Finite Group Databasebeta

← #20249326

Subgroups — #20249326

Order 6016.

500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13094022C211yesmaximal, characteristic, complemented
2C2×#13094010C211yesmaximal, characteristic
3#15689052C212yesmaximal, complemented
4#15689051C212yesmaximal, complemented
5#15689036C211yesmaximal, characteristic, complemented
6#15689035C211yesmaximal, characteristic, complemented
7#15689034C211yesmaximal, characteristic, complemented
8#15689027C212yesmaximal, complemented
9#15689023C212yesmaximal
10#15688968C211yesmaximal, characteristic, complemented
11C47×#393C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×Dic94C2211yescharacteristic
14C22×C22⋊D47C2211yescharacteristic
15#13094022—24no—
16#13094010—24no—
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2212yes—
19C2×C22⋊Dic47C2211yescharacteristic
20C2×C22⋊Dic47C2212yes—
21C2×(C2×D47)⋊C4C2211yescharacteristic
22C2×(C2×D47)⋊C4C2211yescharacteristic
23C2×(C2×D47)⋊C4C2212yes—
24C2×(C2×D47)⋊C4C2212yes—
25C2×C4×Dic47C2212yes—
26C2×C4×Dic47C2211yescharacteristic
27C47⋊#95C2211yescharacteristic
28C47⋊#95C2212yes—
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×C47C2312yes—
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—22no—
46C2×C22⋊D47—24no—
47C22×Dic47C2312yes—
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2312yes—
50C22×Dic47C2311yescharacteristic
51C22×Dic47C2311yescharacteristic
52C2×Dic94—22no—
53C2×Dic94—22no—
54C2×Dic94—24no—
55C2×Dic94—42no—
56C22⋊C4×C47—22no—
57C22⋊C4×C47—42no—
58C22⋊Dic47—22no—
59C22⋊Dic47—42no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—22no—
62(C2×D47)⋊C4—42no—
63(C2×D47)⋊C4—42no—
64Dic47⋊C4—24no—
65Dic47⋊C4—24no—
66C4×Dic47—24no—
67C4×Dic47D414yes—
68C23×C47—21no—
69C23×C47—22no—
70C23×C47—22no—
71C23×C47—21no—
72C23×C47—21no—
73C23×C47C2411yescharacteristic
74C22×D47—21no—
75C22×D47—22no—
76C22×D47—22no—
77C22×D47—21no—
78C22×D47—21no—
79Q8×C47—44no—
80C2×C4×C47—22no—
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×C47C2×D412yes—
90C22⋊D47—44no—
91C2×Dic47—21no—
92C2×Dic47—21no—
93C2×Dic47—22no—
94C2×Dic47—21no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47C2×D412yes—
102C2×Dic47C2×D412yes—
103C2×Dic47#4114yes—
104Dic94—44no—
105Dic94—44no—
106C22×C47—41no—
107C22×C47—41no—
108C22×C47—41no—
109C22×C47—42no—
110C22×C47—42no—
111C22×C47C22×D411yescharacteristic
112C22×C47C2×#4112yes—
113C22×C47H(5,𝔽2)12yes—
114C22×C472−1+411yescharacteristic
115C22×C472−1+411yescharacteristic
116C2×D47—41no—
117C2×D47—41no—
118C2×D47—41no—
119C2×D47—42no—
120C2×D47—42no—
121C4×C47—22no—
122C4×C47—41no—
123C4×C47—42no—
124C4×C47—42no—
125Dic47—22no—
126Dic47—41no—
127Dic47—42no—
128Dic47—42no—
129Dic47#12414yes—
130#2640—471nomaximal, Sylow
131C2×C47—81no—
132C2×C47C2×#12411yescharacteristic
133C2×C47#53511yescharacteristic
134C2×C47#53611yescharacteristic
