Finite Group Databasebeta

← #29598741

Subgroups — #29598741

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#21455400C212yesmaximal, complemented
3#21447556C212yesmaximal, complemented
4#21443921C211yesmaximal, characteristic, complemented
5C61×#2112C211yesmaximal, characteristic, complemented
6C2×#14519799C2212yes—
7#16840273—22no—
8#16840205—22no—
9#16840200—22no—
10#16840194—22no—
11#16840003—22no—
12#16839998—22no—
13#16839991—24no—
14#16839800C2212yes—
15#16839759—22no—
16#16839573—24no—
17C23×C8×C61C2211yescharacteristic
18C2×M32×C61C2211yescharacteristic
19C2×M32×C61C2211yescharacteristic
20C61×C22⋊C16—22no—
21C2×#11758222—22no—
22#14519799—22no—
23#14519799—22no—
24#14519799—22no—
25#14519799—22no—
26C2×Dic244D412yescomplemented
27C2×#11758190—22no—
28C2×D488D412yescomplemented
29#14519760—42no—
30#14519756—24no—
31#14519751—24no—
32#14519746—42no—
33C4×C22⋊D61—44no—
34#14519736—22no—
35Dic488—22no—
36#14519722—24no—
37D976—22no—
38#14519711—22no—
39#14519709D414yescomplemented
40#14519702—24no—
41#14519699—24no—
42C23×C4×C61D411yescharacteristic
43C22×C8×C61—22no—
44C22×C8×C61—22no—
45C22×C8×C61—21no—
46C22×C8×C61—21no—
47C22×C8×C61D411yescharacteristic
48C22×C8×C61C2311yescharacteristic
49M32×C61—22no—
50M32×C61—22no—
51C2×C16×C61—21no—
52C2×C16×C61D412yescomplemented
53C24×C61D811yescharacteristic
54C22×C4×C61—22no—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—22no—
58C22×C4×C61D811yescharacteristic
59C22×C4×C61C2×D411yescharacteristic
60C2×C22⋊D61—44no—
61C2×C22⋊D61—42no—
62#11758222—42no—
63#11758222—42no—
64#11758222—42no—
65#11758222—42no—
66C2×D244—22no—
67C2×C4×D61—42no—
68C2×Dic122—22no—
69C2×C8×C61—22no—
70C2×C8×C61—21no—
71C2×C8×C61—41no—
72C2×C8×C61—42no—
73C2×C8×C61—41no—
74C2×C8×C61C2×D412yes—
75C2×C8×C61C2×D411yescharacteristic
76C2×C8×C61C2×D412yes—
77C2×C8×C61#4111yescharacteristic
78C22⋊Dic61—44no—
79C22⋊Dic61—42no—
80#11758198—44no—
81C4⋊Dic61—24no—
82#11758196—44no—
83C4×Dic61—42no—
84Dic244—22no—
85Dic244—22no—
86D488—22no—
87D488—22no—
88#11758190—42no—
89#11758190—42no—
90C16×C61—22no—
91C16×C61—41no—
92C23×C61—22no—
93C23×C61—21no—
94C23×C61—42no—
95C23×C61C2×D811yescharacteristic
96C22×D61—42no—
97C2×C4×C61—22no—
98C2×C4×C61—21no—
99C2×C4×C61—41no—
100C2×C4×C61—42no—
101C2×C4×C61—41no—
102C2×C4×C61#12012yes—
103C2×C4×C61#12111yescharacteristic
104C2×C4×C61#13511yescharacteristic
105C2×C4×C61AGL(1,ℤ/8)12yes—
106C22⋊D61—88no—
107C22⋊D61—82no—
108C22⋊D61—82no—
109C2×Dic61—44no—
110C2×Dic61—42no—
111D244—42no—
112D244—42no—
113C4×D61—82no—
114C4×D61—82no—
115Dic122—42no—
116Dic122—42no—
117C8×C61—41no—
118C8×C61#12011yescharacteristic
119C8×C61#12112yes—
120C8×C61#12711yescharacteristic
121#13309—611nomaximal, Sylow
122C22×C61—24no—
123C22×C61—22no—
124C22×C61—41no—
125C22×C61—42no—
126C22×C61—41no—
127C22×C61—41no—
128C22×C61#44712yes—
129C22×C61#46611yescharacteristic
130C2×D61—84no—
131C2×D61—82no—
132C4×C61—41no—
133C4×C61#39211yescharacteristic
134C4×C61#44912yes—
135C4×C61#46911yescharacteristic
136Dic61—84no—
137Dic61—82no—
138#3414—611no—
139#3050—612no—
140#2145—612no—
141#2112D6111yescharacteristic, complemented
142#1384—611no—
143C2×C61—22no—
144C2×C61—21no—
145C2×C61—42no—
