Finite Group Databasebeta

← #29577451

Subgroups — #29577451

Order 15616.

618 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 107 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#21451199C211yesmaximal, characteristic
2#21448176C211yesmaximal, characteristic
3#21444340C212yesmaximal
4#21443704C212yesmaximal
5C61×#1463C211yesmaximal, characteristic
6C2×#14519756C2211yescharacteristic
7C2×#14519736—21no—
8#16839692C412yescomplemented
9#16839682C412yescomplemented
10#16839657—22no—
11#16839635—21no—
12#16839635—21no—
13C4⋊C4×Dic61—24no—
14C4×C22⋊Dic61—21no—
15C4×C22⋊Dic61C2211yescharacteristic
16C4×C22⋊Dic61C2212yes—
17#16839500—24no—
18C22×C4⋊C4×C61C2211yescharacteristic
19C61×#407C2212yes—
20C61×#324—22no—
21C22×Dic122C2×C411yescharacteristic
22#14519756—22no—
23#14519756—22no—
24#14519736—28no—
25C2×C4⋊Dic61—22no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×#11758196—22no—
28C2×#11758196—21no—
29C2×#11758196—22no—
30C2×C22⋊Dic61—22no—
31C2×C22⋊Dic61—21no—
32C2×C22⋊Dic61—21no—
33C2×C4×Dic61—22no—
34C2×C4×Dic61—22no—
35C2×C4×Dic61—22no—
36C2×C4×Dic61—21no—
37#14519684—22no—
38#14519684—22no—
39#14519684—22no—
40#14519684C2×C412yes—
41#14519684D414yes—
42C23×C4×C61D411yescharacteristic
43C23×C4×C61D411yescharacteristic
44C23×C4×C61C2311yescharacteristic
45C2×M16×C61—22no—
46C2×C4⋊C4×C61—22no—
47C2×C4⋊C4×C61—22no—
48C2×C4⋊C4×C61C2×C412yes—
49C2×C4⋊C4×C61D412yes—
50C22⋊C8×C61—22no—
51C22⋊C8×C61—22no—
52C24×C61C2×D411yescharacteristic
53C22×C4×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61—24no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—81no—
59C22×C4×C61—81no—
60C22×C4×C61C22⋊C412yes—
61C22×C4×C61C22⋊C412yes—
62C22×C4×C61C22×C411yescharacteristic
63C22×C4×C61C2×D412yes—
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61#4112yes—
66C22×Dic61—22no—
67C22×Dic61—24no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C2×Dic122—22no—
71C2×Dic122—81no—
72M16×C61—82no—
73C2×C8×C61—42no—
74C4⋊C4×C61—24no—
75C4⋊C4×C61—24no—
76C22⋊Dic61—24no—
77C22⋊Dic61—28no—
78C22⋊Dic61—41no—
79C22⋊Dic61—41no—
80C4⋊Dic61—28no—
81C4⋊Dic61—22no—
82#11758196—44no—
83#11758196—42no—
84#11758196—82no—
85C4×Dic61—28no—
86C4×Dic61—82no—
87C4×Dic61—82no—
88C4×Dic61—81no—
89C23×C61—22no—
90C23×C61—22no—
91C23×C61—41no—
92C23×C61C2×C22⋊C411yescharacteristic
93C23×C61#12011yescharacteristic
94C23×C61#12311yescharacteristic
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—24no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61—41no—
102C2×C4×C61—42no—
103C2×C4×C61—42no—
104C2×C4×C61—41no—
105C2×C4×C61—42no—
106C2×C4×C61—42no—
107C2×C4×C61—81no—
108C2×C4×C61#10414yes—
109C2×C4×C61C4×D412yes—
110C2×C4×C61#12112yes—
111C2×Dic61—28no—
112C2×Dic61—24no—
113C2×Dic61—44no—
114C2×Dic61—42no—
115C2×Dic61—42no—
116C2×Dic61—44no—
117C2×Dic61—42no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—42no—
121Dic122—82no—
122C8×C61—82no—
123#9408—611nomaximal, Sylow
124C22×C61—21no—
125C22×C61—21no—
126C22×C61—21no—
127C22×C61—21no—
128C22×C61—21no—
129C22×C61—21no—
130C22×C61—21no—
131C22×C61—44no—
132C22×C61#38611yescharacteristic
133C22×C61C2×#10412yes—
134C22×C61#45612yes—
135C4×C61—24no—
136C4×C61—22no—
137C4×C61—22no—
138C4×C61—42no—
139Dic61—48no—
140Dic61—44no—
141Dic61—81no—
142Dic61—81no—
