Finite Group Databasebeta

← #11800581

Subgroups — #11800581

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#10592611C211yesmaximal, characteristic, complemented
2C3⋊D3×D16C211yesmaximal, characteristic, complemented
3C32×D32C211yesmaximal, characteristic, complemented
4#10589386C211yesmaximal, characteristic, complemented
5#10589385C211yesmaximal, characteristic, complemented
6#10589315C211yesmaximal, characteristic, complemented
7#10589313C211yesmaximal, characteristic, complemented
8#69377—34nomaximal
9#64121—21no—
10D8×C3⋊D3—21no—
11C32×D16C2211yescharacteristic
12C32×D16C2211yescharacteristic, complemented
13#63654—21no—
14#63653—21no—
15#63628C2211yescharacteristic, complemented
16#63626C2211yescharacteristic
17C16×C3⋊D3C2211yescharacteristic
18C32×C32C2211yescharacteristic, complemented
19C3⋊(C3⋊C32)C2211yescharacteristic, complemented
20#4912—34no—
21D3×D16—34no—
22C3×D32D314yescomplemented
23#4520—34no—
24#4519—34no—
25#4449—34no—
26#4447—34no—
27#3830—41no—
28D4×C3⋊D3—41no—
29C32×D8—21no—
30C32×D8—21no—
31#3754—41no—
32#3753—41no—
33#3746—21no—
34#3745—21no—
35C8×C3⋊D3D411yescharacteristic
36C32×C16C2311yescharacteristic
37C3⋊(C3⋊C16)D411yescharacteristic
38#2263—91noSylow
39#912—64no—
40D3×D8—64no—
41C3×D16C2×D314yes—
42C3×D16C2×D314yescomplemented
43#827—64no—
44#826—64no—
45Dic24—34no—
46D48—34no—
47D3×C16—34no—
48C3×C32C2×D314yescomplemented
49C3⋊C32—34no—
50C22×C3⋊D3—81no—
51C32×D4—41no—
52C32×D4—41no—
53#638—81no—
54#638—81no—
55C2×C3⋊Dic3—81no—
56C4⋊(C3⋊D3)—41no—
57C4×C3⋊D3D811yescharacteristic
58#634—41no—
59C32×C8C2×D411yescharacteristic
60C3⋊(C3⋊C8)D811yescharacteristic
61#508—91no—
62C2×D16—91no—
63SD64—91no—
64SD64—91no—
65D32—91no—
66D32C3⋊D311yescharacteristic, complemented
67M64—91no—
68#237—124no—
69D3×D4—124no—
70C3×D8—24no—
71C3×D8—24no—
72#214—124no—
73#213—124no—
74Dic12—64no—
75D24—64no—
76D3×C8—34no—
77C3×C16C22×D314yes—
78C3⋊C16—34no—
79C22×C32—81no—
80C22×C32—81no—
81C2×C3⋊D3—81no—
82C2×C3⋊D3—162no—
83C2×C3⋊D3D1611yescharacteristic
84C32×C4C2×D811yescharacteristic
85C3⋊Dic3—81no—
86C3⋊Dic3D1611yescharacteristic
87#135—181no—
88C2×D8—181no—
89Q32—91no—
90SD32—181no—
91D16—91no—
92D16—181no—
93D16C2×C3⋊D311yescharacteristic
94D16C2×C3⋊D311yescharacteristic, complemented
95C2×C16—91no—
96C32—91no—
97C32C2×C3⋊D311yescharacteristic, complemented
98C22×D3—244no—
99C3×D4—44no—
100C3×D4—44no—
101#67—244no—
102#67—244no—
103C2×Dic3—244no—
104D12—124no—
105C4×D3—34no—
106Dic6—124no—
107C3×C8D3×D414yes—
108C3⋊C8—34no—
109C2×C32—161no—
110C2×C32—161no—
111C2×C32C2×D1611yescharacteristic
112C3⋊D3—21no—
113C3⋊D3—161no—
114#41—361no—
115C2×D4—361no—
116Q16—181no—
117SD16—361no—
118D8—21no—
119D8—21no—
120D8—181no—
121D8—361no—
122C2×C8—91no—
123C16—91no—
124C16C22×C3⋊D311yescharacteristic
125C22×C3—84no—
126C22×C3—84no—
127C2×D3—34no—
128C2×D3—244no—
129C2×D3—488no—
130C3×C4D3×D814yes—
131Dic3—34no—
132Dic3—244no—
133C32#226311yescharacteristic, complemented, Sylow
134C23—721no—
135Q8—361no—
136D4—41no—
137D4—41no—
138D4—361no—
139D4—721no—
140D4—721no—
141C2×C4—91no—
142C2×C4—721no—
143C8—91no—
144C8D4×C3⋊D311yescharacteristic
145C2×C3—164no—
146C2×C3—164no—
147C2×C3D3×D1614yes—
148D3—64no—
149D3—484no—
150C22—81no—
151C22—81no—
152C22—91no—
153C22—721no—
154C22—1442no—
155C4—91no—
156C4—721no—
157C4D8×C3⋊D311yescharacteristic
158C3#6937714yescomplemented
159C2—161no—
160C2—161no—
161C2—181no—
162C2—1441no—
163C2C3⋊D3×D1611yescharacteristic
subgroupG/H
centerC2C3⋊D3×D16
commutator, cosocleC32×C16C23
FrattiniC16C22×C3⋊D3
FittingC32×D32C2
socleC2×C32C2×D16
hypercenterD32C3⋊D3
hypocenterC32#2263
LCSG ▷ C32×C16 ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D32

Complements

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

NH ≅ G/Ntype
1. #10592611C2semidirect
2. C3⋊D3×D16C2semidirect
3. C32×D32C2semidirect
4. #10589386C2semidirect
5. #10589385C2semidirect
6. #10589315C2semidirect
7. #10589313C2semidirect
12. C32×D16C22semidirect
15. #63628C22semidirect
18. C32×C32C22semidirect
19. C3⋊(C3⋊C32)C22semidirect
22. C3×D32D3semidirect
42. C3×D16C2×D3semidirect
48. C3×C32C2×D3semidirect
66. D32C3⋊D3semidirect
94. D16C2×C3⋊D3semidirect
97. C32C2×C3⋊D3semidirect
133. C32#2263semidirect
158. C3#69377semidirect

Maximal subgroups

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

subgroupindex
#105926112
C3⋊D3×D162
C32×D322
#105893862
#105893852
#105893152
#105893132
#693773