Finite Group Databasebeta

← #20247676

Subgroups — #20247676

Order 6016.

512 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 139 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×#13093982C211yesmaximal, characteristic
2C2×C4⋊C4×D47C211yesmaximal, characteristic
3#15689061C211yesmaximal, characteristic, complemented
4#15689055C211yesmaximal, characteristic, complemented
5#15689053C211yesmaximal, characteristic, complemented
6#15689010C212yesmaximal, complemented
7#15689006C212yesmaximal, complemented
8#15688997C212yesmaximal
9#15688985C211yesmaximal, characteristic
10#15688985C212yesmaximal
11C47×#400C211yesmaximal, characteristic, complemented
12C22×C4×D47C2211yescharacteristic
13C22×C4×D47C2211yescharacteristic
14C22×C4×D47C2211yescharacteristic
15#13093982—24no—
16C2×C4⋊Dic47C2212yes—
17C2×C4⋊Dic47C2211yescharacteristic
18C2×C4⋊Dic47C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C4⋊C4×D47—24no—
23C2×(C2×D47)⋊C4C2212yes—
24C2×(C2×D47)⋊C4C2212yes—
25C2×C4×Dic47C2212yes—
26C47⋊#95C2212yes—
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2211yescharacteristic
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34#95×C47C2212yes—
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C23×D47C2311yescharacteristic
38C22×C4×C47C2312yes—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2312yes—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C22×Dic47C2312yes—
44C22×Dic47C2311yescharacteristic
45C22×Dic47C2312yes—
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2311yescharacteristic
48C2×C4×D47—22no—
49C2×C4×D47—24no—
50C2×C4×D47—22no—
51C2×C4×D47—22no—
52C2×C4×D47—22no—
53C2×C4×D47—24no—
54C2×C4×D47D414yes—
55C4⋊C4×C47—22no—
56C4⋊C4×C47—22no—
57(C2×D47)⋊C4—24no—
58(C2×D47)⋊C4—24no—
59C4⋊Dic47—22no—
60C4⋊Dic47—22no—
61C4⋊Dic47—24no—
62Dic47⋊C4—22no—
63Dic47⋊C4—24no—
64Dic47⋊C4—22no—
65C4×Dic47—24no—
66C23×C47C2411yescharacteristic
67C22×D47—21no—
68C22×D47—21no—
69C22×D47—22no—
70C22×D47C2×D412yes—
71C22×D47#4114yes—
72C2×C4×C47—21no—
73C2×C4×C47—22no—
74C2×C4×C47—21no—
75C2×C4×C47—22no—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—24no—
81C2×C4×C47—22no—
82C2×C4×C47C2×D412yes—
83C2×C4×C47#4112yes—
84C2×Dic47—21no—
85C2×Dic47—22no—
86C2×Dic47—21no—
87C2×Dic47—22no—
88C2×Dic47—21no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47C2×D412yes—
96C2×Dic47#4112yes—
97C4×D47—28no—
98C4×D47—28no—
99C4×D47—44no—
100C22×C47C22×D411yescharacteristic
101C22×C47C2×#4112yes—
102C22×C47C2×#4111yescharacteristic
103C22×C47C2×#4111yescharacteristic
104C22×C472−1+412yes—
105C2×D47—22no—
106C2×D47—22no—
107C2×D47—24no—
108C2×D47—24no—
109C2×D47#12314yes—
110C4×C47—22no—
111C4×C47—22no—
112C4×C47—41no—
113C4×C47—42no—
114C4×C47—42no—
115Dic47—22no—
116Dic47—22no—
117Dic47—41no—
118Dic47—42no—
119Dic47—42no—
120#2484—471nomaximal, Sylow
121C2×C47C2×#12311yescharacteristic
122C2×C47#52511yescharacteristic
123C2×C47#53611yescharacteristic
124C2×C47#55212yes—
125C2×C47#55212yes—
126D47—24no—
127C2×#117—471no—
128C22×C4⋊C4—471no—
129#400—471no—
130#400D4711yescharacteristic, complemented
131#398—471no—
132#398—471no—
133#387—472no—
134#387—472no—
135#385—472no—
136#381—471no—
137#381—472no—
138C47#248411yescharacteristic, complemented, Sylow
139C23×C4—471no—
140C23×C4—471no—
141C23×C4—471no—
142#117—944no—
143C2×C4⋊C4—471no—
144C2×C4⋊C4—471no—
145C2×C4⋊C4—471no—
146C2×C4⋊C4—471no—
147C2×C4⋊C4—472no—
148C2×C4⋊C4—472no—
149C2×C4⋊C4—944no—
150C2×C4⋊C4C2×D4711yescharacteristic
151C2×C4⋊C4C2×D4711yescharacteristic
152C2×C22⋊C4—472no—
153C2×C22⋊C4—472no—
154C2×C42—472no—
155#95—472no—
156#95—472no—
157#95—472no—
158#95—472no—
159#95—471no—
160#95—472no—
161#95C2×D4712yes—
162#95C2×D4711yescharacteristic
163#95C2×D4712yes—
164C24—471no—
165C22×C4—471no—
166C22×C4—471no—
167C22×C4—474no—
168C22×C4—472no—
169C22×C4—471no—
170C22×C4—472no—
171C22×C4—942no—
172C22×C4—942no—
173C22×C4—944no—
174C22×C4—942no—
175C22×C4—944no—
176C22×C4—942no—
177C22×C4C22×D4712yes—
178C22×C4C22×D4712yes—
179C22×C4C22×D4711yescharacteristic
180C22×C4C22×D4711yescharacteristic
181C22×C4C22×D4711yescharacteristic
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—942no—
185C4⋊C4—944no—
186C4⋊C4—942no—
187C4⋊C4—942no—
188C4⋊C4—942no—
189C4⋊C4—944no—
190C22⋊C4—944no—
191C22⋊C4—944no—
192C42—944no—
193C23—472no—
194C23—474no—
195C23—941no—
196C23—941no—
197C23—942no—
198C23C23×D4711yescharacteristic
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—24no—
209C2×C4—472no—
210C2×C4—472no—
211C2×C4—948no—
212C2×C4—948no—
213C2×C4—941no—
214C2×C4—942no—
215C2×C4—941no—
216C2×C4—942no—
217C2×C4—941no—
218C2×C4—942no—
219C2×C4—942no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4—942no—
223C2×C4—942no—
224C2×C4—1884no—
225C2×C4D4×D4712yes—
226C2×C4#1062535412yes—
227C22—474no—
228C22—944no—
229C22—944no—
230C22—942no—
231C22—942no—
232C22C2×D4×D4711yescharacteristic
233C22#41×D4711yescharacteristic
234C22#41×D4712yes—
235C22C2×#1062535411yescharacteristic
236C22#1309407112yes—
237C4—22no—
238C4—22no—
239C4—42no—
240C4—41no—
241C4—42no—
242C4—942no—
243C4—942no—
244C4—1882no—
245C4—1881no—
246C4—1882no—
247C2—944no—
248C2#123×D4711yescharacteristic
249C2#1568963611yescharacteristic
250C2#1568969311yescharacteristic
251C2#1568980912yes—
252C2#1568981112yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#400C2
hypercenter#400D47
hypocenterC47#2484
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #15689061C2semidirect
4. #15689055C2semidirect
5. #15689053C2semidirect
6. #15689010C2semidirect
7. #15689006C2semidirect
11. C47×#400C2semidirect
130. #400D47semidirect
138. C47#2484semidirect