Finite Group Databasebeta

← #20252884

Subgroups — #20252884

Order 6016.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13094049C211yesmaximal, characteristic
2C2×#13094013C211yesmaximal, characteristic, complemented
3#41×Dic47C211yesmaximal, characteristic, complemented
4#15689347C214yesmaximal, complemented
5#15689340C214yesmaximal, complemented
6#15689146C211yesmaximal, characteristic, complemented
7#15689132C211yesmaximal, characteristic, complemented
8#15689129C211yesmaximal, characteristic, complemented
9C2×#137×C47C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11#13094049—24no—
12C2×#10625336C2212yes—
13C2×#10625334C2212yes—
14C2×#10625329C2211yescharacteristic
15#13094013—21no—
16#13094013—21no—
17#13094013C2214yes—
18Q8×Dic47C2212yescomplemented
19D4×Dic47—22no—
20D4×Dic47C2212yescomplemented
21#13093983—21no—
22#13093983C2211yescharacteristic
23C2×(C2×D47)⋊C4—22no—
24C2×C4×Dic47—21no—
25C2×C4×Dic47C2211yescharacteristic
26Dic47⋊C8C2214yescomplemented
27#13093948C2214yescomplemented
28#13093946C2214yes—
29C2×#41×C47C2211yescharacteristic
30C22×Q8×C47C2211yescharacteristic
31#137×C47—24no—
32C2×Q16×C47C2212yescomplemented
33C2×SD16×C47C2212yescomplemented
34C2×M16×C47C2211yescharacteristic
35C23×D47—21no—
36#41×C47—22no—
37#41×C47D414yes—
38C2×Q8×C47—21no—
39C2×Q8×C47—22no—
40C2×Q8×C47—22no—
41C2×Q8×C47C2312yes—
42C2×Q8×C47C2311yescharacteristic
43C2×D4×C47—21no—
44C2×D4×C47C2311yescharacteristic
45C22×C4×C47—21no—
46C22×C4×C47—21no—
47C22×C4×C47C2311yescharacteristic
48C22×Dic47—22no—
49C22×Dic47D412yes—
50C2×D188—22no—
51C2×D188—22no—
52C2×D188—21no—
53C2×D188C2312yes—
54Q16×C47—24no—
55SD16×C47—24no—
56M16×C47—22no—
57C2×C8×C47C2312yes—
58C22⋊Dic47—21no—
59C22⋊Dic47—22no—
60#10625336—24no—
61#10625334—24no—
62(C2×D47)⋊C4—24no—
63(C2×D47)⋊C4—24no—
64C4⋊Dic47—22no—
65C4⋊Dic47C2312yes—
66C4×Dic47—21no—
67C4×Dic47—22no—
68C4×Dic47D411yescharacteristic
69C4×Dic47D411yescharacteristic
70C4×Dic47C2312yes—
71#10625329—22no—
72C2×C47⋊C8C2312yes—
73C23×C47—21no—
74C23×C47C2×D411yescharacteristic
75C22×D47—22no—
76C22×D47—44no—
77C22×D47—42no—
78Q8×C47—21no—
79Q8×C47—22no—
80Q8×C47—22no—
81Q8×C47—42no—
82Q8×C47C2×D412yes—
83D4×C47—24no—
84D4×C47—21no—
85D4×C47C2×D412yes—
86C2×C4×C47—21no—
87C2×C4×C47—24no—
88C2×C4×C47—22no—
89C2×C4×C47—42no—
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2×D412yes—
92C2×C4×C47#4112yes—
93C2×C4×C47C2411yescharacteristic
94C2×Dic47—22no—
95C2×Dic47—42no—
96C2×Dic47—44no—
97C2×Dic47C2×D412yes—
98C2×Dic47C2×D412yes—
99D188—22no—
100D188—22no—
101D188—42no—
102C8×C47—22no—
103C47⋊C8—22no—
104C22×C47—22no—
105C22×C47—22no—
106C22×C47—42no—
107C22×C47#12112yes—
108C22×C47C22×D411yescharacteristic
109C2×D47—42no—
110C2×D47—44no—
111C2×D47—84no—
112C4×C47—22no—
113C4×C47—42no—
114C4×C47#12112yes—
115C4×C47C22×D411yescharacteristic
116C4×C47C2×#4111yescharacteristic
117Dic47—22no—
118Dic47—22no—
119Dic47—42no—
120#3040—471nomaximal, Sylow
121C2×C47—22no—
122C2×C47—42no—
123C2×C47C2×#12111yescharacteristic
