Finite Group Databasebeta

← #20248762

Subgroups — #20248762

Order 6016.

544 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 159 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×#13094004C211yesmaximal, characteristic
2C2×C4⋊C4×D47C211yesmaximal, characteristic
3#15689054C211yesmaximal, characteristic, complemented
4#15689044C211yesmaximal, characteristic, complemented
5#15689043C211yesmaximal, characteristic, complemented
6#15689022C212yesmaximal, complemented
7#15689020C212yesmaximal, complemented
8#15688997C212yesmaximal
9#15688994C212yesmaximal
10#15688970C211yesmaximal, characteristic
11C47×#398C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×C4×D47C2211yescharacteristic
14C22×C4×D47C2211yescharacteristic
15C22×C4×D47C2211yescharacteristic
16#13094004—24no—
17C2×C4⋊Dic47C2212yes—
18C2×C4⋊Dic47C2211yescharacteristic
19C2×C4⋊Dic47C2212yes—
20C2×Dic47⋊C4C2212yes—
21C2×Dic47⋊C4C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2212yes—
24C4⋊C4×D47—24no—
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2212yes—
27C2×C4×Dic47C2212yes—
28C47⋊#95C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2212yes—
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C4⋊C4×C47C2211yescharacteristic
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C23×D47C2311yescharacteristic
38C22×C4×C47C2312yes—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C22×Dic47C2312yes—
44C22×Dic47C2311yescharacteristic
45C22×Dic47C2311yescharacteristic
46C22×Dic47C2312yes—
47C22×Dic47C2311yescharacteristic
48C2×C4×D47—22no—
49C2×C4×D47—22no—
50C2×C4×D47—22no—
51C2×C4×D47—22no—
52C2×C4×D47—42no—
53C2×C4×D47—42no—
54C2×C4×D47D414yes—
55C2×Dic94—22no—
56C2×Dic94—42no—
57C4⋊C4×C47—22no—
58C4⋊C4×C47—22no—
59C4⋊C4×C47—24no—
60(C2×D47)⋊C4—24no—
61(C2×D47)⋊C4Q818yescomplemented
62C4⋊Dic47—22no—
63C4⋊Dic47—24no—
64C4⋊Dic47—42no—
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67Dic47⋊C4—24no—
68Dic47⋊C4—42no—
69C4×Dic47—42no—
70C23×C47C2411yescharacteristic
71C22×D47—21no—
72C22×D47—21no—
73C22×D47—22no—
74C22×D47C2×D412yes—
75C22×D47C2×Q814yes—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
78C2×C4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—21no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—22no—
86C2×C4×C47C2×D412yes—
87C2×C4×C47C2×Q814yes—
88C2×C4×C47#4112yes—
89C2×Dic47—21no—
90C2×Dic47—22no—
91C2×Dic47—21no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—21no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47C2×D412yes—
100C2×Dic47C2×Q814yes—
101C2×Dic47#4112yes—
102C4×D47—28no—
103C4×D47—44no—
104C4×D47—44no—
105Dic94—44no—
106C22×C47C22×D411yescharacteristic
107C22×C47C22×Q812yes—
108C22×C47C2×#4111yescharacteristic
109C22×C47C2×#4111yescharacteristic
110C22×C47H(5,𝔽2)12yes—
111C2×D47—22no—
112C2×D47—22no—
113C2×D47—24no—
114C2×D47—24no—
115C2×D47C4⋊Q814yes—
116C4×C47—22no—
117C4×C47—22no—
118C4×C47—24no—
119C4×C47—42no—
120C4×C47—41no—
121Dic47—22no—
122Dic47—22no—
123Dic47—24no—
