Finite Group Databasebeta

← #20254462

Subgroups — #20254462

Order 6016.

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

normal subgroups only

This group has 396 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#15689735C211yesmaximal, characteristic, complemented
2#15689692C211yesmaximal, characteristic
3#15689517C211yesmaximal, characteristic, complemented
4#15689496C211yesmaximal, characteristic, complemented
5#15689488C211yesmaximal, characteristic, complemented
6#15689478C211yesmaximal, characteristic, complemented
7#15689346C212yesmaximal, complemented
8#15689324C212yesmaximal, complemented
9#15689287C212yesmaximal, complemented
10#15689276C212yesmaximal, complemented
11C47×#433C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13C22×D188C2211yescharacteristic
14C2×Dic188C2212yescomplemented
15C2×#10625325C2212yes—
16C2×#10625325C2212yes—
17C2×#10625325C2212yescomplemented
18#13094024C2211yescharacteristic, complemented
19#13094021C2211yescharacteristic
20#13094021C2211yescharacteristic
21#13094017—22no—
22#13094016C2211yescharacteristic, complemented
23#13094014—22no—
24#13094012C2211yescharacteristic
25#13094012C2211yescharacteristic
26#13094003C2212yes—
27#13093999—22no—
28#13093994—22no—
29C4×Dic94C2212yescomplemented
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—
42#10625350—42no—
43C2×D188—21no—
44C2×D188—22no—
45C2×D188—22no—
46C2×D188—42no—
47C2×D188C2311yescharacteristic
48C2×D188C2311yescharacteristic
49C2×D188C2311yescharacteristic
50C2×C4×D47—21no—
51C2×Dic94C2311yescharacteristic
52C2×Dic94C2312yes—
53C2×C8×C47C2312yes—
54C2×C8×C47C2312yes—
55C4⋊C4×C47D412yes—
56C22⋊C4×C47D412yes—
57C42×C47C2311yescharacteristic
58C42×C47C2311yescharacteristic
59C22⋊Dic47—22no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—22no—
62C4⋊Dic47—22no—
63C4⋊Dic47C2312yes—
64Dic47⋊C4—22no—
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67C4×Dic47—22no—
68Dic188—42no—
69#10625325—42no—
70#10625325—42no—
71#10625325—42no—
72C23×C47C2×D411yescharacteristic
73C22×D47—21no—
74C22×D47—21no—
75C22×D47—21no—
76C22×D47—42no—
77C22×D47—82no—
78C2×C4×C47—22no—
79C2×C4×C47C2×D412yes—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D412yes—
82C2×C4×C47C2411yescharacteristic
83C22⋊D47—42no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—21no—
87D188—22no—
88D188—22no—
89D188—22no—
90D188—42no—
91D188—82no—
92D188—82no—
93C4×D47—42no—
94Dic94—22no—
95Dic94—22no—
96Dic94—22no—
97C8×C47—22no—
98C8×C47—22no—
99C22×C47—21no—
100C22×C47—22no—
101C22×C47C22×D411yescharacteristic
102C2×D47—41no—
103C2×D47—41no—
104C2×D47—41no—
105C2×D47—42no—
106C2×D47—42no—
107C2×D47—42no—
108C2×D47—84no—
109C4×C47—21no—
110C4×C47—22no—
111C4×C47—22no—
112C4×C47H(5,𝔽2)12yes—
113Dic47—41no—
114Dic47—42no—
115Dic47—42no—
116#3222—471nomaximal, Sylow
117C2×C47—41no—
118C2×C47#53511yescharacteristic
119C2×C47#57712yes—
120D47—81no—
121D47—81no—
122D47—81no—
123#541—471no—
124#535—471no—
125#497—471no—
126#492—471no—
