Finite Group Databasebeta

← #20253785

Subgroups — #20253785

Order 6016.

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

normal subgroups only

This group has 392 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#15689672C211yesmaximal, characteristic
2#125×D47C211yesmaximal, characteristic, complemented
3#15689490C212yesmaximal, complemented
4#15689486C212yesmaximal, complemented
5#15689480C211yesmaximal, characteristic, complemented
6#15689478C211yesmaximal, characteristic, complemented
7#15689477C211yesmaximal, characteristic, complemented
8#15689123C212yesmaximal, complemented
9#15689121C212yesmaximal, complemented
10C4×#10625324C211yesmaximal, characteristic, complemented
11C47×#488C211yesmaximal, characteristic, complemented
12C2×#10625354C2211yescharacteristic
13C2×#10625352C2211yescharacteristic
14C2×#10625324C2212yes—
15#13094022C2211yescharacteristic
16#13094020C2211yescharacteristic
17#13094016C2211yescharacteristic
18#13094015C2212yes—
19#13094014—22no—
20#13094012C2211yescharacteristic
21#13093997—22no—
22(C22⋊D47)⋊C4—22no—
23C4⋊C4×D47—22no—
24C4⋊C4×D47C2212yes—
25C42×D47C2211yescharacteristic
26#13093949C2212yes—
27#13093948C2212yes—
28#13093947C2212yes—
29#13093946C2212yes—
30#13093945C2212yes—
31#13093944C2212yes—
32#13093934C2212yes—
33C4×C47⋊C8C2211yescharacteristic
34#125×C47C2211yescharacteristic
35#124×C47C2211yescharacteristic
36#103×C47C2212yes—
37#102×C47C2212yes—
38C4×C8×C47C2211yescharacteristic
39C2×Q8×C47C2311yescharacteristic
40C2×D4×C47C2311yescharacteristic
41C2×C22⋊D47—21no—
42C2×C22⋊D47—22no—
43C22×Dic47—21no—
44#10625354—24no—
45#10625352—24no—
46C2×D188—21no—
47C2×D188C2311yescharacteristic
48C2×C4×D47—22no—
49C2×C4×D47—21no—
50C2×C4×D47D412yes—
51C2×C4×D47C2311yescharacteristic
52C2×Dic94C2311yescharacteristic
53C2×C8×C47C2312yes—
54C4⋊C4×C47—22no—
55C4⋊C4×C47C2312yes—
56C22⋊C4×C47—22no—
57C42×C47C2311yescharacteristic
58(C2×D47)⋊C4—22no—
59C4⋊Dic47—22no—
60C4⋊Dic47C2312yes—
61Dic47⋊C4—22no—
62Dic47⋊C4—22no—
63Dic47⋊C4—22no—
64Dic47⋊C4—22no—
65C4×Dic47D412yes—
66C4×Dic47C2311yescharacteristic
67C2×C47⋊C8C2312yes—
68#10625324—24no—
69C23×C47—21no—
70C22×D47—21no—
71C22×D47C2×D411yescharacteristic
72Q8×C47—22no—
73D4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47C2×D412yes—
77C2×C4×C47C2411yescharacteristic
78C22⋊D47—44no—
79C22⋊D47—42no—
80C2×Dic47—22no—
81C2×Dic47—21no—
82C2×Dic47—42no—
83C2×Dic47C2×D412yes—
84C2×Dic47C2×D411yescharacteristic
85D188—22no—
86D188—42no—
87C4×D47—42no—
88C4×D47—44no—
89C4×D47—42no—
90C4×D47#4114yes—
91Dic94—22no—
92C8×C47—22no—
93C47⋊C8—22no—
94C22×C47—41no—
95C22×C47—42no—
96C22×C47C22×D411yescharacteristic
97C2×D47—22no—
98C2×D47—41no—
99C2×D47—42no—
100C2×D47#12412yes—
101C4×C47—22no—
