Finite Group Databasebeta

← #20252685

Subgroups — #20252685

Order 6016.

700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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
2C2×#13094057C211yesmaximal, characteristic, complemented
3C22×Dic188C211yesmaximal, characteristic, complemented
4#15689694C211yesmaximal, characteristic, complemented
5#15689287C214yesmaximal, complemented
6#15689281C214yesmaximal, complemented
7#15689133C211yesmaximal, characteristic, complemented
8#15689120C211yesmaximal, characteristic, complemented
9C47×#408C211yesmaximal, characteristic, complemented
10#13094071—24no—
11#13094071—24no—
12C2×#10625350C2212yes—
13C2×#10625350C2211yescharacteristic
14C2×#10625352—22no—
15C2×#10625352—21no—
16C22×Dic94C2212yes—
17C22×Dic94C2211yescharacteristic
18C22×Dic94C2211yescharacteristic
19C2×Q8×D47—21no—
20#13094057—24no—
21C2×Dic188—24no—
22C2×Dic188C2212yes—
23C2×Dic188C2214yes—
24C2×#10625325C2212yes—
25#13094022—21no—
26#13094011—21no—
27#13094005—22no—
28#13094003C2214yes—
29#13093983C2211yescharacteristic
30#13093949C2212yes—
31#13093949C2214yes—
32#13093946C2212yes—
33C2×#41×C47C2211yescharacteristic
34C2×M16×C47C2211yescharacteristic
35C22×C8×C47C2211yescharacteristic
36C22⋊C8×C47C2214yes—
37#41×C47—22no—
38#41×C47—22no—
39C2×Q8×C47D411yescharacteristic
40C2×D4×C47D412yes—
41C2×D4×C47D411yescharacteristic
42C22×C4×C47C2312yes—
43C22×C4×C47C2311yescharacteristic
44C2×C22⋊D47—22no—
45C2×C22⋊D47—21no—
46C22×Dic47—22no—
47C22×Dic47—21no—
48C22×Dic47—21no—
49Q8×D47—28no—
50#10625352—216no—
51#10625352—28no—
52#10625350—22no—
53#10625350—24no—
54#10625350—24no—
55#10625350D414yes—
56C2×D188C2311yescharacteristic
57C2×C4×D47—22no—
58C2×C4×D47—21no—
59C2×Dic94—22no—
60C2×Dic94—21no—
61C2×Dic94—22no—
62C2×Dic94—24no—
63C2×Dic94—24no—
64C2×Dic94—22no—
65C2×Dic94—22no—
66C2×Dic94—21no—
67C2×Dic94D414yes—
68C2×Dic94C2312yes—
69C2×Dic94C2311yescharacteristic
70C2×Dic94C2312yes—
71M16×C47—22no—
72C2×C8×C47—22no—
73C2×C8×C47C2312yes—
74C2×C8×C47C2312yes—
75C22⋊Dic47—21no—
76C22⋊Dic47—24no—
77C4⋊Dic47C2312yes—
78Dic47⋊C4—24no—
79C4×Dic47—21no—
80Dic188—28no—
81Dic188—24no—
82#10625325—24no—
83C23×C47C2×D412yes—
84C23×C47C2×D411yescharacteristic
85C22×D47—21no—
86Q8×C47—22no—
87D4×C47—24no—
88D4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47C2×D412yes—
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47C2×D412yes—
94C2×C4×C47C2×D412yes—
95C2×C4×C47C2411yescharacteristic
96C22⋊D47—28no—
97C22⋊D47—24no—
98C2×Dic47—28no—
99C2×Dic47—24no—
100C2×Dic47—21no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—42no—
105D188—21no—
106D188C2×D412yes—
107C4×D47—28no—
108C4×D47—24no—
109Dic94—28no—
110Dic94—24no—
111Dic94—22no—
112Dic94—21no—
113Dic94—22no—
114Dic94—22no—
115Dic94—42no—
116Dic94C2×D412yes—
117Dic94C2×D414yes—
118C8×C47—22no—
119C8×C47—22no—
120C22×C47—22no—
121C22×C47—22no—
122C22×C47—24no—
123C22×C47#12012yes—
124C22×C47C22×D411yescharacteristic
125C2×D47—22no—
126C2×D47—42no—
127C4×C47—22no—
128C4×C47#12012yes—
129C4×C47C22×D411yescharacteristic
130C4×C47C22×D411yescharacteristic
131Dic47—22no—
