Finite Group Databasebeta

← #30604078

Subgroups — #30604078

Order 15616.

662 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 80 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#21461070C212yesmaximal, complemented
2#21460745C212yesmaximal, complemented
3#21460743C212yesmaximal
4#21448202C211yesmaximal, characteristic
5#16840782—22no—
6#16840607—22no—
7#16840605C2214yes—
8C2×#14519736C411yescharacteristic
9C2×#14519736C2211yescharacteristic
10#16839625C411yescharacteristic
11#16839625C2211yescharacteristic
12#16839622—22no—
13#16839618C411yescharacteristic
14#16839618C2211yescharacteristic
15C4×C22⋊Dic61—22no—
16C24×C4×C61C411yescharacteristic
17#14519844—42no—
18C22⋊#92420—24no—
19#14519832—42no—
20#14519736—42no—
21#14519736—42no—
22C2×C4⋊Dic61—21no—
23C2×C4⋊Dic61D412yes—
24C2×C22⋊Dic61—22no—
25C2×C22⋊Dic61—22no—
26C2×C22⋊Dic61C2×C411yescharacteristic
27C2×C22⋊Dic61C2×C411yescharacteristic
28C2×C22⋊Dic61C2×C411yescharacteristic
29C2×C22⋊Dic61C2311yescharacteristic
30C2×C4×Dic61—21no—
31C2×C4×Dic61D412yes—
32#14519684—22no—
33#14519684—22no—
34C25×C61C2×C411yescharacteristic
35C23×C4×C61—22no—
36C23×C4×C61—21no—
37C23×C4×C61—21no—
38C23×C4×C61—22no—
39C23×C4×C61—42no—
40C23×C4×C61—42no—
41C23×C4×C61C2×C411yescharacteristic
42C23×C4×C61C2×C411yescharacteristic
43C24×C61—21no—
44C24×C61—21no—
45C24×C61—41no—
46C24×C61—41no—
47C24×C61—44no—
48C24×C61M1612yes—
49C24×C61C22×C411yescharacteristic
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61—22no—
53C22×C4×C61—22no—
54C22×C4×C61—24no—
55C22×C4×C61—24no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—48no—
59C22×C4×C61—48no—
60C22×C4×C61—42no—
61C22×C4×C61—42no—
62C22×C4×C61—42no—
63C22×C4×C61—42no—
64C22×C4×C61—41no—
65C22×C4×C61—41no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61M1612yes—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61C22⋊C412yes—
72C22×Dic61C2×D412yes—
73C2×#92420—44no—
74C22⋊Dic61—41no—
75C22⋊Dic61—41no—
76C22⋊Dic61—44no—
77C22⋊Dic61—44no—
78C22⋊Dic61—41no—
79C22⋊Dic61—41no—
80C4⋊Dic61—42no—
81C4⋊Dic61—42no—
82C4×Dic61—22no—
83C4×Dic61—22no—
84C4×Dic61—42no—
85C23×C61—24no—
86C23×C61—22no—
87C23×C61—21no—
88C23×C61—21no—
89C23×C61—42no—
90C23×C61—42no—
91C23×C61—44no—
92C23×C61—42no—
93C23×C61—44no—
94C23×C61—42no—
95C23×C61—48no—
96C23×C61—44no—
97C23×C61—41no—
98C23×C61—41no—
99C23×C61—44no—
100C23×C61C2×C22⋊C411yescharacteristic
101C23×C61C2×M1611yescharacteristic
102C23×C61C2×M1611yescharacteristic
103C2×C4×C61—24no—
104C2×C4×C61—24no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—22no—
110C2×C4×C61—48no—
111C2×C4×C61—48no—
112C2×C4×C61—42no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—42no—
116C2×C4×C61#9912yes—
117C2×C4×C61#10012yes—
118C2×Dic61—22no—
119C2×Dic61—22no—
120C2×Dic61—42no—
121C2×Dic61—42no—
122C2×Dic61—42no—
123C2×Dic61—42no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126#92420—84no—
127#11501—611nomaximal, Sylow
128C22×C61—22no—
129C22×C61—24no—
130C22×C61—21no—
131C22×C61—21no—
132C22×C61—41no—
133C22×C61—41no—
134C22×C61—44no—
135C22×C61—42no—
136C22×C61—42no—
137C22×C61—44no—
138C22×C61—48no—
139C22×C61—44no—
140C22×C61—44no—
141C22×C61—42no—
142C22×C61—42no—
143C22×C61#40711yescharacteristic
144C22×C61C2×#9911yescharacteristic
