Finite Group Databasebeta

← #37548705

Subgroups — #37548705

Order 23168.

124 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 30 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#26042159C211yesmaximal, characteristic
2#26042125C211yesmaximal, characteristic
3#26041210C211yesmaximal, characteristic
4C2×#15668458—21no—
5C22⋊#13089685—21no—
6C2×#15668428—21no—
7C2×#15668428C2211yescharacteristic
8#19153723—21no—
9#19153723C411yescharacteristic
10C2×C4⋊C4×C181C411yescharacteristic
11#15668458—22no—
12#15668458—41no—
13C2×#13089685—41no—
14C2×#13089685—41no—
15C22×Dic181—21no—
16C22×Dic181D411yescharacteristic
17C22×Dic181D411yescharacteristic
18#15668428—41no—
19#15668428—41no—
20#15668428—41no—
21C22×C4×C181—21no—
22C22×C4×C181C2×C411yescharacteristic
23C4⋊C4×C181—41no—
24#13089685—42no—
25#13089685—81no—
26C2×Dic181—21no—
27C2×Dic181—21no—
28C2×Dic181—22no—
29C2×Dic181—21no—
30C2×Dic181—41no—
31C2×Dic181—41no—
32C2×Dic181—41no—
33C2×Dic181D811yescharacteristic
34C2×Dic181SD1611yescharacteristic
35C23×C181C22⋊C411yescharacteristic
36C2×C4×C181—21no—
37C2×C4×C181—41no—
38C2×C4×C181—41no—
39C2×C4×C181—41no—
40C2×C4×C181—41no—
41C22×C181—21no—
42C22×C181—21no—
43C22×C181#9911yescharacteristic
44C22×C181#10211yescharacteristic
45C22×C181#10411yescharacteristic
46C4×C181—41no—
47C4×C181—81no—
48Dic181—21no—
49Dic181—21no—
50Dic181—42no—
51Dic181—41no—
52C2×C181—21no—
53C2×C181—21no—
54C2×C181#32711yescharacteristic
55C2×C181#35211yescharacteristic
56C2×C181#35611yescharacteristic
57C181#134611yescharacteristic, complemented, Sylow
58#1346—1811nomaximal, Sylow
59#398—1811no—
60#343—1811no—
61#324—1811no—
62C2×M16—3621no—
63C2×C4⋊C4—3621no—
64C2×C4⋊C4—1811no—
65C2×C4⋊C4#1062438211yescharacteristic
66C22⋊C8—3621no—
67#95—3621no—
68#95—1811no—
69C22×C4—21no—
70C22×C4—3621no—
71C22×C4—1811no—
72C22×C4—1811no—
73C22×C4C2×#1062438211yescharacteristic
74M16—3622no—
75M16—7241no—
76C2×C8—7241no—
77C2×C8—7241no—
78C4⋊C4—41no—
79C4⋊C4—7241no—
80C4⋊C4—7241no—
81C4⋊C4—7241no—
82C23C22⋊#1062438211yescharacteristic
83C2×C4—21no—
84C2×C4—41no—
85C2×C4—41no—
86C2×C4—41no—
87C2×C4—41no—
88C2×C4—3621no—
89C2×C4—3621no—
90C2×C4—3622no—
91C2×C4—3621no—
92C2×C4—1811no—
93C2×C4—1811no—
94C2×C4—7241no—
95C2×C4—7241no—
96C2×C4—7241no—
97C8—14481no—
98C8—7242no—
99C22—21no—
100C22—21no—
101C22#1915387411yescharacteristic
102C22#1915387811yescharacteristic
103C22#1915388011yescharacteristic
104C4—41no—
105C4—81no—
106C4—3621no—
107C4—3621no—
108C4—7242no—
109C4—7241no—
110C2—21no—
111C2—21no—
112C2#2604213011yescharacteristic
113C2#2604218111yescharacteristic
114C2#2604218911yescharacteristic
subgroupG/H
centerC22#19153874
commutatorC22×C4×C181C2×C4
FrattiniC22×C4C2×#10624382
FittingC2×C4⋊C4×C181C4
socleC22×C181#99
prime radicalC23×C181C22⋊C4
cosocleC2×#15668428C22
hypercenterC2×C4⋊C4#10624382
hypocenterC181#1346
LCSG ▷ C22×C4×C181 ▷ C23×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
57. C181#1346semidirect

Maximal subgroups

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

subgroupindex
#260421592
#260421252
#260412102
#1346181