Finite Group Databasebeta

← #20249152

Subgroups — #20249152

Order 6016.

612 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13094013C211yesmaximal, characteristic, complemented
2C2×#13094000C211yesmaximal, characteristic, complemented
3C2×#13093999C211yesmaximal, characteristic
4C2×#13093981C211yesmaximal, characteristic, complemented
5#15689047C214yesmaximal, complemented
6#15689041C214yesmaximal, complemented
7#15689025C211yesmaximal, characteristic, complemented
8#15688992C211yesmaximal, characteristic, complemented
9C47×#391C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C22×D188C2212yes—
12C22×C4×D47C2211yescharacteristic
13#13094013—24no—
14#13094000—24no—
15#13093999—24no—
16#13093981—24no—
17C2×C4⋊Dic47C2211yescharacteristic
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2214yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2214yes—
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2214yes—
26C2×C4×Dic47C2211yescharacteristic
27C22×Q8×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C42×C47C2211yescharacteristic
30#95×C47C2214yes—
31C23×D47C2312yes—
32C23×D47C2311yescharacteristic
33C2×Q8×C47—22no—
34C2×Q8×C47—22no—
35C2×Q8×C47—22no—
36C22×C4×C47C2312yes—
37C22×C4×C47C2312yes—
38C22×C4×C47C2312yes—
39C22×C4×C47C2311yescharacteristic
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C22×Dic47C2311yescharacteristic
43C2×D188—24no—
44C2×D188—22no—
45C2×D188—22no—
46C2×D188—22no—
47C2×D188—44no—
48C2×C4×D47—22no—
49C2×C4×D47—22no—
50C2×C4×D47D414yes—
51C4⋊C4×C47—22no—
52C42×C47—22no—
53(C2×D47)⋊C4—24no—
54(C2×D47)⋊C4—24no—
55(C2×D47)⋊C4—24no—
56(C2×D47)⋊C4—28no—
57(C2×D47)⋊C4—44no—
58C4⋊Dic47—22no—
59Dic47⋊C4—24no—
60Dic47⋊C4—24no—
61Dic47⋊C4—44no—
62C4×Dic47D414yescomplemented
63C23×C47C2411yescharacteristic
64C22×D47—21no—
65C22×D47—21no—
66C22×D47—22no—
67C22×D47—22no—
68C22×D47—22no—
69C22×D47—22no—
70C22×D47—22no—
71C22×D47—24no—
72C22×D47—24no—
73C22×D47C2×D412yes—
74Q8×C47—44no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—24no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47C2×D412yes—
84C2×C4×C47C2×D412yes—
85C2×C4×C47#4112yes—
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—24no—
92C2×Dic47C2×D414yes—
93C2×Dic47C2×D412yes—
94D188—48no—
95D188—44no—
96C4×D47—28no—
97C22×C47C22×D411yescharacteristic
98C22×C47C22×D411yescharacteristic
99C22×C47C2×#4111yescharacteristic
100C22×C47H(5,𝔽2)12yes—
101C22×C472−1+412yes—
102C2×D47—22no—
103C2×D47—22no—
104C2×D47—22no—
105C2×D47—42no—
106C2×D47—42no—
107C2×D47—42no—
108C2×D47—42no—
109C2×D47—42no—
110C2×D47—44no—
111C2×D47—44no—
112C4×C47—42no—
113C4×C47—42no—
114C4×C47—42no—
115C4×C47#12114yes—
116Dic47—22no—
117Dic47—24no—
118Dic47—42no—
119#2620—471nomaximal, Sylow
120C2×C47C2×#12111yescharacteristic
121C2×C47#53511yescharacteristic
122C2×C47#53611yescharacteristic
123C2×C47#53712yes—
124C2×C47#54212yes—
125D47—42no—
126D47—82no—
127C2×#124—471no—
128C2×C22⋊Q8—471no—
129C2×#121—471no—
130C2×#117—471no—
131#396—474no—
132#394—474no—
133#391D4711yescharacteristic, complemented
134#390—471no—
135#384—471no—
136C47#262011yescharacteristic, complemented, Sylow
137C22×Q8C2×D4711yescharacteristic
138C22×D4—471no—
139C22×D4—472no—
140C23×C4—471no—
141#124—944no—
142C22⋊Q8—944no—
143#121—944no—
144#117—944no—
145C2×C4⋊C4—472no—
146C2×C4⋊C4—472no—
147C2×C4⋊C4—471no—
148C2×C4⋊C4—474no—
149C2×C4⋊C4C2×D4711yescharacteristic
150C2×C22⋊C4—472no—
151C2×C22⋊C4—472no—
152C2×C22⋊C4—472no—
153C2×C22⋊C4—474no—
154C2×C22⋊C4—474no—
155C2×C42—471no—
156C2×C42C2×D4711yescharacteristic
157#95C2×D4714yes—
158C24—471no—
159C24—472no—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—22no—
163C2×D4—944no—
164C2×D4—942no—
165C2×D4—942no—
166C2×D4—942no—
167C2×D4—1884no—
168C22×C4—472no—
169C22×C4—471no—
170C22×C4—474no—
171C22×C4—472no—
172C22×C4—942no—
173C22×C4—942no—
174C22×C4C22×D4712yes—
175C22×C4C22×D4712yes—
176C22×C4C22×D4712yes—
177C22×C4C22×D4711yescharacteristic
178C4⋊C4—22no—
179C4⋊C4—944no—
180C4⋊C4—944no—
181C4⋊C4—942no—
182C4⋊C4—1884no—
183C22⋊C4—944no—
184C22⋊C4—944no—
185C22⋊C4—948no—
186C22⋊C4—944no—
187C22⋊C4—1884no—
188C42—22no—
189C42—474no—
190C23—472no—
191C23—941no—
192C23—941no—
193C23—942no—
194C23—942no—
195C23—942no—
196C23—942no—
197C23—942no—
198C23—944no—
199C23—944no—
200C23C23×D4711yescharacteristic
201Q8—44no—
202D4—1888no—
203D4—1884no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—24no—
211C2×C4—22no—
212C2×C4—474no—
213C2×C4—472no—
214C2×C4—941no—
215C2×C4—941no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—948no—
219C2×C4—942no—
220C2×C4—944no—
221C2×C4#1062535012yes—
222C2×C4D4×D4712yes—
223C2×C4D4×D4712yes—
224C22—942no—
225C22—942no—
226C22—942no—
227C22—1884no—
228C22—1882no—
229C22—1882no—
230C22—1882no—
231C22—1884no—
232C22—1882no—
233C22—1882no—
234C22C2×D4×D4711yescharacteristic
235C22C2×D4×D4711yescharacteristic
236C22C2×#1062535011yescharacteristic
237C22#1309407012yes—
238C22#1309407212yes—
239C4—42no—
240C4—42no—
241C4—42no—
242C4—942no—
243C4—944no—
244C4—1882no—
245C4#1309399714yes—
246C2—3762no—
247C2—1882no—
248C2C2×#1309399711yescharacteristic
249C2#1568969111yescharacteristic
250C2#1568969811yescharacteristic
251C2#1568970312yes—
252C2#1568974512yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#391C2
hypercenter#391D47
hypocenterC47#2620
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#13094013C2semidirect
2. C2×#13094000C2semidirect
4. C2×#13093981C2semidirect
5. #15689047C2semidirect
6. #15689041C2semidirect
7. #15689025C2semidirect
8. #15688992C2semidirect
9. C47×#391C2semidirect
62. C4×Dic47D4semidirect
133. #391D47semidirect
136. C47#2620semidirect