Finite Group Databasebeta

← #29590558

Subgroups — #29590558

Order 15616.

292 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 65 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#21456473C211yesmaximal, characteristic
2#21447632C211yesmaximal, characteristic
3#21445573C211yesmaximal, characteristic
4#21443814C211yesmaximal, characteristic
5#21443813C211yesmaximal, characteristic
6#21443806C211yesmaximal, characteristic
7C61×#1340C211yesmaximal, characteristic
8#16840372—21no—
9#16840162C411yescharacteristic, complemented
10#16840140C411yescharacteristic, complemented
11#16840129—21no—
12#16840020C2211yescharacteristic
13#16840001—21no—
14#16839869C411yescharacteristic, complemented
15#16839868C411yescharacteristic, complemented
16#16839854—21no—
17#16839720C2211yescharacteristic
18#16839718—21no—
19#16839582—21no—
20#16839544C2211yescharacteristic
21#16839539—21no—
22#16839520C2211yescharacteristic
23#16839518—21no—
24C61×#470C2211yescharacteristic
25C61×#349C2211yescharacteristic
26C61×H(3,ℤ/4)C2211yescharacteristic
27C2×Dic244C2×C411yescharacteristic
28C2×#11758202—21no—
29C2×#11758194—21no—
30C22×#92418D411yescharacteristic
31#14519775—21no—
32#14519770—41no—
33#14519770—41no—
34#14519768—21no—
35#14519768—41no—
36#14519767—41no—
37#14519756—21no—
38Q8×Dic61—21no—
39#14519742—21no—
40#14519736D411yescharacteristic
41#14519717—21no—
42#14519710—21no—
43#14519709C2×C411yescharacteristic
44#14519702—21no—
45#14519701—21no—
46#14519700—21no—
47#14519688—22no—
48#14519687C2×C411yescharacteristic
49#14519687D411yescharacteristic
50C4×#92418—22no—
51C8×Dic61C2×C411yescharacteristic
52C8×Dic61D411yescharacteristic
53C2×Q16×C61C2×C411yescharacteristic
54C2×M16×C61C2311yescharacteristic
55C22⋊Q8×C61—21no—
56#117×C61—21no—
57M32×C61—21no—
58#106×C61C2×C411yescharacteristic
59#103×C61—21no—
60C2×Q8×C61—21no—
61C22×C4×C61C2×D411yescharacteristic
62C2×Dic122—21no—
63Q16×C61—41no—
64M16×C61—41no—
65C2×C8×C61C22×C411yescharacteristic
66C2×C8×C61C2×D411yescharacteristic
67C4⋊C4×C61—21no—
68C4⋊C4×C61—41no—
69C4⋊C4×C61—41no—
70C22⋊C4×C61—41no—
71C22⋊C4×C61—41no—
72C42×C61—22no—
73C22⋊Dic61—21no—
74C22⋊Dic61—41no—
75#11758202—41no—
76#11758202—41no—
77C4⋊Dic61—21no—
78C4⋊Dic61—21no—
79C4⋊Dic61—41no—
80C4⋊Dic61—41no—
81#11758196—41no—
82#11758196—41no—
83#11758196—41no—
84#11758196—41no—
85#11758196—41no—
86C4×Dic61—41no—
87C4×Dic61—41no—
88C4×Dic61C22⋊C411yescharacteristic
89C4×Dic61C22⋊C411yescharacteristic
90#11758194—41no—
91#11758194—41no—
92C2×#92418—21no—
93C2×#92418—21no—
94C2×#92418—22no—
95C2×#92418C22⋊C411yescharacteristic
96C2×#92418C22⋊C411yescharacteristic
97Dic244—41no—
98C16×C61—41no—
99#11758185—41no—
100C23×C61AGL(1,ℤ/8)11yescharacteristic
101Q8×C61—41no—
102Q8×C61—41no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—42no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61C2×C22⋊C411yescharacteristic
109C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114Dic122—41no—
115Dic122—41no—
116C8×C61—21no—
117C8×C61—21no—
118#92418—21no—
119#92418—42no—
120#92418#10411yescharacteristic
121#92418#10411yescharacteristic
122#11771—611nomaximal, Sylow
123C22×C61—21no—
124C22×C61—41no—
125C22×C61#41811yescharacteristic
126C4×C61—21no—
