Finite Group Databasebeta

← #20253019

Subgroups — #20253019

Order 6016.

496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094057C211yesmaximal, characteristic, complemented
2C2×M16×D47C211yesmaximal, characteristic, complemented
3#15689635C211yesmaximal, characteristic
4C2×#13094004C211yesmaximal, characteristic, complemented
5#15689382C212yesmaximal, complemented
6#15689370C212yesmaximal, complemented
7#15689365C212yesmaximal, complemented
8#15689353C212yesmaximal, complemented
9#15689131C211yesmaximal, characteristic, complemented
10#15689122C211yesmaximal, characteristic, complemented
11C47×#428C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13C22×Dic94C2211yescharacteristic
14C22×C4×D47C2211yescharacteristic
15#13094057—24no—
16C2×Dic188C2212yescomplemented
17C2×#10625325C2212yescomplemented
18C2×#10625329C2211yescharacteristic
19C2×#10625324C2212yes—
20M16×D47—24no—
21C2×C8×D47C2212yes—
22#13094008—21no—
23#13094004—21no—
24#13094004—21no—
25#13094004C2212yes—
26#13094004C2211yescharacteristic
27#13094004C2212yes—
28#13094004C2211yescharacteristic
29#13093999C2211yescharacteristic
30#13093999C2211yescharacteristic
31#13093994—21no—
32C4×D188—21no—
33C4×D188—21no—
34C2×C4⋊Dic47—21no—
35C2×(C2×D47)⋊C4—21no—
36#13093947C2212yescomplemented
37#13093947C2212yescomplemented
38#13093947C2212yescomplemented
39#13093944C2212yescomplemented
40C2×M16×C47C2211yescharacteristic
41#117×C47C2211yescharacteristic
42C2×C4⋊C4×C47C2211yescharacteristic
43#107×C47C2212yescomplemented
44#106×C47C2212yescomplemented
45C23×D47D411yescharacteristic
46C22×C4×C47—21no—
47C22×C4×C47C2311yescharacteristic
48C2×C22⋊D47—21no—
49C22×Dic47—21no—
50C22×Dic47D411yescharacteristic
51#10625350—22no—
52#10625350—22no—
53C2×D188—21no—
54C2×D188—21no—
55C2×D188C2311yescharacteristic
56C2×C4×D47—22no—
57C2×C4×D47—22no—
58C2×C4×D47—21no—
59C2×C4×D47D411yescharacteristic
60C2×C4×D47D411yescharacteristic
61C2×C4×D47C2311yescharacteristic
62C2×C4×D47C2311yescharacteristic
63C2×Dic94—22no—
64C2×Dic94—22no—
65C2×Dic94—21no—
66C2×Dic94C2312yes—
67C2×Dic94C2311yescharacteristic
68M16×C47D414yescomplemented
69C2×C8×C47C2312yes—
70C4⋊C4×C47—21no—
71C4⋊C4×C47C2311yescharacteristic
72C4⋊C4×C47C2312yes—
73C4⋊C4×C47C2311yescharacteristic
74C22⋊C4×C47—21no—
75C42×C47—21no—
76(C2×D47)⋊C4—22no—
77(C2×D47)⋊C4—22no—
78(C2×D47)⋊C4—21no—
79(C2×D47)⋊C4—21no—
80(C2×D47)⋊C4—21no—
81(C2×D47)⋊C4—21no—
82C4⋊Dic47—22no—
83C4⋊Dic47—22no—
84C4⋊Dic47—21no—
85C4⋊Dic47—21no—
86#10625329—22no—
87C2×C47⋊C8C2312yes—
88Dic188—24no—
89#10625325—24no—
90#10625324—24no—
91C8×D47—24no—
92C23×C47C2×D411yescharacteristic
93C22×D47—22no—
94C22×D47—22no—
95C22×D47—21no—
96C22×D47—41no—
97C22×D47C2×D411yescharacteristic
98C22×D47C2×D411yescharacteristic
99C2×C4×C47—22no—
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—42no—
103C2×C4×C47C2×D412yes—
104C2×C4×C47C2×D411yescharacteristic
105C2×C4×C47#4112yes—
106C2×C4×C47C2411yescharacteristic
107C22⋊D47—42no—
108C2×Dic47—22no—
109C2×Dic47—22no—
110C2×Dic47—21no—
111C2×Dic47—42no—
112C2×Dic47C2×D411yescharacteristic
113C2×Dic47C2×D411yescharacteristic
114D188—21no—
115D188—21no—
116D188—42no—
117D188—42no—
118C4×D47—22no—
119C4×D47—22no—
120C4×D47—21no—
121C4×D47—21no—
122C4×D47—21no—
123C4×D47—21no—
124C4×D47—42no—
125Dic94—22no—
126Dic94—21no—
127Dic94—22no—
128Dic94—21no—
129Dic94—42no—
130C8×C47C2×D414yes—
131C47⋊C8—22no—
132C22×C47—21no—
133C22×C47—21no—
134C22×C47#12112yes—
135C22×C47C22×D411yescharacteristic
136C2×D47—21no—
137C2×D47—21no—
138C2×D47—21no—
139C2×D47—21no—
140C2×D47—21no—
141C2×D47—44no—
142C2×D47—41no—
143C2×D47—41no—
144C2×D47—41no—
145C2×D47#13712yescomplemented
146C4×C47—41no—
147C4×C47—41no—
148C4×C47—42no—
149C4×C47#12112yes—
150C4×C47C22×D411yescharacteristic
151C4×C47C2×#4111yescharacteristic
152Dic47—21no—
153Dic47—21no—
154Dic47—42no—
155Dic47—41no—
156#3056—471nomaximal, Sylow
157C2×C47—22no—
