Finite Group Databasebeta

← #20253180

Subgroups — #20253180

Order 6016.

440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 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
1#15689678C211yesmaximal, characteristic, complemented
2C4×D4×D47C211yesmaximal, characteristic
3#15689426C212yesmaximal, complemented
4#15689425C212yesmaximal, complemented
5#15689414C211yesmaximal, characteristic, complemented
6#15689413C211yesmaximal, characteristic, complemented
7#15689400C211yesmaximal, characteristic, complemented
8#15689164C212yesmaximal, complemented
9#15689145C211yesmaximal, characteristic, complemented
10#15689126C212yesmaximal
11C47×#474C211yesmaximal, characteristic, complemented
12C2×D4×D47C2211yescharacteristic
13C22×C4×D47—21no—
14C2×#10625324C2212yes—
15#13094024C2211yescharacteristic, complemented
16#13094015C2212yescomplemented
17#13094004—21no—
18#13094000—21no—
19Q8×Dic47—21no—
20#13093989—21no—
21C4×D188C2211yescharacteristic
22D4×Dic47C2211yescharacteristic
23#13093986C2211yescharacteristic
24C4×C22⋊D47—21no—
25(C22⋊D47)⋊C4—21no—
26#13093982C2212yes—
27C4⋊C4×D47C2211yescharacteristic
28C22⋊C4×D47—21no—
29C42×D47C2211yescharacteristic
30#13093957C2212yescomplemented
31#13093956C2212yescomplemented
32#13093955C2212yescomplemented
33C4⋊(C47⋊C8)C2211yescharacteristic, complemented
34Dic47⋊C8C2212yescomplemented
35#13093946C2212yes—
36#13093945C2212yes—
37#13093944C2212yes—
38C4⋊Q8×C47C2211yescharacteristic, complemented
39C4×D4×C47C2211yescharacteristic
40#107×C47C2212yescomplemented
41C4⋊C8×C47C2211yescharacteristic, complemented
42#102×C47C2212yes—
43C23×D47—21no—
44C2×Q8×C47—21no—
45C2×D4×C47C2311yescharacteristic
46C22×C4×C47—21no—
47C2×C22⋊D47—21no—
48C22×Dic47—21no—
49D4×D47—22no—
50D4×D47Q814yescomplemented
51C2×D188C2311yescharacteristic
52C2×C4×D47—21no—
53C2×C4×D47—21no—
54C2×C4×D47—21no—
55C2×C4×D47—44no—
56C2×C4×D47D411yescharacteristic
57C2×C4×D47D411yescharacteristic
58C2×C4×D47C2311yescharacteristic
59C2×Dic94—21no—
60C2×C8×C47C2312yes—
61C4⋊C4×C47—21no—
62C4⋊C4×C47C2311yescharacteristic
63C4⋊C4×C47C2312yes—
64C22⋊C4×C47—21no—
65C42×C47C2311yescharacteristic
66C22⋊Dic47—21no—
67(C2×D47)⋊C4—22no—
68(C2×D47)⋊C4—21no—
69(C2×D47)⋊C4—21no—
70C4⋊Dic47—21no—
71C4⋊Dic47—22no—
72C4⋊Dic47C2312yes—
73C4⋊Dic47C2311yescharacteristic
74Dic47⋊C4—21no—
75Dic47⋊C4—22no—
76C4×Dic47—22no—
77C4×Dic47D411yescharacteristic
78C4×Dic47D411yescharacteristic
79C4×Dic47C2311yescharacteristic
80C2×C47⋊C8C2312yes—
81#10625324—24no—
82C23×C47—21no—
83C22×D47—21no—
84C22×D47—24no—
85C22×D47—42no—
86C22×D47—42no—
87C22×D47C2×D411yescharacteristic
88Q8×C47—42no—
89D4×C47—21no—
90D4×C47C2×Q812yes—
91C2×C4×C47—22no—
92C2×C4×C47—21no—
93C2×C4×C47—42no—
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47C2411yescharacteristic
97C22⋊D47—24no—
98C2×Dic47—22no—
99C2×Dic47—21no—
100C2×Dic47—42no—
101C2×Dic47C2×D411yescharacteristic
102C2×Dic47C2×D411yescharacteristic
103C2×Dic47C2×D411yescharacteristic
104D188—21no—
105D188C2×Q812yes—
106C4×D47—22no—
107C4×D47—41no—
108C4×D47—42no—
109C4×D47—42no—
110C4×D47—42no—
111C4×D47C2×Q812yes—
112C4×D47#4112yes—
113Dic94—42no—
114C8×C47—22no—
115C47⋊C8—22no—
116C22×C47—22no—
117C22×C47—41no—
118C22×C47—41no—
119C22×C47C22×D411yescharacteristic
120C2×D47—21no—
121C2×D47—21no—
122C2×D47—22no—
123C2×D47—48no—
124C2×D47—41no—
125C2×D47—41no—
126C2×D47C22⋊Q812yes—
127C4×C47—21no—
128C4×C47—41no—
129C4×C47—42no—
130C4×C47AGL(1,ℤ/8)12yes—
131C4×C47C22×Q811yescharacteristic
132C4×C47C2×#4111yescharacteristic
133Dic47—21no—
134Dic47—21no—
135Dic47—41no—
136Dic47—42no—
137Dic47C22⋊Q812yes—
