Finite Group Databasebeta

← #29590950

Subgroups — #29590950

Order 15616.

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

normal subgroups only

This group has 324 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#21456390C211yesmaximal, characteristic
2#21447615C211yesmaximal, characteristic, complemented
3#21445948C211yesmaximal, characteristic, complemented
4#21443831C211yesmaximal, characteristic, complemented
5#21443829C211yesmaximal, characteristic
6#21443827C211yesmaximal, characteristic
7C61×#1348C211yesmaximal, characteristic, complemented
8#16840298—21no—
9#16840163C411yescharacteristic, complemented
10#16840147C411yescharacteristic, complemented
11#16840118—21no—
12#16839998C2211yescharacteristic
13#16839993—21no—
14Q16×Dic61C411yescharacteristic, complemented
15#16839847—21no—
16#16839844C411yescharacteristic, complemented
17C2×C8×Dic61C2211yescharacteristic
18#16839627—21no—
19#16839580—21no—
20C22⋊#11758185C2211yescharacteristic
21C16×Dic61—21no—
22#16839525C2211yescharacteristic
23#16839524—21no—
24C61×#467C2211yescharacteristic
25C61×C22⋊C16C2211yescharacteristic
26C61×#340C2211yescharacteristic
27C2×#11758201—21no—
28C2×D488C2×C411yescharacteristic
29C22×#92418D411yescharacteristic
30#14519772—41no—
31#14519768—21no—
32#14519766—21no—
33#14519761—41no—
34#14519751—21no—
35Q8×Dic61—21no—
36#14519739—21no—
37#14519737—41no—
38#14519735—41no—
39C2×C4⋊Dic61—21no—
40C2×C4×Dic61D411yescharacteristic
41C2×#11758185—21no—
42#14519711C2×C411yescharacteristic
43#14519708—21no—
44#14519701—21no—
45#14519699—21no—
46#14519697—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
63C2×C22⋊D61—41no—
64C22×Dic61—41no—
65C22×Dic61D811yescharacteristic
66C22×Dic61D811yescharacteristic
67C2×D244—21no—
68C2×C4×D61—41no—
69Q16×C61—41no—
70C2×C8×C61—41no—
71C2×C8×C61C22×C411yescharacteristic
72C2×C8×C61C2×D411yescharacteristic
73C4⋊C4×C61—21no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C22⋊C4×C61—41no—
78#11758201—42no—
79#11758198—41no—
80#11758198—41no—
81#11758198—41no—
82#11758198—41no—
83C4⋊Dic61—21no—
84C4⋊Dic61—41no—
85C4⋊Dic61—41no—
86C4⋊Dic61—41no—
87C4⋊Dic61—41no—
88#11758196—41no—
89C4×Dic61—41no—
90C4×Dic61C22⋊C411yescharacteristic
91C4×Dic61C22⋊C411yescharacteristic
92C4×Dic61SD1611yescharacteristic
93C4×Dic61SD1611yescharacteristic
94C2×#92418—41no—
95C2×#92418C22⋊C411yescharacteristic
96C2×#92418C22⋊C411yescharacteristic
97D488—41no—
98C16×C61—41no—
99#11758185—41no—
100C23×C61C2×D811yescharacteristic
101C22×D61—41no—
102Q8×C61—41no—
103Q8×C61—41no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—81no—
109C2×C4×C61—81no—
110C2×C4×C61—81no—
111C2×C4×C61C2×C22⋊C411yescharacteristic
112C2×C4×C61C2×SD1611yescharacteristic
113C22⋊D61—81no—
114C22⋊D61—81no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—81no—
120C2×Dic61—81no—
121C2×Dic61—81no—
122C2×Dic61#10211yescharacteristic
123C2×Dic61#10211yescharacteristic
124C2×Dic61#10211yescharacteristic
125C2×Dic61#10211yescharacteristic
126D244—41no—
127D244—41no—
128C4×D61—82no—
129C8×C61—21no—
130C8×C61—21no—
131#92418—21no—
132#92418—21no—
133#11855—611nomaximal, Sylow
134C22×C61—21no—
135C22×C61—21no—
136C22×C61C2×#10211yescharacteristic
137C22×C61#50811yescharacteristic
138C22×C61#50811yescharacteristic
139C2×D61—81no—
140C2×D61—81no—
141C2×D61—81no—
142C4×C61—21no—
143C4×C61—81no—
144C4×C61—81no—
145C4×C61—161no—
146C4×C61#41011yescharacteristic
147C4×C61#42111yescharacteristic
148Dic61—21no—
149Dic61—21no—
150Dic61—21no—
151Dic61—21no—
152Dic61—81no—
153Dic61—161no—
154#3168—611no—
155#2162—611no—
156#1835—611no—
157#1348—611no—
