Finite Group Databasebeta

← #20254739

Subgroups — #20254739

Order 6016.

360 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#15689658C211yesmaximal, characteristic, complemented
2#15689655C211yesmaximal, characteristic, complemented
3#15689433C211yesmaximal, characteristic, complemented
4#15689427C211yesmaximal, characteristic, complemented
5#15689426C211yesmaximal, characteristic, complemented
6#15689365C211yesmaximal, characteristic, complemented
7#15689358C211yesmaximal, characteristic
8#15689353C211yesmaximal, characteristic, complemented
9#15689351C211yesmaximal, characteristic, complemented
10#15689346C211yesmaximal, characteristic, complemented
11#15689344C211yesmaximal, characteristic, complemented
12#15689338C211yesmaximal, characteristic, complemented
13#15689337C211yesmaximal, characteristic, complemented
14C4⋊C8×D47C211yesmaximal, characteristic, complemented
15C47×#478C211yesmaximal, characteristic, complemented
16C2×Dic188C2211yescharacteristic
17C2×#10625325C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20C2×C8×D47C2211yescharacteristic
21C2×C8×D47C2211yescharacteristic
22#13094019—21no—
23#13094017—21no—
24#13094015C2211yescharacteristic
25#13094012C2211yescharacteristic
26#13094011C2211yescharacteristic
27#13094009—21no—
28#13094006—21no—
29#13094004C2211yescharacteristic
30#13094004C2211yescharacteristic
31#13093999C2211yescharacteristic
32#13093995C2211yescharacteristic
33C4×Dic94C2211yescharacteristic
34#13093989C2211yescharacteristic
35#13093986—21no—
36#13093986C2211yescharacteristic
37C4×C22⋊D47—21no—
38#13093983—21no—
39#13093982—21no—
40C42×D47C2211yescharacteristic
41#13093957C2211yescharacteristic
42#13093955C2211yescharacteristic
43C4⋊(C47⋊C8)C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093947C2211yescharacteristic
49#13093947C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093944C2211yescharacteristic
52#125×C47C2211yescharacteristic
53C4×D4×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×D4×C47C2311yescharacteristic
60C22×C4×C47—21no—
61C2×C22⋊D47—21no—
62C2×D188—21no—
63C2×D188C2311yescharacteristic
64C2×C4×D47—21no—
65C2×C4×D47D411yescharacteristic
66C2×C4×D47D411yescharacteristic
67C2×C4×D47C2311yescharacteristic
68C2×Dic94C2311yescharacteristic
69C2×Dic94C2311yescharacteristic
70C2×C8×C47C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C22⋊C4×C47—21no—
78C42×C47C2311yescharacteristic
79C22⋊Dic47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82#10625335—41no—
83#10625334—41no—
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—
90C4⋊Dic47—21no—
91C4⋊Dic47—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47C2311yescharacteristic
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47D411yescharacteristic
100C4×Dic47D411yescharacteristic
101C4×Dic47C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104Dic188—41no—
105#10625325—41no—
106C8×D47—41no—
107C8×D47—41no—
108C23×C47—21no—
109C22×D47—21no—
110C22×D47C2×D411yescharacteristic
111D4×C47—21no—
112D4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—42no—
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2411yescharacteristic
120C22⋊D47—42no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47C2×D411yescharacteristic
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127D188—21no—
128D188—21no—
129D188—42no—
130C4×D47—22no—
131C4×D47—21no—
132C4×D47—21no—
133C4×D47—41no—
134C4×D47—42no—
135Dic94—21no—
136Dic94—21no—
137Dic94—21no—
138Dic94—21no—
139C8×C47—21no—
140C8×C47—21no—
141C47⋊C8—21no—
142C47⋊C8—21no—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47C22×D411yescharacteristic
147C2×D47—21no—
148C2×D47—21no—
149C2×D47—41no—
150C2×D47—41no—
151C2×D47—41no—
152C2×D47#13512yes—
