Finite Group Databasebeta

← #20254785

Subgroups — #20254785

Order 6016.

354 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689659C211yesmaximal, characteristic, complemented
2#15689654C211yesmaximal, characteristic, complemented
3#15689432C211yesmaximal, characteristic, complemented
4#15689429C211yesmaximal, characteristic, complemented
5#15689426C211yesmaximal, characteristic, complemented
6#15689421C211yesmaximal, characteristic, complemented
7#15689379C211yesmaximal, characteristic, complemented
8#15689374C211yesmaximal, characteristic
9#15689369C211yesmaximal, characteristic, complemented
10#15689348C211yesmaximal, characteristic, complemented
11#15689343C211yesmaximal, characteristic, complemented
12#15689340C211yesmaximal, characteristic, complemented
13#15689337C211yesmaximal, characteristic, complemented
14#15689146C211yesmaximal, characteristic, complemented
15C47×#468C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C2×#10625325C2211yescharacteristic
18C2×#10625334C2211yescharacteristic
19C2×#10625329C2211yescharacteristic
20#13094019—21no—
21#13094017—21no—
22#13094015C2211yescharacteristic
23#13094015C2211yescharacteristic
24#13094013C2211yescharacteristic
25#13094011C2211yescharacteristic
26#13094008—21no—
27#13094005—21no—
28#13094003C2211yescharacteristic
29#13093998C2211yescharacteristic
30Q8×Dic47C2211yescharacteristic
31#13093989C2211yescharacteristic
32D4×Dic47—21no—
33D4×Dic47C2211yescharacteristic
34#13093986C2211yescharacteristic
35(C22⋊D47)⋊C4—21no—
36#13093982—21no—
37#13093980—21no—
38C2×C4×Dic47C2211yescharacteristic
39#13093958C2211yescharacteristic
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
53C2×M16×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C22×Dic47—21no—
65C22×Dic47D411yescharacteristic
66C22×Dic47D411yescharacteristic
67C2×D188C2311yescharacteristic
68C2×C4×D47—21no—
69C2×Dic94C2311yescharacteristic
70SD16×C47—41no—
71M16×C47—41no—
72C2×C8×C47C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C4⋊C4×C47—21no—
75C4⋊C4×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C22⋊C4×C47—21no—
78C22⋊C4×C47—21no—
79C22⋊Dic47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83#10625337—41no—
84#10625334—41no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47—21no—
91C4⋊Dic47—21no—
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47D411yescharacteristic
101C4×Dic47D411yescharacteristic
102C4×Dic47C2311yescharacteristic
103C4×Dic47C2311yescharacteristic
104#10625329—41no—
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107#10625325—41no—
108C23×C47—21no—
109C23×C47C2×D411yescharacteristic
110C22×D47—21no—
111Q8×C47—21no—
112Q8×C47—21no—
113D4×C47—21no—
114D4×C47—21no—
115D4×C47—42no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2411yescharacteristic
123C22⋊D47—42no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—41no—
128C2×Dic47—41no—
129C2×Dic47—42no—
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133C2×Dic47C2×D411yescharacteristic
134D188—21no—
135D188—21no—
136C4×D47—42no—
137Dic94—21no—
138Dic94—21no—
139C8×C47—21no—
140C8×C47—21no—
141C47⋊C8—21no—
142C47⋊C8—21no—
143C22×C47—21no—
144C22×C47—21no—
145C22×C47—21no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47—41no—
149C22×C47C22×D411yescharacteristic
150C2×D47—41no—
151C2×D47—41no—
152C2×D47—41no—
153C4×C47—21no—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47H(5,𝔽2)11yescharacteristic
158C4×C472−1+411yescharacteristic
159Dic47—21no—
160Dic47—21no—
161Dic47—21no—
162Dic47—21no—
163Dic47—41no—
164Dic47—41no—
