Finite Group Databasebeta

← #11800590

Subgroups — #11800590

Order 1152.

336 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 71 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#10592618C211yesmaximal, characteristic, complemented
2C3⋊D3×D16C211yesmaximal, characteristic, complemented
3C32×SD64C211yesmaximal, characteristic, complemented
4#10589387C211yesmaximal, characteristic, complemented
5#10589385C211yesmaximal, characteristic, complemented
6#10589314C211yesmaximal, characteristic, complemented
7#10589313C211yesmaximal, characteristic, complemented
8#69380—34nomaximal
9#64128—21no—
10D8×C3⋊D3—21no—
11C32×Q32C2211yescharacteristic, complemented
12C32×D16C2211yescharacteristic
13#63655—21no—
14#63653—21no—
15#63626C2211yescharacteristic
16#63626C2211yescharacteristic, complemented
17C16×C3⋊D3C2211yescharacteristic
18C32×C32C2211yescharacteristic, complemented
19C3⋊(C3⋊C32)C2211yescharacteristic, complemented
20#4919—34no—
21D3×D16—34no—
22C3×SD64D314yescomplemented
23#4521—34no—
24#4519—34no—
25D96—34no—
26#4447—34no—
27#3832—41no—
28D4×C3⋊D3—41no—
29C32×Q16—21no—
30C32×D8—21no—
31#3755—41no—
32#3753—41no—
33#3745—21no—
34#3745—21no—
35C8×C3⋊D3D411yescharacteristic
36C32×C16C2311yescharacteristic
37C3⋊(C3⋊C16)D411yescharacteristic
38#2263—91noSylow
39#919—64no—
40D3×D8—64no—
41C3×Q32C2×D314yescomplemented
42C3×D16C2×D314yes—
43#828—64no—
44#826—64no—
45D48—34no—
46D48—34no—
47D3×C16—34no—
48C3×C32C2×D314yescomplemented
49C3⋊C32—34no—
50C22×C3⋊D3—81no—
51C32×Q8—41no—
52C32×D4—41no—
53#638—81no—
54C4⋊(C3⋊D3)—41no—
55C4⋊(C3⋊D3)—41no—
56C4⋊(C3⋊D3)—81no—
57C4×C3⋊D3—81no—
58C4×C3⋊D3D811yescharacteristic
59C32×C8C2×D411yescharacteristic
60C3⋊(C3⋊C8)D811yescharacteristic
61#508—91no—
62C2×D16—91no—
63SD64—91no—
64SD64C3⋊D311yescharacteristic, complemented
65D32—91no—
66D32—91no—
67M64—91no—
68#239—124no—
69D3×D4—124no—
70C3×Q16—24no—
71C3×D8—24no—
72#215—124no—
73#213—124no—
74D24—64no—
75D24—64no—
76D3×C8—34no—
77C3×C16C22×D314yes—
78C3⋊C16—34no—
79C22×C32—81no—
80C2×C3⋊D3—81no—
81C2×C3⋊D3—81no—
82C2×C3⋊D3—162no—
83C2×C3⋊D3D1611yescharacteristic
84C32×C4—81no—
85C32×C4C2×D811yescharacteristic
86C3⋊Dic3D1611yescharacteristic
87#135—181no—
88C2×D8—181no—
89Q32C2×C3⋊D311yescharacteristic, complemented
90SD32—181no—
91D16—91no—
92D16—91no—
93D16—181no—
94D16C2×C3⋊D311yescharacteristic
95C2×C16—91no—
96C32—91no—
97C32C2×C3⋊D311yescharacteristic, complemented
98C22×D3—244no—
99C3×Q8—44no—
100C3×D4—44no—
101#67—244no—
102D12—124no—
103D12—124no—
104D12—244no—
105C4×D3—34no—
106C4×D3—244no—
107C3×C8D3×D414yes—
108C3⋊C8—34no—
109C2×C32—161no—
110C2×C32C2×D1611yescharacteristic
111C3⋊D3—21no—
112C3⋊D3—161no—
113C3⋊D3—161no—
114#41—361no—
115C2×D4—361no—
116Q16—21no—
117SD16—361no—
118D8—21no—
119D8—181no—
120D8—181no—
121D8—361no—
122C2×C8—91no—
123C16—91no—
124C16C22×C3⋊D311yescharacteristic
125C22×C3—84no—
126C2×D3—34no—
127C2×D3—244no—
128C2×D3—244no—
129C2×D3—488no—
130C3×C4—84no—
131C3×C4D3×D814yes—
132Dic3—34no—
133C32#226311yescharacteristic, complemented, Sylow
134C23—721no—
135Q8—41no—
136D4—41no—
137D4—361no—
138D4—361no—
139D4—721no—
140D4—721no—
141C2×C4—91no—
142C2×C4—721no—
143C8—91no—
144C8D4×C3⋊D311yescharacteristic
145C2×C3—164no—
146C2×C3D3×D1614yes—
147D3—64no—
148D3—484no—
149D3—484no—
150C22—81no—
151C22—91no—
152C22—721no—
153C22—721no—
154C22—1442no—
155C4—81no—
156C4—91no—
157C4D8×C3⋊D311yescharacteristic
158C3#6938014yescomplemented
159C2—161no—
160C2—181no—
161C2—1441no—
162C2—1441no—
163C2C3⋊D3×D1611yescharacteristic
subgroupG/H
centerC2C3⋊D3×D16
commutator, cosocleC32×C16C23
FrattiniC16C22×C3⋊D3
FittingC32×SD64C2
socleC2×C32C2×D16
hypercenterSD64C3⋊D3
hypocenterC32#2263
LCSG ▷ C32×C16 ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ SD64

Complements

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

NH ≅ G/Ntype
1. #10592618C2semidirect
2. C3⋊D3×D16C2semidirect
3. C32×SD64C2semidirect
4. #10589387C2semidirect
5. #10589385C2semidirect
6. #10589314C2semidirect
7. #10589313C2semidirect
11. C32×Q32C22semidirect
16. #63626C22semidirect
18. C32×C32C22semidirect
19. C3⋊(C3⋊C32)C22semidirect
22. C3×SD64D3semidirect
41. C3×Q32C2×D3semidirect
48. C3×C32C2×D3semidirect
64. SD64C3⋊D3semidirect
89. Q32C2×C3⋊D3semidirect
97. C32C2×C3⋊D3semidirect
133. C32#2263semidirect
158. C3#69380semidirect

Maximal subgroups

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

subgroupindex
#105926182
C3⋊D3×D162
C32×SD642
#105893872
#105893852
#105893142
#105893132
#693803