Finite Group Databasebeta

← #30604075

Subgroups — #30604075

Order 15616.

706 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 88 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#21461064C212yesmaximal
2#21460745C214yesmaximal, complemented
3C2×#16839625C211yesmaximal, characteristic
4#16840732—22no—
5#16840605—22no—
6#16840605C2214yes—
7C22×C22⋊Dic61C411yescharacteristic
8C22×C22⋊Dic61C2211yescharacteristic
9#16839625—22no—
10#16839625C412yes—
11#16839625C2212yes—
12C2×#14519684—22no—
13C24×C4×C61C411yescharacteristic
14C2×#11758217—42no—
15C22⋊#92420—24no—
16C22⋊#92420—42no—
17C23×Dic61—21no—
18C23×Dic61D412yes—
19C2×C22⋊Dic61—21no—
20C2×C22⋊Dic61—42no—
21C2×C22⋊Dic61—42no—
22C2×C22⋊Dic61C2×C412yes—
23C2×C22⋊Dic61C2×C411yescharacteristic
24C2×C22⋊Dic61D412yes—
25C2×C22⋊Dic61C2311yescharacteristic
26#14519684—24no—
27#14519684—24no—
28C25×C61C2×C411yescharacteristic
29C23×C4×C61—21no—
30C23×C4×C61—21no—
31C23×C4×C61—24no—
32C23×C4×C61—42no—
33C23×C4×C61—42no—
34C23×C4×C61C2×C412yes—
35C24×C61—22no—
36C24×C61—22no—
37C24×C61—22no—
38C24×C61—44no—
39C24×C61C22⋊C411yescharacteristic
40C24×C61C22⋊C411yescharacteristic
41C24×C61C22×C411yescharacteristic
42C22×C4×C61—24no—
43C22×C4×C61—24no—
44C22×C4×C61—22no—
45C22×C4×C61—22no—
46C22×C4×C61—416no—
47C22×C4×C61—42no—
48C22×C4×C61—42no—
49C22×C4×C61—42no—
50C22×C4×C61—42no—
51C22×C4×C61—42no—
52C22×C4×C61—42no—
53C22×C4×C61M1614yescomplemented
54C22×Dic61—22no—
55C22×Dic61—22no—
56C22×Dic61—22no—
57C22×Dic61—44no—
58C22×Dic61—44no—
59C22×Dic61—42no—
60C22×Dic61C22⋊C412yes—
61C22×Dic61C2×D412yes—
62#11758217—84no—
63C2×#92420—44no—
64C22⋊Dic61—41no—
65C22⋊Dic61—42no—
66C22⋊Dic61—41no—
67C22⋊Dic61—42no—
68C22⋊Dic61—42no—
69C23×C61—24no—
70C23×C61—21no—
71C23×C61—21no—
72C23×C61—28no—
73C23×C61—21no—
74C23×C61—21no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—48no—
78C23×C61—48no—
79C23×C61—44no—
80C23×C61—42no—
81C23×C61—42no—
82C23×C61—44no—
83C23×C61#9912yes—
84C23×C61#10012yes—
85C23×C61C2×C22⋊C411yescharacteristic
86C23×C61C2×M1612yes—
87C2×C4×C61—24no—
88C2×C4×C61—48no—
89C2×C4×C61—48no—
90C2×C4×C61—44no—
91C2×C4×C61—42no—
92C2×C4×C61—42no—
93C2×C4×C61—44no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—44no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61—44no—
100C2×Dic61—42no—
101C2×Dic61—82no—
102C2×Dic61—84no—
103#92420—84no—
104#11500—611nomaximal, Sylow
105C22×C61—24no—
106C22×C61—24no—
107C22×C61—22no—
108C22×C61—22no—
109C22×C61—22no—
110C22×C61—22no—
111C22×C61—22no—
112C22×C61—42no—
113C22×C61—42no—
114C22×C61—42no—
115C22×C61—416no—
116C22×C61—42no—
117C22×C61—42no—
118C22×C61—42no—
119C22×C61#35214yes—
120C22×C61#40711yescharacteristic
121C22×C61C2×#9911yescharacteristic
122C22×C61C2×#10011yescharacteristic
123C4×C61—44no—
124Dic61—42no—
125Dic61—42no—
126Dic61—82no—
127C2×#381—611no—
128#1462—612no—
129#1317—614no—
130C2×C61—21no—
131C2×C61—24no—
132C2×C61—21no—
133C2×C61—42no—
