Finite Group Databasebeta

← #29580868

Subgroups — #29580868

Order 15616.

566 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 105 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#21455851C212yesmaximal
2#21449112C211yesmaximal, characteristic, complemented
3#21446651C211yesmaximal, characteristic
4#21444249C212yesmaximal, complemented
5C61×#1274C211yesmaximal, characteristic, complemented
6#16840312C2211yescharacteristic
7C2×C4×Dic122C2212yes—
8#16840081—22no—
9#16840048—22no—
10#16839963—22no—
11#16839903—22no—
12C4×#11758190—24no—
13#16839786C2211yescharacteristic
14C2×#14519705—22no—
15#16839694—22no—
16#16839683—22no—
17C4×C4⋊Dic61—22no—
18#16839494—24no—
19C61×#431C2212yes—
20C61×#376C2211yescharacteristic
21C2×#11758222—21no—
22C22×Dic122D412yes—
23C2×#11758190—24no—
24C2×#11758194—21no—
25#14519777D411yescharacteristic
26#14519774D411yescharacteristic
27#14519765—21no—
28#14519751—22no—
29C4×Dic122—22no—
30C4×Dic122—22no—
31C4×Dic122—22no—
32C4×Dic122—22no—
33C4×D244—22no—
34C2×C4⋊Dic61—24no—
35C2×C4⋊Dic61D412yes—
36C2×#11758196—22no—
37C2×C4×Dic61—22no—
38#14519709—24no—
39C4⋊#92418—22no—
40#14519705—44no—
41#14519702—24no—
42#14519699—24no—
43#14519684—22no—
44#14519684—22no—
45C2×C42×C61D412yes—
46C2×C42×C61C2311yescharacteristic
47C4⋊C8×C61—22no—
48C22⋊C8×C61—22no—
49C4×C8×C61D414yes—
50#95×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61C2×D412yes—
53C22×C4×C61C2×D411yescharacteristic
54C2×C22⋊D61—41no—
55C22×Dic61—22no—
56C22×Dic61—22no—
57#11758222—42no—
58#11758222—42no—
59C2×D244—22no—
60C2×D244—21no—
61C2×C4×D61—41no—
62C2×Dic122—22no—
63C2×Dic122—22no—
64C2×Dic122—21no—
65C2×Dic122—44no—
66C2×C8×C61—24no—
67C42×C61—22no—
68C42×C61SD1614yescomplemented
69C42×C61C2×D411yescharacteristic
70C42×C61C2×D412yes—
71C42×C61#4111yescharacteristic
72#11758198—42no—
73C4⋊Dic61—22no—
74C4⋊Dic61—22no—
75C4⋊Dic61—22no—
76C4⋊Dic61—48no—
77#11758196—42no—
78#11758196—42no—
79C4×Dic61—42no—
80C4×Dic61—42no—
81#11758194—42no—
82C2×#92418—41no—
83#11758190—48no—
84C23×C61#12011yescharacteristic
85C22×D61—41no—
86C2×C4×C61—24no—
87C2×C4×C61—42no—
88C2×C4×C61—44no—
89C2×C4×C61#12012yes—
90C2×C4×C61#12112yes—
91C2×C4×C61#12111yescharacteristic
92C2×C4×C61#12711yescharacteristic
93C2×C4×C61C2×SD1612yes—
94C2×C4×C61#13712yes—
95C22⋊D61—82no—
96C2×Dic61—24no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61—44no—
100C2×Dic61—42no—
101C2×Dic61—41no—
102D244—44no—
103D244—42no—
104C4×D61—81no—
105C4×D61—81no—
106Dic122—24no—
107Dic122—24no—
108Dic122—42no—
109Dic122—42no—
110Dic122—42no—
111C8×C61—44no—
112#92418—81no—
113#10014—611nomaximal, Sylow
114C22×C61—22no—
115C22×C61#39211yescharacteristic
116C22×C61#44812yes—
117C2×D61—82no—
118C2×D61—81no—
119C4×C61—22no—
120C4×C61—22no—
121C4×C61—44no—
122C4×C61#46112yes—
123C4×C61#49211yescharacteristic
124C4×C61#49711yescharacteristic
125Dic61—44no—
126Dic61—82no—
127Dic61—81no—
128#3103—612no—
129#2399—611no—
130#1963—611no—
131#1487—612no—
132#1274D6111yescharacteristic, complemented
