Finite Group Databasebeta

← #20249311

Subgroups — #20249311

Order 6016.

520 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 131 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×#13094000C211yesmaximal, characteristic, complemented
2C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic
3#15689055C211yesmaximal, characteristic, complemented
4#15689052C212yesmaximal, complemented
5#15689048C211yesmaximal, characteristic, complemented
6#15689042C211yesmaximal, characteristic, complemented
7#15689039C212yesmaximal
8#15689006C212yesmaximal, complemented
9#15688995C212yesmaximal, complemented
10#15688985C211yesmaximal, characteristic, complemented
11C47×#393C211yesmaximal, characteristic, complemented
12C22×C22⋊D47C2211yescharacteristic
13C23×Dic47C2211yescharacteristic
14C22×C4×D47C2211yescharacteristic
15#13094000—24no—
16(C22⋊D47)⋊C4—24no—
17C2×C4⋊Dic47C2212yes—
18C2×C4⋊Dic47C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2212yes—
22C2×C22⋊Dic47C2212yes—
23C2×(C2×D47)⋊C4C2212yes—
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2212yes—
26C2×C4×Dic47C2211yescharacteristic
27C47⋊#95C2212yes—
28C47⋊#95C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×Q8×C47C2211yescharacteristic
33C2×C22⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2212yes—
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C24×C47C2311yescharacteristic
38C23×D47C2311yescharacteristic
39C2×Q8×C47—22no—
40C2×Q8×C47—42no—
41C22×C4×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2312yes—
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—22no—
46C2×C22⋊D47—22no—
47C2×C22⋊D47—22no—
48C22×Dic47—22no—
49C22×Dic47—42no—
50C22×Dic47C2312yes—
51C22×Dic47C2312yes—
52C22×Dic47C2311yescharacteristic
53C22×Dic47C2311yescharacteristic
54C22×Dic47C2311yescharacteristic
55C2×C4×D47—42no—
56C2×C4×D47D414yes—
57C22⋊C4×C47—22no—
58C22⋊C4×C47—42no—
59C22⋊Dic47—24no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—24no—
62(C2×D47)⋊C4—42no—
63C4⋊Dic47—22no—
64C4⋊Dic47—24no—
65Dic47⋊C4—22no—
66Dic47⋊C4—24no—
67Dic47⋊C4—42no—
68C4×Dic47—22no—
69C23×C47—21no—
70C23×C47—21no—
71C23×C47—22no—
72C23×C47—22no—
73C23×C47#4112yes—
74C23×C47C2411yescharacteristic
75C22×D47—21no—
76C22×D47—21no—
77C22×D47—22no—
78C22×D47—22no—
79C22×D47C2×D412yes—
80Q8×C47—44no—
81C2×C4×C47—22no—
82C2×C4×C47—21no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—22no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47C2×D412yes—
91C22⋊D47—28no—
92C2×Dic47—21no—
93C2×Dic47—21no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—21no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—44no—
104C2×Dic47C2×D412yes—
105C2×Dic47#4112yes—
106C4×D47—44no—
107C22×C47—22no—
108C22×C47—24no—
109C22×C47—41no—
110C22×C47—41no—
111C22×C47—42no—
112C22×C47C22×D411yescharacteristic
113C22×C47C2×#4111yescharacteristic
114C22×C47C2×#4111yescharacteristic
115C22×C47H(5,𝔽2)12yes—
116C22×C472−1+412yes—
117C2×D47—22no—
118C2×D47—22no—
119C2×D47—22no—
120C2×D47—42no—
121C2×D47—42no—
122C4×C47—22no—
123C4×C47—42no—
124C4×C47—41no—
125C4×C47—42no—
126Dic47—22no—
127Dic47—22no—
