Finite Group Databasebeta

← #29593797

Subgroups — #29593797

Order 15616.

366 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 67 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#21457577C211yesmaximal, characteristic
2#21447958C211yesmaximal, characteristic, complemented
3#21445205C211yesmaximal, characteristic, complemented
4#21443865C211yesmaximal, characteristic, complemented
5#21443784C211yesmaximal, characteristic, complemented
6#21443775C211yesmaximal, characteristic, complemented
7C61×#2240C211yesmaximal, characteristic, complemented
8C2×#14519796—21no—
9#16840432—21no—
10#16839995—21no—
11#16839964—21no—
12#16839959—21no—
13#16839904—22no—
14C4×Dic244C2211yescharacteristic
15C8×D244C2211yescharacteristic
16#16839589—21no—
17C4⋊#11758185C2211yescharacteristic
18#16839565—21no—
19#16839515C2211yescharacteristic
20#16839508—21no—
21C61×#500C2211yescharacteristic
22C61×#493C2211yescharacteristic
23C61×#357—22no—
24C4×C16×C61C2211yescharacteristic
25C2×#11758224—22no—
26#14519796—42no—
27#14519796—42no—
28C2×Dic244D411yescharacteristic
29C2×#11758200—22no—
30C2×#11758201—41no—
31C2×C8×D61—21no—
32#14519773—41no—
33#14519749—42no—
34#14519748—22no—
35C4×Dic122—21no—
36C4×D244D411yescharacteristic
37D4×Dic61—41no—
38C2×#11758185—21no—
39#14519711D411yescharacteristic
40C4⋊#92418—21no—
41C4⋊#92418D411yescharacteristic
42#14519702—21no—
43#14519701—41no—
44#14519698—22no—
45#14519689—21no—
46C2×D8×C61—21no—
47C2×D8×C61D412yes—
48C4⋊Q8×C61—21no—
49#127×C61—21no—
50C2×C16×C61—21no—
51#107×C61—21no—
52#107×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—41no—
55C2×D4×C61—22no—
56C2×D4×C61—41no—
57C2×D4×C61—41no—
58C2×C22⋊D61—42no—
59C2×C22⋊D61—42no—
60C22×Dic61—42no—
61#11758224—44no—
62#11758224—82no—
63C2×D244D811yescharacteristic
64C2×C4×D61—21no—
65C2×Dic122—21no—
66D8×C61—42no—
67D8×C61—41no—
68D8×C61—41no—
69C2×C8×C61C2×D411yescharacteristic
70C2×C8×C61C2×D411yescharacteristic
71C4⋊C4×C61—41no—
72C4⋊C4×C61—41no—
73C42×C61C2×D411yescharacteristic
74C22⋊Dic61—42no—
75#11758201—82no—
76#11758200—44no—
77#11758198—21no—
78C4⋊Dic61—21no—
79C4⋊Dic61D811yescharacteristic
80#11758196—41no—
81C4×Dic61—41no—
82C2×#92418—21no—
83C2×#92418—41no—
84Dic244—21no—
85Dic244SD1612yescomplemented
86C8×D61—41no—
87C8×D61—41no—
88C16×C61—41no—
89#11758185—41no—
90C23×C61—42no—
91C22×D61—21no—
92Q8×C61—81no—
93Q8×C61—81no—
94D4×C61—42no—
95D4×C61—42no—
96D4×C61—81no—
97D4×C61—81no—
98D4×C61—161no—
99C2×C4×C61—81no—
100C2×C4×C61#12011yescharacteristic
101C2×C4×C61C2×D811yescharacteristic
102C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
103C22⋊D61—84no—
104C22⋊D61—162no—
105C2×Dic61—21no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—84no—
109D244—21no—
110D244—21no—
111C4×D61—41no—
112C4×D61—41no—
113Dic122—22no—
114Dic122—41no—
115C8×C61—21no—
116C8×C61C2×SD1611yescharacteristic
117C8×C61AGL(1,ℤ/8)11yescharacteristic
118#92418—41no—
119#92418—81no—
120#12369—611nomaximal, Sylow
121C22×C61—82no—
122C22×C61—82no—
123C22×C61—82no—
124C22×C61#44711yescharacteristic
125C2×D61—41no—
126C2×D61—41no—
127C2×D61—41no—
128C4×C61—21no—
129C4×C61—161no—
130C4×C61#45011yescharacteristic
131C4×C61#45511yescharacteristic
132C4×C61#50811yescharacteristic
133C4×C61#50911yescharacteristic
134Dic61—42no—
135Dic61—41no—
136Dic61—81no—
137#3287—611no—
138#2240D6111yescharacteristic, complemented
139#2225—611no—