158#1348D6111yescharacteristic, complemented
159#1347—611no—
160#1347—611no—
161C2×C61—21no—
162C2×C61—21no—
163C2×C61#151711yescharacteristic
164C2×C61#213811yescharacteristic
165C2×C61#214511yescharacteristic
166D61—161no—
167#529—1221no—
168#499—611no—
169#495—611no—
170#488—1221no—
171#467C2×D6111yescharacteristic
172#466—611no—
173#465—1221no—
174C4×Q16—611no—
175C4×SD16—1221no—
176C4×D8—611no—
177C2×C4×C8—611no—
178#382—1221no—
179C4⋊C16—1221no—
180C22⋊C16—611no—
181C22⋊C16C2×D6111yescharacteristic
182C4×C16—1221no—
183#340—611no—
184#340—1221no—
185#340C2×D6111yescharacteristic
186C61#1185511yescharacteristic, complemented, Sylow
187C2×Q16C4×D6111yescharacteristic
188C2×SD16—1221no—
189C2×D8—611no—
190C22×C8—611no—
191C22×C8C22×D6111yescharacteristic
192#126—2441no—
193#125—1221no—
194#124—1221no—
195#123—2441no—
196C22⋊Q8—21no—
197#121—1221no—
198C4×Q8—1221no—
199C4×D4—1221no—
200C4×D4—2441no—
201#117—2441no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—1221no—
204C2×C42—611no—
205C2×C16—21no—
206C2×C16—1221no—
207#107—611no—
208#107C4×D6111yescharacteristic
209#106—1221no—
210#103—21no—
211#103—1221no—
212#102—1221no—
213#102—1221no—
214C4×C8—611no—
215C4×C8—611no—
216C4×C8—611no—
217C4×C8—611no—
218#95—2441no—
219#95—2441no—
220C2×Q8—21no—
221C2×D4—1221no—
222C2×D4—2441no—
223C22×C4—41no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—2441no—
227C22×C4—2441no—
228C22×C4D4×D6111yescharacteristic
229Q16—41no—
230SD16—2442no—
231D8—2441no—
232C2×C8—41no—
233C2×C8—611no—
234C2×C8—611no—
235C2×C8—2441no—
236C2×C8C2×C4×D6111yescharacteristic
237C2×C8D4×D6111yescharacteristic
238C4⋊C4—21no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—1221no—
243C4⋊C4—2441no—
244C4⋊C4—2441no—
245C4⋊C4—2441no—
246C4⋊C4—2441no—
247C4⋊C4—2441no—
248C22⋊C4—41no—
249C22⋊C4—2441no—
250C22⋊C4—2441no—
251C22⋊C4—2441no—
252C22⋊C4—2441no—
253C42—611no—
254C42—611no—
255C42—611no—
256C42—611no—
257C42—2441no—
258C16—41no—
259C16—2441no—
260C23—2441no—
261C23D8×D6111yescharacteristic
262Q8—41no—
263Q8—41no—
264D4—4881no—
265D4—4881no—
266D4—2441no—
267D4—2441no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—611no—
276C2×C4—611no—
277C2×C4—611no—
278C2×C4—611no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—4882no—
282C2×C4—4881no—
283C2×C4—4881no—
284C2×C4—4881no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4C22⋊C4×D6111yescharacteristic
288C2×C4SD16×D6111yescharacteristic
289C8—21no—
290C8—21no—
291C8—1221no—
292C8—1221no—
293C22—21no—
294C22—21no—
295C22—4881no—
296C22—4881no—
297C22—4881no—
298C22#102×D6111yescharacteristic
299C22#1684019311yescharacteristic
300C22#1684019511yescharacteristic
301C4—21no—
302C4—81no—
303C4—81no—
304C4—161no—
305C4—1221no—
306C4—1221no—
307C4—1221no—
308C4—1221no—
309C4—9761no—
310C4—4881no—
311C4#1683973411yescharacteristic
312C4#1683977711yescharacteristic
313C2—21no—
314C2—21no—
315C2—9761no—
316C2#2144437711yescharacteristic
317C2#2144752511yescharacteristic
318C2#2144755311yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1348C2
socleC22×C61C2×#102
prime radical#16839998C22
cosocleC22×C8×C61C23
hypercenter#1348D61
hypocenterC61#11855
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
2. #21447615C2semidirect
3. #21445948C2semidirect
4. #21443831C2semidirect
7. C61×#1348C2semidirect
9. #16840163C4semidirect
10. #16840147C4semidirect
14. Q16×Dic61C4semidirect
16. #16839844C4semidirect
158. #1348D61semidirect
186. C61#11855semidirect

Maximal subgroups

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

subgroupindex
#214563902
#214476152
#214459482
#214438312
#214438292
#214438272
C61×#13482
#1185561