Finite Group Databasebeta

← #30604113

Subgroups — #30604113

Order 15616.

490 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 78 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#21461068C212yesmaximal
2#21460760C212yesmaximal, complemented
3#21460759C212yesmaximal, complemented
4#382×D61C211yesmaximal, characteristic
5#16840733—22no—
6#16840608—22no—
7#16840607C2214yes—
8C2×C4⋊C4×D61C411yescharacteristic
9C2×C4⋊C4×D61C2211yescharacteristic
10C2×C42×D61C411yescharacteristic
11#16839628C2211yescharacteristic
12#16839627C411yescharacteristic
13#16839627C2211yescharacteristic
14#16839626—22no—
15#95×D61—22no—
16C61×#382C411yescharacteristic
17C2×#11758213—42no—
18#14519834—42no—
19C22⋊#92420—24no—
20C22×C4×D61—21no—
21C22×C4×D61—21no—
22C22×C4×D61C2×C411yescharacteristic
23C22×C4×D61D412yes—
24C2×C4⋊Dic61C2×C411yescharacteristic
25C2×C4⋊Dic61C2311yescharacteristic
26C2×#11758196—21no—
27C2×#11758196D412yes—
28C4⋊C4×D61—41no—
29C4⋊C4×D61—41no—
30C4⋊C4×D61—41no—
31C4⋊C4×D61—41no—
32C2×C4×Dic61—21no—
33C2×C4×Dic61C2×C411yescharacteristic
34C42×D61—22no—
35C42×D61—22no—
36#14519684—22no—
37#14519684—22no—
38#14519684—22no—
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C2×C42×C61C2×C411yescharacteristic
42#95×C61—22no—
43C23×D61C22⋊C411yescharacteristic
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61C22⋊C412yes—
47C22×C4×C61C22×C411yescharacteristic
48C22×Dic61—21no—
49C22×Dic61—21no—
50C22×Dic61C22⋊C411yescharacteristic
51C22×Dic61C2×D412yes—
52C2×C4×D61—21no—
53C2×C4×D61—21no—
54C2×C4×D61—21no—
55C2×C4×D61—21no—
56C2×C4×D61—22no—
57C2×C4×D61—24no—
58C2×C4×D61—22no—
59C2×C4×D61—22no—
60C2×C4×D61—42no—
61C2×C4×D61—42no—
62C2×C4×D61—44no—
63C2×C4×D61—44no—
64C2×C4×D61—41no—
65C2×C4×D61—41no—
66C2×#92420—44no—
67#11758213—84no—
68C4⋊C4×C61—41no—
69C4⋊C4×C61—41no—
70C42×C61—21no—
71C42×C61M1612yescomplemented
72C4⋊Dic61—41no—
73C4⋊Dic61—41no—
74#11758196—42no—
75#11758196—42no—
76C4×Dic61—24no—
77C4×Dic61—21no—
78C4×Dic61M1612yescomplemented
79C23×C61C2×C22⋊C411yescharacteristic
80C22×D61—21no—
81C22×D61—21no—
82C22×D61—22no—
83C22×D61—22no—
84C22×D61#9911yescharacteristic
85C22×D61#9911yescharacteristic
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61—42no—
93C2×C4×C61—42no—
94C2×C4×C61—41no—
95C2×C4×C61C2×M1611yescharacteristic
96C2×C4×C61C2×M1611yescharacteristic
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103C2×Dic61—42no—
104C2×Dic61—42no—
105C2×Dic61—41no—
106C2×Dic61#10112yes—
107C4×D61—22no—
108C4×D61—22no—
109C4×D61—22no—
110C4×D61—22no—
111C4×D61—48no—
112C4×D61—44no—
113C4×D61—82no—
114C4×D61—82no—
115C4×D61—82no—
116#92420—84no—
117#11511—611nomaximal, Sylow
118C22×C61—21no—
119C22×C61—21no—
120C22×C61#40711yescharacteristic
121C22×C61C2×#9911yescharacteristic
122C22×C61C2×#10111yescharacteristic
123C2×D61—24no—
124C2×D61—24no—
125C2×D61—21no—
126C2×D61—21no—
127C2×D61—21no—
128C2×D61—21no—
129C2×D61#35412yes—
130C2×D61#35512yes—
131C4×C61—21no—
132C4×C61—21no—
133C4×C61—42no—
134C4×C61—42no—
135C4×C61—81no—
136Dic61—22no—
137Dic61—42no—
138Dic61—42no—
139Dic61—81no—
140C2×#382—611no—
141#1463—612no—
142#1324—612no—
143#1324—612no—
144C2×C61—21no—
