Finite Group Databasebeta

← #37549634

Subgroups — #37549634

Order 23168.

272 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 62 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
1C2×#19153876C212yesmaximal
2#26042160C214yesmaximal, complemented
3#26041752C211yesmaximal, characteristic
4C2×#15668458C2214yes—
5#19153876—22no—
6#19153876—22no—
7C22×C22⋊D181C2211yescharacteristic
8C4×C22⋊D181—22no—
9#19153776—22no—
10#19153772C2212yes—
11C2×C22⋊Dic181C411yescharacteristic
12C22⋊C4×D181C412yes—
13C2×C22⋊C4×C181C411yescharacteristic
14#15668458—24no—
15#15668458—24no—
16C2×#13089685—24no—
17C23×D181C2×C411yescharacteristic
18C2×C22⋊D181—24no—
19C2×C22⋊D181D412yes—
20C2×C22⋊D181D412yes—
21C22×Dic181—21no—
22C22×Dic181C2311yescharacteristic
23C2×C4×D181—22no—
24#15668428—22no—
25C22⋊Dic181—21no—
26C22⋊Dic181C2×C412yes—
27#15668426—22no—
28C4×Dic181—22no—
29C24×C181C2×C411yescharacteristic
30C22×C4×C181—21no—
31C22⋊C4×C181—21no—
32C22⋊C4×C181C2×C412yes—
33#13089685—44no—
34C22×D181—22no—
35C22×D181—81no—
36C22×D181C22⋊C412yes—
37C22⋊D181—24no—
38C22⋊D181—24no—
39C2×Dic181—22no—
40C2×Dic181—81no—
41C2×Dic181C2×D412yes—
42C2×Dic181#4114yes—
43C4×D181—82no—
44C23×C181—22no—
45C23×C181—81no—
46C23×C181C22⋊C411yescharacteristic
47C23×C181C22⋊C411yescharacteristic
48C23×C181C22×C411yescharacteristic
49C2×C4×C181—22no—
50C2×C4×C181—81no—
51C22×C181—21no—
52C22×C181—21no—
53C22×C181—41no—
54C22×C181—41no—
55C22×C181—41no—
56C22×C181—82no—
57C22×C181C2×C22⋊C411yescharacteristic
58C22×C181#11712yes—
59C2×D181—22no—
60C2×D181—42no—
61C2×D181—82no—
62C4×C181—42no—
63Dic181—42no—
64Dic181#12314yes—
65C2×C181—21no—
66C2×C181—22no—
67C2×C181—41no—
68C2×C181—41no—
69C2×C181#38111yescharacteristic
70D181—42no—
71C181#182911yescharacteristic, complemented, Sylow
72#1829—1811nomaximal, Sylow
73#518—1811no—
74C2×#100—1812no—
75#344—1814no—
76C22×D4—1811no—
77C2×M16—1814no—
78C4×D4—3622no—
79C4×D4—3622no—
80#117—1812no—
81C2×C22⋊C4—1811no—
82C2×C22⋊C4—1812no—
83C2×C22⋊C4#1062438211yescharacteristic
84#100—3622no—
85#100—3622no—
86C24—1811no—
87C24C2×#1062438211yescharacteristic
88C2×D4—3624no—
89C2×D4—1812no—
90C2×D4—1812no—
91C22×C4—21no—
92C22×C4—3622no—
93C22×C4—3621no—
94C22×C4—1811no—
95M16—3624no—
96M16—3624no—
97C2×C8—3624no—
98C4⋊C4—3622no—
99C22⋊C4—21no—
100C22⋊C4—3622no—
101C22⋊C4—3621no—
102C22⋊C4—1812no—
103C22⋊C4C2×#1062438212yes—
104C42—3622no—
105C23—22no—
106C23—81no—
107C23—3622no—
108C23—14481no—
109C23—1812no—
110C23C22⋊#1062438211yescharacteristic
111C23C22⋊#1062438211yescharacteristic
112C23C22×#1062438211yescharacteristic
113D4—3624no—
114D4—3624no—
115C2×C4—22no—
116C2×C4—81no—
117C2×C4—3622no—
118C2×C4—14482no—
119C2×C4—14481no—
120C2×C4—1812no—
121C2×C4—1814no—
122C8—7244no—
123C22—21no—
124C22—21no—
125C22—41no—
126C22—41no—
127C22—41no—
128C22—82no—
129C22—3622no—
130C22—14482no—
131C22—7242no—
132C22C2×C22⋊#1062438211yescharacteristic
133C22#1915389512yes—
134C4—42no—
135C4—1814no—
136C4—7242no—
137C2—21no—
138C2—22no—
139C2—41no—
140C2—41no—
141C2—7242no—
142C2#2604222211yescharacteristic
subgroupG/H
centerC2#26042222
commutatorC23×C181C22×C4
FrattiniC23C22×#10624382
FittingC2×C22⋊C4×C181C4
socleC2×C181#381
prime radicalC22×C22⋊D181C22
cosocleC22×Dic181C23
hypercenterC2×C22⋊C4#10624382
hypocenterC181#1829
LCSG ▷ C23×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #26042160C2semidirect
71. C181#1829semidirect

Maximal subgroups

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

subgroupindex
C2×#191538762
#260421602
#260417522
#1829181