138#3077—471nomaximal, Sylow
139C2×C47—42no—
140C2×C47C2×C22⋊Q811yescharacteristic
141C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
142C2×C47#57511yescharacteristic
143D47—22no—
144D47—42no—
145#533—471no—
146C2×C4×D4—471no—
147#478—472no—
148#478—472no—
149#476—471no—
150#476—471no—
151#474—471no—
152#474D4711yescharacteristic, complemented
153#428—472no—
154#423—471no—
155#418—472no—
156C47#307711yescharacteristic, complemented, Sylow
157C22×D4—471no—
158C23×C4—941no—
159C2×M16—472no—
160C4⋊Q8—471no—
161C4⋊Q8C2×D4711yescharacteristic, complemented
162#125—472no—
163C22⋊Q8—941no—
164C22⋊Q8—941no—
165C4×Q8—941no—
166C4×Q8—941no—
167C4×D4—471no—
168C4×D4—471no—
169C4×D4—471no—
170C4×D4—941no—
171C4×D4—941no—
172C4×D4C2×D4711yescharacteristic
173#117—472no—
174C2×C4⋊C4—471no—
175C2×C22⋊C4—941no—
176C2×C42—471no—
177#107—472no—
178#107C2×D4712yescomplemented
179#106—472no—
180#106—472no—
181C4⋊C8—472no—
182C4⋊C8—471no—
183C4⋊C8C2×D4711yescharacteristic, complemented
184#102—472no—
185#102—472no—
186#102—472no—
187#102C2×D4712yes—
188C24—941no—
189C2×Q8—21no—
190C2×Q8—941no—
191C2×D4—474no—
192C2×D4—471no—
193C2×D4—942no—
194C2×D4—941no—
195C2×D4C22×D4711yescharacteristic
196C22×C4—21no—
197C22×C4—471no—
198C22×C4—471no—
199C22×C4—471no—
200C22×C4—941no—
201C22×C4—941no—
202C22×C4—941no—
203C22×C4—941no—
204C22×C4—1884no—
205M16—944no—
206C2×C8—472no—
207C2×C8C22×D4712yes—
208C4⋊C4—21no—
209C4⋊C4—472no—
210C4⋊C4—471no—
211C4⋊C4—941no—
212C4⋊C4—942no—
213C4⋊C4—942no—
214C4⋊C4—941no—
215C4⋊C4C22×D4712yes—
216C4⋊C4C22×D4711yescharacteristic
217C22⋊C4—21no—
218C22⋊C4—941no—
219C22⋊C4—942no—
220C22⋊C4—941no—
221C22⋊C4—941no—
222C42—471no—
223C42—471no—
224C42—471no—
225C42—942no—
226C42C22×D4711yescharacteristic
227C23—21no—
228C23—471no—
229C23—944no—
230C23—941no—
231C23—1882no—
232C23—1882no—
233Q8—42no—
234Q8—1882no—
235D4—21no—
236D4—472no—
237D4—944no—
238D4—941no—
239D4Q8×D4712yes—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—471no—
244C2×C4—472no—
245C2×C4—472no—
246C2×C4—471no—
247C2×C4—471no—
248C2×C4—942no—
249C2×C4—942no—
250C2×C4—941no—
251C2×C4—1881no—
252C2×C4—1882no—
253C2×C4—1882no—
254C2×C4—1882no—
255C2×C4—1882no—
256C2×C4D4×D4711yescharacteristic
257C2×C4D4×D4711yescharacteristic
258C2×C4C23×D4711yescharacteristic
259C8—22no—
260C8—942no—
261C22—22no—
262C22—41no—
263C22—41no—
264C22—472no—
265C22—941no—
266C22—941no—
267C22—942no—
268C22—1888no—
269C22—1881no—
270C22—1881no—
271C22C2×D4×D4711yescharacteristic
272C4—21no—
273C4—41no—
274C4—42no—
275C4—472no—
276C4—941no—
277C4—941no—
278C4—1881no—
279C4—1882no—
280C4#1309404812yes—
281C4C2×Q8×D4711yescharacteristic
282C4#41×D4711yescharacteristic
283C2—42no—
284C2—942no—
285C2—1882no—
286C2C22⋊Q8×D4711yescharacteristic
287C2C2×#1309404811yescharacteristic
288C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#474C2
socleC22×C47C22×D4
hypercenter#474D47
hypocenterC47#3077
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #15689678C2semidirect
3. #15689426C2semidirect
4. #15689425C2semidirect
5. #15689414C2semidirect
6. #15689413C2semidirect
7. #15689400C2semidirect
8. #15689164C2semidirect
9. #15689145C2semidirect
11. C47×#474C2semidirect
15. #13094024C22semidirect
16. #13094015C22semidirect
30. #13093957C22semidirect
31. #13093956C22semidirect
32. #13093955C22semidirect
33. C4⋊(C47⋊C8)C22semidirect
34. Dic47⋊C8C22semidirect
38. C4⋊Q8×C47C22semidirect
40. #107×C47C22semidirect
41. C4⋊C8×C47C22semidirect
50. D4×D47Q8semidirect
152. #474D47semidirect
156. C47#3077semidirect
161. C4⋊Q8C2×D47semidirect
178. #107C2×D47semidirect
183. C4⋊C8C2×D47semidirect