Finite Group Databasebeta

← #29577548

Subgroups — #29577548

Order 15616.

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

normal subgroups only

This group has 534 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#21456193C211yesmaximal, characteristic
2#21448996C211yesmaximal, characteristic
3#21444371C212yesmaximal, complemented
4#21443685C212yesmaximal, complemented
5C61×#1555C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7#16840126—22no—
8#16840108C414yescomplemented
9#16839767—22no—
10C4×#11758194C2211yescharacteristic
11#16839642—24no—
12#16839642—22no—
13#16839630C2212yes—
14#16839500—24no—
15C2×#127×C61C2211yescharacteristic
16C61×#432C2212yes—
17C61×#331—22no—
18C23×Dic61—22no—
19C2×#11758194—21no—
20#14519777C2×C412yescomplemented
21#14519769—21no—
22#14519756—22no—
23C4×Dic122—22no—
24#14519736—21no—
25C2×C22⋊Dic61—24no—
26C2×C22⋊Dic61—22no—
27#14519698—28no—
28#14519688—21no—
29C4×#92418C2×C412yescomplemented
30#14519684—22no—
31#14519684—22no—
32#14519684D414yes—
33C22×D4×C61—22no—
34C22×D4×C61D412yes—
35#127×C61—22no—
36#127×C61C2×C412yes—
37#127×C61D412yes—
38C2×C42×C61C2311yescharacteristic
39C4⋊C8×C61—22no—
40C22⋊C8×C61—22no—
41#97×C61—22no—
42C24×C61—22no—
43C2×D4×C61—24no—
44C2×D4×C61—24no—
45C2×D4×C61—22no—
46C2×D4×C61—42no—
47C2×D4×C61—42no—
48C2×D4×C61—82no—
49C2×D4×C61—82no—
50C2×D4×C61C22⋊C414yes—
51C22×C4×C61C2×D411yescharacteristic
52C22×C4×C61C2×D412yes—
53C22×Dic61—24no—
54C22×Dic61—84no—
55C22×Dic61—82no—
56C2×Dic122—22no—
57C2×C8×C61—42no—
58C42×C61C22×C411yescharacteristic
59C42×C61C2×D411yescharacteristic
60C42×C61#4112yes—
61C22⋊Dic61—41no—
62C22⋊Dic61—84no—
63C22⋊Dic61—82no—
64C4⋊Dic61—22no—
65C4⋊Dic61—22no—
66#11758196—42no—
67C4×Dic61—41no—
68#11758194—42no—
69C2×#92418—22no—
70C23×C61—24no—
71C23×C61—44no—
72C23×C61—44no—
73C23×C61—42no—
74C23×C61—42no—
75C23×C61#12011yescharacteristic
76D4×C61—44no—
77D4×C61—82no—
78D4×C61—84no—
79D4×C61—84no—
80C2×C4×C61—22no—
81C2×C4×C61—42no—
82C2×C4×C61C2×C22⋊C411yescharacteristic
83C2×C4×C61C4×D412yes—
84C2×C4×C61#12112yes—
85C2×C4×C61#12311yescharacteristic
86C2×Dic61—48no—
87C2×Dic61—42no—
88C2×Dic61—44no—
89C2×Dic61—88no—
90Dic122—82no—
91C8×C61—82no—
92#92418—42no—
93#9425—611nomaximal, Sylow
94C22×C61—22no—
95C22×C61—44no—
96C22×C61—48no—
97C22×C61—82no—
98C22×C61—82no—
99C22×C61—84no—
100C22×C61#38611yescharacteristic
101C22×C61#45512yes—
102C4×C61—21no—
103C4×C61—21no—
104C4×C61—22no—
105C4×C61—22no—
106Dic61—84no—
107Dic61—82no—
108#3138—611no—
109#2380—611no—
110#1555D6111yescharacteristic
111#1515—612no—
112#1288—612no—
113C2×C61—22no—
114C2×C61—84no—
115C2×C61#188511yescharacteristic
116C2×C61#190412yes—
117#533—611no—
118C2×#127C2×D6111yescharacteristic
119#490—1222no—
120#486—614no—
121#432C2×D6112yes—
122#418—1222no—
123C4×M16—611no—
124#386—1224no—
125#386—1222no—
126#383—612no—
127#331—22no—
128#328—1224no—
129C61#942511yescharacteristic, complemented, Sylow
130C22×D4—22no—
131C22×D4D24412yes—
132C23×C4—1222no—
133C2×M16—1221no—
134C4⋊Q8—612no—
135#127—22no—
136#127C4×D6112yes—
137#127C22⋊D6112yes—
138#125—1221no—
139C22⋊Q8—1222no—
140C4×Q8—1222no—
141#117—1221no—
142C2×C22⋊C4—1224no—
143C2×C22⋊C4—1222no—
144C2×C42C22×D6111yescharacteristic
145C4⋊C8—22no—
146#102—1228no—
147C22⋊C8—22no—
148#97—22no—
149#97—1221no—
150C4×C8—612no—
151#95—614no—
152#95—1222no—
153#95—1222no—
154C24—22no—
155C2×Q8—1222no—
156C2×D4—24no—
157C2×D4—24no—
158C2×D4—22no—
159C2×D4—42no—
160C2×D4—42no—
161C2×D4—82no—
162C2×D4—82no—
163C2×D4#1175819814yes—
164C22×C4—1224no—
165C22×C4—4884no—
166C22×C4—4882no—
167C22×C4C2×D24411yescharacteristic
168C22×C4D4×D6112yes—
169M16—2442no—
170C2×C8—42no—
171C2×C8—1222no—
172C4⋊C4—1222no—
173C4⋊C4—1222no—
174C4⋊C4—2442no—
175C22⋊C4—4884no—
176C22⋊C4—4882no—
177C22⋊C4—2441no—
178C42—2441no—
179C42C2×C4×D6111yescharacteristic
180C42#1175822412yes—
181C42C2×C22⋊D6111yescharacteristic
182C23—24no—
183C23—44no—
184C23—44no—
185C23—42no—
186C23—42no—
187C23#1451974711yescharacteristic
188Q8—4882no—
189D4—44no—
190D4—82no—
191D4—84no—
192D4—84no—
193C2×C4—22no—
194C2×C4—42no—
195C2×C4—4888no—
196C2×C4—2448no—
197C2×C4—2444no—
198C2×C4—2442no—
199C2×C4C2×#1175819811yescharacteristic
200C2×C4#1451973712yes—
201C2×C4#1451974912yes—
202C2×C4#1451976111yescharacteristic
203C8—82no—
204C8—2442no—
205C22—22no—
206C22—44no—
207C22—48no—
208C22—82no—
209C22—82no—
210C22—84no—
211C22#1683963911yescharacteristic
212C22#1683994212yes—
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—4884no—
218C4—4882no—
219C2—22no—
220C2—84no—
221C2#2144620511yescharacteristic
222C2#2144630412yes—
subgroupG/H
centerC22#16839639
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1555C2
socleC22×C61#386
prime radicalC2×#127×C61C22
cosocleC2×C42×C61C23
hypercenter#1555D61
hypocenterC61#9425
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1555

Complements

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

NH ≅ G/Ntype
3. #21444371C2semidirect
4. #21443685C2semidirect
8. #16840108C4semidirect
20. #14519777C2×C4semidirect
29. C4×#92418C2×C4semidirect
129. C61#9425semidirect

Maximal subgroups

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

subgroupindex
#214561932
#214489962
#214443712
#214436852
C61×#15552
#942561