Finite Group Databasebeta

← #20247871

Subgroups — #20247871

Order 6016.

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

normal subgroups only

This group has 512 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×#13094001C211yesmaximal, characteristic
2C22×Dic47⋊C4C211yesmaximal, characteristic
3#15689065C212yesmaximal, complemented
4#15689064C212yesmaximal, complemented
5#15689027C212yesmaximal, complemented
6#15688987C212yesmaximal, complemented
7#15688986C211yesmaximal, characteristic
8#15688984C211yesmaximal, characteristic
9#15688984C211yesmaximal, characteristic
10C22⋊C4×Dic47C211yesmaximal, characteristic
11C47×#381C211yesmaximal, characteristic
12C22×Dic94C2211yescharacteristic
13C23×Dic47C2211yescharacteristic
14C23×Dic47C2211yescharacteristic
15#13094001—24no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4—24no—
18C2×Dic47⋊C4C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2212yes—
21C2×Dic47⋊C4C2211yescharacteristic
22C2×C22⋊Dic47C2211yescharacteristic
23C2×C22⋊Dic47C2211yescharacteristic
24C2×C4×Dic47C2212yes—
25C47⋊#95C2212yes—
26C47⋊#95C2212yes—
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C23×C4×C47C2211yescharacteristic
33C2×C22⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2211yescharacteristic
35#95×C47C2212yes—
36#95×C47C2212yes—
37C24×C47C2311yescharacteristic
38C22×C4×C47—22no—
39C22×C4×C47—22no—
40C22×C4×C47—22no—
41C22×C4×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2312yes—
45C22×Dic47—24no—
46C22×Dic47—22no—
47C22×Dic47—22no—
48C22×Dic47—22no—
49C22×Dic47D414yes—
50C22×Dic47C2312yes—
51C22×Dic47C2311yescharacteristic
52C22×Dic47C2311yescharacteristic
53C22×Dic47C2312yes—
54C22×Dic47C2311yescharacteristic
55C22×Dic47C2311yescharacteristic
56C2×Dic94—22no—
57C2×Dic94—24no—
58C22⋊C4×C47—22no—
59C22⋊C4×C47—22no—
60C22⋊Dic47—22no—
61C22⋊Dic47—22no—
62C4⋊Dic47—22no—
63Dic47⋊C4—24no—
64Dic47⋊C4—24no—
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67C4×Dic47—24no—
68C23×C47—22no—
69C23×C47—22no—
70C23×C47C2×D412yes—
71C23×C47#4112yes—
72C23×C47#4112yes—
73C23×C47C2411yescharacteristic
74C2×C4×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—44no—
85C2×Dic47—22no—
86C2×Dic47—28no—
87C2×Dic47—21no—
88C2×Dic47—22no—
89C2×Dic47—21no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—44no—
98C2×Dic47C2×D412yes—
99C2×Dic47C2×D412yes—
100C2×Dic47#4114yes—
101Dic94—44no—
102C22×C47—22no—
103C22×C47—22no—
104C22×C47—24no—
105C22×C47—24no—
106C22×C47#12414yes—
107C22×C47C22×D411yescharacteristic
108C22×C47C2×#4112yes—
109C22×C47C2×#4111yescharacteristic
110C22×C47C2×#4111yescharacteristic
111C22×C472−1+412yes—
112C4×C47—41no—
113C4×C47—42no—
114C4×C47—41no—
115C4×C47—42no—
116Dic47—22no—
117Dic47—41no—
118Dic47—42no—
119Dic47—41no—
120Dic47—42no—
121Dic47#12314yes—
122#2503—471nomaximal, Sylow
123C2×C47—24no—
124C2×C47C2×#12311yescharacteristic
125C2×C47C2×#12411yescharacteristic
126C2×C47#53611yescharacteristic
127C2×C47#55212yes—
128C2×C47#55212yes—
129C2×C22⋊Q8—471no—
130C22×C4⋊C4—471no—
131#400—472no—
132#400—472no—
133#391—472no—
134#382—472no—
135#381—471no—
136#381—471no—
137#381—471no—
138#381D4711yescharacteristic
139C4×C22⋊C4—471no—
140C47#250311yescharacteristic, complemented, Sylow
141C22×Q8—471no—
142C23×C4—471no—
143C23×C4—471no—
144C23×C4C2×D4711yescharacteristic
145C22⋊Q8—944no—
146C2×C4⋊C4—472no—
147C2×C4⋊C4—472no—
148C2×C4⋊C4—471no—
149C2×C4⋊C4—471no—
150C2×C4⋊C4—471no—
151C2×C4⋊C4—944no—
152C2×C22⋊C4—471no—
153C2×C22⋊C4—471no—
154C2×C22⋊C4C2×D4711yescharacteristic
155C2×C22⋊C4C2×D4711yescharacteristic
156C2×C42—472no—
157#95—472no—
158#95—472no—
159#95—472no—
160#95—472no—
161#95—472no—
162#95—472no—
163#95—472no—
164#95C2×D4712yes—
165#95C2×D4712yes—
166C24C22×D4711yescharacteristic
167C2×Q8—942no—
168C2×Q8—944no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—471no—
173C22×C4—474no—
174C22×C4—471no—
175C22×C4—472no—
176C22×C4—471no—
177C22×C4—471no—
178C22×C4—472no—
179C22×C4—944no—
180C22×C4—942no—
181C22×C4—942no—
182C22×C4—942no—
183C22×C4C22×D4712yes—
184C22×C4C22×D4711yescharacteristic
185C22×C4C22×D4711yescharacteristic
186C22×C4C22×D4712yes—
187C4⋊C4—944no—
188C4⋊C4—944no—
189C4⋊C4—942no—
190C4⋊C4—942no—
191C4⋊C4—942no—
192C22⋊C4—22no—
193C22⋊C4—22no—
194C22⋊C4—942no—
195C22⋊C4—942no—
196C42—944no—
197C23—22no—
198C23—22no—
199C23#1062535012yes—
200C23D4×D4712yes—
201C23#1062535212yes—
202C23C23×D4711yescharacteristic
203Q8—1884no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—44no—
215C2×C4—472no—
216C2×C4—474no—
217C2×C4—472no—
218C2×C4—948no—
219C2×C4—942no—
220C2×C4—941no—
221C2×C4—941no—
222C2×C4—942no—
223C2×C4—942no—
224C2×C4—942no—
225C2×C4—942no—
226C2×C4—942no—
227C2×C4—942no—
228C2×C4—942no—
229C2×C4—942no—
230C2×C4—1884no—
231C22—24no—
232C22—24no—
233C22—22no—
234C22—22no—
235C22#1309401014yes—
236C22C2×D4×D4711yescharacteristic
237C22#41×D4712yes—
238C22C2×#1062535211yescharacteristic
239C22C2×#1062535011yescharacteristic
240C22#1309407112yes—
241C4—42no—
242C4—41no—
243C4—42no—
244C4—41no—
245C4—474no—
246C4—942no—
247C4—1882no—
248C4—1881no—
249C4—1882no—
250C4—1881no—
251C2—24no—
252C2#123×D4711yescharacteristic
253C2C2×#1309401011yescharacteristic
254C2#1568969511yescharacteristic
255C2#1568980612yes—
256C2#1568981012yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#381C2
hypercenter#381D47
hypocenterC47#2503
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
3. #15689065C2semidirect
4. #15689064C2semidirect
5. #15689027C2semidirect
6. #15688987C2semidirect
140. C47#2503semidirect