Finite Group Databasebeta

← #29590866

Subgroups — #29590866

Order 15616.

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

normal subgroups only

This group has 280 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#21456559C211yesmaximal, characteristic
2#21447628C211yesmaximal, characteristic
3#21445969C211yesmaximal, characteristic
4#21443812C211yesmaximal, characteristic
5#21443808C211yesmaximal, characteristic
6#21443807C211yesmaximal, characteristic
7C61×#1342C211yesmaximal, characteristic
8#16840314—21no—
9#16840159C411yescharacteristic, complemented
10#16840140C411yescharacteristic, complemented
11#16840111—21no—
12#16840020C2211yescharacteristic
13#16840018—21no—
14#16839869C411yescharacteristic, complemented
15#16839868C411yescharacteristic, complemented
16#16839866—21no—
17M16×Dic61C2211yescharacteristic
18#16839582—21no—
19#16839544C2211yescharacteristic
20#16839539—21no—
21#16839534—21no—
22#16839523—21no—
23#16839519C2211yescharacteristic
24C61×#470C2211yescharacteristic
25C61×#349C2211yescharacteristic
26C61×#338C2211yescharacteristic
27C2×Dic244C2×C411yescharacteristic
28C2×#11758202—21no—
29C2×#11758194D411yescharacteristic
30#14519776—21no—
31#14519775—21no—
32#14519767—41no—
33#14519756—21no—
34#14519754—41no—
35Q8×Dic61—21no—
36#14519742—21no—
37#14519742—41no—
38#14519736—21no—
39#14519733—41no—
40C2×C4×Dic61D411yescharacteristic
41#14519717—21no—
42#14519709C2×C411yescharacteristic
43#14519708—21no—
44#14519702—21no—
45#14519701—21no—
46#14519700—21no—
47#14519687C2×C411yescharacteristic
48#14519687D411yescharacteristic
49C8×Dic61C2×C411yescharacteristic
50C8×Dic61D411yescharacteristic
51C2×Q16×C61C2×C411yescharacteristic
52C2×M16×C61—21no—
53C2×M16×C61C2311yescharacteristic
54C22⋊Q8×C61—21no—
55M32×C61—21no—
56#106×C61C2×C411yescharacteristic
57#103×C61—21no—
58C2×Q8×C61—21no—
59C22×C4×C61C2×D411yescharacteristic
60C22×Dic61—21no—
61C2×Dic122—21no—
62C2×Dic122—41no—
63Q16×C61—41no—
64M16×C61—41no—
65M16×C61—41no—
66M16×C61—41no—
67C2×C8×C61—41no—
68C2×C8×C61C22×C411yescharacteristic
69C2×C8×C61C2×D411yescharacteristic
70C4⋊C4×C61—21no—
71C4⋊C4×C61—41no—
72C22⋊C4×C61—41no—
73C22⋊Dic61—41no—
74C22⋊Dic61—41no—
75#11758202—42no—
76C4⋊Dic61—21no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79#11758196—41no—
80#11758196—41no—
81#11758196—41no—
82#11758196—41no—
83#11758196—41no—
84C4×Dic61—21no—
85C4×Dic61—41no—
86C4×Dic61—41no—
87C4×Dic61—41no—
88C4×Dic61C22⋊C411yescharacteristic
89C4×Dic61C22⋊C411yescharacteristic
90#11758194—41no—
91C2×#92418C22⋊C411yescharacteristic
92C2×#92418C22⋊C411yescharacteristic
93Dic244—41no—
94C16×C61—41no—
95#11758185—41no—
96C23×C61AGL(1,ℤ/8)11yescharacteristic
97Q8×C61—41no—
98Q8×C61—41no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61C2×C22⋊C411yescharacteristic
104C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—42no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—81no—
111Dic122—41no—
112Dic122—41no—
113Dic122—82no—
114C8×C61—21no—
115C8×C61—21no—
116C8×C61—81no—
117#92418—21no—
118#92418—21no—
119#11838—611nomaximal, Sylow
120C22×C61—21no—
121C22×C61—41no—
122C22×C61#41811yescharacteristic
123C4×C61—21no—
124C4×C61—81no—
125C4×C61—81no—
