Finite Group Databasebeta

← #30599345

Subgroups — #30599345

Order 15616.

814 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 80 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
1#21461645C212yesmaximal
2#21460718C214yesmaximal, complemented
3#21448394C211yesmaximal, characteristic
4C2×#14519835—22no—
5C2×#14519835—22no—
6#16840703C2214yes—
7C23×C22⋊D61C2211yescharacteristic
8C22×C22⋊Dic61C411yescharacteristic, complemented
9#16839641—22no—
10#16839639—22no—
11#16839623C412yescomplemented
12#16839617C2212yes—
13C22×C22⋊C4×C61C411yescharacteristic, complemented
14C2×C22⋊#6923—24no—
15C2×C22⋊#6923—28no—
16#14519835—44no—
17#14519835—44no—
18C24×D61C2311yescharacteristic
19C22×C22⋊D61—24no—
20C22×C22⋊D61—42no—
21C22×C22⋊D61—42no—
22C22×C22⋊D61D412yes—
23C22×C22⋊D61D412yes—
24C23×Dic61—21no—
25C23×Dic61C2×C411yescharacteristic
26C2×C22⋊Dic61—21no—
27C2×C22⋊Dic61—42no—
28C2×C22⋊Dic61C2×C412yes—
29C2×#11758198—24no—
30#14519684—24no—
31C25×C61C2×C411yescharacteristic
32C23×C4×C61—21no—
33C2×C22⋊C4×C61—21no—
34C2×C22⋊C4×C61—42no—
35C2×C22⋊C4×C61C2×C412yes—
36C24×C61—22no—
37C24×C61—22no—
38C24×C61—22no—
39C24×C61—82no—
40C24×C61C22⋊C411yescharacteristic
41C24×C61C22⋊C411yescharacteristic
42C24×C61C22×C411yescharacteristic
43C23×D61—41no—
44C23×D61—41no—
45C23×D61—82no—
46C23×D61C2×D412yes—
47C23×D61#4114yes—
48C22×#6923—44no—
49C22×C4×C61—22no—
50C22×C4×C61—42no—
51C22×C4×C61—82no—
52C2×C22⋊D61—24no—
53C2×C22⋊D61—24no—
54C2×C22⋊D61—24no—
55C2×C22⋊D61—24no—
56C2×C22⋊D61—42no—
57C2×C22⋊D61—42no—
58C2×C22⋊D61—416no—
59C22×Dic61—22no—
60C22×Dic61—22no—
61C22×Dic61—41no—
62C22×Dic61—41no—
63C22×Dic61—42no—
64C22×Dic61—82no—
65C22×Dic61C22⋊C412yes—
66C22⋊#6923—44no—
67C22⋊#6923—44no—
68C22⋊#6923—88no—
69C22⋊C4×C61—42no—
70C22⋊C4×C61—42no—
71C22⋊Dic61—42no—
72C22⋊Dic61—42no—
73#11758198—84no—
74C23×C61—28no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—21no—
78C23×C61—21no—
79C23×C61—21no—
80C23×C61—21no—
81C23×C61—42no—
82C23×C61—42no—
83C23×C61—42no—
84C23×C61—84no—
85C23×C61—84no—
86C23×C61—84no—
87C23×C61#9912yes—
88C23×C61#9912yes—
89C23×C61C2×C22⋊C411yescharacteristic
90C23×C61#11712yes—
91C22×D61—22no—
92C22×D61—22no—
93C22×D61—44no—
94C22×D61—48no—
95C22×D61—44no—
96C22×D61—84no—
97C22×D61—84no—
98C22×D61#12314yes—
99C2×#6923—84no—
100C2×#6923—88no—
101C2×C4×C61—44no—
102C2×C4×C61—42no—
103C2×C4×C61—84no—
104C22⋊D61—48no—
105C22⋊D61—48no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—44no—
110C2×Dic61—44no—
111C2×Dic61—42no—
112C2×Dic61—84no—
113#8747—611nomaximal, Sylow
114C22×C61—22no—
115C22×C61—22no—
116C22×C61—22no—
117C22×C61—22no—
118C22×C61—24no—
119C22×C61—42no—
120C22×C61—42no—
121C22×C61—42no—
122C22×C61—42no—
123C22×C61—42no—
124C22×C61—42no—
125C22×C61—42no—
126C22×C61—42no—
127C22×C61—88no—
128C22×C61#38111yescharacteristic
129C22×C61C2×#9911yescharacteristic
130C22×C61C2×#9911yescharacteristic
131C2×D61—24no—
132C2×D61—28no—
133C2×D61—82no—
134C2×D61—82no—
135C2×D61—88no—
136#6923—164no—
137C4×C61—82no—
138Dic61—42no—
139Dic61—82no—
140#2308—611no—
141#1781—612no—
142#1304—614no—
143C2×C61—21no—
144C2×C61—21no—
145C2×C61—42no—
146C2×C61—42no—
147C2×C61—42no—
