Finite Group Databasebeta

← #30596908

Subgroups — #30596908

Order 15616.

726 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 184 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×#16840782C212yesmaximal
2#21460697C214yesmaximal, complemented
3C2×#16839631C211yesmaximal, characteristic
4#16840782—24no—
5#16840782C418yescomplemented
6C2×#14519844C2214yes—
7C2×C22⋊#92420—22no—
8C2×#14519832—22no—
9C22×C4⋊Dic61C411yescharacteristic
10C22×#11758196—22no—
11C22×C4×Dic61C2211yescharacteristic
12#16839631—22no—
13#16839631C412yes—
14#16839631C2212yes—
15C22×C4⋊C4×C61C411yescharacteristic
16C22×#92420—24no—
17#14519844—24no—
18#14519844C2×C418yescomplemented
19C22⋊#92420—28no—
20#14519832—28no—
21C23×Dic61—21no—
22C23×Dic61D412yes—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61—42no—
25C2×C4⋊Dic61C2×C412yes—
26C2×#11758196—24no—
27C2×#11758196—24no—
28C2×#11758196—48no—
29C2×C4×Dic61C2×C411yescharacteristic
30C2×C4×Dic61C2×C414yes—
31C2×C4×Dic61D412yes—
32C2×C4×Dic61D412yes—
33C2×C4×Dic61Q812yes—
34C2×C4×Dic61C2311yescharacteristic
35C23×C4×C61—21no—
36C23×C4×C61C2×C411yescharacteristic
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—42no—
39C2×C4⋊C4×C61C2×C412yes—
40C24×C61C22⋊C411yescharacteristic
41C22×C4×C61—22no—
42C22×C4×C61—22no—
43C22×C4×C61—22no—
44C22×C4×C61—44no—
45C22×C4×C61—42no—
46C22×C4×C61C4212yes—
47C22×C4×C61C22⋊C411yescharacteristic
48C22×C4×C61C4⋊C412yes—
49C22×C4×C61C22×C411yescharacteristic
50C22×Dic61—24no—
51C22×Dic61—24no—
52C22×Dic61—22no—
53C22×Dic61—44no—
54C22×Dic61—42no—
55C22×Dic61C22⋊C412yes—
56C22×Dic61C22⋊C414yes—
57C22×Dic61C4⋊C414yes—
58C22×Dic61C2×D412yes—
59C2×#92420—28no—
60C2×#92420—44no—
61C2×#92420—44no—
62C4⋊C4×C61—42no—
63C4⋊C4×C61—42no—
64C4⋊Dic61—42no—
65C4⋊Dic61—42no—
66#11758196—48no—
67#11758196—48no—
68C4×Dic61C4212yes—
69C4×Dic61C22⋊C414yes—
70C4×Dic61C4⋊C412yes—
71C4×Dic61C4⋊C414yes—
72C4×Dic61C22×C412yes—
73C4×Dic61C2×D411yescharacteristic
74C4×Dic61C2×Q811yescharacteristic
75C23×C61—22no—
76C23×C61—22no—
77C23×C61#9512yes—
78C23×C61#10012yes—
79C23×C61#10112yes—
80C23×C61C2×C22⋊C411yescharacteristic
81C2×C4×C61—24no—
82C2×C4×C61—24no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—42no—
88C2×C4×C61—44no—
89C2×C4×C61—84no—
90C2×C4×C61#9512yes—
91C2×C4×C61C2×C4211yescharacteristic
92C2×C4×C61C2×C4⋊C411yescharacteristic
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—28no—
96C2×Dic61—28no—
97C2×Dic61—42no—
98C2×Dic61—44no—
99C2×Dic61—84no—
100C2×Dic61#9514yes—
101C2×Dic61C2×C22⋊C412yes—
102C2×Dic61C2×C4⋊C412yes—
103C2×Dic61AGL(1,ℤ/8)14yes—
104C2×Dic61#13714yes—
105#92420—48no—
106#8040—611nomaximal, Sylow
107C22×C61—22no—
108C22×C61—24no—
109C22×C61—22no—
110C22×C61—24no—
111C22×C61#34314yes—
112C22×C61C2×#9511yescharacteristic
113C22×C61C2×#10011yescharacteristic
114C22×C61C2×#10111yescharacteristic
115C22×C61#41812yes—
116C22×C61#41912yes—
117C4×C61—22no—
118C4×C61—21no—
119C4×C61—21no—
120C4×C61—82no—
121Dic61—24no—
122Dic61—82no—
