no—
343C4—941no—
344C4—941no—
345C4—1881no—
346C4—1881no—
347C4—1881no—
348C4—1881no—
349C4C2×#1062535211yescharacteristic
350C4#1309406911yescharacteristic
351C2—41no—
352C2—81no—
353C2—1881no—
354C2#1568976011yescharacteristic
355C2#1568992211yescharacteristic
356C2#1568993711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#452C2
socleC22×C47C22×D4
hypercenter#452D47
hypocenterC47#3327
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #15689815C2semidirect
3. #15689476C2semidirect
4. #15689459C2semidirect
5. #15689445C2semidirect
6. #15689432C2semidirect
7. #15689379C2semidirect
8. #15689366C2semidirect
9. #15689343C2semidirect
10. #15689277C2semidirect
11. Q16×Dic47C2semidirect
12. #15689198C2semidirect
13. #15689130C2semidirect
14. #15689124C2semidirect
15. C47×#452C2semidirect
188. #452D47semidirect
194. C47#3327semidirect