127#490—471no—
128#488—471no—
129#464—472no—
130#460—472no—
131#452—472no—
132#450—472no—
133#433D4711yescharacteristic, complemented
134C47#322211yescharacteristic, complemented, Sylow
135C2×#41—471no—
136C22×D4—471no—
137C2×Q16—472no—
138C2×SD16—472no—
139C2×SD16—472no—
140C2×SD16—472no—
141C4⋊Q8—471no—
142#127—471no—
143#127—471no—
144#126—942no—
145#125—471no—
146#125—942no—
147#124—471no—
148#124—471no—
149C22⋊Q8—472no—
150#121—942no—
151#120—942no—
152C4×Q8—472no—
153#117C2×D4711yescharacteristic
154C4⋊C8C2×D4712yescomplemented
155#103—472no—
156#102—472no—
157#102—472no—
158#102—472no—
159C22⋊C8C2×D4712yes—
160#97C2×D4711yescharacteristic, complemented
161C4×C8C2×D4711yescharacteristic, complemented
162C24—941no—
163#41—1882no—
164C2×Q8—471no—
165C2×Q8—472no—
166C2×D4—471no—
167C2×D4—471no—
168C2×D4—471no—
169C2×D4—941no—
170C2×D4—942no—
171C2×D4—942no—
172C2×D4—941no—
173C2×D4—1882no—
174C22×C4—941no—
175C22×C4C22×D4711yescharacteristic
176Q16—1882no—
177SD16—1882no—
178SD16—1882no—
179SD16—1882no—
180C2×C8C22×D4712yes—
181C2×C8C22×D4712yes—
182C4⋊C4—472no—
183C4⋊C4—942no—
184C4⋊C4—942no—
185C4⋊C4—942no—
186C4⋊C4—942no—
187C4⋊C4D18812yes—
188C22⋊C4—942no—
189C22⋊C4—942no—
190C22⋊C4—942no—
191C22⋊C4D18812yes—
192C42—942no—
193C42C22×D4711yescharacteristic
194C42C22×D4711yescharacteristic
195C23—941no—
196C23—941no—
197C23—941no—
198C23—3762no—
199C23—1882no—
200C23C2×D18811yescharacteristic
201Q8—942no—
202Q8—942no—
203Q8—942no—
204D4—942no—
205D4—942no—
206D4—942no—
207D4—3762no—
208D4—3762no—
209D4—1882no—
210D4—1882no—
211C2×C4—22no—
212C2×C4—942no—
213C2×C4—942no—
214C2×C4—941no—
215C2×C4—1882no—
216C2×C4C2×D18812yes—
217C2×C4C2×D18812yes—
218C2×C4C2×D18811yescharacteristic
219C2×C4C23×D4711yescharacteristic
220C8—22no—
221C8—22no—
222C22—22no—
223C22—21no—
224C22—3764no—
225C22—1882no—
226C22—1882no—
227C22—1882no—
228C22—1881no—
229C22—1881no—
230C22—1881no—
231C22C22×D18811yescharacteristic
232C4—22no—
233C4—22no—
234C4—21no—
235C4—1882no—
236C4—1881no—
237C4—1882no—
238C4#1309407012yes—
239C2—41no—
240C2—3761no—
241C2—3761no—
242C2—3761no—
243C2#1568969211yescharacteristic
244C2#1568993512yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#433C2
socleC22×C47C22×D4
hypercenter#433D47
hypocenterC47#3222
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. #15689735C2semidirect
3. #15689517C2semidirect
4. #15689496C2semidirect
5. #15689488C2semidirect
6. #15689478C2semidirect
7. #15689346C2semidirect
8. #15689324C2semidirect
9. #15689287C2semidirect
10. #15689276C2semidirect
11. C47×#433C2semidirect
14. C2×Dic188C22semidirect
17. C2×#10625325C22semidirect
18. #13094024C22semidirect
22. #13094016C22semidirect
29. C4×Dic94C22semidirect
30. #13093949C22semidirect
33. #13093946C22semidirect
35. C4⋊C8×C47C22semidirect
37. #97×C47C22semidirect
38. C4×C8×C47C22semidirect
133. #433D47semidirect
134. C47#3222semidirect
154. C4⋊C8C2×D47semidirect
160. #97C2×D47semidirect
161. C4×C8C2×D47semidirect