Finite Group Databasebeta

← #37548822

Subgroups — #37548822

Order 23168.

162 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 40 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#26042265C211yesmaximal, characteristic
2#26042258C211yesmaximal, characteristic
3#26041247C211yesmaximal, characteristic
4D181⋊M16—21no—
5#19153895—21no—
6#19153877C412yescomplemented
7#19153876—21no—
8#19153875C412yes—
9#19153874—21no—
10C2×#15668449C2211yescharacteristic
11C22×#13089678C411yescharacteristic, complemented
12#19153728—21no—
13#19153728—21no—
14C2×M16×C181C411yescharacteristic, complemented
15#15668459—41no—
16#15668458—22no—
17D181⋊C8—41no—
18C4⋊#10624382—41no—
19C22⋊#10624382—22no—
20C4×#10624382—41no—
21#15668449—41no—
22#15668449—41no—
23C2×Dic362C2×C411yescharacteristic
24C2×D724C2×C411yescharacteristic
25C2×C22⋊D181D411yescharacteristic
26C2×C22⋊D181Q811yescharacteristic
27C2×C4×D181D411yescharacteristic
28C2×C4×D181D411yescharacteristic
29C2×#13089678—21no—
30C2×#13089678—41no—
31C22×C4×C181C2×C411yescharacteristic
32M16×C181—41no—
33C2×C8×C181—21no—
34C2×#10624382—42no—
35#13089685—42no—
36C22×D181C22⋊C411yescharacteristic
37C22×D181C4⋊C411yescharacteristic
38Dic362—41no—
39D724—41no—
40C22⋊D181—41no—
41C22⋊D181—41no—
42C2×Dic181C22⋊C411yescharacteristic
43C2×Dic181C4⋊C411yescharacteristic
44C4×D181—21no—
45C4×D181—21no—
46C4×D181—21no—
47C4×D181—21no—
48#13089678—41no—
49C23×C181C4⋊C411yescharacteristic
50C2×C4×C181—21no—
51C2×C4×C181—21no—
52C2×C4×C181C4211yescharacteristic
53C2×C4×C181C22⋊C411yescharacteristic
54C8×C181—41no—
55C22×C181—21no—
56C22×C181—41no—
57C22×C181#9511yescharacteristic
58C2×D181—21no—
59C2×D181—21no—
60C2×D181—41no—
61C2×D181—41no—
62#10624382—82no—
63C4×C181—21no—
64C4×C181#9911yescharacteristic
65C4×C181#9911yescharacteristic
66Dic181—21no—
67Dic181—21no—
68C2×C181—21no—
69C2×C181—41no—
70C2×C181#34211yescharacteristic
71D181—41no—
72D181—41no—
73C181#139511yescharacteristic, complemented, Sylow
74#1395—1811nomaximal, Sylow
75#413—1811no—
76#410—1811no—
77#408—1811no—
78C2×#41—1811no—
79C2×M16—3621no—
80C2×M16#1062438211yescharacteristic, complemented
81C22×C8—1811no—
82#117—3621no—
83#101—1812no—
84#100—3621no—
85#99—3621no—
86#99—1812no—
87C22⋊C8—3621no—
88C22⋊C8—3621no—
89#41—7241no—
90#41—7241no—
91C2×Q8—1811no—
92C2×D4—1811no—
93C2×D4—1811no—
94C2×D4—1811no—
95C22×C4—1811no—
96C22×C4—1811no—
97C22×C4C2×#1062438211yescharacteristic
98M16—41no—
99M16—3622no—
100M16—7241no—
101C2×C8—21no—
102C2×C8—3621no—
103C2×C8—7241no—
104C2×C8—7241no—
105C4⋊C4—7241no—
106C22⋊C4—3622no—
107C42—7241no—
108C23—1811no—
109C23—1811no—
110C23C4⋊#1062438211yescharacteristic
111Q8—7241no—
112D4—7241no—
113D4—7241no—
114D4—7241no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—3621no—
118C2×C4—3621no—
119C2×C4—3621no—
120C2×C4—3621no—
121C2×C4—1811no—
122C2×C4—1811no—
123C2×C4—7242no—
124C2×C4C4×#1062438211yescharacteristic
125C2×C4C22⋊#1062438211yescharacteristic
126C8—41no—
127C8—7242no—
128C8—7241no—
129C22—21no—
130C22—41no—
131C22—3621no—
132C22—3621no—
133C22—7241no—
134C22—7241no—
135C22(C2×#10624382)⋊C411yescharacteristic
136C4—21no—
137C4—3621no—
138C4—3621no—
139C4—14482no—
140C4#1915387411yescharacteristic
141C4#1915387511yescharacteristic
142C2—21no—
143C2—41no—
144C2—7241no—
145C2—7241no—
146C2#2604215711yescharacteristic
subgroupG/H
centerC4#19153874
commutatorC2×C4×C181C42
FrattiniC22×C4C2×#10624382
FittingC2×M16×C181C4
socleC2×C181#342
prime radical, cosocleC2×#15668449C22
hypercenterC2×M16#10624382
hypocenterC181#1395
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
6. #19153877C4semidirect
11. C22×#13089678C4semidirect
14. C2×M16×C181C4semidirect
73. C181#1395semidirect
80. C2×M16#10624382semidirect

Maximal subgroups

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

subgroupindex
#260422652
#260422582
#260412472
#1395181