Finite Group Databasebeta

← #20255748

Subgroups — #20255748

Order 6016.

388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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#15689833C211yesmaximal, characteristic, complemented
2#15689776C211yesmaximal, characteristic
3#15689519C211yesmaximal, characteristic, complemented
4#15689452C212yesmaximal, complemented
5#15689443C212yesmaximal, complemented
6#15689414C211yesmaximal, characteristic, complemented
7#15689355C212yesmaximal, complemented
8C4×#10625336C211yesmaximal, characteristic, complemented
9#15689188C211yesmaximal, characteristic, complemented
10#106×D47C212yesmaximal, complemented
11C47×#475C211yesmaximal, characteristic, complemented
12C2×#10625354—21no—
13C2×#10625336C2211yescharacteristic
14C2×C8×D47C2212yes—
15#13094024C2211yescharacteristic
16#13094016—21no—
17#13094009—22no—
18#13094002—22no—
19#13094000—21no—
20#13094000C2212yes—
21#13093999C2212yes—
22C4×D188—21no—
23C4×D188C2211yescharacteristic
24C4×D188C2211yescharacteristic
25C4⋊C4×D47C2212yes—
26C4⋊C4×D47C2212yes—
27#13093956C2212yes—
28#13093955C2212yes—
29#13093955C2212yes—
30#13093955C2211yescharacteristic
31#13093948C2211yescharacteristic
32#13093946C2212yes—
33#13093944C2211yescharacteristic
34(C2×D47)⋊C8C2212yes—
35C4×C47⋊C8C2211yescharacteristic
36C4⋊Q8×C47C2211yescharacteristic
37C4×Q8×C47C2211yescharacteristic
38#106×C47C2212yes—
39C4⋊C8×C47C2211yescharacteristic
40#103×C47C2212yes—
41C2×Q8×C47—21no—
42C2×Q8×C47C2311yescharacteristic
43#10625354—44no—
44C2×D188—22no—
45C2×D188D411yescharacteristic
46C2×D188C2311yescharacteristic
47C2×C4×D47—22no—
48C2×C4×D47—21no—
49C2×C4×D47—22no—
50C2×C4×D47C2312yes—
51C2×Dic94—21no—
52C2×C8×C47C2312yes—
53C4⋊C4×C47—21no—
54C4⋊C4×C47—21no—
55C4⋊C4×C47C2312yes—
56C4⋊C4×C47C2311yescharacteristic
57C42×C47—21no—
58C42×C47C2311yescharacteristic
59#10625336—22no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—21no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4D412yes—
64C4⋊Dic47—21no—
65C4⋊Dic47D411yescharacteristic
66C4⋊Dic47C2312yes—
67C4⋊Dic47C2311yescharacteristic
68Dic47⋊C4—22no—
69Dic47⋊C4—22no—
70Dic47⋊C4—22no—
71C2×C47⋊C8C2311yescharacteristic
72C2×C47⋊C8C2311yescharacteristic
73C8×D47—24no—
74C22×D47—21no—
75C22×D47C2×D412yes—
76Q8×C47—21no—
77Q8×C47—21no—
78Q8×C47—42no—
79C2×C4×C47—21no—
80C2×C4×C47—21no—
81C2×C4×C47—22no—
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2411yescharacteristic
85C2×Dic47—22no—
86C2×Dic47—21no—
87C2×Dic47C2×D412yes—
88D188—21no—
89D188—21no—
90D188—44no—
91D188SD1614yescomplemented
92C4×D47—22no—
93C4×D47—22no—
94C4×D47—44no—
95C4×D47—42no—
96C4×D47—82no—
97Dic94—81no—
98C8×C47—22no—
99C47⋊C8—21no—
100C47⋊C8#4112yescomplemented
101C22×C47C22×D411yescharacteristic
102C2×D47—22no—
103C2×D47—22no—
104C2×D47—41no—
105C2×D47—41no—
106C2×D47—41no—
107C2×D47C2×SD1614yes—
108C4×C47—21no—
109C4×C47—41no—
110C4×C47—42no—
111C4×C47—41no—
112C4×C47C2×SD1612yes—
113C4×C47C2×#4111yescharacteristic
