Finite Group Databasebeta

← #30599360

Subgroups — #30599360

Order 15616.

566 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461653C212yesmaximal
2#21460722C214yesmaximal
3#21448404C211yesmaximal, characteristic
4C2×#14519838—24no—
5#16840732C2214yes—
6C23×Dic122C2211yescharacteristic
7C2×#14519733C412yes—
8#16839666—24no—
9#16839625C411yescharacteristic
10#16839623C2212yes—
11C61×#381C411yescharacteristic
12C2×#11758217—24no—
13#14519838—48no—
14C22⋊#92420—28no—
15C22×Dic122—24no—
16C22×Dic122—44no—
17C22×Dic122D414yes—
18C23×Dic61C2×C411yescharacteristic
19C23×Dic61C2311yescharacteristic
20#14519733—44no—
21C2×#11758196—22no—
22C2×C22⋊Dic61C2×C412yes—
23C2×C4×Dic61—22no—
24#14519684—22no—
25#14519684—24no—
26C23×C4×C61C2×C411yescharacteristic
27C2×C22⋊C4×C61C2×C412yes—
28#95×C61—22no—
29C24×C61C22×C411yescharacteristic
30C22×C4×C61—22no—
31C22×C4×C61—22no—
32C22×C4×C61—42no—
33C22×C4×C61C22⋊C412yes—
34C22×Dic61—22no—
35C22×Dic61—24no—
36C22×Dic61—22no—
37C22×Dic61—42no—
38C22×Dic61C22⋊C412yes—
39C22×Dic61C2×D412yes—
40C22×Dic61#4114yes—
41C2×Dic122—28no—
42C2×Dic122—28no—
43C2×Dic122—44no—
44C2×Dic122—416no—
45#11758217—48no—
46C2×#92420—44no—
47C22⋊C4×C61—42no—
48C22⋊Dic61—42no—
49#11758196—44no—
50C4×Dic61—44no—
51C23×C61—22no—
52C23×C61—42no—
53C23×C61C2×C22⋊C411yescharacteristic
54C23×C61#11712yes—
55C2×C4×C61—22no—
56C2×C4×C61—24no—
57C2×C4×C61—44no—
58C2×C4×C61—44no—
59C2×C4×C61—42no—
60C2×Dic61—28no—
61C2×Dic61—22no—
62C2×Dic61—22no—
63C2×Dic61—24no—
64C2×Dic61—44no—
65C2×Dic61—44no—
66C2×Dic61—42no—
67C2×Dic61#9914yes—
68C2×Dic61#12314yes—
69Dic122—416no—
70#92420—84no—
71#8754—611nomaximal, Sylow
72C22×C61—22no—
73C22×C61—22no—
74C22×C61—24no—
75C22×C61—44no—
76C22×C61#38111yescharacteristic
77C22×C61C2×#9912yes—
78C4×C61—42no—
79C4×C61—82no—
80Dic61—24no—
81Dic61—24no—
82Dic61—82no—
83#2310—611no—
84#1784—612no—
85#1306—614no—
86C2×C61—22no—
87C2×C61—42no—
88C2×C61#181911yescharacteristic
89C2×C61#183012yes—
90C23×Q8—611no—
91C2×#117—612no—
92C2×#101—1224no—
93#407—614no—
94#391—1224no—
95#381—611no—
96#381—612no—
97#381#692311yescharacteristic
98C61#875411yescharacteristic, complemented, Sylow
99C22×Q8—614no—
100C22×Q8—1224no—
101C22×Q8—2444no—
102C23×C4—611no—
103C23×C4—611no—
104C23×C4C2×#692311yescharacteristic
105C2×M16—1224no—
106#117—2444no—
107C2×C4⋊C4—1222no—
108C2×C22⋊C4—612no—
109C2×C22⋊C4C2×#692312yes—
110C2×C42—1222no—
111#101—2448no—
112C22⋊C8—1228no—
113#95—22no—
114#95—1224no—
115#95—1222no—
116C24C22×#692311yescharacteristic
117C2×Q8—1228no—
118C2×Q8—1228no—
119C2×Q8—2444no—
120C2×Q8—24416no—
121C22×C4—22no—
122C22×C4—22no—
123C22×C4—42no—
124C22×C4—612no—
125C22×C4—612no—
126C22×C4—614no—
127C22×C4—1224no—
128C22×C4—1222no—
129C22×C4—1222no—
130C22×C4—2442no—
131C22×C4C22⋊#692312yes—
132M16—2448no—
133C2×C8—2444no—
134C4⋊C4—2444no—
135C22⋊C4—42no—
136C22⋊C4—2442no—
137C42—2444no—
138C23—22no—
139C23—42no—
140C23C2×C22⋊#692311yescharacteristic
141C23#1451985612yes—
142Q8—24416no—
143C2×C4—22no—
144C2×C4—24no—
145C2×C4—44no—
146C2×C4—44no—
147C2×C4—42no—
148C2×C4—614no—
149C2×C4—614no—
150C2×C4—1228no—
151C2×C4—1222no—
152C2×C4—1222no—
153C2×C4—1224no—
154C2×C4—2444no—
155C2×C4—2444no—
156C2×C4—2442no—
157C8—4884no—
158C22—22no—
159C22—22no—
160C22—24no—
161C22—44no—
162C22#1684070511yescharacteristic
163C22D61⋊#9912yes—
164C4—42no—
165C4—82no—
166C4—1224no—
167C4—1224no—
168C4—4882no—
169C2—22no—
170C2—42no—
171C2#2146171511yescharacteristic
172C2#2146173312yes—
subgroupG/H
centerC22#16840705
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC61×#381C4
socleC22×C61#381
cosocleC23×Dic61C23
hypercenter#381#6923
hypocenterC61#8754
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
98. C61#8754semidirect

Maximal subgroups

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

subgroupindex
#214616532
#214607222
#214484042
#875461