Finite Group Databasebeta

← #20254597

Subgroups — #20254597

Order 6016.

322 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 111 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
1#15689679C211yesmaximal, characteristic
2#15689678C211yesmaximal, characteristic
3#15689533C211yesmaximal, characteristic, complemented
4#15689532C211yesmaximal, characteristic, complemented
5#15689491C211yesmaximal, characteristic, complemented
6#15689463C212yesmaximal
7#15689462C212yesmaximal
8#15689416C212yesmaximal, complemented
9#15689406C212yesmaximal, complemented
10#15689178C211yesmaximal, characteristic
11C47×#491C211yesmaximal, characteristic, complemented
12#13094024C2211yescharacteristic
13#13094023C2211yescharacteristic
14#13094023C2211yescharacteristic
15#13094016C2211yescharacteristic
16#13094015—21no—
17#13094004—21no—
18#13094002—21no—
19#13094002—21no—
20#13094000C2212yes—
21Q8×Dic47C2212yes—
22#13093989—21no—
23#13093989—21no—
24#13093989—21no—
25#13093982—21no—
26#13093982C2211yescharacteristic
27#13093982C2211yescharacteristic
28C42×D47C2211yescharacteristic
29#13093958C2212yes—
30#13093957C2212yes—
31#13093956C2212yes—
32#13093955C2212yes—
33Dic47⋊C8C2212yes—
34#13093948C2212yes—
35#13093948C2212yes—
36(C2×D47)⋊C8C2212yes—
37#13093935C2211yescharacteristic
38C4⋊Q8×C47C2211yescharacteristic
39#125×C47C2211yescharacteristic
40#103×C47C2212yes—
41#103×C47C2212yes—
42#97×C47C2211yescharacteristic
43C2×Q8×C47C2312yes—
44C2×C4×D47D411yescharacteristic
45C2×C4×D47D411yescharacteristic
46C2×C4×D47C2311yescharacteristic
47C2×Dic94—21no—
48C2×Dic94—21no—
49C2×Dic94—21no—
50C2×C8×C47C2312yes—
51C4⋊C4×C47—21no—
52C4⋊C4×C47—21no—
53C4⋊C4×C47—21no—
54C4⋊C4×C47—21no—
55C4⋊C4×C47C2311yescharacteristic
56C4⋊C4×C47C2311yescharacteristic
57C42×C47C2311yescharacteristic
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—21no—
60(C2×D47)⋊C4—21no—
61C4⋊Dic47—21no—
62C4⋊Dic47—22no—
63C4⋊Dic47C2311yescharacteristic
64C4⋊Dic47C2311yescharacteristic
65C4⋊Dic47C2312yes—
66Dic47⋊C4—21no—
67Dic47⋊C4—21no—
68Dic47⋊C4—22no—
69Dic47⋊C4—21no—
70Dic47⋊C4—21no—
71C4×Dic47—22no—
72C4×Dic47—21no—
73C4×Dic47—21no—
74C4×Dic47D411yescharacteristic
75C4×Dic47D411yescharacteristic
76C4×Dic47C2311yescharacteristic
77C2×C47⋊C8C2312yes—
78C22×D47C2×D411yescharacteristic
79Q8×C47—24no—
80C2×C4×C47—22no—
81C2×C4×C47—21no—
82C2×C4×C47—21no—
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2411yescharacteristic
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—22no—
89C2×Dic47C2×D411yescharacteristic
90C2×Dic47C2×D411yescharacteristic
91C2×Dic47C2×D411yescharacteristic
92C4×D47—22no—
93C4×D47—22no—
94C4×D47—41no—
95Dic94—42no—
96Dic94—42no—
97Dic94—42no—
98C8×C47—22no—
99C47⋊C8—22no—
100C22×C47C22×D411yescharacteristic
101C2×D47—21no—
102C2×D47—21no—
103C2×D47—21no—
104C4×C47—21no—
