Finite Group Databasebeta

← #20256456

Subgroups — #20256456

Order 6016.

368 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#15689858C211yesmaximal, characteristic, complemented
2#15689846C211yesmaximal, characteristic, complemented
3#15689517C211yesmaximal, characteristic, complemented
4#15689512C211yesmaximal, characteristic
5#15689507C211yesmaximal, characteristic, complemented
6#15689346C211yesmaximal, characteristic, complemented
7#15689346C211yesmaximal, characteristic, complemented
8#15689339C211yesmaximal, characteristic, complemented
9#15689339C211yesmaximal, characteristic, complemented
10#15689329C211yesmaximal, characteristic, complemented
11#15689324C211yesmaximal, characteristic, complemented
12#15689236C211yesmaximal, characteristic, complemented
13#15689231C211yesmaximal, characteristic, complemented
14C4×#10625325C211yesmaximal, characteristic, complemented
15C47×#446C211yesmaximal, characteristic, complemented
16C2×Dic188C2211yescharacteristic
17C2×Dic188C2211yescharacteristic
18C2×#10625325C2211yescharacteristic
19C2×#10625325C2211yescharacteristic
20C2×#10625325C2211yescharacteristic
21C2×#10625325C2211yescharacteristic
22C2×#10625325C2211yescharacteristic
23C2×D376C2211yescharacteristic
24C2×D376C2211yescharacteristic
25#13094024C2211yescharacteristic
26#13094021C2211yescharacteristic
27#13094019—21no—
28#13094019—21no—
29#13094013—21no—
30#13094012C2211yescharacteristic
31#13094012C2211yescharacteristic
32#13094012C2211yescharacteristic
33#13094012C2211yescharacteristic
34#13094009—21no—
35#13094009—21no—
36#13094000—21no—
37C4×Dic94C2211yescharacteristic
38C4×Dic94C2211yescharacteristic
39C4×Dic94C2211yescharacteristic
40C4×D188C2211yescharacteristic
41C4×D188C2211yescharacteristic
42C4×D188C2211yescharacteristic
43#13093986—21no—
44#13093982—21no—
45#13093956C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093949C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52C4×Q8×C47C2211yescharacteristic
53C4⋊C8×C47C2211yescharacteristic
54C4⋊C8×C47C2211yescharacteristic
55C4⋊C8×C47C2211yescharacteristic
56#97×C47C2211yescharacteristic
57#97×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C2×Q8×C47D411yescharacteristic
60C2×D188—21no—
61C2×D188—21no—
62C2×D188C2311yescharacteristic
63C2×D188C2311yescharacteristic
64C2×D188C2311yescharacteristic
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×Dic94C2311yescharacteristic
69C2×Dic94C2311yescharacteristic
70C2×Dic94C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C4⋊C4×C47D411yescharacteristic
76C4⋊C4×C47D411yescharacteristic
77C4⋊C4×C47D411yescharacteristic
78C42×C47C2311yescharacteristic
79C42×C47C2311yescharacteristic
80C42×C47C2311yescharacteristic
81(C2×D47)⋊C4—21no—
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)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47—21no—
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102Dic188—22no—
103Dic188—41no—
104D376—22no—
105D376—41no—
106#10625325—22no—
107#10625325—41no—
108#10625325—41no—
109#10625325—41no—
110#10625325—41no—
111C22×D47—21no—
112C22×D47—21no—
113C22×D47—21no—
114Q8×C47—41no—
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127D188—21no—
128D188—21no—
129D188—21no—
130D188—21no—
131D188—21no—
132D188—21no—
133D188—42no—
134D188—81no—
135C4×D47—42no—
136C4×D47—81no—
137C4×D47—81no—
138Dic94—21no—
139Dic94—21no—
140Dic94—21no—
141Dic94—21no—
142Dic94—21no—
143Dic94—21no—
144C8×C47—21no—
145C8×C47—21no—
146C8×C47—21no—
147C8×C47#4112yes—
148C22×C47C22×D411yescharacteristic
149C2×D47—41no—
150C2×D47—41no—
151C2×D47—41no—
152C2×D47—41no—
153C2×D47—41no—
154C2×D47—41no—
155C2×D47—41no—
156C2×D47—41no—
157C2×D47—41no—
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47C2×#4111yescharacteristic
165C4×C47H(5,𝔽2)11yescharacteristic
166Dic47—41no—
167Dic47—41no—
168Dic47—41no—
