Finite Group Databasebeta

← #37542044

Subgroups — #37542044

Order 23168.

582 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 157 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×#19153799C211yesmaximal, characteristic
2C22×C4×Dic181C211yesmaximal, characteristic, complemented
3#26041171C214yesmaximal, complemented
4#26041164C214yesmaximal, complemented
5#26041156C212yesmaximal
6#26041154C212yesmaximal, complemented
7#381×C181C211yesmaximal, characteristic, complemented
8C22×C22⋊D181C2211yescharacteristic
9C23×Dic181C2212yes—
10#19153799—24no—
11C2×C4⋊Dic181C2214yes—
12C2×#15668428C2212yes—
13C2×C22⋊Dic181C2211yescharacteristic
14C2×#15668426C2214yes—
15C2×#15668426C2212yes—
16C2×C4×Dic181—24no—
17C2×C4×Dic181C2214yes—
18#19153723C2214yes—
19#19153723C2214yes—
20C23×C4×C181C2211yescharacteristic
21C2×C22⋊C4×C181C2212yes—
22#95×C181C2214yes—
23C23×D181C2311yescharacteristic
24C2×C22⋊D181—22no—
25C2×C22⋊D181—24no—
26C22×Dic181—28no—
27C22×Dic181—24no—
28C22×Dic181C2311yescharacteristic
29C22×Dic181C2312yes—
30C22×Dic181C2314yes—
31C4⋊Dic181—28no—
32#15668428—24no—
33C22⋊Dic181—22no—
34#15668426—28no—
35#15668426—24no—
36C4×Dic181—28no—
37C24×C181C2311yescharacteristic
38C22×C4×C181—24no—
39C22×C4×C181D414yes—
40C22×C4×C181C2314yes—
41C22×C4×C181C2312yes—
42C22⋊C4×C181—24no—
43C22×D181—21no—
44C22×D181—24no—
45C22×D181—22no—
46C22⋊D181—44no—
47C2×Dic181—216no—
48C2×Dic181—24no—
49C2×Dic181—24no—
50C2×Dic181—22no—
51C2×Dic181—21no—
52C2×Dic181—24no—
53C2×Dic181—22no—
54C2×Dic181#4118yes—
55C23×C181—24no—
56C23×C181C2×D412yes—
57C23×C181#4114yes—
58C23×C181C2411yescharacteristic
59C2×C4×C181—28no—
60C2×C4×C181—24no—
61C2×C4×C181—24no—
62C2×C4×C181—24no—
63C2×C4×C181—24no—
64C2×C4×C181C2×D414yes—
65C22×C181—24no—
66C22×C181—28no—
67C22×C181#12314yes—
68C22×C181C22×D411yescharacteristic
69C22×C181C2×#4114yes—
70C22×C181C2×#4112yes—
71C2×D181—41no—
72C2×D181—42no—
73C2×D181—44no—
74C4×C181—24no—
75C4×C181—44no—
76Dic181—28no—
77Dic181—41no—
78Dic181—42no—
79C2×C181—24no—
80C2×C181C2×#12311yescharacteristic
81C2×C181#52512yes—
82C2×C181#52914yes—
83D181—81no—
84C181#285311yescharacteristic, complemented, Sylow
85#2853—1811nomaximal, Sylow
86C2×#123—1811no—
87C22×C42—1811no—
88#388—1814no—
89#387—1814no—
90#386—1812no—
91#385—1812no—
92#381D18111yescharacteristic, complemented
93C22×D4—1811no—
94C23×C4—1812no—
95C23×C4C2×D18111yescharacteristic
96#123—3624no—
97C2×C4⋊C4—1812no—
98C2×C4⋊C4—1814no—
99C2×C22⋊C4—1811no—
100C2×C22⋊C4—1812no—
101C2×C22⋊C4—1814no—
102C2×C22⋊C4C2×D18112yes—
103C2×C42—3624no—
104C2×C42—1814no—
105#95—1814no—
106#95—1814no—
107#95C2×D18114yes—
108C24—1811no—
109C24C22×D18111yescharacteristic
110C2×D4—3622no—
111C2×D4—3624no—
112C22×C4—24no—
113C22×C4—3624no—
114C22×C4—3628no—
115C22×C4—1811no—
116C22×C4—1812no—
117C22×C4—1814no—
118C22×C4D72414yes—
119C22×C4C22×D18114yes—
120C22×C4C22×D18112yes—
121C4⋊C4—3628no—
122C4⋊C4—3624no—
123C22⋊C4—24no—
124C22⋊C4—3628no—
125C22⋊C4—3622no—
126C22⋊C4—3624no—
127C42—3628no—
128C23—24no—
129C23—3621no—
130C23—3624no—
131C23—3622no—
132C23C2×D72412yes—
133C23#1566844814yes—
134C23C23×D18111yescharacteristic
135D4—7244no—
136C2×C4—28no—
137C2×C4—24no—
138C2×C4—24no—
139C2×C4—24no—
140C2×C4—24no—
141C2×C4—36216no—
142C2×C4—3624no—
143C2×C4—3624no—
144C2×C4—3622no—
145C2×C4—3621no—
146C2×C4—3624no—
147C2×C4—3622no—
148C2×C4—1818no—
149C2×C4C2×D72414yes—
150C22—24no—
151C22—28no—
152C22—7241no—
153C22—7242no—
154C22—7244no—
155C22#1915380014yes—
156C22C22×D72411yescharacteristic
157C22#41×D18114yes—
158C22C2×#1566844812yes—
159C4—24no—
160C4—44no—
161C4—3628no—
162C4—7241no—
163C4—7242no—
164C2—24no—
165C2—14481no—
166C2C2×#1915380011yescharacteristic
167C2#2604179112yes—
168C2#2604180614yes—
subgroupG/H
center, FrattiniC23C23×D181
commutator, socle, cosocleC23×C181C24
Fitting#381×C181C2
prime radicalC22×C22⋊D181C22
hypercenter#381D181
hypocenterC181#2853
LCSG ▷ C23×C181 ▷ C181
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic181C2semidirect
3. #26041171C2semidirect
4. #26041164C2semidirect
6. #26041154C2semidirect
7. #381×C181C2semidirect
84. C181#2853semidirect
92. #381D181semidirect

Maximal subgroups

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

subgroupindex
C2×#191537992
C22×C4×Dic1812
#260411712
#260411642
#260411562
#260411542
#381×C1812
#2853181