Finite Group Databasebeta

← #30603890

Subgroups — #30603890

Order 15616.

454 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C2×#16840607C212yesmaximal
2#21460761C212yesmaximal, complemented
3#21460759C212yesmaximal, complemented
4#21448442C211yesmaximal, characteristic
5C2×C22⋊#92420—22no—
6#16840607—22no—
7#16840607C2214yes—
8C2×#14519736C411yescharacteristic
9C22×C4⋊Dic61C2211yescharacteristic
10#16839661—22no—
11#16839637—22no—
12#16839632C411yescharacteristic
13#16839632C2211yescharacteristic
14#16839628C411yescharacteristic
15#16839628C2211yescharacteristic
16C2×#117×C61C411yescharacteristic
17C22×#92420—42no—
18C22⋊#92420—24no—
19C22⋊#92420—42no—
20C23×Dic61D412yes—
21#14519736—42no—
22C2×C4⋊Dic61—22no—
23C2×C4⋊Dic61—22no—
24C2×C4⋊Dic61—42no—
25C2×C4⋊Dic61C2×C411yescharacteristic
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×C4⋊Dic61D412yes—
29C2×C4⋊Dic61C2311yescharacteristic
30C2×C22⋊Dic61—21no—
31C2×C4×Dic61—21no—
32#14519684—22no—
33#14519684—22no—
34C23×C4×C61C2×C411yescharacteristic
35#117×C61—22no—
36#117×C61C814yescomplemented
37C2×C4⋊C4×C61—21no—
38C2×C22⋊C4×C61—21no—
39C2×C42×C61C2×C411yescharacteristic
40C2×C42×C61C2×C411yescharacteristic
41C24×C61C22⋊C411yescharacteristic
42C22×C4×C61—22no—
43C22×C4×C61—22no—
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61C22⋊C411yescharacteristic
47C22×C4×C61C2×C812yes—
48C22×C4×C61M1612yes—
49C22×C4×C61C22×C411yescharacteristic
50C22×Dic61—22no—
51C22×Dic61—22no—
52C22×Dic61—21no—
53C22×Dic61—21no—
54C22×Dic61—82no—
55C22×Dic61C22⋊C412yes—
56C22×Dic61C2×D412yes—
57C2×#92420—44no—
58C2×#92420—84no—
59C4⋊C4×C61—24no—
60C22⋊C4×C61—24no—
61C42×C61—21no—
62C42×C61—21no—
63C42×C61C2×C812yescomplemented
64C42×C61C2×C812yescomplemented
65C22⋊Dic61—42no—
66C4⋊Dic61—41no—
67C4⋊Dic61—42no—
68C4⋊Dic61—41no—
69C4⋊Dic61—41no—
70C4⋊Dic61—41no—
71C4⋊Dic61—82no—
72C4⋊Dic61—82no—
73C4×Dic61—42no—
74C23×C61—41no—
75C23×C61—41no—
76C23×C61C22⋊C812yes—
77C23×C61#9912yes—
78C23×C61#10112yes—
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—22no—
87C2×C4×C61—22no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61C22⋊C812yes—
93C2×C4×C61C22×C811yescharacteristic
94C2×C4×C61C2×M1611yescharacteristic
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—44no—
98C2×Dic61—42no—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61—42no—
102C2×Dic61—41no—
103C2×Dic61—41no—
104C2×Dic61—82no—
105#92420—84no—
106#11448—611nomaximal, Sylow
107C22×C61—21no—
108C22×C61—22no—
109C22×C61—21no—
110C22×C61—22no—
111C22×C61—42no—
112C22×C61—42no—
113C22×C61#32414yes—
114C22×C61C2×C22⋊C811yescharacteristic
115C22×C61C2×#9911yescharacteristic
116C22×C61C2×#10111yescharacteristic
117C4×C61—22no—
118C4×C61—21no—
119C4×C61—21no—
120C4×C61—42no—
121C4×C61—42no—
122Dic61—42no—
123Dic61—42no—
124Dic61—81no—
125Dic61—81no—
126#2317—611no—
