Finite Group Databasebeta

← #29589408

Subgroups — #29589408

Order 15616.

490 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 81 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#382×D61C211yesmaximal, characteristic
2#21444147C212yesmaximal
3#21443763C211yesmaximal, characteristic, complemented
4#21443762C212yesmaximal, complemented
5C61×#1324C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D61C411yescharacteristic
7C2×C4⋊C4×D61C2211yescharacteristic
8C2×C42×D61C411yescharacteristic
9#16839724—22no—
10#16839628C411yescharacteristic
11#16839627C411yescharacteristic
12#16839627C2211yescharacteristic
13#16839626—22no—
14#95×D61—22no—
15#16839488C2212yes—
16#16839487—22no—
17C61×#382C2211yescharacteristic
18C61×#324C2212yes—
19C22×C4×D61—21no—
20C22×C4×D61—21no—
21C22×C4×D61C2×C411yescharacteristic
22C22×C4×D61D412yes—
23C2×#11758189—42no—
24C2×C4⋊Dic61C2×C411yescharacteristic
25C2×C4⋊Dic61C2×C411yescharacteristic
26C2×#11758196—21no—
27C2×#11758196D412yes—
28C4⋊C4×D61—41no—
29C4⋊C4×D61—41no—
30C4⋊C4×D61—41no—
31C4⋊C4×D61—41no—
32C2×C4×Dic61—21no—
33C2×C4×Dic61C2×C411yescharacteristic
34C42×D61—22no—
35C42×D61—22no—
36C22⋊#92418—22no—
37#14519689—42no—
38#14519684—22no—
39#14519684—22no—
40#14519684—22no—
41C2×C4⋊C4×C61C2×C411yescharacteristic
42C2×C4⋊C4×C61C2311yescharacteristic
43C2×C42×C61C2×C411yescharacteristic
44C22⋊C8×C61—22no—
45#95×C61—22no—
46C23×D61C22⋊C411yescharacteristic
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61C22×C411yescharacteristic
50C22×C4×C61C2×D412yes—
51C22×Dic61—21no—
52C22×Dic61—21no—
53C22×Dic61C22⋊C411yescharacteristic
54C22×Dic61C22⋊C412yes—
55C2×C4×D61—21no—
56C2×C4×D61—21no—
57C2×C4×D61—21no—
58C2×C4×D61—21no—
59C2×C4×D61—22no—
60C2×C4×D61—24no—
61C2×C4×D61—22no—
62C2×C4×D61—22no—
63C2×C4×D61—42no—
64C2×C4×D61—42no—
65C2×C4×D61—44no—
66C2×C4×D61—44no—
67C2×C4×D61—41no—
68C2×C4×D61—41no—
69C2×C8×C61—42no—
70C4⋊C4×C61—41no—
71C4⋊C4×C61—41no—
72C42×C61—21no—
73C42×C61M1612yescomplemented
74C4⋊Dic61—41no—
75C4⋊Dic61—41no—
76#11758196—42no—
77#11758196—42no—
78C4×Dic61—24no—
79C4×Dic61—21no—
80C4×Dic61M1612yescomplemented
81C2×#92418—42no—
82#11758189—84no—
83C23×C61C2×C22⋊C411yescharacteristic
84C22×D61—21no—
85C22×D61—21no—
86C22×D61—22no—
87C22×D61—22no—
88C22×D61#9911yescharacteristic
89C22×D61#9911yescharacteristic
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61—42no—
97C2×C4×C61—42no—
98C2×C4×C61—41no—
99C2×C4×C61C2×M1611yescharacteristic
100C2×C4×C61C2×M1611yescharacteristic
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61—42no—
108C2×Dic61—42no—
109C2×Dic61—41no—
110C2×Dic61#10112yes—
111C4×D61—22no—
112C4×D61—22no—
113C4×D61—22no—
114C4×D61—22no—
115C4×D61—48no—
116C4×D61—44no—
117C4×D61—82no—
118C4×D61—82no—
119C4×D61—82no—
120C8×C61—82no—
121#92418—82no—
122#11511—611nomaximal, Sylow
123C22×C61—21no—
124C22×C61—21no—
125C22×C61#40711yescharacteristic
126C22×C61C2×#9911yescharacteristic
127C22×C61C2×#10111yescharacteristic
128C2×D61—24no—
129C2×D61—24no—
130C2×D61—21no—
131C2×D61—21no—
132C2×D61—21no—
133C2×D61—21no—
134C2×D61#35412yes—
135C2×D61#35512yes—
136C4×C61—21no—
137C4×C61—21no—
138C4×C61—42no—
139C4×C61—42no—
140C4×C61—81no—
141Dic61—22no—
142Dic61—42no—
143Dic61—42no—
144Dic61—81no—
145C2×#382—611no—
146#1463—612no—
147#1324—611no—
148#1324—612no—
149#1324D6111yescharacteristic, complemented
