Finite Group Databasebeta

← #29590856

Subgroups — #29590856

Order 15616.

286 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 71 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#21456548C211yesmaximal, characteristic
2#21445968C211yesmaximal, characteristic, complemented
3#21443814C211yesmaximal, characteristic, complemented
4#21443811C211yesmaximal, characteristic
5#21443808C211yesmaximal, characteristic, complemented
6#21443805C211yesmaximal, characteristic
7C61×#2165C211yesmaximal, characteristic, complemented
8#16840296—21no—
9#16840164C411yescharacteristic, complemented
10#16840146C411yescharacteristic, complemented
11#16840117—21no—
12#16840020C2211yescharacteristic
13#16840015C2211yescharacteristic
14#16840008—21no—
15#16839875C411yescharacteristic, complemented
16#16839870C411yescharacteristic, complemented
17#16839864—21no—
18#16839533—21no—
19#16839522—21no—
20#16839520C2211yescharacteristic
21#16839519C2211yescharacteristic
22C4×M16×C61C2211yescharacteristic
23C61×#364—21no—
24C61×#349C2211yescharacteristic
25C61×#349C2211yescharacteristic
26C61×#347—21no—
27C2×Dic244C2×C411yescharacteristic
28C2×#11758190—21no—
29C2×D488C2×C411yescharacteristic
30C2×#11758194—21no—
31#14519771—41no—
32#14519769—21no—
33#14519765—21no—
34#14519760—41no—
35#14519756—21no—
36#14519751—21no—
37C4×Dic122—21no—
38C4×D244—21no—
39C4×C22⋊D61—41no—
40#14519736—21no—
41#14519734—41no—
42#14519711—21no—
43#14519709C2×C411yescharacteristic
44#14519709C2×C411yescharacteristic
45#14519702—21no—
46#14519702—21no—
47#14519699—21no—
48#14519699—21no—
49C2×M16×C61D411yescharacteristic
50C2×M16×C61C2311yescharacteristic
51C2×C42×C61D411yescharacteristic
52M32×C61—21no—
53M32×C61—21no—
54#97×C61C2×C411yescharacteristic
55#97×C61D411yescharacteristic
56C4×C8×C61C2×C411yescharacteristic
57C4×C8×C61D411yescharacteristic
58C22×C4×C61—21no—
59C22×C4×C61C2×D411yescharacteristic
60C2×C22⋊D61—41no—
61C2×D244—21no—
62C2×C4×D61—41no—
63C2×Dic122—21no—
64M16×C61—41no—
65M16×C61—41no—
66C2×C8×C61C22⋊C411yescharacteristic
67C2×C8×C61C22⋊C411yescharacteristic
68C2×C8×C61C22×C411yescharacteristic
69C2×C8×C61C2×D411yescharacteristic
70C42×C61—21no—
71C42×C61C22⋊C411yescharacteristic
72C42×C61C22⋊C411yescharacteristic
73C22⋊Dic61—41no—
74C22⋊Dic61—41no—
75#11758198—41no—
76#11758198—41no—
77#11758198—41no—
78#11758198—41no—
79C4⋊Dic61—21no—
80C4⋊Dic61—21no—
81C4⋊Dic61—41no—
82#11758196—41no—
83#11758196—41no—
84#11758196—41no—
85#11758196—41no—
86C4×Dic61—41no—
87C4×Dic61—41no—
88#11758194—41no—
89#11758194—41no—
90C2×#92418—41no—
91Dic244—41no—
92D488—41no—
93#11758190—42no—
94C16×C61—41no—
95C16×C61—41no—
96C23×C61AGL(1,ℤ/8)11yescharacteristic
97C22×D61—41no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—81no—
103C2×C4×C61C2×C22⋊C411yescharacteristic
104C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
105C22⋊D61—82no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61—81no—
110D244—41no—
111D244—41no—
112C4×D61—82no—
113Dic122—41no—
114Dic122—41no—
115C8×C61—21no—
116C8×C61—21no—
117C8×C61—21no—
118C8×C61—21no—
119#92418—81no—
120#11836—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—41no—
123C22×C61#41811yescharacteristic
124C2×D61—81no—
125C2×D61—81no—
126C2×D61—81no—
127C4×C61—21no—
128C4×C61—41no—
129C4×C61—41no—
130C4×C61#41011yescharacteristic
131C4×C61#42111yescharacteristic
132Dic61—81no—
133Dic61—81no—
134Dic61—81no—