124Dic47—42no—
125Dic47—41no—
126#2583—471nomaximal, Sylow
127C2×C47#52511yescharacteristic
128C2×C47C2×C4⋊Q811yescharacteristic
129C2×C47#53411yescharacteristic
130C2×C47#55412yes—
131C2×C47#55412yes—
132D47—24no—
133C2×C22⋊Q8—471no—
134C22×C4⋊C4—471no—
135#398—471no—
136#398D4711yescharacteristic, complemented
137#395—471no—
138#395—471no—
139#389—472no—
140#389—472no—
141#385—472no—
142#385—472no—
143C4×C22⋊C4—471no—
144C47#258311yescharacteristic, complemented, Sylow
145C22×Q8—471no—
146C23×C4—471no—
147C23×C4—471no—
148C23×C4—471no—
149C22⋊Q8—944no—
150C2×C4⋊C4—471no—
151C2×C4⋊C4—471no—
152C2×C4⋊C4—471no—
153C2×C4⋊C4—472no—
154C2×C4⋊C4—472no—
155C2×C4⋊C4—472no—
156C2×C4⋊C4—472no—
157C2×C4⋊C4—944no—
158C2×C4⋊C4C2×D4711yescharacteristic
159C2×C4⋊C4C2×D4711yescharacteristic
160C2×C4⋊C4C2×D4712yes—
161C2×C22⋊C4—472no—
162C2×C22⋊C4—472no—
163C2×C42—472no—
164#95—471no—
165#95—472no—
166#95—472no—
167#95—472no—
168#95C2×D4711yescharacteristic
169#95C2×D4712yes—
170C24—471no—
171C2×Q8—942no—
172C2×Q8—1882no—
173C22×C4—472no—
174C22×C4—471no—
175C22×C4—471no—
176C22×C4—474no—
177C22×C4—472no—
178C22×C4—471no—
179C22×C4—942no—
180C22×C4—942no—
181C22×C4—942no—
182C22×C4—942no—
183C22×C4—1882no—
184C22×C4—1882no—
185C22×C4C22×D4712yes—
186C22×C4C22×D4711yescharacteristic
187C22×C4C22×D4711yescharacteristic
188C22×C4C22×D4711yescharacteristic
189C22×C4C22×D4712yes—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—24no—
193C4⋊C4—944no—
194C4⋊C4—942no—
195C4⋊C4—942no—
196C4⋊C4—944no—
197C4⋊C4—942no—
198C4⋊C4—1882no—
199C4⋊C4—1882no—
200C22⋊C4—478no—
201C22⋊C4—944no—
202C42—1882no—
203C23—472no—
204C23—474no—
205C23—941no—
206C23—941no—
207C23—942no—
208C23C23×D4711yescharacteristic
209Q8—1884no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—472no—
221C2×C4—474no—
222C2×C4—472no—
223C2×C4—948no—
224C2×C4—941no—
225C2×C4—942no—
226C2×C4—941no—
227C2×C4—942no—
228C2×C4—942no—
229C2×C4—942no—
230C2×C4—941no—
231C2×C4—942no—
232C2×C4—942no—
233C2×C4—942no—
234C2×C4—1884no—
235C2×C4—1884no—
236C2×C4D4×D4712yes—
237C2×C4#1062535212yes—
238C2×C4Q8×D4714yes—
239C22—474no—
240C22—944no—
241C22—944no—
242C22—942no—
243C22—942no—
244C22C2×D4×D4711yescharacteristic
245C22C2×Q8×D4712yes—
246C22#41×D4711yescharacteristic
247C22C2×#1062535211yescharacteristic
248C22#1309407012yes—
249C4—24no—
250C4—22no—
251C4—22no—
252C4—42no—
253C4—41no—
254C4—944no—
255C4—942no—
256C4—942no—
257C4—1881no—
258C4—1882no—
259C2—944no—
260C2#1568963311yescharacteristic
261C2C4⋊Q8×D4711yescharacteristic
262C2#1568968411yescharacteristic
263C2#1568982912yes—
264C2#1568983112yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#398C2
hypercenter#398D47
hypocenterC47#2583
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. #15689054C2semidirect
4. #15689044C2semidirect
5. #15689043C2semidirect
6. #15689022C2semidirect
7. #15689020C2semidirect
11. C47×#398C2semidirect
61. (C2×D47)⋊C4Q8semidirect
136. #398D47semidirect
144. C47#2583semidirect