145C22×C61C2×#10011yescharacteristic
146C4×C61—22no—
147C4×C61—22no—
148C4×C61—42no—
149Dic61—42no—
150Dic61—42no—
151Dic61—81no—
152Dic61—81no—
153#2280—611no—
154#1464—612no—
155#1317—612no—
156#1316—612no—
157C2×C61—21no—
158C2×C61—21no—
159C2×C61—44no—
160C2×C61—41no—
161C2×C61—41no—
162C2×C61#146211yescharacteristic
163C2×C61#212012yes—
164C24×C4#692311yescharacteristic
165C2×#117—611no—
166C2×#117—611no—
167#432—1222no—
168#381—611no—
169#381—611no—
170#380—1222no—
171#379—611no—
172#379—611no—
173C4×C22⋊C4—1222no—
174#324—1222no—
175#323—614no—
176C61#1150111yescharacteristic, complemented, Sylow
177C25C2×#692311yescharacteristic
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—42no—
183C23×C4—42no—
184C23×C4C2×#692311yescharacteristic
185C23×C4C2×#692311yescharacteristic
186#117—2442no—
187#117—2442no—
188C2×C4⋊C4—612no—
189C2×C4⋊C4—1221no—
190C2×C22⋊C4—611no—
191C2×C22⋊C4—611no—
192C2×C22⋊C4—611no—
193C2×C22⋊C4—611no—
194C2×C22⋊C4—1222no—
195C2×C22⋊C4—1222no—
196C2×C42—612no—
197C2×C42—1221no—
198C4⋊C8—2442no—
199C22⋊C8—1224no—
200#97—2442no—
201#95—1222no—
202#95—1222no—
203C24—21no—
204C24—21no—
205C24—41no—
206C24—41no—
207C24—44no—
208C24#1175821712yes—
209C24C22×#692311yescharacteristic
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—24no—
215C22×C4—24no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—48no—
219C22×C4—48no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—612no—
227C22×C4—612no—
228C22×C4—1221no—
229C22×C4—1221no—
230C22×C4#1175821712yes—
231C22×C4C22⋊#692311yescharacteristic
232C22×C4C22⋊#692311yescharacteristic
233C2×C8—2444no—
234C4⋊C4—2442no—
235C4⋊C4—2442no—
236C22⋊C4—2441no—
237C22⋊C4—2441no—
238C22⋊C4—2444no—
239C22⋊C4—2444no—
240C22⋊C4—2441no—
241C22⋊C4—2441no—
242C42—1222no—
243C42—1222no—
244C42—2442no—
245C23—24no—
246C23—22no—
247C23—21no—
248C23—21no—
249C23—42no—
250C23—44no—
251C23—42no—
252C23—42no—
253C23—42no—
254C23—44no—
255C23—44no—
256C23—48no—
257C23—44no—
258C23—41no—
259C23—41no—
260C23C2×C22⋊#692311yescharacteristic
261C23C2×#1175821711yescharacteristic
262C23C2×#1175821711yescharacteristic
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—48no—
271C2×C4—48no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—1222no—
277C2×C4—1222no—
278C2×C4—2442no—
279C2×C4—2442no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2442no—
283C2×C4—2442no—
284C2×C4#1451983512yes—
285C2×C4#1451983712yes—
286C8—4884no—
287C22—22no—
288C22—24no—
289C22—21no—
290C22—21no—
291C22—41no—
292C22—41no—
293C22—44no—
294C22—42no—
295C22—42no—
296C22—44no—
297C22—44no—
298C22—48no—
299C22—44no—
300C22—42no—
301C22—42no—
302C22#1684073211yescharacteristic
303C22C2×#1451983511yescharacteristic
304C22C2×#1451983711yescharacteristic
305C4—22no—
306C4—22no—
307C4—42no—
308C4—4881no—
309C4—4881no—
310C4—2442no—
311C4—2442no—
312C2—21no—
313C2—21no—
314C2—44no—
315C2—41no—
316C2—41no—
317C2#2146106411yescharacteristic
318C2#2146207012yes—
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#11501
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. #21461070C2semidirect
2. #21460745C2semidirect
176. C61#11501semidirect

Maximal subgroups

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

subgroupindex
#214610702
#214607452
#214607432
#214482022
#1150161