Finite Group Databasebeta

← #30594768

Subgroups — #30594768

Order 15616.

244 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 50 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#21461070C212yesmaximal
2#21445888C211yesmaximal, characteristic
3#16840782—22no—
4#16840607—22no—
5#16840605C414yes—
6C2×#14519736C2211yescharacteristic
7C2×C22⋊#92418C411yescharacteristic
8#16839516—22no—
9C2×C22⋊C8×C61C411yescharacteristic
10#14519844—42no—
11C22⋊#92420—24no—
12#14519832—42no—
13C22×#92418—21no—
14#14519736—41no—
15#14519736—41no—
16C2×C4⋊Dic61D411yescharacteristic
17C2×C4⋊Dic61Q811yescharacteristic
18C2×C22⋊Dic61C2×C412yes—
19C2×C4×Dic61D412yes—
20C22⋊#92418—41no—
21C23×C4×C61C2×C411yescharacteristic
22C22×C8×C61—21no—
23C22⋊C8×C61—41no—
24C24×C61C4211yescharacteristic
25C22×C4×C61—21no—
26C22×C4×C61—21no—
27C22×C4×C61—42no—
28C22×C4×C61C22⋊C411yescharacteristic
29C22×C4×C61C4⋊C411yescharacteristic
30C22×Dic61C22⋊C412yes—
31C22×Dic61C4⋊C412yes—
32C2×#92420—44no—
33C2×C8×C61—42no—
34C2×C8×C61—41no—
35C22⋊Dic61—42no—
36C4⋊Dic61—41no—
37C4⋊Dic61—41no—
38C4×Dic61—22no—
39C4×Dic61—22no—
40C2×#92418—42no—
41C2×#92418—41no—
42C23×C61—21no—
43C23×C61—22no—
44C23×C61—41no—
45C23×C61—41no—
46C23×C61#9511yescharacteristic
47C2×C4×C61—22no—
48C2×C4×C61—21no—
49C2×C4×C61—22no—
50C2×C4×C61—42no—
51C2×C4×C61—42no—
52C2×C4×C61#9911yescharacteristic
53C2×C4×C61#9911yescharacteristic
54C2×Dic61—22no—
55C2×Dic61—22no—
56C2×Dic61—42no—
57C2×Dic61—42no—
58#92420—84no—
59C8×C61—81no—
60#92418—81no—
61#7325—611nomaximal, Sylow
62C22×C61—21no—
63C22×C61—21no—
64C22×C61—41no—
65C22×C61—41no—
66C22×C61—41no—
67C22×C61—82no—
68C22×C61#34211yescharacteristic
69C22×C61#34412yes—
70C4×C61—21no—
71C4×C61—21no—
72C4×C61—41no—
73Dic61—42no—
74Dic61—42no—
75#1818—611no—
76#1464—612no—
77C2×C61—22no—
78C2×C61—81no—
79C2×C61#130611yescharacteristic
80C2×C61#139111yescharacteristic
81C2×C61#139211yescharacteristic
82C2×#117—611no—
83#432—1222no—
84C2×C22⋊C8—611no—
85C2×C22⋊C8#692311yescharacteristic
86#336—1222no—
87#324—1222no—
88#323—614no—
89C61#732511yescharacteristic, complemented, Sylow
90C23×C4C2×#692311yescharacteristic
91C22×C8—21no—
92C22×C8—1221no—
93#117—2441no—
94#117—2441no—
95C2×C4⋊C4—611no—
96C2×C4⋊C4—611no—
97C2×C22⋊C4—612no—
98C2×C42—612no—
99C4⋊C8—2442no—
100C22⋊C8—41no—
101C22⋊C8—1224no—
102C22⋊C8—2441no—
103#97—2442no—
104C24C4×#692311yescharacteristic
105C22×C4—21no—
106C22×C4—21no—
107C22×C4—42no—
108C22×C4—612no—
109C22×C4—612no—
110C22×C4C4⋊#692311yescharacteristic
111C22×C4C22⋊#692311yescharacteristic
112C2×C8—42no—
113C2×C8—41no—
114C2×C8—2442no—
115C2×C8—2444no—
116C2×C8—2441no—
117C4⋊C4—2441no—
118C4⋊C4—2441no—
119C22⋊C4—2442no—
120C42—1222no—
121C42—1222no—
122C23—21no—
123C23—22no—
124C23—41no—
125C23—41no—
126C23(C2×#6923)⋊C411yescharacteristic
127C2×C4—22no—
128C2×C4—21no—
129C2×C4—22no—
130C2×C4—42no—
131C2×C4—42no—
132C2×C4—1222no—
133C2×C4—1222no—
134C2×C4—2442no—
135C2×C4—2442no—
136C2×C4#1451983511yescharacteristic
137C2×C4#1451983611yescharacteristic
138C8—81no—
139C8—4881no—
140C8—4884no—
141C22—21no—
142C22—21no—
143C22—41no—
144C22—41no—
145C22—41no—
146C22—82no—
147C22#1684064011yescharacteristic
148C22#1684064312yes—
149C4—21no—
150C4—21no—
151C4—41no—
152C4—2442no—
153C4—2442no—
154C2—22no—
155C2—81no—
156C2#2146072211yescharacteristic
157C2#2146090811yescharacteristic
158C2#2146091011yescharacteristic
subgroupG/H
centerC22#16840640
commutator, prime radicalC24×C61C42
FrattiniC23×C4C2×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61#342
cosocleC2×#14519736C22
hypercenterC2×C22⋊C8#6923
hypocenterC61#7325
LCSG ▷ C24×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
89. C61#7325semidirect

Maximal subgroups

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

subgroupindex
#214610702
#214458882
#732561