Finite Group Databasebeta

← #20251850

Subgroups — #20251850

Order 6016.

716 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 209 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
1C2×#13094071C211yesmaximal, characteristic
2#15689600C212yesmaximal, complemented
3#15689097C211yesmaximal, characteristic, complemented
4#15689096C212yesmaximal, complemented
5#15689095C218yesmaximal, complemented
6C47×#410C211yesmaximal, characteristic, complemented
7#13094071—24no—
8#13094071—24no—
9C2×#10625350C412yescomplemented
10C2×#10625350C2211yescharacteristic
11C2×#10625352C412yescomplemented
12C2×#10625352C2214yes—
13C22×Dic94C412yescomplemented
14C22×Dic94C2211yescharacteristic
15C2×Q8×D47C412yescomplemented
16C4×Dic94—24no—
17#13093989—24no—
18#13093983C2212yes—
19#13093980C2218yes—
20#13093939C2214yes—
21#13093938C2218yes—
22C2×#41×C47C2211yescharacteristic
23#117×C47C2212yes—
24#99×C47C2214yes—
25#41×C47—22no—
26#41×C47—22no—
27C2×Q8×C47C2×C411yescharacteristic
28C2×D4×C47C2×C411yescharacteristic
29C2×D4×C47C2312yes—
30C22×C4×C47C2×C412yes—
31C22×C4×C47C2311yescharacteristic
32C2×C22⋊D47C2×C414yes—
33C2×C22⋊D47C2312yes—
34C22×Dic47C2×C414yes—
35C22×Dic47C2312yes—
36Q8×D47—28no—
37#10625352—216no—
38#10625352—28no—
39#10625350—22no—
40#10625350—22no—
41#10625350—24no—
42#10625350—24no—
43C2×D188C2×C411yescharacteristic
44C2×C4×D47C2×C412yes—
45C2×C4×D47C2×C414yes—
46C2×Dic94—24no—
47C2×Dic94—24no—
48C2×Dic94C2×C414yes—
49C2×Dic94C2×C411yescharacteristic
50C2×Dic94C2×C412yes—
51C2×Dic94C2×C412yes—
52C2×Dic94D414yes—
53C2×Dic94D414yes—
54C4⋊C4×C47—22no—
55C22⋊C4×C47C2314yes—
56C42×C47—22no—
57C22⋊Dic47C2314yes—
58C4⋊Dic47—22no—
59Dic47⋊C4—28no—
60C4×Dic47—22no—
61C4×Dic47—28no—
62C23×C47C22×C412yes—
63C23×C47C2411yescharacteristic
64C22×D47C22×C412yes—
65Q8×C47—22no—
66D4×C47—24no—
67D4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—24no—
71C2×C4×C47C22×C412yes—
72C2×C4×C47C22×C411yescharacteristic
73C2×C4×C47C22×C411yescharacteristic
74C2×C4×C47C2×D412yes—
75C2×C4×C47C2×D412yes—
76C22⋊D47—24no—
77C22⋊D47—28no—
78C2×Dic47—28no—
79C2×Dic47—24no—
80C2×Dic47C22×C412yes—
81C2×Dic47C22×C414yes—
82C2×Dic47C2×D418yes—
83D188—21no—
84D188—21no—
85C4×D47—24no—
86C4×D47—28no—
87Dic94—21no—
88Dic94—21no—
89Dic94—28no—
90Dic94C22⋊C414yes—
91Dic94C22⋊C414yes—
92Dic94C22⋊C418yes—
93C22×C47—22no—
94C22×C47—41no—
95C22×C47—42no—
96C22×C47C23×C411yescharacteristic
97C22×C47C22×D412yes—
98C2×D47—22no—
99C2×D47—42no—
100C4×C47—22no—
101C4×C47—44no—
102C4×C47C2×C22⋊C411yescharacteristic
103C4×C47C2×C22⋊C411yescharacteristic
104C4×C47C2×C22⋊C412yes—
105Dic47—22no—
106Dic47—44no—
107Dic47C2×C22⋊C418yes—