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47H(5,𝔽2)11yescharacteristic
159C4×C472−1+411yescharacteristic
160Dic47—21no—
161Dic47—21no—
162Dic47—21no—
163Dic47—41no—
164Dic47—41no—
165Dic47—41no—
166#3250—471nomaximal, Sylow
167C2×C47—81no—
168C2×C47#53711yescharacteristic
169C2×C47C2×#13511yescharacteristic
170C2×C47#57511yescharacteristic
171D47—22no—
172D47—81no—
173#529—471no—
174#529—471no—
175#479—471no—
176#479—471no—
177#478—471no—
178#478D4711yescharacteristic, complemented
179#467—471no—
180#466—471no—
181#465—471no—
182#465—471no—
183#464—471no—
184#464—471no—
185#463—471no—
186#463—471no—
187C2×C4⋊C8—471no—
188C47#325011yescharacteristic, complemented, Sylow
189C2×Q16—471no—
190C2×SD16—471no—
191C2×SD16—471no—
192C2×D8—471no—
193C22×C8—471no—
194C22×C8—471no—
195#126—941no—
196#126—941no—
197#125—471no—
198#125C2×D4711yescharacteristic
199#124—471no—
200#124—471no—
201#123—941no—
202#123—941no—
203C22⋊Q8—471no—
204C22⋊Q8—471no—
205#121—471no—
206#121—471no—
207C4×Q8—471no—
208C4×Q8—471no—
209C4×D4—471no—
210C4×D4—941no—
211C4×D4—941no—
212C4×D4C2×D4711yescharacteristic
213#117—941no—
214#117—941no—
215C2×C42—471no—
216#107—471no—
217#107C2×D4711yescharacteristic
218#106—471no—
219#106C2×D4711yescharacteristic
220C4⋊C8—471no—
221C4⋊C8—471no—
222C4⋊C8—471no—
223C4⋊C8C2×D4711yescharacteristic
224#103—471no—
225#103—471no—
226#103—471no—
227#103—471no—
228#102—471no—
229#102—471no—
230#102C2×D4711yescharacteristic
231#102C2×D4711yescharacteristic
232C2×Q8—471no—
233C2×Q8—471no—
234C2×D4—471no—
235C2×D4—941no—
236C2×D4—941no—
237C2×D4C22×D4711yescharacteristic
238C22×C4—21no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4—471no—
242C22×C4—941no—
243Q16—1881no—
244SD16—1881no—
245SD16—1881no—
246D8—1881no—
247C2×C8—471no—
248C2×C8—471no—
249C2×C8—1881no—
250C2×C8—1881no—
251C2×C8C22×D4711yescharacteristic
252C2×C8C22×D4711yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—471no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4C22×D4711yescharacteristic
263C4⋊C4C22×D4711yescharacteristic
264C4⋊C4C22×D4711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—941no—
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—941no—
279C42—941no—
280C42C22×D4711yescharacteristic
281C23—21no—
282C23—471no—
283C23—941no—
284Q8—941no—
285Q8—941no—
286Q8—941no—
287Q8—941no—
288D4—21no—
289D4—21no—
290D4—941no—
291D4—941no—
292D4—1882no—
293D4—1882no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—471no—
299C2×C4—471no—
300C2×C4—471no—
301C2×C4—942no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—1881no—
308C2×C4—1882no—
309C2×C4D4×D4711yescharacteristic
310C2×C4D4×D4711yescharacteristic
311C2×C4C23×D4711yescharacteristic
312C8—21no—
313C8—21no—
314C8—941no—
315C8—941no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—472no—
320C22—941no—
321C22—941no—
322C22—1881no—
323C22—1881no—
324C22—1881no—
325C22C2×D4×D4711yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—941no—
332C4—941no—
333C4—941no—
334C4—1881no—
335C4—1881no—
336C4—1881no—
337C4#1309407011yescharacteristic
338C4#1309407211yescharacteristic
339C2—81no—
340C2—942no—
341C2—3761no—
342C2#1568970311yescharacteristic
343C2#135×D4711yescharacteristic
344C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#478C2
socleC22×C47C22×D4
hypercenter#478D47
hypocenterC47#3250
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #15689658C2semidirect
2. #15689655C2semidirect
3. #15689433C2semidirect
4. #15689427C2semidirect
5. #15689426C2semidirect
6. #15689365C2semidirect
8. #15689353C2semidirect
9. #15689351C2semidirect
10. #15689346C2semidirect
11. #15689344C2semidirect
12. #15689338C2semidirect
13. #15689337C2semidirect
14. C4⋊C8×D47C2semidirect
15. C47×#478C2semidirect
178. #478D47semidirect
188. C47#3250semidirect