134C2×C61—42no—
135C2×C61#146211yescharacteristic
136C2×C61C2×#35212yes—
137C24×C4#692311yescharacteristic
138C22×C22⋊C4—611no—
139C22×C22⋊C4—611no—
140#407—1222no—
141#381—612no—
142#381—612no—
143#381—1222no—
144C2×#95—1222no—
145#323—614no—
146#323—1222no—
147C61#1150011yescharacteristic, complemented, Sylow
148C25C2×#692311yescharacteristic
149C23×C4—21no—
150C23×C4—21no—
151C23×C4—24no—
152C23×C4—42no—
153C23×C4—42no—
154C23×C4—612no—
155C23×C4—1221no—
156C23×C4C2×#692312yes—
157C2×M16—2442no—
158C2×C22⋊C4—612no—
159C2×C22⋊C4—611no—
160C2×C22⋊C4—611no—
161C2×C22⋊C4—612no—
162C2×C22⋊C4—1221no—
163C2×C22⋊C4—2442no—
164C2×C22⋊C4—2442no—
165C22⋊C8—1224no—
166C22⋊C8—2442no—
167#95—1224no—
168#95—1224no—
169C24—22no—
170C24—22no—
171C24—22no—
172C24—44no—
173C24C22⋊#692311yescharacteristic
174C24C22⋊#692311yescharacteristic
175C24C22×#692311yescharacteristic
176C22×C4—24no—
177C22×C4—24no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—416no—
181C22×C4—42no—
182C22×C4—42no—
183C22×C4—42no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4—612no—
188C22×C4—612no—
189C22×C4—1222no—
190C22×C4—1222no—
191C22×C4—1222no—
192C22×C4—2442no—
193C22×C4—2444no—
194C22×C4—2444no—
195C22×C4#1175821714yescomplemented
196M16—4884no—
197C2×C8—2444no—
198C22⋊C4—2441no—
199C22⋊C4—2442no—
200C22⋊C4—2441no—
201C22⋊C4—2442no—
202C22⋊C4—2442no—
203C23—21no—
204C23—21no—
205C23—24no—
206C23—28no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—42no—
212C23—42no—
213C23—48no—
214C23—48no—
215C23—44no—
216C23—44no—
217C23#1451983512yes—
218C23#1451983712yes—
219C23C2×C22⋊#692311yescharacteristic
220C23C2×#1175821712yes—
221C2×C4—24no—
222C2×C4—48no—
223C2×C4—48no—
224C2×C4—44no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—44no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4—4884no—
231C2×C4—4882no—
232C2×C4—2444no—
233C2×C4—2442no—
234C2×C4—2444no—
235C2×C4—2442no—
236C2×C4—2442no—
237C8—4884no—
238C22—24no—
239C22—24no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—42no—
249C22—416no—
250C22—42no—
251C22—42no—
252C22#1684066414yes—
253C22#1684073211yescharacteristic
254C22C2×#1451983511yescharacteristic
255C22C2×#1451983711yescharacteristic
256C4—44no—
257C4—4882no—
258C4—2442no—
259C4—2442no—
260C2—21no—
261C2—21no—
262C2—24no—
263C2—42no—
264C2—42no—
265C2#2146106411yescharacteristic
266C2C2×#1684066412yes—
subgroupG/H
centerC22C2×#14519835
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC24×C4×C61C4
socleC22×C61C2×#99
prime radicalC25×C61C2×C4
cosocleC2×C22⋊Dic61C23
hypercenterC24×C4#6923
hypocenterC61#11500
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C25 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
2. #21460745C2semidirect
53. C22×C4×C61M16semidirect
147. C61#11500semidirect
195. C22×C4#11758217semidirect

Maximal subgroups

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

subgroupindex
#214610642
#214607452
C2×#168396252
#1150061