132Dic47—24no—
133Dic47—42no—
134Dic47—42no—
135#3011—471nomaximal, Sylow
136C2×C47—22no—
137C2×C47—42no—
138C2×C47C2×#12011yescharacteristic
139C2×C47#57812yes—
140D47—42no—
141C2×2−1+4—471no—
142C2×#137—471no—
143C22×Q16—471no—
144#536—471no—
145#452—474no—
146#451—474no—
147#419—471no—
148#416—471no—
149#408D4711yescharacteristic, complemented
150C47#301111yescharacteristic, complemented, Sylow
1512−1+4—944no—
1522−1+4—944no—
153C2×#41—471no—
154C2×#41—472no—
155C2×#41—942no—
156C2×#41—941no—
157C2×#41C2×D4711yescharacteristic
158C22×Q8—471no—
159C22×Q8—471no—
160C22×Q8—472no—
161C22×Q8—941no—
162#137—944no—
163C2×Q16—474no—
164C2×Q16—472no—
165C2×Q16—944no—
166C2×SD16—472no—
167C2×M16C2×D4711yescharacteristic
168C22×C8C2×D4711yescharacteristic
169C4⋊Q8—941no—
170#124—941no—
171#123—942no—
172C22⋊Q8—474no—
173#117—471no—
174#103—472no—
175#103—474no—
176#102—472no—
177C22⋊C8C2×D4714yes—
178#41—22no—
179#41—22no—
180#41—474no—
181#41—944no—
182#41—944no—
183#41—9416no—
184#41—948no—
185#41—942no—
186C2×Q8—474no—
187C2×Q8—472no—
188C2×Q8—471no—
189C2×Q8—472no—
190C2×Q8—944no—
191C2×Q8—944no—
192C2×Q8—948no—
193C2×Q8—942no—
194C2×Q8—941no—
195C2×Q8—941no—
196C2×Q8—942no—
197C2×Q8—942no—
198C2×Q8—942no—
199C2×Q8D18811yescharacteristic
200C2×D4—471no—
201C2×D4—942no—
202C2×D4—941no—
203C2×D4D18812yes—
204C2×D4D18811yescharacteristic
205C22×C4—942no—
206C22×C4—941no—
207C22×C4—942no—
208C22×C4—941no—
209C22×C4—941no—
210C22×C4C22×D4712yes—
211C22×C4C22×D4711yescharacteristic
212Q16—948no—
213Q16—944no—
214SD16—944no—
215M16—22no—
216C2×C8—22no—
217C2×C8C22×D4712yes—
218C2×C8C22×D4712yes—
219C4⋊C4—472no—
220C4⋊C4—944no—
221C22⋊C4—941no—
222C22⋊C4—944no—
223C42—941no—
224C23—941no—
225C23C2×D18812yes—
226C23C2×D18811yescharacteristic
227Q8—22no—
228Q8—474no—
229Q8—472no—
230Q8—948no—
231Q8—944no—
232Q8—942no—
233Q8—941no—
234Q8—942no—
235Q8—942no—
236Q8—1882no—
237D4—24no—
238D4—22no—
239D4—472no—
240D4—948no—
241D4—944no—
242D4—941no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—948no—
246C2×C4—948no—
247C2×C4—944no—
248C2×C4—942no—
249C2×C4—941no—
250C2×C4—944no—
251C2×C4—942no—
252C2×C4—942no—
253C2×C4—1882no—
254C2×C4C2×D18812yes—
255C2×C4C2×D18811yescharacteristic
256C2×C4D4×D4712yes—
257C2×C4D4×D4712yes—
258C2×C4C23×D4711yescharacteristic
259C8—22no—
260C8—22no—
261C22—22no—
262C22—22no—
263C22—24no—
264C22—942no—
265C22—1882no—
266C22#1309399412yes—
267C22C22×D18811yescharacteristic
268C4—22no—
269C4—944no—
270C4—942no—
271C4—1882no—
272C4—1882no—
273C4#1309399412yes—
274C4C2×D4×D4711yescharacteristic
275C4C2×D4×D4711yescharacteristic
276C2—22no—
277C2—42no—
278C2—1882no—
279C2C2×#1309399411yescharacteristic
280C2#1568994012yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#408C2
socleC22×C47C22×D4
hypercenter#408D47
hypocenterC47#3011
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. C2×#13094057C2semidirect
3. C22×Dic188C2semidirect
4. #15689694C2semidirect
5. #15689287C2semidirect
6. #15689281C2semidirect
7. #15689133C2semidirect
8. #15689120C2semidirect
9. C47×#408C2semidirect
149. #408D47semidirect
150. C47#3011semidirect