Finite Group Databasebeta

← #29580992

Subgroups — #29580992

Order 15616.

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

normal subgroups only

This group has 584 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#21456265C211yesmaximal, characteristic
2#21455851C212yesmaximal, complemented
3#21446759C211yesmaximal, characteristic, complemented
4#21444219C212yesmaximal, complemented
5C61×#1275C211yesmaximal, characteristic, complemented
6C2×#14519799—22no—
7#16840312C2212yes—
8C2×C4×Dic122C2211yescharacteristic
9#16840156—22no—
10#16840151—22no—
11#16840081—22no—
12#16840048—22no—
13#16839963—22no—
14#16839903—22no—
15C4×#11758190—24no—
16C2×C4⋊#92418C2211yescharacteristic
17#16839516—22no—
18#16839491—24no—
19C61×#431C2212yes—
20C2×#97×C61C2211yescharacteristic
21C2×#11758222—22no—
22C22×Dic122D411yescharacteristic
23#14519799—44no—
24#14519799—44no—
25C2×Dic244—22no—
26C2×#11758190—24no—
27C2×#11758190—24no—
28C2×D488—22no—
29C22×#92418—21no—
30#14519777D412yes—
31#14519774D412yes—
32#14519765—22no—
33#14519751—22no—
34#14519751—22no—
35C4×Dic122—22no—
36C4×Dic122—22no—
37C4×D244—22no—
38C4×D244—22no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×C4×Dic61—21no—
42#14519709—24no—
43C4⋊#92418—22no—
44#14519702—24no—
45#14519699—24no—
46C22×C8×C61D412yes—
47C2×C42×C61C2311yescharacteristic
48C4⋊C8×C61—22no—
49C22⋊C8×C61—22no—
50#97×C61—22no—
51C4×C8×C61D414yes—
52C22×C4×C61C2×D411yescharacteristic
53C22×C4×C61C2×D411yescharacteristic
54C22×C4×C61#4111yescharacteristic
55C2×C22⋊D61—42no—
56C22×Dic61—21no—
57C22×Dic61—21no—
58#11758222—44no—
59#11758222—44no—
60C2×D244—22no—
61C2×D244—22no—
62C2×D244—22no—
63C2×C4×D61—42no—
64C2×Dic122—22no—
65C2×Dic122—22no—
66C2×Dic122—42no—
67C2×C8×C61—22no—
68C2×C8×C61—22no—
69C2×C8×C61—24no—
70C2×C8×C61SD1614yescomplemented
71C42×C61C2×D412yes—
72C42×C61C2×D412yes—
73#11758198—42no—
74#11758198—42no—
75C4⋊Dic61—22no—
76C4⋊Dic61—22no—
77C4⋊Dic61—22no—
78#11758196—42no—
79C4×Dic61—41no—
80C4×Dic61—41no—
81C2×#92418—41no—
82C2×#92418—42no—
83Dic244—44no—
84D488—44no—
85#11758190—48no—
86#11758190—48no—
87C23×C61#12111yescharacteristic
88C22×D61—42no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61#12012yes—
92C2×C4×C61#12011yescharacteristic
93C2×C4×C61#12112yes—
94C2×C4×C61#12711yescharacteristic
95C2×C4×C61C2×SD1612yes—
96C2×C4×C61AGL(1,ℤ/8)12yes—
97C22⋊D61—84no—
98C2×Dic61—22no—
99C2×Dic61—41no—
100C2×Dic61—41no—
101C2×Dic61—42no—
102C2×Dic61—41no—
103C2×Dic61—42no—
104D244—44no—
105D244—44no—
106D244—44no—
107C4×D61—82no—
108C4×D61—82no—
109Dic122—24no—
110Dic122—42no—
111Dic122—44no—
112C8×C61—24no—
113C8×C61—44no—
114#92418—81no—
115#10034—611nomaximal, Sylow
116C22×C61—21no—
117C22×C61—21no—
118C22×C61#39211yescharacteristic
119C22×C61#46012yes—
120C2×D61—82no—
121C2×D61—82no—
122C2×D61—82no—
123C4×C61—22no—
124C4×C61—22no—
125C4×C61#45012yes—
126C4×C61#49211yescharacteristic
127C4×C61#49611yescharacteristic
128Dic61—42no—
129Dic61—82no—
130Dic61—81no—
131#3150—611no—
132#3103—612no—
133#1985—611no—
134#1480—612no—
135#1275D6111yescharacteristic, complemented
136C2×C61—22no—
137C2×C61#201011yescharacteristic
