Finite Group Databasebeta

← #26106405

Subgroups — #26106405

Order 12032.

604 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 151 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#20252017C211yesmaximal, characteristic
2#20245782C212yesmaximal
3#20241274C212yesmaximal
4#20241273C211yesmaximal, characteristic
5C47×#1297C211yesmaximal, characteristic
6C22×C4×Dic47C2211yescharacteristic
7#15689177—22no—
8#15689173—22no—
9#15689146C412yescomplemented
10#15689087C2211yescharacteristic
11M16×Dic47C412yescomplemented
12#15688990C414yescomplemented
13#15688987C414yescomplemented
14#15688984—22no—
15#15688981—22no—
16C4×Dic47⋊C4—22no—
17C4×C22⋊Dic47C2212yes—
18#15688969—22no—
19C47×#407C2211yescharacteristic
20C4×C22⋊C4×C47C2212yes—
21C23×Dic47D412yes—
22C2×#10625329C2×C412yes—
23C2×Dic47⋊C4—24no—
24C2×C22⋊Dic47—22no—
25C2×C4×Dic47—22no—
26C2×C4×Dic47C2×C411yescharacteristic
27C2×C4×Dic47C2×C411yescharacteristic
28C2×C4×Dic47C2×C412yes—
29C2×C4×Dic47C2×C412yes—
30C2×C4×Dic47D412yes—
31C2×C4×Dic47D412yes—
32C2×C4×Dic47Q812yes—
33Dic47⋊C8—24no—
34C22⋊(C47⋊C8)—22no—
35#13093934—22no—
36C8×Dic47—22no—
37C47⋊#95—24no—
38C47⋊#95—24no—
39C47⋊#95—24no—
40C47⋊#95C2×C414yes—
41C23×C4×C47C2311yescharacteristic
42C2×M16×C47C2×C412yes—
43C2×C22⋊C4×C47—22no—
44C2×C42×C47—22no—
45C22⋊C8×C47—22no—
46#95×C47C2×C414yes—
47C24×C47C2×D411yescharacteristic
48C22×C4×C47—24no—
49C22×C4×C47—42no—
50C22×C4×C47C22×C411yescharacteristic
51C22×C4×C47C22×C412yes—
52C22×C4×C47C2×D412yes—
53C22×C4×C47C2×Q811yescharacteristic
54C22×Dic47—24no—
55C22×Dic47—44no—
56C22×Dic47C22⋊C412yes—
57C22×Dic47C22⋊C412yes—
58C22×Dic47C22⋊C412yes—
59C22×Dic47C22⋊C412yes—
60C22×Dic47C4⋊C412yes—
61C22×Dic47C4⋊C412yes—
62M16×C47—42no—
63C2×C8×C47—22no—
64C22⋊C4×C47—44no—
65C42×C47—44no—
66C22⋊Dic47—44no—
67Dic47⋊C4—48no—
68C4×Dic47—44no—
69C4×Dic47C4212yes—
70C4×Dic47C4211yescharacteristic
71C4×Dic47C4211yescharacteristic
72C4×Dic47C22⋊C411yescharacteristic
73C4×Dic47C22⋊C411yescharacteristic
74C4×Dic47C22⋊C412yes—
75C4×Dic47C4⋊C412yes—
76C4×Dic47C4⋊C412yes—
77C4×Dic47C4⋊C412yes—
78C4×Dic47C4⋊C412yes—
79#10625329—42no—
80C2×C47⋊C8—22no—
81C23×C47—24no—
82C23×C47—41no—
83C23×C47C2×C22⋊C412yes—
84C23×C47C2×C4⋊C411yescharacteristic
85C2×C4×C47—22no—
86C2×C4×C47—24no—
87C2×C4×C47—42no—
88C2×C4×C47—41no—
89C2×C4×C47—44no—
90C2×C4×C47—44no—
91C2×C4×C47—44no—
92C2×C4×C47C2×C4211yescharacteristic
93C2×C4×C47C2×C22⋊C411yescharacteristic
94C2×C4×C47C2×C4⋊C412yes—
95C2×Dic47—24no—
96C2×Dic47—24no—
97C2×Dic47—42no—
98C2×Dic47—42no—
99C2×Dic47—42no—
100C2×Dic47—42no—
101C2×Dic47—44no—
102C2×Dic47—44no—
103C2×Dic47—44no—
104C2×Dic47#9512yes—
105C2×Dic47#9512yes—
106C2×Dic47#9512yes—
107C2×Dic47#9512yes—
108C8×C47—42no—
109C47⋊C8—42no—
110#8050—471nomaximal, Sylow
111C22×C47—22no—
112C22×C47—22no—
113C22×C47—22no—
114C22×C47—21no—
115C22×C47—44no—
116C22×C47C2×#9511yescharacteristic
117C22×C47#42114yes—
118C4×C47—21no—
119C4×C47—22no—
120C4×C47—84no—
