Finite Group Databasebeta

← #29598742

Subgroups — #29598742

Order 15616.

568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 95 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#21458955C211yesmaximal, characteristic, complemented
2#21455401C212yesmaximal, complemented
3#21447554C212yesmaximal, complemented
4#21447429C211yesmaximal, characteristic, complemented
5C61×#1384C211yesmaximal, characteristic, complemented
6C2×#14519799C2212yes—
7C22×C8×D61C2211yescharacteristic
8#16840274—22no—
9#16840205—22no—
10#16840200—22no—
11#16840194—22no—
12C2×#14519717C2211yescharacteristic
13#16840004—22no—
14#16839999—22no—
15#16839992—24no—
16#16839756—22no—
17#16839571—24no—
18#16839541—22no—
19C2×M32×C61C2211yescharacteristic
20C61×#427C2212yes—
21C2×#11758222—22no—
22C22×C4×D61D411yescharacteristic
23#14519799—22no—
24#14519799—22no—
25#14519799—22no—
26#14519799—22no—
27C2×Dic244D412yescomplemented
28C2×#11758190—22no—
29C2×D488D412yescomplemented
30C22×#92418D411yescharacteristic
31C2×C8×D61—22no—
32C2×C8×D61—22no—
33C2×C8×D61—21no—
34C2×C8×D61—21no—
35#14519761—42no—
36#14519757—24no—
37#14519752—24no—
38#14519747—42no—
39C4×D244—44no—
40Dic488—22no—
41#14519722—24no—
42D976—22no—
43#14519717—22no—
44C2×#11758185—21no—
45#14519700—24no—
46#14519697—24no—
47C22×C8×C61C2311yescharacteristic
48#117×C61—22no—
49M32×C61—22no—
50C2×C16×C61D412yescomplemented
51#107×C61—22no—
52#106×C61D414yescomplemented
53C23×D61D811yescharacteristic
54C22×C4×C61C2×D411yescharacteristic
55C2×C22⋊D61—42no—
56C22×Dic61D811yescharacteristic
57#11758222—42no—
58#11758222—42no—
59#11758222—42no—
60#11758222—42no—
61C2×D244—22no—
62C2×D244—44no—
63C2×C4×D61—22no—
64C2×C4×D61—21no—
65C2×C4×D61—21no—
66C2×C4×D61—22no—
67C2×C4×D61—42no—
68C2×Dic122—22no—
69C2×C8×C61C2×D412yes—
70C2×C8×C61C2×D411yescharacteristic
71C2×C8×C61C2×D412yes—
72C2×C8×C61#4111yescharacteristic
73C4⋊C4×C61—24no—
74C22⋊C4×C61—42no—
75C42×C61—42no—
76#11758198—44no—
77#11758198—44no—
78C4⋊Dic61—44no—
79C2×#92418—22no—
80C2×#92418—21no—
81Dic244—22no—
82Dic244—22no—
83D488—22no—
84D488—22no—
85#11758190—42no—
86#11758190—42no—
87C8×D61—41no—
88C8×D61—42no—
89C8×D61—41no—
90C16×C61—22no—
91#11758185—41no—
92C23×C61C2×D811yescharacteristic
93C22×D61—22no—
94C22×D61—21no—
95C22×D61—42no—
96C22×D61—42no—
97C2×C4×C61—44no—
98C2×C4×C61#12012yes—
99C2×C4×C61#12111yescharacteristic
100C2×C4×C61#13511yescharacteristic
101C2×C4×C61AGL(1,ℤ/8)12yes—
102C22⋊D61—82no—
103C22⋊D61—82no—
104C2×Dic61—22no—
105C2×Dic61—21no—
106C2×Dic61—42no—
107D244—42no—
108D244—42no—
109D244—88no—
110C4×D61—41no—
111C4×D61—42no—
112C4×D61—41no—
113C4×D61—82no—
114C4×D61—82no—
115Dic122—42no—
116Dic122—42no—
117C8×C61#12011yescharacteristic
118C8×C61#12112yes—
119C8×C61#12711yescharacteristic
120#92418—41no—
121#13309—611nomaximal, Sylow
122C22×C61—41no—
123C22×C61#44712yes—
124C22×C61#46611yescharacteristic
125C2×D61—24no—
126C2×D61—22no—
127C2×D61—42no—
128C2×D61—41no—
129C2×D61—41no—
130C2×D61—84no—
131C2×D61—82no—
132C4×C61—84no—
133C4×C61#39211yescharacteristic
134C4×C61#44912yes—
135C4×C61#46911yescharacteristic
136Dic61—41no—
137Dic61—82no—
138#3414—611no—
139#3050—612no—
140#2145—612no—
141#2112—611no—
142#1384D6111yescharacteristic, complemented
143C2×C61—22no—
144C2×C61—21no—
145C2×C61#199911yescharacteristic
146D61—42no—
147D61—162no—
