Finite Group Databasebeta

← #30603828

Subgroups — #30603828

Order 15616.

526 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 90 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#21461051C212yesmaximal
2#21460746C212yesmaximal
3#21460745C212yesmaximal
4#21448404C211yesmaximal, characteristic
5#16840779—22no—
6#16840608—22no—
7#16840605C2214yes—
8C23×Dic122C411yescharacteristic
9C2×#14519733C411yescharacteristic
10C2×#14519733C2211yescharacteristic
11#16839666—22no—
12#16839666—22no—
13#16839625C2211yescharacteristic
14#16839623C411yescharacteristic
15#16839623C2211yescharacteristic
16C61×#381C411yescharacteristic
17#14519844—42no—
18C22⋊#92420—24no—
19C4×#92420—42no—
20C22×Dic122—21no—
21C22×Dic122—21no—
22C22×Dic122—22no—
23C22×Dic122—42no—
24C22×Dic122—42no—
25C22×Dic122C814yescomplemented
26C23×Dic61C2×C411yescharacteristic
27C23×Dic61C2×C411yescharacteristic
28#14519733—42no—
29#14519733—42no—
30C2×#11758196—21no—
31C2×#11758196D412yes—
32C2×C22⋊Dic61C2×C411yescharacteristic
33C2×C22⋊Dic61C2311yescharacteristic
34C2×C4×Dic61—21no—
35C2×C4×Dic61D412yes—
36#14519684—22no—
37#14519684—22no—
38#14519684—22no—
39C23×C4×C61C2×C411yescharacteristic
40C2×C22⋊C4×C61C2×C411yescharacteristic
41C2×C22⋊C4×C61C2×C411yescharacteristic
42#95×C61—22no—
43C24×C61C22×C411yescharacteristic
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61—41no—
48C22×C4×C61—41no—
49C22×C4×C61C22⋊C412yes—
50C22×C4×C61C2×C812yes—
51C22×Dic61—22no—
52C22×Dic61—22no—
53C22×Dic61—21no—
54C22×Dic61—21no—
55C22×Dic61—21no—
56C22×Dic61—41no—
57C22×Dic61—41no—
58C22×Dic61C22⋊C411yescharacteristic
59C22×Dic61C22⋊C411yescharacteristic
60C22×Dic61C2×C812yes—
61C22×Dic61C2×C812yes—
62C22×Dic61M1612yes—
63C22×Dic61C2×D412yes—
64C2×Dic122—24no—
65C2×Dic122—24no—
66C2×Dic122—42no—
67C2×Dic122—42no—
68C2×Dic122—48no—
69C2×Dic122—42no—
70C2×Dic122—42no—
71C2×Dic122—48no—
72C2×#92420—44no—
73C22⋊C4×C61—41no—
74C22⋊C4×C61—41no—
75C22⋊Dic61—41no—
76C22⋊Dic61—41no—
77#11758196—42no—
78#11758196—42no—
79C4×Dic61—22no—
80C4×Dic61—22no—
81C4×Dic61—42no—
82C23×C61—21no—
83C23×C61—21no—
84C23×C61—42no—
85C23×C61C2×C22⋊C411yescharacteristic
86C23×C61C22×C811yescharacteristic
87C23×C61C2×M1611yescharacteristic
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—42no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—42no—
94C2×C4×C61—42no—
95C2×C4×C61—42no—
96C2×C4×C61—41no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—24no—
100C2×Dic61—24no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—42no—
104C2×Dic61—41no—
105C2×Dic61—41no—
106C2×Dic61—42no—
107C2×Dic61—42no—
108C2×Dic61—42no—
109C2×Dic61—41no—
110C2×Dic61C22⋊C812yes—
111C2×Dic61C22⋊C812yes—
112C2×Dic61#9912yes—
113C2×Dic61#10012yes—
114Dic122—48no—
115Dic122—48no—
116#92420—84no—
117#11428—611nomaximal, Sylow
118C22×C61—22no—
119C22×C61—21no—
120C22×C61—21no—
121C22×C61—41no—
122C22×C61—41no—
123C22×C61—42no—
124C22×C61—42no—
125C22×C61C2×C22⋊C811yescharacteristic
126C22×C61C2×#9911yescharacteristic
127C22×C61C2×#10011yescharacteristic
128C4×C61—42no—
129C4×C61—42no—
130C4×C61—81no—
131Dic61—22no—
132Dic61—42no—
133Dic61—42no—
