Finite Group Databasebeta

← #30596902

Subgroups — #30596902

Order 15616.

650 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 650 conjugacy classes of subgroups — too many to draw. Only its 176 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×#16840780C212yesmaximal
2#21460697C214yesmaximal, complemented
3#21448225C211yesmaximal, characteristic
4#16840780—24no—
5#16840780C418yescomplemented
6C2×#14519844C2214yes—
7C2×#14519834—22no—
8C2×C4×#92420—22no—
9C2×#14519735C412yes—
10C2×C42×D61C2211yescharacteristic
11#16839631C2212yes—
12#16839628C411yescharacteristic
13#16839621—22no—
14#16839613—22no—
15C61×#382C411yescharacteristic
16C22×#92420—24no—
17#14519844—24no—
18#14519844C2×C418yes—
19#14519834—28no—
20C4×#92420—28no—
21C22×C4×D61C2×C411yescharacteristic
22C22×C4×D61D412yes—
23#14519735—44no—
24C2×C4⋊Dic61C2×C412yes—
25C2×#11758196—24no—
26C2×#11758198—22no—
27C2×C4×Dic61—22no—
28C2×C4×Dic61D412yes—
29C2×C4×Dic61C2311yescharacteristic
30C42×D61C2×C414yes—
31C42×D61D412yes—
32C42×D61Q812yes—
33#14519684—22no—
34C2×C4⋊C4×C61C2×C412yes—
35C2×C42×C61C2×C411yescharacteristic
36#95×C61—22no—
37C23×D61C22⋊C411yescharacteristic
38C22×C4×C61—22no—
39C22×C4×C61C22⋊C412yes—
40C22×C4×C61C22×C411yescharacteristic
41C22×Dic61—22no—
42C22×Dic61C22⋊C411yescharacteristic
43C22×Dic61C2×D412yes—
44C2×C4×D61—22no—
45C2×C4×D61—22no—
46C2×C4×D61—28no—
47C2×C4×D61C4212yes—
48C2×C4×D61C22⋊C414yes—
49C2×C4×D61C4⋊C412yes—
50C2×C4×D61C4⋊C414yes—
51C2×#92420—28no—
52C2×#92420—48no—
53C4⋊C4×C61—42no—
54C42×C61C4212yes—
55C42×C61C4⋊C412yes—
56#11758198—44no—
57C4⋊Dic61—42no—
58#11758196—48no—
59C4×Dic61—44no—
60C4×Dic61C22⋊C414yes—
61C4×Dic61C4⋊C414yes—
62C4×Dic61C22×C412yes—
63C4×Dic61C2×D411yescharacteristic
64C4×Dic61C2×Q811yescharacteristic
65C23×C61C2×C22⋊C411yescharacteristic
66C22×D61—21no—
67C22×D61—21no—
68C22×D61—24no—
69C22×D61#9512yes—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—24no—
73C2×C4×C61—42no—
74C2×C4×C61—44no—
75C2×C4×C61#9514yes—
76C2×C4×C61C2×C4211yescharacteristic
77C2×C4×C61C2×C4⋊C411yescharacteristic
78C2×Dic61—42no—
79C2×Dic61—44no—
80C2×Dic61#9512yes—
81C2×Dic61#10012yes—
82C2×Dic61#10112yes—
83C2×Dic61C2×C22⋊C412yes—
84C2×Dic61C2×C4⋊C412yes—
85C2×Dic61#13518yes—
86C4×D61—24no—
87C4×D61—24no—
88C4×D61—28no—
89C4×D61—28no—
90#92420—48no—
91#8038—611nomaximal, Sylow
92C22×C61C2×#9511yescharacteristic
93C22×C61C2×#10011yescharacteristic
94C22×C61C2×#10111yescharacteristic
95C22×C61#41614yes—
96C2×D61—24no—
97C2×D61—22no—
98C2×D61—42no—
99C2×D61—42no—
100C4×C61—24no—
101C4×C61—21no—
102C4×C61—21no—
103C4×C61—82no—
104Dic61—82no—