146C2×C61#199911yescharacteristic
147D61—162no—
148C2×#135—612no—
149C23×C8C2×D6111yescharacteristic
150#525—1222no—
151#510—1222no—
152#509—1222no—
153#508—1222no—
154C2×M32C2×D6111yescharacteristic
155C2×M32C2×D6111yescharacteristic
156#467—1222no—
157#466—1222no—
158#465—1224no—
159#427—612no—
160#416—1222no—
161#360—1224no—
162C22⋊C16—22no—
163C61#1330911yescharacteristic, complemented, Sylow
164C2×#41—1222no—
165C23×C4D24411yescharacteristic
166#135—1222no—
167#135—1222no—
168#135—1222no—
169#135—1222no—
170C2×Q16—612no—
171C2×SD16—1222no—
172C2×D8—612no—
173C22×C8—21no—
174C22×C8—22no—
175C22×C8—22no—
176C22×C8—21no—
177C22×C8D24411yescharacteristic
178C22×C8C22×D6111yescharacteristic
179#123—2442no—
180C22⋊Q8—1224no—
181#121—1224no—
182#120—2442no—
183C4×D4—2444no—
184#117—1222no—
185Q32—1222no—
186SD32—1224no—
187D16—1222no—
188M32—22no—
189M32—22no—
190C2×C16—21no—
191C2×C16C22⋊D6112yescomplemented
192#107—1222no—
193#106—614no—
194#103—1224no—
195#102—1224no—
196C24D48811yescharacteristic
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—22no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—2442no—
210C22×C4D48811yescharacteristic
211C22×C4C2×D24411yescharacteristic
212Q16—1222no—
213Q16—1222no—
214SD16—2442no—
215SD16—2442no—
216D8—1222no—
217D8—1222no—
218C2×C8—22no—
219C2×C8—21no—
220C2×C8—41no—
221C2×C8—42no—
222C2×C8—41no—
223C2×C8#1175822211yescharacteristic
224C2×C8D4×D6112yes—
225C2×C8D4×D6112yes—
226C2×C8C2×C22⋊D6111yescharacteristic
227C4⋊C4—1224no—
228C4⋊C4—2444no—
229C22⋊C4—2444no—
230C22⋊C4—2444no—
231C22⋊C4—2442no—
232C42—2442no—
233C16—22no—
234C16—41no—
235C23—21no—
236C23—22no—
237C23—42no—
238C23—2442no—
239C23C2×D48811yescharacteristic
240Q8—2442no—
241Q8—2442no—
242D4—4888no—
243D4—4882no—
244D4—4882no—
245D4—2442no—
246D4—2442no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—4882no—
253C2×C4—4882no—
254C2×C4—2444no—
255C2×C4—2442no—
256C2×C4#1451974712yes—
257C2×C4#1451975111yescharacteristic
258C2×C4#1451979911yescharacteristic
259C2×C4#1451980512yes—
260C8—41no—
261C8#1451974511yescharacteristic
262C8#1451975012yes—
263C8#1451977311yescharacteristic
264C22—24no—
265C22—22no—
266C22—41no—
267C22—42no—
268C22—41no—
269C22—41no—
270C22—4884no—
271C22—4882no—
272C22#1683989812yes—
273C22#1683999811yescharacteristic
274C4—41no—
275C4—4884no—
276C4—4882no—
277C4#1683967111yescharacteristic
278C4#1683990912yes—
279C4#1684001511yescharacteristic
280C2—22no—
281C2—21no—
282C2—42no—
283C2—9762no—
284C2#2144681711yescharacteristic
subgroupG/H
centerC4#16840015
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#2112C2
socleC2×C61#1999
hypercenter#2112D61
hypocenterC61#13309
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ C23×C8 ◁ #2112

Complements

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

NH ≅ G/Ntype
1. #21458955C2semidirect
2. #21455400C2semidirect
3. #21447556C2semidirect
4. #21443921C2semidirect
5. C61×#2112C2semidirect
26. C2×Dic244D4semidirect
28. C2×D488D4semidirect
39. #14519709D4semidirect
52. C2×C16×C61D4semidirect
141. #2112D61semidirect
163. C61#13309semidirect
191. C2×C16C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214589552
#214554002
#214475562
#214439212
C61×#21122
#1330961