Finite Group Databasebeta

← #20254009

Subgroups — #20254009

Order 6016.

362 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#15689733C211yesmaximal, characteristic, complemented
2#15689726C211yesmaximal, characteristic
3#15689523C211yesmaximal, characteristic, complemented
4#15689494C211yesmaximal, characteristic, complemented
5#15689490C211yesmaximal, characteristic, complemented
6#15689486C211yesmaximal, characteristic, complemented
7#15689371C211yesmaximal, characteristic, complemented
8#15689367C211yesmaximal, characteristic, complemented
9#15689352C211yesmaximal, characteristic, complemented
10#15689226C211yesmaximal, characteristic, complemented
11#15689220C211yesmaximal, characteristic, complemented
12SD16×Dic47C211yesmaximal, characteristic, complemented
13#15689210C211yesmaximal, characteristic, complemented
14#15689078C211yesmaximal, characteristic, complemented
15C47×#465C211yesmaximal, characteristic, complemented
16C2×#10625325C2211yescharacteristic
17C2×#10625335C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19C2×#10625329C2211yescharacteristic
20#13094022C2211yescharacteristic
21#13094020C2211yescharacteristic
22#13094017—21no—
23#13094017—21no—
24#13094015—21no—
25#13094015C2211yescharacteristic
26#13094015C2211yescharacteristic
27#13094014—21no—
28#13094008—21no—
29#13094006—21no—
30#13094003C2211yescharacteristic
31#13093998C2211yescharacteristic
32#13093996—21no—
33#13093995—21no—
34Q8×Dic47C2211yescharacteristic
35#13093989C2211yescharacteristic
36D4×Dic47C2211yescharacteristic
37#13093986C2211yescharacteristic
38#13093983C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093948C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093934C2211yescharacteristic
49#13093934C2211yescharacteristic
50C8×Dic47C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C22×C8×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C22×Dic47—21no—
67C2×D188C2311yescharacteristic
68C2×C4×D47—21no—
69C2×Dic94C2311yescharacteristic
70SD16×C47—22no—
71C2×C8×C47—22no—
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⋊Dic47D411yescharacteristic
82C22⋊Dic47D411yescharacteristic
83#10625336—22no—
84#10625335—22no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47D411yescharacteristic
91C4⋊Dic47D411yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47C2311yescharacteristic
103C4×Dic47C2311yescharacteristic
104#10625329—22no—
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107#10625325—22no—
108C23×C47—21no—
109C23×C47C2×D411yescharacteristic
110C22×D47—21no—
111Q8×C47—21no—
112Q8×C47—21no—
113D4×C47—21no—
114D4×C47—21no—
115D4×C47—81no—
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—81no—
124C22⋊D47—81no—
125C22⋊D47—81no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—81no—
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133C2×Dic47C2×D411yescharacteristic
134D188—21no—
135D188—21no—
136C4×D47—81no—
137Dic94—21no—
138Dic94—21no—
139C8×C47—21no—
140C8×C47#4112yes—
141C47⋊C8—21no—
142C47⋊C8#4112yes—
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×C47C2×#4111yescharacteristic
158C4×C47C2×#4111yescharacteristic
159Dic47—21no—
160Dic47—21no—
161Dic47—21no—
162Dic47—21no—
163Dic47—41no—
164Dic47—41no—
165Dic47—41no—
166#3174—471nomaximal, Sylow
167C2×C47—41no—
168C2×C47—81no—
169C2×C47#53211yescharacteristic
170C2×C47#57711yescharacteristic
171C2×C47#57711yescharacteristic
172D47—81no—
173#541—471no—
174#540—471no—
175#499—471no—
176#492—471no—
177#491—471no—
178#490—471no—
179#468—471no—
180#468—471no—
181#465—471no—
182#465D4711yescharacteristic, complemented
183#440—471no—
184#440—471no—
185C4×SD16—471no—
186C4×SD16—471no—
187#405—471no—
188C47#317411yescharacteristic, complemented, Sylow
189C2×SD16—471no—
190C2×SD16—471no—
191C2×SD16—471no—
192C2×SD16C2×D4711yescharacteristic
193C2×M16—471no—
194C22×C8C2×D4711yescharacteristic
195C4⋊Q8—471no—
196#127—471no—
197#126—941no—
198#126—941no—
199#125—471no—
200#125—471no—
201#125—941no—
202#125—941no—
203#123—941no—
204#123—941no—
205C22⋊Q8—471no—
206C22⋊Q8C2×D4711yescharacteristic
207#121—471no—
208#121—941no—
209#121—941no—
210#121C2×D4711yescharacteristic
211C4×Q8—471no—
212C4×Q8—471no—
213C4×D4—471no—
214C4×D4—471no—
215#117—471no—
216#107—471no—
217#107—471no—
218#106—471no—
219#106C2×D4711yescharacteristic
220#103—471no—
221#103—471no—
222#103—471no—
223#103C2×D4711yescharacteristic
224#102—471no—
225#102—471no—
226#102—471no—
227#102C2×D4711yescharacteristic
228#97—471no—
229#97—471no—
230C4×C8—471no—
231C4×C8—471no—
232C2×Q8—471no—
233C2×Q8C22×D4711yescharacteristic
234C2×D4—21no—
235C2×D4—471no—
236C2×D4—941no—
237C2×D4—941no—
238C2×D4—941no—
239C2×D4C22×D4711yescharacteristic
240C22×C4—941no—
241C22×C4—941no—
242C22×C4C22×D4711yescharacteristic
243SD16—22no—
244SD16—942no—
245SD16—942no—
246SD16—942no—
247M16—942no—
248C2×C8—22no—
249C2×C8—471no—
250C2×C8—471no—
251C2×C8C22×D4711yescharacteristic
252C2×C8C22×D4711yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—471no—
255C4⋊C4—471no—
256C4⋊C4—471no—
257C4⋊C4—471no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4C22×D4711yescharacteristic
268C4⋊C4C22×D4711yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—471no—
272C22⋊C4—471no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
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—81no—
291D4—941no—
292D4—941no—
293D4—3761no—
294D4—3761no—
295D4—3761no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—471no—
302C2×C4—471no—
303C2×C4—471no—
304C2×C4—471no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—3761no—
309C2×C4—3761no—
310C2×C4D4×D4711yescharacteristic
311C2×C4C23×D4711yescharacteristic
312C8—21no—
313C8—472no—
314C8—941no—
315C8#1062535212yes—
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#41×D4711yescharacteristic
338C4C2×#1062535211yescharacteristic
339C2—41no—
340C2—81no—
341C2—3761no—
342C2#1568966811yescharacteristic
343C2#1568992911yescharacteristic
344C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#465C2
socleC22×C47C22×D4
hypercenter#465D47
hypocenterC47#3174
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #15689733C2semidirect
3. #15689523C2semidirect
4. #15689494C2semidirect
5. #15689490C2semidirect
6. #15689486C2semidirect
7. #15689371C2semidirect
8. #15689367C2semidirect
9. #15689352C2semidirect
10. #15689226C2semidirect
11. #15689220C2semidirect
12. SD16×Dic47C2semidirect
13. #15689210C2semidirect
14. #15689078C2semidirect
15. C47×#465C2semidirect
182. #465D47semidirect
188. C47#3174semidirect