Finite Group Databasebeta

← #37548846

Subgroups — #37548846

Order 23168.

106 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 20 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#26042189C211yesmaximal, characteristic, complemented
2#26042139C211yesmaximal, characteristic, complemented
3#26041462C211yesmaximal, characteristic
4#19153883—21no—
5#19153877—21no—
6#19153846—21no—
7#19153814C2211yescharacteristic
8#19153743—21no—
9#19153735C411yescharacteristic
102−1+4×C181C411yescharacteristic
11#15668458—41no—
12C2×#13089685—41no—
13C2×Dic362D411yescharacteristic
14#15668439—41no—
15#15668437—41no—
16#15668433—21no—
17#15668428—41no—
18C4×Dic181D411yescharacteristic
19#41×C181—21no—
20#41×C181—41no—
21#41×C181—41no—
22C2×Q8×C181—41no—
23C2×Q8×C181C2×C411yescharacteristic
24#13089685—81no—
25#13089685—81no—
26Dic362—41no—
27C2×Dic181—21no—
28C2×Dic181—21no—
29#13089678—41no—
30Q8×C181—21no—
31Q8×C181—41no—
32Q8×C181—41no—
33D4×C181—21no—
34D4×C181—41no—
35D4×C181—41no—
36C2×C4×C181—21no—
37C2×C4×C181—41no—
38C2×C4×C181—42no—
39C2×C4×C181C22⋊C411yescharacteristic
40C22×C181—41no—
41C22×C181#9911yescharacteristic
42C4×C181—21no—
43C4×C181—41no—
44C4×C181—41no—
45Dic181—21no—
46Dic181—21no—
47Dic181—41no—
48C2×C181—21no—
49C2×C181—81no—
50C2×C181AΣL(1,𝔽16)11yescharacteristic
51C181#140511yescharacteristic, complemented, Sylow
52#1405—1811nomaximal, Sylow
53#456—1811no—
54#356—1811no—
55#333—1811no—
562−1+4#1062438211yescharacteristic
57#137—3621no—
58C4⋊Q8—1811no—
59C4⋊C8—3621no—
60#104—3621no—
61#101—3621no—
62#101—1811no—
63#41—21no—
64#41—41no—
65#41—41no—
66C2×Q8—41no—
67C2×Q8—1811no—
68C2×Q8C2×#1062438211yescharacteristic
69Q16—7241no—
70SD16—7241no—
71M16—3621no—
72M16—7241no—
73C2×C8—7241no—
74C4⋊C4—7241no—
75C42—1811no—
76Q8—21no—
77Q8—41no—
78Q8—41no—
79Q8—7241no—
80D4—21no—
81D4—41no—
82D4—41no—
83C2×C4—21no—
84C2×C4—41no—
85C2×C4—42no—
86C2×C4—3621no—
87C2×C4—3621no—
88C2×C4C22⋊#1062438211yescharacteristic
89C8—14481no—
90C8—14481no—
91C8—7241no—
92C22—41no—
93C22#1915387411yescharacteristic
94C4—21no—
95C4—41no—
96C4—41no—
97C4—3621no—
98C4—3621no—
99C4—7241no—
100C2—21no—
101C2—81no—
102C2#2604217911yescharacteristic
subgroupG/H
centerC2#26042179
commutatorC2×Q8×C181C2×C4
FrattiniC2×Q8C2×#10624382
Fitting, prime radical2−1+4×C181C4
socleC2×C181AΣL(1,𝔽16)
cosocle#19153814C22
hypercenter2−1+4#10624382
hypocenterC181#1405
LCSG ▷ C2×Q8×C181 ▷ C2×C4×C181 ▷ C22×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. #26042189C2semidirect
2. #26042139C2semidirect
51. C181#1405semidirect

Maximal subgroups

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

subgroupindex
#260421892
#260421392
#260414622
#1405181