Finite Group Databasebeta

← #30604080

Subgroups — #30604080

Order 15616.

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

normal subgroups only

This group has 662 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#21461070C212yesmaximal, complemented
2#21460746C212yesmaximal, complemented
3#21460744C212yesmaximal
4#21448198C211yesmaximal, characteristic
5#16840782—22no—
6#16840607—22no—
7#16840605C2214yes—
8C23×C4×D61C411yescharacteristic
9C2×#14519736C2211yescharacteristic
10#16839623C411yescharacteristic
11#16839623C2211yescharacteristic
12#16839619—22no—
13#16839617C411yescharacteristic
14#16839617C2211yescharacteristic
15C4×#11758198—22no—
16C2×#117×C61C411yescharacteristic
17#14519844—42no—
18C22⋊#92420—24no—
19#14519832—42no—
20C24×D61C2×C411yescharacteristic
21C23×Dic61C2×C411yescharacteristic
22C22×C4×D61—22no—
23C22×C4×D61—21no—
24C22×C4×D61—21no—
25C22×C4×D61—22no—
26C22×C4×D61—42no—
27C22×C4×D61—42no—
28#14519736—42no—
29C2×C4⋊Dic61D412yes—
30C2×C22⋊Dic61C2×C411yescharacteristic
31C2×C22⋊Dic61C2311yescharacteristic
32C2×#11758198—22no—
33C2×#11758198—22no—
34C2×C4×Dic61D412yes—
35#14519684—22no—
36#14519684—22no—
37C23×C4×C61C2×C411yescharacteristic
38#117×C61—42no—
39C2×C4⋊C4×C61—21no—
40C2×C22⋊C4×C61C2×C411yescharacteristic
41C2×C22⋊C4×C61C2×C411yescharacteristic
42C2×C42×C61—21no—
43C24×C61C22×C411yescharacteristic
44C23×D61—21no—
45C23×D61—21no—
46C23×D61—44no—
47C23×D61—41no—
48C23×D61—41no—
49C23×D61M1612yes—
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61—22no—
53C22×C4×C61—22no—
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22⋊C411yescharacteristic
58C22×Dic61—21no—
59C22×Dic61—21no—
60C22×Dic61—41no—
61C22×Dic61—41no—
62C22×Dic61C22⋊C412yes—
63C22×Dic61M1612yes—
64C22×Dic61C2×D412yes—
65C2×C4×D61—24no—
66C2×C4×D61—24no—
67C2×C4×D61—48no—
68C2×C4×D61—42no—
69C2×C4×D61—42no—
70C2×C4×D61—48no—
71C2×C4×D61—42no—
72C2×C4×D61—42no—
73C2×#92420—44no—
74C4⋊C4×C61—42no—
75C22⋊C4×C61—41no—
76C22⋊C4×C61—41no—
77C42×C61—42no—
78C22⋊Dic61—41no—
79C22⋊Dic61—41no—
80#11758198—44no—
81#11758198—44no—
82C4⋊Dic61—42no—
83C4×Dic61—22no—
84C4×Dic61—22no—
85C23×C61—21no—
86C23×C61—21no—
87C23×C61—42no—
88C23×C61C2×C22⋊C411yescharacteristic
89C23×C61C2×M1611yescharacteristic
90C23×C61C2×M1611yescharacteristic
91C22×D61—24no—
92C22×D61—22no—
93C22×D61—44no—
94C22×D61—44no—
95C22×D61—42no—
96C22×D61—42no—
97C22×D61—48no—
98C22×D61—44no—
99C22×D61—41no—
100C22×D61—41no—
101C22×D61—42no—
102C22×D61—44no—
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—42no—
110C2×C4×C61—42no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61#9912yes—
114C2×C4×C61#10012yes—
115C2×Dic61—22no—
116C2×Dic61—22no—
117C2×Dic61—22no—
118C2×Dic61—42no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—42no—
122C2×Dic61—42no—
123C2×Dic61—42no—
124C4×D61—48no—
125C4×D61—48no—
126#92420—84no—
127#11501—611nomaximal, Sylow
128C22×C61—22no—
129C22×C61—21no—
130C22×C61—21no—
131C22×C61—41no—
132C22×C61—41no—
133C22×C61—42no—
134C22×C61—42no—
135C22×C61#40711yescharacteristic
136C22×C61C2×#9911yescharacteristic
137C22×C61C2×#10011yescharacteristic
138C2×D61—24no—
139C2×D61—44no—
140C2×D61—42no—
141C2×D61—48no—
142C2×D61—44no—
143C2×D61—44no—
144C2×D61—42no—
145C2×D61—44no—
146C4×C61—22no—
147C4×C61—22no—