127C4×C61—81no—
128C4×C61—82no—
129C4×C61—81no—
130C4×C61#41011yescharacteristic
131C4×C61C2×#10411yescharacteristic
132Dic61—41no—
133Dic61—41no—
134Dic61—81no—
135Dic61—81no—
136#3177—611no—
137#2166—611no—
138#1747—611no—
139#1342—611no—
140#1342—611no—
141#1340—611no—
142#1340D6111yescharacteristic
143C2×C61—21no—
144C2×C61—41no—
145C2×C61#150511yescharacteristic
146#541—1221no—
147#499—611no—
148#494—611no—
149#491—1221no—
150#470—611no—
151#470C2×D6111yescharacteristic
152#467—1221no—
153#441—611no—
154#441—611no—
155C4×Q16—1221no—
156#405—611no—
157#405—1221no—
158#364—1221no—
159#349—611no—
160#349C2×D6111yescharacteristic
161#347—1221no—
162#338—611no—
163H(3,ℤ/4)—1221no—
164H(3,ℤ/4)C2×D6111yescharacteristic
165C61#1177111yescharacteristic, complemented, Sylow
166C2×Q16—611no—
167C2×Q16—1221no—
168C2×Q16C4×D6111yescharacteristic
169C2×M16—1221no—
170C2×M16C22×D6111yescharacteristic
171C22×C8—611no—
172C4⋊Q8—1221no—
173#126—2441no—
174#126—2441no—
175#125—1221no—
176#125—2441no—
177#125—2441no—
178C22⋊Q8—21no—
179C22⋊Q8—1221no—
180C4×Q8—1221no—
181C4×Q8—1221no—
182#117—21no—
183#117—611no—
184M32—21no—
185M32—1221no—
186#107—1221no—
187#106—611no—
188#106C4×D6111yescharacteristic
189#103—21no—
190#103—1221no—
191#103—1221no—
192#103—1221no—
193#97—611no—
194#97—611no—
195#97—1222no—
196C4×C8—611no—
197C4×C8—611no—
198C4×C8—1222no—
199C2×Q8—21no—
200C2×Q8—1221no—
201C22×C4D4×D6111yescharacteristic
202Q16—41no—
203Q16—2441no—
204Q16—2441no—
205Q16—2441no—
206M16—41no—
207M16—2441no—
208M16—2441no—
209C2×C8—611no—
210C2×C8—611no—
211C2×C8—1221no—
212C2×C8—1221no—
213C2×C8—1222no—
214C2×C8C2×C4×D6111yescharacteristic
215C2×C8D4×D6111yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—1221no—
220C4⋊C4—1221no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C4⋊C4—2441no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C4⋊C4—2441no—
227C4⋊C4—2441no—
228C22⋊C4—41no—
229C22⋊C4—41no—
230C22⋊C4—1221no—
231C22⋊C4—2441no—
232C42—22no—
233C42—611no—
234C42—611no—
235C42—2441no—
236C42—2441no—
237C16—41no—
238C16—2441no—
239C23#1451980111yescharacteristic
240Q8—41no—
241Q8—41no—
242Q8—2441no—
243Q8—2441no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4C22⋊C4×D6111yescharacteristic
254C2×C4#1451980411yescharacteristic
255C8—21no—
256C8—21no—
257C8—611no—
258C8—611no—
259C8—1221no—
260C8—2442no—
261C22—21no—
262C22—41no—
263C22#1683976511yescharacteristic
264C4—21no—
265C4—81no—
266C4—82no—
267C4—81no—
268C4—4881no—
269C4—4881no—
270C4—2441no—
271C4—2441no—
272C4#1683973411yescharacteristic
273C4#104×D6111yescharacteristic
274C2—21no—
275C2—41no—
276C2#2144432511yescharacteristic
subgroupG/H
centerC2#21444325
commutatorC2×C8×C61C22×C4
FrattiniC2×M16C22×D61
FittingC61×#1340C2
socleC2×C61#1505
prime radicalC23×C61AGL(1,ℤ/8)
cosocleC2×M16×C61C23
hypercenter#1340D61
hypocenterC61#11771
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
9. #16840162C4semidirect
10. #16840140C4semidirect
14. #16839869C4semidirect
15. #16839868C4semidirect
165. C61#11771semidirect

Maximal subgroups

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

subgroupindex
#214564732
#214476322
#214455732
#214438142
#214438132
#214438062
C61×#13402
#1177161