121C4×C47#41012yes—
122Dic47—22no—
123Dic47—22no—
124Dic47—22no—
125Dic47—22no—
126Dic47—84no—
127#2920—471no—
128#2283—472no—
129#1297—471no—
130#1297—472no—
131#1297D4711yescharacteristic
132C2×C47—24no—
133C2×C47—41no—
134C2×C47#173312yes—
135C2×C47#174011yescharacteristic
136C22×C42—471no—
137#432—942no—
138#431—942no—
139#423—472no—
140#407—471no—
141#407C2×D4711yescharacteristic
142C4×M16—472no—
143#383—474no—
144#382—474no—
145#381—942no—
146#380—942no—
147C4×C4⋊C4—942no—
148C4×C22⋊C4—472no—
149C4×C22⋊C4C2×D4712yes—
150#376—942no—
151C47#805011yescharacteristic, complemented, Sylow
152C23×C4—472no—
153C23×C4C22×D4711yescharacteristic
154C2×M16—472no—
155C2×M16C4×D4712yes—
156C2×C4⋊C4—944no—
157C2×C22⋊C4—22no—
158C2×C22⋊C4—942no—
159C2×C42—22no—
160C2×C42—472no—
161C2×C42—472no—
162C2×C42—471no—
163C2×C42—471no—
164C2×C42—472no—
165C2×C42—472no—
166C2×C42—472no—
167C2×C42—942no—
168C4⋊C8—944no—
169C22⋊C8—22no—
170C22⋊C8—942no—
171#97—942no—
172C4×C8—942no—
173#95—474no—
174#95—944no—
175#95—944no—
176#95—944no—
177#95C4×D4714yes—
178C24D4×D4711yescharacteristic
179C22×C4—24no—
180C22×C4—42no—
181C22×C4—472no—
182C22×C4—472no—
183C22×C4—472no—
184C22×C4—472no—
185C22×C4—472no—
186C22×C4—472no—
187C22×C4—944no—
188C22×C4—1884no—
189C22×C4C2×C4×D4711yescharacteristic
190C22×C4C2×C4×D4712yes—
191C22×C4D4×D4712yes—
192C22×C4Q8×D4711yescharacteristic
193M16—42no—
194M16—1882no—
195C2×C8—22no—
196C2×C8—942no—
197C4⋊C4—1888no—
198C22⋊C4—44no—
199C22⋊C4—1884no—
200C42—44no—
201C42—471no—
202C42—472no—
203C42—471no—
204C42—471no—
205C42—471no—
206C42—472no—
207C42—472no—
208C42—472no—
209C42—472no—
210C42—472no—
211C42—1884no—
212C23—24no—
213C23—41no—
214C23C22⋊C4×D4712yes—
215C23C4⋊C4×D4711yescharacteristic
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—41no—
220C2×C4—44no—
221C2×C4—44no—
222C2×C4—44no—
223C2×C4—472no—
224C2×C4—472no—
225C2×C4—472no—
226C2×C4—472no—
227C2×C4—944no—
228C2×C4—944no—
229C2×C4—1882no—
230C2×C4—1882no—
231C2×C4—1882no—
232C2×C4—1882no—
233C2×C4—1884no—
234C2×C4—1884no—
235C2×C4—1884no—
236C2×C4C42×D4711yescharacteristic
237C2×C4C22⋊C4×D4711yescharacteristic
238C2×C4C4⋊C4×D4712yes—
239C8—42no—
240C8—1882no—
241C22—22no—
242C22—22no—
243C22—22no—
244C22—21no—
245C22—44no—
246C22#95×D4711yescharacteristic
247C22#1568913814yes—
248C4—21no—
249C4—22no—
250C4—84no—
251C4—942no—
252C4—942no—
253C4—942no—
254C4—942no—
255C4—3764no—
256C4#1568909512yes—
257C2—24no—
258C2—41no—
259C2#2024309612yes—
260C2#2024311911yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC47×#1297C2
socleC22×C47C2×#95
prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenter#1297D47
hypocenterC47#8050
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
9. #15689146C4semidirect
11. M16×Dic47C4semidirect
12. #15688990C4semidirect
13. #15688987C4semidirect
151. C47#8050semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202520172
#202457822
#202412742
#202412732
C47×#12972
#805047