Finite Group Databasebeta

← #16855103

Subgroups — #16855103

Order 3968.

766 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 161 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#14521556C213yesmaximal, complemented
2#14521239C214yesmaximal, complemented
3#14521236C214yesmaximal, complemented
4#14521023C213yesmaximal, complemented
5C31×#585C211yesmaximal, characteristic, complemented
6C31×2−1+4—23no—
7C31×H(5,𝔽2)—23no—
8C31×H(5,𝔽2)C2214yes—
9C2×#41×C31—26no—
10C2×#41×C31C2213yes—
11C22×C4×D31C2211yescharacteristic, complemented
12#11758523—23no—
13#11758515—23no—
14#11758514C2216yescomplemented
15#11758512C2216yescomplemented
16C4×C22⋊D31—26no—
17#11758503C2213yescomplemented
18#11758422C22112yescomplemented
19C23×D31C2311yescharacteristic
20#41×C31—24no—
21#41×C31—212no—
22#41×C31—26no—
23#41×C31—212no—
24#41×C31—26no—
25C2×Q8×C31—26no—
26C2×Q8×C31D413yescomplemented
27C2×D4×C31—26no—
28C2×D4×C31—212no—
29C2×D4×C31D413yescomplemented
30C2×D4×C31C2316yes—
31C22×C4×C31—24no—
32C22×C4×C31D416yescomplemented
33C22×C4×C31C2311yescharacteristic
34C2×C22⋊D31—26no—
35C22×Dic31C2311yescharacteristic
36C2×C4×D31—23no—
37C2×C4×D31—23no—
38C22⋊Dic31—26no—
39C22⋊Dic31C2316yes—
40(C2×D31)⋊C4—26no—
41C4⋊Dic31—23no—
42Dic31⋊C4—26no—
43C4×Dic31—23no—
44C23×C31—24no—
45C23×C31C2×D416yes—
46C23×C31C2411yescharacteristic
47C22×D31—23no—
48C22×D31—42no—
49Q8×C31—24no—
50Q8×C31—26no—
51D4×C31—212no—
52D4×C31—212no—
53D4×C31—26no—
54C2×C4×C31—212no—
55C2×C4×C31—26no—
56C2×C4×C31—26no—
57C2×C4×C31C2×D416yes—
58C2×C4×C31C2×D413yes—
59C2×C4×C31C2×D413yes—
60C22⋊D31—412no—
61C2×Dic31—26no—
62C2×Dic31—23no—
63C4×D31—43no—
64C4×D31—41no—
65#3025—311nomaximal, Sylow
66C22×C31—26no—
67C22×C31—41no—
68C22×C31—46no—
69C22×C31—84no—
70C22×C31C22×D413yes—
71C2×D31—26no—
72C2×D31—43no—
73C2×D31—41no—
74C4×C31—26no—
75C4×C31#12013yes—
76C4×C31#12011yescharacteristic
77Dic31—46no—
78Dic31—41no—
79#585D3111yescharacteristic, complemented
80#525—313no—
81#458—314no—
82B(4,𝔽2)—314no—
83#410—313no—
84C2×C31—23no—
85C2×C31—46no—
86C2×C31C2×#12011yescharacteristic
87D31—42no—
882−1+4—23no—
89H(5,𝔽2)—23no—
90H(5,𝔽2)C2×D3114yes—
91C2×#41—26no—
92C2×#41C2×D3113yes—
93C23×C4—311no—
94#123—316no—
95C22⋊Q8—623no—
96#121—623no—
97#120—316no—
98C4×D4—626no—
99#117—313no—
100#99—3112no—
101C31#302511yescharacteristic, complemented, Sylow
102C24—311no—
103#41—24no—
104#41—212no—
105#41—26no—
106#41—212no—
107#41—26no—
108C2×Q8—26no—
109C2×Q8C22⋊D3113yescomplemented
110C2×D4—26no—
111C2×D4—212no—
112C2×D4—626no—
113C2×D4C22⋊D3113yescomplemented
114C2×D4C22×D3116yes—
115C22×C4—24no—
116C22×C4—311no—
117C22×C4—623no—
118C22×C4—623no—
119C22×C4C22⋊D3116yescomplemented
120C22×C4C22×D3111yescharacteristic
121C4⋊C4—626no—
122C4⋊C4—623no—
123C22⋊C4—316no—
124C22⋊C4—626no—
125C22⋊C4—626no—
126C42—623no—
127C23—24no—
128C23—623no—
129C23—1242no—
130C23C2×C22⋊D3116yes—
131C23C23×D3111yescharacteristic
132Q8—24no—
133Q8—26no—
134D4—212no—
135D4—212no—
136D4—26no—
137D4—12412no—
138C2×C4—212no—
139C2×C4—26no—
140C2×C4—26no—
141C2×C4—626no—
142C2×C4—623no—
143C2×C4—1243no—
144C2×C4—1241no—
145C2×C4C2×C22⋊D3116yes—
146C2×C4C2×C22⋊D3113yes—
147C2×C4C2×C22⋊D3113yes—
148C22—26no—
149C22—41no—
150C22—46no—
151C22—84no—
152C22—626no—
153C22—1243no—
154C22—1241no—
155C22C22×C22⋊D3113yes—
156C4—26no—
157C4—1246no—
158C4—1241no—
159C4#1175853013yes—
160C4#1175853011yescharacteristic
161C2—23no—
162C2—46no—
163C2—1242no—
164C2C2×#1175853011yescharacteristic
subgroupG/H
centerC4#11758530
commutator, cosocleC23×C31C24
FrattiniC23C23×D31
FittingC31×#585C2
socleC2×C31C2×#120
hypercenter#585D31
hypocenterC31#3025
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C4 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #14521556C2semidirect
2. #14521239C2semidirect
3. #14521236C2semidirect
4. #14521023C2semidirect
5. C31×#585C2semidirect
11. C22×C4×D31C22semidirect
14. #11758514C22semidirect
15. #11758512C22semidirect
17. #11758503C22semidirect
18. #11758422C22semidirect
26. C2×Q8×C31D4semidirect
29. C2×D4×C31D4semidirect
32. C22×C4×C31D4semidirect
79. #585D31semidirect
101. C31#3025semidirect
109. C2×Q8C22⋊D31semidirect
113. C2×D4C22⋊D31semidirect
119. C22×C4C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
#145215562
#145212392
#145212362
#145210232
C31×#5852
#302531