Finite Group Databasebeta

← #29577565

Subgroups — #29577565

Order 15616.

620 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 95 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#21456269C211yesmaximal, characteristic
2#21448996C211yesmaximal, characteristic, complemented
3#21444367C212yesmaximal, complemented
4#21443685C212yesmaximal, complemented
5C61×#1555C211yesmaximal, characteristic, complemented
6C2×#14519803—22no—
7#16840312C2211yescharacteristic
8#16840149—22no—
9#16840138C412yescomplemented
10#16840134C412yescomplemented
11C4×#11758194C2211yescharacteristic
12#16839642—24no—
13#16839642—22no—
14#16839630C2212yes—
15#16839497—24no—
16C2×#127×C61C2211yescharacteristic
17C61×#432C2212yes—
18C61×#331—22no—
19C2×#11758222—21no—
20C23×Dic61—22no—
21#14519803—44no—
22#14519803—44no—
23C2×#11758200—24no—
24C2×#11758199—24no—
25C2×#11758194—21no—
26#14519777C2×C411yescharacteristic, complemented
27#14519774C2×C411yescharacteristic, complemented
28#14519765—21no—
29#14519751—22no—
30C4×D244—22no—
31C2×C22⋊Dic61—24no—
32C2×C22⋊Dic61—22no—
33#14519688—21no—
34C4×#92418C2×C412yescomplemented
35#14519684—22no—
36#14519684—22no—
37#14519684D414yes—
38C22×D4×C61—22no—
39C22×D4×C61D412yes—
40#127×C61—22no—
41#127×C61C2×C412yes—
42#127×C61D412yes—
43C2×C42×C61C2311yescharacteristic
44C4⋊C8×C61—22no—
45C22⋊C8×C61—22no—
46#97×C61—22no—
47C24×C61—22no—
48C2×D4×C61—24no—
49C2×D4×C61—24no—
50C2×D4×C61—22no—
51C2×D4×C61—42no—
52C2×D4×C61—42no—
53C2×D4×C61—82no—
54C2×D4×C61—82no—
55C2×D4×C61C22⋊C414yes—
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61C2×D412yes—
58C2×C22⋊D61—41no—
59C22×Dic61—24no—
60C22×Dic61—84no—
61C22×Dic61—82no—
62#11758222—42no—
63#11758222—42no—
64C2×D244—21no—
65C2×D244—22no—
66C2×C4×D61—41no—
67C2×Dic122—21no—
68C2×C8×C61—42no—
69C42×C61C22×C411yescharacteristic
70C42×C61C2×D411yescharacteristic
71C42×C61#4112yes—
72C22⋊Dic61—84no—
73C22⋊Dic61—82no—
74#11758200—48no—
75#11758199—48no—
76#11758198—42no—
77C4⋊Dic61—22no—
78#11758194—24no—
79C2×#92418—22no—
80C23×C61—24no—
81C23×C61—44no—
82C23×C61—44no—
83C23×C61—42no—
84C23×C61—42no—
85C23×C61#12011yescharacteristic
86C22×D61—41no—
87D4×C61—44no—
88D4×C61—82no—
89D4×C61—84no—
90D4×C61—84no—
91C2×C4×C61—22no—
92C2×C4×C61—42no—
93C2×C4×C61C2×C22⋊C411yescharacteristic
94C2×C4×C61C4×D412yes—
95C2×C4×C61#12112yes—
96C2×C4×C61#12311yescharacteristic
97C22⋊D61—82no—
98C2×Dic61—48no—
99C2×Dic61—41no—
100C2×Dic61—44no—
101C2×Dic61—88no—
102D244—42no—
103D244—82no—
104C4×D61—81no—
105C4×D61—81no—
106Dic122—42no—
107C8×C61—82no—
108#92418—24no—
109#9428—611nomaximal, Sylow
110C22×C61—22no—
111C22×C61—44no—
112C22×C61—48no—
113C22×C61—82no—
114C22×C61—82no—
115C22×C61—84no—
116C22×C61#38611yescharacteristic
117C22×C61#45312yes—
118C2×D61—81no—
119C2×D61—82no—
120C4×C61—21no—
121C4×C61—21no—
122C4×C61—22no—
123C4×C61—22no—
124Dic61—84no—
125Dic61—81no—
126#3151—611no—
127#2380—611no—
128#1555D6111yescharacteristic, complemented
129#1514—612no—
130#1288—612no—
131C2×C61—22no—
132C2×C61—84no—
