Finite Group Databasebeta

← #37548842

Subgroups — #37548842

Order 23168.

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

normal subgroups only

This group has 112 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#26042187C211yesmaximal, characteristic, complemented
2#26042134C211yesmaximal, characteristic, complemented
3#26041457C211yesmaximal, characteristic
4#19153877—21no—
5#19153871—21no—
6#19153846—21no—
7#19153803C2211yescharacteristic
8#19153743—21no—
9#19153733C411yescharacteristic
10H(5,𝔽2)×C181C411yescharacteristic
11#15668458—41no—
12C2×#13089685—41no—
13C2×Dic362D411yescharacteristic
14#15668439—41no—
15#15668437—41no—
16#15668433—21no—
17C22⋊Dic181—41no—
18C4×Dic181D411yescharacteristic
19#41×C181—21no—
20#41×C181—41no—
21C2×D4×C181—41no—
22C2×D4×C181—41no—
23C2×D4×C181C2×C411yescharacteristic
24#13089685—42no—
25#13089685—81no—
26Dic362—41no—
27C2×Dic181—21no—
28C2×Dic181—21no—
29#13089678—41no—
30C23×C181—21no—
31C23×C181—41no—
32Q8×C181—21no—
33D4×C181—21no—
34D4×C181—41no—
35D4×C181—42no—
36D4×C181—41no—
37C2×C4×C181—41no—
38C2×C4×C181—41no—
39C2×C4×C181C22⋊C411yescharacteristic
40C22×C181—41no—
41C22×C181—41no—
42C22×C181—81no—
43C22×C181—161no—
44C22×C181#9911yescharacteristic
45C4×C181—21no—
46C4×C181—41no—
47Dic181—41no—
48Dic181—41no—
49C2×C181—21no—
50C2×C181—81no—
51C2×C181—81no—
52C2×C181AΣL(1,𝔽16)11yescharacteristic
53C181#140311yescharacteristic, complemented, Sylow
54#1403—1811nomaximal, Sylow
55#455—1811no—
56#355—1811no—
57#329—1811no—
58H(5,𝔽2)#1062438211yescharacteristic
59#137—3621no—
60#124—1811no—
61#104—3621no—
62#101—3621no—
63#100—1811no—
64#97—3621no—
65#41—21no—
66#41—41no—
67C2×Q8—1811no—
68C2×D4—41no—
69C2×D4—41no—
70C2×D4C2×#1062438211yescharacteristic
71Q16—7241no—
72SD16—7241no—
73M16—3621no—
74M16—7241no—
75C2×C8—7241no—
76C22⋊C4—7241no—
77C42—1811no—
78C23—21no—
79C23—41no—
80Q8—21no—
81Q8—7241no—
82D4—21no—
83D4—41no—
84D4—42no—
85D4—41no—
86C2×C4—41no—
87C2×C4—41no—
88C2×C4—3621no—
89C2×C4—3621no—
90C2×C4C22⋊#1062438211yescharacteristic
91C8—14481no—
92C8—7241no—
93C8—7242no—
94C22—41no—
95C22—41no—
96C22—81no—
97C22—161no—
98C22#1915387411yescharacteristic
99C4—21no—
100C4—41no—
101C4—7241no—
102C4—7241no—
103C2—21no—
104C2—81no—
105C2—81no—
106C2#2604217911yescharacteristic
subgroupG/H
centerC2#26042179
commutatorC2×D4×C181C2×C4
FrattiniC2×D4C2×#10624382
Fitting, prime radicalH(5,𝔽2)×C181C4
socleC2×C181AΣL(1,𝔽16)
cosocle#19153803C22
hypercenterH(5,𝔽2)#10624382
hypocenterC181#1403
LCSG ▷ C2×D4×C181 ▷ C2×C4×C181 ▷ C22×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #26042187C2semidirect
2. #26042134C2semidirect
53. C181#1403semidirect

Maximal subgroups

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

subgroupindex
#260421872
#260421342
#260414572
#1403181