Finite Group Databasebeta

← #20253495

Subgroups — #20253495

Order 6016.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689655C211yesmaximal, characteristic, complemented
2C4×#10625354C211yesmaximal, characteristic, complemented
3#15689466C211yesmaximal, characteristic, complemented
4#15689445C211yesmaximal, characteristic, complemented
5#15689432C211yesmaximal, characteristic, complemented
6#15689426C211yesmaximal, characteristic, complemented
7#15689343C211yesmaximal, characteristic, complemented
8#15689337C211yesmaximal, characteristic, complemented
9#15689288C211yesmaximal, characteristic, complemented
10#15689267C211yesmaximal, characteristic
11#15689233C211yesmaximal, characteristic, complemented
12#15689228C211yesmaximal, characteristic, complemented
13#15689225C211yesmaximal, characteristic, complemented
14#15689178C211yesmaximal, characteristic, complemented
15C47×#440C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625325C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20#13094017—21no—
21#13094015C2211yescharacteristic
22#13094011C2211yescharacteristic
23#13094006—21no—
24#13094004C2211yescharacteristic
25#13093995C2211yescharacteristic
26Q8×Dic47C2211yescharacteristic
27C4×Dic94C2211yescharacteristic
28C4×D188—21no—
29C4×D188C2211yescharacteristic
30#13093986—21no—
31#13093986C2211yescharacteristic
32C4×C22⋊D47—21no—
33#13093983—21no—
34#13093982—21no—
35#13093982C2211yescharacteristic
36C42×D47—21no—
37C42×D47C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093955C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51#13093935C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C2×C22⋊D47—21no—
63#10625354—22no—
64#10625354—22no—
65C2×D188—21no—
66C2×D188C2311yescharacteristic
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47D411yescharacteristic
71C2×C4×D47D411yescharacteristic
72C2×C4×D47C2311yescharacteristic
73C2×Dic94C2311yescharacteristic
74SD16×C47—22no—
75C2×C8×C47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C4⋊C4×C47—21no—
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C22⋊C4×C47—21no—
81C42×C47—21no—
82C42×C47C2311yescharacteristic
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86#10625337—22no—
87#10625334—22no—
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⋊Dic47—21no—
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47D411yescharacteristic
103C4×Dic47D411yescharacteristic
104C4×Dic47C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107#10625325—22no—
108C23×C47—21no—
109C22×D47—21no—
110C22×D47C2×D411yescharacteristic
111Q8×C47—21no—
112Q8×C47#4112yes—
113D4×C47—21no—
114D4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—42no—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C22⋊D47—42no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129D188—24no—
130D188—21no—
131D188#4112yes—
132C4×D47—24no—
133C4×D47—21no—
134C4×D47—21no—
135C4×D47—41no—
136C4×D47—41no—
137C4×D47—42no—
138C4×D47—42no—
139Dic94—21no—
140Dic94—21no—
141C8×C47—21no—
142C8×C47—21no—
143C47⋊C8—21no—
144C47⋊C8—21no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47C22×D411yescharacteristic
149C2×D47—21no—
150C2×D47—22no—
151C2×D47—21no—
152C2×D47—21no—
153C2×D47—41no—
154C2×D47—41no—
155C4×C47—22no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47C2×#4111yescharacteristic
161C4×C47C2×#4111yescharacteristic
162Dic47—21no—
163Dic47—21no—
164Dic47—21no—
165Dic47—41no—
166Dic47—41no—
167Dic47—41no—
168#3111—471nomaximal, Sylow
169C2×C47—81no—
170C2×C47#52511yescharacteristic
171C2×C47#57511yescharacteristic
