Finite Group Databasebeta

← #30596876

Subgroups — #30596876

Order 15616.

610 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 160 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×#16840785C212yesmaximal
2#21460695C214yesmaximal, complemented
3#21448224C211yesmaximal, characteristic
4#16840785—24no—
5#16840785C418yescomplemented
6C2×#14519844—22no—
7C2×#14519834—22no—
8C2×#14519832C2214yes—
9C2×#14519735C412yes—
10C2×C42×D61C2211yescharacteristic
11#16839632C411yescharacteristic
12#16839627C2212yes—
13#16839619—22no—
14C4⋊C4×Dic61—22no—
15C61×#384C411yescharacteristic
16C22×#92420—24no—
17#14519844—28no—
18#14519834—28no—
19#14519832—24no—
20#14519832C2×C418yes—
21C22×C4×D61C2×C411yescharacteristic
22C22×C4×D61D412yes—
23#14519735—44no—
24C2×C4⋊Dic61—22no—
25C2×C4⋊Dic61C2×C412yes—
26C2×#11758198—22no—
27C2×C4×Dic61—22no—
28C2×C4×Dic61D412yes—
29C2×C4×Dic61C2311yescharacteristic
30C42×D61C2×C414yes—
31C42×D61D412yes—
32C42×D61Q812yes—
33#14519684—24no—
34C2×C4⋊C4×C61—22no—
35C2×C4⋊C4×C61C2×C412yes—
36C2×C42×C61C2×C411yescharacteristic
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—42no—
47C2×C4×D61—42no—
48C2×C4×D61C4212yes—
49C2×C4×D61C22⋊C414yes—
50C2×C4×D61C4⋊C412yes—
51C2×C4×D61C4⋊C414yes—
52C2×#92420—28no—
53C2×#92420—44no—
54C2×#92420—44no—
55C4⋊C4×C61—44no—
56C4⋊C4×C61—42no—
57C42×C61C4212yes—
58C42×C61C4⋊C412yes—
59#11758198—44no—
60C4⋊Dic61—44no—
61C4⋊Dic61—42no—
62C4×Dic61—44no—
63C4×Dic61C22⋊C414yes—
64C4×Dic61C4⋊C414yes—
65C4×Dic61C22×C412yes—
66C4×Dic61C2×D411yescharacteristic
67C4×Dic61C2×Q811yescharacteristic
68C23×C61C2×C22⋊C411yescharacteristic
69C22×D61—21no—
70C22×D61—21no—
71C22×D61—22no—
72C22×D61—22no—
73C22×D61#9512yes—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—42no—
79C2×C4×C61—44no—
80C2×C4×C61#9514yes—
81C2×C4×C61C2×C4211yescharacteristic
82C2×C4×C61C2×C4⋊C411yescharacteristic
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—42no—
86C2×Dic61—44no—
87C2×Dic61#9512yes—
88C2×Dic61#10012yes—
89C2×Dic61#10112yes—
90C2×Dic61C2×C22⋊C412yes—
91C2×Dic61C2×C4⋊C412yes—
92C4×D61—24no—
93C4×D61—24no—
94C4×D61—44no—
95C4×D61—44no—
96#92420—48no—
97#8031—611nomaximal, Sylow
98C22×C61C2×#9511yescharacteristic
99C22×C61C2×#10011yescharacteristic
100C22×C61C2×#10111yescharacteristic
101C22×C61#42112yes—
102C22×C61#42112yes—
103C2×D61—24no—
104C2×D61—22no—
105C2×D61—41no—
106C2×D61—41no—
107C2×D61—42no—
108C4×C61—24no—
109C4×C61—21no—
110C4×C61—21no—
111C4×C61—82no—
112Dic61—22no—
113Dic61—22no—
114Dic61—82no—
115Dic61#34314yes—
116C2×#432—612no—
117#2285—611no—
118#1295—614no—
119C2×C61#153611yescharacteristic
120C2×C61#153611yescharacteristic
121C2×C61#153712yes—
122C2×C61#173312yes—