124C2×C47#57512yes—
125D47—82no—
126C2×#137D4711yescharacteristic, complemented
127C2×AGL(1,ℤ/8)—471no—
128C2×#124—471no—
129C4×#41—471no—
130#464—474no—
131#463—474no—
132#423—471no—
133#419—471no—
134#418—471no—
135C47#304011yescharacteristic, complemented, Sylow
136C2×#41C2×D4711yescharacteristic
137C22×Q8C2×D4711yescharacteristic
138C22×D4—471no—
139#137—24no—
140AGL(1,ℤ/8)—944no—
141C2×Q16C2×D4712yescomplemented
142C2×SD16—472no—
143C2×SD16C2×D4712yescomplemented
144C2×D8—472no—
145C2×M16—471no—
146C2×M16C2×D4711yescharacteristic
147#124—474no—
148#124—941no—
149#124—941no—
150C4×Q8—472no—
151C4×D4—472no—
152C4×D4—942no—
153#117—471no—
154#117—941no—
155C2×C22⋊C4—942no—
156C2×C42—471no—
157C2×C42—941no—
158C4⋊C8—474no—
159#103—474no—
160#102—474no—
161C24—941no—
162#41—22no—
163#41C22⋊D4714yes—
164C2×Q8—21no—
165C2×Q8—22no—
166C2×Q8—22no—
167C2×Q8C22×D4712yes—
168C2×Q8C22×D4711yescharacteristic
169C2×D4—21no—
170C2×D4—472no—
171C2×D4—941no—
172C2×D4—942no—
173C2×D4—942no—
174C2×D4C22×D4711yescharacteristic
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—472no—
178C22×C4—942no—
179C22×C4C22×D4711yescharacteristic
180Q16—24no—
181SD16—24no—
182SD16—944no—
183D8—944no—
184M16—22no—
185M16—942no—
186C2×C8—472no—
187C2×C8C22×D4712yes—
188C4⋊C4—472no—
189C4⋊C4—942no—
190C22⋊C4—944no—
191C22⋊C4—944no—
192C22⋊C4—942no—
193C22⋊C4—941no—
194C42—471no—
195C42—471no—
196C42—472no—
197C42—942no—
198C42—941no—
199C23—21no—
200C23—942no—
201C23—1884no—
202C23—1882no—
203C23D4×D4711yescharacteristic
204Q8—21no—
205Q8—22no—
206Q8—22no—
207Q8—42no—
208Q8C2×C22⋊D4712yes—
209D4—24no—
210D4—21no—
211D4—942no—
212D4—942no—
213D4—1882no—
214D4C2×C22⋊D4712yes—
215C2×C4—21no—
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—472no—
220C2×C4—472no—
221C2×C4—942no—
222C2×C4—1882no—
223C2×C4—1884no—
224C2×C4D4×D4711yescharacteristic
225C2×C4#1062535212yes—
226C2×C4C2×C22⋊D4712yes—
227C2×C4C23×D4711yescharacteristic
228C8—22no—
229C8—942no—
230C22—22no—
231C22—22no—
232C22—42no—
233C22—3764no—
234C22—1882no—
235C22—1884no—
236C22#1309399612yes—
237C22C2×D4×D4711yescharacteristic
238C4—22no—
239C4—42no—
240C4—942no—
241C4—942no—
242C4—1882no—
243C4#1309399612yes—
244C4C22×C22⋊D4711yescharacteristic
245C4C2×#1062535211yescharacteristic
246C2—22no—
247C2—42no—
248C2—3762no—
249C2C2×#1309399611yescharacteristic
250C2#1568992212yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#137×C47C2
socleC22×C47C22×D4
hypercenterC2×#137D47
hypocenterC47#3040
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C2×#13094013C2semidirect
3. #41×Dic47C2semidirect
4. #15689347C2semidirect
5. #15689340C2semidirect
6. #15689146C2semidirect
7. #15689132C2semidirect
8. #15689129C2semidirect
9. C2×#137×C47C2semidirect
18. Q8×Dic47C22semidirect
20. D4×Dic47C22semidirect
26. Dic47⋊C8C22semidirect
27. #13093948C22semidirect
32. C2×Q16×C47C22semidirect
33. C2×SD16×C47C22semidirect
126. C2×#137D47semidirect
135. C47#3040semidirect
141. C2×Q16C2×D47semidirect
143. C2×SD16C2×D47semidirect