Finite Group Databasebeta

← #29573333

Subgroups — #29573333

Order 15616.

384 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#21454794C211yesmaximal, characteristic
2#21444582C211yesmaximal, characteristic, complemented
3#21444342C212yesmaximal
4#21443675C212yesmaximal, complemented
5C4×#107×C61C211yesmaximal, characteristic, complemented
6#16840296C2211yescharacteristic
7#16839892C411yescharacteristic, complemented
8C8×Dic122C411yescharacteristic, complemented
9#16839841C411yescharacteristic, complemented
10#16839833—21no—
11C8×D244C411yescharacteristic, complemented
12C8×C22⋊D61—21no—
13#16839821—21no—
14#16839819C2212yes—
15#16839819C2211yescharacteristic
16#16839716—21no—
17#16839515—21no—
18#16839513—21no—
19#16839498—22no—
20#16839495—22no—
21C2×#107×C61—21no—
22C2×C4×C8×C61C2211yescharacteristic
23C4×C4⋊C4×C61C2212yes—
24C61×#340—21no—
25C2×#11758189—21no—
26C2×C8×D61—21no—
27#14519771—21no—
28#14519769Q811yescharacteristic
29#14519765Q811yescharacteristic
30#14519760—21no—
31#14519756D411yescharacteristic
32#14519751D411yescharacteristic
33C4×Dic122C2×C411yescharacteristic
34C4×D244C2×C411yescharacteristic
35C4×C22⋊D61—21no—
36#14519734—21no—
37C4⋊#92418—22no—
38C4⋊#92418C2×C411yescharacteristic
39C4⋊#92418C2×C411yescharacteristic
40#14519706—21no—
41#14519706—21no—
42C22⋊#92418—21no—
43C22⋊#92418—22no—
44#14519689—21no—
45#14519689—21no—
46#14519688—21no—
47#14519688—22no—
48#14519687—21no—
49C8×Dic61—21no—
50C22×C8×C61D411yescharacteristic
51C22×C8×C61D411yescharacteristic
52C2×C4⋊C4×C61—22no—
53C2×C42×C61—22no—
54C2×C42×C61C2311yescharacteristic
55#107×C61—24no—
56C4×C8×C61C2×C411yescharacteristic
57C4×C8×C61C2×C411yescharacteristic
58C4×C8×C61D411yescharacteristic
59C4×C8×C61D411yescharacteristic
60#95×C61—22no—
61C22×C4×C61—42no—
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61#4111yescharacteristic
65C2×C22⋊D61—21no—
66C2×D244C4⋊C411yescharacteristic
67C2×C4×D61—21no—
68C2×Dic122C4⋊C411yescharacteristic
69C2×C8×C61—22no—
70C2×C8×C61—41no—
71C2×C8×C61C22⋊C411yescharacteristic
72C2×C8×C61C22⋊C411yescharacteristic
73C2×C8×C61C22⋊C411yescharacteristic
74C2×C8×C61C22⋊C411yescharacteristic
75C4⋊C4×C61—24no—
76C4⋊C4×C61—42no—
77C42×C61—82no—
78C42×C61C22×C411yescharacteristic
79C42×C61C2×D411yescharacteristic
80C42×C61C2×Q811yescharacteristic
81C42×C61#4111yescharacteristic
82C22⋊Dic61—21no—
83#11758198—21no—
84#11758198—21no—
85#11758198—21no—
86#11758198—21no—
87C4⋊Dic61C4⋊C411yescharacteristic
88C4⋊Dic61C4⋊C411yescharacteristic
89#11758196—21no—
90#11758196—21no—
91#11758196—21no—
92#11758196—21no—
93C4×Dic61—21no—
94C2×#92418—21no—
95C2×#92418—21no—
96C2×#92418—42no—
97#11758189—42no—
98C8×D61—42no—
99C23×C61#12111yescharacteristic
100C22×D61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—41no—
106C2×C4×C61—44no—
107C2×C4×C61—82no—
108C2×C4×C61—82no—
109C2×C4×C61C2×C22⋊C411yescharacteristic
110C2×C4×C61C2×C4⋊C411yescharacteristic
111C2×C4×C61#11711yescharacteristic
112C2×C4×C61#12111yescharacteristic
113C2×C4×C61C22⋊Q811yescharacteristic
114C2×C4×C61C22⋊Q811yescharacteristic
115C22⋊D61—41no—
116C22⋊D61—41no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120D244—41no—
121C4×D61—41no—
122C4×D61—41no—
123Dic122—41no—
124C8×C61—21no—
125C8×C61—21no—
126C8×C61—21no—
127C8×C61#10412yes—
128#92418—41no—
129#92418—41no—
130#92418—82no—
131#8697—611nomaximal, Sylow
132C22×C61—21no—
133C22×C61—21no—
134C22×C61#38011yescharacteristic
135C22×C61#47211yescharacteristic
136C22×C61#47311yescharacteristic
137C2×D61—41no—
138C2×D61—41no—
139C2×D61—41no—
140C4×C61—21no—
141C4×C61—21no—
142C4×C61—21no—
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—84no—
146C4×C61C2×#10411yescharacteristic
147C4×C61#42111yescharacteristic
148Dic61—41no—
149Dic61—41no—
150Dic61—41no—
151#2966—611no—
152C4×#107D6111yescharacteristic, complemented
153#1568—611no—