172C2×C47#57511yescharacteristic
173D47—41no—
174D47—42no—
175#529—471no—
176C4×#41—471no—
177#485—471no—
178#482—471no—
179#479—471no—
180#478—471no—
181#464—471no—
182#463—471no—
183#452—471no—
184#449—471no—
185#442—471no—
186#441—471no—
187#440—471no—
188#440D4711yescharacteristic, complemented
189#432—471no—
190C47#311111yescharacteristic, complemented, Sylow
191C2×#41—471no—
192C2×Q16—471no—
193C2×SD16—471no—
194C2×SD16C2×D4711yescharacteristic
195C2×D8—471no—
196#126—941no—
197#125—471no—
198#124—471no—
199#123—941no—
200C22⋊Q8—471no—
201#121—471no—
202C4×Q8—471no—
203C4×Q8—471no—
204C4×Q8C2×D4711yescharacteristic
205C4×D4—471no—
206C4×D4—471no—
207C4×D4—941no—
208C4×D4—941no—
209C4×D4—941no—
210C4×D4C2×D4711yescharacteristic
211#117—471no—
212#117—941no—
213#117—941no—
214C2×C42—471no—
215C2×C42—941no—
216#107—471no—
217#107C2×D4711yescharacteristic
218#106—471no—
219#106—471no—
220C4⋊C8—471no—
221C4⋊C8—471no—
222#103—471no—
223#103—471no—
224#103—471no—
225#103C2×D4711yescharacteristic
226#102—471no—
227#102—471no—
228#102—471no—
229#102C2×D4711yescharacteristic
230C22⋊C8—471no—
231C22⋊C8—471no—
232#97—471no—
233#97C2×D4711yescharacteristic
234#41—942no—
235#41—942no—
236C2×Q8—471no—
237C2×Q8C22×D4711yescharacteristic
238C2×D4—471no—
239C2×D4—941no—
240C2×D4—941no—
241C2×D4C22×D4711yescharacteristic
242C22×C4—21no—
243C22×C4—471no—
244C22×C4—471no—
245C22×C4—471no—
246C22×C4—941no—
247C22×C4—941no—
248C22×C4—941no—
249Q16—942no—
250SD16—22no—
251SD16—942no—
252D8—942no—
253C2×C8—471no—
254C2×C8—471no—
255C2×C8C22×D4711yescharacteristic
256C2×C8C22×D4711yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—471no—
259C4⋊C4—471no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4C22×D4711yescharacteristic
266C4⋊C4C22×D4711yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C42—21no—
276C42—471no—
277C42—471no—
278C42—471no—
279C42—941no—
280C42—941no—
281C42—941no—
282C42C22×D4711yescharacteristic
283C23—21no—
284C23—471no—
285C23—941no—
286Q8—21no—
287Q8—941no—
288Q8—941no—
289Q8#1062535012yes—
290D4—21no—
291D4—21no—
292D4—472no—
293D4—944no—
294D4—941no—
295D4—1882no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—471no—
301C2×C4—471no—
302C2×C4—471no—
303C2×C4—944no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—1881no—
310C2×C4—1881no—
311C2×C4—1882no—
312C2×C4—1882no—
313C2×C4D4×D4711yescharacteristic
314C2×C4D4×D4711yescharacteristic
315C2×C4C23×D4711yescharacteristic
316C8—21no—
317C8—21no—
318C8—941no—
319C8—941no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—942no—
324C22—941no—
325C22—941no—
326C22—941no—
327C22—1881no—
328C22—1881no—
329C22C2×D4×D4711yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—941no—
336C4—941no—
337C4—941no—
338C4—1881no—
339C4—1881no—
340C4—1881no—
341C4#41×D4711yescharacteristic
342C4C2×#1062535011yescharacteristic
343C2—81no—
344C2—1881no—
345C2—1882no—
346C2#1568963211yescharacteristic
347C2#1568991911yescharacteristic
348C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#440C2
socleC22×C47C22×D4
hypercenter#440D47
hypocenterC47#3111
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #15689655C2semidirect
2. C4×#10625354C2semidirect
3. #15689466C2semidirect
4. #15689445C2semidirect
5. #15689432C2semidirect
6. #15689426C2semidirect
7. #15689343C2semidirect
8. #15689337C2semidirect
9. #15689288C2semidirect
11. #15689233C2semidirect
12. #15689228C2semidirect
13. #15689225C2semidirect
14. #15689178C2semidirect
15. C47×#440C2semidirect
188. #440D47semidirect
190. C47#3111semidirect