133C2×C61#188711yescharacteristic
134C2×C61#190412yes—
135D61—161no—
136C2×AGL(1,ℤ/8)—1222no—
137#532—611no—
138C2×#127C2×D6111yescharacteristic
139#496—1222no—
140#493—612no—
141#492—612no—
142#432C2×D6112yes—
143C4×M16—611no—
144#386—1224no—
145#386—1222no—
146#383—612no—
147#331—22no—
148#327—1224no—
149C61#942811yescharacteristic, complemented, Sylow
150C2×#41—1221no—
151C22×D4—22no—
152C22×D4D24412yes—
153C23×C4—1222no—
154AGL(1,ℤ/8)—2444no—
155AGL(1,ℤ/8)—2444no—
156C2×SD16—1224no—
157C2×D8—1224no—
158C2×M16—1221no—
159C4⋊Q8—611no—
160#127—22no—
161#127—611no—
162#127C4×D6112yes—
163#127C22⋊D6112yes—
164#124—1221no—
165#121—1222no—
166C4×D4—1222no—
167C2×C22⋊C4—1224no—
168C2×C22⋊C4—1222no—
169C2×C42C22×D6111yescharacteristic
170C4⋊C8—22no—
171C22⋊C8—22no—
172#97—22no—
173#97—1221no—
174C4×C8—612no—
175#95—614no—
176#95—1222no—
177#95—1222no—
178C24—22no—
179#41—2442no—
180#41—2442no—
181C2×Q8—1221no—
182C2×D4—24no—
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—42no—
186C2×D4—42no—
187C2×D4—82no—
188C2×D4—82no—
189C2×D4—1221no—
190C2×D4—1222no—
191C2×D4—2441no—
192C2×D4#1175819814yes—
193C22×C4—1224no—
194C22×C4—4884no—
195C22×C4—4882no—
196C22×C4—2441no—
197C22×C4C2×D24411yescharacteristic
198C22×C4D4×D6112yes—
199SD16—2448no—
200D8—2448no—
201M16—1224no—
202C2×C8—42no—
203C2×C8—1222no—
204C4⋊C4—1222no—
205C22⋊C4—4884no—
206C22⋊C4—4882no—
207C22⋊C4—2442no—
208C42C2×C4×D6111yescharacteristic
209C42#1175822412yes—
210C42C2×C22⋊D6111yescharacteristic
211C23—24no—
212C23—44no—
213C23—44no—
214C23—42no—
215C23—42no—
216C23—2441no—
217C23#1451974711yescharacteristic
218Q8—2442no—
219D4—44no—
220D4—82no—
221D4—84no—
222D4—84no—
223D4—4882no—
224D4—4882no—
225D4—2442no—
226C2×C4—22no—
227C2×C4—42no—
228C2×C4—4881no—
229C2×C4—4881no—
230C2×C4—4888no—
231C2×C4—2448no—
232C2×C4—2441no—
233C2×C4—2444no—
234C2×C4C2×#1175819811yescharacteristic
235C2×C4#1451973712yes—
236C2×C4#1451974912yes—
237C2×C4#1451976111yescharacteristic
238C8—82no—
239C8—1224no—
240C22—22no—
241C22—44no—
242C22—48no—
243C22—82no—
244C22—82no—
245C22—84no—
246C22—4881no—
247C22—4882no—
248C22#1683963911yescharacteristic
249C22#1683993212yes—
250C4—21no—
251C4—21no—
252C4—22no—
253C4—22no—
254C4—4884no—
255C4—4881no—
256C2—22no—
257C2—84no—
258C2—9761no—
259C2#2144621511yescharacteristic
260C2#2144630412yes—
subgroupG/H
centerC22#16839639
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1555C2
socleC22×C61#386
prime radical#21456269C2
cosocleC2×C42×C61C23
hypercenter#1555D61
hypocenterC61#9428
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1555

Complements

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

NH ≅ G/Ntype
2. #21448996C2semidirect
3. #21444367C2semidirect
4. #21443685C2semidirect
5. C61×#1555C2semidirect
9. #16840138C4semidirect
10. #16840134C4semidirect
26. #14519777C2×C4semidirect
27. #14519774C2×C4semidirect
34. C4×#92418C2×C4semidirect
128. #1555D61semidirect
149. C61#9428semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214562692
#214489962
#214443672
#214436852
C61×#15552
#942861