134Dic61—81no—
135Dic61#32314yes—
136#2310—611no—
137#1458—612no—
138#1317—612no—
139#1317—612no—
140C2×C61—21no—
141C2×C61—21no—
142C2×C61—41no—
143C2×C61—41no—
144C2×C61C2×#32311yescharacteristic
145C2×C61#212312yes—
146C23×Q8—611no—
147C2×#117—611no—
148C2×#117—611no—
149#431—1222no—
150#391—1222no—
151#391—1222no—
152#381—611no—
153#381—611no—
154#381—611no—
155#381#692311yescharacteristic
156#324—1222no—
157#323—614no—
158C61#1142811yescharacteristic, complemented, Sylow
159C22×Q8—614no—
160C22×Q8—1222no—
161C22×Q8—1221no—
162C22×Q8—1221no—
163C22×Q8—2442no—
164C22×Q8—2442no—
165C23×C4—611no—
166C23×C4—611no—
167C23×C4C2×#692311yescharacteristic
168#117—2442no—
169#117—2442no—
170C2×C4⋊C4—612no—
171C2×C4⋊C4—1221no—
172C2×C22⋊C4—611no—
173C2×C22⋊C4—611no—
174C2×C22⋊C4C2×#692311yescharacteristic
175C2×C22⋊C4C2×#692311yescharacteristic
176C2×C42—612no—
177C2×C42—1221no—
178C4⋊C8—2442no—
179C22⋊C8—1224no—
180C4×C8—2442no—
181#95—22no—
182#95—1222no—
183#95—1222no—
184#95—1222no—
185C24C22×#692311yescharacteristic
186C2×Q8—1224no—
187C2×Q8—1224no—
188C2×Q8—2442no—
189C2×Q8—2442no—
190C2×Q8—2448no—
191C2×Q8—2448no—
192C2×Q8—2442no—
193C2×Q8—2442no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—611no—
200C22×C4—611no—
201C22×C4—612no—
202C22×C4—612no—
203C22×C4—612no—
204C22×C4—612no—
205C22×C4—1222no—
206C22×C4—1222no—
207C22×C4—1221no—
208C22×C4—1221no—
209C22×C4—1221no—
210C22×C4—2441no—
211C22×C4—2441no—
212C22×C4D61⋊C812yes—
213C22×C4C22⋊#692312yes—
214C2×C8—2444no—
215C4⋊C4—2442no—
216C4⋊C4—2442no—
217C22⋊C4—41no—
218C22⋊C4—41no—
219C22⋊C4—2441no—
220C22⋊C4—2441no—
221C42—1222no—
222C42—1222no—
223C42—2442no—
224C23—21no—
225C23—21no—
226C23—42no—
227C23C2×C22⋊#692311yescharacteristic
228C23C2×D61⋊C811yescharacteristic
229C23D61⋊M1611yescharacteristic
230Q8—2448no—
231Q8—2448no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—612no—
242C2×C4—612no—
243C2×C4—612no—
244C2×C4—612no—
245C2×C4—1224no—
246C2×C4—1224no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1222no—
250C2×C4—1222no—
251C2×C4—2442no—
252C2×C4—2441no—
253C2×C4—2442no—
254C2×C4—2441no—
255C2×C4—2441no—
256C2×C4—2442no—
257C2×C4—2442no—
258C8—4884no—
259C22—22no—
260C22—21no—
261C22—21no—
262C22—41no—
263C22—41no—
264C22—42no—
265C22—42no—
266C22D61⋊(C22⋊C8)11yescharacteristic
267C22D61⋊#9911yescharacteristic
268C22D61⋊#10011yescharacteristic
269C4—42no—
270C4—42no—
271C4—81no—
272C4—614no—
273C4—1222no—
274C4—4881no—
275C4—2442no—
276C4—2442no—
277C2—21no—
278C2—21no—
279C2—41no—
280C2—41no—
281C2D61⋊#32311yescharacteristic
282C2#2146208212yes—
subgroupG/H
centerC22D61⋊#99
commutatorC23×C61C22×C8
FrattiniC24C22×#6923
FittingC61×#381C4
socleC22×C61C2×#99
prime radicalC24×C61C22×C4
cosocleC2×C22⋊Dic61C23
hypercenter#381#6923
hypocenterC61#11428
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #381

Complements

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

NH ≅ G/Ntype
25. C22×Dic122C8semidirect
158. C61#11428semidirect

Maximal subgroups

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

subgroupindex
#214610512
#214607462
#214607452
#214484042
#1142861