Finite Group Databasebeta

← #20251724

Subgroups — #20251724

Order 6016.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13094001C211yesmaximal, characteristic
2C22×C4×Dic47C211yesmaximal, characteristic
3#15689027C212yesmaximal, complemented
4#15689018C212yesmaximal, complemented
5#15689009C212yesmaximal, complemented
6#15689005C212yesmaximal, complemented
7#15688996C211yesmaximal, characteristic
8#15688984C211yesmaximal, characteristic
9#15688984C211yesmaximal, characteristic
10#15688981C211yesmaximal, characteristic
11C47×#385C211yesmaximal, characteristic
12C22×Dic94C2211yescharacteristic
13C23×Dic47C2211yescharacteristic
14C23×Dic47C2211yescharacteristic
15#13094001—24no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×C22⋊Dic47C2211yescharacteristic
22C2×C22⋊Dic47C2211yescharacteristic
23C2×C4×Dic47—24no—
24C2×C4×Dic47C2212yes—
25C2×C4×Dic47C2212yes—
26C47⋊#95C2212yes—
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C23×C4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2212yes—
34C2×C22⋊C4×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2211yescharacteristic
36#95×C47C2212yes—
37C24×C47C2311yescharacteristic
38C22×C4×C47—22no—
39C22×C4×C47—24no—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2312yes—
44C22×Dic47—22no—
45C22×Dic47—22no—
46C22×Dic47—24no—
47C22×Dic47D414yes—
48C22×Dic47Q814yescomplemented
49C22×Dic47C2312yes—
50C22×Dic47C2311yescharacteristic
51C22×Dic47C2311yescharacteristic
52C22×Dic47C2311yescharacteristic
53C22×Dic47C2312yes—
54C22×Dic47C2311yescharacteristic
55C2×Dic94—22no—
56C2×Dic94—24no—
57C4⋊C4×C47—24no—
58C22⋊C4×C47—22no—
59C22⋊C4×C47—22no—
60C22⋊Dic47—22no—
61C22⋊Dic47—22no—
62C4⋊Dic47—22no—
63Dic47⋊C4—24no—
64Dic47⋊C4—22no—
65Dic47⋊C4—22no—
66Dic47⋊C4—24no—
67C4×Dic47—24no—
68C4×Dic47—24no—
69C23×C47—22no—
70C23×C47—22no—
71C23×C47C2×D412yes—
72C23×C47C2×Q812yes—
73C23×C47#4112yes—
74C23×C47C2411yescharacteristic
75C2×C4×C47—28no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47#4114yes—
86C2×Dic47—28no—
87C2×Dic47—22no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—28no—
91C2×Dic47—21no—
92C2×Dic47—21no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47C2×D412yes—
99C2×Dic47C2×D412yes—
100C2×Dic47C2×Q814yes—
101C2×Dic47#4114yes—
102Dic94—44no—
103C22×C47—22no—
104C22×C47—22no—
105C22×C47—24no—
106C22×C47—24no—
107C22×C47C22⋊Q814yes—
108C22×C47C22×D411yescharacteristic
109C22×C47C22×Q811yescharacteristic
110C22×C47C2×#4112yes—
111C22×C47C2×#4112yes—
112C22×C47C2×#4111yescharacteristic
113C4×C47—24no—
114C4×C47—41no—
115C4×C47—41no—
116C4×C47—42no—
117Dic47—24no—
118Dic47—22no—
119Dic47—41no—
120Dic47—41no—
121Dic47—42no—
122Dic47#12314yes—
123#2855—471nomaximal, Sylow
124C2×C47—24no—
125C2×C47C2×C22⋊Q811yescharacteristic
126C2×C47C2×#12311yescharacteristic
127C2×C47#52511yescharacteristic
128C2×C47#52912yes—
129C2×C47#53312yes—
130C2×C22⋊Q8—471no—
131C22×C42—471no—
132#391—472no—
133#389—472no—
134#387—472no—
135#387—472no—
136#385—471no—
137#385D4711yescharacteristic
138#381—471no—
139#381—471no—
140#380—471no—
141C47#285511yescharacteristic, complemented, Sylow
142C22×Q8—471no—
143C23×C4—471no—
144C23×C4—471no—
145C23×C4C2×D4711yescharacteristic
146C22⋊Q8—944no—
147C2×C4⋊C4—471no—
148C2×C4⋊C4—471no—
149C2×C4⋊C4—471no—
150C2×C4⋊C4—472no—
151C2×C4⋊C4—472no—
152C2×C4⋊C4C2×D4712yes—
153C2×C22⋊C4—471no—
154C2×C22⋊C4—471no—
155C2×C22⋊C4C2×D4711yescharacteristic
156C2×C22⋊C4C2×D4711yescharacteristic
157C2×C42—472no—
158C2×C42—472no—
159C2×C42—944no—
160#95—472no—
161#95—472no—
162#95—472no—
163#95—472no—
164#95—472no—
165#95—472no—
166#95C2×D4712yes—
167C24C22×D4711yescharacteristic
168C2×Q8—942no—
169C2×Q8—944no—
170C22×C4—22no—
171C22×C4—24no—
172C22×C4—471no—
173C22×C4—474no—
174C22×C4—474no—
175C22×C4—472no—
176C22×C4—471no—
177C22×C4—472no—
178C22×C4—471no—
179C22×C4—471no—
180C22×C4—944no—
181C22×C4—942no—
182C22×C4—942no—
183C22×C4C22×D4712yes—
184C22×C4C22×D4711yescharacteristic
185C22×C4C22×D4711yescharacteristic
186C22×C4C22×D4712yes—
187C4⋊C4—24no—
188C4⋊C4—944no—
189C4⋊C4—942no—
190C4⋊C4—942no—
191C4⋊C4—942no—
192C4⋊C4—944no—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—942no—
196C22⋊C4—942no—
197C42—944no—
198C42—944no—
199C23—22no—
200C23—22no—
201C23#1062535012yes—
202C23D4×D4712yes—
203C23Q8×D4712yes—
204C23C23×D4711yescharacteristic
205Q8—1884no—
206C2×C4—28no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—472no—
217C2×C4—474no—
218C2×C4—472no—
219C2×C4—474no—
220C2×C4—948no—
221C2×C4—948no—
222C2×C4—942no—
223C2×C4—942no—
224C2×C4—942no—
225C2×C4—941no—
226C2×C4—941no—
227C2×C4—942no—
228C2×C4—942no—
229C2×C4—942no—
230C2×C4—942no—
231C2×C4—942no—
232C2×C4#1062535214yes—
233C22—22no—
234C22—22no—
235C22—24no—
236C22—24no—
237C22#1309400214yes—
238C22C2×D4×D4711yescharacteristic
239C22C2×Q8×D4711yescharacteristic
240C22#41×D4712yes—
241C22C2×#1062535212yes—
242C22C2×#1062535011yescharacteristic
243C4—24no—
244C4—41no—
245C4—41no—
246C4—42no—
247C4—474no—
248C4—944no—
249C4—942no—
250C4—1881no—
251C4—1881no—
252C4—1882no—
253C2—24no—
254C2C2×#1309400211yescharacteristic
255C2#123×D4711yescharacteristic
256C2#1568962911yescharacteristic
257C2#1568965312yes—
258C2#1568967512yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#385C2
hypercenter#385D47
hypocenterC47#2855
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. #15689027C2semidirect
4. #15689018C2semidirect
5. #15689009C2semidirect
6. #15689005C2semidirect
48. C22×Dic47Q8semidirect
141. C47#2855semidirect