Finite Group Databasebeta

← #20253473

Subgroups — #20253473

Order 6016.

390 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689658C211yesmaximal, characteristic
2C4×Q8×D47C211yesmaximal, characteristic, complemented
3#15689455C211yesmaximal, characteristic, complemented
4#15689438C211yesmaximal, characteristic
5#15689427C211yesmaximal, characteristic, complemented
6#15689346C211yesmaximal, characteristic, complemented
7#15689345C211yesmaximal, characteristic, complemented
8#15689280C211yesmaximal, characteristic, complemented
9#15689263C211yesmaximal, characteristic
10#15689217C211yesmaximal, characteristic, complemented
11#15689215C211yesmaximal, characteristic, complemented
12#15689210C211yesmaximal, characteristic, complemented
13#15689208C211yesmaximal, characteristic, complemented
14#15689175C211yesmaximal, characteristic, complemented
15C47×#479C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×Dic188C2211yescharacteristic
18C2×#10625337C2211yescharacteristic
19C2×#10625325C2211yescharacteristic
20C2×#10625336C2211yescharacteristic
21#13094019—21no—
22#13094012C2211yescharacteristic
23#13094009—21no—
24#13094004C2211yescharacteristic
25#13093999C2211yescharacteristic
26Q8×Dic47C2211yescharacteristic
27C4×Dic94—21no—
28C4×Dic94C2211yescharacteristic
29#13093989—21no—
30#13093989C2211yescharacteristic
31#13093989C2211yescharacteristic
32#13093986—21no—
33#13093986C2211yescharacteristic
34#13093982—21no—
35C4⋊C4×D47—21no—
36C4⋊C4×D47C2211yescharacteristic
37C42×D47—21no—
38C42×D47C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093955C2211yescharacteristic
41C4⋊(C47⋊C8)C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093947C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093944C2211yescharacteristic
48(C2×D47)⋊C8C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50C8×Dic47C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52#125×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60Q8×D47—22no—
61Q8×D47—22no—
62C2×D188—21no—
63C2×D188C2311yescharacteristic
64C2×C4×D47—21no—
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×C4×D47D411yescharacteristic
68C2×C4×D47D411yescharacteristic
69C2×C4×D47C2311yescharacteristic
70C2×Dic94—21no—
71C2×Dic94C2311yescharacteristic
72C2×Dic94C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C42×C47—21no—
82C42×C47C2311yescharacteristic
83#10625337—22no—
84#10625336—22no—
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⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47D411yescharacteristic
102C4×Dic47D411yescharacteristic
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106Dic188—22no—
107#10625325—22no—
108C22×D47—21no—
109C22×D47C2×D411yescharacteristic
110Q8×C47—21no—
111Q8×C47#4112yes—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2411yescharacteristic
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124C2×Dic47C2×D411yescharacteristic
125D188—21no—
126D188—21no—
127D188—42no—
128C4×D47—24no—
129C4×D47—22no—
130C4×D47—21no—
131C4×D47—21no—
132C4×D47—22no—
133C4×D47—42no—
134C4×D47—42no—
135Dic94—24no—
136Dic94—21no—
137Dic94—21no—
138Dic94—21no—
139Dic94#4112yes—
140C8×C47—21no—
141C8×C47—21no—
142C47⋊C8—21no—
143C47⋊C8—21no—
144C22×C47C22×D411yescharacteristic
145C2×D47—21no—
146C2×D47—21no—
147C2×D47—41no—
148C2×D47—41no—
149C2×D47—41no—
150C2×D47#13512yes—
151C4×C47—22no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47C2×#4111yescharacteristic
158C4×C47C2×#4111yescharacteristic
159Dic47—21no—
160Dic47—22no—
161Dic47—21no—
