Finite Group Databasebeta

← #29573356

Subgroups — #29573356

Order 15616.

486 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 115 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×#16839629C211yesmaximal, characteristic
2#21445885C212yesmaximal
3#21443662C211yesmaximal, characteristic
4#21443661C212yesmaximal
5C61×#1280C211yesmaximal, characteristic
6C22×C4×Dic61C2211yescharacteristic
7C2×C22⋊#92418C2212yes—
8#16839629—24no—
9C2×#14519684C412yes—
10C2×#14519684C412yes—
11C2×#14519684C2211yescharacteristic
12#16839516—24no—
13C2×C22⋊C8×C61C2212yes—
14C2×#95×C61C2211yescharacteristic
15C23×Dic61C2×C411yescharacteristic
16C23×Dic61C2×C412yes—
17C23×Dic61C2×C411yescharacteristic
18C22×#92418—22no—
19C2×C4×Dic61—22no—
20C2×C4×Dic61—21no—
21C2×C4×Dic61—21no—
22C2×C4×Dic61D414yes—
23C22⋊#92418—22no—
24C22⋊#92418—22no—
25#14519684—22no—
26#14519684—24no—
27#14519684—24no—
28C23×C4×C61C2×C412yes—
29C23×C4×C61C2311yescharacteristic
30C22×C8×C61—22no—
31C22⋊C8×C61—22no—
32C22⋊C8×C61—22no—
33#95×C61—22no—
34C24×C61C22×C411yescharacteristic
35C22×C4×C61—22no—
36C22×C4×C61—22no—
37C22×C4×C61—22no—
38C22×C4×C61—42no—
39C22×C4×C61—42no—
40C22×C4×C61—42no—
41C22×C4×C61C2×D412yes—
42C22×C4×C61#4112yes—
43C22×C4×C61#4111yescharacteristic
44C22×C4×C61#4111yescharacteristic
45C22×Dic61—21no—
46C22×Dic61—21no—
47C22×Dic61—21no—
48C22×Dic61—21no—
49C22×Dic61—22no—
50C22×Dic61—22no—
51C22×Dic61—22no—
52C22×Dic61—22no—
53C22×Dic61—22no—
54C22×Dic61—41no—
55C22×Dic61—41no—
56C22×Dic61—42no—
57C22×Dic61—42no—
58C22×Dic61C22⋊C412yes—
59C22×Dic61C22⋊C412yes—
60C2×C8×C61—44no—
61C2×C8×C61—42no—
62C4×Dic61—24no—
63C4×Dic61—24no—
64C2×#92418—44no—
65C2×#92418—42no—
66C23×C61—22no—
67C23×C61—21no—
68C23×C61—21no—
69C23×C61C2×C22⋊C411yescharacteristic
70C23×C61#11711yescharacteristic
71C23×C61#11711yescharacteristic
72C23×C61#13112yes—
73C23×C61#13112yes—
74C2×C4×C61—24no—
75C2×C4×C61—41no—
76C2×C4×C61—42no—
77C2×C4×C61—41no—
78C2×C4×C61—42no—
79C2×C4×C61—42no—
80C2×C4×C61—42no—
81C2×C4×C61—82no—
82C2×C4×C61—82no—
83C2×C4×C61#12312yes—
84C2×C4×C61#12312yes—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—24no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—42no—
91C2×Dic61—42no—
92C2×Dic61—41no—
93C2×Dic61—42no—
94C2×Dic61—41no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97C2×Dic61—42no—
98C2×Dic61—82no—
99C2×Dic61—82no—
100C8×C61—82no—
101#92418—82no—
102#8705—611nomaximal, Sylow
103C22×C61—21no—
104C22×C61—21no—
105C22×C61—21no—
106C22×C61—21no—
107C22×C61—22no—
108C22×C61—22no—
109C22×C61—22no—
110C22×C61—22no—
111C22×C61#38111yescharacteristic
112C22×C61#40812yes—
113C22×C61#41012yes—
114C22×C61#41311yescharacteristic
115C22×C61#41311yescharacteristic
116C22×C61#43311yescharacteristic
117C22×C61#43312yes—
118C22×C61#43311yescharacteristic
119C4×C61—22no—
120C4×C61—22no—
121C4×C61—82no—
122Dic61—42no—
123Dic61—42no—
124Dic61—82no—
125C2×#383—611no—
126#1817—612no—
127#1280—612no—
128#1280—611no—
129#1280D6111yescharacteristic
