Finite Group Databasebeta

← #29580991

Subgroups — #29580991

Order 15616.

584 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 103 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#21455850C212yesmaximal, complemented
3#21444217C212yesmaximal, complemented
4#21443650C211yesmaximal, characteristic, complemented
5C61×#1985C211yesmaximal, characteristic, complemented
6C2×#14519799—22no—
7#16840312C2212yes—
8#16840156—22no—
9#16840151—22no—
10#16840080—22no—
11#16840047—22no—
12#16839962—22no—
13#16839901—22no—
14C4×#11758201—24no—
15#16839815C2212yes—
16#16839489—24no—
17C2×C4×Q8×C61C2211yescharacteristic
18C2×C4⋊C8×C61C2211yescharacteristic
19C2×#97×C61C2211yescharacteristic
20C61×#336—22no—
21C2×#11758222—22no—
22#14519799—44no—
23#14519799—44no—
24C2×Dic244—22no—
25C2×#11758190—24no—
26C2×#11758201—24no—
27C2×D488—22no—
28#14519777D412yes—
29#14519774D412yes—
30#14519765—22no—
31#14519751—22no—
32#14519751—22no—
33C4×D244—22no—
34C4×D244—22no—
35#14519708—24no—
36C4⋊#92418—22no—
37#14519701—24no—
38#14519697—24no—
39C22⋊#92418—22no—
40C4×#92418D414yes—
41C22×Q8×C61D411yescharacteristic
42C22×C8×C61—21no—
43C22×C8×C61D412yes—
44C4×Q8×C61—22no—
45C4×Q8×C61—22no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61D411yescharacteristic
48C2×C42×C61—21no—
49C2×C42×C61C2311yescharacteristic
50C4⋊C8×C61—22no—
51#97×C61—22no—
52C2×Q8×C61—22no—
53C2×Q8×C61—42no—
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61C2×D411yescharacteristic
58C22×C4×C61#4111yescharacteristic
59C2×C22⋊D61—42no—
60#11758222—44no—
61#11758222—44no—
62C2×D244—22no—
63C2×D244—22no—
64C2×D244—22no—
65C2×C4×D61—42no—
66C2×Dic122—22no—
67C2×C8×C61—22no—
68C2×C8×C61—22no—
69C2×C8×C61—41no—
70C2×C8×C61—42no—
71C2×C8×C61SD1614yescomplemented
72C4⋊C4×C61—22no—
73C4⋊C4×C61—42no—
74C42×C61—41no—
75C42×C61—41no—
76C42×C61C2×D412yes—
77C42×C61C2×D412yes—
78#11758201—48no—
79#11758198—42no—
80#11758198—42no—
81C4⋊Dic61—22no—
82C4⋊Dic61—22no—
83C2×#92418—24no—
84Dic244—44no—
85D488—44no—
86#11758190—48no—
87C23×C61#12111yescharacteristic
88C22×D61—42no—
89Q8×C61—24no—
90Q8×C61—42no—
91C2×C4×C61—22no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61—42no—
97C2×C4×C61—41no—
98C2×C4×C61#12012yes—
99C2×C4×C61#12011yescharacteristic
100C2×C4×C61#12112yes—
101C2×C4×C61#12711yescharacteristic
102C2×C4×C61C2×SD1612yes—
103C2×C4×C61AGL(1,ℤ/8)12yes—
104C22⋊D61—84no—
105C2×Dic61—42no—
106D244—44no—
107D244—44no—
108D244—44no—
109C4×D61—82no—
110C4×D61—82no—
111Dic122—44no—
112C8×C61—24no—
113C8×C61—81no—
114#92418—44no—
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—42no—
126C4×C61—81no—
127C4×C61#45012yes—
128C4×C61#49211yescharacteristic
129C4×C61#49611yescharacteristic
130Dic61—82no—
131#3150—611no—
132#3103—612no—
133#1985D6111yescharacteristic, complemented
134#1480—612no—
135#1275—611no—
136C2×C61—22no—
137C2×C61#201011yescharacteristic
138C2×C61#201411yescharacteristic
139C2×C61#201711yescharacteristic
140D61—162no—
141C2×#135—1222no—