148C2×#135—612no—
149C23×C8—611no—
150#525—1222no—
151#510—1222no—
152#509—1222no—
153#508—1222no—
154C2×M32—611no—
155C2×M32C2×D6111yescharacteristic
156#467—1222no—
157#466—1222no—
158#465—1224no—
159#427C2×D6112yes—
160#416—1222no—
161#360—1224no—
162C22⋊C16—1222no—
163C61#1330911yescharacteristic, complemented, Sylow
164C2×#41—1222no—
165C23×C4—611no—
166#135—1222no—
167#135—1222no—
168#135—1222no—
169#135—1222no—
170C2×Q16—612no—
171C2×SD16—1222no—
172C2×D8—612no—
173C22×C8—611no—
174C22×C8—1221no—
175C22×C8—1222no—
176C22×C8—1222no—
177C22×C8—1221no—
178C22×C8C22×D6111yescharacteristic
179#123—2442no—
180C22⋊Q8—1224no—
181#121—1224no—
182#120—2442no—
183C4×D4—2444no—
184#117—22no—
185Q32—1222no—
186SD32—1224no—
187D16—1222no—
188M32—22no—
189M32—1222no—
190C2×C16—1221no—
191C2×C16D24412yescomplemented
192#107—22no—
193#106D24414yescomplemented
194#103—1224no—
195#102—1224no—
196C24—611no—
197#41—2442no—
198#41—2442no—
199#41—2442no—
200#41—2442no—
201C2×Q8—1222no—
202C2×D4—1222no—
203C2×D4—2444no—
204C2×D4—2442no—
205C22×C4—611no—
206C22×C4—1222no—
207C22×C4—1221no—
208C22×C4—1221no—
209C22×C4—1222no—
210C22×C4—2442no—
211C22×C4D4×D6111yescharacteristic
212Q16—1222no—
213Q16—1222no—
214SD16—2442no—
215SD16—2442no—
216D8—1222no—
217D8—1222no—
218C2×C8—1222no—
219C2×C8—1221no—
220C2×C8—2441no—
221C2×C8—2442no—
222C2×C8—2441no—
223C2×C8C2×D24411yescharacteristic
224C2×C8C2×D24412yes—
225C2×C8D4×D6112yes—
226C2×C8#1175822611yescharacteristic
227C4⋊C4—24no—
228C4⋊C4—2444no—
229C22⋊C4—42no—
230C22⋊C4—2444no—
231C22⋊C4—2444no—
232C42—42no—
233C16—22no—
234C16—2441no—
235C23—1221no—
236C23—1222no—
237C23—2442no—
238C23—2442no—
239C23D8×D6111yescharacteristic
240Q8—2442no—
241Q8—2442no—
242D4—4888no—
243D4—4882no—
244D4—4882no—
245D4—2442no—
246D4—2442no—
247C2×C4—44no—
248C2×C4—1221no—
249C2×C4—1222no—
250C2×C4—4882no—
251C2×C4—4882no—
252C2×C4—2442no—
253C2×C4—2441no—
254C2×C4—2442no—
255C2×C4—2441no—
256C2×C4#1451974712yes—
257C2×C4#1451975211yescharacteristic
258C2×C4#1451980011yescharacteristic
259C2×C4#1451980412yes—
260C8—2441no—
261C8#1451974711yescharacteristic
262C8#1451975212yes—
263C8#1451977411yescharacteristic
264C22—41no—
265C22—1224no—
266C22—1222no—
267C22—4884no—
268C22—4882no—
269C22—2442no—
270C22—2441no—
271C22—2441no—
272C22#1683989712yes—
273C22#1683999911yescharacteristic
274C4—84no—
275C4—4882no—
276C4—2441no—
277C4#1683967211yescharacteristic
278C4#1683991012yes—
279C4#1684001611yescharacteristic
280C2—22no—
281C2—21no—
282C2—9762no—
283C2—2442no—
284C2#2144681811yescharacteristic
subgroupG/H
centerC4#16840016
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#1384C2
socleC2×C61#1999
hypercenter#1384D61
hypocenterC61#13309
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #1384

Complements

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

NH ≅ G/Ntype
1. #21458955C2semidirect
2. #21455401C2semidirect
3. #21447554C2semidirect
4. #21447429C2semidirect
5. C61×#1384C2semidirect
27. C2×Dic244D4semidirect
29. C2×D488D4semidirect
50. C2×C16×C61D4semidirect
52. #106×C61D4semidirect
142. #1384D61semidirect
163. C61#13309semidirect
191. C2×C16D244semidirect
193. #106D244semidirect

Maximal subgroups

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

subgroupindex
#214589552
#214554012
#214475542
#214474292
C61×#13842
#1330961