158C2×C47C2×#12111yescharacteristic
159C2×C47C2×#13711yescharacteristic
160C2×C47#57511yescharacteristic
161D47—22no—
162D47—41no—
163D47—81no—
164C2×#137—471no—
165C22×M16—471no—
166#525—471no—
167C2×C22⋊Q8—471no—
168#470—472no—
169#468—472no—
170#467—472no—
171#465—472no—
172#428D4711yescharacteristic, complemented
173#419—471no—
174#417—471no—
175C47#305611yescharacteristic, complemented, Sylow
176C2×#41—471no—
177C22×Q8—471no—
178C23×C4—471no—
179#137—944no—
180C2×Q16—472no—
181C2×SD16—472no—
182C2×M16—471no—
183C2×M16—472no—
184C2×M16—944no—
185C2×M16C2×D4711yescharacteristic
186C22×C8—472no—
187#123—941no—
188C22⋊Q8—472no—
189C22⋊Q8—472no—
190C22⋊Q8—471no—
191C22⋊Q8—471no—
192C22⋊Q8—941no—
193C22⋊Q8—941no—
194#121—471no—
195#121—471no—
196#120—941no—
197C4×D4—941no—
198C4×D4—941no—
199#117C2×D4711yescharacteristic
200C2×C4⋊C4—941no—
201C2×C4⋊C4C2×D4711yescharacteristic
202C2×C22⋊C4—941no—
203#107C2×D4712yescomplemented
204#106C2×D4712yescomplemented
205#103—472no—
206#103—472no—
207#103—472no—
208#102—472no—
209C24—471no—
210#41—942no—
211#41—942no—
212C2×Q8—472no—
213C2×Q8—471no—
214C2×Q8—941no—
215C2×Q8—942no—
216C2×Q8—942no—
217C2×D4—471no—
218C2×D4—941no—
219C2×D4—941no—
220C2×D4—941no—
221C22×C4—21no—
222C22×C4—471no—
223C22×C4—471no—
224C22×C4—471no—
225C22×C4—471no—
226C22×C4—471no—
227C22×C4—942no—
228C22×C4—942no—
229C22×C4—941no—
230C22×C4—941no—
231C22×C4C22×D4711yescharacteristic
232Q16—944no—
233SD16—944no—
234M16—942no—
235M16—944no—
236M16D18814yescomplemented
237C2×C8—472no—
238C2×C8—944no—
239C2×C8C22×D4712yes—
240C4⋊C4—21no—
241C4⋊C4—942no—
242C4⋊C4—942no—
243C4⋊C4—941no—
244C4⋊C4—941no—
245C4⋊C4C22×D4712yes—
246C4⋊C4C22×D4711yescharacteristic
247C4⋊C4C22×D4711yescharacteristic
248C22⋊C4—21no—
249C22⋊C4—941no—
250C22⋊C4—941no—
251C22⋊C4—942no—
252C22⋊C4—942no—
253C22⋊C4—941no—
254C22⋊C4—941no—
255C42—21no—
256C23—471no—
257C23—471no—
258C23—942no—
259C23—942no—
260C23—941no—
261C23—1881no—
262C23D4×D4711yescharacteristic
263Q8—942no—
264Q8—941no—
265Q8—942no—
266Q8—941no—
267Q8—1882no—
268D4—941no—
269D4—941no—
270D4—1882no—
271D4—1882no—
272D4—1882no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—42no—
277C2×C4—471no—
278C2×C4—471no—
279C2×C4—942no—
280C2×C4—942no—
281C2×C4—942no—
282C2×C4—941no—
283C2×C4—941no—
284C2×C4—941no—
285C2×C4—941no—
286C2×C4—941no—
287C2×C4—942no—
288C2×C4—1882no—
289C2×C4—1882no—
290C2×C4C2×D18812yes—
291C2×C4D4×D4711yescharacteristic
292C2×C4#1062535412yes—
293C2×C4C23×D4711yescharacteristic
294C8—942no—
295C8C2×D18814yes—
296C22—21no—
297C22—21no—
298C22—472no—
299C22—941no—
300C22—941no—
301C22—941no—
302C22—941no—
303C22—941no—
304C22—1884no—
305C22—1881no—
306C22—1881no—
307C22—1881no—
308C22#1309399912yes—
309C22C2×D4×D4711yescharacteristic
310C4—41no—
311C4—42no—
312C4—41no—
313C4—941no—
314C4—941no—
315C4—1881no—
316C4—1882no—
317C4#1309399912yes—
318C4C22×D18811yescharacteristic
319C4C2×#1062535411yescharacteristic
320C2—22no—
321C2—942no—
322C2—3761no—
323C2—1881no—
324C2C2×#1309399911yescharacteristic
325C2#137×D4711yescharacteristic
326C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#428C2
socleC22×C47C22×D4
hypercenter#428D47
hypocenterC47#3056
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. C2×#13094057C2semidirect
2. C2×M16×D47C2semidirect
4. C2×#13094004C2semidirect
5. #15689382C2semidirect
6. #15689370C2semidirect
7. #15689365C2semidirect
8. #15689353C2semidirect
9. #15689131C2semidirect
10. #15689122C2semidirect
11. C47×#428C2semidirect
16. C2×Dic188C22semidirect
17. C2×#10625325C22semidirect
36. #13093947C22semidirect
37. #13093947C22semidirect
38. #13093947C22semidirect
39. #13093944C22semidirect
43. #107×C47C22semidirect
44. #106×C47C22semidirect
68. M16×C47D4semidirect
145. C2×D47#137semidirect
172. #428D47semidirect
175. C47#3056semidirect
203. #107C2×D47semidirect
204. #106C2×D47semidirect
236. M16D188semidirect