Finite Group Databasebeta

← #37532055

Subgroups — #37532055

Order 23168.

252 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 85 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#26041336C212yesmaximal, complemented
2#26041005C212yesmaximal, complemented
3#26041003C212yesmaximal
4C2×#117×C181C211yesmaximal, characteristic
5C4⋊#13089678—22no—
6C22⋊#13089678C2214yes—
7#19153727—22no—
8C23×C4×C181C411yescharacteristic
9#117×C181—22no—
10#117×C181—22no—
11C2×C4⋊C4×C181C411yescharacteristic
12C2×C4⋊C4×C181C2211yescharacteristic
13C2×C22⋊C4×C181C411yescharacteristic
14C2×C22⋊C4×C181C2211yescharacteristic
15C2×C42×C181C411yescharacteristic
16C2×C42×C181C2211yescharacteristic
17C2×#13089678—24no—
18C24×C181C2×C411yescharacteristic
19C22×C4×C181—22no—
20C22×C4×C181—21no—
21C22×C4×C181—21no—
22C22×C4×C181—22no—
23C22×C4×C181C2×C411yescharacteristic
24C22×C4×C181C2×C411yescharacteristic
25C22×C4×C181C2×C411yescharacteristic
26C22×C4×C181C2×C411yescharacteristic
27C22×C4×C181C2×C411yescharacteristic
28C22×C4×C181C2311yescharacteristic
29C4⋊C4×C181—22no—
30C4⋊C4×C181—22no—
31C22⋊C4×C181—22no—
32C22⋊C4×C181—22no—
33C42×C181—21no—
34C42×C181—21no—
35C42×C181D412yes—
36C42×C181D412yes—
37#13089678—44no—
38C23×C181—21no—
39C23×C181—21no—
40C23×C181—41no—
41C23×C181—41no—
42C23×C181M1612yes—
43C23×C181C22×C411yescharacteristic
44C2×C4×C181—24no—
45C2×C4×C181—24no—
46C2×C4×C181—21no—
47C2×C4×C181—21no—
48C2×C4×C181—21no—
49C2×C4×C181—21no—
50C2×C4×C181—21no—
51C2×C4×C181—21no—
52C2×C4×C181—41no—
53C2×C4×C181—41no—
54C2×C4×C181—41no—
55C2×C4×C181—41no—
56C2×C4×C181C22⋊C411yescharacteristic
57C2×C4×C181C22⋊C411yescharacteristic
58C2×C4×C181C22⋊C412yes—
59C2×C4×C181M1612yes—
60C2×C4×C181C2×D412yes—
61C22×C181—21no—
62C22×C181—21no—
63C22×C181—22no—
64C22×C181—42no—
65C22×C181—42no—
66C22×C181—41no—
67C22×C181—41no—
68C22×C181C2×C22⋊C411yescharacteristic
69C22×C181C2×M1611yescharacteristic
70C22×C181C2×M1611yescharacteristic
71C4×C181—21no—
72C4×C181—21no—
73C4×C181—22no—
74C4×C181—22no—
75C4×C181—22no—
76C4×C181—41no—
77C4×C181—41no—
78C2×C181—21no—
79C2×C181—21no—
80C2×C181—42no—
81C2×C181#40711yescharacteristic
82C2×C181#41011yescharacteristic
83C2×C181#41311yescharacteristic
84C181#146411yescharacteristic, complemented, Sylow
85#1464—1811nomaximal, Sylow
86C2×#117D18111yescharacteristic
87#432—1812no—
88#324—1812no—
89#323—1812no—
90C23×C4Dic18111yescharacteristic
91#117—22no—
92#117—22no—
93C2×C4⋊C4Dic18111yescharacteristic
94C2×C4⋊C4C2×D18111yescharacteristic
95C2×C22⋊C4Dic18111yescharacteristic
96C2×C22⋊C4C2×D18111yescharacteristic
97C2×C42Dic18111yescharacteristic
98C2×C42C2×D18111yescharacteristic
99C4⋊C8—3622no—
100C22⋊C8—1814no—
101#97—3622no—
102C24C2×Dic18111yescharacteristic
103C22×C4—22no—
104C22×C4—21no—
105C22×C4—21no—
106C22×C4—22no—
107C22×C4C2×Dic18111yescharacteristic
108C22×C4C2×Dic18111yescharacteristic
109C22×C4C2×Dic18111yescharacteristic
110C22×C4C2×Dic18111yescharacteristic
111C22×C4C2×Dic18111yescharacteristic
112C22×C4C22×D18111yescharacteristic
113C2×C8—3624no—
114C4⋊C4—22no—
115C4⋊C4—22no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C42—21no—
119C42—21no—
120C42C22⋊D18112yes—
121C42C22⋊D18112yes—
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23#1566843312yes—
127C23C22×Dic18111yescharacteristic
128C2×C4—24no—
129C2×C4—24no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4C22⋊Dic18111yescharacteristic
141C2×C4C22⋊Dic18111yescharacteristic
142C2×C4C22⋊Dic18112yes—
143C2×C4#1566843312yes—
144C2×C4C2×C22⋊D18112yes—
145C8—7244no—
146C22—21no—
147C22—21no—
148C22—22no—
149C22—42no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22C2×C22⋊Dic18111yescharacteristic
154C22C2×#1566843311yescharacteristic
155C22C2×#1566843311yescharacteristic
156C4—21no—
157C4—21no—
158C4—22no—
159C4—22no—
160C4—22no—
161C4—41no—
162C4—41no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#2604124311yescharacteristic
167C2#2604125311yescharacteristic
168C2#2604126311yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic181
commutatorC23×C181C22×C4
FrattiniC22×C4C22×D181
FittingC2×#117×C181C2
socleC22×C181C2×C22⋊C4
prime radicalC24×C181C2×C4
cosocleC22×C4×C181C23
hypercenterC2×#117D181
hypocenterC181#1464
LCSG ▷ C23×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #26041336C2semidirect
2. #26041005C2semidirect
84. C181#1464semidirect

Maximal subgroups

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

subgroupindex
#260413362
#260410052
#260410032
C2×#117×C1812
#1464181