Finite Group Databasebeta

← #29590853

Subgroups — #29590853

Order 15616.

286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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#21456549C211yesmaximal, characteristic
2#21447628C211yesmaximal, characteristic, complemented
3#21445966C211yesmaximal, characteristic, complemented
4#21443813C211yesmaximal, characteristic, complemented
5#21443811C211yesmaximal, characteristic
6#21443803C211yesmaximal, characteristic
7C61×#1340C211yesmaximal, characteristic, complemented
8#16840298—21no—
9#16840162C411yescharacteristic, complemented
10#16840147C411yescharacteristic, complemented
11#16840118—21no—
12#16840015C2211yescharacteristic
13#16840010—21no—
14#16839873C411yescharacteristic, complemented
15#16839869C411yescharacteristic, complemented
16#16839865—21no—
17M16×Dic61C2211yescharacteristic
18#16839582—21no—
19#16839544C2211yescharacteristic
20#16839539—21no—
21#16839532—21no—
22#16839521—21no—
23#16839520C2211yescharacteristic
24C61×#470C2211yescharacteristic
25C61×#349C2211yescharacteristic
26C61×H(3,ℤ/4)C2211yescharacteristic
27C2×#11758201—21no—
28C2×D488C2×C411yescharacteristic
29C2×#11758194—21no—
30C2×#11758194D411yescharacteristic
31#14519772—41no—
32#14519768—21no—
33#14519766—21no—
34#14519761—41no—
35#14519751—21no—
36Q8×Dic61—21no—
37#14519739—21no—
38#14519737—41no—
39#14519735—41no—
40C2×C4×Dic61D411yescharacteristic
41#14519717—21no—
42#14519710—21no—
43#14519709C2×C411yescharacteristic
44#14519701—21no—
45#14519699—21no—
46#14519697—21no—
47#14519687C2×C411yescharacteristic
48#14519687D411yescharacteristic
49C8×Dic61C2×C411yescharacteristic
50C8×Dic61D411yescharacteristic
51C2×Q16×C61C2×C411yescharacteristic
52C2×M16×C61C2311yescharacteristic
53C22⋊Q8×C61—21no—
54#117×C61—21no—
55M32×C61—21no—
56#106×C61C2×C411yescharacteristic
57#103×C61—21no—
58C2×Q8×C61—21no—
59C22×C4×C61C2×D411yescharacteristic
60C2×C22⋊D61—41no—
61C22×Dic61—21no—
62C2×D244—21no—
63C2×C4×D61—41no—
64Q16×C61—41no—
65M16×C61—41no—
66C2×C8×C61C22×C411yescharacteristic
67C2×C8×C61C2×D411yescharacteristic
68C4⋊C4×C61—21no—
69C4⋊C4×C61—41no—
70C4⋊C4×C61—41no—
71C22⋊C4×C61—41no—
72C22⋊C4×C61—41no—
73C42×C61—41no—
74#11758201—42no—
75#11758198—41no—
76#11758198—41no—
77#11758198—41no—
78#11758198—41no—
79C4⋊Dic61—21no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82#11758196—41no—
83C4×Dic61—21no—
84C4×Dic61—41no—
85C4×Dic61C22⋊C411yescharacteristic
86C4×Dic61C22⋊C411yescharacteristic
87#11758194—41no—
88#11758194—41no—
89#11758194—41no—
90C2×#92418—41no—
91C2×#92418C22⋊C411yescharacteristic
92C2×#92418C22⋊C411yescharacteristic
93D488—41no—
94C16×C61—41no—
95#11758185—41no—
96C23×C61AGL(1,ℤ/8)11yescharacteristic
97C22×D61—41no—
98Q8×C61—41no—
99Q8×C61—41no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—81no—
105C2×C4×C61C2×C22⋊C411yescharacteristic
106C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
107C22⋊D61—82no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—41no—
111C2×Dic61—81no—
112D244—41no—
113D244—41no—
114C4×D61—82no—
115C8×C61—21no—
116C8×C61—21no—
117#92418—21no—
118#92418—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—81no—
129C4×C61—81no—
130C4×C61—161no—
131C4×C61#41011yescharacteristic
132C4×C61#42111yescharacteristic
