Finite Group Databasebeta

← #29577578

Subgroups — #29577578

Order 15616.

444 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 89 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#21456213C211yesmaximal, characteristic
2#21448999C211yesmaximal, characteristic, complemented
3#21444537C211yesmaximal, characteristic, complemented
4#21444367C211yesmaximal, characteristic
5#21444365C211yesmaximal, characteristic
6#21443684C211yesmaximal, characteristic, complemented
7C61×#1288C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9C2×#14519777C2211yescharacteristic
10#16840122—22no—
11#16840113C412yescomplemented
12#16840109C412yescomplemented
13#16839819C2211yescharacteristic
14#16839764—22no—
15#16839666—22no—
16#16839647—22no—
17#16839645—22no—
18#16839630C2211yescharacteristic
19#16839509—22no—
20#16839497—22no—
21#16839495—22no—
22C61×#432C2211yescharacteristic
23C4×M16×C61C2211yescharacteristic
24C61×#383C2211yescharacteristic
25C2×#11758222—21no—
26C22×Dic122—21no—
27#14519777—21no—
28#14519777—21no—
29#14519777C2×C411yescharacteristic
30#14519777C2×C412yes—
31#14519777D412yes—
32#14519774C2×C411yescharacteristic
33#14519765—21no—
34#14519751—21no—
35#14519751—21no—
36C4×D244—21no—
37C4×D244—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61D412yes—
40C2×#11758196—22no—
41C2×C4×Dic61—22no—
42C4⋊#92418—21no—
43#14519702—24no—
44#14519699—24no—
45C22⋊#92418—21no—
46#14519688—21no—
47#14519684—24no—
48#14519684—21no—
49#14519684—21no—
50#14519684D412yes—
51C2×M16×C61—21no—
52C2×C42×C61C2311yescharacteristic
53C4⋊C8×C61—21no—
54C22⋊C8×C61—21no—
55#97×C61—21no—
56#97×C61—21no—
57C4×C8×C61C2×C412yes—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61D412yes—
61C22×C4×C61—22no—
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C2×C22⋊D61—41no—
66C22×Dic61—22no—
67C22×Dic61—22no—
68#11758222—44no—
69C2×D244—21no—
70C2×D244—21no—
71C2×D244—21no—
72C2×C4×D61—41no—
73C2×Dic122—21no—
74C2×Dic122—22no—
75C2×Dic122—22no—
76C2×Dic122—81no—
77C2×Dic122—81no—
78M16×C61—42no—
79C2×C8×C61—22no—
80C2×C8×C61—41no—
81C42×C61C22×C411yescharacteristic
82C42×C61C2×D411yescharacteristic
83C42×C61#4111yescharacteristic
84C42×C61#4111yescharacteristic
85#11758198—41no—
86#11758198—41no—
87C4⋊Dic61—22no—
88C4⋊Dic61—22no—
89C4⋊Dic61—22no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61C22⋊C414yes—
93#11758196—82no—
94C4×Dic61—82no—
95C2×#92418—41no—
96C23×C61#12011yescharacteristic
97C22×D61—41no—
98C2×C4×C61—22no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—42no—
102C2×C4×C61—42no—
103C2×C4×C61—42no—
104C2×C4×C61C2×C22⋊C411yescharacteristic
105C2×C4×C61C4×D411yescharacteristic
106C2×C4×C61C4×D411yescharacteristic
107C2×C4×C61#12111yescharacteristic
108C2×C4×C61#12111yescharacteristic
109C2×C4×C61#12311yescharacteristic
110C22⋊D61—82no—
111C2×Dic61—24no—
112C2×Dic61—42no—
113C2×Dic61—42no—
114C2×Dic61—42no—
115C2×Dic61—42no—
116C2×Dic61—41no—
117C2×Dic61—42no—
118D244—42no—
119D244—81no—
120D244—81no—
121C4×D61—82no—
122Dic122—42no—
123Dic122—82no—
124Dic122—82no—
125C8×C61—42no—
126C8×C61—81no—
127#92418—81no—
128#9430—611nomaximal, Sylow
129C22×C61—21no—
130C22×C61—21no—
131C22×C61#38611yescharacteristic
132C22×C61#45412yes—
133C2×D61—81no—
134C2×D61—81no—
135C2×D61—81no—
136C4×C61—21no—
137C4×C61—21no—
138C4×C61—21no—
139C4×C61—21no—
140C4×C61—21no—
141C4×C61—21no—
142C4×C61—82no—
143Dic61—44no—
144Dic61—82no—
145Dic61—81no—
146#3141—611no—
147#2381—611no—
148#1556—611no—
149#1514—611no—
150#1514—611no—
151#1288—611no—
