Finite Group Databasebeta

← #30599316

Subgroups — #30599316

Order 15616.

418 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C2×#16840607C212yesmaximal
2#21460662C214yesmaximal
3#21448420C211yesmaximal, characteristic
4C2×C22⋊#92420C2214yes—
5#16840607—22no—
6#16840607—22no—
7C22×C4⋊Dic61C2211yescharacteristic
8#16839647—22no—
9#16839645—22no—
10#16839625C411yescharacteristic
11#16839620C412yes—
12C22⋊C4×Dic61C2212yes—
13C61×#381C411yescharacteristic
14C22×#92420—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—24no—
36C22×C4×C61—22no—
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—
46C2×#92420—44no—
47C2×#92420—84no—
48C22⋊C4×C61—24no—
49C22⋊Dic61—24no—
50C4⋊Dic61—24no—
51C4⋊Dic61—24no—
52#11758196—82no—
53C4×Dic61—82no—
54C23×C61—41no—
55C23×C61—41no—
56C23×C61C2×C22⋊C411yescharacteristic
57C23×C61#11712yes—
58C23×C61#13114yes—
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#8737—611nomaximal, Sylow
78C22×C61—21no—
79C22×C61—22no—
80C22×C61—21no—
81C22×C61—22no—
82C22×C61—44no—
83C22×C61#38111yescharacteristic
84C22×C61#40812yes—
85C22×C61#43314yes—
86C4×C61—41no—
87C4×C61—41no—
88C4×C61—82no—
89Dic61—24no—
90Dic61—42no—
91Dic61—82no—
92#2313—611no—
93C2×#324—612no—
94#1282—614no—
95C2×C61—22no—
96C2×C61—24no—
97C2×C61#181811yescharacteristic
98C2×C61#182811yescharacteristic
99C2×C61#183011yescharacteristic
100C22×C4⋊C4—611no—
101C2×C22⋊C8—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#873711yescharacteristic, complemented, Sylow
111C23×C4—611no—
112C23×C4—611no—
113C23×C4C2×#692311yescharacteristic
114C22×C8—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—24no—
133C22×C4—22no—
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
143C2×C8—4884no—
144C2×C8—2444no—
145C4⋊C4—1224no—
146C4⋊C4—1224no—
147C4⋊C4—4882no—
148C22⋊C4—24no—
149C22⋊C4—1224no—
150C42—4882no—
151C23—41no—
152C23—41no—
153C23C2×C22⋊#692311yescharacteristic
154C23#1451985612yes—
155C23#1451986414yes—
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—22no—
176C22—21no—
177C22—22no—
178C22—44no—
179C22#1684070511yescharacteristic
180C22#1684073512yes—
181C22#1684078614yes—
182C4—41no—
183C4—41no—
184C4—82no—
185C4—1224no—
186C4—4882no—
187C4—2442no—
188C2—22no—
189C2—24no—
190C2#2146171211yescharacteristic
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#8737
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
110. C61#8737semidirect

Maximal subgroups

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

subgroupindex
C2×#168406072
#214606622
#214484202
#873761