Finite Group Databasebeta

← #20245978

Subgroups — #20245978

Order 6016.

880 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 880 conjugacy classes of subgroups — too many to draw. Only its 229 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
1C22×#10625352C211yesmaximal, characteristic
2C2×#13093981C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×D47C211yesmaximal, characteristic, complemented
4#15689029C211yesmaximal, characteristic, complemented
5#15689028C211yesmaximal, characteristic, complemented
6#15689026C211yesmaximal, characteristic, complemented
7#15688999C214yesmaximal, complemented
8#15688981C214yesmaximal, complemented
9C47×#390C211yesmaximal, characteristic, complemented
10C2×#10625352—24no—
11C2×#10625352—24no—
12C2×#10625352C418yescomplemented
13C22×Dic94C2211yescharacteristic
14C22×C22⋊D47C2212yes—
15C23×Dic47C2212yes—
16C22×C4×D47C2212yes—
17C22×C4×D47C2211yescharacteristic
18#13093981—24no—
19C2×C4⋊Dic47C2211yescharacteristic
20C2×Dic47⋊C4C2212yes—
21C2×Dic47⋊C4C2212yes—
22C4⋊C4×D47—24no—
23C2×C22⋊Dic47C2214yes—
24C2×(C2×D47)⋊C4C2212yes—
25C2×C4×Dic47C2211yescharacteristic
26C47⋊#95C2214yes—
27C47⋊#95C2214yes—
28C22×D4×C47C2211yescharacteristic
29C2×C4⋊C4×C47C2211yescharacteristic
30C2×C22⋊C4×C47C2214yes—
31C2×C42×C47C2211yescharacteristic
32C24×C47C2312yes—
33C23×D47C2311yescharacteristic
34C2×D4×C47—22no—
35C2×D4×C47—22no—
36C2×D4×C47C2×C414yescomplemented
37C22×C4×C47C2312yes—
38C22×C4×C47C2312yes—
39C22×C4×C47C2311yescharacteristic
40C2×C22⋊D47—24no—
41C2×C22⋊D47—24no—
42C2×C22⋊D47C2×C418yes—
43C22×Dic47—24no—
44C22×Dic47—24no—
45C22×Dic47C2×C418yescomplemented
46C22×Dic47C2312yes—
47C22×Dic47C2312yes—
48C22×Dic47C2312yes—
49C22×Dic47C2311yescharacteristic
50#10625352—232no—
51C2×C4×D47—24no—
52C2×C4×D47—44no—
53C2×C4×D47C2×C414yes—
54C2×C4×D47D414yes—
55C2×C4×D47D414yes—
56C2×Dic94—22no—
57C2×Dic94—22no—
58C2×Dic94C2×C414yescomplemented
59C4⋊C4×C47—22no—
60C22⋊C4×C47—44no—
61C42×C47—22no—
62C22⋊Dic47—44no—
63(C2×D47)⋊C4—24no—
64C4⋊Dic47—22no—
65Dic47⋊C4—24no—
66Dic47⋊C4—24no—
67C4×Dic47—22no—
68C23×C47—22no—
69C23×C47—22no—
70C23×C47—24no—
71C23×C47—24no—
72C23×C47C22×C414yes—
73C23×C47C2411yescharacteristic
74C22×D47—22no—
75C22×D47—22no—
76C22×D47C22×C412yes—
77C22×D47C2×D412yes—
78C22×D47C2×D412yes—
79D4×C47—28no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—24no—
84C2×C4×C47—22no—
85C2×C4×C47C22×C412yes—
86C2×C4×C47C2×D412yes—
87C2×C4×C47C2×D412yes—
88C22⋊D47—216no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—216no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—24no—
96C2×Dic47—22no—
97C2×Dic47C22×C414yes—
98C2×Dic47C22×C412yes—
99C2×Dic47C2×D412yes—
100C2×Dic47C2×D412yes—
101C4×D47—48no—
102C4×D47C22⋊C4116yescomplemented
103Dic94—28no—
104C22×C47—24no—
105C22×C47—28no—
106C22×C47—42no—
107C22×C47—42no—
108C22×C47—44no—
109C22×C47C23×C411yescharacteristic
110C22×C47C22×D411yescharacteristic
111C22×C47C22×D411yescharacteristic
112C22×C47H(5,𝔽2)12yes—
113C22×C472−1+412yes—
114C2×D47—24no—
115C2×D47—22no—
116C2×D47—22no—
117C2×D47—24no—
118C2×D47C2×C22⋊C414yes—
119C4×C47—42no—
120C4×C47—42no—
121C4×C47C2×C22⋊C414yes—
122Dic47—24no—
123Dic47—42no—
124Dic47—42no—
125Dic47C2×C22⋊C414yes—
