Finite Group Databasebeta

← #20254440

Subgroups — #20254440

Order 6016.

420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689728C211yesmaximal, characteristic, complemented
2#15689692C211yesmaximal, characteristic, complemented
3#15689512C211yesmaximal, characteristic, complemented
4#15689500C211yesmaximal, characteristic, complemented
5#15689488C211yesmaximal, characteristic, complemented
6#15689478C211yesmaximal, characteristic, complemented
7#15689339C212yesmaximal, complemented
8#15689319C212yesmaximal, complemented
9#15689270C212yesmaximal, complemented
10#15689259C212yesmaximal, complemented
11C47×#433C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13C22×D188C2211yescharacteristic
14C2×#10625325C2212yescomplemented
15C2×D376C2212yes—
16C2×D376C2212yes—
17C2×D376C2212yescomplemented
18#13094021C2211yescharacteristic
19#13094021C2211yescharacteristic
20#13094021C2211yescharacteristic, complemented
21#13094016C2211yescharacteristic, complemented
22#13094012C2211yescharacteristic
23#13094012C2211yescharacteristic
24#13094009—22no—
25#13093999—22no—
26#13093998C2212yes—
27#13093997—22no—
28#13093994—22no—
29C4×D188C2212yescomplemented
30#13093949C2212yescomplemented
31#13093946C2212yes—
32#13093946C2212yes—
33#13093946C2212yescomplemented
34#117×C47C2211yescharacteristic
35C4⋊C8×C47C2212yescomplemented
36C22⋊C8×C47C2212yes—
37#97×C47C2211yescharacteristic, complemented
38C4×C8×C47C2211yescharacteristic, complemented
39C23×D47—21no—
40C22×C4×C47C2311yescharacteristic
41C2×C22⋊D47—21no—
42C2×C22⋊D47—22no—
43#10625350—42no—
44C2×D188—21no—
45C2×D188—22no—
46C2×D188—22no—
47C2×D188—22no—
48C2×D188—42no—
49C2×D188C2311yescharacteristic
50C2×D188C2311yescharacteristic
51C2×D188C2311yescharacteristic
52C2×D188C2312yes—
53C2×C4×D47—21no—
54C2×C4×D47—22no—
55C2×Dic94C2311yescharacteristic
56C2×C8×C47C2312yes—
57C2×C8×C47C2312yes—
58C4⋊C4×C47D412yes—
59C22⋊C4×C47D412yes—
60C42×C47C2311yescharacteristic
61C42×C47C2311yescharacteristic
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—22no—
64(C2×D47)⋊C4—22no—
65(C2×D47)⋊C4—22no—
66C4⋊Dic47C2312yes—
67Dic47⋊C4—22no—
68D376—42no—
69D376—42no—
70D376—42no—
71#10625325—42no—
72C23×C47C2×D411yescharacteristic
73C22×D47—22no—
74C22×D47—21no—
75C22×D47—21no—
76C22×D47—21no—
77C22×D47—42no—
78C22×D47—82no—
79C2×C4×C47—22no—
80C2×C4×C47C2×D412yes—
81C2×C4×C47C2×D412yes—
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2411yescharacteristic
84C22⋊D47—42no—
85C22⋊D47—82no—
86C2×Dic47—22no—
87C2×Dic47—21no—
88D188—22no—
89D188—22no—
90D188—22no—
91D188—22no—
92D188—22no—
93D188—42no—
94D188—82no—
95D188—82no—
96D188—82no—
97C4×D47—42no—
98C4×D47—82no—
99Dic94—22no—
100C8×C47—22no—
101C8×C47—22no—
102C22×C47—21no—
103C22×C47—22no—
104C22×C47C22×D411yescharacteristic
105C2×D47—41no—
106C2×D47—41no—
107C2×D47—41no—
108C2×D47—42no—
109C2×D47—42no—
110C2×D47—42no—
111C2×D47—42no—
112C2×D47—42no—
113C2×D47—42no—
114C2×D47—84no—
115C4×C47—21no—
116C4×C47—22no—
117C4×C47—22no—
118C4×C47H(5,𝔽2)12yes—
119Dic47—41no—
120Dic47—42no—
121#3220—471nomaximal, Sylow
122C2×C47—41no—
123C2×C47#53511yescharacteristic
124C2×C47#57612yes—
125D47—81no—
