Finite Group Databasebeta

← #20253467

Subgroups — #20253467

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#15689652C211yesmaximal, characteristic
2C4×Q8×D47C211yesmaximal, characteristic, complemented
3#15689452C211yesmaximal, characteristic, complemented
4#15689435C211yesmaximal, characteristic
5#15689431C211yesmaximal, characteristic, complemented
6#15689430C211yesmaximal, characteristic, complemented
7#15689342C211yesmaximal, characteristic, complemented
8#15689277C211yesmaximal, characteristic, complemented
9#15689260C211yesmaximal, characteristic
10Q16×Dic47C211yesmaximal, characteristic, complemented
11#15689215C211yesmaximal, characteristic, complemented
12#15689214C211yesmaximal, characteristic, complemented
13SD16×Dic47C211yesmaximal, characteristic, complemented
14#15689175C211yesmaximal, characteristic, complemented
15C47×#464C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19#13094017—21no—
20#13094016C2211yescharacteristic
21#13094006—21no—
22#13094000C2211yescharacteristic
23#13093995C2211yescharacteristic
24Q8×Dic47C2211yescharacteristic
25Q8×Dic47C2211yescharacteristic
26C4×Dic94—21no—
27C4×Dic94C2211yescharacteristic
28#13093989—21no—
29#13093989C2211yescharacteristic
30D4×Dic47C2211yescharacteristic
31(C22⋊D47)⋊C4—21no—
32#13093980—21no—
33C4⋊C4×D47—21no—
34C4⋊C4×D47C2211yescharacteristic
35C42×D47—21no—
36C42×D47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41C4⋊(C47⋊C8)C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093945C2211yescharacteristic
48(C2×D47)⋊C8C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50C8×Dic47C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×Q16×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54#124×C47C2211yescharacteristic
55C4×Q8×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C22×Dic47—21no—
64Q8×D47—22no—
65Q8×D47—22no—
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×C4×D47D411yescharacteristic
69C2×C4×D47D411yescharacteristic
70C2×C4×D47C2311yescharacteristic
71C2×Dic94—21no—
72C2×Dic94C2311yescharacteristic
73Q16×C47—22no—
74SD16×C47—22no—
75C2×C8×C47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C4⋊C4×C47—21no—
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C42×C47—21no—
82C42×C47C2311yescharacteristic
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85#10625337—22no—
86#10625335—22no—
87(C2×D47)⋊C4—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47D411yescharacteristic
104C4×Dic47D411yescharacteristic
105C4×Dic47C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47—21no—
109C22×D47C2×D411yescharacteristic
110Q8×C47—21no—
111Q8×C47—21no—
112Q8×C47—21no—
113Q8×C47#4112yes—
114D4×C47—21no—
115D4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C22⋊D47—42no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—42no—
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131C4×D47—24no—
132C4×D47—22no—
133C4×D47—21no—
134C4×D47—21no—
135C4×D47—22no—
136C4×D47—42no—
137Dic94—24no—
138Dic94—21no—
139Dic94#4112yes—
140C8×C47—21no—
141C8×C47—21no—
142C47⋊C8—21no—
143C47⋊C8—21no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47C22×D411yescharacteristic
148C2×D47—21no—
149C2×D47—21no—
150C2×D47#13512yes—
151C4×C47—22no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47C2×#4111yescharacteristic
157C4×C47C2×#4111yescharacteristic
158Dic47—21no—
159Dic47—22no—
160Dic47—21no—
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164Dic47#13712yes—
165#3108—471nomaximal, Sylow
166C2×C47—81no—
167C2×C47#52511yescharacteristic
168C2×C47C2×#13511yescharacteristic
169C2×C47C2×#13711yescharacteristic
170D47—22no—
171#529—471no—
172C2×C4×Q8—471no—
173#483—471no—
174#480—471no—
175#479—471no—
176#479—471no—
177#464—471no—
178#464D4711yescharacteristic, complemented
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×Q16C2×D4711yescharacteristic
190C2×SD16—471no—
191C2×SD16C2×D4711yescharacteristic
192#126—941no—
193#125—471no—
194#124C2×D4711yescharacteristic
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#107—471no—
214#106—471no—
215#106—471no—
216C4⋊C8—471no—
217C4⋊C8C2×D4711yescharacteristic
218#103—471no—
219#103—471no—
220#103—471no—
221#103—471no—
222#103—471no—
223#103C2×D4711yescharacteristic
224#102—471no—
225#102C2×D4711yescharacteristic
226C22⋊C8—471no—
227C22⋊C8—471no—
228C4×C8—471no—
229C4×C8—471no—
230C2×Q8—471no—
231C2×Q8—941no—
232C2×Q8—942no—
233C2×Q8—942no—
234C2×Q8C22×D4711yescharacteristic
235C2×Q8C22×D4711yescharacteristic
236C2×D4—941no—
237C2×D4C22×D4711yescharacteristic
238C22×C4—471no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4—941no—
242C22×C4—941no—
243C22×C4—941no—
244Q16—22no—
245Q16—942no—
246SD16—22no—
247SD16—942no—
248C2×C8—471no—
249C2×C8—471no—
250C2×C8C22×D4711yescharacteristic
251C2×C8C22×D4711yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—471no—
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⋊C4—941no—
264C4⋊C4C22×D4711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
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—21no—
280C23—471no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—472no—
285Q8—944no—
286Q8—941no—
287Q8#1062535212yes—
288D4—21no—
289D4—21no—
290D4—1882no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—471no—
295C2×C4—471no—
296C2×C4—471no—
297C2×C4—942no—
298C2×C4—942no—
299C2×C4—944no—
300C2×C4—941no—
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—41no—
316C22—41no—
317C22—41no—
318C22—472no—
319C22—941no—
320C22—941no—
321C22C2×D4×D4711yescharacteristic
322C4—22no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—472no—
328C4—941no—
329C4—942no—
330C4—941no—
331C4—1881no—
332C4—1881no—
333C4—1881no—
334C4#41×D4711yescharacteristic
335C4C2×#1062535211yescharacteristic
336C2—81no—
337C2—942no—
338C2#1568963311yescharacteristic
339C2#135×D4711yescharacteristic
340C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#464C2
socleC22×C47C22×D4
hypercenter#464D47
hypocenterC47#3108
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D47C2semidirect
3. #15689452C2semidirect
5. #15689431C2semidirect
6. #15689430C2semidirect
7. #15689342C2semidirect
8. #15689277C2semidirect
10. Q16×Dic47C2semidirect
11. #15689215C2semidirect
12. #15689214C2semidirect
13. SD16×Dic47C2semidirect
14. #15689175C2semidirect
15. C47×#464C2semidirect
178. #464D47semidirect
186. C47#3108semidirect