162Dic47—41no—
163Dic47—41no—
164Dic47#13712yes—
165#3108—471nomaximal, Sylow
166C2×C47#52511yescharacteristic
167C2×C47C2×#13511yescharacteristic
168C2×C47C2×#13711yescharacteristic
169D47—22no—
170D47—81no—
171#529—471no—
172C2×C4×Q8—471no—
173#483—471no—
174#480—471no—
175#479—471no—
176#479D4711yescharacteristic, complemented
177#464—471no—
178#464—471no—
179#451—471no—
180#448—471no—
181C4×Q16—471no—
182C4×Q16—471no—
183C4×SD16—471no—
184C4×SD16—471no—
185#431—471no—
186C47#310811yescharacteristic, complemented, Sylow
187C22×Q8—471no—
188C2×Q16—471no—
189C2×Q16—471no—
190C2×SD16—471no—
191C2×SD16—471no—
192#126—941no—
193#125C2×D4711yescharacteristic
194#124—471no—
195#123—941no—
196C22⋊Q8—471no—
197#121—471no—
198C4×Q8—471no—
199C4×Q8—471no—
200C4×Q8—471no—
201C4×Q8—471no—
202C4×Q8—941no—
203C4×Q8—941no—
204C4×Q8C2×D4711yescharacteristic
205C4×D4—471no—
206C4×D4—941no—
207#117—941no—
208C2×C4⋊C4—471no—
209C2×C4⋊C4—941no—
210C2×C42—471no—
211C2×C42—941no—
212#107—471no—
213#107C2×D4711yescharacteristic
214#106—471no—
215#106C2×D4711yescharacteristic
216C4⋊C8—471no—
217C4⋊C8C2×D4711yescharacteristic
218#103—471no—
219#103—471no—
220#103—471no—
221#103—471no—
222#103C2×D4711yescharacteristic
223#103C2×D4711yescharacteristic
224#102—471no—
225#102—471no—
226C22⋊C8—471no—
227C22⋊C8—471no—
228C4×C8—471no—
229C4×C8—471no—
230C2×Q8—471no—
231C2×Q8—471no—
232C2×Q8—941no—
233C2×Q8—942no—
234C2×Q8—942no—
235C2×Q8C22×D4711yescharacteristic
236C2×D4—471no—
237C2×D4—941no—
238C22×C4—471no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4—941no—
242C22×C4—941no—
243C22×C4—941no—
244Q16—942no—
245Q16—942no—
246SD16—942no—
247SD16—942no—
248C2×C8—471no—
249C2×C8—471no—
250C2×C8C22×D4711yescharacteristic
251C2×C8C22×D4711yescharacteristic
252C4⋊C4—21no—
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—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C42—21no—
271C42—471no—
272C42—471no—
273C42—471no—
274C42—941no—
275C42—941no—
276C42—941no—
277C42—941no—
278C42C22×D4711yescharacteristic
279C23—471no—
280C23—941no—
281Q8—21no—
282Q8—472no—
283Q8—944no—
284Q8—941no—
285Q8—941no—
286Q8—941no—
287Q8#1062535412yes—
288D4—941no—
289D4—941no—
290D4—1882no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—471no—
296C2×C4—471no—
297C2×C4—471no—
298C2×C4—942no—
299C2×C4—942no—
300C2×C4—944no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—1882no—
307C2×C4—1882no—
308C2×C4D4×D4711yescharacteristic
309C2×C4D4×D4711yescharacteristic
310C2×C4C23×D4711yescharacteristic
311C8—21no—
312C8—21no—
313C8—941no—
314C8—941no—
315C22—472no—
316C22—941no—
317C22—941no—
318C22—1881no—
319C22—1881no—
320C22—1881no—
321C22C2×D4×D4711yescharacteristic
322C4—22no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—472no—
329C4—941no—
330C4—942no—
331C4—941no—
332C4—1881no—
333C4—1881no—
334C4#41×D4711yescharacteristic
335C4C2×#1062535411yescharacteristic
336C2—942no—
337C2—3761no—
338C2#1568963611yescharacteristic
339C2#135×D4711yescharacteristic
340C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#479C2
socleC22×C47C22×D4
hypercenter#479D47
hypocenterC47#3108
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D47C2semidirect
3. #15689455C2semidirect
5. #15689427C2semidirect
6. #15689346C2semidirect
7. #15689345C2semidirect
8. #15689280C2semidirect
10. #15689217C2semidirect
11. #15689215C2semidirect
12. #15689210C2semidirect
13. #15689208C2semidirect
14. #15689175C2semidirect
15. C47×#479C2semidirect
176. #479D47semidirect
186. C47#3108semidirect