135Dic61—161no—
136#3183—611no—
137#2165D6111yescharacteristic, complemented
138#1841—611no—
139#1342—611no—
140#1341—611no—
141#1340—611no—
142#1339—611no—
143C2×C61—21no—
144C2×C61—41no—
145C2×C61#151411yescharacteristic
146D61—161no—
147#529—1221no—
148#499—611no—
149#495—611no—
150#488—1221no—
151#470—611no—
152#469—611no—
153#468—1221no—
154#442—611no—
155#441—611no—
156#440—1221no—
157C4×M16C2×D6111yescharacteristic
158#364—21no—
159#349C2×D6111yescharacteristic
160#349C2×D6111yescharacteristic
161#347—21no—
162#344—1221no—
163#339—1221no—
164#338—611no—
165H(3,ℤ/4)—611no—
166C61#1183611yescharacteristic, complemented, Sylow
167C2×Q16—611no—
168C2×SD16—1221no—
169C2×D8—611no—
170C2×M16—1221no—
171C2×M16D24411yescharacteristic
172C2×M16C22×D6111yescharacteristic
173#126—2441no—
174#125—1221no—
175#124—1221no—
176#123—2441no—
177C22⋊Q8—1221no—
178#121—1221no—
179C4×Q8—1221no—
180C4×D4—1221no—
181C4×D4—2441no—
182#117—1221no—
183#117—2441no—
184C2×C42D24411yescharacteristic
185M32—21no—
186M32—21no—
187#107—1221no—
188#106—611no—
189#106—611no—
190#103—1221no—
191#103—1221no—
192#102—1221no—
193#102—1221no—
194#97C4×D6111yescharacteristic
195#97C22⋊D6111yescharacteristic
196C4×C8C4×D6111yescharacteristic
197C4×C8C22⋊D6111yescharacteristic
198C2×Q8—1221no—
199C2×D4—1221no—
200C2×D4—2441no—
201C22×C4—21no—
202C22×C4—2441no—
203C22×C4C2×D24411yescharacteristic
204Q16—2441no—
205SD16—2442no—
206D8—2441no—
207M16—41no—
208M16—41no—
209M16—2441no—
210M16—2441no—
211C2×C8—2441no—
212C2×C8#1175819811yescharacteristic
213C2×C8#1175819811yescharacteristic
214C2×C8C2×C4×D6111yescharacteristic
215C2×C8C2×C22⋊D6111yescharacteristic
216C4⋊C4—1221no—
217C4⋊C4—1221no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C22⋊C4—2441no—
224C22⋊C4—2441no—
225C22⋊C4—2441no—
226C22⋊C4—2441no—
227C22⋊C4—2441no—
228C22⋊C4—2441no—
229C42—21no—
230C42—2441no—
231C42—2441no—
232C42#1175819811yescharacteristic
233C42#1175819811yescharacteristic
234C16—41no—
235C16—41no—
236C23—2441no—
237C23#1451980511yescharacteristic
238Q8—2441no—
239Q8—2441no—
240D4—4882no—
241D4—2441no—
242D4—2441no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—81no—
248C2×C4—4882no—
249C2×C4—4881no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4C2×#1175819811yescharacteristic
254C2×C4#1451980511yescharacteristic
255C8—21no—
256C8—21no—
257C8—21no—
258C8—21no—
259C8—4881no—
260C22—21no—
261C22—41no—
262C22—4881no—
263C22—4881no—
264C22—4881no—
265C22#1683976811yescharacteristic
266C4—21no—
267C4—41no—
268C4—41no—
269C4—9761no—
270C4—4881no—
271C4—4881no—
272C4—4881no—
273C4#1683973511yescharacteristic
274C4#1683977811yescharacteristic
275C2—21no—
276C2—41no—
277C2—9761no—
278C2#2144436711yescharacteristic
subgroupG/H
centerC2#21444367
commutatorC2×C8×C61C22×C4
FrattiniC2×M16C22×D61
FittingC61×#2165C2
socleC2×C61#1514
prime radical#16840015C22
cosocleC2×M16×C61C23
hypercenter#2165D61
hypocenterC61#11836
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
2. #21445968C2semidirect
3. #21443814C2semidirect
5. #21443808C2semidirect
7. C61×#2165C2semidirect
9. #16840164C4semidirect
10. #16840146C4semidirect
15. #16839875C4semidirect
16. #16839870C4semidirect
137. #2165D61semidirect
166. C61#11836semidirect

Maximal subgroups

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

subgroupindex
#214565482
#214459682
#214438142
#214438112
#214438082
#214438052
C61×#21652
#1183661