Finite Group Databasebeta

← C2×#21460762 #30603885

Subgroups — C2×#21460762 #30603885

Order 15616.

598 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 120 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#21460762C214yesmaximal, direct product factor
3C2×#16839631C211yesmaximal, characteristic
4C2×C22⋊#92420—22no—
5#16840607—22no—
6#16840607C2214yes—
7C22×C4⋊Dic61C2211yescharacteristic
8C22×#11758196—22no—
9C22×C4×Dic61C411yescharacteristic
10#16839631—22no—
11#16839631C412yes—
12#16839631C2212yes—
13C22×C4⋊C4×C61C411yescharacteristic
14C22×#92420—42no—
15C22⋊#92420—24no—
16C22⋊#92420—42no—
17C23×Dic61—21no—
18C23×Dic61D412yes—
19C2×C4⋊Dic61—41no—
20C2×C4⋊Dic61—41no—
21C2×C4⋊Dic61C2×C411yescharacteristic
22C2×C4⋊Dic61D412yes—
23C2×C4⋊Dic61C2311yescharacteristic
24C2×#11758196—24no—
25C2×#11758196—24no—
26C2×#11758196—48no—
27C2×C4×Dic61—21no—
28C2×C4×Dic61—22no—
29C2×C4×Dic61C814yescomplemented
30C2×C4×Dic61C2×C412yes—
31C23×C4×C61—21no—
32C23×C4×C61C2×C411yescharacteristic
33C2×C4⋊C4×C61—21no—
34C2×C4⋊C4×C61—41no—
35C2×C4⋊C4×C61—41no—
36C2×C4⋊C4×C61C2×C412yes—
37C24×C61C22⋊C411yescharacteristic
38C22×C4×C61—21no—
39C22×C4×C61—21no—
40C22×C4×C61—22no—
41C22×C4×C61—22no—
42C22×C4×C61—44no—
43C22×C4×C61—41no—
44C22×C4×C61—41no—
45C22×C4×C61C22⋊C411yescharacteristic
46C22×C4×C61C2×C812yes—
47C22×C4×C61M1612yes—
48C22×C4×C61C22×C411yescharacteristic
49C22×Dic61—24no—
50C22×Dic61—24no—
51C22×Dic61—24no—
52C22×Dic61—22no—
53C22×Dic61—22no—
54C22×Dic61—22no—
55C22×Dic61—44no—
56C22×Dic61C22⋊C412yes—
57C22×Dic61C2×D412yes—
58C2×#92420—44no—
59C2×#92420—84no—
60C4⋊C4×C61—42no—
61C4⋊C4×C61—42no—
62C4⋊Dic61—41no—
63C4⋊Dic61—42no—
64C4⋊Dic61—41no—
65#11758196—48no—
66#11758196—48no—
67C4×Dic61—24no—
68C4×Dic61—22no—
69C4×Dic61C2×C814yescomplemented
70C23×C61—22no—
71C23×C61—22no—
72C23×C61C22⋊C812yes—
73C23×C61#9911yescharacteristic
74C23×C61#9911yescharacteristic
75C23×C61#10112yes—
76C23×C61C2×C22⋊C411yescharacteristic
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—44no—
86C2×C4×C61—42no—
87C2×C4×C61—82no—
88C2×C4×C61—82no—
89C2×C4×C61C22⋊C812yes—
90C2×C4×C61C22×C811yescharacteristic
91C2×C4×C61C2×M1611yescharacteristic
92C2×Dic61—24no—
93C2×Dic61—216no—
94C2×Dic61—24no—
95C2×Dic61—24no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—44no—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61—82no—
102#92420—84no—
103C2×#1325—611nomaximal, Sylow
104C22×C61—24no—
105C22×C61—24no—
106C22×C61—21no—
107C22×C61—21no—
108C22×C61—21no—
109C22×C61—21no—
110C22×C61#32412yes—
111C22×C61#32412yes—
112C22×C61#35312yes—
113C22×C61#35612yes—
114C22×C61C2×C22⋊C811yescharacteristic
115C22×C61C2×#9911yescharacteristic
116C22×C61C2×#10111yescharacteristic
117C4×C61—22no—
118C4×C61—21no—
119C4×C61—21no—
120C4×C61—82no—
121Dic61—28no—
122Dic61—42no—
123Dic61—42no—
124C2×#384—611no—
125C2×#324—612no—
126#1325—614no—
127C2×C61—21no—
128C2×C61—22no—
129C2×C61—21no—
130C2×C61#132514yescomplemented
