Finite Group Databasebeta

← C2×#21460759 #30603880

Subgroups — C2×#21460759 #30603880

Order 15616.

510 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 128 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#21460759C214yesmaximal, direct product factor
3C2×#16839628C211yesmaximal, characteristic
4C2×C22⋊#92420—22no—
5#16840607—22no—
6#16840607C2214yes—
7C22×C4⋊Dic61C411yescharacteristic
8C22×C4⋊Dic61C2211yescharacteristic
9#16839628—22no—
10#16839628C412yes—
11#16839628C2212yes—
12C2×#14519684—22no—
13C22×C42×C61C411yescharacteristic
14C22×#92420—42no—
15C22⋊#92420—24no—
16C22⋊#92420—42no—
17C23×Dic61—21no—
18C23×Dic61D412yes—
19C2×C4⋊Dic61—21no—
20C2×C4⋊Dic61—41no—
21C2×C4⋊Dic61—41no—
22C2×C4⋊Dic61—41no—
23C2×C4⋊Dic61—41no—
24C2×C4⋊Dic61C2×C412yes—
25C2×C4⋊Dic61C2×C411yescharacteristic
26C2×C4⋊Dic61D412yes—
27C2×C4⋊Dic61C2311yescharacteristic
28#14519684—24no—
29#14519684—24no—
30C23×C4×C61—21no—
31C23×C4×C61C2×C411yescharacteristic
32C2×C42×C61—21no—
33C2×C42×C61—22no—
34C2×C42×C61C814yescomplemented
35C2×C42×C61C2×C412yes—
36C24×C61C22⋊C411yescharacteristic
37C22×C4×C61—21no—
38C22×C4×C61—21no—
39C22×C4×C61—22no—
40C22×C4×C61—24no—
41C22×C4×C61—22no—
42C22×C4×C61—42no—
43C22×C4×C61—42no—
44C22×C4×C61C22⋊C411yescharacteristic
45C22×C4×C61C2×C812yes—
46C22×C4×C61M1612yes—
47C22×C4×C61C22×C411yescharacteristic
48C22×Dic61—22no—
49C22×Dic61—22no—
50C22×Dic61—22no—
51C22×Dic61—44no—
52C22×Dic61—44no—
53C22×Dic61—41no—
54C22×Dic61—41no—
55C22×Dic61C22⋊C412yes—
56C22×Dic61C2×D412yes—
57C2×#92420—44no—
58C2×#92420—84no—
59C42×C61—24no—
60C42×C61—22no—
61C42×C61C2×C814yescomplemented
62C4⋊Dic61—41no—
63C4⋊Dic61—42no—
64C4⋊Dic61—41no—
65C4⋊Dic61—42no—
66C4⋊Dic61—42no—
67C23×C61—22no—
68C23×C61—22no—
69C23×C61C22⋊C812yes—
70C23×C61#9911yescharacteristic
71C23×C61#9911yescharacteristic
72C23×C61#10112yes—
73C23×C61C2×C22⋊C411yescharacteristic
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—24no—
83C2×C4×C61—48no—
84C2×C4×C61—42no—
85C2×C4×C61—42no—
86C2×C4×C61C22⋊C812yes—
87C2×C4×C61C22×C811yescharacteristic
88C2×C4×C61C2×M1611yescharacteristic
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—44no—
92C2×Dic61—42no—
93C2×Dic61—42no—
94C2×Dic61—44no—
95C2×Dic61—42no—
96C2×Dic61—82no—
97C2×Dic61—82no—
98C2×Dic61—82no—
99#92420—84no—
100C2×#1324—611nomaximal, Sylow
101C22×C61—24no—
102C22×C61—24no—
103C22×C61—21no—
104C22×C61—21no—
105C22×C61—21no—
106C22×C61—21no—
107C22×C61#32412yes—
108C22×C61#32412yes—
109C22×C61#35412yes—
110C22×C61#35512yes—
111C22×C61C2×C22⋊C811yescharacteristic
112C22×C61C2×#9911yescharacteristic
113C22×C61C2×#10111yescharacteristic
114C4×C61—22no—
115C4×C61—21no—
116C4×C61—21no—
117C4×C61—44no—
118Dic61—42no—
119Dic61—42no—
120Dic61—82no—
121C2×#382—611no—
122C2×#324—612no—
123#1324—614no—
124C2×C61—21no—
125C2×C61—22no—
126C2×C61—21no—
127C2×C61#132414yescomplemented
128C2×C61C2×#32411yescharacteristic
129C2×C61C2×#35411yescharacteristic
130C2×C61C2×#35511yescharacteristic
