Finite Group Databasebeta

← #16855113

Subgroups — #16855113

Order 3968.

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

normal subgroups only

This group has 772 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#14521613C213yesmaximal, complemented
2#14521236C218yesmaximal, complemented
3#14521023C213yesmaximal, complemented
4C31×#585C211yesmaximal, characteristic, complemented
5C31×2−1+4—23no—
6C31×H(5,𝔽2)—23no—
7C31×H(5,𝔽2)C2214yes—
8C2×#41×C31—26no—
9C2×#41×C31C2213yes—
10C22×D124C2211yescharacteristic, complemented
11#11758524—23no—
12#11758517—23no—
13#11758514C22112yescomplemented
14#11758507—26no—
15#11758503C2213yescomplemented
16#11758422C22112yescomplemented
17C23×D31C2312yes—
18#41×C31—24no—
19#41×C31—212no—
20#41×C31—26no—
21#41×C31—212no—
22#41×C31—26no—
23C2×Q8×C31—26no—
24C2×Q8×C31D413yescomplemented
25C2×D4×C31—26no—
26C2×D4×C31—212no—
27C2×D4×C31D413yescomplemented
28C2×D4×C31C2316yes—
29C22×C4×C31—24no—
30C22×C4×C31D416yescomplemented
31C22×C4×C31C2311yescharacteristic
32C2×C22⋊D31—212no—
33C2×D124—23no—
34C2×D124—23no—
35C22⋊Dic31C2316yes—
36(C2×D31)⋊C4—212no—
37C4⋊Dic31—23no—
38C4×Dic31—23no—
39C23×C31—24no—
40C23×C31C2×D416yes—
41C23×C31C2411yescharacteristic
42C22×D31—26no—
43C22×D31—82no—
44Q8×C31—24no—
45Q8×C31—26no—
46D4×C31—212no—
47D4×C31—212no—
48D4×C31—26no—
49C2×C4×C31—212no—
50C2×C4×C31—26no—
51C2×C4×C31—26no—
52C2×C4×C31C2×D416yes—
53C2×C4×C31C2×D413yes—
54C2×C4×C31C2×D413yes—
55C22⋊D31—812no—
56C2×Dic31—26no—
57D124—41no—
58D124—43no—
59#3027—311nomaximal, Sylow
60C22×C31—26no—
61C22×C31—41no—
62C22×C31—46no—
63C22×C31—84no—
64C22×C31C22×D413yes—
65C2×D31—412no—
66C2×D31—42no—
67C4×C31—26no—
68C4×C31#12011yescharacteristic
69C4×C31#12013yes—
70Dic31—46no—
71#585D3111yescharacteristic, complemented
72#535—313no—
73B(4,𝔽2)—318no—
74#410—313no—
75C2×C31—23no—
76C2×C31—46no—
77C2×C31C2×#12011yescharacteristic
78D31—82no—
792−1+4—23no—
80H(5,𝔽2)—23no—
81H(5,𝔽2)C2×D3114yes—
82C2×#41—26no—
83C2×#41C2×D3113yes—
84C22×D4—311no—
85#127—623no—
86#124—623no—
87#121—626no—
88#120—3112no—
89#117—313no—
90#99—3112no—
91C31#302711yescharacteristic, complemented, Sylow
92C24—312no—
93#41—24no—
94#41—212no—
95#41—26no—
96#41—212no—
97#41—26no—
98C2×Q8—26no—
99C2×Q8C22⋊D3113yescomplemented
100C2×D4—26no—
101C2×D4—212no—
102C2×D4—6212no—
103C2×D4—623no—
104C2×D4—623no—
105C2×D4C22⋊D3113yescomplemented
106C2×D4C22×D3116yes—
107C22×C4—24no—
108C22×C4C22⋊D3116yescomplemented
109C22×C4C22×D3111yescharacteristic
110C4⋊C4—623no—
111C22⋊C4—316no—
112C22⋊C4—6212no—
113C42—623no—
114C23—24no—
115C23—626no—
116C23—2482no—
117C23C2×C22⋊D3116yes—
118C23C23×D3111yescharacteristic
119Q8—24no—
120Q8—26no—
121D4—212no—
122D4—212no—
123D4—26no—
124D4—1241no—
125D4—1243no—
126D4—24812no—
127C2×C4—212no—
128C2×C4—26no—
129C2×C4—26no—
130C2×C4—626no—
131C2×C4C2×C22⋊D3116yes—
132C2×C4C2×C22⋊D3113yes—
133C2×C4C2×C22⋊D3113yes—
134C22—26no—
135C22—41no—
136C22—46no—
137C22—84no—
138C22—12412no—
139C22—1242no—
140C22C22×C22⋊D3113yes—
141C4—26no—
142C4—1246no—
143C4#1175853011yescharacteristic
144C4#1175853013yes—
145C2—23no—
146C2—46no—
147C2—2482no—
148C2C2×#1175853011yescharacteristic
subgroupG/H
centerC2C2×#11758530
commutator, cosocleC23×C31C24
FrattiniC23C23×D31
FittingC31×#585C2
socleC2×C31C2×#120
hypercenter#585D31
hypocenterC31#3027
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #14521613C2semidirect
2. #14521236C2semidirect
3. #14521023C2semidirect
4. C31×#585C2semidirect
10. C22×D124C22semidirect
13. #11758514C22semidirect
15. #11758503C22semidirect
16. #11758422C22semidirect
24. C2×Q8×C31D4semidirect
27. C2×D4×C31D4semidirect
30. C22×C4×C31D4semidirect
71. #585D31semidirect
91. C31#3027semidirect
99. C2×Q8C22⋊D31semidirect
105. C2×D4C22⋊D31semidirect
108. C22×C4C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
#145216132
#145212362
#145210232
C31×#5852
#302731