Finite Group Databasebeta

← #20252791

Subgroups — #20252791

Order 6016.

772 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 145 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#15689959C211yesmaximal, characteristic, complemented
2#15689692C212yesmaximal, complemented
3#15689687C211yesmaximal, characteristic, complemented
4#15689311C218yesmaximal, complemented
5#15689096C212yesmaximal, complemented
6C47×#410C211yesmaximal, characteristic, complemented
7#13094072—21no—
8#13094071—22no—
9#13094070—22no—
10#13094069—21no—
11#13094069C2214yes—
12C2×#10625350—22no—
13C2×#10625350C2212yes—
14#41×D47—24no—
15C22×D188C2211yescharacteristic, complemented
16#13094021—22no—
17#13094020—21no—
18#13094013—21no—
19#13094012—22no—
20#13093999—24no—
21#13093998—22no—
22#13093994C2218yescomplemented
23#13093992C2214yescomplemented
24#13093983C2211yescharacteristic, complemented
25#13093938C2218yescomplemented
26C2×#41×C47C2211yescharacteristic
27#117×C47C2212yescomplemented
28#99×C47C2214yescomplemented
29C23×D47C2312yes—
30#41×C47—22no—
31#41×C47—22no—
32C2×Q8×C47D411yescharacteristic, complemented
33C2×D4×C47D411yescharacteristic, complemented
34C2×D4×C47C2312yes—
35C22×C4×C47D412yescomplemented
36C22×C4×C47C2311yescharacteristic
37C2×C22⋊D47—24no—
38C2×C22⋊D47—24no—
39C2×C22⋊D47C2314yes—
40#10625354—24no—
41Q8×D47—24no—
42#10625352—24no—
43#10625352—28no—
44D4×D47—24no—
45D4×D47—28no—
46#10625350—24no—
47#10625350—24no—
48#10625350—22no—
49#10625350—22no—
50#10625350—24no—
51#10625350—22no—
52#10625350—22no—
53C2×D188—22no—
54C2×D188—21no—
55C2×D188—22no—
56C2×D188—22no—
57C2×D188—21no—
58C2×D188—28no—
59C2×D188D412yescomplemented
60C2×C4×D47—24no—
61C2×C4×D47D414yescomplemented
62C2×Dic94—22no—
63C2×Dic94D412yescomplemented
64C4⋊C4×C47—22no—
65C22⋊C4×C47C2314yes—
66C42×C47—22no—
67C22⋊Dic47C2312yes—
68(C2×D47)⋊C4—24no—
69(C2×D47)⋊C4—28no—
70C4⋊Dic47—21no—
71C4×Dic47—21no—
72C23×C47C2×D412yes—
73C23×C47C2411yescharacteristic
74C22×D47—24no—
75C22×D47—24no—
76C22×D47—22no—
77C22×D47—82no—
78C22×D47C2×D414yes—
79Q8×C47—22no—
80D4×C47—24no—
81D4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—24no—
85C2×C4×C47C2×D412yes—
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2×D412yes—
89C2×C4×C47C2×D412yes—
90C22⋊D47—28no—
91C22⋊D47—24no—
92C22⋊D47—24no—
93C22⋊D47—84no—
94C2×Dic47—24no—
95C2×Dic47—22no—
96C2×Dic47C2×D414yes—
97D188—24no—
98D188—22no—
99D188—22no—
100D188—41no—
101D188—42no—
102D188—41no—
103D188—88no—
104C4×D47—28no—
105C4×D47—24no—
106C4×D47—24no—
107Dic94—24no—
108Dic94—22no—
109Dic94—22no—
110C22×C47—22no—
111C22×C47—41no—
112C22×C47—42no—
113C22×C47C22×D412yes—
114C22×C47C22×D411yescharacteristic
115C2×D47—24no—
116C2×D47—44no—
117C2×D47—48no—
118C2×D47—44no—
119C2×D47—42no—
120C2×D47—84no—
121C4×C47—22no—
122C4×C47—44no—
123C4×C47#12011yescharacteristic
124C4×C47#12012yes—
125C4×C47#12011yescharacteristic
126Dic47—24no—
127Dic47—42no—
128#3027—471nomaximal, Sylow
129C2×C47—21no—
130C2×C47—22no—
131C2×C47—42no—
132C2×C47C2×#12011yescharacteristic
133D47—44no—
134D47—82no—
135#585—471no—
136#535—471no—
137#535—472no—
138B(4,𝔽2)—478no—
139#410—472no—
140#410D4711yescharacteristic, complemented
