Finite Group Databasebeta

← #29576016

Subgroups — #29576016

Order 15616.

504 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451640C211yesmaximal, characteristic
2#21444501C212yesmaximal, complemented
3#21444133C211yesmaximal, characteristic
4#21443679C212yesmaximal, complemented
5C61×#2905C211yesmaximal, characteristic
6C2×#14519777C2211yescharacteristic
7#16839815C2212yes—
8#16839701—21no—
9#16839698—21no—
10#16839682C412yes—
11#16839674C412yes—
12#16839660—21no—
13#16839628C2211yescharacteristic
14#16839622—21no—
15#16839510—24no—
16#16839488—21no—
17#16839486—21no—
18C22×M16×C61—21no—
19C2×#117×C61C2211yescharacteristic
20C61×#424—24no—
21C61×#423—21no—
22C61×#423C2212yes—
23C22×Dic122C2×C412yes—
24#14519777—22no—
25#14519777—22no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—21no—
29C2×#11758196—22no—
30C2×C22⋊Dic61—22no—
31C4⋊#92418—22no—
32C22⋊#92418—22no—
33C4×#92418—22no—
34#14519684—22no—
35#14519684—22no—
36#14519684—21no—
37#14519684C2×C412yes—
38C23×C4×C61D411yescharacteristic
39C2×M16×C61—22no—
40C2×M16×C61—22no—
41C2×M16×C61—42no—
42C2×M16×C61—42no—
43C22×C8×C61—22no—
44#117×C61—22no—
45#117×C61—22no—
46C2×C4⋊C4×C61C2×C411yescharacteristic
47C2×C4⋊C4×C61D411yescharacteristic
48C2×C22⋊C4×C61C2×C411yescharacteristic
49C2×C22⋊C4×C61D411yescharacteristic
50C2×C42×C61D411yescharacteristic
51C2×C42×C61C2311yescharacteristic
52C4⋊C8×C61—24no—
53C4⋊C8×C61—22no—
54C4⋊C8×C61D414yes—
55C24×C61C22⋊C411yescharacteristic
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61SD1612yes—
64C22×C4×C61Q1612yes—
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—22no—
69C22×Dic61—22no—
70C2×Dic122—24no—
71C2×Dic122—82no—
72M16×C61—44no—
73M16×C61—42no—
74M16×C61—42no—
75C2×C8×C61—24no—
76C2×C8×C61—44no—
77C4⋊C4×C61—22no—
78C4⋊C4×C61—22no—
79C22⋊C4×C61—22no—
80C22⋊C4×C61—22no—
81C42×C61—21no—
82C42×C61—21no—
83C42×C61C2×D412yes—
84C42×C61#4112yes—
85C22⋊Dic61—82no—
86C4⋊Dic61—41no—
87C4⋊Dic61—42no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91#11758196—82no—
92C2×#92418—42no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—41no—
96C23×C61—41no—
97C23×C61#10312yes—
98C23×C61C2×C22⋊C411yescharacteristic
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—22no—
104C2×C4×C61—22no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61#10312yes—
112C2×C4×C61C4×D412yes—
113C2×C4×C61#12011yescharacteristic
114C2×C4×C61#12112yes—
115C2×C4×C61#12311yescharacteristic
116C2×C4×C61C2×SD1611yescharacteristic
117C2×C4×C61C2×Q1611yescharacteristic
118C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C61#13711yescharacteristic
120C2×Dic61—42no—
121C2×Dic61—42no—
122C2×Dic61—42no—
123C2×Dic61—42no—
124C2×Dic61—42no—
125C2×Dic61—42no—
126Dic122—84no—
127C8×C61—44no—
128#92418—82no—
129#9191—611nomaximal, Sylow
130C22×C61—21no—
131C22×C61—21no—
132C22×C61—22no—
133C22×C61—42no—
134C22×C61—41no—
135C22×C61—41no—
136C22×C61—81no—
137C22×C61#38611yescharacteristic
138C22×C61C2×#10311yescharacteristic
139C22×C61#41711yescharacteristic
140C4×C61—22no—
141C4×C61—22no—
142C4×C61—22no—
143C4×C61—41no—
144C4×C61—41no—
145C4×C61#45011yescharacteristic
146C4×C61#45111yescharacteristic
147C4×C61#48311yescharacteristic
148C4×C61#48411yescharacteristic
149Dic61—82no—
150Dic61—82no—
151#2905D6111yescharacteristic
152#2628—611no—
153#1548—612no—
154#1458—611no—
155#1286—612no—
156C2×C61—21no—
157C2×C61—21no—
158C2×C61—42no—
159C2×C61#187211yescharacteristic
160C2×C61#190911yescharacteristic
161C2×C61#191411yescharacteristic
162C22×M16—21no—
163C2×C4⋊Q8—611no—
