Finite Group Databasebeta

← #30596872

Subgroups — #30596872

Order 15616.

638 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 168 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#21460695C214yesmaximal, complemented
3C2×#16839627C211yesmaximal, characteristic
4#16840782—24no—
5#16840782C418yescomplemented
6C2×#14519844—22no—
7C2×C22⋊#92420—22no—
8C2×#14519832C2214yes—
9C22×C4⋊Dic61C411yescharacteristic
10C22×C4×Dic61C2211yescharacteristic
11#16839627—22no—
12#16839627C412yes—
13#16839627C2212yes—
14C2×#14519684—22no—
15C22×C4⋊C4×C61C411yescharacteristic
16C22×#92420—24no—
17#14519844—28no—
18C22⋊#92420—28no—
19#14519832—24no—
20#14519832C2×C418yescomplemented
21C23×Dic61—21no—
22C23×Dic61D412yes—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61—42no—
25C2×C4⋊Dic61C2×C412yes—
26C2×C4×Dic61C2×C411yescharacteristic
27C2×C4×Dic61C2×C414yes—
28C2×C4×Dic61D412yes—
29C2×C4×Dic61D412yes—
30C2×C4×Dic61Q812yes—
31C2×C4×Dic61C2311yescharacteristic
32#14519684—24no—
33#14519684—24no—
34C23×C4×C61—21no—
35C23×C4×C61C2×C411yescharacteristic
36C2×C4⋊C4×C61—21no—
37C2×C4⋊C4×C61—42no—
38C2×C4⋊C4×C61C2×C412yes—
39C24×C61C22⋊C411yescharacteristic
40C22×C4×C61—22no—
41C22×C4×C61—22no—
42C22×C4×C61—22no—
43C22×C4×C61—44no—
44C22×C4×C61—42no—
45C22×C4×C61C4212yes—
46C22×C4×C61C22⋊C411yescharacteristic
47C22×C4×C61C4⋊C412yes—
48C22×C4×C61C22×C411yescharacteristic
49C22×Dic61—22no—
50C22×Dic61—42no—
51C22×Dic61—42no—
52C22×Dic61—44no—
53C22×Dic61—42no—
54C22×Dic61C22⋊C412yes—
55C22×Dic61C22⋊C414yes—
56C22×Dic61C4⋊C414yes—
57C22×Dic61C2×D412yes—
58C2×#92420—28no—
59C2×#92420—44no—
60C2×#92420—44no—
61C4⋊C4×C61—42no—
62C4⋊C4×C61—42no—
63C4⋊Dic61—42no—
64C4⋊Dic61—42no—
65C4×Dic61C4212yes—
66C4×Dic61C22⋊C414yes—
67C4×Dic61C4⋊C412yes—
68C4×Dic61C4⋊C414yes—
69C4×Dic61C22×C412yes—
70C4×Dic61C2×D411yescharacteristic
71C4×Dic61C2×Q811yescharacteristic
72C23×C61—22no—
73C23×C61—22no—
74C23×C61#9512yes—
75C23×C61#10012yes—
76C23×C61#10112yes—
77C23×C61C2×C22⋊C411yescharacteristic
78C2×C4×C61—24no—
79C2×C4×C61—24no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—42no—
85C2×C4×C61—44no—
86C2×C4×C61—84no—
87C2×C4×C61#9512yes—
88C2×C4×C61C2×C4211yescharacteristic
89C2×C4×C61C2×C4⋊C411yescharacteristic
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—44no—
95C2×Dic61—44no—
96C2×Dic61—42no—
97C2×Dic61—44no—
98C2×Dic61—84no—
99C2×Dic61#9514yes—
100C2×Dic61C2×C22⋊C412yes—
101C2×Dic61C2×C4⋊C412yes—
102#92420—48no—
103#8030—611nomaximal, Sylow
104C22×C61—24no—
105C22×C61—22no—
106C22×C61—22no—
107C22×C61—24no—
108C22×C61#34314yes—
109C22×C61C2×#9511yescharacteristic
110C22×C61C2×#10011yescharacteristic
111C22×C61C2×#10111yescharacteristic
112C22×C61#42112yes—
113C22×C61#42112yes—
114C4×C61—22no—
115C4×C61—21no—
116C4×C61—21no—
117C4×C61—82no—
118Dic61—22no—
119Dic61—24no—
120Dic61—22no—
121Dic61—82no—
122C2×#432—612no—
123C2×#382—611no—
124#1295—614no—
