Finite Group Databasebeta

← #11799709

Subgroups — #11799709

Order 1152.

378 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 115 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#10592399C211yesmaximal, characteristic
2#10592379C211yesmaximal, characteristic, complemented
3C32×#364C211yesmaximal, characteristic, complemented
4#10589384C212yesmaximal
5#10589379C212yesmaximal, complemented
6#69307—34nomaximal
7#64113C2211yescharacteristic
8#64110—21no—
9#64078—21no—
10C32×M32C2212yes—
11C32×C4×C8C2211yescharacteristic
12#63646C2211yescharacteristic
13#63644—21no—
14#63644C2212yes—
15#63632—21no—
16#4700—34no—
17#4680—34no—
18C3×#364D314yescomplemented
19#4518—38no—
20#4513—38no—
21#3828—21no—
22C2×#634—41no—
23C2×C32×C8D411yescharacteristic
24C2×C32×C8C2311yescharacteristic
25C32×C42D411yescharacteristic
26C4⋊(C3⋊Dic3)—22no—
27C4⋊(C3⋊Dic3)—41no—
28#3748—21no—
29#3746Q811yescharacteristic, complemented
30#3745Q811yescharacteristic, complemented
31#3744—21no—
32#3743—41no—
33C8×C3⋊D3—41no—
34C32×C16—22no—
35#2230—91noSylow
36#904—34no—
37#901—64no—
38#869—64no—
39C3×M32C2×D318yes—
40C3×C4×C8C2×D314yes—
41#819—34no—
42#817—38no—
43#817—64no—
44#805—64no—
45C2×C32×C4—21no—
46C2×C32×C4C2×D411yescharacteristic
47#638—41no—
48C2×C3⋊Dic3—42no—
49C4⋊(C3⋊D3)—21no—
50C4×C3⋊D3—41no—
51#634—21no—
52#634—82no—
53C32×C8SD1611yescharacteristic
54C32×C8SD1611yescharacteristic
55C32×C8C2×Q811yescharacteristic
56C32×C8#4111yescharacteristic
57C3⋊(C3⋊C8)—41no—
58#498—91no—
59#443—91no—
60#365—92no—
61#364C3⋊D311yescharacteristic, complemented
62#360—92no—
63#235—64no—
64C2×Dic6—124no—
65C2×C3×C8D1214yes—
66C2×C3×C8C22×D314yes—
67C3×C42D1214yes—
68C4⋊Dic3—68no—
69C4⋊Dic3—124no—
70#208—64no—
71Dic12—34no—
72D24—34no—
73#204—64no—
74ΓL(1,𝔽25)—124no—
75D3×C8—124no—
76C3×C16—28no—
77C22×C32AGL(1,ℤ/8)11yescharacteristic
78C2×C3⋊D3—41no—
79C32×C4—22no—
80C32×C4C22⋊Q811yescharacteristic
81C32×C4C2×SD1611yescharacteristic
82C3⋊Dic3—41no—
83C3⋊Dic3—82no—
84#135—91no—
85#131—181no—
86C4⋊Q8—181no—
87M32C2×C3⋊D312yes—
88#108—91no—
89#106—92no—
90#106—181no—
91#104—181no—
92C4×C8C2×C3⋊D311yescharacteristic
93C2×C3×C4—24no—
94C2×C3×C4C2×D1214yes—
95#67—124no—
96C2×Dic3—128no—
97D12—64no—
98C4×D3—124no—
99Dic6—64no—
100Dic6—248no—
101C3×C8#20414yes—
102C3×C8#20414yes—
103C3×C8#23714yes—
104C3×C8D3×Q814yes—
105C3⋊C8—124no—
106C2×C32—21no—
107C2×C32#47611yescharacteristic
108C3⋊D3—81no—
109#41—181no—
110C2×Q8—361no—
111Q16—91no—
112SD16—181no—
113D8—91no—
114M16—181no—
115M16—361no—
116C2×C8—361no—
117C2×C8C4⋊(C3⋊D3)11yescharacteristic
118C2×C8C22×C3⋊D311yescharacteristic
119C4⋊C4—182no—
120C4⋊C4—361no—
121C42C4⋊(C3⋊D3)11yescharacteristic
122C16—22no—
123C22×C3#90814yes—
124C2×D3—124no—
125C3×C4—28no—
126C3×C4#89714yes—
127C3×C4C2×#20414yes—
128Dic3—124no—
129Dic3—248no—
130C32#223011yescharacteristic, complemented, Sylow
131Q8—181no—
132Q8—722no—
133D4—181no—
134D4—361no—
135C2×C4—21no—
136C2×C4—361no—
137C2×C4—362no—
138C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
139C8—361no—
140C8#374411yescharacteristic
141C8#374411yescharacteristic
142C8#383011yescharacteristic
143C8Q8×C3⋊D311yescharacteristic
144C2×C3—24no—
145C2×C3#484214yes—
146D3—244no—
147C22—361no—
148C22#6411711yescharacteristic
149C4—22no—
150C4—361no—
151C4—722no—
152C4#6410611yescharacteristic
153C4C2×#374411yescharacteristic
154C3#6930714yescomplemented
155C2—21no—
156C2—721no—
157C2#1059254111yescharacteristic
subgroupG/H
centerC2#10592541
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#364C2
socleC2×C32#476
prime radical#64113C22
hypercenter#364C3⋊D3
hypocenterC32#2230
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #364

Complements

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

NH ≅ G/Ntype
2. #10592379C2semidirect
3. C32×#364C2semidirect
5. #10589379C2semidirect
18. C3×#364D3semidirect
29. #3746Q8semidirect
30. #3745Q8semidirect
61. #364C3⋊D3semidirect
130. C32#2230semidirect
154. C3#69307semidirect

Maximal subgroups

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

subgroupindex
#105923992
#105923792
C32×#3642
#105893842
#105893792
#693073