Finite Group Databasebeta

← #29590965

Subgroups — #29590965

Order 15616.

314 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 79 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#21447619C211yesmaximal, characteristic
3#21445948C211yesmaximal, 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#16839627—21no—
19#16839580—21no—
20C22⋊#11758185C2211yescharacteristic
21#16839537—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×C4×Dic61D411yescharacteristic
41C2×#11758185—21no—
42#14519711C2×C411yescharacteristic
43#14519710—21no—
44#14519702—21no—
45#14519701—21no—
46#14519700—21no—
47C8×Dic61C2×C411yescharacteristic
48C8×Dic61C2×C411yescharacteristic
49C8×Dic61D411yescharacteristic
50C8×Dic61D411yescharacteristic
51#14519684—41no—
52#14519684—41no—
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—
88C4×Dic61—41no—
89C4×Dic61—41no—
90C4×Dic61C22⋊C411yescharacteristic
91C4×Dic61C22⋊C411yescharacteristic
92C4×Dic61SD1611yescharacteristic
93C4×Dic61SD1611yescharacteristic
94C2×#92418—41no—
95C2×#92418C22⋊C411yescharacteristic
96C2×#92418C22⋊C411yescharacteristic
97Dic244—41no—
98C16×C61—41no—
99#11758185—41no—
100C23×C61C2×D811yescharacteristic
101Q8×C61—41no—
102Q8×C61—41no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—81no—
108C2×C4×C61—81no—
109C2×C4×C61—81no—
110C2×C4×C61C2×C22⋊C411yescharacteristic
111C2×C4×C61C2×SD1611yescharacteristic
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—41no—
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
124Dic122—41no—
125Dic122—41no—
126Dic122—82no—
127C8×C61—21no—
128C8×C61—21no—
129#92418—21no—
130#92418—21no—
131#11859—611nomaximal, Sylow
132C22×C61—21no—
133C22×C61—21no—
134C22×C61C2×#10211yescharacteristic
135C22×C61#51011yescharacteristic
136C22×C61#51011yescharacteristic
137C4×C61—21no—
138C4×C61—81no—
139C4×C61—81no—
140C4×C61—161no—
141C4×C61#41011yescharacteristic
142C4×C61#42111yescharacteristic
143Dic61—21no—
144Dic61—21no—
145Dic61—21no—
146Dic61—21no—
147Dic61—81no—
148Dic61—81no—
149Dic61—161no—
150#3170—611no—
151#2163—611no—
152#1835—611no—
153#1348—611no—
154#1348—611no—
155#1348—611no—
156#1348D6111yescharacteristic
157C2×C61—21no—
158C2×C61—21no—
159C2×C61#151711yescharacteristic
160C2×C61#214111yescharacteristic
161C2×C61#214511yescharacteristic
162#533—1221no—
163#500—611no—
164#494—611no—
165#487—1221no—
166#467—611no—
167#467—1221no—
168#467C2×D6111yescharacteristic
169C4×Q16—611no—
170C4×Q16—611no—
171C4×Q16—1221no—
172C2×C4×C8—611no—
173#382—1221no—
174C4⋊C16—1221no—
175C22⋊C16—611no—
176C22⋊C16C2×D6111yescharacteristic
177#346—1221no—
178#340—611no—
179#340—1221no—
180#340C2×D6111yescharacteristic
181C61#1185911yescharacteristic, complemented, Sylow
182C2×Q16—611no—
183C2×Q16—1221no—
184C2×Q16C4×D6111yescharacteristic
185C22×C8—611no—
186C22×C8C22×D6111yescharacteristic
187C4⋊Q8—1221no—
188C4⋊Q8—1221no—
189#125—2441no—
190C22⋊Q8—21no—
191C22⋊Q8—1221no—
192C22⋊Q8—2441no—
193C4×Q8—1221no—
194C4×Q8—1221no—
195C4×Q8—2441no—
196#117—2441no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—1221no—
199C2×C42—611no—
200C2×C16—21no—
201C2×C16—1221no—
202#107—611no—
203#107—1221no—
204#107C4×D6111yescharacteristic
205#103—21no—
206#103—1221no—
207#103—1221no—
208#103—1221no—
209C4×C8—611no—
210C4×C8—611no—
211C4×C8—611no—
212C4×C8—611no—
213#95—2441no—
214#95—2441no—
215C2×Q8—21no—
216C2×Q8—1221no—
217C2×Q8—2441no—
218C22×C4—41no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—2441no—
222C22×C4D4×D6111yescharacteristic
223Q16—41no—
224Q16—2441no—
225Q16—2442no—
226C2×C8—41no—
227C2×C8—611no—
228C2×C8—611no—
229C2×C8—2441no—
230C2×C8C2×C4×D6111yescharacteristic
231C2×C8D4×D6111yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—1221no—
237C4⋊C4—2441no—
238C4⋊C4—2441no—
239C4⋊C4—2441no—
240C4⋊C4—2441no—
241C4⋊C4—2441no—
242C4⋊C4—2441no—
243C4⋊C4—2441no—
244C4⋊C4—2441no—
245C22⋊C4—41no—
246C22⋊C4—2441no—
247C42—611no—
248C42—611no—
249C42—611no—
250C42—611no—
251C42—2441no—
252C42—2441no—
253C16—41no—
254C16—2441no—
255C23D8×D6111yescharacteristic
256Q8—41no—
257Q8—41no—
258Q8—4882no—
259Q8—2441no—
260Q8—2441no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—611no—
269C2×C4—611no—
270C2×C4—611no—
271C2×C4—611no—
272C2×C4—1221no—
273C2×C4—1221no—
274C2×C4—4881no—
275C2×C4—4881no—
276C2×C4—4881no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4C22⋊C4×D6111yescharacteristic
281C2×C4SD16×D6111yescharacteristic
282C8—21no—
283C8—21no—
284C8—1221no—
285C8—1221no—
286C22—21no—
287C22—21no—
288C22#102×D6111yescharacteristic
289C22#1684020111yescharacteristic
290C22#1684020411yescharacteristic
291C4—21no—
292C4—81no—
293C4—81no—
294C4—161no—
295C4—1221no—
296C4—1221no—
297C4—1221no—
298C4—1221no—
299C4—9761no—
300C4—4881no—
301C4—4881no—
302C4#1683973411yescharacteristic
303C4#1683977711yescharacteristic
304C2—21no—
305C2—21no—
306C2#2144437711yescharacteristic
307C2#2144753711yescharacteristic
308C2#2144755311yescharacteristic
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#11859
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
181. C61#11859semidirect

Maximal subgroups

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

subgroupindex
#214564002
#214476192
#214459482
#214438322
#214438312
#214438302
C61×#13482
#1185961