Finite Group Databasebeta

← #20253308

Subgroups — #20253308

Order 6016.

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

normal subgroups only

This group has 458 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
1C22×C4⋊Dic47C211yesmaximal, characteristic, complemented
2#15689456C212yesmaximal, complemented
3#15689451C212yesmaximal, complemented
4#15689439C212yesmaximal, complemented
5#15689434C212yesmaximal, complemented
6#15689166C212yesmaximal, complemented
7#15689124C212yesmaximal, complemented
8#15689087C211yesmaximal, characteristic, complemented
9C47×#525C211yesmaximal, characteristic
10C23×Dic47—21no—
11C2×#10625329C2212yes—
12C2×C4⋊Dic47—21no—
13C2×C4⋊Dic47—21no—
14C2×C4⋊Dic47—21no—
15C2×C4⋊Dic47C2212yes—
16C2×C4⋊Dic47C2212yes—
17C2×C4⋊Dic47C2212yes—
18#13093957C2214yescomplemented
19#13093955C2214yescomplemented
20#13093948C2214yescomplemented
21#13093945C2214yescomplemented
22C22⋊(C47⋊C8)C2212yes—
23C22⋊(C47⋊C8)C2212yes—
24C2×#41×C47C2211yescharacteristic
25C23×C4×C47C2211yescharacteristic
26#123×C47—21no—
27C22⋊Q8×C47C2211yescharacteristic
28C22⋊Q8×C47C2211yescharacteristic
29#121×C47C2211yescharacteristic
30#121×C47C2211yescharacteristic
31#120×C47—21no—
32C4×D4×C47—21no—
33C4×D4×C47—21no—
34#117×C47C2211yescharacteristic
35C24×C47D411yescharacteristic
36#41×C47—24no—
37C2×Q8×C47C2311yescharacteristic
38C2×D4×C47—21no—
39C2×D4×C47—21no—
40C2×D4×C47—21no—
41C2×D4×C47C2311yescharacteristic
42C22×C4×C47—24no—
43C22×C4×C47—21no—
44C22×C4×C47D411yescharacteristic
45C22×C4×C47D411yescharacteristic
46C22×C4×C47D411yescharacteristic
47C22×C4×C47C2311yescharacteristic
48C22×C4×C47C2311yescharacteristic
49C22×C4×C47C2311yescharacteristic
50C22×Dic47—22no—
51C22×Dic47—22no—
52C22×Dic47—22no—
53C22×Dic47—44no—
54C4⋊C4×C47—21no—
55C4⋊C4×C47—21no—
56C4⋊C4×C47C2311yescharacteristic
57C4⋊C4×C47C2311yescharacteristic
58C22⋊C4×C47—21no—
59C22⋊C4×C47—21no—
60C22⋊C4×C47—21no—
61C22⋊C4×C47—21no—
62C22⋊C4×C47—21no—
63C42×C47—21no—
64C4⋊Dic47—22no—
65C4⋊Dic47—22no—
66C4⋊Dic47—22no—
67C4⋊Dic47C2314yes—
68#10625329—24no—
69C2×C47⋊C8C2314yes—
70C23×C47—22no—
71C23×C47—22no—
72C23×C47—22no—
73C23×C47—21no—
74C23×C47C2×D411yescharacteristic
75C23×C47C2×D411yescharacteristic
76C23×C47C2×D411yescharacteristic
77Q8×C47—22no—
78D4×C47—22no—
79D4×C47—42no—
80D4×C47—42no—
81D4×C47—42no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—22no—
86C2×C4×C47—22no—
87C2×C4×C47—21no—
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47—42no—
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47#4114yes—
95C2×C4×C47C2411yescharacteristic
96C2×Dic47—24no—
97C2×Dic47—44no—
98C2×Dic47—44no—
99C2×Dic47—44no—
100C47⋊C8—24no—
101C22×C47—28no—
102C22×C47—21no—
103C22×C47—21no—
104C22×C47—21no—
105C22×C47—21no—
106C22×C47—21no—
107C22×C47—21no—
108C22×C47—41no—
109C22×C47—41no—
110C22×C47—41no—
111C22×C47#12312yes—
112C22×C47AGL(1,ℤ/8)12yes—
113C22×C47#13712yes—
114C22×C47C22×D411yescharacteristic
115C4×C47—21no—
116C4×C47—21no—
117C4×C47—41no—
118C4×C47—41no—
119C4×C47—41no—
120C4×C47#12312yes—
121C4×C47C2×#4112yes—
122Dic47—44no—
123#3092—471nomaximal, Sylow
124C2×C47—22no—
125C2×C47—22no—
126C2×C47—22no—
