Finite Group Databasebeta

← #30604124

Subgroups — #30604124

Order 15616.

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

normal subgroups only

This group has 434 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#21461067C212yesmaximal
2#21460762C212yesmaximal, complemented
3#21460760C212yesmaximal, complemented
4#21448439C211yesmaximal, characteristic
5#16840732—22no—
6#16840607—22no—
7#16840607C2214yes—
8C2×#14519736C411yescharacteristic
9C22×C4⋊Dic61C2211yescharacteristic
10#16839660—22no—
11#16839634—22no—
12#16839631C411yescharacteristic
13#16839631C2211yescharacteristic
14#16839627C411yescharacteristic
15#16839627C2211yescharacteristic
16C2×#117×C61C411yescharacteristic
17C2×#11758217—42no—
18C22⋊#92420—24no—
19C22⋊#92420—42no—
20C23×Dic61D412yes—
21#14519736—22no—
22#14519736—22no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61—42no—
25C2×C4⋊Dic61C2×C411yescharacteristic
26C2×C4⋊Dic61D412yes—
27C2×C4⋊Dic61C2311yescharacteristic
28C2×#11758196—22no—
29C2×#11758196—22no—
30C2×C22⋊Dic61—21no—
31C2×C4×Dic61C2×C411yescharacteristic
32C2×C4×Dic61C2×C411yescharacteristic
33#14519684—22no—
34#14519684—22no—
35C23×C4×C61C2×C411yescharacteristic
36#117×C61—42no—
37C2×C4⋊C4×C61C2×C411yescharacteristic
38C2×C4⋊C4×C61C2×C411yescharacteristic
39C2×C22⋊C4×C61—21no—
40C2×C42×C61—21no—
41C24×C61C22⋊C411yescharacteristic
42C22×C4×C61—22no—
43C22×C4×C61—22no—
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61C22⋊C411yescharacteristic
49C22×C4×C61C22×C411yescharacteristic
50C22×Dic61—22no—
51C22×Dic61—21no—
52C22×Dic61—21no—
53C22×Dic61—22no—
54C22×Dic61—82no—
55C22×Dic61C22⋊C412yes—
56C22×Dic61C2×D412yes—
57#11758217—84no—
58C2×#92420—44no—
59C4⋊C4×C61—41no—
60C4⋊C4×C61—41no—
61C22⋊C4×C61—42no—
62C42×C61—42no—
63C22⋊Dic61—24no—
64C4⋊Dic61—24no—
65C4⋊Dic61—41no—
66C4⋊Dic61—42no—
67C4⋊Dic61—41no—
68#11758196—82no—
69#11758196—82no—
70C4×Dic61—21no—
71C4×Dic61—21no—
72C4×Dic61M1612yescomplemented
73C4×Dic61M1612yescomplemented
74C23×C61—21no—
75C23×C61—21no—
76C23×C61—41no—
77C23×C61—41no—
78C23×C61#9912yes—
79C23×C61C2×C22⋊C411yescharacteristic
80C2×C4×C61—24no—
81C2×C4×C61—24no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—42no—
87C2×C4×C61—42no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61#10112yes—
91C2×C4×C61C2×M1611yescharacteristic
92C2×C4×C61C2×M1611yescharacteristic
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—41no—
98C2×Dic61—41no—
99C2×Dic61—44no—
100C2×Dic61—41no—
101C2×Dic61—41no—
102C2×Dic61—42no—
103C2×Dic61—42no—
104C2×Dic61—82no—
105#92420—84no—
106#11514—611nomaximal, Sylow
107C22×C61—21no—
108C22×C61—21no—
109C22×C61—22no—
110C22×C61—22no—
111C22×C61—22no—
112C22×C61—42no—
113C22×C61—42no—
114C22×C61#40711yescharacteristic
115C22×C61C2×#9911yescharacteristic
116C22×C61C2×#10111yescharacteristic
117C4×C61—22no—
118C4×C61—21no—
119C4×C61—21no—
120C4×C61—81no—
121C4×C61—81no—