126D47—82no—
127D47—81no—
128D47—81no—
129#540—471no—
130#535—471no—
131#496—471no—
132#493—471no—
133#490—471no—
134#488—471no—
135#463—472no—
136#459—472no—
137#449—472no—
138#447—472no—
139#433D4711yescharacteristic, complemented
140C47#322011yescharacteristic, complemented, Sylow
141C2×#41—471no—
142C22×D4—471no—
143C2×SD16—472no—
144C2×D8—472no—
145C2×D8—472no—
146C2×D8—472no—
147#127—471no—
148#127—471no—
149#127—471no—
150#125—471no—
151#124—471no—
152#124—471no—
153#123—942no—
154#121—472no—
155#121—942no—
156#121—942no—
157#120—942no—
158C4×D4—472no—
159#117C2×D4711yescharacteristic
160C4⋊C8C2×D4712yescomplemented
161#103—472no—
162#102—472no—
163#102—472no—
164#102—472no—
165C22⋊C8C2×D4712yes—
166#97C2×D4711yescharacteristic, complemented
167C4×C8C2×D4711yescharacteristic, complemented
168C24—941no—
169#41—1882no—
170C2×Q8—471no—
171C2×D4—471no—
172C2×D4—471no—
173C2×D4—471no—
174C2×D4—472no—
175C2×D4—942no—
176C2×D4—941no—
177C2×D4—942no—
178C2×D4—942no—
179C2×D4—942no—
180C2×D4—941no—
181C2×D4—1882no—
182C22×C4—942no—
183C22×C4—941no—
184C22×C4C22×D4711yescharacteristic
185SD16—1882no—
186D8—1882no—
187D8—1882no—
188D8—1882no—
189C2×C8C22×D4712yes—
190C2×C8C22×D4712yes—
191C4⋊C4—472no—
192C4⋊C4—942no—
193C4⋊C4D18812yes—
194C22⋊C4—942no—
195C22⋊C4—942no—
196C22⋊C4—942no—
197C22⋊C4—942no—
198C22⋊C4D18812yes—
199C42C22×D4711yescharacteristic
200C42C22×D4711yescharacteristic
201C23—942no—
202C23—941no—
203C23—941no—
204C23—941no—
205C23—3762no—
206C23—1882no—
207C23C2×D18811yescharacteristic
208Q8—942no—
209D4—942no—
210D4—942no—
211D4—942no—
212D4—942no—
213D4—942no—
214D4—3762no—
215D4—3762no—
216D4—3762no—
217D4—3762no—
218D4—1882no—
219D4—1882no—
220C2×C4—22no—
221C2×C4—941no—
222C2×C4—942no—
223C2×C4—3762no—
224C2×C4—1882no—
225C2×C4C2×D18812yes—
226C2×C4C2×D18812yes—
227C2×C4C2×D18811yescharacteristic
228C2×C4C23×D4711yescharacteristic
229C8—22no—
230C8—22no—
231C22—22no—
232C22—21no—
233C22—3764no—
234C22—1882no—
235C22—1882no—
236C22—1882no—
237C22—1882no—
238C22—1882no—
239C22—1881no—
240C22—1881no—
241C22—1881no—
242C22—1882no—
243C22C22×D18811yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—1882no—
248C4—1881no—
249C4#1309407012yes—
250C2—41no—
251C2—3761no—
252C2—3761no—
253C2—3762no—
254C2—3761no—
255C2#1568969211yescharacteristic
256C2#1568992812yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#433C2
socleC22×C47C22×D4
hypercenter#433D47
hypocenterC47#3220
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #15689728C2semidirect
2. #15689692C2semidirect
3. #15689512C2semidirect
4. #15689500C2semidirect
5. #15689488C2semidirect
6. #15689478C2semidirect
7. #15689339C2semidirect
8. #15689319C2semidirect
9. #15689270C2semidirect
10. #15689259C2semidirect
11. C47×#433C2semidirect
14. C2×#10625325C22semidirect
17. C2×D376C22semidirect
20. #13094021C22semidirect
21. #13094016C22semidirect
29. C4×D188C22semidirect
30. #13093949C22semidirect
33. #13093946C22semidirect
35. C4⋊C8×C47C22semidirect
37. #97×C47C22semidirect
38. C4×C8×C47C22semidirect
139. #433D47semidirect
140. C47#3220semidirect
160. C4⋊C8C2×D47semidirect
166. #97C2×D47semidirect
167. C4×C8C2×D47semidirect