Finite Group Databasebeta

← #20247856

Subgroups — #20247856

Order 6016.

708 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 169 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×#13094009C214yesmaximal, complemented
2C2×#13093999C211yesmaximal, characteristic
3C2×C4⋊C4×D47C211yesmaximal, characteristic, complemented
4#15689058C214yesmaximal, complemented
5#15689025C211yesmaximal, characteristic, complemented
6#15689024C211yesmaximal, characteristic, complemented
7#15688992C211yesmaximal, characteristic, complemented
8C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
9C47×#384C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C22×D188C2212yes—
12C22×C4×D47C2212yes—
13C22×C4×D47C2211yescharacteristic
14#13094009—216no—
15#13093999—24no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4C2214yes—
18C2×Dic47⋊C4C2212yes—
19C4⋊C4×D47—24no—
20C2×(C2×D47)⋊C4C2214yes—
21C2×(C2×D47)⋊C4C2214yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2212yes—
24C2×C4×Dic47C2211yescharacteristic
25C47⋊#95C2212yes—
26C2×C4⋊C4×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2214yes—
29C2×C42×C47C2211yescharacteristic
30C23×D47C2312yes—
31C23×D47C2311yescharacteristic
32C22×C4×C47C2312yes—
33C22×C4×C47C2312yes—
34C22×C4×C47C2312yes—
35C22×C4×C47C2311yescharacteristic
36C22×Dic47C2312yes—
37C22×Dic47C2311yescharacteristic
38C22×Dic47C2312yes—
39C2×D188—24no—
40C2×D188—28no—
41C2×D188—22no—
42C2×D188—22no—
43C2×D188—22no—
44C2×C4×D47—22no—
45C2×C4×D47—22no—
46C2×C4×D47—24no—
47C2×C4×D47—28no—
48C2×C4×D47D414yes—
49C4⋊C4×C47—22no—
50C4⋊C4×C47—22no—
51C4⋊C4×C47—28no—
52C42×C47—22no—
53(C2×D47)⋊C4—28no—
54(C2×D47)⋊C4—24no—
55(C2×D47)⋊C4—28no—
56(C2×D47)⋊C4D418yescomplemented
57C4⋊Dic47—22no—
58Dic47⋊C4—24no—
59Dic47⋊C4—28no—
60C4×Dic47—22no—
61C23×C47C2411yescharacteristic
62C22×D47—21no—
63C22×D47—21no—
64C22×D47—22no—
65C22×D47—24no—
66C22×D47—22no—
67C22×D47—22no—
68C22×D47—22no—
69C22×D47—24no—
70C22×D47C2×D414yes—
71C22×D47C2×D412yes—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—24no—
76C2×C4×C47—24no—
77C2×C4×C47—22no—
78C2×C4×C47C2×D414yes—
79C2×C4×C47C2×D412yes—
80C2×C4×C47#4112yes—
81C2×C4×C47#4112yes—
82C2×Dic47—22no—
83C2×Dic47—21no—
84C2×Dic47—21no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—24no—
88C2×Dic47C2×D414yes—
89C2×Dic47C2×D412yes—
90D188—48no—
91D188—44no—
92C4×D47—28no—
93C4×D47—48no—
94C22×C47C22×D411yescharacteristic
95C22×C47C22×D412yes—
96C22×C47C2×#4111yescharacteristic
97C22×C47C2×#4111yescharacteristic
98C22×C472−1+412yes—
99C2×D47—22no—
100C2×D47—22no—
101C2×D47—24no—
102C2×D47—24no—
103C2×D47—42no—
104C2×D47—42no—
105C2×D47—42no—
106C2×D47—44no—
107C2×D47—44no—
108C2×D47#12714yes—
109C4×C47—24no—
110C4×C47—42no—
111C4×C47—42no—
112C4×C47#12314yescomplemented
113Dic47—22no—
114Dic47—24no—
115Dic47—42no—
116#2501—471nomaximal, Sylow
117C2×C47C2×#12311yescharacteristic
118C2×C47C2×#12711yescharacteristic
