Finite Group Databasebeta

← #29577550

Subgroups — #29577550

Order 15616.

534 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 99 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#21444533C211yesmaximal, characteristic
3#21444369C212yesmaximal, complemented
4#21443683C212yesmaximal, complemented
5C61×#2380C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7#16840126—22no—
8#16840108C414yescomplemented
9#16839819C2212yes—
10#16839767—22no—
11C4×#11758194C2211yescharacteristic
12#16839506—22no—
13#16839498—24no—
14C2×#127×C61C2211yescharacteristic
15C61×#386—22no—
16C61×#386—24no—
17C61×#383C2212yes—
18C2×#11758194—21no—
19#14519777C2×C412yescomplemented
20#14519769—21no—
21#14519756—22no—
22C4×Dic122—22no—
23#14519736—21no—
24C4⋊#92418—22no—
25#14519698—28no—
26C22⋊#92418—22no—
27#14519688—21no—
28#14519688—22no—
29C4×#92418C2×C412yescomplemented
30C22×D4×C61—22no—
31C22×D4×C61D412yes—
32C23×C4×C61—22no—
33#127×C61—22no—
34#127×C61C2×C412yes—
35#127×C61D412yes—
36C2×C22⋊C4×C61—24no—
37C2×C22⋊C4×C61—22no—
38C2×C42×C61C2311yescharacteristic
39#95×C61—22no—
40#95×C61—22no—
41#95×C61D414yes—
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×C61—24no—
52C22×C4×C61—84no—
53C22×C4×C61—82no—
54C22×C4×C61C2×D411yescharacteristic
55C22×C4×C61C2×D412yes—
56C2×Dic122—22no—
57C22⋊C4×C61—84no—
58C22⋊C4×C61—82no—
59C42×C61C22×C411yescharacteristic
60C42×C61C2×D411yescharacteristic
61C42×C61#4112yes—
62C22⋊Dic61—41no—
63C4⋊Dic61—22no—
64C4⋊Dic61—22no—
65#11758196—42no—
66C4×Dic61—41no—
67#11758194—42no—
68C2×#92418—22no—
69C2×#92418—42no—
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×C61—48no—
83C2×C4×C61—44no—
84C2×C4×C61—88no—
85C2×C4×C61C2×C22⋊C411yescharacteristic
86C2×C4×C61C4×D412yes—
87C2×C4×C61#12112yes—
88C2×C4×C61#12311yescharacteristic
89C2×Dic61—42no—
90Dic122—82no—
91#92418—42no—
92#92418—82no—
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—
106C4×C61—84no—
107Dic61—82no—
108#3138—611no—
109#2380D6111yescharacteristic
110#1555—611no—
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#432—612no—
122#418—1222no—
123C4×M16—611no—
124#386—22no—
125#386—24no—
126#383C2×D6112yes—
127#331—1222no—
128#328—1224no—
129C61#942511yescharacteristic, complemented, Sylow
130C22×D4—22no—
131C22×D4C22⋊D6112yes—
132C23×C4—22no—
133C2×M16—1221no—
134C4⋊Q8—612no—
135#127—22no—
136#127C4×D6112yes—
137#127D24412yes—
138#125—1221no—
139C22⋊Q8—1222no—
140C4×Q8—1222no—
141#117—1221no—
142C2×C22⋊C4—24no—
143C2×C22⋊C4—22no—
144C2×C42C22×D6111yescharacteristic
145C4⋊C8—1222no—
146#102—1228no—
147C22⋊C8—1222no—
148#97—1221no—
149#97—1222no—
150C4×C8—612no—
151#95—22no—
152#95—22no—
153#95C22⋊D6114yes—
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—24no—
165C22×C4—84no—
166C22×C4—82no—
167C22×C4C2×C22⋊D6111yescharacteristic
168C22×C4C2×C22⋊D6112yes—
169M16—2442no—
170C2×C8—1222no—
171C2×C8—2442no—
172C4⋊C4—1222no—
173C4⋊C4—1222no—
174C4⋊C4—2442no—
175C22⋊C4—84no—
176C22⋊C4—82no—
177C22⋊C4—2441no—
178C42—2441no—
179C42C2×C4×D6111yescharacteristic
180C42C2×D24411yescharacteristic
181C42#1175822212yes—
182C23—24no—
183C23—44no—
184C23—44no—
185C23—42no—
186C23—42no—
187C23#1451974611yescharacteristic
188Q8—4882no—
189D4—44no—
190D4—82no—
191D4—84no—
192D4—84no—
193C2×C4—22no—
194C2×C4—42no—
195C2×C4—48no—
196C2×C4—44no—
197C2×C4—88no—
198C2×C4—2442no—
199C2×C4C2×#1175819811yescharacteristic
200C2×C4C4×C22⋊D6112yes—
201C2×C4#1451975112yes—
202C2×C4#1451976011yescharacteristic
203C8—4882no—
204C8—2442no—
205C22—22no—
206C22—44no—
207C22—48no—
208C22—82no—
209C22—82no—
210C22—84no—
211C22#1683964111yescharacteristic
212C22#1683994012yes—
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—84no—
218C4—4882no—
219C2—22no—
220C2—84no—
221C2#2144620711yescharacteristic
222C2#2144630612yes—
subgroupG/H
centerC22#16839641
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2380C2
socleC22×C61#386
prime radicalC2×#127×C61C22
cosocleC2×C42×C61C23
hypercenter#2380D61
hypocenterC61#9425
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2380

Complements

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

NH ≅ G/Ntype
3. #21444369C2semidirect
4. #21443683C2semidirect
8. #16840108C4semidirect
19. #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
#214445332
#214443692
#214436832
C61×#23802
#942561