164C2×#117C2×D6111yescharacteristic
165#431—612no—
166#424—24no—
167#423—21no—
168#423C2×D6112yes—
169#400—1221no—
170#399—1221no—
171#395—612no—
172#393—612no—
173#389—1221no—
174#382—611no—
175#380—1221no—
176#333—1224no—
177#324—1221no—
178#323—1221no—
179C61#919111yescharacteristic, complemented, Sylow
180C22×Q8—612no—
181C23×C4C22⋊D6111yescharacteristic
182C2×M16—22no—
183C2×M16—22no—
184C2×M16—42no—
185C2×M16—42no—
186C22×C8—22no—
187C4⋊Q8—1222no—
188C4⋊Q8—1222no—
189#117—22no—
190#117—22no—
191C2×C4⋊C4—1222no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4—1221no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4C4×D6111yescharacteristic
196C2×C4⋊C4D24411yescharacteristic
197C2×C22⋊C4—1222no—
198C2×C22⋊C4C4×D6111yescharacteristic
199C2×C22⋊C4D24411yescharacteristic
200C2×C42C22⋊D6111yescharacteristic
201C2×C42C22×D6111yescharacteristic
202C4⋊C8—24no—
203C4⋊C8—22no—
204C4⋊C8—1222no—
205C4⋊C8C22⋊D6114yes—
206C22⋊C8—1222no—
207C4×C8—1222no—
208#95—612no—
209#95—1222no—
210#95—1222no—
211#95—1221no—
212C24#1175819811yescharacteristic
213C2×Q8—1224no—
214C2×Q8—4882no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—1222no—
220C22×C4—1222no—
221C22×C4#1175819811yescharacteristic
222C22×C4#1175819811yescharacteristic
223C22×C4#1175819811yescharacteristic
224C22×C4#1175820012yes—
225C22×C4#1175820212yes—
226C22×C4C2×C4×D6111yescharacteristic
227C22×C4C2×D24411yescharacteristic
228C22×C4C2×C22⋊D6111yescharacteristic
229M16—44no—
230M16—42no—
231M16—42no—
232C2×C8—24no—
233C2×C8—44no—
234C2×C8—2442no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—4882no—
238C4⋊C4—2441no—
239C4⋊C4—2441no—
240C4⋊C4—2442no—
241C4⋊C4—2441no—
242C4⋊C4—2441no—
243C22⋊C4—22no—
244C22⋊C4—22no—
245C22⋊C4—4882no—
246C42—21no—
247C42—21no—
248C42#1175822212yes—
249C42C2×C22⋊D6112yes—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23#1451970012yes—
255C23C2×#1175819811yescharacteristic
256Q8—4884no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—2442no—
270C2×C4—2442no—
271C2×C4—2442no—
272C2×C4—2442no—
273C2×C4—2442no—
274C2×C4—2442no—
275C2×C4#1451970012yes—
276C2×C4C4×C22⋊D6112yes—
277C2×C4#1451974611yescharacteristic
278C2×C4#1451975112yes—
279C2×C4#1451976011yescharacteristic
280C2×C4C2×#1175820011yescharacteristic
281C2×C4C2×#1175820211yescharacteristic
282C2×C4#1451980311yescharacteristic
283C2×C4#1451980811yescharacteristic
284C8—44no—
285C8—4882no—
286C22—21no—
287C22—21no—
288C22—22no—
289C22—42no—
290C22—41no—
291C22—41no—
292C22—81no—
293C22#1683964111yescharacteristic
294C22C2×#1451970011yescharacteristic
295C22#1683976111yescharacteristic
296C4—22no—
297C4—22no—
298C4—22no—
299C4—41no—
300C4—41no—
301C4—4882no—
302C4—4882no—
303C4#1683991311yescharacteristic
304C4#1683991811yescharacteristic
305C4#1684009211yescharacteristic
306C4#1684009711yescharacteristic
307C2—21no—
308C2—21no—
309C2—42no—
310C2#2144612611yescharacteristic
311C2#2144634111yescharacteristic
312C2#2144636611yescharacteristic
subgroupG/H
centerC22#16839641
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2905C2
socleC22×C61#386
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2905D61
hypocenterC61#9191
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2905

Complements

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

NH ≅ G/Ntype
2. #21444501C2semidirect
4. #21443679C2semidirect
179. C61#9191semidirect

Maximal subgroups

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

subgroupindex
#214516402
#214445012
#214441332
#214436792
C61×#29052
#919161