143#2583—611no—
144#2274—611no—
145#1508—612no—
146#1463D6111yescharacteristic
147#1297—612no—
148C2×C61—22no—
149C2×C61—22no—
150C2×C61—41no—
151C2×C61#188611yescharacteristic
152C2×C61#189611yescharacteristic
153C2×C61#191311yescharacteristic
154C2×C22⋊Q8—611no—
155C2×#117—1221no—
156C22×C4⋊C4C2×D6111yescharacteristic
157#407C2×D6112yes—
158#398—612no—
159#395—612no—
160#389—1222no—
161#385—1221no—
162#385—1221no—
163C4×C4⋊C4—1224no—
164C4×C22⋊C4—611no—
165C4×C22⋊C4—612no—
166C4×C22⋊C4—1221no—
167#328—1224no—
168#324—22no—
169C61#940811yescharacteristic, complemented, Sylow
170C22×Q8—611no—
171C23×C4D24411yescharacteristic
172C23×C4D24411yescharacteristic
173C23×C4C22×D6111yescharacteristic
174C2×M16—22no—
175C22⋊Q8—1222no—
176C22⋊Q8—1222no—
177#117—1228no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—611no—
181C2×C4⋊C4—1222no—
182C2×C4⋊C4—1222no—
183C2×C4⋊C4—1222no—
184C2×C4⋊C4—1221no—
185C2×C4⋊C4C4×D6112yes—
186C2×C4⋊C4C22⋊D6112yes—
187C2×C22⋊C4—1222no—
188C2×C22⋊C4—1221no—
189C2×C22⋊C4—1221no—
190C2×C42—1222no—
191C2×C42—1222no—
192C2×C42—1222no—
193C2×C42—1221no—
194C22⋊C8—22no—
195C22⋊C8—22no—
196#95—612no—
197#95—614no—
198#95—1222no—
199#95—1222no—
200#95—1222no—
201C24C2×D24411yescharacteristic
202C2×Q8—1222no—
203C2×Q8—4881no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—24no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—81no—
210C22×C4—81no—
211C22×C4—1222no—
212C22×C4—1224no—
213C22×C4—1221no—
214C22×C4—1221no—
215C22×C4#1175819812yes—
216C22×C4#1175819812yes—
217C22×C4C2×C4×D6111yescharacteristic
218C22×C4D4×D6112yes—
219C22×C4#1175822412yes—
220C22×C4C2×C22⋊D6111yescharacteristic
221M16—82no—
222C2×C8—42no—
223C4⋊C4—24no—
224C4⋊C4—24no—
225C4⋊C4—1228no—
226C4⋊C4—1222no—
227C4⋊C4—4882no—
228C4⋊C4—2444no—
229C4⋊C4—2442no—
230C22⋊C4—1228no—
231C22⋊C4—1224no—
232C22⋊C4—2441no—
233C22⋊C4—2441no—
234C42—1228no—
235C42—4882no—
236C42—4881no—
237C42—4882no—
238C23—22no—
239C23—22no—
240C23—41no—
241C23C2×#1175819811yescharacteristic
242C23#1451974711yescharacteristic
243C23#1451976111yescharacteristic
244Q8—4882no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—24no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—81no—
258C2×C4—1228no—
259C2×C4—1224no—
260C2×C4—2442no—
261C2×C4—2442no—
262C2×C4—2441no—
263C2×C4—2441no—
264C2×C4—2444no—
265C2×C4—2442no—
266C2×C4—2444no—
267C2×C4—2442no—
268C2×C4#1451970314yes—
269C2×C4#1451973712yes—
270C2×C4#1451974912yes—
271C8—82no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—44no—
280C22#1683963911yescharacteristic
281C22C2×#1451970312yes—
282C22#1683994712yes—
283C4—24no—
284C4—22no—
285C4—22no—
286C4—42no—
287C4—4881no—
288C4—4881no—
289C4—2448no—
290C4—2444no—
291C2—22no—
292C2—22no—
293C2—41no—
294C2#2144621011yescharacteristic
295C2#2144626011yescharacteristic
296C2#2144635911yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1463C2
socleC22×C61#386
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#1463D61
hypocenterC61#9408
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
8. #16839692C4semidirect
9. #16839682C4semidirect
169. C61#9408semidirect

Maximal subgroups

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

subgroupindex
#214511992
#214481762
#214443402
#214437042
C61×#14632
#940861