Finite Group Databasebeta

← #20251681

Subgroups — #20251681

Order 6016.

1102 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C23×C4×D47C211yesmaximal, characteristic, complemented
2C2×#13094008C211yesmaximal, characteristic, complemented
3C2×#13094007C211yesmaximal, characteristic, complemented
4C2×#13093994C211yesmaximal, characteristic
5#15689001C214yesmaximal, complemented
6#15688997C214yesmaximal, complemented
7#15688984C211yesmaximal, characteristic, complemented
8#15688978C211yesmaximal, characteristic, complemented
9C47×#381C211yesmaximal, characteristic, complemented
10C24×D47C2211yescharacteristic
11C22×D188C2212yes—
12C22×C22⋊D47C2211yescharacteristic
13C23×Dic47C2211yescharacteristic
14C22×C4×D47—24no—
15C22×C4×D47—24no—
16C22×C4×D47—24no—
17C22×C4×D47C2214yes—
18#13094008—24no—
19#13094007—24no—
20#13093994—24no—
21C2×C4⋊Dic47C2212yescomplemented
22C2×Dic47⋊C4C2212yescomplemented
23C2×C22⋊Dic47C2211yescharacteristic
24C2×(C2×D47)⋊C4C2214yes—
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2212yescomplemented
27C2×(C2×D47)⋊C4C2212yescomplemented
28C47⋊#95C2214yescomplemented
29C23×C4×C47C2211yescharacteristic
30C2×C22⋊C4×C47C2211yescharacteristic
31C2×C22⋊C4×C47C2211yescharacteristic
32#95×C47C2214yescomplemented
33C24×C47C2311yescharacteristic
34C23×D47—22no—
35C23×D47—22no—
36C23×D47—28no—
37C23×D47D414yes—
38C23×D47C2311yescharacteristic
39C23×D47C2312yes—
40C22×C4×C47—22no—
41C22×C4×C47—22no—
42C22×C4×C47D414yescomplemented
43C22×C4×C47C2312yes—
44C22×C4×C47C2312yes—
45C22×C4×C47C2312yes—
46C2×C22⋊D47—22no—
47C2×C22⋊D47—22no—
48C2×C22⋊D47—22no—
49C22×Dic47—22no—
50C22×Dic47—22no—
51C22×Dic47D414yescomplemented
52C22×Dic47C2312yes—
53C22×Dic47C2311yescharacteristic
54C22×Dic47C2312yes—
55C2×D188—24no—
56C2×D188—28no—
57C2×C4×D47—232no—
58C2×C4×D47—28no—
59C2×C4×D47—28no—
60C2×C4×D47—28no—
61C22⋊C4×C47—22no—
62C22⋊C4×C47—22no—
63C22⋊Dic47—22no—
64(C2×D47)⋊C4—24no—
65(C2×D47)⋊C4—28no—
66(C2×D47)⋊C4—24no—
67(C2×D47)⋊C4—24no—
68C4⋊Dic47—24no—
69Dic47⋊C4—24no—
70C23×C47—24no—
71C23×C47C2×D412yes—
72C23×C47C2×D412yes—
73C23×C47C2×D412yes—
74C23×C47C2411yescharacteristic
75C22×D47—216no—
76C22×D47—216no—
77C22×D47—28no—
78C22×D47—22no—
79C22×D47—22no—
80C22×D47—24no—
81C22×D47—216no—
82C22×D47—21no—
83C22×D47—21no—
84C22×D47—21no—
85C22×D47—24no—
86C22×D47C2×D414yes—
87C22×D47#4118yes—
88C2×C4×C47—28no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—24no—
94C2×C4×C47—24no—
95C2×C4×C47C2×D414yes—
96C22⋊D47—44no—
97C2×Dic47—28no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—21no—
101C2×Dic47—22no—
102C2×Dic47—21no—
103C2×Dic47—21no—
104C2×Dic47—24no—
105C2×Dic47C2×D414yes—
106D188—48no—
107C4×D47—232no—
108C22×C47—24no—
109C22×C47—24no—
110C22×C47—24no—
111C22×C47#12014yes—
112C22×C47C22×D411yescharacteristic
113C22×C47C22×D411yescharacteristic
114C22×C47C22×D411yescharacteristic
115C22×C47C2×#4114yes—
116C2×D47—232no—
117C2×D47—24no—
118C2×D47—24no—
119C2×D47—28no—
120C2×D47—28no—
121C2×D47—41no—
122C2×D47—42no—
123C2×D47—42no—
124C2×D47—42no—
125C2×D47#12318yescomplemented
126C4×C47—24no—
127C4×C47—42no—
128C4×C47—42no—
129Dic47—24no—
130Dic47—41no—
131Dic47—42no—
132#2849—471nomaximal, Sylow
133C2×C47—24no—
134C2×C47C2×#12011yescharacteristic
135C2×C47C2×#12312yes—