148C2×C61#181911yescharacteristic
149C2×C61#182812yes—
150D61—44no—
151C23×D4—611no—
152C22×C22⋊C4—611no—
153C22×C22⋊C4#692311yescharacteristic, complemented
154C2×#99—1222no—
155C2×#99—1222no—
156#386—1222no—
157#386—1222no—
158#381—612no—
159#379—612no—
160#379—614no—
161C61#874711yescharacteristic, complemented, Sylow
162C25—611no—
163C25C2×#692311yescharacteristic
164C22×D4—612no—
165C22×D4—612no—
166C22×D4—1224no—
167C22×D4—2442no—
168C22×D4—2442no—
169C23×C4—21no—
170C23×C4—611no—
171C23×C4—1221no—
172C2×C22⋊C4—21no—
173C2×C22⋊C4—42no—
174C2×C22⋊C4—612no—
175C2×C22⋊C4—1224no—
176C2×C22⋊C4—1228no—
177C2×C22⋊C4—1221no—
178C2×C22⋊C4—1224no—
179C2×C22⋊C4—2442no—
180C2×C22⋊C4C2×#692312yes—
181#99—2444no—
182#99—2444no—
183#95—1224no—
184C24—22no—
185C24—22no—
186C24—22no—
187C24—82no—
188C24—612no—
189C24—614no—
190C24—4882no—
191C24—2441no—
192C24—2441no—
193C24C22⋊#692311yescharacteristic
194C24C22⋊#692311yescharacteristic
195C24C22×#692311yescharacteristic
196C2×D4—1224no—
197C2×D4—1224no—
198C2×D4—1224no—
199C2×D4—1224no—
200C2×D4—2442no—
201C2×D4—2442no—
202C2×D4—24416no—
203C22×C4—22no—
204C22×C4—42no—
205C22×C4—82no—
206C22×C4—612no—
207C22×C4—1222no—
208C22×C4—1222no—
209C22×C4—4882no—
210C22×C4—2441no—
211C22×C4—2441no—
212C22×C4—2444no—
213C22×C4—2442no—
214C22⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—4884no—
217C22⋊C4—4888no—
218C22⋊C4—2444no—
219C22⋊C4—2444no—
220C22⋊C4—2442no—
221C22⋊C4—2442no—
222C23—28no—
223C23—21no—
224C23—21no—
225C23—21no—
226C23—21no—
227C23—21no—
228C23—21no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—84no—
233C23—84no—
234C23—84no—
235C23—614no—
236C23—1222no—
237C23—1222no—
238C23—4884no—
239C23—4884no—
240C23—2444no—
241C23—2448no—
242C23—2444no—
243C23#1451983512yes—
244C23#1451983612yes—
245C23C2×C22⋊#692311yescharacteristic
246C23#1451985612yes—
247D4—2448no—
248D4—2448no—
249C2×C4—44no—
250C2×C4—42no—
251C2×C4—84no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—1222no—
255C2×C4—4888no—
256C2×C4—4884no—
257C2×C4—4884no—
258C2×C4—2444no—
259C2×C4—2442no—
260C2×C4—2444no—
261C22—22no—
262C22—22no—
263C22—22no—
264C22—22no—
265C22—24no—
266C22—42no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—42no—
272C22—42no—
273C22—42no—
274C22—88no—
275C22—1224no—
276C22—1228no—
277C22—4882no—
278C22—4882no—
279C22—4888no—
280C22#1684070511yescharacteristic
281C22C2×#1451983511yescharacteristic
282C22C2×#1451983611yescharacteristic
283C4—82no—
284C4—9764no—
285C4—4882no—
286C4—2442no—
287C2—21no—
288C2—21no—
289C2—42no—
290C2—42no—
291C2—42no—
292C2—2444no—
293C2#2146171411yescharacteristic
294C2#2146173012yes—
subgroupG/H
centerC22#16840705
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C22⋊C4×C61C4
socleC22×C61#381
prime radicalC23×C22⋊D61C22
cosocleC24×D61C23
hypercenterC22×C22⋊C4#6923
hypocenterC61#8747
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #21460718C2semidirect
8. C22×C22⋊Dic61C4semidirect
11. #16839623C4semidirect
13. C22×C22⋊C4×C61C4semidirect
153. C22×C22⋊C4#6923semidirect
161. C61#8747semidirect

Maximal subgroups

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

subgroupindex
#214616452
#214607182
#214483942
#874761