130C2×C61—21no—
131C2×C61—22no—
132C2×C61—21no—
133C2×C61#147312yes—
134C2×C61#147312yes—
135C2×C61#181811yescharacteristic
136C2×C61#182011yescharacteristic
137C2×C61#182211yescharacteristic
138C22×C42—611no—
139C2×C22⋊C8—612no—
140C2×C22⋊C8C2×D6112yes—
141#383—1224no—
142C2×#95—612no—
143C2×#95—612no—
144C2×#95—611no—
145C2×#95C2×D6111yescharacteristic
146#336—1224no—
147C61#870511yescharacteristic, complemented, Sylow
148C23×C4—611no—
149C23×C4—611no—
150C23×C4—612no—
151C23×C4C4×D6112yes—
152C23×C4C22×D6111yescharacteristic
153C22×C8—22no—
154C22×C8—1222no—
155C2×C42—614no—
156C2×C42—1222no—
157C2×C42—1221no—
158C2×C42—1221no—
159C22⋊C8—22no—
160C22⋊C8—22no—
161C22⋊C8—1222no—
162C22⋊C8—1222no—
163#95—22no—
164#95—1224no—
165#95—1224no—
166#95—1222no—
167C24C2×C4×D6111yescharacteristic
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—42no—
172C22×C4—42no—
173C22×C4—42no—
174C22×C4—612no—
175C22×C4—612no—
176C22×C4—1221no—
177C22×C4—1221no—
178C22×C4—1221no—
179C22×C4—1221no—
180C22×C4—1222no—
181C22×C4—1222no—
182C22×C4—1222no—
183C22×C4—1222no—
184C22×C4—1222no—
185C22×C4—2441no—
186C22×C4—2441no—
187C22×C4—2442no—
188C22×C4—2442no—
189C22×C4#1175822212yes—
190C22×C4D4×D6112yes—
191C22×C4#1175822411yescharacteristic
192C22×C4#1175822611yescharacteristic
193C2×C8—44no—
194C2×C8—42no—
195C2×C8—2444no—
196C2×C8—2442no—
197C42—1224no—
198C42—1224no—
199C23—22no—
200C23—21no—
201C23—21no—
202C23C22⋊C4×D6111yescharacteristic
203C23#1451973411yescharacteristic
204C23#1451973511yescharacteristic
205C23#1451978312yes—
206C23#1451978512yes—
207C2×C4—24no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—82no—
215C2×C4—82no—
216C2×C4—1224no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—4882no—
222C2×C4—4882no—
223C2×C4—2442no—
224C2×C4—2442no—
225C2×C4—2442no—
226C2×C4—2442no—
227C2×C4—2442no—
228C2×C4—2441no—
229C2×C4—2442no—
230C2×C4—2441no—
231C2×C4#1451975912yes—
232C2×C4#1451976212yes—
233C8—82no—
234C8—4882no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—22no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22#1683962411yescharacteristic
244C22#1683972712yes—
245C22#1683973412yes—
246C22#1683974311yescharacteristic
247C22#1683974511yescharacteristic
248C22#1683982111yescharacteristic
249C22#1683982212yes—
250C22#1683982411yescharacteristic
251C4—22no—
252C4—22no—
253C4—82no—
254C4—4882no—
255C4—2442no—
256C4—2442no—
257C2—21no—
258C2—22no—
259C2—21no—
260C2#2144418512yes—
261C2#2144418712yes—
262C2#2144588911yescharacteristic
263C2#2144589511yescharacteristic
264C2#2144590111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutator, prime radicalC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1280C2
socleC23×C61C2×C22⋊C4
cosocleC23×C4×C61C23
hypercenter#1280D61
hypocenterC61#8705
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
147. C61#8705semidirect

Maximal subgroups

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

subgroupindex
C2×#168396292
#214458852
#214436622
#214436612
C61×#12802
#870561