126C4×C61#41011yescharacteristic
127C4×C61#42111yescharacteristic
128Dic61—22no—
129Dic61—41no—
130Dic61—81no—
131Dic61—81no—
132Dic61—161no—
133#3185—611no—
134#2165—611no—
135#1841—611no—
136#1342—611no—
137#1342D6111yescharacteristic
138#1340—611no—
139#1340—611no—
140C2×C61—21no—
141C2×C61—41no—
142C2×C61#151411yescharacteristic
143#533—1221no—
144#498—611no—
145#494—611no—
146#487—1221no—
147#470—611no—
148#470—1221no—
149#470C2×D6111yescharacteristic
150#441—611no—
151#441—611no—
152#441—1221no—
153C4×M16—611no—
154#364—1221no—
155#349—611no—
156#349C2×D6111yescharacteristic
157#347—1221no—
158#344—1221no—
159#339—1221no—
160#338C2×D6111yescharacteristic
161H(3,ℤ/4)—611no—
162C61#1183811yescharacteristic, complemented, Sylow
163C2×Q16—611no—
164C2×Q16—1221no—
165C2×Q16C4×D6111yescharacteristic
166C2×M16—21no—
167C2×M16—611no—
168C2×M16C22×D6111yescharacteristic
169C4⋊Q8—1221no—
170C4⋊Q8—1221no—
171#125—2441no—
172C22⋊Q8—21no—
173C22⋊Q8—1221no—
174C22⋊Q8—2441no—
175C4×Q8—1221no—
176C4×Q8—1221no—
177C4×Q8—2441no—
178#117—1221no—
179#117—2441no—
180C2×C42—611no—
181M32—21no—
182M32—1221no—
183#106—611no—
184#106—1221no—
185#106C4×D6111yescharacteristic
186#103—21no—
187#103—1221no—
188#103—1221no—
189#103—1221no—
190#97—611no—
191#97—611no—
192C4×C8—611no—
193C4×C8—611no—
194C2×Q8—21no—
195C2×Q8—1221no—
196C2×Q8—2441no—
197C22×C4—1221no—
198C22×C4D4×D6111yescharacteristic
199Q16—41no—
200Q16—2441no—
201Q16—2442no—
202M16—41no—
203M16—41no—
204M16—41no—
205M16—2441no—
206C2×C8—41no—
207C2×C8—611no—
208C2×C8—611no—
209C2×C8C2×C4×D6111yescharacteristic
210C2×C8D4×D6111yescharacteristic
211C4⋊C4—21no—
212C4⋊C4—41no—
213C4⋊C4—1221no—
214C4⋊C4—2441no—
215C4⋊C4—2441no—
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C22⋊C4—41no—
222C22⋊C4—2441no—
223C22⋊C4—2441no—
224C42—611no—
225C42—611no—
226C42—1221no—
227C42—2441no—
228C42—2441no—
229C42—2441no—
230C16—41no—
231C16—2441no—
232C23#1451980411yescharacteristic
233Q8—41no—
234Q8—41no—
235Q8—4882no—
236Q8—2441no—
237Q8—2441no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—4881no—
245C2×C4—2442no—
246C2×C4—2441no—
247C2×C4—2441no—
248C2×C4C22⋊C4×D6111yescharacteristic
249C2×C4#1451980111yescharacteristic
250C8—21no—
251C8—21no—
252C8—81no—
253C8—1221no—
254C8—1221no—
255C22—21no—
256C22—41no—
257C22#1683976511yescharacteristic
258C4—21no—
259C4—81no—
260C4—81no—
261C4—1222no—
262C4—9761no—
263C4—4881no—
264C4—4881no—
265C4—2441no—
266C4#1683973411yescharacteristic
267C4#1683977711yescharacteristic
268C2—21no—
269C2—41no—
270C2#2144436411yescharacteristic
subgroupG/H
centerC2#21444364
commutatorC2×C8×C61C22×C4
FrattiniC2×M16C22×D61
FittingC61×#1342C2
socleC2×C61#1514
prime radicalC23×C61AGL(1,ℤ/8)
cosocleC2×M16×C61C23
hypercenter#1342D61
hypocenterC61#11838
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1342

Complements

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

NH ≅ G/Ntype
9. #16840159C4semidirect
10. #16840140C4semidirect
14. #16839869C4semidirect
15. #16839868C4semidirect
162. C61#11838semidirect

Maximal subgroups

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

subgroupindex
#214565592
#214476282
#214459692
#214438122
#214438082
#214438072
C61×#13422
#1183861