Finite Group Databasebeta

← #30594024

Subgroups — #30594024

Order 15616.

194 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 44 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#21460739C212yesmaximal
2#21445888C211yesmaximal, characteristic
3C22⋊#11758187—22no—
4C2×#14519736C411yescharacteristic
5C2×C22⋊#92418C2211yescharacteristic
6#16839516—22no—
7C2×C22⋊C8×C61C411yescharacteristic
8C2×#11758187—42no—
9C22×#92418D412yes—
10#14519736—41no—
11#14519736—41no—
12C2×C4⋊Dic61C811yescharacteristic
13C2×C4⋊Dic61C811yescharacteristic
14C2×C22⋊Dic61—21no—
15C2×C4×Dic61—21no—
16C22⋊#92418—41no—
17C23×C4×C61C2×C411yescharacteristic
18C22×C8×C61—21no—
19C22⋊C8×C61—41no—
20C24×C61M1611yescharacteristic
21C22×C4×C61—21no—
22C22×C4×C61—21no—
23C22×C4×C61—42no—
24C22×C4×C61C22⋊C411yescharacteristic
25C22×C4×C61C2×C811yescharacteristic
26C22×Dic61—21no—
27C22×Dic61—21no—
28C2×C8×C61—42no—
29C2×C8×C61—41no—
30C22⋊Dic61—42no—
31C4⋊Dic61—41no—
32C4⋊Dic61—41no—
33C4×Dic61—41no—
34C4×Dic61—41no—
35C2×#92418—22no—
36C2×#92418—42no—
37#11758187—82no—
38C23×C61—21no—
39C23×C61—22no—
40C23×C61—41no—
41C23×C61—41no—
42C23×C61C22⋊C811yescharacteristic
43C2×C4×C61—22no—
44C2×C4×C61—21no—
45C2×C4×C61—42no—
46C2×C4×C61—42no—
47C2×C4×C61—41no—
48C2×C4×C61#9911yescharacteristic
49C2×C4×C61#10011yescharacteristic
50C2×Dic61—42no—
51C2×Dic61—41no—
52C2×Dic61—41no—
53C2×Dic61—42no—
54C8×C61—81no—
55#92418—42no—
56#7059—611nomaximal, Sylow
57C22×C61—21no—
58C22×C61—21no—
59C22×C61—41no—
60C22×C61—41no—
61C22×C61—41no—
62C22×C61—82no—
63C22×C61#32311yescharacteristic
64C22×C61#35012yes—
65C4×C61—21no—
66C4×C61—41no—
67C4×C61#35212yes—
68Dic61—81no—
69Dic61—81no—
70#1818—611no—
71#1314—612no—
72C2×C61—22no—
73C2×C61—81no—
74C2×C61#131511yescharacteristic
75C2×C61#131711yescharacteristic
76C2×C61#132111yescharacteristic
77C2×#117—611no—
78C2×C22⋊C8—611no—
79C2×C22⋊C8#692311yescharacteristic
80C22⋊C16—1222no—
81#336—1222no—
82C61#705911yescharacteristic, complemented, Sylow
83C23×C4C2×#692311yescharacteristic
84C22×C8—21no—
85C22×C8—612no—
86#117—2441no—
87#117—2441no—
88C2×C4⋊C4—611no—
89C2×C4⋊C4—611no—
90C2×C22⋊C4—1221no—
91C2×C42—1221no—
92C2×C16—2442no—
93C22⋊C8—41no—
94C22⋊C8—2441no—
95C24#1175821311yescharacteristic
96C22×C4—21no—
97C22×C4—21no—
98C22×C4—42no—
99C22×C4—1221no—
100C22×C4—1221no—
101C22×C4D61⋊C811yescharacteristic
102C22×C4C22⋊#692311yescharacteristic
103C2×C8—42no—
104C2×C8—41no—
105C2×C8—1222no—
106C2×C8—2442no—
107C4⋊C4—2441no—
108C4⋊C4—2441no—
109C22⋊C4—2442no—
110C42—2441no—
111C42—2441no—
112C16—4882no—
113C23—21no—
114C23—22no—
115C23—41no—
116C23—41no—
117C23#1451983411yescharacteristic
118C2×C4—22no—
119C2×C4—21no—
120C2×C4—42no—
121C2×C4—42no—
122C2×C4—41no—
123C2×C4—2442no—
124C2×C4—2441no—
125C2×C4—2441no—
126C2×C4—2442no—
127C2×C4#1451983611yescharacteristic
128C2×C4#1451983711yescharacteristic
129C8—81no—
130C8—2442no—
131C22—21no—
132C22—21no—
133C22—41no—
134C22—41no—
135C22—41no—
136C22—82no—
137C22#1684060611yescharacteristic
138C22#1684066112yes—
139C4—21no—
140C4—41no—
141C4—4881no—
142C4—4881no—
143C4#1684066512yes—
144C2—22no—
145C2—81no—
146C2#2146074211yescharacteristic
147C2#2146074611yescharacteristic
148C2#2146075411yescharacteristic
subgroupG/H
centerC2×C4#14519836
commutatorC22×C4×C61C2×C8
FrattiniC23×C4C2×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61#323
prime radicalC24×C61M16
cosocleC2×C22⋊#92418C22
hypercenterC2×C22⋊C8#6923
hypocenterC61#7059
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
82. C61#7059semidirect

Maximal subgroups

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

subgroupindex
#214607392
#214458882
#705961