150C2×C61—21no—
151C2×C61—21no—
152C2×C61#146311yescharacteristic
153C2×C61C2×#35411yescharacteristic
154C2×C61C2×#35511yescharacteristic
155D61—22no—
156D61—22no—
157C22×C4⋊C4—611no—
158C22×C4⋊C4—611no—
159C22×C42—611no—
160#407—1222no—
161#382—611no—
162#382—611no—
163#382—611no—
164#382—1222no—
165#382C2×D6111yescharacteristic
166C2×#95—1222no—
167#324—612no—
168#324—1222no—
169#324C2×D6112yes—
170C61#1151111yescharacteristic, complemented, Sylow
171C23×C4—611no—
172C23×C4—612no—
173C23×C4—1221no—
174C23×C4—1221no—
175C2×M16—2442no—
176C2×C4⋊C4—611no—
177C2×C4⋊C4—612no—
178C2×C4⋊C4—611no—
179C2×C4⋊C4—1221no—
180C2×C4⋊C4—2441no—
181C2×C4⋊C4—2441no—
182C2×C4⋊C4—2441no—
183C2×C4⋊C4—2441no—
184C2×C4⋊C4C4×D6111yescharacteristic
185C2×C4⋊C4C22×D6111yescharacteristic
186C2×C42—611no—
187C2×C42—1222no—
188C2×C42—1221no—
189C2×C42—1222no—
190C2×C42C4×D6111yescharacteristic
191C22⋊C8—22no—
192C22⋊C8—1222no—
193C22⋊C8—2442no—
194#95—22no—
195#95—1222no—
196#95—1222no—
197#95—1222no—
198C24—611no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—611no—
202C22×C4—612no—
203C22×C4—1222no—
204C22×C4—1221no—
205C22×C4—1221no—
206C22×C4—1222no—
207C22×C4—1222no—
208C22×C4—1224no—
209C22×C4—1221no—
210C22×C4—1221no—
211C22×C4—1221no—
212C22×C4—1221no—
213C22×C4—2441no—
214C22×C4—2441no—
215C22×C4—2444no—
216C22×C4—2444no—
217C22×C4—2442no—
218C22×C4—2442no—
219C22×C4C2×C4×D6111yescharacteristic
220C22×C4D4×D6112yes—
221M16—4884no—
222C2×C8—42no—
223C2×C8—2442no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—2442no—
227C4⋊C4—2441no—
228C4⋊C4—2441no—
229C4⋊C4—2442no—
230C42—21no—
231C42—612no—
232C42—1224no—
233C42—1221no—
234C42#1175818912yescomplemented
235C23—611no—
236C23—611no—
237C23—1222no—
238C23—1222no—
239C23—1221no—
240C23—1221no—
241C23C22⋊C4×D6111yescharacteristic
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—612no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—1222no—
255C2×C4—1222no—
256C2×C4—1221no—
257C2×C4—1221no—
258C2×C4—1222no—
259C2×C4—1222no—
260C2×C4—4882no—
261C2×C4—4882no—
262C2×C4—4882no—
263C2×C4—2444no—
264C2×C4—2448no—
265C2×C4—2442no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4—2442no—
270C2×C4M16×D6111yescharacteristic
271C2×C4C2×#1175818911yescharacteristic
272C8—82no—
273C8—4882no—
274C22—21no—
275C22—21no—
276C22—612no—
277C22—612no—
278C22—1224no—
279C22—1224no—
280C22—1221no—
281C22—1221no—
282C22—1221no—
283C22—1221no—
284C22#1683972411yescharacteristic
285C22#99×D6111yescharacteristic
286C22#101×D6111yescharacteristic
287C4—21no—
288C4—21no—
289C4—42no—
290C4—42no—
291C4—81no—
292C4—1222no—
293C4—4881no—
294C4—2442no—
295C4—2442no—
296C2—21no—
297C2—21no—
298C2—1222no—
299C2—1222no—
300C2#2144414711yescharacteristic
301C2#354×D6111yescharacteristic
302C2#355×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1324C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1324D61
hypocenterC61#11511
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
3. #21443763C2semidirect
4. #21443762C2semidirect
5. C61×#1324C2semidirect
73. C42×C61M16semidirect
80. C4×Dic61M16semidirect
149. #1324D61semidirect
170. C61#11511semidirect
234. C42#11758189semidirect

Maximal subgroups

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

subgroupindex
#382×D612
#214441472
#214437632
#214437622
C61×#13242
#1151161