114C4×C472−1+411yescharacteristic
115Dic47—22no—
116Dic47—41no—
117Dic47—42no—
118#3335—471nomaximal, Sylow
119C2×C47#54711yescharacteristic
120C2×C47C22×SD1611yescharacteristic
121C2×C47#57711yescharacteristic
122D47—24no—
123D47—81no—
124#554—471no—
125#547—471no—
126#498—471no—
127#483—472no—
128#481—472no—
129#476—471no—
130#475D4711yescharacteristic, complemented
131#465—472no—
132C4×SD16—471no—
133C8×D4—471no—
134C2×#106—472no—
135C47#333511yescharacteristic, complemented, Sylow
136C2×#41—941no—
137C2×SD16—471no—
138C22×C8—472no—
139C4⋊Q8—471no—
140C4⋊Q8C2×D4711yescharacteristic
141#125—941no—
142#123—942no—
143C22⋊Q8—472no—
144C22⋊Q8—942no—
145C22⋊Q8—941no—
146#121—472no—
147C4×Q8C2×D4711yescharacteristic
148C4×D4—471no—
149C4×D4—471no—
150C4×D4—941no—
151C2×C4⋊C4—472no—
152C2×C4⋊C4—472no—
153#106—472no—
154#106—471no—
155#106—472no—
156#106—472no—
157#106C2×D4712yes—
158C4⋊C8C2×D4711yescharacteristic
159#103—471no—
160#103C2×D4712yes—
161#102—472no—
162#102—471no—
163C22⋊C8—472no—
164C4×C8—471no—
165#41—1884no—
166C2×Q8—21no—
167C2×Q8—941no—
168C2×Q8C22×D4711yescharacteristic
169C2×D4—471no—
170C2×D4—471no—
171C2×D4—942no—
172C22×C4—472no—
173C22×C4—942no—
174C22×C4—942no—
175C22×C4—941no—
176SD16—942no—
177C2×C8—471no—
178C2×C8—471no—
179C2×C8—944no—
180C2×C8C22×D4712yes—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—471no—
184C4⋊C4—472no—
185C4⋊C4—471no—
186C4⋊C4—942no—
187C4⋊C4—942no—
188C4⋊C4—942no—
189C4⋊C4—941no—
190C4⋊C4C22×D4711yescharacteristic
191C4⋊C4C22×D4712yes—
192C22⋊C4—472no—
193C22⋊C4—942no—
194C22⋊C4—942no—
195C22⋊C4—941no—
196C42—21no—
197C42C22×D4711yescharacteristic
198C23—472no—
199C23—941no—
200Q8—21no—
201Q8—21no—
202Q8—42no—
203Q8—3761no—
204D4—474no—
205D4—941no—
206D4—941no—
207D4—1884no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—472no—
212C2×C4—942no—
213C2×C4—942no—
214C2×C4—942no—
215C2×C4—941no—
216C2×C4—3762no—
217C2×C4—1884no—
218C2×C4—1882no—
219C2×C4D4×D4711yescharacteristic
220C2×C4D4×D4711yescharacteristic
221C2×C4C23×D4711yescharacteristic
222C8—22no—
223C8—472no—
224C8—941no—
225C22—474no—
226C22—942no—
227C22—942no—
228C22—1881no—
229C22—1881no—
230C22—1881no—
231C22C2×D4×D4711yescharacteristic
232C4—21no—
233C4—41no—
234C4—42no—
235C4—41no—
236C4—942no—
237C4—1881no—
238C4—1882no—
239C4SD16×D4712yes—
240C4#41×D4711yescharacteristic
241C4#1309407211yescharacteristic
242C2—944no—
243C2—3761no—
244C2#1568977511yescharacteristic
245C2C2×SD16×D4711yescharacteristic
246C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#475C2
socleC22×C47C22×D4
hypercenter#475D47
hypocenterC47#3335
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #15689833C2semidirect
3. #15689519C2semidirect
4. #15689452C2semidirect
5. #15689443C2semidirect
6. #15689414C2semidirect
7. #15689355C2semidirect
8. C4×#10625336C2semidirect
9. #15689188C2semidirect
10. #106×D47C2semidirect
11. C47×#475C2semidirect
91. D188SD16semidirect
100. C47⋊C8#41semidirect
130. #475D47semidirect
135. C47#3335semidirect