Finite Group Databasebeta

← #20253999

Subgroups — #20253999

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#15689744C211yesmaximal, characteristic, complemented
2#15689519C211yesmaximal, characteristic, complemented
3#15689505C211yesmaximal, characteristic, complemented
4#15689485C211yesmaximal, characteristic, complemented
5#15689482C211yesmaximal, characteristic, complemented
6#15689379C211yesmaximal, characteristic, complemented
7#15689374C211yesmaximal, characteristic
8#15689354C211yesmaximal, characteristic, complemented
9#15689350C211yesmaximal, characteristic, complemented
10#15689233C211yesmaximal, characteristic, complemented
11#15689228C211yesmaximal, characteristic, complemented
12C4×#10625336C211yesmaximal, characteristic, complemented
13C4×#10625335C211yesmaximal, characteristic, complemented
14#15689079C211yesmaximal, characteristic, complemented
15C47×#542C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C2×#10625335C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20C2×#10625329C2211yescharacteristic
21C22×C47⋊C8C2211yescharacteristic
22#13094024C2211yescharacteristic
23#13094019—21no—
24#13094012C2211yescharacteristic
25#13094010—21no—
26#13094006—21no—
27#13094003C2211yescharacteristic
28#13094002—21no—
29#13093998C2211yescharacteristic
30C4×Dic94C2211yescharacteristic
31C4×D188C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34#13093955C2211yescharacteristic
35#13093955C2211yescharacteristic
36#13093948C2211yescharacteristic
37#13093948C2211yescharacteristic
38#13093947C2211yescharacteristic
39#13093947C2211yescharacteristic
40#13093945C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44#13093935C2211yescharacteristic
45#13093935C2211yescharacteristic
46C4×C47⋊C8C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48C4⋊Q8×C47C2211yescharacteristic
49#126×C47—21no—
50#124×C47—21no—
51#124×C47C2211yescharacteristic
52#123×C47—21no—
53C22⋊Q8×C47—21no—
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56C4×Q8×C47C2211yescharacteristic
57C4×D4×C47C2211yescharacteristic
58#117×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47—21no—
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C22×C4×C47C2311yescharacteristic
65C2×C22⋊D47—21no—
66C2×D188C2311yescharacteristic
67C2×C4×D47—21no—
68C2×Dic94—21no—
69C2×Dic94C2311yescharacteristic
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47D411yescharacteristic
74C4⋊C4×C47D411yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C22⋊C4×C47—21no—
78C22⋊C4×C47—21no—
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C22⋊C4×C47—21no—
82C22⋊C4×C47D411yescharacteristic
83C22⋊C4×C47D411yescharacteristic
84C42×C47—21no—
85C42×C47C2311yescharacteristic
86C42×C47C2311yescharacteristic
87C22⋊Dic47—21no—
88#10625337—22no—
89#10625336—22no—
90#10625335—22no—
91#10625334—22no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101C4×Dic47—21no—
102#10625329—22no—
103C2×C47⋊C8—22no—
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47—21no—
109C23×C47C2×D411yescharacteristic
110C22×D47—21no—
111Q8×C47—21no—
112Q8×C47—21no—
113Q8×C47—81no—
114D4×C47—21no—
115D4×C47—21no—
116D4×C47—81no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—81no—
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2411yescharacteristic
129C22⋊D47—81no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133D188—21no—
134D188—21no—
135C4×D47—81no—
136Dic94—21no—
137Dic94—21no—
138Dic94—81no—
139C47⋊C8—21no—
140C47⋊C8—21no—
141C47⋊C8#4112yes—
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—21no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47C2×#4111yescharacteristic
162C4×C47C2×#4111yescharacteristic
163Dic47—41no—
164Dic47—41no—
165Dic47—41no—