108#2884—471nomaximal, Sylow
109C2×C47—22no—
110C2×C47—21no—
111C2×C47—42no—
112C2×C47C22×C22⋊C411yescharacteristic
113D47—42no—
114C2×2−1+4—471no—
115#519—472no—
116#410—471no—
117#410—472no—
118#410—478no—
119#410D4711yescharacteristic, complemented
120C47#288411yescharacteristic, complemented, Sylow
1212−1+4—944no—
1222−1+4—944no—
123C2×#41—472no—
124C2×#41—474no—
125C2×#41—472no—
126C2×#41—471no—
127C2×#41C2×D4711yescharacteristic
128C22×Q8—472no—
129C22×Q8—472no—
130C22×Q8—471no—
131C4×Q8—944no—
132C4×Q8—944no—
133#117—472no—
134#117—478no—
135#117C2×D4712yes—
136#99—474no—
137#99—478no—
138#99C2×D4714yes—
139#41—22no—
140#41—22no—
141#41—944no—
142#41—944no—
143#41—9416no—
144#41—948no—
145#41—942no—
146#41—942no—
147C2×Q8—472no—
148C2×Q8—472no—
149C2×Q8—474no—
150C2×Q8—471no—
151C2×Q8—474no—
152C2×Q8—474no—
153C2×Q8—944no—
154C2×Q8—944no—
155C2×Q8—948no—
156C2×Q8C4×D4711yescharacteristic
157C2×D4—474no—
158C2×D4—472no—
159C2×D4—471no—
160C2×D4C4×D4711yescharacteristic
161C2×D4C22×D4712yes—
162C22×C4—472no—
163C22×C4—474no—
164C22×C4—474no—
165C22×C4—472no—
166C22×C4C4×D4712yes—
167C22×C4C22×D4711yescharacteristic
168C4⋊C4—22no—
169C4⋊C4—948no—
170C4⋊C4—942no—
171C22⋊C4—474no—
172C22⋊C4C22×D4714yes—
173C42—22no—
174C42—948no—
175C42—942no—
176C23—472no—
177C23C2×C4×D4712yes—
178C23C23×D4711yescharacteristic
179Q8—22no—
180Q8—474no—
181Q8—474no—
182Q8—478no—
183Q8—948no—
184Q8—941no—
185Q8—941no—
186D4—24no—
187D4—22no—
188D4—948no—
189D4—944no—
190D4—941no—
191D4—941no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4—474no—
196C2×C4—478no—
197C2×C4—472no—
198C2×C4—948no—
199C2×C4—948no—
200C2×C4—944no—
201C2×C4—944no—
202C2×C4C2×C4×D4712yes—
203C2×C4C2×C4×D4711yescharacteristic
204C2×C4C2×C4×D4711yescharacteristic
205C2×C4D4×D4712yes—
206C2×C4D4×D4712yes—
207C22—22no—
208C22—41no—
209C22—42no—
210C22—942no—
211C22—1882no—
212C22C22×C4×D4711yescharacteristic
213C22C2×D4×D4712yes—
214C4—22no—
215C4—44no—
216C4—478no—
217C4—942no—
218C4—1884no—
219C4C22⋊C4×D4711yescharacteristic
220C4C22⋊C4×D4711yescharacteristic
221C4C22⋊C4×D4712yes—
222C2—22no—
223C2—21no—
224C2—42no—
225C2—1882no—
226C2C2×C22⋊C4×D4711yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D47
commutatorC22×C47C23×C4
FrattiniC23C23×D47
FittingC47×#410C2
socleC2×C47C22×C22⋊C4
hypercenter#410D47
hypocenterC47#2884
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #15689600C2semidirect
3. #15689097C2semidirect
4. #15689096C2semidirect
5. #15689095C2semidirect
6. C47×#410C2semidirect
9. C2×#10625350C4semidirect
11. C2×#10625352C4semidirect
13. C22×Dic94C4semidirect
15. C2×Q8×D47C4semidirect
119. #410D47semidirect
120. C47#2884semidirect