133C2×C61—22no—
134C2×C61#201012yes—
135C2×C61#201311yescharacteristic
136D61—161no—
137#532—611no—
138C2×C4×Q8—612no—
139#481—1222no—
140#475—1222no—
141#460—1222no—
142#448—1222no—
143C4×SD16—1224no—
144#431C2×D6112yes—
145#423—611no—
146C2×#104—1222no—
147#398—1222no—
148#395—1222no—
149C4×C4⋊C4—1222no—
150#376C2×D6111yescharacteristic
151Q8⋊C8—1224no—
152C61#1001411yescharacteristic, complemented, Sylow
153C2×#41—1221no—
154C22×Q8—612no—
155C2×SD16—1224no—
156C2×M16—1221no—
157C4⋊Q8—611no—
158#127—611no—
159#124—1221no—
160#121—1222no—
161C4×Q8—1222no—
162C4×Q8—1222no—
163C4×Q8—1222no—
164C4×Q8—1222no—
165C4×D4—1222no—
166C2×C4⋊C4—612no—
167C2×C4⋊C4—1224no—
168C2×C4⋊C4—1222no—
169C2×C42—1222no—
170C2×C42D24412yes—
171C2×C42C22×D6111yescharacteristic
172#106—1224no—
173C4⋊C8—22no—
174C4⋊C8—1222no—
175#104—2444no—
176#103—1224no—
177#102—1224no—
178C22⋊C8—22no—
179C4×C8D24414yes—
180#95—22no—
181#95—1222no—
182#95—1222no—
183#41—2442no—
184#41—2442no—
185C2×Q8—1222no—
186C2×Q8—1222no—
187C2×Q8—1221no—
188C2×Q8—2444no—
189C2×D4—1222no—
190C2×D4—1221no—
191C2×D4—2441no—
192C22×C4—22no—
193C22×C4—1222no—
194C22×C4—1222no—
195C22×C4—2441no—
196C22×C4C2×D24411yescharacteristic
197C22×C4D4×D6112yes—
198SD16—2448no—
199M16—2442no—
200C2×C8—24no—
201C2×C8—2441no—
202C4⋊C4—1222no—
203C4⋊C4—1222no—
204C4⋊C4—1222no—
205C4⋊C4—2448no—
206C4⋊C4—2442no—
207C4⋊C4—2442no—
208C22⋊C4—2442no—
209C42—22no—
210C42—2442no—
211C42—2442no—
212C42#1175819014yescomplemented
213C42C2×D24412yes—
214C42D4×D6111yescharacteristic
215C42#1175822611yescharacteristic
216C23—2441no—
217C23#1451974711yescharacteristic
218Q8—1224no—
219Q8—1224no—
220Q8—2442no—
221Q8—2442no—
222Q8—2442no—
223D4—4882no—
224D4—2444no—
225D4—2442no—
226C2×C4—24no—
227C2×C4—42no—
228C2×C4—44no—
229C2×C4—1224no—
230C2×C4—4881no—
231C2×C4—4881no—
232C2×C4—2444no—
233C2×C4—2442no—
234C2×C4—2441no—
235C2×C4—2442no—
236C2×C4—2442no—
237C2×C4#1451974712yes—
238C2×C4#1451975212yes—
239C2×C4#1451975211yescharacteristic
240C2×C4#1451977411yescharacteristic
241C2×C4C2×#1175819012yes—
242C2×C4#1451981012yes—
243C8—44no—
244C8—4881no—
245C22—22no—
246C22—4882no—
247C22—4881no—
248C22#1683967211yescharacteristic
249C22#1683990312yes—
250C4—22no—
251C4—22no—
252C4—44no—
253C4—4882no—
254C4—4881no—
255C4—2444no—
256C4#1683996812yes—
257C4#1684013511yescharacteristic
258C4#1684015611yescharacteristic
259C2—22no—
260C2—9761no—
261C2#2144688712yes—
262C2#2144690411yescharacteristic
subgroupG/H
centerC2×C4#14519774
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1274C2
socleC22×C61#392
prime radical#16840312C22
hypercenter#1274D61
hypocenterC61#10014
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
2. #21449112C2semidirect
4. #21444249C2semidirect
5. C61×#1274C2semidirect
68. C42×C61SD16semidirect
132. #1274D61semidirect
152. C61#10014semidirect
212. C42#11758190semidirect

Maximal subgroups

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

subgroupindex
#214558512
#214491122
#214466512
#214442492
C61×#12742
#1001461