166#3173—471nomaximal, Sylow
167C2×C47—41no—
168C2×C47—81no—
169C2×C47#53211yescharacteristic
170C2×C47#57711yescharacteristic
171C2×C47#57711yescharacteristic
172D47—81no—
173#542—471no—
174#542D4711yescharacteristic, complemented
175#498—471no—
176#495—471no—
177#489—471no—
178#489—471no—
179#470—471no—
180#469—471no—
181#465—471no—
182#465—471no—
183#442—471no—
184#441—471no—
185C4×SD16—471no—
186C4×SD16—471no—
187#405—471no—
188C47#317311yescharacteristic, complemented, Sylow
189C2×Q16—471no—
190C2×SD16—471no—
191C2×SD16—471no—
192C2×D8—471no—
193C2×M16—471no—
194C22×C8—471no—
195C4⋊Q8—471no—
196C4⋊Q8C2×D4711yescharacteristic
197#126—21no—
198#126—941no—
199#124—21no—
200#124—471no—
201#124—941no—
202#124C2×D4711yescharacteristic
203#123—21no—
204#123—941no—
205C22⋊Q8—21no—
206C22⋊Q8—471no—
207C22⋊Q8—941no—
208C22⋊Q8C2×D4711yescharacteristic
209#121—471no—
210#121C2×D4711yescharacteristic
211C4×Q8—471no—
212C4×Q8C2×D4711yescharacteristic
213C4×D4—471no—
214C4×D4C2×D4711yescharacteristic
215#117C2×D4711yescharacteristic
216#106—471no—
217#106—471no—
218#106—471no—
219#106—471no—
220#103—471no—
221#103—471no—
222#103—471no—
223#103—471no—
224#102—471no—
225#102—471no—
226#102—471no—
227#102—471no—
228#97—471no—
229#97—471no—
230C4×C8—471no—
231C4×C8—471no—
232C2×Q8—21no—
233C2×Q8—471no—
234C2×Q8—941no—
235C2×Q8C22×D4711yescharacteristic
236C2×D4—21no—
237C2×D4—471no—
238C2×D4—941no—
239C2×D4C22×D4711yescharacteristic
240C22×C4—21no—
241C22×C4—941no—
242C22×C4C22×D4711yescharacteristic
243Q16—942no—
244SD16—942no—
245SD16—942no—
246D8—942no—
247M16—942no—
248C2×C8—471no—
249C2×C8—471no—
250C2×C8—471no—
251C2×C8—471no—
252C2×C8—942no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—471no—
257C4⋊C4—471no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4C22⋊D4711yescharacteristic
262C4⋊C4C22⋊D4711yescharacteristic
263C4⋊C4C22×D4711yescharacteristic
264C4⋊C4C22×D4711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4C22⋊D4711yescharacteristic
276C22⋊C4C22⋊D4711yescharacteristic
277C42—21no—
278C42—941no—
279C42C22×D4711yescharacteristic
280C42C22×D4711yescharacteristic
281C23—21no—
282C23—941no—
283C23C2×C22⋊D4711yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—941no—
288Q8—941no—
289Q8—3761no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—941no—
294D4—941no—
295D4—3761no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—81no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—3761no—
306C2×C4C2×C22⋊D4711yescharacteristic
307C2×C4C2×C22⋊D4711yescharacteristic
308C2×C4C2×C22⋊D4711yescharacteristic
309C2×C4C2×C22⋊D4711yescharacteristic
310C2×C4C2×C22⋊D4711yescharacteristic
311C2×C4C23×D4711yescharacteristic
312C8—472no—
313C8—472no—
314C8—941no—
315C8—941no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—1881no—
323C22—1881no—
324C22—1881no—
325C22C22×C22⋊D4711yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—1881no—
335C4—1881no—
336C4—1881no—
337C4#41×D4711yescharacteristic
338C4#41×D4711yescharacteristic
339C2—41no—
340C2—81no—
341C2—3761no—
342C2#1568966911yescharacteristic
343C2#1568993111yescharacteristic
344C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#542C2
socleC22×C47C22×D4
hypercenter#542D47
hypocenterC47#3173
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #15689744C2semidirect
2. #15689519C2semidirect
3. #15689505C2semidirect
4. #15689485C2semidirect
5. #15689482C2semidirect
6. #15689379C2semidirect
8. #15689354C2semidirect
9. #15689350C2semidirect
10. #15689233C2semidirect
11. #15689228C2semidirect
12. C4×#10625336C2semidirect
13. C4×#10625335C2semidirect
14. #15689079C2semidirect
15. C47×#542C2semidirect
174. #542D47semidirect
188. C47#3173semidirect