123C2×C61C2×#34311yescharacteristic
124D61—42no—
125C2×#117—612no—
126C22×C42—611no—
127#432—618no—
128#432—1224no—
129C2×C4⋊C8—1222no—
130C2×C22⋊C8—1222no—
131C2×#97—614no—
132#384—611no—
133#384#692311yescharacteristic
134#382—612no—
135#380—1222no—
136C4×C4⋊C4—1222no—
137C61#803111yescharacteristic, complemented, Sylow
138C23×C4—611no—
139C23×C4—612no—
140C22×C8—1224no—
141#117—2444no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—612no—
144C2×C4⋊C4—1222no—
145C2×C4⋊C4C2×#692312yes—
146C2×C22⋊C4—1222no—
147C2×C42—612no—
148C2×C42—611no—
149C2×C42—614no—
150C2×C42—612no—
151C2×C42—612no—
152C2×C42—1222no—
153C2×C42C2×#692311yescharacteristic
154C4⋊C8—1228no—
155C22⋊C8—1228no—
156#97—618no—
157#97—1224no—
158#95—1224no—
159C24—611no—
160C22×C4—22no—
161C22×C4—611no—
162C22×C4—612no—
163C22×C4—612no—
164C22×C4—612no—
165C22×C4—614no—
166C22×C4—614no—
167C22×C4—1222no—
168C22×C4—1222no—
169C22×C4—1222no—
170C22×C4—2442no—
171C22×C4—2442no—
172C22×C4C22⋊#692312yes—
173C22×C4C22×#692311yescharacteristic
174C2×C8—1228no—
175C2×C8—2444no—
176C2×C8—2444no—
177C4⋊C4—42no—
178C4⋊C4—44no—
179C4⋊C4—2442no—
180C4⋊C4—2444no—
181C22⋊C4—2444no—
182C42—614no—
183C42—614no—
184C42—612no—
185C42—611no—
186C42—611no—
187C42—2444no—
188C42C4×#692312yes—
189C42C4⋊#692312yes—
190C23—612no—
191C23—1221no—
192C23—1221no—
193C23—1222no—
194C23—1222no—
195C23C2×C22⋊#692311yescharacteristic
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—42no—
201C2×C4—44no—
202C2×C4—612no—
203C2×C4—612no—
204C2×C4—612no—
205C2×C4—612no—
206C2×C4—612no—
207C2×C4—1224no—
208C2×C4—1224no—
209C2×C4—1222no—
210C2×C4—1222no—
211C2×C4—2444no—
212C2×C4—2444no—
213C2×C4—2442no—
214C2×C4—2444no—
215C2×C4(C2×#6923)⋊C414yes—
216C2×C4C2×C4×#692311yescharacteristic
217C2×C4C2×C4⋊#692311yescharacteristic
218C8—2448no—
219C22—1222no—
220C22—1224no—
221C22—2441no—
222C22—2441no—
223C22—2442no—
224C22C2×(C2×#6923)⋊C411yescharacteristic
225C22D61⋊#10011yescharacteristic
226C22D61⋊#10111yescharacteristic
227C22#1684076012yes—
228C22#1684076112yes—
229C4—21no—
230C4—21no—
231C4—24no—
232C4—82no—
233C4—614no—
234C4—1222no—
235C4—1222no—
236C4—4882no—
237C2—2442no—
238C2#2146130811yescharacteristic
239C2#2146130911yescharacteristic
240C2#2146131112yes—
241C2#2146149812yes—
242C2#2146152211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#384C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#384#6923
hypocenterC61#8031
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
2. #21460695C2semidirect
5. #16840785C4semidirect
137. C61#8031semidirect

Maximal subgroups

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

subgroupindex
C2×#168407852
#214606952
#214482242
#803161