145C2×C61—21no—
146C2×C61#146311yescharacteristic
147C2×C61C2×#35411yescharacteristic
148C2×C61C2×#35511yescharacteristic
149D61—22no—
150D61—22no—
151C22×C4⋊C4—611no—
152C22×C4⋊C4—611no—
153C22×C42—611no—
154#407—1222no—
155#382—611no—
156#382—611no—
157#382—611no—
158#382—1222no—
159#382#692311yescharacteristic
160C2×#95—1222no—
161#324—614no—
162#324—1222no—
163C61#1151111yescharacteristic, complemented, Sylow
164C23×C4—611no—
165C23×C4—612no—
166C23×C4—1221no—
167C23×C4—1221no—
168C2×M16—2442no—
169C2×C4⋊C4—612no—
170C2×C4⋊C4—611no—
171C2×C4⋊C4—611no—
172C2×C4⋊C4—1221no—
173C2×C4⋊C4—2441no—
174C2×C4⋊C4—2441no—
175C2×C4⋊C4—2441no—
176C2×C4⋊C4—2441no—
177C2×C4⋊C4C2×#692311yescharacteristic
178C2×C4⋊C4C2×#692311yescharacteristic
179C2×C42—611no—
180C2×C42—1222no—
181C2×C42—1221no—
182C2×C42—1222no—
183C2×C42C2×#692311yescharacteristic
184C22⋊C8—1224no—
185C22⋊C8—2442no—
186#95—22no—
187#95—1222no—
188#95—1222no—
189#95—1222no—
190C24—611no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—611no—
194C22×C4—612no—
195C22×C4—1222no—
196C22×C4—1221no—
197C22×C4—1221no—
198C22×C4—1222no—
199C22×C4—1222no—
200C22×C4—1224no—
201C22×C4—1221no—
202C22×C4—1221no—
203C22×C4—1221no—
204C22×C4—1221no—
205C22×C4—2441no—
206C22×C4—2441no—
207C22×C4—2444no—
208C22×C4—2444no—
209C22×C4—2442no—
210C22×C4—2442no—
211C22×C4C22⋊#692312yes—
212C22×C4C22×#692311yescharacteristic
213M16—4884no—
214C2×C8—2444no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—2442no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C4⋊C4—2442no—
221C42—21no—
222C42—612no—
223C42—1224no—
224C42—1221no—
225C42#1175821312yescomplemented
226C23—611no—
227C23—611no—
228C23—1222no—
229C23—1222no—
230C23—1221no—
231C23—1221no—
232C23C2×C22⋊#692311yescharacteristic
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—612no—
243C2×C4—1222no—
244C2×C4—1222no—
245C2×C4—1222no—
246C2×C4—1222no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1222no—
250C2×C4—1222no—
251C2×C4—4882no—
252C2×C4—4882no—
253C2×C4—4882no—
254C2×C4—2444no—
255C2×C4—2448no—
256C2×C4—2442no—
257C2×C4—2441no—
258C2×C4—2441no—
259C2×C4—2441no—
260C2×C4—2442no—
261C2×C4D61⋊M1611yescharacteristic
262C2×C4C2×#1175821311yescharacteristic
263C8—4884no—
264C22—21no—
265C22—21no—
266C22—612no—
267C22—612no—
268C22—1224no—
269C22—1224no—
270C22—1221no—
271C22—1221no—
272C22—1221no—
273C22—1221no—
274C22#1684073311yescharacteristic
275C22D61⋊#9911yescharacteristic
276C22D61⋊#10111yescharacteristic
277C4—21no—
278C4—21no—
279C4—42no—
280C4—42no—
281C4—81no—
282C4—1222no—
283C4—4881no—
284C4—2442no—
285C4—2442no—
286C2—21no—
287C2—21no—
288C2—1222no—
289C2—1222no—
290C2#2146106811yescharacteristic
291C2D61⋊#35411yescharacteristic
292C2D61⋊#35511yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenter#382#6923
hypocenterC61#11511
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #21460760C2semidirect
3. #21460759C2semidirect
71. C42×C61M16semidirect
78. C4×Dic61M16semidirect
163. C61#11511semidirect
225. C42#11758213semidirect

Maximal subgroups

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

subgroupindex
#214610682
#214607602
#214607592
#382×D612
#1151161