123Dic61#41714yes—
124Dic61#42814yes—
125C2×#432—612no—
126C2×#384—611no—
127#1296—614no—
128C2×C61—24no—
129C2×C61#155511yescharacteristic
130C2×C61#155612yes—
131C2×C61#155811yescharacteristic
132C2×C61#173612yes—
133C2×C61C2×#34311yescharacteristic
134C22×C4⋊C4—611no—
135C22×C4⋊C4—1222no—
136C22×C4⋊C4#692311yescharacteristic
137C22×C42—611no—
138#432—618no—
139#432—1224no—
140C2×C4⋊C8—614no—
141C2×C22⋊C8—1222no—
142C2×#97—1222no—
143#384—612no—
144#384—612no—
145#384—1222no—
146C61#804011yescharacteristic, complemented, Sylow
147C23×C4—21no—
148C23×C4—612no—
149C23×C4—1221no—
150C23×C4C2×#692311yescharacteristic
151C22×C8—1224no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—42no—
154C2×C4⋊C4—612no—
155C2×C4⋊C4—1224no—
156C2×C4⋊C4—1224no—
157C2×C4⋊C4—1221no—
158C2×C4⋊C4—2442no—
159C2×C4⋊C4—2448no—
160C2×C4⋊C4C2×#692312yes—
161C2×C42—614no—
162C2×C42—612no—
163C2×C42—612no—
164C2×C42—612no—
165C2×C42—611no—
166C2×C42—611no—
167C4⋊C8—618no—
168C4⋊C8—1224no—
169C22⋊C8—1228no—
170#97—1228no—
171C24C22⋊#692311yescharacteristic
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—44no—
176C22×C4—42no—
177C22×C4—612no—
178C22×C4—614no—
179C22×C4—614no—
180C22×C4—612no—
181C22×C4—1224no—
182C22×C4—1224no—
183C22×C4—1222no—
184C22×C4—2444no—
185C22×C4—2442no—
186C22×C4C4×#692312yes—
187C22×C4C4⋊#692312yes—
188C22×C4C22⋊#692311yescharacteristic
189C22×C4C22×#692311yescharacteristic
190C2×C8—1228no—
191C2×C8—2444no—
192C2×C8—2444no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—2442no—
196C4⋊C4—2442no—
197C4⋊C4—2448no—
198C4⋊C4—2448no—
199C42—614no—
200C42—614no—
201C42—612no—
202C42—612no—
203C42—611no—
204C42—612no—
205C42—611no—
206C23—22no—
207C23—22no—
208C23(C2×#6923)⋊C412yes—
209C23#1451983712yes—
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—42no—
219C2×C4—44no—
220C2×C4—84no—
221C2×C4—614no—
222C2×C4—614no—
223C2×C4—612no—
224C2×C4—612no—
225C2×C4—614no—
226C2×C4—1228no—
227C2×C4—1228no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4—4884no—
231C2×C4—2442no—
232C2×C4—2444no—
233C2×C4(C2×#6923)⋊C412yes—
234C2×C4C2×C4×#692311yescharacteristic
235C2×C4C2×C4⋊#692311yescharacteristic
236C8—2448no—
237C22—24no—
238C22—22no—
239C22—24no—
240C22—22no—
241C22#1684064214yes—
242C22C2×(C2×#6923)⋊C411yescharacteristic
243C22C2×#1451983711yescharacteristic
244C22C2×#1451983811yescharacteristic
245C22#1684075412yes—
246C22#1684075512yes—
247C4—22no—
248C4—21no—
249C4—21no—
250C4—82no—
251C4—614no—
252C4—614no—
253C4—1224no—
254C4—4882no—
255C2—24no—
256C2#2146134611yescharacteristic
257C2#2146134812yes—
258C2#2146135211yescharacteristic
259C2#2146150612yes—
260C2C2×#1684064211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#8040
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #21460697C2semidirect
5. #16840782C4semidirect
18. #14519844C2×C4semidirect
146. C61#8040semidirect

Maximal subgroups

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

subgroupindex
C2×#168407822
#214606972
C2×#168396312
#804061