141C47#302711yescharacteristic, complemented, Sylow
1422−1+4—942no—
1432−1+4—941no—
144H(5,𝔽2)—474no—
145H(5,𝔽2)—942no—
146H(5,𝔽2)—941no—
147C2×#41—472no—
148C2×#41—944no—
149C2×#41—942no—
150C2×#41C2×D4711yescharacteristic
151C22×D4—471no—
152#127—942no—
153#127—941no—
154#124—942no—
155#124—941no—
156#121—944no—
157#121—942no—
158#120—474no—
159#120—478no—
160#117—471no—
161#117C2×D4712yescomplemented
162#99—478no—
163#99C2×D4714yescomplemented
164C24—472no—
165#41—22no—
166#41—22no—
167#41—944no—
168#41—944no—
169#41—948no—
170#41—944no—
171#41—944no—
172#41—942no—
173#41—942no—
174#41—944no—
175#41—942no—
176#41—942no—
177C2×Q8—472no—
178C2×Q8—942no—
179C2×Q8—944no—
180C2×Q8D18811yescharacteristic, complemented
181C2×D4—474no—
182C2×D4—472no—
183C2×D4—942no—
184C2×D4—948no—
185C2×D4—948no—
186C2×D4—944no—
187C2×D4—944no—
188C2×D4—944no—
189C2×D4—941no—
190C2×D4—941no—
191C2×D4—942no—
192C2×D4—942no—
193C2×D4D18811yescharacteristic, complemented
194C2×D4C22×D4712yes—
195C22×C4—474no—
196C22×C4—944no—
197C22×C4D18812yescomplemented
198C22×C4C22×D4711yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—941no—
201C22⋊C4—472no—
202C22⋊C4—948no—
203C22⋊C4—944no—
204C22⋊C4C22×D4714yes—
205C42—22no—
206C42—941no—
207C23—474no—
208C23—944no—
209C23—944no—
210C23—942no—
211C23—3762no—
212C23C2×D18812yes—
213C23C23×D4711yescharacteristic
214Q8—22no—
215Q8—944no—
216Q8—942no—
217Q8—942no—
218D4—24no—
219D4—22no—
220D4—944no—
221D4—948no—
222D4—944no—
223D4—944no—
224D4—942no—
225D4—942no—
226D4—3768no—
227D4—3764no—
228D4—1881no—
229D4—1881no—
230D4—1882no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—24no—
234C2×C4—474no—
235C2×C4—948no—
236C2×C4—944no—
237C2×C4—944no—
238C2×C4—944no—
239C2×C4—942no—
240C2×C4C2×D18812yes—
241C2×C4C2×D18811yescharacteristic
242C2×C4C2×D18811yescharacteristic
243C2×C4D4×D4712yes—
244C2×C4D4×D4712yes—
245C22—22no—
246C22—41no—
247C22—42no—
248C22—944no—
249C22—3764no—
250C22—1888no—
251C22—1884no—
252C22—1884no—
253C22—1882no—
254C22C2×D4×D4712yes—
255C22C22×D18811yescharacteristic
256C4—22no—
257C4—44no—
258C4—944no—
259C4—1882no—
260C4#1309399411yescharacteristic
261C4#1309399411yescharacteristic
262C4#1309399412yes—
263C2—22no—
264C2—21no—
265C2—42no—
266C2—3762no—
267C2—1884no—
268C2C2×#1309399411yescharacteristic
subgroupG/H
centerC2C2×#13093994
commutatorC23×C47C24
FrattiniC23C23×D47
FittingC47×#410C2
socleC2×C47C2×#120
hypercenter#410D47
hypocenterC47#3027
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #15689959C2semidirect
2. #15689692C2semidirect
3. #15689687C2semidirect
4. #15689311C2semidirect
5. #15689096C2semidirect
6. C47×#410C2semidirect
15. C22×D188C22semidirect
22. #13093994C22semidirect
23. #13093992C22semidirect
24. #13093983C22semidirect
25. #13093938C22semidirect
27. #117×C47C22semidirect
28. #99×C47C22semidirect
32. C2×Q8×C47D4semidirect
33. C2×D4×C47D4semidirect
35. C22×C4×C47D4semidirect
59. C2×D188D4semidirect
61. C2×C4×D47D4semidirect
63. C2×Dic94D4semidirect
140. #410D47semidirect
141. C47#3027semidirect
161. #117C2×D47semidirect
163. #99C2×D47semidirect
180. C2×Q8D188semidirect
193. C2×D4D188semidirect
197. C22×C4D188semidirect