142#532—612no—
143C2×C4×Q8C2×D6111yescharacteristic
144#497—1222no—
145#496—1222no—
146#481—1222no—
147#475—1222no—
148#460—1222no—
149#448—1222no—
150C4×SD16—1224no—
151#431—612no—
152C2×C4⋊C8C2×D6111yescharacteristic
153C2×#97C2×D6111yescharacteristic
154#336—22no—
155D4⋊C8—1224no—
156C61#1003411yescharacteristic, complemented, Sylow
157C2×#41—1222no—
158C22×Q8D24411yescharacteristic
159#135—2444no—
160#135—2444no—
161C2×Q16—1222no—
162C2×SD16—1224no—
163C2×SD16—1224no—
164C2×D8—1222no—
165C22×C8—21no—
166C22×C8C22⋊D6112yes—
167C4⋊Q8—612no—
168#127—612no—
169#124—1222no—
170#121—1222no—
171#121—1222no—
172C4×Q8—22no—
173C4×Q8—22no—
174C4×D4—1222no—
175C4×D4—1222no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4D24411yescharacteristic
178C2×C42—21no—
179C2×C42C22×D6111yescharacteristic
180#106—1224no—
181C4⋊C8—22no—
182C4⋊C8—1222no—
183#103—1224no—
184#102—1224no—
185C22⋊C8—1222no—
186#97—22no—
187C4×C8—614no—
188#41—2444no—
189#41—2444no—
190C2×Q8—22no—
191C2×Q8—42no—
192C2×Q8—1222no—
193C2×D4—1222no—
194C2×D4—1222no—
195C2×D4—1222no—
196C2×D4—2442no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—2442no—
200C22×C4C2×D24411yescharacteristic
201C22×C4#1175822211yescharacteristic
202C22×C4C2×C22⋊D6111yescharacteristic
203Q16—2444no—
204SD16—2448no—
205SD16—2448no—
206D8—2444no—
207C2×C8—22no—
208C2×C8—22no—
209C2×C8—41no—
210C2×C8—42no—
211C2×C8—1224no—
212C2×C8#1175820114yescomplemented
213C4⋊C4—22no—
214C4⋊C4—42no—
215C4⋊C4—1222no—
216C4⋊C4—1222no—
217C22⋊C4—2442no—
218C22⋊C4—2442no—
219C42—41no—
220C42—41no—
221C42D4×D6112yes—
222C42D4×D6112yes—
223C23—2442no—
224C23#1451975111yescharacteristic
225Q8—24no—
226Q8—42no—
227Q8—2444no—
228D4—4884no—
229D4—2444no—
230D4—2444no—
231D4—2444no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—4882no—
240C2×C4—4882no—
241C2×C4—2442no—
242C2×C4#1451974511yescharacteristic
243C2×C4#1451974712yes—
244C2×C4#1451975012yes—
245C2×C4#1451977311yescharacteristic
246C2×C4C2×#1175820112yes—
247C2×C4#1451980212yes—
248C8—24no—
249C8—81no—
250C8—2444no—
251C22—21no—
252C22—21no—
253C22—4882no—
254C22—4882no—
255C22—4882no—
256C22#1683967111yescharacteristic
257C22#1683996212yes—
258C4—22no—
259C4—22no—
260C4—42no—
261C4—81no—
262C4—4882no—
263C4#1683991212yes—
264C4#1684013611yescharacteristic
265C4#1684015211yescharacteristic
266C2—22no—
267C2—9762no—
268C2#2144688611yescharacteristic
269C2#2144690611yescharacteristic
270C2#2144692311yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1985C2
socleC22×C61#392
prime radical#21456265C2
hypercenter#1985D61
hypocenterC61#10034
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
2. #21455850C2semidirect
3. #21444217C2semidirect
4. #21443650C2semidirect
5. C61×#1985C2semidirect
71. C2×C8×C61SD16semidirect
133. #1985D61semidirect
156. C61#10034semidirect
212. C2×C8#11758201semidirect

Maximal subgroups

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

subgroupindex
#214562652
#214558502
#214442172
#214436502
C61×#19852
#1003461