Finite Group Databasebeta

← #20243304

Subgroups — #20243304

Order 6016.

612 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#10625352C211yesmaximal, characteristic
2C2×#13093939C211yesmaximal, characteristic, complemented
3C2×#13093938C212yesmaximal, complemented
4#15688984C212yesmaximal, complemented
5C2×#99×C47C211yesmaximal, characteristic, complemented
6C2×#10625352—22no—
7C2×#10625352—22no—
8C2×#10625352—24no—
9C2×#10625352—24no—
10C22×Dic94C411yescharacteristic, complemented
11C22×C22⋊D47C411yescharacteristic, complemented
12C22×C22⋊D47C2211yescharacteristic
13C23×Dic47C411yescharacteristic, complemented
14C23×Dic47C2211yescharacteristic
15C22×C4×D47C411yescharacteristic, complemented
16C2×C22⋊Dic47C2212yes—
17#13093939—22no—
18#13093938—24no—
19C47⋊#95—24no—
20C22×D4×C47C2211yescharacteristic
21C2×C22⋊C4×C47C2212yes—
22#99×C47—22no—
23C24×C47C2×C411yescharacteristic
24C24×C47C2311yescharacteristic
25C23×D47C2×C411yescharacteristic
26C2×D4×C47—22no—
27C2×D4×C47—22no—
28C2×D4×C47D412yes—
29C2×D4×C47D412yes—
30C22×C4×C47—22no—
31C22×C4×C47C2×C411yescharacteristic
32C2×C22⋊D47—22no—
33C2×C22⋊D47—21no—
34C2×C22⋊D47—22no—
35C2×C22⋊D47—21no—
36C2×C22⋊D47—22no—
37C2×C22⋊D47—22no—
38C2×C22⋊D47D414yes—
39C22×Dic47—22no—
40C22×Dic47—21no—
41C22×Dic47—22no—
42C22×Dic47—21no—
43C22×Dic47—22no—
44C22×Dic47—22no—
45C22×Dic47—22no—
46C22×Dic47C2×C411yescharacteristic
47C22×Dic47C2×C411yescharacteristic
48C22×Dic47C2×C411yescharacteristic
49C22×Dic47D414yes—
50#10625352—216no—
51#10625352—216no—
52C2×C4×D47—22no—
53C2×C4×D47—22no—
54C2×C4×D47—22no—
55C2×Dic94—22no—
56C2×Dic94—22no—
57C2×Dic94—22no—
58C22⋊C4×C47—22no—
59C22⋊C4×C47—22no—
60C22⋊Dic47—22no—
61C22⋊Dic47—22no—
62C23×C47—21no—
63C23×C47—21no—
64C23×C47—42no—
65C23×C47—42no—
66C23×C47C22⋊C412yes—
67C23×C47C22×C411yescharacteristic
68C23×C47C2×D411yescharacteristic
69C23×C47C2×D412yes—
70C23×C47C2×D412yes—
71C23×C47C2×D411yescharacteristic
72C22×D47—21no—
73C22×D47—21no—
74C22×D47—42no—
75C22×D47C22⋊C412yes—
76D4×C47—24no—
77D4×C47—24no—
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47—44no—
81C2×C4×C47—42no—
82C2×C4×C47C22⋊C412yes—
83C22⋊D47—28no—
84C22⋊D47—24no—
85C22⋊D47—24no—
86C2×Dic47—28no—
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47—21no—
90C2×Dic47—21no—
91C2×Dic47—21no—
92C2×Dic47—21no—
93C2×Dic47—24no—
94C2×Dic47—24no—
95C2×Dic47—44no—
96C2×Dic47—42no—
97C2×Dic47C22⋊C412yes—
98C2×Dic47C22⋊C412yes—
99C2×Dic47C22⋊C412yes—
100C4×D47—28no—
101Dic94—28no—
102C22×C47—24no—
103C22×C47—22no—
104C22×C47—22no—
105C22×C47—41no—
106C22×C47—42no—
107C22×C47—41no—
108C22×C47—42no—
109C22×C47—42no—
110C22×C47—42no—
111C22×C47C2×C22⋊C411yescharacteristic
112C22×C47C2×C22⋊C411yescharacteristic
113C22×C47C2×C22⋊C411yescharacteristic
114C22×C47#12012yes—
115C22×C47#12012yes—
116C2×D47—22no—
117C2×D47—42no—
118C2×D47—42no—
119C2×D47—42no—
120C4×C47—22no—
121C4×C47—82no—
122Dic47—22no—
123Dic47—22no—
124Dic47—22no—
125Dic47—82no—
126#1782—471nomaximal, Sylow
127C2×C47—22no—
128C2×C47—22no—