102C4×C47—41no—
103C4×C47—42no—
104C4×C47C2×#4112yes—
105Dic47—22no—
106Dic47—41no—
107Dic47—42no—
108Dic47#12412yes—
109#3142—471nomaximal, Sylow
110C2×C47—81no—
111C2×C47C2×#12411yescharacteristic
112C2×C47#57512yes—
113D47—22no—
114D47—81no—
115#532—471no—
116C2×#125—471no—
117#491—472no—
118#490—472no—
119#488—471no—
120#488—471no—
121#488—471no—
122#488D4711yescharacteristic, complemented
123#417—472no—
124#417—472no—
125C4×M16—471no—
126C47#314211yescharacteristic, complemented, Sylow
127C2×#41—471no—
128C2×#41—471no—
129C2×M16—472no—
130C4⋊Q8—471no—
131#127—471no—
132#125—472no—
133#125—471no—
134#125—942no—
135#125C2×D4711yescharacteristic
136#124—471no—
137#124C2×D4711yescharacteristic
138#121—942no—
139C4×D4—942no—
140C2×C4⋊C4—472no—
141C2×C4⋊C4—942no—
142C2×C42—471no—
143#103—472no—
144#103—472no—
145#103—472no—
146#103C2×D4712yes—
147#102—472no—
148#102—472no—
149#102—472no—
150#102C2×D4712yes—
151#97—472no—
152C4×C8—471no—
153C4×C8C2×D4711yescharacteristic
154#41—944no—
155#41—944no—
156C2×Q8—471no—
157C2×Q8C22×D4711yescharacteristic
158C2×D4—471no—
159C2×D4—941no—
160C2×D4—942no—
161C2×D4—941no—
162C2×D4C22×D4711yescharacteristic
163C22×C4—471no—
164C22×C4—472no—
165C22×C4—941no—
166C22×C4—942no—
167C22×C4—941no—
168M16—944no—
169C2×C8—472no—
170C2×C8C22×D4712yes—
171C4⋊C4—22no—
172C4⋊C4—472no—
173C4⋊C4—942no—
174C4⋊C4—942no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4C22×D4712yes—
179C22⋊C4—22no—
180C22⋊C4—942no—
181C42—472no—
182C42—471no—
183C42C22×D4711yescharacteristic
184C23—21no—
185C23—471no—
186C23—941no—
187Q8—22no—
188Q8—942no—
189D4—22no—
190D4—942no—
191D4—1882no—
192D4—1884no—
193D4—1882no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—471no—
197C2×C4—474no—
198C2×C4—472no—
199C2×C4—941no—
200C2×C4—942no—
201C2×C4—1882no—
202C2×C4—1882no—
203C2×C4—1884no—
204C2×C4—1882no—
205C2×C4D4×D4712yes—
206C2×C4C23×D4711yescharacteristic
207C8—22no—
208C8—942no—
209C22—41no—
210C22—42no—
211C22—472no—
212C22—942no—
213C22—1881no—
214C22—1882no—
215C22C2×D4×D4711yescharacteristic
216C4—22no—
217C4—41no—
218C4—42no—
219C4—472no—
220C4—942no—
221C4—1881no—
222C4—1882no—
223C4#41×D4712yes—
224C2—81no—
225C2—942no—
226C2—3761no—
227C2#124×D4711yescharacteristic
228C2#1568992012yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#488C2
socleC22×C47C22×D4
hypercenter#488D47
hypocenterC47#3142
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
2. #125×D47C2semidirect
3. #15689490C2semidirect
4. #15689486C2semidirect
5. #15689480C2semidirect
6. #15689478C2semidirect
7. #15689477C2semidirect
8. #15689123C2semidirect
9. #15689121C2semidirect
10. C4×#10625324C2semidirect
11. C47×#488C2semidirect
122. #488D47semidirect
126. C47#3142semidirect