136C2×C47#52512yes—
137C2×C47#52512yes—
138D47—28no—
139D47—81no—
140C24×C4—471no—
141C2×#123—471no—
142C2×#123—471no—
143C2×#120—471no—
144#386—474no—
145#385—474no—
146#381—471no—
147#381D4711yescharacteristic, complemented
148#379—471no—
149C47#284911yescharacteristic, complemented, Sylow
150C25—471no—
151C22×D4—471no—
152C22×D4—472no—
153C23×C4—471no—
154C23×C4—474no—
155C23×C4—944no—
156C23×C4—944no—
157C23×C4—944no—
158C23×C4C2×D4711yescharacteristic
159#123—944no—
160#123—944no—
161#120—944no—
162C2×C4⋊C4—472no—
163C2×C4⋊C4—472no—
164C2×C22⋊C4—471no—
165C2×C22⋊C4—472no—
166C2×C22⋊C4—472no—
167C2×C22⋊C4—472no—
168C2×C22⋊C4—474no—
169C2×C22⋊C4C2×D4711yescharacteristic
170C2×C22⋊C4C2×D4711yescharacteristic
171#95—474no—
172#95C2×D4714yescomplemented
173C24—472no—
174C24—474no—
175C24—471no—
176C24—948no—
177C24—942no—
178C24—942no—
179C24C22×D4711yescharacteristic
180C2×D4—944no—
181C2×D4—948no—
182C2×D4—942no—
183C2×D4—942no—
184C2×D4—942no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—474no—
188C22×C4—472no—
189C22×C4—472no—
190C22×C4—471no—
191C22×C4—948no—
192C22×C4—948no—
193C22×C4—9432no—
194C22×C4—942no—
195C22×C4—942no—
196C22×C4—948no—
197C22×C4D18814yescomplemented
198C22×C4C22×D4712yes—
199C22×C4C22×D4712yes—
200C22×C4C22×D4712yes—
201C4⋊C4—944no—
202C4⋊C4—944no—
203C22⋊C4—22no—
204C22⋊C4—22no—
205C22⋊C4—944no—
206C22⋊C4—948no—
207C22⋊C4—944no—
208C22⋊C4—942no—
209C22⋊C4—944no—
210C23—24no—
211C23—474no—
212C23—478no—
213C23—9416no—
214C23—9416no—
215C23—9416no—
216C23—948no—
217C23—942no—
218C23—942no—
219C23—944no—
220C23—941no—
221C23—941no—
222C23—941no—
223C23—944no—
224C23C2×D18812yes—
225C23D4×D4712yes—
226C23D4×D4712yes—
227C23C23×D4711yescharacteristic
228D4—1888no—
229D4—1884no—
230C2×C4—28no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—24no—
236C2×C4—24no—
237C2×C4—474no—
238C2×C4—9432no—
239C2×C4—948no—
240C2×C4—942no—
241C2×C4—942no—
242C2×C4—941no—
243C2×C4—941no—
244C2×C4—942no—
245C2×C4—941no—
246C2×C4—944no—
247C2×C4C2×D18814yes—
248C22—24no—
249C22—24no—
250C22—24no—
251C22—478no—
252C22—9432no—
253C22—944no—
254C22—944no—
255C22—948no—
256C22—948no—
257C22—1881no—
258C22—1882no—
259C22—1882no—
260C22—1882no—
261C22#1309399414yes—
262C22C2×D4×D4711yescharacteristic
263C22C2×D4×D4711yescharacteristic
264C22C22×D18811yescharacteristic
265C22#41×D4714yes—
266C4—24no—
267C4—42no—
268C4—42no—
269C4—944no—
270C4—1881no—
271C4—1882no—
272C2—24no—
273C2—948no—
274C2—3761no—
275C2C2×#1309399411yescharacteristic
276C2#123×D4712yes—
277C2#1568963112yes—
278C2#1568963512yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#381C2
hypercenter#381D47
hypocenterC47#2849
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C23×C4×D47C2semidirect
2. C2×#13094008C2semidirect
3. C2×#13094007C2semidirect
5. #15689001C2semidirect
6. #15688997C2semidirect
7. #15688984C2semidirect
8. #15688978C2semidirect
9. C47×#381C2semidirect
21. C2×C4⋊Dic47C22semidirect
22. C2×Dic47⋊C4C22semidirect
26. C2×(C2×D47)⋊C4C22semidirect
27. C2×(C2×D47)⋊C4C22semidirect
28. C47⋊#95C22semidirect
32. #95×C47C22semidirect
42. C22×C4×C47D4semidirect
51. C22×Dic47D4semidirect
125. C2×D47#123semidirect
147. #381D47semidirect
149. C47#2849semidirect
172. #95C2×D47semidirect
197. C22×C4D188semidirect