119C2×C47#53611yescharacteristic
120C2×C47#54712yes—
121C2×C47#54712yes—
122D47—24no—
123D47—82no—
124C2×#123—474no—
125C2×#121—471no—
126C22×C4⋊C4—471no—
127#399—474no—
128#390—471no—
129#390—471no—
130#384—471no—
131#384D4711yescharacteristic, complemented
132C4×C22⋊C4—471no—
133C47#250111yescharacteristic, complemented, Sylow
134C22×D4—472no—
135C22×D4—471no—
136C23×C4—471no—
137C23×C4—472no—
138#123—9416no—
139#121—944no—
140C2×C4⋊C4—472no—
141C2×C4⋊C4—471no—
142C2×C4⋊C4—474no—
143C2×C4⋊C4—944no—
144C2×C4⋊C4C2×D4711yescharacteristic
145C2×C4⋊C4C2×D4711yescharacteristic
146C2×C4⋊C4C2×D4714yes—
147C2×C22⋊C4—472no—
148C2×C22⋊C4—472no—
149C2×C22⋊C4—474no—
150C2×C22⋊C4—474no—
151C2×C42—471no—
152C2×C42C2×D4711yescharacteristic
153#95—472no—
154C24—471no—
155C24—472no—
156C2×D4—944no—
157C2×D4—948no—
158C2×D4—942no—
159C2×D4—942no—
160C2×D4—942no—
161C22×C4—471no—
162C22×C4—472no—
163C22×C4—474no—
164C22×C4—472no—
165C22×C4—944no—
166C22×C4—948no—
167C22×C4—942no—
168C22×C4—942no—
169C22×C4C22×D4712yes—
170C22×C4C22×D4712yes—
171C22×C4C22×D4712yes—
172C22×C4C22×D4711yescharacteristic
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—28no—
176C4⋊C4—944no—
177C4⋊C4—948no—
178C4⋊C4—942no—
179C22⋊C4—478no—
180C22⋊C4—944no—
181C22⋊C4—948no—
182C22⋊C4—948no—
183C42—22no—
184C42—942no—
185C23—474no—
186C23—472no—
187C23—941no—
188C23—941no—
189C23—942no—
190C23—944no—
191C23—942no—
192C23—942no—
193C23—942no—
194C23—944no—
195C23C23×D4711yescharacteristic
196D4—1888no—
197D4—1884no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—24no—
204C2×C4—474no—
205C2×C4—472no—
206C2×C4—941no—
207C2×C4—942no—
208C2×C4—941no—
209C2×C4—942no—
210C2×C4—948no—
211C2×C4—944no—
212C2×C4—942no—
213C2×C4—1888no—
214C2×C4#1062535012yes—
215C2×C4D4×D4714yes—
216C2×C4D4×D4712yes—
217C2×C4#1062535412yes—
218C22—474no—
219C22—944no—
220C22—944no—
221C22—942no—
222C22—942no—
223C22—1884no—
224C22—1884no—
225C22—1882no—
226C22—1882no—
227C22—1882no—
228C22C2×D4×D4712yes—
229C22C2×D4×D4711yescharacteristic
230C22C2×#1062535011yescharacteristic
231C22C2×#1062535411yescharacteristic
232C22#1309407212yes—
233C4—24no—
234C4—42no—
235C4—42no—
236C4—944no—
237C4—942no—
238C4—1882no—
239C4#1309400914yescomplemented
240C2—944no—
241C2—3762no—
242C2C2×#1309400911yescharacteristic
243C2#127×D4711yescharacteristic
244C2#1568969811yescharacteristic
245C2#1568977412yes—
246C2#1568977612yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#384C2
hypercenter#384D47
hypocenterC47#2501
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
1. C2×#13094009C2semidirect
3. C2×C4⋊C4×D47C2semidirect
4. #15689058C2semidirect
5. #15689025C2semidirect
6. #15689024C2semidirect
7. #15688992C2semidirect
8. C4×(C2×D47)⋊C4C2semidirect
9. C47×#384C2semidirect
56. (C2×D47)⋊C4D4semidirect
112. C4×C47#123semidirect
131. #384D47semidirect
133. C47#2501semidirect
239. C4#13094009semidirect