154#1509—612no—
155#1285—612no—
156C2×C61—21no—
157C2×C61—21no—
158C2×C61#180611yescharacteristic
159C2×C61#181211yescharacteristic
160C2×C61#181611yescharacteristic
161D61—81no—
162#529—611no—
163#446—611no—
164C8×Q8—611no—
165#436—611no—
166#435—1221no—
167C8×D4—611no—
168C8×D4—1221no—
169#433—1221no—
170#432—611no—
171#432—612no—
172C2×#107—21no—
173#405—1221no—
174C2×C4×C8C2×D6111yescharacteristic
175C4×C4⋊C4C2×D6112yes—
176#340—21no—
177#335—1221no—
178#334—1221no—
179#328—1222no—
180#327—1222no—
181C61#869711yescharacteristic, complemented, Sylow
182C2×M16—1221no—
183C22×C8—1221no—
184C22×C8C22⋊D6111yescharacteristic
185C22×C8C22⋊D6111yescharacteristic
186#126—1221no—
187#125—611no—
188#124—611no—
189#123—1221no—
190C22⋊Q8—611no—
191#121—611no—
192C4×Q8—611no—
193C4×D4—611no—
194C4×D4—1221no—
195#117—1221no—
196C2×C4⋊C4—22no—
197C2×C42—22no—
198C2×C42C22×D6111yescharacteristic
199#107—24no—
200C4⋊C8—611no—
201C4⋊C8—611no—
202C4⋊C8—1221no—
203C4⋊C8—1221no—
204C4⋊C8—1222no—
205C22⋊C8—1221no—
206C22⋊C8—1221no—
207C22⋊C8—1221no—
208C22⋊C8—1222no—
209#97—1221no—
210#97—1221no—
211#97—1222no—
212C4×C8—1221no—
213C4×C8C4×D6111yescharacteristic
214C4×C8C4×D6111yescharacteristic
215C4×C8D24411yescharacteristic
216C4×C8D24411yescharacteristic
217#95—22no—
218C2×Q8—611no—
219C2×D4—611no—
220C2×D4—1221no—
221C22×C4—42no—
222C22×C4—1221no—
223C22×C4D4×D6111yescharacteristic
224C22×C4#1175822411yescharacteristic
225C22×C4C2×C22⋊D6111yescharacteristic
226M16—2442no—
227C2×C8—22no—
228C2×C8—41no—
229C2×C8—1221no—
230C2×C8—1221no—
231C2×C8—2442no—
232C2×C8—2442no—
233C2×C8#1175819811yescharacteristic
234C2×C8#1175819811yescharacteristic
235C2×C8#1175819811yescharacteristic
236C2×C8#1175819811yescharacteristic
237C4⋊C4—24no—
238C4⋊C4—42no—
239C4⋊C4—611no—
240C4⋊C4—611no—
241C4⋊C4—1221no—
242C4⋊C4—1221no—
243C4⋊C4—1221no—
244C4⋊C4—1221no—
245C22⋊C4—1221no—
246C22⋊C4—1221no—
247C22⋊C4—1221no—
248C22⋊C4—1221no—
249C22⋊C4—1221no—
250C42—82no—
251C42—1221no—
252C42C2×C4×D6111yescharacteristic
253C42C2×D24411yescharacteristic
254C42Q8×D6111yescharacteristic
255C42#1175822611yescharacteristic
256C23—1221no—
257C23#1451974811yescharacteristic
258Q8—2441no—
259D4—2441no—
260D4—2441no—
261D4—2441no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—44no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—1221no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4C2×#1175819811yescharacteristic
276C2×C4C4⋊C4×D6111yescharacteristic
277C2×C4#1451973511yescharacteristic
278C2×C4#1451975211yescharacteristic
279C2×C4#1451975311yescharacteristic
280C2×C4#1451975711yescharacteristic
281C8—21no—
282C8—21no—
283C8—21no—
284C8—4882no—
285C8—2441no—
286C8—2441no—
287C8#1451970512yes—
288C22—21no—
289C22—21no—
290C22—2441no—
291C22—2441no—
292C22—2441no—
293C22#1683961911yescharacteristic
294C22#1684002911yescharacteristic
295C22#1684003411yescharacteristic
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—84no—
302C4—2441no—
303C4—2441no—
304C4—2441no—
305C4C2×#1451970511yescharacteristic
306C4#1683978011yescharacteristic
307C2—21no—
308C2—21no—
309C2—4881no—
310C2#2144584011yescharacteristic
311C2#2144586211yescharacteristic
312C2#2144588411yescharacteristic
subgroupG/H
centerC22#16839619
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC4×#107×C61C2
socleC22×C61#380
prime radical#14519751D4
cosocleC2×C42×C61C23
hypercenterC4×#107D61
hypocenterC61#8697
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
2. #21444582C2semidirect
4. #21443675C2semidirect
5. C4×#107×C61C2semidirect
7. #16839892C4semidirect
8. C8×Dic122C4semidirect
9. #16839841C4semidirect
11. C8×D244C4semidirect
152. C4×#107D61semidirect
181. C61#8697semidirect

Maximal subgroups

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

subgroupindex
#214547942
#214445822
#214443422
#214436752
C4×#107×C612
#869761