Finite Group Databasebeta

← #29590957

Subgroups — #29590957

Order 15616.

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

normal subgroups only

This group has 334 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#21456400C211yesmaximal, characteristic
2#21447615C211yesmaximal, characteristic
3#21445945C211yesmaximal, characteristic
4#21443832C211yesmaximal, characteristic
5#21443831C211yesmaximal, characteristic
6#21443830C211yesmaximal, characteristic
7C61×#1348C211yesmaximal, characteristic
8#16840314—21no—
9#16840166C411yescharacteristic, complemented
10#16840140C411yescharacteristic, complemented
11#16840111—21no—
12#16840003C2211yescharacteristic
13#16840001—21no—
14Q16×Dic61C411yescharacteristic, complemented
15#16839856C411yescharacteristic, complemented
16#16839854—21no—
17C2×C8×Dic61C2211yescharacteristic
18#16839631—21no—
19#16839580—21no—
20C22⋊#11758185C2211yescharacteristic
21C16×Dic61—21no—
22#16839525C2211yescharacteristic
23#16839524—21no—
24C61×#467C2211yescharacteristic
25C61×C22⋊C16C2211yescharacteristic
26C61×#340C2211yescharacteristic
27C2×Dic244C2×C411yescharacteristic
28C2×#11758202—21no—
29C22×#92418D411yescharacteristic
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#14519733—41no—
39C2×C4⋊Dic61—21no—
40C2×#11758196—41no—
41C2×#11758196—41no—
42C2×C4×Dic61D411yescharacteristic
43C2×#11758185—21no—
44#14519711C2×C411yescharacteristic
45#14519710—21no—
46#14519702—21no—
47#14519701—21no—
48#14519700—21no—
49C8×Dic61C2×C411yescharacteristic
50C8×Dic61C2×C411yescharacteristic
51C8×Dic61D411yescharacteristic
52C8×Dic61D411yescharacteristic
53C2×Q16×C61C2×C411yescharacteristic
54C22×C8×C61C2311yescharacteristic
55C22⋊Q8×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C16×C61—21no—
58#107×C61C2×C411yescharacteristic
59#103×C61—21no—
60C2×Q8×C61—21no—
61C22×C4×C61—41no—
62C22×C4×C61C2×D411yescharacteristic
63C22×Dic61—41no—
64C22×Dic61D811yescharacteristic
65C22×Dic61D811yescharacteristic
66C2×Dic122—21no—
67C2×Dic122—41no—
68Q16×C61—41no—
69C2×C8×C61—41no—
70C2×C8×C61C22×C411yescharacteristic
71C2×C8×C61C2×D411yescharacteristic
72C4⋊C4×C61—21no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C22⋊C4×C61—41no—
77C22⋊Dic61—41no—
78#11758202—42no—
79C4⋊Dic61—21no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83#11758196—41no—
84#11758196—41no—
85#11758196—41no—
86#11758196—41no—
87#11758196—41no—
88#11758196—82no—
89#11758196—82no—
90C4×Dic61—41no—
91C4×Dic61—41no—
92C4×Dic61C22⋊C411yescharacteristic
93C4×Dic61C22⋊C411yescharacteristic
94C4×Dic61SD1611yescharacteristic
95C4×Dic61SD1611yescharacteristic
96C2×#92418—41no—
97C2×#92418C22⋊C411yescharacteristic
98C2×#92418C22⋊C411yescharacteristic
99Dic244—41no—
100C16×C61—41no—
101#11758185—41no—
102C23×C61C2×D811yescharacteristic
103Q8×C61—41no—
104Q8×C61—41no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—81no—
110C2×C4×C61—81no—
111C2×C4×C61—81no—
112C2×C4×C61C2×C22⋊C411yescharacteristic
113C2×C4×C61C2×SD1611yescharacteristic
114C2×Dic61—22no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—81no—
118C2×Dic61—81no—
119C2×Dic61—81no—
120C2×Dic61#10211yescharacteristic
121C2×Dic61#10211yescharacteristic
122C2×Dic61#10211yescharacteristic
123C2×Dic61#10211yescharacteristic
124C2×Dic61SD3212yes—
125C2×Dic61Q3212yes—
126Dic122—41no—
127Dic122—41no—
128Dic122—82no—
129C8×C61—21no—
130C8×C61—21no—
131#92418—21no—
132#92418—21no—
133#11857—611nomaximal, Sylow
134C22×C61—21no—
135C22×C61—21no—
136C22×C61C2×#10211yescharacteristic
137C22×C61C2×SD3211yescharacteristic
138C22×C61C2×Q3211yescharacteristic
139C4×C61—21no—
140C4×C61—81no—
141C4×C61—81no—
142C4×C61—161no—
143C4×C61#41011yescharacteristic
