Finite Group Databasebeta

← #20254757

Subgroups — #20254757

Order 6016.

348 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#15689678C211yesmaximal, characteristic, complemented
2#15689655C211yesmaximal, characteristic
3#15689432C212yesmaximal, complemented
4#15689419C211yesmaximal, characteristic, complemented
5#15689413C211yesmaximal, characteristic, complemented
6#15689380C212yesmaximal, complemented
7#15689366C212yesmaximal
8#15689343C212yesmaximal, complemented
9#15689330C211yesmaximal, characteristic, complemented
10#15689145C211yesmaximal, characteristic, complemented
11C47×#461C211yesmaximal, characteristic, complemented
12C2×#10625337C2212yes—
13C2×#10625324C2212yes—
14#13094024C2211yescharacteristic
15#13094017—21no—
16#13094015—21no—
17#13094015C2211yescharacteristic
18#13094011C2211yescharacteristic
19#13094006—21no—
20#13094004—21no—
21#13094004C2211yescharacteristic
22#13094000C2212yes—
23#13093995C2211yescharacteristic
24Q8×Dic47C2212yes—
25C4×Dic94C2211yescharacteristic
26#13093989—21no—
27C4×C22⋊D47—21no—
28#13093983—21no—
29#13093982—21no—
30C42×D47C2211yescharacteristic
31#13093958C2212yes—
32#13093955C2212yes—
33C4⋊(C47⋊C8)C2211yescharacteristic
34Dic47⋊C8C2212yes—
35#13093949C2212yes—
36#13093948C2212yes—
37#13093945C2212yes—
38C2×SD16×C47C2212yes—
39C4⋊Q8×C47C2211yescharacteristic
40C4×D4×C47C2211yescharacteristic
41C4⋊C8×C47C2211yescharacteristic
42#103×C47C2212yes—
43C2×Q8×C47C2312yes—
44C2×D4×C47C2311yescharacteristic
45C22×C4×C47—21no—
46C2×C22⋊D47—21no—
47C2×C4×D47D411yescharacteristic
48C2×C4×D47D411yescharacteristic
49C2×C4×D47C2311yescharacteristic
50C2×Dic94—21no—
51C2×Dic94C2311yescharacteristic
52SD16×C47—42no—
53C2×C8×C47C2312yes—
54C4⋊C4×C47—21no—
55C4⋊C4×C47—21no—
56C4⋊C4×C47C2311yescharacteristic
57C22⋊C4×C47—21no—
58C42×C47C2311yescharacteristic
59C22⋊Dic47—21no—
60C22⋊Dic47—21no—
61C22⋊Dic47—21no—
62#10625337—42no—
63(C2×D47)⋊C4—22no—
64(C2×D47)⋊C4—21no—
65C4⋊Dic47—21no—
66C4⋊Dic47—21no—
67C4⋊Dic47—21no—
68C4⋊Dic47—22no—
69C4⋊Dic47C2312yes—
70C4⋊Dic47C2311yescharacteristic
71Dic47⋊C4—21no—
72Dic47⋊C4—21no—
73Dic47⋊C4—22no—
74C4×Dic47—21no—
75C4×Dic47—22no—
76C4×Dic47D411yescharacteristic
77C4×Dic47D411yescharacteristic
78C4×Dic47C2311yescharacteristic
79C2×C47⋊C8C2312yes—
80#10625324—42no—
81C23×C47—21no—
82C22×D47C2×D411yescharacteristic
83Q8×C47—22no—
84Q8×C47—22no—
85D4×C47—21no—
86D4×C47—21no—
87C2×C4×C47—22no—
88C2×C4×C47—21no—
89C2×C4×C47—42no—
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47C2411yescharacteristic
93C22⋊D47—42no—
94C2×Dic47—21no—
95C2×Dic47—22no—
96C2×Dic47—21no—
97C2×Dic47C2×D411yescharacteristic
98C2×Dic47C2×D411yescharacteristic
99C2×Dic47C2×D411yescharacteristic
100C4×D47—22no—
101C4×D47—21no—
102C4×D47—21no—
103C4×D47—41no—
104Dic94—21no—
105Dic94—21no—
106Dic94—42no—
107C8×C47—22no—
108C47⋊C8—22no—
109C22×C47—41no—
110C22×C47—41no—
111C22×C47—41no—
112C22×C47C22×D411yescharacteristic
113C2×D47—21no—
114C2×D47—21no—
115C2×D47—21no—
116C4×C47—21no—
117C4×C47—42no—
118C4×C47—41no—
119C4×C47#13712yes—
120C4×C47H(5,𝔽2)11yescharacteristic