127C2×C47—81no—
128C2×C47C2×#12311yescharacteristic
129C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
130C2×C47C2×#13711yescharacteristic
131#525D4711yescharacteristic
132C22×C4⋊C4—471no—
133#484—472no—
134#483—472no—
135#481—472no—
136#480—472no—
137#428—472no—
138#417—472no—
139#407—471no—
140C47#309211yescharacteristic, complemented, Sylow
141C2×#41C2×D4711yescharacteristic
142C23×C4—941no—
143C23×C4C2×D4711yescharacteristic
144C2×M16—472no—
145#123—21no—
146C22⋊Q8C2×D4711yescharacteristic
147C22⋊Q8C2×D4711yescharacteristic
148#121C2×D4711yescharacteristic
149#121C2×D4711yescharacteristic
150#120—21no—
151C4×D4—21no—
152C4×D4—21no—
153#117C2×D4711yescharacteristic
154C2×C4⋊C4—472no—
155C2×C4⋊C4—472no—
156C2×C4⋊C4—472no—
157C2×C4⋊C4—941no—
158C2×C4⋊C4—941no—
159C2×C4⋊C4—941no—
160#107—474no—
161#106—474no—
162#103—474no—
163#102—474no—
164C22⋊C8—472no—
165C22⋊C8—472no—
166C24C22⋊D4711yescharacteristic
167#41—24no—
168C2×Q8C22×D4711yescharacteristic
169C2×D4—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4C22×D4711yescharacteristic
173C22×C4—24no—
174C22×C4—21no—
175C22×C4—942no—
176C22×C4—942no—
177C22×C4—942no—
178C22×C4—1884no—
179C22×C4C22⋊D4711yescharacteristic
180C22×C4C22⋊D4711yescharacteristic
181C22×C4C22⋊D4711yescharacteristic
182C22×C4C22×D4711yescharacteristic
183C22×C4C22×D4711yescharacteristic
184C22×C4C22×D4711yescharacteristic
185M16—944no—
186C2×C8—474no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—474no—
190C4⋊C4—942no—
191C4⋊C4—942no—
192C4⋊C4—942no—
193C4⋊C4C22×D4711yescharacteristic
194C4⋊C4C22×D4711yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—21no—
197C22⋊C4—21no—
198C22⋊C4—21no—
199C22⋊C4—21no—
200C42—21no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—21no—
205C23C2×C22⋊D4711yescharacteristic
206C23C2×C22⋊D4711yescharacteristic
207C23C2×C22⋊D4711yescharacteristic
208Q8—22no—
209D4—22no—
210D4—42no—
211D4—42no—
212D4—42no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—42no—
222C2×C4—944no—
223C2×C4—1884no—
224C2×C4—1884no—
225C2×C4—1884no—
226C2×C4#1062535214yes—
227C2×C4C2×C22⋊D4711yescharacteristic
228C2×C4C2×C22⋊D4711yescharacteristic
229C2×C4C2×C22⋊D4711yescharacteristic
230C2×C4C23×D4711yescharacteristic
231C8—944no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22#1309400512yes—
243C22#1309404912yes—
244C22#1309405412yes—
245C22C22×C22⋊D4711yescharacteristic
246C4—21no—
247C4—21no—
248C4—41no—
249C4—41no—
250C4—41no—
251C4—1884no—
252C4#1309400512yes—
253C4C2×#1062535212yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—81no—
258C2C2×#1309400511yescharacteristic
259C2C2×#1309404911yescharacteristic
260C2C2×#1309405411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#525C2
socleC22×C47C22×D4
hypercenter#525D47
hypocenterC47#3092
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊Dic47C2semidirect
2. #15689456C2semidirect
3. #15689451C2semidirect
4. #15689439C2semidirect
5. #15689434C2semidirect
6. #15689166C2semidirect
7. #15689124C2semidirect
8. #15689087C2semidirect
18. #13093957C22semidirect
19. #13093955C22semidirect
20. #13093948C22semidirect
21. #13093945C22semidirect
140. C47#3092semidirect