144C4×C61#42111yescharacteristic
145Dic61—21no—
146Dic61—81no—
147Dic61—81no—
148Dic61—161no—
149Dic61#35812yes—
150Dic61#35812yes—
151Dic61#36012yes—
152#3170—611no—
153#2162—611no—
154#1834—611no—
155#1348—611no—
156#1348—611no—
157#1348—611no—
158#1348D6111yescharacteristic
159C2×C61—21no—
160C2×C61—21no—
161C2×C61#151711yescharacteristic
162C2×C61C2×#35811yescharacteristic
163C2×C61C2×#36011yescharacteristic
164#533—1221no—
165#500—611no—
166#494—611no—
167#487—1221no—
168#467—611no—
169#467—1221no—
170#467C2×D6111yescharacteristic
171C4×Q16—611no—
172C4×Q16—611no—
173C4×Q16—1221no—
174C2×C4×C8—611no—
175#384—1221no—
176C4⋊C16—1221no—
177C22⋊C16—611no—
178C22⋊C16C2×D6111yescharacteristic
179C4×C16—1221no—
180#340—611no—
181#340—1221no—
182#340C2×D6111yescharacteristic
183C61#1185711yescharacteristic, complemented, Sylow
184C2×Q16—611no—
185C2×Q16—1221no—
186C2×Q16C4×D6111yescharacteristic
187C22×C8—611no—
188C22×C8C22×D6111yescharacteristic
189C4⋊Q8—1221no—
190C4⋊Q8—1221no—
191#125—2441no—
192C22⋊Q8—21no—
193C22⋊Q8—1221no—
194C22⋊Q8—2441no—
195C4×Q8—1221no—
196C4×Q8—1221no—
197C4×Q8—2441no—
198#117—2441no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4—2441no—
202C2×C4⋊C4—2441no—
203C2×C42—611no—
204C2×C16—21no—
205C2×C16—1221no—
206#107—611no—
207#107—1221no—
208#107C4×D6111yescharacteristic
209#103—21no—
210#103—1221no—
211#103—1221no—
212#103—1221no—
213C4×C8—611no—
214C4×C8—611no—
215C4×C8—611no—
216C4×C8—611no—
217C2×Q8—21no—
218C2×Q8—1221no—
219C2×Q8—2441no—
220C22×C4—41no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—2441no—
224C22×C4D4×D6111yescharacteristic
225Q16—41no—
226Q16—2441no—
227Q16—2442no—
228C2×C8—41no—
229C2×C8—611no—
230C2×C8—611no—
231C2×C8—2441no—
232C2×C8C2×C4×D6111yescharacteristic
233C2×C8D4×D6111yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—1221no—
239C4⋊C4—4882no—
240C4⋊C4—4882no—
241C4⋊C4—2441no—
242C4⋊C4—2441no—
243C4⋊C4—2441no—
244C4⋊C4—2441no—
245C4⋊C4—2441no—
246C4⋊C4—2441no—
247C4⋊C4—2441no—
248C4⋊C4—2441no—
249C22⋊C4—41no—
250C22⋊C4—2441no—
251C42—611no—
252C42—611no—
253C42—611no—
254C42—611no—
255C42—2441no—
256C42—2441no—
257C16—41no—
258C16—2441no—
259C23D8×D6111yescharacteristic
260Q8—41no—
261Q8—41no—
262Q8—4882no—
263Q8—2441no—
264Q8—2441no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—611no—
273C2×C4—611no—
274C2×C4—611no—
275C2×C4—612no—
276C2×C4—612no—
277C2×C4—611no—
278C2×C4—1222no—
279C2×C4—4881no—
280C2×C4—4881no—
281C2×C4—4881no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4C22⋊C4×D6111yescharacteristic
285C2×C4SD16×D6111yescharacteristic
286C8—21no—
287C8—21no—
288C8—1221no—
289C8—1221no—
290C22—21no—
291C22—21no—
292C22#102×D6111yescharacteristic
293C22SD32×D6111yescharacteristic
294C22Q32×D6111yescharacteristic
295C4—21no—
296C4—81no—
297C4—81no—
298C4—161no—
299C4—612no—
300C4—612no—
301C4—612no—
302C4—1221no—
303C4—9761no—
304C4—4881no—
305C4—4881no—
306C4#1683973411yescharacteristic
307C4#1683977711yescharacteristic
308C2—21no—
309C2—21no—
310C2#2144437711yescharacteristic
311C2#358×D6111yescharacteristic
312C2#360×D6111yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1348C2
socleC22×C61C2×#102
prime radicalC23×C61C2×D8
cosocleC22×C8×C61C23
hypercenter#1348D61
hypocenterC61#11857
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1348

Complements

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

NH ≅ G/Ntype
9. #16840166C4semidirect
10. #16840140C4semidirect
14. Q16×Dic61C4semidirect
15. #16839856C4semidirect
183. C61#11857semidirect

Maximal subgroups

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

subgroupindex
#214564002
#214476152
#214459452
#214438322
#214438312
#214438302
C61×#13482
#1185761