105Dic61#34314yes—
106Dic61#41614yes—
107Dic61#42714yes—
108C2×#431—612no—
109#2285—611no—
110#1296—614no—
111C2×C61#154312yes—
112C2×C61#154412yes—
113C2×C61#173512yes—
114C2×C61C2×#34311yescharacteristic
115D61—42no—
116C2×#117—612no—
117C22×C42—611no—
118#431—618no—
119#431—1224no—
120C2×C4⋊C8—614no—
121C2×C22⋊C8—1222no—
122C2×C4×C8—1222no—
123#384—612no—
124#382—611no—
125#382#692311yescharacteristic
126#380—1222no—
127C4×C4⋊C4—1222no—
128C61#803811yescharacteristic, complemented, Sylow
129C23×C4—612no—
130C23×C4—611no—
131C22×C8—1224no—
132#117—2444no—
133C2×C4⋊C4—612no—
134C2×C4⋊C4—1224no—
135C2×C4⋊C4C2×#692312yes—
136C2×C22⋊C4—1222no—
137C2×C42—612no—
138C2×C42—611no—
139C2×C42—614no—
140C2×C42—612no—
141C2×C42—612no—
142C2×C42—1222no—
143C2×C42C2×#692311yescharacteristic
144C4⋊C8—618no—
145C4⋊C8—1224no—
146C22⋊C8—1228no—
147C4×C8—1228no—
148#95—22no—
149#95—1222no—
150C24—611no—
151C22×C4—22no—
152C22×C4—611no—
153C22×C4—612no—
154C22×C4—614no—
155C22×C4—614no—
156C22×C4—612no—
157C22×C4—612no—
158C22×C4—1222no—
159C22×C4—1222no—
160C22×C4—1228no—
161C22×C4—1222no—
162C22×C4C22⋊#692312yes—
163C22×C4C22×#692311yescharacteristic
164C2×C8—1228no—
165C2×C8—2448no—
166C4⋊C4—42no—
167C4⋊C4—2442no—
168C4⋊C4—2448no—
169C22⋊C4—2444no—
170C42—614no—
171C42—614no—
172C42—612no—
173C42—611no—
174C42—611no—
175C42—2444no—
176C42C4×#692312yes—
177C42C4⋊#692312yes—
178C23—612no—
179C23—1221no—
180C23—1221no—
181C23—1224no—
182C23C2×C22⋊#692311yescharacteristic
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—24no—
186C2×C4—42no—
187C2×C4—44no—
188C2×C4—612no—
189C2×C4—612no—
190C2×C4—618no—
191C2×C4—612no—
192C2×C4—612no—
193C2×C4—612no—
194C2×C4—1228no—
195C2×C4—1228no—
196C2×C4—1224no—
197C2×C4—1224no—
198C2×C4—2442no—
199C2×C4—2444no—
200C2×C4(C2×#6923)⋊C414yes—
201C2×C4C2×C4×#692311yescharacteristic
202C2×C4C2×C4⋊#692311yescharacteristic
203C8—2448no—
204C22—1224no—
205C22—1222no—
206C22—2442no—
207C22—2442no—
208C22C2×(C2×#6923)⋊C411yescharacteristic
209C22D61⋊#10011yescharacteristic
210C22D61⋊#10111yescharacteristic
211C22#1684075214yes—
212C4—24no—
213C4—21no—
214C4—21no—
215C4—82no—
216C4—614no—
217C4—614no—
218C4—614no—
219C4—4882no—
220C2—2442no—
221C2#2146132312yes—
222C2#2146132512yes—
223C2#2146150412yes—
224C2#2146152211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#382#6923
hypocenterC61#8038
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #21460697C2semidirect
5. #16840780C4semidirect
128. C61#8038semidirect

Maximal subgroups

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

subgroupindex
C2×#168407802
#214606972
#214482252
#803861