135C2×C47#54212yes—
136C2×C47#54212yes—
137D47—81no—
138C2×C4⋊Q8—471no—
139C2×#124—471no—
140#397—472no—
141#397—472no—
142#393—471no—
143#393—471no—
144#393—471no—
145#393D4711yescharacteristic, complemented
146#391—472no—
147#390—472no—
148#376—471no—
149C47#264011yescharacteristic, complemented, Sylow
150C22×Q8—471no—
151C22×Q8—471no—
152C22×Q8C2×D4711yescharacteristic
153C22×D4—471no—
154C4⋊Q8—944no—
155#124—944no—
156C2×C4⋊C4—472no—
157C2×C4⋊C4—472no—
158C2×C22⋊C4—471no—
159C2×C22⋊C4—471no—
160C2×C22⋊C4—471no—
161C2×C22⋊C4—472no—
162C2×C22⋊C4—472no—
163C2×C22⋊C4—472no—
164C2×C22⋊C4C2×D4711yescharacteristic
165C2×C22⋊C4C2×D4712yes—
166C2×C42—471no—
167C2×C42—472no—
168#95—471no—
169#95—472no—
170#95—472no—
171#95—472no—
172#95—472no—
173#95C2×D4711yescharacteristic
174#95C2×D4712yes—
175C24—471no—
176C24C22×D4711yescharacteristic
177C2×Q8—22no—
178C2×Q8—42no—
179C2×Q8—942no—
180C2×Q8—944no—
181C2×Q8—942no—
182C2×Q8—1882no—
183C2×D4—942no—
184C2×D4—944no—
185C22×C4—471no—
186C22×C4—471no—
187C22×C4—472no—
188C22×C4—471no—
189C22×C4—472no—
190C22×C4C22×D4712yes—
191C22×C4C22×D4711yescharacteristic
192C22×C4C22×D4712yes—
193C22×C4C22×D4711yescharacteristic
194C4⋊C4—944no—
195C4⋊C4—944no—
196C22⋊C4—22no—
197C22⋊C4—42no—
198C22⋊C4—942no—
199C22⋊C4—942no—
200C22⋊C4—942no—
201C22⋊C4—1882no—
202C22⋊C4—1882no—
203C22⋊C4—1882no—
204C42—474no—
205C42—944no—
206C23—21no—
207C23—22no—
208C23—22no—
209C23—21no—
210C23—21no—
211C23—941no—
212C23—942no—
213C23—942no—
214C23—941no—
215C23—941no—
216C23C23×D4711yescharacteristic
217Q8—44no—
218Q8—1884no—
219Q8—1884no—
220D4—1884no—
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—474no—
232C2×C4—472no—
233C2×C4—941no—
234C2×C4—941no—
235C2×C4—941no—
236C2×C4—942no—
237C2×C4—942no—
238C2×C4—942no—
239C2×C4—942no—
240C2×C4—942no—
241C2×C4—942no—
242C2×C4—942no—
243C2×C4D4×D4712yes—
244C22—42no—
245C22—42no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—1882no—
250C22—1882no—
251C22—1881no—
252C22—1881no—
253C22—1881no—
254C22C2×D4×D4711yescharacteristic
255C22#41×D4712yes—
256C22#1309406912yes—
257C22#1309407111yescharacteristic
258C22#1309407211yescharacteristic
259C4—22no—
260C4—42no—
261C4—41no—
262C4—42no—
263C4—474no—
264C4—942no—
265C4—1882no—
266C4—1881no—
267C4—1882no—
268C2—81no—
269C2—3761no—
270C2#124×D4711yescharacteristic
271C2#1568968811yescharacteristic
272C2#1568969611yescharacteristic
273C2#1568973712yes—
274C2#1568974312yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#393C2
hypercenter#393D47
hypocenterC47#2640
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#13094022C2semidirect
3. #15689052C2semidirect
4. #15689051C2semidirect
5. #15689036C2semidirect
6. #15689035C2semidirect
7. #15689034C2semidirect
8. #15689027C2semidirect
10. #15688968C2semidirect
11. C47×#393C2semidirect
145. #393D47semidirect
149. C47#2640semidirect