105C4×C47—21no—
106C4×C47—42no—
107C4×C47—41no—
108C4×C47—41no—
109C4×C472−1+412yes—
110Dic47—21no—
111Dic47—21no—
112Dic47—41no—
113Dic47—41no—
114Dic47—42no—
115Dic47#13712yes—
116#3237—471nomaximal, Sylow
117C2×C47#53611yescharacteristic
118C2×C47C2×#13711yescharacteristic
119C2×C47#57511yescharacteristic
120D47—41no—
121#533—471no—
122#533—471no—
123#501—471no—
124#501—471no—
125#491—471no—
126#491D4711yescharacteristic, complemented
127#485—472no—
128#485—472no—
129#477—472no—
130#475—472no—
131#432—471no—
132C47#323711yescharacteristic, complemented, Sylow
133C4⋊Q8—471no—
134C4⋊Q8—471no—
135C4⋊Q8—471no—
136C4⋊Q8C2×D4711yescharacteristic
137#125—471no—
138#125—941no—
139#125C2×D4711yescharacteristic
140C22⋊Q8—472no—
141C22⋊Q8—941no—
142C22⋊Q8—941no—
143C22⋊Q8—941no—
144C4×Q8—472no—
145C4×Q8—941no—
146C4×Q8—941no—
147C4×Q8—941no—
148#117—471no—
149#117—471no—
150#117—941no—
151C2×C42—471no—
152#107—472no—
153#107—472no—
154#106—472no—
155#106—472no—
156C4⋊C8—472no—
157#103—472no—
158#103—472no—
159#103C2×D4712yes—
160#103C2×D4712yes—
161C22⋊C8—472no—
162#97—471no—
163#97C2×D4711yescharacteristic
164C2×Q8—941no—
165C2×Q8—941no—
166C2×Q8—941no—
167C2×Q8C22×D4712yes—
168C22×C4—471no—
169C22×C4—471no—
170C22×C4—471no—
171C2×C8—472no—
172C2×C8C22×D4712yes—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—471no—
178C4⋊C4—471no—
179C4⋊C4—472no—
180C4⋊C4—942no—
181C4⋊C4—941no—
182C4⋊C4—941no—
183C4⋊C4—942no—
184C4⋊C4—941no—
185C4⋊C4—941no—
186C4⋊C4—941no—
187C4⋊C4C22×D4711yescharacteristic
188C4⋊C4C22×D4711yescharacteristic
189C22⋊C4—941no—
190C22⋊C4—941no—
191C22⋊C4—942no—
192C42—471no—
193C42—471no—
194C42—471no—
195C42—941no—
196C42—941no—
197C42—942no—
198C42C22×D4711yescharacteristic
199C23—471no—
200Q8—24no—
201Q8—1882no—
202Q8—1882no—
203Q8—1882no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—471no—
208C2×C4—471no—
209C2×C4—471no—
210C2×C4—942no—
211C2×C4—942no—
212C2×C4—941no—
213C2×C4—941no—
214C2×C4—942no—
215C2×C4—1881no—
216C2×C4D4×D4711yescharacteristic
217C2×C4D4×D4711yescharacteristic
218C2×C4C23×D4711yescharacteristic
219C8—22no—
220C8—942no—
221C22—941no—
222C22—941no—
223C22—941no—
224C22C2×D4×D4711yescharacteristic
225C4—21no—
226C4—21no—
227C4—41no—
228C4—41no—
229C4—42no—
230C4—472no—
231C4—941no—
232C4—941no—
233C4—1881no—
234C4—1882no—
235C4—1881no—
236C4#1309407112yes—
237C2—1881no—
238C2#1568969311yescharacteristic
239C2#137×D4711yescharacteristic
240C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#491C2
socleC22×C47C22×D4
hypercenter#491D47
hypocenterC47#3237
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
3. #15689533C2semidirect
4. #15689532C2semidirect
5. #15689491C2semidirect
8. #15689416C2semidirect
9. #15689406C2semidirect
11. C47×#491C2semidirect
126. #491D47semidirect
132. C47#3237semidirect