128Dic47—42no—
129Dic47—41no—
130Dic47—42no—
131#2638—471nomaximal, Sylow
132C2×C47—42no—
133C2×C47#52511yescharacteristic
134C2×C47#53411yescharacteristic
135C2×C47#53611yescharacteristic
136C2×C47#53912yes—
137C2×C47#54212yes—
138D47—42no—
139C2×C22⋊Q8—471no—
140C2×C4×D4—471no—
141#398—471no—
142#397—471no—
143#397—472no—
144#395—471no—
145#394—472no—
146#393D4711yescharacteristic, complemented
147#387—472no—
148#385—472no—
149#381—471no—
150C47#263811yescharacteristic, complemented, Sylow
151C22×Q8C2×D4711yescharacteristic
152C22×D4—471no—
153C23×C4—471no—
154C23×C4—471no—
155C22⋊Q8—944no—
156C4×D4—944no—
157C2×C4⋊C4—471no—
158C2×C4⋊C4—472no—
159C2×C4⋊C4—471no—
160C2×C4⋊C4—472no—
161C2×C4⋊C4—472no—
162C2×C22⋊C4—472no—
163C2×C22⋊C4—471no—
164C2×C22⋊C4—472no—
165C2×C22⋊C4—472no—
166C2×C22⋊C4C2×D4711yescharacteristic
167C2×C22⋊C4C2×D4712yes—
168C2×C42—471no—
169#95—472no—
170#95—471no—
171#95—472no—
172#95—472no—
173#95—472no—
174#95C2×D4711yescharacteristic
175#95C2×D4712yes—
176C24—471no—
177C24C22×D4711yescharacteristic
178C2×Q8—22no—
179C2×Q8—42no—
180C2×D4—942no—
181C2×D4—942no—
182C2×D4—942no—
183C22×C4—471no—
184C22×C4—471no—
185C22×C4—474no—
186C22×C4—472no—
187C22×C4—472no—
188C22×C4—471no—
189C22×C4—942no—
190C22×C4—1882no—
191C22×C4—1882no—
192C22×C4C22×D4711yescharacteristic
193C22×C4C22×D4712yes—
194C22×C4C22×D4712yes—
195C22×C4C22×D4711yescharacteristic
196C4⋊C4—944no—
197C4⋊C4—944no—
198C4⋊C4—942no—
199C4⋊C4—942no—
200C4⋊C4—1882no—
201C22⋊C4—22no—
202C22⋊C4—42no—
203C22⋊C4—942no—
204C22⋊C4—944no—
205C22⋊C4—944no—
206C22⋊C4—1882no—
207C42—942no—
208C23—21no—
209C23—21no—
210C23—22no—
211C23—22no—
212C23—472no—
213C23—941no—
214C23—941no—
215C23—942no—
216C23—942no—
217C23#1062535412yes—
218C23C23×D4711yescharacteristic
219Q8—44no—
220D4—948no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—472no—
231C2×C4—472no—
232C2×C4—941no—
233C2×C4—941no—
234C2×C4—942no—
235C2×C4—942no—
236C2×C4—941no—
237C2×C4—942no—
238C2×C4—942no—
239C2×C4—942no—
240C2×C4—942no—
241C2×C4—942no—
242C2×C4—942no—
243C2×C4—1884no—
244C2×C4—1884no—
245C2×C4D4×D4712yes—
246C22—22no—
247C22—24no—
248C22—42no—
249C22—41no—
250C22—41no—
251C22—942no—
252C22—942no—
253C22—942no—
254C22—1882no—
255C22—1882no—
256C22C2×D4×D4711yescharacteristic
257C22#41×D4711yescharacteristic
258C22C2×#1062535411yescharacteristic
259C22#1309406912yes—
260C22#1309407112yes—
261C4—22no—
262C4—42no—
263C4—42no—
264C4—41no—
265C4—942no—
266C4—942no—
267C4—1882no—
268C4—1881no—
269C4—1882no—
270C2—42no—
271C2—1882no—
272C2#1568963611yescharacteristic
273C2#1568968311yescharacteristic
274C2#1568969311yescharacteristic
275C2#1568972212yes—
276C2#1568973712yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#393C2
hypercenter#393D47
hypocenterC47#2638
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#13094000C2semidirect
3. #15689055C2semidirect
4. #15689052C2semidirect
5. #15689048C2semidirect
6. #15689042C2semidirect
8. #15689006C2semidirect
9. #15688995C2semidirect
10. #15688985C2semidirect
11. C47×#393C2semidirect
146. #393D47semidirect
150. C47#2638semidirect