Finite Group Databasebeta

← #20247384

Subgroups — #20247384

Order 6016.

668 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 145 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×#13094002C212yesmaximal, complemented
2C2×C4×C22⋊D47C212yesmaximal, complemented
3#15689038C212yesmaximal, complemented
4#15689035C211yesmaximal, characteristic, complemented
5#15689032C211yesmaximal, characteristic
6#15689013C212yesmaximal, complemented
7#15689005C212yesmaximal, complemented
8#15689001C212yesmaximal, complemented
9C47×#385C211yesmaximal, characteristic, complemented
10C22×Dic94C2211yescharacteristic
11C22×D188C2211yescharacteristic
12C22×C22⋊D47C2212yes—
13C22×C4×D47C2212yes—
14#13094002—28no—
15C4×C22⋊D47—28no—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×C22⋊Dic47C2212yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×C4×Dic47C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2211yescharacteristic
26C47⋊#95C2212yes—
27C47⋊#95C2211yescharacteristic
28C23×C4×C47C2211yescharacteristic
29C2×C4⋊C4×C47C2212yes—
30C2×C22⋊C4×C47C2211yescharacteristic
31C2×C22⋊C4×C47C2211yescharacteristic
32#95×C47C2212yes—
33C24×C47C2311yescharacteristic
34C23×D47C2312yes—
35C22×C4×C47—24no—
36C22×C4×C47—41no—
37C22×C4×C47C2311yescharacteristic
38C22×C4×C47C2312yes—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2312yes—
41C2×C22⋊D47—24no—
42C2×C22⋊D47—24no—
43C2×C22⋊D47—24no—
44C22×Dic47C2312yes—
45C22×Dic47C2312yes—
46C22×Dic47C2312yes—
47C2×D188—24no—
48C2×D188—41no—
49C2×C4×D47—24no—
50C2×C4×D47—24no—
51C2×C4×D47—42no—
52C2×Dic94—24no—
53C2×Dic94—41no—
54C4⋊C4×C47—24no—
55C22⋊C4×C47—22no—
56C22⋊C4×C47—41no—
57C22⋊Dic47—24no—
58(C2×D47)⋊C4—24no—
59(C2×D47)⋊C4—24no—
60(C2×D47)⋊C4—24no—
61(C2×D47)⋊C4—24no—
62Dic47⋊C4—24no—
63Dic47⋊C4D418yescomplemented
64C4×Dic47—24no—
65C23×C47—22no—
66C23×C47—22no—
67C23×C47—21no—
68C23×C47—21no—
69C23×C47#4112yes—
70C23×C47C2411yescharacteristic
71C22×D47—22no—
72C22×D47—22no—
73C22×D47—22no—
74C22×D47—22no—
75C22×D47—22no—
76C22×D47—22no—
77C22×D47#4114yes—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—21no—
86C2×C4×C47—21no—
87C2×C4×C47—44no—
88C2×C4×C47C2×D414yes—
89C22⋊D47—216no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47C2×D414yes—
98C2×Dic47C2×D414yes—
99D188—44no—
100C4×D47—48no—
101Dic94—44no—
102C22×C47—24no—
103C22×C47—22no—
104C22×C47—41no—
105C22×C47—42no—
106C22×C47—41no—
107C22×C47C22×D412yes—
108C22×C47C2×#4112yes—
109C22×C47C2×#4111yescharacteristic
110C22×C47H(5,𝔽2)11yescharacteristic
111C22×C472−1+411yescharacteristic
112C2×D47—24no—
113C2×D47—24no—
114C2×D47—24no—
115C2×D47—42no—
116C2×D47—42no—
117C2×D47—42no—
118C2×D47—42no—
119C4×C47—24no—
120C4×C47—42no—
121C4×C47—41no—
122C4×C47—41no—
123Dic47—24no—
124Dic47—24no—
125Dic47—42no—
126#2463—471nomaximal, Sylow
127C2×C47—42no—
128C2×C47#52512yes—
129C2×C47#53911yescharacteristic