169Dic47—41no—
170Dic47—41no—
171#3401—471nomaximal, Sylow
172C2×C47#55011yescharacteristic
173C2×C47#57511yescharacteristic
174C2×C47#57711yescharacteristic
175D47—81no—
176D47—81no—
177D47—81no—
178#559—471no—
179#556—471no—
180#497—471no—
181#496—471no—
182#495—471no—
183#464—471no—
184#464—471no—
185#463—471no—
186#463—471no—
187#461—471no—
188#460—471no—
189#446D4711yescharacteristic, complemented
190#442—471no—
191#441—471no—
192C4×SD16—471no—
193C47#340111yescharacteristic, complemented, Sylow
194C2×Q16—471no—
195C2×Q16—471no—
196C2×SD16—471no—
197C2×SD16—471no—
198C2×SD16—471no—
199C2×SD16—471no—
200C2×SD16—471no—
201C2×D8—471no—
202C2×D8—471no—
203C4⋊Q8—471no—
204#127—471no—
205#126—941no—
206#126—941no—
207#124—471no—
208#124—471no—
209#124—471no—
210#124—471no—
211#124—941no—
212#123—941no—
213#123—941no—
214C22⋊Q8—941no—
215C4×Q8—471no—
216C4×Q8—471no—
217C4×Q8—471no—
218C4×Q8C2×D4711yescharacteristic
219C4×D4—471no—
220C4×D4—471no—
221C4×D4—471no—
222C4×D4—941no—
223#117—941no—
224#106—471no—
225C4⋊C8C2×D4711yescharacteristic
226C4⋊C8C2×D4711yescharacteristic
227C4⋊C8C2×D4711yescharacteristic
228#103—471no—
229#103—471no—
230#103—471no—
231#102—471no—
232#102—471no—
233#102—471no—
234#97C2×D4711yescharacteristic
235#97C2×D4711yescharacteristic
236C4×C8C2×D4711yescharacteristic
237C2×Q8—471no—
238C2×Q8—471no—
239C2×Q8—471no—
240C2×Q8D18811yescharacteristic
241C2×D4—471no—
242C2×D4—471no—
243C2×D4—471no—
244C2×D4—941no—
245C2×D4—941no—
246C22×C4—941no—
247C22×C4—941no—
248C22×C4—941no—
249Q16—942no—
250Q16—1881no—
251SD16—942no—
252SD16—1881no—
253SD16—1881no—
254SD16—1881no—
255SD16—1881no—
256D8—942no—
257D8—1881no—
258C2×C8C22×D4711yescharacteristic
259C2×C8C22×D4711yescharacteristic
260C2×C8C22×D4711yescharacteristic
261C2×C8C22×D4711yescharacteristic
262C4⋊C4—471no—
263C4⋊C4—471no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4D18811yescharacteristic
270C4⋊C4D18811yescharacteristic
271C4⋊C4D18811yescharacteristic
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C42—941no—
284C42—941no—
285C42—941no—
286C42C22×D4711yescharacteristic
287C42C22×D4711yescharacteristic
288C42C22×D4711yescharacteristic
289C23—941no—
290C23—941no—
291C23—941no—
292Q8—41no—
293Q8—941no—
294Q8—941no—
295Q8—941no—
296Q8—941no—
297Q8—941no—
298Q8—941no—
299D4—941no—
300D4—941no—
301D4—941no—
302D4—941no—
303D4—941no—
304D4—941no—
305D4—3761no—
306D4—1882no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—3761no—
313C2×C4—3761no—
314C2×C4—1882no—
315C2×C4C2×D18811yescharacteristic
316C2×C4C2×D18811yescharacteristic
317C2×C4C2×D18811yescharacteristic
318C2×C4C2×D18811yescharacteristic
319C2×C4C2×D18811yescharacteristic
320C2×C4C2×D18811yescharacteristic
321C2×C4C23×D4711yescharacteristic
322C8—21no—
323C8—21no—
324C8—21no—
325C8#1062535412yes—
326C22—1881no—
327C22—1881no—
328C22—1881no—
329C22—1881no—
330C22—1881no—
331C22—1881no—
332C22—1881no—
333C22—1881no—
334C22—1881no—
335C22C22×D18811yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—1881no—
343C4—1881no—
344C4—1881no—
345C4—1881no—
346C4—1881no—
347C4C2×#1062535411yescharacteristic
348C4#1309407011yescharacteristic
349C2—3761no—
350C2—3761no—
351C2—3761no—
352C2#1568979511yescharacteristic
353C2#1568992311yescharacteristic
354C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#446C2
socleC22×C47C22×D4
hypercenter#446D47
hypocenterC47#3401
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #15689858C2semidirect
2. #15689846C2semidirect
3. #15689517C2semidirect
5. #15689507C2semidirect
6. #15689346C2semidirect
7. #15689346C2semidirect
8. #15689339C2semidirect
9. #15689339C2semidirect
10. #15689329C2semidirect
11. #15689324C2semidirect
12. #15689236C2semidirect
13. #15689231C2semidirect
14. C4×#10625325C2semidirect
15. C47×#446C2semidirect
189. #446D47semidirect
193. C47#3401semidirect