Finite Group Databasebeta

← #15682789

Subgroups — #15682789

Order 2944.

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#13092924C213yesmaximal, complemented
2#13092607C214yesmaximal, complemented
3#13092604C214yesmaximal, complemented
4#13092391C213yesmaximal, complemented
5C23×#585C211yesmaximal, characteristic, complemented
6C23×2−1+4—23no—
7C23×H(5,𝔽2)—23no—
8C23×H(5,𝔽2)C2214yes—
9C2×#41×C23—26no—
10C2×#41×C23C2213yes—
11C22×C4×D23C2211yescharacteristic, complemented
12#10625117—23no—
13#10625109—23no—
14#10625108C2216yescomplemented
15#10625106C2216yescomplemented
16C4×C22⋊D23—26no—
17#10625097C2213yescomplemented
18#10625016C22112yescomplemented
19C23×D23C2311yescharacteristic
20#41×C23—24no—
21#41×C23—212no—
22#41×C23—26no—
23#41×C23—212no—
24#41×C23—26no—
25C2×Q8×C23—26no—
26C2×Q8×C23D413yescomplemented
27C2×D4×C23—26no—
28C2×D4×C23—212no—
29C2×D4×C23D413yescomplemented
30C2×D4×C23C2316yes—
31C22×C4×C23—24no—
32C22×C4×C23D416yescomplemented
33C22×C4×C23C2311yescharacteristic
34C2×C22⋊D23—26no—
35C22×Dic23C2311yescharacteristic
36C2×C4×D23—23no—
37C2×C4×D23—23no—
38C22⋊Dic23—26no—
39C22⋊Dic23C2316yes—
40(C2×D23)⋊C4—26no—
41C4⋊Dic23—23no—
42Dic23⋊C4—26no—
43C4×Dic23—23no—
44C23×C23—24no—
45C23×C23C2×D416yes—
46C23×C23C2411yescharacteristic
47C22×D23—23no—
48C22×D23—42no—
49Q8×C23—24no—
50Q8×C23—26no—
51D4×C23—212no—
52D4×C23—212no—
53D4×C23—26no—
54C2×C4×C23—212no—
55C2×C4×C23—26no—
56C2×C4×C23—26no—
57C2×C4×C23C2×D416yes—
58C2×C4×C23C2×D413yes—
59C2×C4×C23C2×D413yes—
60C22⋊D23—412no—
61C2×Dic23—26no—
62C2×Dic23—23no—
63C4×D23—43no—
64C4×D23—41no—
65#3025—231nomaximal, Sylow
66C22×C23—26no—
67C22×C23—41no—
68C22×C23—46no—
69C22×C23—84no—
70C22×C23C22×D413yes—
71C2×D23—26no—
72C2×D23—43no—
73C2×D23—41no—
74C4×C23—26no—
75C4×C23#12013yes—
76C4×C23#12011yescharacteristic
77Dic23—46no—
78Dic23—41no—
79#585D2311yescharacteristic, complemented
80#525—233no—
81#458—234no—
82B(4,𝔽2)—234no—
83#410—233no—
84C2×C23—23no—
85C2×C23—46no—
86C2×C23C2×#12011yescharacteristic
87D23—42no—
882−1+4—23no—
89H(5,𝔽2)—23no—
90H(5,𝔽2)C2×D2314yes—
91C2×#41—26no—
92C2×#41C2×D2313yes—
93C23×C4—231no—
94#123—236no—
95C22⋊Q8—463no—
96#121—463no—
97#120—236no—
98C4×D4—466no—
99#117—233no—
100#99—2312no—
101C23#302511yescharacteristic, complemented, Sylow
102C24—231no—
103#41—24no—
104#41—212no—
105#41—26no—
106#41—212no—
107#41—26no—
108C2×Q8—26no—
109C2×Q8C22⋊D2313yescomplemented
110C2×D4—26no—
111C2×D4—212no—
112C2×D4—466no—
113C2×D4C22⋊D2313yescomplemented
114C2×D4C22×D2316yes—
115C22×C4—24no—
116C22×C4—231no—
117C22×C4—463no—
118C22×C4—463no—
119C22×C4C22⋊D2316yescomplemented
120C22×C4C22×D2311yescharacteristic
121C4⋊C4—463no—
122C4⋊C4—466no—
123C22⋊C4—236no—
124C22⋊C4—466no—
125C22⋊C4—466no—
126C42—463no—
127C23—24no—
128C23—463no—
129C23—922no—
130C23C2×C22⋊D2316yes—
131C23C23×D2311yescharacteristic
132Q8—24no—
133Q8—26no—
134D4—212no—
135D4—212no—
136D4—26no—
137D4—9212no—
138C2×C4—212no—
139C2×C4—26no—
140C2×C4—26no—
141C2×C4—466no—
142C2×C4—463no—
143C2×C4—923no—
144C2×C4—921no—
145C2×C4C2×C22⋊D2316yes—
146C2×C4C2×C22⋊D2313yes—
147C2×C4C2×C22⋊D2313yes—
148C22—26no—
149C22—41no—
150C22—46no—
151C22—84no—
152C22—466no—
153C22—923no—
154C22—921no—
155C22C22×C22⋊D2313yes—
156C4—26no—
157C4—926no—
158C4—921no—
159C4#1062512413yes—
160C4#1062512411yescharacteristic
161C2—23no—
162C2—46no—
163C2—922no—
164C2C2×#1062512411yescharacteristic
subgroupG/H
centerC4#10625124
commutator, cosocleC23×C23C24
FrattiniC23C23×D23
FittingC23×#585C2
socleC2×C23C2×#120
hypercenter#585D23
hypocenterC23#3025
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C4 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #13092924C2semidirect
2. #13092607C2semidirect
3. #13092604C2semidirect
4. #13092391C2semidirect
5. C23×#585C2semidirect
11. C22×C4×D23C22semidirect
14. #10625108C22semidirect
15. #10625106C22semidirect
17. #10625097C22semidirect
18. #10625016C22semidirect
26. C2×Q8×C23D4semidirect
29. C2×D4×C23D4semidirect
32. C22×C4×C23D4semidirect
79. #585D23semidirect
101. C23#3025semidirect
109. C2×Q8C22⋊D23semidirect
113. C2×D4C22⋊D23semidirect
119. C22×C4C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
#130929242
#130926072
#130926042
#130923912
C23×#5852
#302523