130C2×C47D4211yescharacteristic
131C2×C47#54812yes—
132C2×C47#55111yescharacteristic
133D47—44no—
134C2×C22⋊Q8—472no—
135C2×C4×D4—472no—
136#394—472no—
137#393—471no—
138#392—471no—
139#388—472no—
140#387—472no—
141#386—472no—
142#385D4711yescharacteristic, complemented
143C47#246311yescharacteristic, complemented, Sylow
144C22×Q8—471no—
145C22×D4—472no—
146C22×D4—471no—
147C23×C4—472no—
148C23×C4C2×D4711yescharacteristic
149C22⋊Q8—948no—
150C4×D4—948no—
151C2×C4⋊C4—472no—
152C2×C4⋊C4—472no—
153C2×C4⋊C4C2×D4712yes—
154C2×C22⋊C4—472no—
155C2×C22⋊C4—472no—
156C2×C22⋊C4—472no—
157C2×C22⋊C4—472no—
158C2×C22⋊C4—472no—
159C2×C22⋊C4C2×D4711yescharacteristic
160C2×C22⋊C4C2×D4711yescharacteristic
161C2×C42—472no—
162#95—472no—
163#95—471no—
164#95—472no—
165#95—471no—
166#95C2×D4712yes—
167C24—472no—
168C24C22×D4711yescharacteristic
169C2×Q8—944no—
170C2×Q8—1881no—
171C2×D4—944no—
172C2×D4—944no—
173C2×D4—944no—
174C2×D4—944no—
175C2×D4—1881no—
176C22×C4—24no—
177C22×C4—41no—
178C22×C4—472no—
179C22×C4—472no—
180C22×C4—472no—
181C22×C4—944no—
182C22×C4—944no—
183C22×C4—1882no—
184C22×C4C22×D4711yescharacteristic
185C22×C4C22×D4712yes—
186C22×C4C22×D4711yescharacteristic
187C22×C4C22×D4712yes—
188C4⋊C4—24no—
189C4⋊C4—478no—
190C4⋊C4—944no—
191C22⋊C4—22no—
192C22⋊C4—41no—
193C22⋊C4—944no—
194C22⋊C4—944no—
195C22⋊C4—944no—
196C22⋊C4—944no—
197C22⋊C4—944no—
198C42—944no—
199C23—22no—
200C23—22no—
201C23—21no—
202C23—21no—
203C23—474no—
204C23—942no—
205C23—942no—
206C23—942no—
207C23—942no—
208C23—942no—
209C23—942no—
210C23#1062535012yes—
211C23C23×D4711yescharacteristic
212Q8—1884no—
213D4—9416no—
214D4—1884no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—44no—
225C2×C4—474no—
226C2×C4—474no—
227C2×C4—942no—
228C2×C4—942no—
229C2×C4—942no—
230C2×C4—942no—
231C2×C4—942no—
232C2×C4—942no—
233C2×C4—942no—
234C2×C4—1888no—
235C2×C4D4×D4714yes—
236C22—24no—
237C22—22no—
238C22—41no—
239C22—42no—
240C22—41no—
241C22—944no—
242C22—944no—
243C22—944no—
244C22—1882no—
245C22—1882no—
246C22—1882no—
247C22—1882no—
248C22C2×D4×D4712yes—
249C22#41×D4712yes—
250C22C2×#1062535011yescharacteristic
251C22#1309406911yescharacteristic
252C22#1309407211yescharacteristic
253C4—24no—
254C4—41no—
255C4—41no—
256C4—42no—
257C4—944no—
258C4—944no—
259C4—1882no—
260C2—42no—
261C2—1884no—
262C2#1568963212yes—
263C2#1568972011yescharacteristic
264C2#1568975511yescharacteristic
265C2#1568978312yes—
266C2#1568980111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#385C2
hypercenter#385D47
hypocenterC47#2463
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#13094002C2semidirect
2. C2×C4×C22⋊D47C2semidirect
3. #15689038C2semidirect
4. #15689035C2semidirect
6. #15689013C2semidirect
7. #15689005C2semidirect
8. #15689001C2semidirect
9. C47×#385C2semidirect
63. Dic47⋊C4D4semidirect
142. #385D47semidirect
143. C47#2463semidirect