Finite Group Databasebeta

← #30599370

Subgroups — #30599370

Order 15616.

394 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 72 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#21461067C212yesmaximal
2#21460720C214yesmaximal
3#21448420C211yesmaximal, characteristic
4#16840732C2214yes—
5#16840607—22no—
6#16840607—22no—
7C22×C4⋊Dic61C2211yescharacteristic
8#16839647—22no—
9#16839645—22no—
10#16839625C411yescharacteristic
11#16839620C2212yes—
12C22⋊C4×Dic61C412yes—
13C61×#381C411yescharacteristic
14C2×#11758217—24no—
15C22⋊#92420—24no—
16C22⋊#92420—24no—
17C23×Dic61C2×C411yescharacteristic
18C23×Dic61C2311yescharacteristic
19C2×C4⋊Dic61—24no—
20C2×C4⋊Dic61D412yes—
21C2×C4⋊Dic61D412yes—
22C2×#11758196—22no—
23C2×C22⋊Dic61C2×C412yes—
24C2×C4×Dic61—22no—
25#14519684—21no—
26#14519684—21no—
27#14519684—22no—
28#14519684—22no—
29C23×C4×C61C2×C411yescharacteristic
30C2×C22⋊C4×C61C2×C412yes—
31#95×C61—21no—
32#95×C61—21no—
33C24×C61C22×C411yescharacteristic
34C22×C4×C61—22no—
35C22×C4×C61—22no—
36C22×C4×C61—42no—
37C22×C4×C61C22⋊C411yescharacteristic
38C22×C4×C61C22⋊C411yescharacteristic
39C22×Dic61—22no—
40C22×Dic61—22no—
41C22×Dic61—81no—
42C22×Dic61—81no—
43C22×Dic61C22⋊C412yes—
44C22×Dic61C2×D412yes—
45C22×Dic61#4114yes—
46#11758217—84no—
47C2×#92420—44no—
48C22⋊C4×C61—42no—
49C22⋊Dic61—42no—
50C4⋊Dic61—24no—
51C4⋊Dic61—24no—
52#11758196—82no—
53C4×Dic61—82no—
54C23×C61—22no—
55C23×C61—41no—
56C23×C61—41no—
57C23×C61C2×C22⋊C411yescharacteristic
58C23×C61#11712yes—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—44no—
64C2×C4×C61—42no—
65C2×C4×C61—42no—
66C2×C4×C61—42no—
67C2×Dic61—22no—
68C2×Dic61—42no—
69C2×Dic61—44no—
70C2×Dic61—42no—
71C2×Dic61—42no—
72C2×Dic61—42no—
73C2×Dic61—42no—
74C2×Dic61—82no—
75C2×Dic61#12314yes—
76#92420—84no—
77#8758—611nomaximal, Sylow
78C22×C61—21no—
79C22×C61—21no—
80C22×C61—22no—
81C22×C61—22no—
82C22×C61—22no—
83C22×C61—44no—
84C22×C61#38111yescharacteristic
85C22×C61#41312yes—
86C4×C61—41no—
87C4×C61—41no—
88C4×C61—82no—
89Dic61—24no—
90Dic61—42no—
91Dic61—82no—
92#2313—611no—
93#1463—612no—
94#1305—614no—
95C2×C61—22no—
96C2×C61—42no—
97C2×C61#182211yescharacteristic
98C2×C61#182811yescharacteristic
99C2×C61#183011yescharacteristic
100C22×C4⋊C4—611no—
101#407—614no—
102#387—1222no—
103#387—1222no—
104#381—611no—
105#381#692311yescharacteristic
106#380—612no—
107C4×C22⋊C4—612no—
108#324—1222no—
109#324—1222no—
110C61#875811yescharacteristic, complemented, Sylow
111C23×C4—611no—
112C23×C4—611no—
113C23×C4C2×#692311yescharacteristic
114C2×M16—1224no—
115C2×C4⋊C4—612no—
116C2×C4⋊C4—612no—
117C2×C4⋊C4—1224no—
118C2×C4⋊C4—1222no—
119C2×C22⋊C4—612no—
120C2×C22⋊C4C2×#692312yes—
121C2×C42—1222no—
122C22⋊C8—1224no—
123C22⋊C8—1224no—
124#95—21no—
125#95—21no—
126#95—1222no—
127#95—1222no—
128#95—1221no—
129#95—1221no—
130C24C22×#692311yescharacteristic
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—42no—
134C22×C4—612no—
135C22×C4—614no—
136C22×C4—612no—
137C22×C4—1222no—
138C22×C4—1222no—
139C22×C4—4881no—
140C22×C4—4881no—
141C22×C4C22⋊#692311yescharacteristic
142C22×C4C22⋊#692311yescharacteristic
143M16—4884no—
144C2×C8—2444no—
145C4⋊C4—1224no—
146C4⋊C4—1224no—
147C4⋊C4—4882no—
148C22⋊C4—42no—
149C22⋊C4—2442no—
150C42—4882no—
151C23—22no—
152C23—41no—
153C23—41no—
154C23C2×C22⋊#692311yescharacteristic
155C23#1451985612yes—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—44no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—614no—
165C2×C4—1222no—
166C2×C4—4882no—
167C2×C4—2442no—
168C2×C4—2444no—
169C2×C4—2442no—
170C2×C4—2442no—
171C2×C4—2442no—
172C2×C4—2442no—
173C8—4884no—
174C22—21no—
175C22—21no—
176C22—22no—
177C22—22no—
178C22—22no—
179C22—44no—
180C22#1684070511yescharacteristic
181C22#1684074912yes—
182C4—41no—
183C4—41no—
184C4—82no—
185C4—1224no—
186C4—4882no—
187C4—2442no—
188C2—22no—
189C2—42no—
190C2#2146172111yescharacteristic
191C2#2146173111yescharacteristic
192C2#2146173311yescharacteristic
subgroupG/H
centerC22#16840705
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC61×#381C4
socleC22×C61#381
cosocleC23×Dic61C23
hypercenter#381#6923
hypocenterC61#8758
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
110. C61#8758semidirect

Maximal subgroups

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

subgroupindex
#214610672
#214607202
#214484202
#875861