129C2×C47—21no—
130C2×C47—21no—
131C2×C47—42no—
132C2×C47#37911yescharacteristic
133C2×C47#41012yes—
134D47—42no—
135C22×#41—471no—
136C2×#99—471no—
137C2×#99—472no—
138C2×#99D4711yescharacteristic, complemented
139#381—472no—
140C47#178211yescharacteristic, complemented, Sylow
141C2×#41—944no—
142C2×#41—944no—
143C2×#41—942no—
144C2×#41—942no—
145C22×Q8—471no—
146C22×D4—471no—
147C22×D4—471no—
148C22×D4C2×D4711yescharacteristic
149C23×C4—471no—
150C23×C4—471no—
151C23×C4—471no—
152C2×C22⋊C4—472no—
153C2×C22⋊C4C2×D4712yes—
154#99—22no—
155#99—944no—
156#99—942no—
157#95—944no—
158C24—471no—
159C24C4×D4711yescharacteristic
160C24C22×D4711yescharacteristic
161#41—9416no—
162#41—9416no—
163C2×Q8—942no—
164C2×Q8—942no—
165C2×Q8—942no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4—474no—
169C2×D4—942no—
170C2×D4—942no—
171C2×D4—942no—
172C2×D4—941no—
173C2×D4—942no—
174C2×D4—941no—
175C2×D4D18812yes—
176C2×D4C22⋊D4712yes—
177C22×C4—22no—
178C22×C4—471no—
179C22×C4—471no—
180C22×C4—471no—
181C22×C4—474no—
182C22×C4—942no—
183C22×C4—942no—
184C22×C4—942no—
185C22×C4—942no—
186C22×C4—942no—
187C22×C4—941no—
188C22×C4—942no—
189C22×C4—941no—
190C22×C4—942no—
191C22×C4—942no—
192C22×C4C4×D4711yescharacteristic
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—942no—
196C22⋊C4—942no—
197C23—21no—
198C23—21no—
199C23—42no—
200C23—42no—
201C23—472no—
202C23—941no—
203C23—941no—
204C23—1882no—
205C23(C2×D47)⋊C412yes—
206C23C2×C4×D4711yescharacteristic
207C23C2×D18811yescharacteristic
208C23D4×D4712yes—
209C23D4×D4712yes—
210C23C2×C22⋊D4711yescharacteristic
211Q8—948no—
212D4—24no—
213D4—24no—
214D4—948no—
215D4—944no—
216D4—944no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—44no—
220C2×C4—42no—
221C2×C4—472no—
222C2×C4—472no—
223C2×C4—472no—
224C2×C4—948no—
225C2×C4—948no—
226C2×C4—941no—
227C2×C4—941no—
228C2×C4—941no—
229C2×C4—941no—
230C2×C4—941no—
231C2×C4—941no—
232C2×C4—944no—
233C2×C4—944no—
234C2×C4—1884no—
235C2×C4—1882no—
236C2×C4(C2×D47)⋊C412yes—
237C22—24no—
238C22—22no—
239C22—22no—
240C22—41no—
241C22—42no—
242C22—41no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22—942no—
247C22—1882no—
248C22—1882no—
249C22—1882no—
250C22C22⋊C4×D4711yescharacteristic
251C22C22⋊C4×D4711yescharacteristic
252C22C2×(C2×D47)⋊C411yescharacteristic
253C22#1309399212yes—
254C22#1309399412yes—
255C4—22no—
256C4—82no—
257C4—942no—
258C4—942no—
259C4—942no—
260C4—3762no—
261C2—22no—
262C2—22no—
263C2—21no—
264C2—21no—
265C2—42no—
266C2—1882no—
267C2#1568897811yescharacteristic
268C2#1568909512yes—
subgroupG/H
centerC22C22⋊C4×D47
commutatorC23×C47C22×C4
FrattiniC24C22×D47
FittingC2×#99×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC2×#99D47
hypocenterC47#1782
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#13093939C2semidirect
3. C2×#13093938C2semidirect
4. #15688984C2semidirect
5. C2×#99×C47C2semidirect
10. C22×Dic94C4semidirect
11. C22×C22⋊D47C4semidirect
13. C23×Dic47C4semidirect
15. C22×C4×D47C4semidirect
138. C2×#99D47semidirect
140. C47#1782semidirect