121C4×C472−1+411yescharacteristic
122Dic47—21no—
123Dic47—21no—
124Dic47—21no—
125Dic47—41no—
126Dic47—42no—
127Dic47—41no—
128#3252—471nomaximal, Sylow
129C2×C47—81no—
130C2×C47#53711yescharacteristic
131C2×C47C2×#13711yescharacteristic
132C2×C47#57511yescharacteristic
133D47—41no—
134#533—471no—
135#529—471no—
136#479—472no—
137#477—471no—
138#476—471no—
139#470—472no—
140#468—472no—
141#464—472no—
142#462—471no—
143#461D4711yescharacteristic, complemented
144#423—471no—
145C47#325211yescharacteristic, complemented, Sylow
146C2×Q16—472no—
147C2×SD16C2×D4712yes—
148C2×M16—472no—
149C4⋊Q8—471no—
150C4⋊Q8C2×D4711yescharacteristic
151#126—941no—
152#125—471no—
153#125—941no—
154#124—471no—
155#123—941no—
156C22⋊Q8—472no—
157C22⋊Q8—471no—
158C22⋊Q8—941no—
159#121—471no—
160C4×Q8—472no—
161C4×Q8—471no—
162C4×Q8—941no—
163C4×D4—941no—
164C4×D4C2×D4711yescharacteristic
165#117—941no—
166#117—941no—
167C2×C42—471no—
168#107—472no—
169#106—472no—
170C4⋊C8—472no—
171C4⋊C8—471no—
172C4⋊C8C2×D4711yescharacteristic
173#103—472no—
174#103—472no—
175#103C2×D4712yes—
176#102—472no—
177C2×Q8—471no—
178C2×Q8—941no—
179C2×Q8C22×D4712yes—
180C2×D4—941no—
181C2×D4C22×D4711yescharacteristic
182C22×C4—21no—
183C22×C4—471no—
184C22×C4—471no—
185C22×C4—471no—
186Q16—1882no—
187SD16—42no—
188M16—1882no—
189C2×C8—472no—
190C2×C8C22×D4712yes—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—472no—
194C4⋊C4—471no—
195C4⋊C4—941no—
196C4⋊C4—942no—
197C4⋊C4—941no—
198C4⋊C4—941no—
199C4⋊C4—942no—
200C4⋊C4—941no—
201C4⋊C4—941no—
202C4⋊C4C22×D4711yescharacteristic
203C22⋊C4—21no—
204C22⋊C4—942no—
205C22⋊C4—941no—
206C22⋊C4—941no—
207C22⋊C4—941no—
208C22⋊C4—941no—
209C42—471no—
210C42—471no—
211C42—471no—
212C42—942no—
213C42—941no—
214C42C22×D4711yescharacteristic
215C23—21no—
216C23—471no—
217Q8—22no—
218Q8—22no—
219Q8—941no—
220Q8—941no—
221Q8—1882no—
222D4—21no—
223D4—21no—
224D4—1882no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—471no—
229C2×C4—471no—
230C2×C4—471no—
231C2×C4—942no—
232C2×C4—941no—
233C2×C4—941no—
234C2×C4—941no—
235C2×C4—941no—
236C2×C4—942no—
237C2×C4—1881no—
238C2×C4D4×D4711yescharacteristic
239C2×C4D4×D4711yescharacteristic
240C2×C4C23×D4711yescharacteristic
241C8—22no—
242C8—942no—
243C22—41no—
244C22—41no—
245C22—41no—
246C22—941no—
247C22—941no—
248C22—941no—
249C22C2×D4×D4711yescharacteristic
250C4—21no—
251C4—41no—
252C4—42no—
253C4—941no—
254C4—941no—
255C4—941no—
256C4—1881no—
257C4—1882no—
258C4—1881no—
259C4#1309405312yes—
260C4#1309406911yescharacteristic
261C4#1309407111yescharacteristic
262C2—81no—
263C2—1881no—
264C2#1568970211yescharacteristic
265C2C2×#1309405311yescharacteristic
266C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#461C2
socleC22×C47C22×D4
hypercenter#461D47
hypocenterC47#3252
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #15689678C2semidirect
3. #15689432C2semidirect
4. #15689419C2semidirect
5. #15689413C2semidirect
6. #15689380C2semidirect
8. #15689343C2semidirect
9. #15689330C2semidirect
10. #15689145C2semidirect
11. C47×#461C2semidirect
143. #461D47semidirect
145. C47#3252semidirect