131C22×C4⋊C4—611no—
132C22×C4⋊C4—611no—
133C22×C42#692311yescharacteristic
134C2×C22⋊C8—1222no—
135#382—612no—
136#382—612no—
137#382—1222no—
138C2×#95—1222no—
139#324—614no—
140#324—1222no—
141C61C2×#132411yescharacteristic, complemented, Sylow
142C23×C4—21no—
143C23×C4—612no—
144C23×C4—1221no—
145C23×C4C2×#692311yescharacteristic
146C22×C8—2442no—
147C2×C4⋊C4—612no—
148C2×C4⋊C4—611no—
149C2×C4⋊C4—611no—
150C2×C4⋊C4—612no—
151C2×C4⋊C4—1221no—
152C2×C4⋊C4—2441no—
153C2×C4⋊C4—2441no—
154C2×C4⋊C4—2441no—
155C2×C4⋊C4—2441no—
156C2×C42—22no—
157C2×C42—21no—
158C2×C42#9242014yescomplemented
159C2×C42C2×#692312yes—
160C22⋊C8—1224no—
161C22⋊C8—2442no—
162#95—1224no—
163#95—1224no—
164C24C22⋊#692311yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—22no—
168C22×C4—24no—
169C22×C4—22no—
170C22×C4—42no—
171C22×C4—42no—
172C22×C4—612no—
173C22×C4—612no—
174C22×C4—1222no—
175C22×C4—1222no—
176C22×C4—1222no—
177C22×C4—2444no—
178C22×C4—2441no—
179C22×C4—2441no—
180C22×C4—2444no—
181C22×C4C2×#9242012yes—
182C22×C4#1175821712yes—
183C22×C4C22⋊#692311yescharacteristic
184C22×C4C22×#692311yescharacteristic
185C2×C8—4884no—
186C2×C8—2444no—
187C4⋊C4—2442no—
188C4⋊C4—2441no—
189C4⋊C4—2441no—
190C4⋊C4—2442no—
191C4⋊C4—2442no—
192C42—24no—
193C42—22no—
194C42C2×#9242014yescomplemented
195C23—22no—
196C23—22no—
197C23C22⋊#9242012yes—
198C23#1451983611yescharacteristic
199C23#1451983611yescharacteristic
200C23#1451983812yes—
201C23C2×C22⋊#692311yescharacteristic
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—24no—
211C2×C4—48no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—4882no—
217C2×C4—4882no—
218C2×C4—4882no—
219C2×C4—2444no—
220C2×C4—2442no—
221C2×C4—2444no—
222C2×C4—2442no—
223C2×C4—2442no—
224C2×C4C22⋊#9242012yes—
225C2×C4C22×#9242011yescharacteristic
226C2×C4C2×#1175821711yescharacteristic
227C8—4884no—
228C22—24no—
229C22—24no—
230C22—21no—
231C22—21no—
232C22—21no—
233C22—21no—
234C22#1684060712yes—
235C22#1684060712yes—
236C22#1684066912yes—
237C22#1684067112yes—
238C22C2×C22⋊#9242011yescharacteristic
239C22C2×#1451983611yescharacteristic
240C22C2×#1451983811yescharacteristic
241C4—22no—
242C4—21no—
243C4—21no—
244C4—44no—
245C4—4882no—
246C4—2442no—
247C4—2442no—
248C2—21no—
249C2—21no—
250C2—22no—
251C2#2146075914yesdirect product factor
252C2C2×#1684060711yescharacteristic
253C2C2×#1684066911yescharacteristic
254C2C2×#1684067111yescharacteristic
subgroupG/H
centerC23#14519836
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC22×C42×C61C4
socleC23×C61#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenterC22×C42#6923
hypocenterC61C2×#1324
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. #21460759C2direct (N × H)
34. C2×C42×C61C8semidirect
61. C42×C61C2×C8semidirect
127. C2×C61#1324semidirect
141. C61C2×#1324semidirect
158. C2×C42#92420semidirect
194. C42C2×#92420semidirect
251. C2#21460759direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406072
#214607592
C2×#168396282
C2×#132461