138C2×C61#201411yescharacteristic
139C2×C61#201711yescharacteristic
140D61—162no—
141C2×#135—1222no—
142#532—612no—
143C2×C4×Q8—611no—
144#497—1222no—
145#496—1222no—
146#481—1222no—
147#475—1222no—
148#460—1222no—
149#448—1222no—
150C4×SD16—1224no—
151#431C2×D6112yes—
152C2×C4⋊C8—611no—
153C2×#97C2×D6111yescharacteristic
154#336—1222no—
155D4⋊C8—1224no—
156C61#1003411yescharacteristic, complemented, Sylow
157C2×#41—1222no—
158C22×Q8—611no—
159#135—2444no—
160#135—2444no—
161C2×Q16—1222no—
162C2×SD16—1224no—
163C2×SD16—1224no—
164C2×D8—1222no—
165C22×C8—1221no—
166C22×C8D24412yes—
167C4⋊Q8—612no—
168#127—612no—
169#124—1222no—
170#121—1222no—
171#121—1222no—
172C4×Q8—1222no—
173C4×Q8—1222no—
174C4×D4—1222no—
175C4×D4—1222no—
176C2×C4⋊C4—611no—
177C2×C4⋊C4—1221no—
178C2×C42—1221no—
179C2×C42C22×D6111yescharacteristic
180#106—1224no—
181C4⋊C8—22no—
182C4⋊C8—1222no—
183#103—1224no—
184#102—1224no—
185C22⋊C8—22no—
186#97—22no—
187C4×C8D24414yes—
188#41—2444no—
189#41—2444no—
190C2×Q8—1222no—
191C2×Q8—1222no—
192C2×Q8—2442no—
193C2×D4—1222no—
194C2×D4—1222no—
195C2×D4—1222no—
196C2×D4—2442no—
197C22×C4—1221no—
198C22×C4—1221no—
199C22×C4—2442no—
200C22×C4C2×D24411yescharacteristic
201C22×C4D4×D6111yescharacteristic
202C22×C4#1175822611yescharacteristic
203Q16—2444no—
204SD16—2448no—
205SD16—2448no—
206D8—2444no—
207C2×C8—22no—
208C2×C8—22no—
209C2×C8—24no—
210C2×C8—2441no—
211C2×C8—2442no—
212C2×C8#1175819014yescomplemented
213C4⋊C4—1222no—
214C4⋊C4—1222no—
215C4⋊C4—1222no—
216C4⋊C4—2442no—
217C22⋊C4—2442no—
218C22⋊C4—2442no—
219C42—2441no—
220C42—2441no—
221C42C2×D24412yes—
222C42D4×D6112yes—
223C23—2442no—
224C23#1451975211yescharacteristic
225Q8—1224no—
226Q8—2442no—
227Q8—2444no—
228D4—4884no—
229D4—2444no—
230D4—2444no—
231D4—2444no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—1222no—
235C2×C4—4882no—
236C2×C4—4882no—
237C2×C4—2442no—
238C2×C4—2441no—
239C2×C4—2442no—
240C2×C4—2441no—
241C2×C4—2441no—
242C2×C4#1451974712yes—
243C2×C4#1451974711yescharacteristic
244C2×C4#1451975212yes—
245C2×C4#1451977411yescharacteristic
246C2×C4C2×#1175819012yes—
247C2×C4#1451980512yes—
248C8—24no—
249C8—44no—
250C8—4881no—
251C22—21no—
252C22—21no—
253C22—4882no—
254C22—4882no—
255C22—4882no—
256C22#1683967211yescharacteristic
257C22#1683996312yes—
258C4—22no—
259C4—22no—
260C4—4881no—
261C4—4882no—
262C4—2442no—
263C4#1683991512yes—
264C4#1684013511yescharacteristic
265C4#1684015111yescharacteristic
266C2—22no—
267C2—9762no—
268C2#2144688711yescharacteristic
269C2#2144690911yescharacteristic
270C2#2144692411yescharacteristic
subgroupG/H
centerC2×C4#14519774
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1275C2
socleC22×C61#392
prime radical#21456265C2
hypercenter#1275D61
hypocenterC61#10034
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
2. #21455851C2semidirect
3. #21446759C2semidirect
4. #21444219C2semidirect
5. C61×#1275C2semidirect
70. C2×C8×C61SD16semidirect
135. #1275D61semidirect
156. C61#10034semidirect
212. C2×C8#11758190semidirect

Maximal subgroups

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

subgroupindex
#214562652
#214558512
#214467592
#214442192
C61×#12752
#1003461