126#2311—471nomaximal, Sylow
127C2×C47—44no—
128C2×C47C22×C22⋊C411yescharacteristic
129C2×C47#52012yes—
130C2×C47#53511yescharacteristic
131C2×C47#53611yescharacteristic
132C2×C47#53712yes—
133D47—24no—
134C22×#41—471no—
135C2×#117—471no—
136C22×C4⋊C4—471no—
137#391—471no—
138#391—471no—
139#390—471no—
140#390D4711yescharacteristic, complemented
141#386—474no—
142#380—474no—
143C47#231111yescharacteristic, complemented, Sylow
144C2×#41—478no—
145C2×#41—944no—
146C2×#41—944no—
147C22×Q8—471no—
148C22×D4—472no—
149C22×D4C2×D4711yescharacteristic
150C23×C4—471no—
151C23×C4—472no—
152C23×C4—472no—
153#117—944no—
154C2×C4⋊C4—472no—
155C2×C4⋊C4—471no—
156C2×C4⋊C4—472no—
157C2×C4⋊C4—944no—
158C2×C4⋊C4C2×D4711yescharacteristic
159C2×C22⋊C4—472no—
160C2×C22⋊C4—474no—
161C2×C22⋊C4C2×D4714yes—
162C2×C42—471no—
163C2×C42C2×D4711yescharacteristic
164#95—474no—
165#95—474no—
166C24—471no—
167C24C22×D4712yes—
168#41—9432no—
169C2×Q8—474no—
170C2×Q8—942no—
171C2×Q8—942no—
172C2×D4—22no—
173C2×D4—22no—
174C2×D4—478no—
175C2×D4—944no—
176C2×D4—944no—
177C2×D4C4×D4714yescomplemented
178C22×C4—471no—
179C22×C4—474no—
180C22×C4—474no—
181C22×C4—474no—
182C22×C4—478no—
183C22×C4—472no—
184C22×C4—472no—
185C22×C4—472no—
186C22×C4—944no—
187C22×C4—944no—
188C22×C4—944no—
189C22×C4—1884no—
190C22×C4C22×D4712yes—
191C22×C4C22×D4712yes—
192C22×C4C22×D4711yescharacteristic
193C4⋊C4—22no—
194C4⋊C4—944no—
195C4⋊C4—944no—
196C4⋊C4—942no—
197C22⋊C4—44no—
198C22⋊C4—944no—
199C22⋊C4—1884no—
200C42—22no—
201C42—942no—
202C23—22no—
203C23—22no—
204C23—24no—
205C23—24no—
206C23—472no—
207C23—472no—
208C23—472no—
209C23—942no—
210C23—942no—
211C23C2×C4×D4714yes—
212C23C23×D4711yescharacteristic
213Q8—948no—
214D4—28no—
215D4—9416no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—24no—
220C2×C4—22no—
221C2×C4—472no—
222C2×C4—472no—
223C2×C4—472no—
224C2×C4—4716no—
225C2×C4—474no—
226C2×C4—9416no—
227C2×C4—942no—
228C2×C4—942no—
229C2×C4—942no—
230C2×C4—942no—
231C2×C4—942no—
232C2×C4—944no—
233C2×C4—942no—
234C2×C4—1888no—
235C2×C4C2×C4×D4712yes—
236C2×C4D4×D4712yes—
237C2×C4D4×D4712yes—
238C22—24no—
239C22—28no—
240C22—42no—
241C22—42no—
242C22—44no—
243C22—474no—
244C22—944no—
245C22—942no—
246C22—942no—
247C22—944no—
248C22C22×C4×D4711yescharacteristic
249C22C2×D4×D4711yescharacteristic
250C22C2×D4×D4711yescharacteristic
251C22#1309406912yes—
252C22#1309407112yes—
253C4—42no—
254C4—42no—
255C4—474no—
256C4—944no—
257C4—1882no—
258C4—1882no—
259C4C22⋊C4×D4714yes—
260C2—44no—
261C2—944no—
262C2C2×C22⋊C4×D4711yescharacteristic
263C2#1568960212yes—
264C2#1568968611yescharacteristic
265C2#1568969311yescharacteristic
266C2#1568970212yes—
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#390C2
socleC23×C47C24
hypercenter#390D47
hypocenterC47#2311
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#13093981C2semidirect
3. C2×C4⋊C4×D47C2semidirect
4. #15689029C2semidirect
5. #15689028C2semidirect
6. #15689026C2semidirect
7. #15688999C2semidirect
8. #15688981C2semidirect
9. C47×#390C2semidirect
12. C2×#10625352C4semidirect
36. C2×D4×C47C2×C4semidirect
45. C22×Dic47C2×C4semidirect
58. C2×Dic94C2×C4semidirect
102. C4×D47C22⋊C4semidirect
140. #390D47semidirect
143. C47#2311semidirect
177. C2×D4C4×D47semidirect