148C4×C61—81no—
149C4×C61—81no—
150Dic61—42no—
151Dic61—42no—
152Dic61—42no—
153#2280—611no—
154#1464—612no—
155#1317—612no—
156#1316—612no—
157C2×C61—21no—
158C2×C61—21no—
159C2×C61—41no—
160C2×C61—41no—
161C2×C61#146211yescharacteristic
162C2×C61#212012yes—
163D61—44no—
164C24×C4—611no—
165C2×#117—611no—
166C2×#117#692311yescharacteristic
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
177C25—611no—
178C23×C4—611no—
179C23×C4—1222no—
180C23×C4—1222no—
181C23×C4—1221no—
182C23×C4—1221no—
183C23×C4—2442no—
184C23×C4—2442no—
185C23×C4C2×#692311yescharacteristic
186#117—42no—
187#117—2442no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—612no—
190C2×C22⋊C4—611no—
191C2×C22⋊C4—611no—
192C2×C22⋊C4—1222no—
193C2×C22⋊C4—1222no—
194C2×C22⋊C4C2×#692311yescharacteristic
195C2×C22⋊C4C2×#692311yescharacteristic
196C2×C42—21no—
197C2×C42—612no—
198C4⋊C8—2442no—
199C22⋊C8—1224no—
200#97—2442no—
201#95—1222no—
202#95—1222no—
203C24—612no—
204C24—1221no—
205C24—1221no—
206C24—2441no—
207C24—2441no—
208C24—2444no—
209C24C22×#692311yescharacteristic
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—612no—
217C22×C4—612no—
218C22×C4—612no—
219C22×C4—1224no—
220C22×C4—1224no—
221C22×C4—1221no—
222C22×C4—1221no—
223C22×C4—2448no—
224C22×C4—2448no—
225C22×C4—2442no—
226C22×C4—2442no—
227C22×C4—2442no—
228C22×C4—2442no—
229C22×C4—2441no—
230C22×C4—2441no—
231C22×C4C22⋊#692311yescharacteristic
232C22×C4C22⋊#692311yescharacteristic
233C2×C8—2444no—
234C4⋊C4—42no—
235C4⋊C4—2442no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—2444no—
239C22⋊C4—2444no—
240C22⋊C4—2441no—
241C22⋊C4—2441no—
242C42—42no—
243C42—1222no—
244C42—1222no—
245C23—21no—
246C23—21no—
247C23—42no—
248C23—1224no—
249C23—1222no—
250C23—2442no—
251C23—2442no—
252C23—2442no—
253C23—2444no—
254C23—2444no—
255C23—2444no—
256C23—2448no—
257C23—2444no—
258C23—2441no—
259C23—2441no—
260C23C2×C22⋊#692311yescharacteristic
261C23D61⋊M1611yescharacteristic
262C23D61⋊M1611yescharacteristic
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—1222no—
274C2×C4—1222no—
275C2×C4—1222no—
276C2×C4—2448no—
277C2×C4—2448no—
278C2×C4—2442no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2442no—
282C2×C4—2442no—
283C2×C4—2442no—
284C2×C4#1451983612yes—
285C2×C4#1451983712yes—
286C8—4884no—
287C22—22no—
288C22—21no—
289C22—21no—
290C22—41no—
291C22—41no—
292C22—42no—
293C22—42no—
294C22—1224no—
295C22—2444no—
296C22—2442no—
297C22—2444no—
298C22—2444no—
299C22—2448no—
300C22—2444no—
301C22—2442no—
302C22#1684073411yescharacteristic
303C22C2×#1451983611yescharacteristic
304C22C2×#1451983711yescharacteristic
305C4—22no—
306C4—22no—
307C4—81no—
308C4—81no—
309C4—2442no—
310C4—2442no—
311C4—2442no—
312C2—21no—
313C2—21no—
314C2—41no—
315C2—41no—
316C2—2444no—
317C2#2146106611yescharacteristic
318C2#2146207212yes—
subgroupG/H
centerC22C2×#14519836
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#99
prime radicalC24×D61C2×C4
cosocleC2×C22⋊Dic61C23
hypercenterC2×#117#6923
hypocenterC61#11501
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #21461070C2semidirect
2. #21460746C2semidirect
176. C61#11501semidirect

Maximal subgroups

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

subgroupindex
#214610702
#214607462
#214607442
#214481982
#1150161