131C2×C61C2×#32411yescharacteristic
132C2×C61C2×#35311yescharacteristic
133C2×C61C2×#35611yescharacteristic
134C22×C4⋊C4—611no—
135C22×C4⋊C4—1222no—
136C22×C4⋊C4#692311yescharacteristic
137C22×C42—611no—
138C2×C22⋊C8—1222no—
139#384—612no—
140#384—612no—
141#384—1222no—
142#324—614no—
143#324—1222no—
144C61C2×#132511yescharacteristic, complemented, Sylow
145C23×C4—21no—
146C23×C4—612no—
147C23×C4—1221no—
148C23×C4C2×#692311yescharacteristic
149C22×C8—2442no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—612no—
154C2×C4⋊C4—611no—
155C2×C4⋊C4—611no—
156C2×C4⋊C4—1224no—
157C2×C4⋊C4—1224no—
158C2×C4⋊C4—2441no—
159C2×C4⋊C4—2441no—
160C2×C4⋊C4—2448no—
161C2×C4⋊C4C2×#692312yes—
162C2×C42—614no—
163C2×C42—612no—
164C2×C42—1222no—
165C2×C42—1221no—
166C22⋊C8—1224no—
167C22⋊C8—2442no—
168C24C22⋊#692311yescharacteristic
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—44no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—612no—
177C22×C4—612no—
178C22×C4—1224no—
179C22×C4—1224no—
180C22×C4—1224no—
181C22×C4—1222no—
182C22×C4—1222no—
183C22×C4—1222no—
184C22×C4—2444no—
185C22×C4D61⋊C812yes—
186C22×C4#1175821312yes—
187C22×C4C22⋊#692311yescharacteristic
188C22×C4C22×#692311yescharacteristic
189C2×C8—4884no—
190C2×C8—2444no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—2442no—
194C4⋊C4—2441no—
195C4⋊C4—2441no—
196C4⋊C4—2448no—
197C4⋊C4—2448no—
198C42—614no—
199C42—1224no—
200C42—1222no—
201C23—22no—
202C23—22no—
203C23#1451983412yes—
204C23#1451983511yescharacteristic
205C23#1451983511yescharacteristic
206C23#1451983812yes—
207C23C2×C22⋊#692311yescharacteristic
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—44no—
217C2×C4—42no—
218C2×C4—82no—
219C2×C4—82no—
220C2×C4—1224no—
221C2×C4—12216no—
222C2×C4—1224no—
223C2×C4—1224no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—4882no—
227C2×C4—2444no—
228C2×C4—2442no—
229C2×C4—2442no—
230C2×C4#1451983412yes—
231C2×C4C2×D61⋊C811yescharacteristic
232C2×C4C2×#1175821311yescharacteristic
233C8—4884no—
234C22—24no—
235C22—24no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—21no—
240C22#1684060812yes—
241C22#1684060812yes—
242C22#1684066612yes—
243C22#1684067212yes—
244C22C2×#1451983411yescharacteristic
245C22C2×#1451983511yescharacteristic
246C22C2×#1451983811yescharacteristic
247C4—22no—
248C4—21no—
249C4—21no—
250C4—82no—
251C4—1228no—
252C4—2442no—
253C4—2442no—
254C2—21no—
255C2—21no—
256C2—22no—
257C2#2146076214yesdirect product factor
258C2C2×#1684060811yescharacteristic
259C2C2×#1684066611yescharacteristic
260C2C2×#1684067211yescharacteristic
subgroupG/H
centerC23#14519835
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61C2×#1325
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #21460762C2direct (N × H)
29. C2×C4×Dic61C8semidirect
69. C4×Dic61C2×C8semidirect
130. C2×C61#1325semidirect
144. C61C2×#1325semidirect
257. C2#21460762direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406072
#214607622
C2×#168396312
C2×#132561