Finite Group Databasebeta

← #30604143

Subgroups — #30604143

Order 15616.

418 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461070C211yesmaximal, characteristic
2#21461070C211yesmaximal, characteristic
3#21460764C214yesmaximal
4#21448443C211yesmaximal, characteristic
5#16840782—21no—
6#16840782—21no—
7#16840607—21no—
8#16840607—21no—
9#16840605C2212yes—
10#16840605C2212yes—
11C2×#14519736C411yescharacteristic
12C2×#14519736C2211yescharacteristic
13#16839658—21no—
14#16839658—21no—
15#16839635C412yes—
16#16839635C2212yes—
17#16839631—21no—
18#16839627—21no—
19C22×C4⋊C4×C61C411yescharacteristic
20#14519844—41no—
21#14519844—41no—
22C22⋊#92420—22no—
23C22⋊#92420—22no—
24#14519832—41no—
25#14519832—41no—
26#14519736—24no—
27#14519736—41no—
28#14519736—41no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61D411yescharacteristic
31C2×C4⋊Dic61D411yescharacteristic
32C2×#11758196—22no—
33C2×#11758196—22no—
34C2×C22⋊Dic61C2×C412yes—
35C2×C22⋊Dic61C2×C411yescharacteristic
36C2×C22⋊Dic61C2311yescharacteristic
37C2×C4×Dic61—21no—
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40#14519684—22no—
41#14519684—22no—
42C23×C4×C61C2×C412yes—
43C23×C4×C61C2×C411yescharacteristic
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—41no—
47C2×C4⋊C4×C61—41no—
48C24×C61C22×C411yescharacteristic
49C22×C4×C61—22no—
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61—22no—
53C22×C4×C61—22no—
54C22×C4×C61—42no—
55C22×C4×C61—82no—
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22⋊C411yescharacteristic
58C22×Dic61—22no—
59C22×Dic61C22⋊C411yescharacteristic
60C22×Dic61C22⋊C411yescharacteristic
61C22×Dic61C2×D411yescharacteristic
62C22×Dic61C2×D411yescharacteristic
63C2×#92420—42no—
64C2×#92420—42no—
65C4⋊C4×C61—42no—
66C4⋊C4×C61—41no—
67C4⋊C4×C61—41no—
68C22⋊Dic61—22no—
69C22⋊Dic61—41no—
70C22⋊Dic61—41no—
71C22⋊Dic61M1614yes—
72C4⋊Dic61—24no—
73C4⋊Dic61—41no—
74C4⋊Dic61—41no—
75#11758196—82no—
76#11758196—82no—
77C4×Dic61—24no—
78C4×Dic61—21no—
79C4×Dic61—21no—
80C4×Dic61—21no—
81C4×Dic61—21no—
82C23×C61—21no—
83C23×C61—21no—
84C23×C61—41no—
85C23×C61—41no—
86C23×C61C2×C22⋊C411yescharacteristic
87C23×C61C2×M1612yes—
88C2×C4×C61—24no—
89C2×C4×C61—24no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—42no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61—84no—
98C2×C4×C61#9911yescharacteristic
99C2×C4×C61#9911yescharacteristic
100C2×C4×C61#10112yes—
101C2×Dic61—24no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—42no—
107C2×Dic61—42no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112#92420—82no—
113#92420—82no—
114#11520—611nomaximal, Sylow
115C22×C61—21no—
116C22×C61—21no—
117C22×C61—22no—
118C22×C61—42no—
119C22×C61—42no—
120C22×C61—41no—
121C22×C61—41no—
122C22×C61#40711yescharacteristic
123C22×C61C2×#9911yescharacteristic
124C22×C61C2×#10111yescharacteristic
125C4×C61—21no—
126C4×C61—21no—
127C4×C61—22no—
128C4×C61—82no—
129Dic61—44no—
130Dic61—41no—
131Dic61—41no—
132Dic61—41no—
133Dic61—41no—
134#2317—611no—
135#1464—611no—
136#1464—611no—
137#1326—614no—
138C2×C61—21no—
139C2×C61—21no—
140C2×C61—42no—
141C2×C61#146311yescharacteristic
142C2×C61#212211yescharacteristic
143C2×C61#212311yescharacteristic
144C2×#117—611no—
145C2×#117—611no—
146C22×C4⋊C4#692311yescharacteristic
147#432—1221no—
148#432—1221no—
149#389—1221no—
150#389—1221no—
151#385—612no—
152#385—612no—
153#384—1221no—
154#382—1221no—
155#324—1221no—
156#324—1221no—
157#323—612no—
158#323—612no—
159C61#1152011yescharacteristic, complemented, Sylow
160C23×C4C2×#692312yes—
161C23×C4C2×#692311yescharacteristic
162#117—1224no—
163#117—2441no—
164#117—2441no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4—611no—
170C2×C4⋊C4—611no—
171C2×C4⋊C4—1221no—
172C2×C4⋊C4—1222no—
173C2×C4⋊C4—1222no—
174C2×C22⋊C4—612no—
175C2×C22⋊C4—611no—
176C2×C22⋊C4—611no—
177C2×C42—611no—
178C2×C42—611no—
179C2×C42—1221no—
180C4⋊C8—2441no—
181C4⋊C8—2441no—
182C22⋊C8—1222no—
183C22⋊C8—1222no—
184#97—2441no—
185#97—2441no—
186#95—1222no—
187#95—1222no—
188C24C22×#692311yescharacteristic
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—42no—
195C22×C4—82no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—1222no—
201C22×C4C22⋊#692311yescharacteristic
202C22×C4C22⋊#692311yescharacteristic
203C2×C8—2442no—
204C2×C8—2442no—
205C4⋊C4—42no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—1224no—
209C4⋊C4—4882no—
210C4⋊C4—4882no—
211C4⋊C4—2441no—
212C4⋊C4—2441no—
213C22⋊C4—614no—
214C22⋊C4—1222no—
215C22⋊C4—2441no—
216C22⋊C4—2441no—
217C42—1224no—
218C42—1221no—
219C42—1221no—
220C42—1221no—
221C42—1221no—
222C23—21no—
223C23—21no—
224C23—41no—
225C23—41no—
226C23C2×C22⋊#692311yescharacteristic
227C23D61⋊M1612yes—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—84no—
238C2×C4—1224no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—2442no—
244C2×C4—2442no—
245C2×C4—2441no—
246C2×C4—2441no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4#1451983511yescharacteristic
250C2×C4#1451983511yescharacteristic
251C2×C4#1451983812yes—
252C8—4882no—
253C8—4882no—
254C22—21no—
255C22—21no—
256C22—22no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22#1684073411yescharacteristic
262C22C2×#1451983511yescharacteristic
263C22C2×#1451983811yescharacteristic
264C4—21no—
265C4—21no—
266C4—22no—
267C4—82no—
268C4—2444no—
269C4—2441no—
270C4—2441no—
271C4—2441no—
272C4—2441no—
273C2—21no—
274C2—21no—
275C2—42no—
276C2#2146106911yescharacteristic
277C2#2146207811yescharacteristic
278C2#2146208111yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC22×C61C2×#99
cosocleC2×C22⋊Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#11520
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
159. C61#11520semidirect

Maximal subgroups

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

subgroupindex
#214610702
#214607642
#214484432
#1152061