140#1673—611no—
141#1361—611no—
142#1332—611no—
143D4⋊C16—611no—
144C2×C61—162no—
145C2×C61#163911yescharacteristic
146C2×C61#218611yescharacteristic
147C2×C61#219411yescharacteristic
148D61—81no—
149C2×#135—1221no—
150#550—1221no—
151#500C2×D6111yescharacteristic
152#493C2×D6111yescharacteristic
153#466—1221no—
154#461—1221no—
155#460—1221no—
156#449—1222no—
157C4×Q16—611no—
158C8×D4—611no—
159#367—1221no—
160C4⋊C16—611no—
161#358—1221no—
162#357—22no—
163C4×C16C2×D6111yescharacteristic
164#335—611no—
165#332—1221no—
166C61#1236911yescharacteristic, complemented, Sylow
167C2×#41—1222no—
168#135—2442no—
169#135—2442no—
170C2×Q16—611no—
171C2×SD16—1222no—
172C2×SD16—2441no—
173C2×D8—21no—
174C2×D8C22⋊D6112yes—
175C22×C8—1221no—
176C4⋊Q8—21no—
177#127—21no—
178#127—2441no—
179#121—1222no—
180#121—2442no—
181C4×Q8—1221no—
182C4×D4—611no—
183C4×D4—2441no—
184C2×C16—21no—
185C2×C16—1221no—
186#107—21no—
187#107—21no—
188#107—611no—
189C4⋊C8—611no—
190C4⋊C8—1221no—
191#103—1221no—
192#103—2441no—
193#102—1222no—
194C22⋊C8—1221no—
195C4×C8C22×D6111yescharacteristic
196#41—4882no—
197#41—2444no—
198C2×Q8—41no—
199C2×Q8—1221no—
200C2×D4—22no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4—611no—
204C2×D4—2442no—
205C2×D4—2442no—
206C22×C4—1221no—
207C22×C4—2442no—
208Q16—612no—
209Q16—1221no—
210SD16—4882no—
211SD16—2444no—
212D8—42no—
213D8—41no—
214D8—41no—
215C2×C8—1221no—
216C2×C8—2441no—
217C2×C8—2441no—
218C2×C8—2441no—
219C2×C8D4×D6111yescharacteristic
220C2×C8C2×C22⋊D6111yescharacteristic
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—611no—
224C4⋊C4—1221no—
225C4⋊C4—2441no—
226C22⋊C4—1221no—
227C22⋊C4—2442no—
228C42—2441no—
229C42D4×D6111yescharacteristic
230C16—41no—
231C16—2441no—
232C23—42no—
233C23—1221no—
234Q8—81no—
235Q8—81no—
236Q8—1222no—
237Q8—2441no—
238D4—42no—
239D4—42no—
240D4—81no—
241D4—81no—
242D4—161no—
243D4—1221no—
244D4—1221no—
245D4—9762no—
246D4—4884no—
247C2×C4—81no—
248C2×C4—1221no—
249C2×C4—4884no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4—2441no—
254C2×C4#1451974511yescharacteristic
255C2×C4D8×D6111yescharacteristic
256C2×C4#1451980111yescharacteristic
257C8—21no—
258C8—4881no—
259C8—2441no—
260C8SD16×D6111yescharacteristic
261C8#1451980411yescharacteristic
262C22—82no—
263C22—82no—
264C22—82no—
265C22—2441no—
266C22—2441no—
267C22—2441no—
268C22#1683989411yescharacteristic
269C4—21no—
270C4—161no—
271C4—4881no—
272C4—2441no—
273C4—2442no—
274C4#1683991111yescharacteristic
275C4#1683993911yescharacteristic
276C4#1684019111yescharacteristic
277C4#1684019611yescharacteristic
278C2—162no—
279C2—4881no—
280C2#2144499511yescharacteristic
281C2#2144773911yescharacteristic
282C2#2144778911yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2240C2
socleC22×C61#447
prime radical#21457577C2
hypercenter#2240D61
hypocenterC61#12369
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2240

Complements

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

NH ≅ G/Ntype
2. #21447958C2semidirect
3. #21445205C2semidirect
4. #21443865C2semidirect
5. #21443784C2semidirect
6. #21443775C2semidirect
7. C61×#2240C2semidirect
85. Dic244SD16semidirect
138. #2240D61semidirect
166. C61#12369semidirect

Maximal subgroups

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

subgroupindex
#214575772
#214479582
#214452052
#214438652
#214437842
#214437752
C61×#22402
#1236961