122Dic61—42no—
123Dic61—42no—
124Dic61—42no—
125Dic61—42no—
126#2317—611no—
127#1463—612no—
128#1325—612no—
129#1324—612no—
130C2×C61—21no—
131C2×C61—21no—
132C2×C61—42no—
133C2×C61#146311yescharacteristic
134C2×C61#212711yescharacteristic
135C2×C61#213311yescharacteristic
136C2×#117—611no—
137C2×#117#692311yescharacteristic
138C22×C4⋊C4—611no—
139#407—1222no—
140#389—1222no—
141#385—1222no—
142#384—611no—
143#384—611no—
144#382—611no—
145#382—611no—
146#324—614no—
147#324—1222no—
148C61#1151411yescharacteristic, complemented, Sylow
149C23×C4—612no—
150C23×C4C2×#692311yescharacteristic
151C2×M16—2442no—
152#117—42no—
153#117—1222no—
154#117—1222no—
155C2×C4⋊C4—612no—
156C2×C4⋊C4—611no—
157C2×C4⋊C4—611no—
158C2×C4⋊C4—1221no—
159C2×C4⋊C4—1222no—
160C2×C4⋊C4—1222no—
161C2×C4⋊C4—2442no—
162C2×C4⋊C4C2×#692311yescharacteristic
163C2×C4⋊C4C2×#692311yescharacteristic
164C2×C22⋊C4—21no—
165C2×C22⋊C4—1221no—
166C2×C42—21no—
167C2×C42—611no—
168C2×C42—611no—
169C22⋊C8—1224no—
170C22⋊C8—2442no—
171#95—1222no—
172#95—1222no—
173C24C22⋊#692311yescharacteristic
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—612no—
181C22×C4—612no—
182C22×C4—1222no—
183C22×C4—1222no—
184C22×C4—1221no—
185C22×C4—1221no—
186C22×C4—4882no—
187C22×C4C22⋊#692311yescharacteristic
188C22×C4C22×#692311yescharacteristic
189M16—4884no—
190C2×C8—2444no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—1224no—
194C4⋊C4—4882no—
195C4⋊C4—4882no—
196C4⋊C4—2442no—
197C4⋊C4—2441no—
198C4⋊C4—2441no—
199C22⋊C4—42no—
200C22⋊C4—1224no—
201C42—42no—
202C42—612no—
203C42—612no—
204C42—1221no—
205C42—1221no—
206C23—21no—
207C23—21no—
208C23—41no—
209C23—41no—
210C23#1451983512yes—
211C23C2×C22⋊#692311yescharacteristic
212C2×C4—24no—
213C2×C4—24no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—4882no—
227C2×C4—2441no—
228C2×C4—2441no—
229C2×C4—2444no—
230C2×C4—2441no—
231C2×C4—2441no—
232C2×C4—2442no—
233C2×C4—2442no—
234C2×C4#1451983812yes—
235C2×C4D61⋊M1611yescharacteristic
236C2×C4D61⋊M1611yescharacteristic
237C8—4884no—
238C22—21no—
239C22—21no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22—42no—
244C22—42no—
245C22#1684073411yescharacteristic
246C22C2×#1451983511yescharacteristic
247C22C2×#1451983811yescharacteristic
248C4—22no—
249C4—21no—
250C4—21no—
251C4—81no—
252C4—81no—
253C4—2442no—
254C4—2442no—
255C4—2442no—
256C4—2442no—
257C2—21no—
258C2—21no—
259C2—42no—
260C2#2146106911yescharacteristic
261C2#2146209411yescharacteristic
262C2#2146211411yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenterC2×#117#6923
hypocenterC61#11514
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #21460762C2semidirect
3. #21460760C2semidirect
72. C4×Dic61M16semidirect
73. C4×Dic61M16semidirect
148. C61#11514semidirect

Maximal subgroups

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

subgroupindex
#214610672
#214607622
#214607602
#214484392
#1151461