133Dic61—41no—
134Dic61—41no—
135Dic61—81no—
136#3183—611no—
137#2165—611no—
138#1841—611no—
139#1342—611no—
140#1341—611no—
141#1340D6111yescharacteristic, complemented
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#470C2×D6111yescharacteristic
152#469—611no—
153#468—1221no—
154#442—611no—
155#441—611no—
156#440—1221no—
157C4×M16—611no—
158#364—1221no—
159#349—611no—
160#349C2×D6111yescharacteristic
161#347—1221no—
162#344—1221no—
163#339—1221no—
164#338—611no—
165H(3,ℤ/4)C2×D6111yescharacteristic
166C61#1183611yescharacteristic, complemented, Sylow
167C2×Q16C4×D6111yescharacteristic
168C2×SD16—1221no—
169C2×D8—611no—
170C2×M16—611no—
171C2×M16—1221no—
172C2×M16C22×D6111yescharacteristic
173#126—2441no—
174#125—1221no—
175#124—1221no—
176#123—2441no—
177C22⋊Q8—21no—
178#121—1221no—
179C4×Q8—1221no—
180C4×D4—1221no—
181C4×D4—2441no—
182#117—21no—
183#117—2441no—
184C2×C42—611no—
185M32—21no—
186M32—1221no—
187#107—1221no—
188#106—611no—
189#106C4×D6111yescharacteristic
190#103—21no—
191#103—1221no—
192#102—1221no—
193#102—1221no—
194#97—611no—
195#97—611no—
196C4×C8—611no—
197C4×C8—611no—
198C2×Q8—21no—
199C2×D4—1221no—
200C2×D4—2441no—
201C22×C4—1221no—
202C22×C4—2441no—
203C22×C4D4×D6111yescharacteristic
204Q16—41no—
205SD16—2442no—
206D8—2441no—
207M16—41no—
208M16—2441no—
209M16—2441no—
210M16—2441no—
211C2×C8—611no—
212C2×C8—611no—
213C2×C8—2441no—
214C2×C8C2×C4×D6111yescharacteristic
215C2×C8D4×D6111yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—1221no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C22⋊C4—41no—
224C22⋊C4—41no—
225C22⋊C4—2441no—
226C22⋊C4—2441no—
227C22⋊C4—2441no—
228C22⋊C4—2441no—
229C42—41no—
230C42—611no—
231C42—611no—
232C42—1221no—
233C42—2441no—
234C16—41no—
235C16—2441no—
236C23—2441no—
237C23#1451980111yescharacteristic
238Q8—41no—
239Q8—41no—
240D4—4882no—
241D4—2441no—
242D4—2441no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—81no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—4882no—
251C2×C4—4881no—
252C2×C4—2441no—
253C2×C4C22⋊C4×D6111yescharacteristic
254C2×C4#1451980411yescharacteristic
255C8—21no—
256C8—21no—
257C8—1221no—
258C8—1221no—
259C8—4881no—
260C22—21no—
261C22—41no—
262C22—4881no—
263C22—4881no—
264C22—4881no—
265C22#1683976511yescharacteristic
266C4—21no—
267C4—81no—
268C4—81no—
269C4—161no—
270C4—4881no—
271C4—2441no—
272C4—2441no—
273C4#1683973411yescharacteristic
274C4#1683977711yescharacteristic
275C2—21no—
276C2—41no—
277C2—9761no—
278C2#2144436411yescharacteristic
subgroupG/H
centerC2#21444364
commutatorC2×C8×C61C22×C4
FrattiniC2×M16C22×D61
FittingC61×#1340C2
socleC2×C61#1514
prime radical#16840015C22
cosocleC2×M16×C61C23
hypercenter#1340D61
hypocenterC61#11836
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1340

Complements

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

NH ≅ G/Ntype
2. #21447628C2semidirect
3. #21445966C2semidirect
4. #21443813C2semidirect
7. C61×#1340C2semidirect
9. #16840162C4semidirect
10. #16840147C4semidirect
14. #16839873C4semidirect
15. #16839869C4semidirect
141. #1340D61semidirect
166. C61#11836semidirect

Maximal subgroups

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

subgroupindex
#214565492
#214476282
#214459662
#214438132
#214438112
#214438032
C61×#13402
#1183661