165Dic47—41no—
166#3256—471nomaximal, Sylow
167C2×C47—41no—
168C2×C47—81no—
169C2×C47#53711yescharacteristic
170C2×C47#57511yescharacteristic
171C2×C47#57511yescharacteristic
172D47—81no—
173#529—471no—
174#529—471no—
175#479—471no—
176#479—471no—
177#478—471no—
178#478—471no—
179#470—471no—
180#469—471no—
181#468—471no—
182#468D4711yescharacteristic, complemented
183#464—471no—
184#464—471no—
185#463—471no—
186#463—471no—
187#423—471no—
188C47#325611yescharacteristic, complemented, Sylow
189C2×Q16—471no—
190C2×SD16—471no—
191C2×SD16C2×D4711yescharacteristic
192C2×D8—471no—
193C2×M16—471no—
194C2×M16C2×D4711yescharacteristic
195#126—941no—
196#126—941no—
197#125—471no—
198#125—471no—
199#124—471no—
200#124—471no—
201#123—941no—
202#123—941no—
203C22⋊Q8—471no—
204C22⋊Q8C2×D4711yescharacteristic
205#121—471no—
206#121C2×D4711yescharacteristic
207C4×Q8—471no—
208C4×Q8—471no—
209C4×D4—471no—
210C4×D4—471no—
211C4×D4—941no—
212C4×D4—941no—
213#117—941no—
214#117—941no—
215C2×C42—471no—
216#107—471no—
217#107C2×D4711yescharacteristic
218#106—471no—
219#106—471no—
220C4⋊C8—471no—
221C4⋊C8—471no—
222C4⋊C8—471no—
223C4⋊C8—471no—
224#103—471no—
225#103—471no—
226#103—471no—
227#103C2×D4711yescharacteristic
228#102—471no—
229#102—471no—
230#102—471no—
231#102C2×D4711yescharacteristic
232C2×Q8—471no—
233C2×Q8C22×D4711yescharacteristic
234C2×D4—21no—
235C2×D4—471no—
236C2×D4—941no—
237C2×D4C22×D4711yescharacteristic
238C22×C4—471no—
239C22×C4—471no—
240C22×C4—941no—
241C22×C4—941no—
242C22×C4C22×D4711yescharacteristic
243Q16—1881no—
244SD16—41no—
245SD16—1881no—
246D8—1881no—
247M16—41no—
248M16—1881no—
249C2×C8—471no—
250C2×C8—471no—
251C2×C8C22×D4711yescharacteristic
252C2×C8C22×D4711yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—471no—
255C4⋊C4—471no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4C22×D4711yescharacteristic
264C4⋊C4C22×D4711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C42—471no—
276C42—471no—
277C42—471no—
278C42—471no—
279C42—941no—
280C42—941no—
281C23—21no—
282C23—941no—
283C23D4×D4711yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—941no—
287Q8—941no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—941no—
292D4—941no—
293D4—1882no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—471no—
300C2×C4—471no—
301C2×C4—471no—
302C2×C4—471no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—1882no—
307C2×C4—1881no—
308C2×C4—1881no—
309C2×C4—1882no—
310C2×C4D4×D4711yescharacteristic
311C2×C4C23×D4711yescharacteristic
312C8—21no—
313C8—21no—
314C8—941no—
315C8—941no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—1881no—
323C22—1881no—
324C22—1881no—
325C22C2×D4×D4711yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—941no—
331C4—941no—
332C4—941no—
333C4—941no—
334C4—1881no—
335C4—1881no—
336C4—1881no—
337C4#1309406911yescharacteristic
338C4#1309407111yescharacteristic
339C2—41no—
340C2—81no—
341C2—3761no—
342C2#1568970011yescharacteristic
343C2#1568991911yescharacteristic
344C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#468C2
socleC22×C47C22×D4
hypercenter#468D47
hypocenterC47#3256
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #15689659C2semidirect
2. #15689654C2semidirect
3. #15689432C2semidirect
4. #15689429C2semidirect
5. #15689426C2semidirect
6. #15689421C2semidirect
7. #15689379C2semidirect
9. #15689369C2semidirect
10. #15689348C2semidirect
11. #15689343C2semidirect
12. #15689340C2semidirect
13. #15689337C2semidirect
14. #15689146C2semidirect
15. C47×#468C2semidirect
182. #468D47semidirect
188. C47#3256semidirect