125C2×C61—24no—
126C2×C61#153311yescharacteristic
127C2×C61#153311yescharacteristic
128C2×C61#153412yes—
129C2×C61#173312yes—
130C2×C61C2×#34311yescharacteristic
131C22×C4⋊C4—611no—
132C22×C4⋊C4#692311yescharacteristic
133C22×C42—611no—
134#432—618no—
135#432—1224no—
136C2×C4⋊C8—1222no—
137C2×C22⋊C8—1222no—
138C2×#97—614no—
139#382—612no—
140#382—612no—
141#382—1222no—
142C2×#95—1222no—
143C61#803011yescharacteristic, complemented, Sylow
144C23×C4—21no—
145C23×C4—612no—
146C23×C4—1221no—
147C23×C4C2×#692311yescharacteristic
148C22×C8—1224no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—42no—
151C2×C4⋊C4—612no—
152C2×C4⋊C4—1221no—
153C2×C4⋊C4—2442no—
154C2×C4⋊C4C2×#692312yes—
155C2×C42—614no—
156C2×C42—612no—
157C2×C42—612no—
158C2×C42—612no—
159C2×C42—611no—
160C2×C42—611no—
161C4⋊C8—1228no—
162C22⋊C8—1228no—
163#97—618no—
164#97—1224no—
165#95—1224no—
166#95—1224no—
167C24C22⋊#692311yescharacteristic
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—44no—
172C22×C4—42no—
173C22×C4—612no—
174C22×C4—612no—
175C22×C4—614no—
176C22×C4—614no—
177C22×C4—1222no—
178C22×C4—2442no—
179C22×C4—2442no—
180C22×C4—2444no—
181C22×C4—2442no—
182C22×C4C4×#692312yes—
183C22×C4C4⋊#692312yes—
184C22×C4C22⋊#692311yescharacteristic
185C22×C4C22×#692311yescharacteristic
186C2×C8—1228no—
187C2×C8—2444no—
188C2×C8—2444no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—2442no—
192C4⋊C4—2442no—
193C42—614no—
194C42—614no—
195C42—612no—
196C42—612no—
197C42—611no—
198C42—612no—
199C42—611no—
200C23—22no—
201C23—22no—
202C23(C2×#6923)⋊C412yes—
203C23#1451983712yes—
204C23#1451983812yes—
205C23C2×C22⋊#692311yescharacteristic
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—24no—
211C2×C4—24no—
212C2×C4—42no—
213C2×C4—44no—
214C2×C4—84no—
215C2×C4—614no—
216C2×C4—612no—
217C2×C4—612no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—4884no—
223C2×C4—2444no—
224C2×C4—2444no—
225C2×C4—2442no—
226C2×C4—2444no—
227C2×C4(C2×#6923)⋊C412yes—
228C2×C4C2×C4×#692311yescharacteristic
229C2×C4C2×C4⋊#692311yescharacteristic
230C8—2448no—
231C22—22no—
232C22—22no—
233C22—24no—
234C22—24no—
235C22#1684064214yes—
236C22C2×(C2×#6923)⋊C411yescharacteristic
237C22C2×#1451983711yescharacteristic
238C22C2×#1451983811yescharacteristic
239C22#1684076012yes—
240C22#1684076112yes—
241C4—22no—
242C4—21no—
243C4—21no—
244C4—82no—
245C4—1222no—
246C4—1224no—
247C4—1222no—
248C4—4882no—
249C2—24no—
250C2#2146129811yescharacteristic
251C2#2146130011yescharacteristic
252C2#2146130112yes—
253C2#2146149812yes—
254C2C2×#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#8030
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. #21460695C2semidirect
5. #16840782C4semidirect
20. #14519832C2×C4semidirect
143. C61#8030semidirect

Maximal subgroups

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

subgroupindex
C2×#168407822
#214606952
C2×#168396272
#803061