127C2×#324—612no—
128#1325—612no—
129#1324—612no—
130C2×C61—21no—
131C2×C61—24no—
132C2×C61—21no—
133C2×C61C2×#32411yescharacteristic
134C2×C61#212711yescharacteristic
135C2×C61#213311yescharacteristic
136C2×#117—611no—
137C2×#117#692311yescharacteristic
138C22×C4⋊C4—611no—
139C2×C22⋊C8—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#1144811yescharacteristic, complemented, Sylow
149C23×C4—612no—
150C23×C4C2×#692311yescharacteristic
151C22×C8—2442no—
152#117—22no—
153#117—2442no—
154#117#9242014yescomplemented
155C2×C4⋊C4—21no—
156C2×C4⋊C4—612no—
157C2×C4⋊C4—611no—
158C2×C4⋊C4—611no—
159C2×C4⋊C4—611no—
160C2×C4⋊C4—611no—
161C2×C4⋊C4—1222no—
162C2×C4⋊C4—1222no—
163C2×C4⋊C4—2442no—
164C2×C22⋊C4—21no—
165C2×C22⋊C4—1221no—
166C2×C42—1221no—
167C2×C42C2×#692311yescharacteristic
168C2×C42C2×#692311yescharacteristic
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—612no—
179C22×C4—612no—
180C22×C4—1222no—
181C22×C4—1222no—
182C22×C4—1221no—
183C22×C4—1221no—
184C22×C4—4882no—
185C22×C4C2×#9242012yes—
186C22×C4#1175821712yes—
187C22×C4C22⋊#692311yescharacteristic
188C22×C4C22×#692311yescharacteristic
189C2×C8—4884no—
190C2×C8—2444no—
191C4⋊C4—24no—
192C4⋊C4—4882no—
193C4⋊C4—4882no—
194C4⋊C4—2442no—
195C4⋊C4—2441no—
196C4⋊C4—2441no—
197C4⋊C4—2441no—
198C4⋊C4—2441no—
199C22⋊C4—24no—
200C22⋊C4—2442no—
201C42—21no—
202C42—21no—
203C42—2442no—
204C42C2×#9242012yescomplemented
205C42C2×#9242012yescomplemented
206C23—41no—
207C23—41no—
208C23C22⋊#9242012yes—
209C23#1451983612yes—
210C23#1451983812yes—
211C23C2×C22⋊#692311yescharacteristic
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—4882no—
227C2×C4—2442no—
228C2×C4—2442no—
229C2×C4—2441no—
230C2×C4—2441no—
231C2×C4—2444no—
232C2×C4—2442no—
233C2×C4—2442no—
234C2×C4C22⋊#9242012yes—
235C2×C4C22×#9242011yescharacteristic
236C2×C4C2×#1175821711yescharacteristic
237C8—4884no—
238C22—21no—
239C22—22no—
240C22—21no—
241C22—22no—
242C22—42no—
243C22—42no—
244C22#1684060714yes—
245C22C2×C22⋊#9242011yescharacteristic
246C22C2×#1451983611yescharacteristic
247C22C2×#1451983811yescharacteristic
248C4—22no—
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—4881no—
254C4—4881no—
255C4—2442no—
256C4—2442no—
257C2—21no—
258C2—21no—
259C2—24no—
260C2C2×#1684060711yescharacteristic
261C2#2146209611yescharacteristic
262C2#2146211611yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenterC2×#117#6923
hypocenterC61#11448
LCSG ▷ C2×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. #21460761C2semidirect
3. #21460759C2semidirect
36. #117×C61C8semidirect
63. C42×C61C2×C8semidirect
64. C42×C61C2×C8semidirect
148. C61#11448semidirect
154. #117#92420semidirect
204. C42C2×#92420semidirect
205. C42C2×#92420semidirect

Maximal subgroups

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

subgroupindex
C2×#168406072
#214607612
#214607592
#214484422
#1144861