152#1288D6111yescharacteristic, complemented
153C2×C61—22no—
154C2×C61#188811yescharacteristic
155C2×C61#190411yescharacteristic
156C2×C61#190511yescharacteristic
157D61—161no—
158#532—611no—
159C2×C4⋊Q8—611no—
160#489—1222no—
161#487—612no—
162#486—612no—
163#432—611no—
164#432C2×D6111yescharacteristic
165#417—1222no—
166C4×M16C2×D6111yescharacteristic
167#391—1222no—
168#387—1222no—
169#387—1222no—
170#383—611no—
171#383C2×D6111yescharacteristic
172#332—1222no—
173#327—1222no—
174#327—1222no—
175C61#943011yescharacteristic, complemented, Sylow
176C2×#41—1221no—
177C22×Q8—1221no—
178C2×M16—21no—
179C4⋊Q8—612no—
180C4⋊Q8—611no—
181C4⋊Q8—612no—
182C4⋊Q8—1221no—
183C4⋊Q8—1221no—
184#127—611no—
185#124—1221no—
186#121—1221no—
187#121—1221no—
188C4×D4—1221no—
189C4×D4—1221no—
190C2×C4⋊C4—612no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4—1222no—
193C2×C42—1222no—
194C2×C42C22×D6111yescharacteristic
195C4⋊C8—21no—
196C4⋊C8—1221no—
197#103—1224no—
198#102—1224no—
199C22⋊C8—21no—
200C22⋊C8—1221no—
201#97—21no—
202#97—21no—
203#97—1221no—
204C4×C8C4×D6112yes—
205#95—21no—
206#95—21no—
207#95—612no—
208#95—1224no—
209#95—1221no—
210#95—1221no—
211#95D24412yes—
212#41—2444no—
213C2×Q8—1222no—
214C2×Q8—1222no—
215C2×Q8—1221no—
216C2×Q8—4881no—
217C2×Q8—4881no—
218C2×D4—1221no—
219C2×D4—1221no—
220C2×D4—1221no—
221C2×D4—2441no—
222C22×C4—22no—
223C22×C4—1222no—
224C22×C4—1222no—
225C22×C4—2441no—
226C22×C4C2×D24411yescharacteristic
227C22×C4D4×D6111yescharacteristic
228C22×C4D4×D6111yescharacteristic
229M16—42no—
230C2×C8—22no—
231C2×C8—41no—
232C2×C8—2441no—
233C4⋊C4—614no—
234C4⋊C4—1222no—
235C4⋊C4—1222no—
236C4⋊C4—1222no—
237C4⋊C4—1221no—
238C4⋊C4—1221no—
239C4⋊C4—4882no—
240C22⋊C4—2441no—
241C22⋊C4—2441no—
242C42—4882no—
243C42C2×C4×D6111yescharacteristic
244C42#1175822211yescharacteristic
245C42D4×D6111yescharacteristic
246C42#1175822611yescharacteristic
247C23—2441no—
248C23#1451974711yescharacteristic
249Q8—4882no—
250Q8—4882no—
251Q8—2442no—
252D4—4881no—
253D4—4881no—
254D4—4882no—
255D4—2442no—
256C2×C4—22no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—1224no—
263C2×C4—4882no—
264C2×C4—2442no—
265C2×C4—2442no—
266C2×C4—2442no—
267C2×C4—2441no—
268C2×C4—2442no—
269C2×C4—2442no—
270C2×C4C22⋊C4×D6111yescharacteristic
271C2×C4#1451973911yescharacteristic
272C2×C4C4×D24411yescharacteristic
273C2×C4#1451975011yescharacteristic
274C2×C4#1451975211yescharacteristic
275C2×C4#1451976211yescharacteristic
276C8—42no—
277C8—81no—
278C8—4881no—
279C22—21no—
280C22—21no—
281C22—4881no—
282C22—4881no—
283C22—4881no—
284C22#1683964011yescharacteristic
285C22#1683993612yes—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—82no—
293C4—4882no—
294C4—4881no—
295C4—2444no—
296C2—22no—
297C2—9761no—
298C2#2144622111yescharacteristic
299C2#2144630711yescharacteristic
300C2#2144631211yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1288C2
socleC22×C61#386
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1288D61
hypocenterC61#9430
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1288

Complements

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

NH ≅ G/Ntype
2. #21448999C2semidirect
3. #21444537C2semidirect
6. #21443684C2semidirect
7. C61×#1288C2semidirect
11. #16840113C4semidirect
12. #16840109C4semidirect
152. #1288D61semidirect
175. C61#9430semidirect

Maximal subgroups

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

subgroupindex
#214562132
#214489992
#214445372
#214443672
#214443652
#214436842
C61×#12882
#943061