Finite Group Databasebeta

← #11772034

Subgroups — #11772034

Order 1152.

244 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 28 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#10592784C211yesmaximal, characteristic
2#10590150C212yesmaximal, complemented
3C32×C4⋊Q8C411yescharacteristic
4C2×#3755—22no—
5#64083C411yescharacteristic
6#63773—22no—
7C4×C3⋊(C3⋊C8)C2211yescharacteristic
8#5085—62no—
9C2×C32×Q8—21no—
10C2×C4⋊(C3⋊D3)—21no—
11C2×C4⋊(C3⋊D3)—41no—
12C32×C4⋊C4—41no—
13C32×C42C2×C411yescharacteristic
14#3755—42no—
15#3755—42no—
16C2×C3⋊(C3⋊C8)D412yes—
17#3708—42no—
18#1359—91nomaximal, Sylow
19C3×C4⋊Q8—22no—
20C2×#215—68no—
21#874—62no—
22C4×C3⋊C8—62no—
23C22×C3⋊D3—41no—
24C32×Q8—42no—
25C2×C32×C4—21no—
26C2×C32×C4—41no—
27C2×C32×C4C22⋊C411yescharacteristic
28C4⋊(C3⋊D3)—42no—
29C4⋊(C3⋊D3)—82no—
30C3⋊(C3⋊C8)D812yes—
31C3⋊(C3⋊C8)SD1612yes—
32#492—91no—
33#364—92no—
34C2×C3×Q8—24no—
35C2×D12—64no—
36C2×D12—124no—
37C3×C4⋊C4—44no—
38C3×C42—22no—
39#215—128no—
40#215—128no—
41C2×C3⋊C8—64no—
42C22×C32#10011yescharacteristic
43C2×C3⋊D3—82no—
44C2×C3⋊D3—81no—
45C32×C4—22no—
46C32×C4—81no—
47C32×C4#10212yes—
48C2×SD16—182no—
49C4⋊Q8#15711yescharacteristic
50#127—91no—
51M32—182no—
52C4×C8—91no—
53C22×D3—124no—
54C3×Q8—48no—
55C2×C3×C4—24no—
56C2×C3×C4—22no—
57C2×C3×C4—44no—
58D12—128no—
59D12—248no—
60C3⋊C8—64no—
61C3⋊C8—64no—
62C2×C32—21no—
63C2×C32#33111yescharacteristic
64C3⋊D3—161no—
65C2×Q8—21no—
66C2×D4—181no—
67C2×D4—361no—
68SD16—362no—
69SD16—362no—
70C2×C8—92no—
71C4⋊C4—41no—
72C42C2×#15711yescharacteristic
73C16—362no—
74C22×C3—22no—
75C2×D3—244no—
76C2×D3—248no—
77C3×C4—28no—
78C3×C4—24no—
79C3×C4—84no—
80C32#135911yescharacteristic, complemented, Sylow
81C23—361no—
82Q8—42no—
83D4—362no—
84D4—722no—
85C2×C4—21no—
86C2×C4—41no—
87C2×C4C22⋊#15711yescharacteristic
88C8—92no—
89C8—92no—
90C2×C3—24no—
91C2×C3—22no—
92D3—484no—
93C22—722no—
94C22—721no—
95C22#6378811yescharacteristic
96C4—22no—
97C4—81no—
98C4#6378212yes—
99C3—22no—
100C2—21no—
101C2—1441no—
102C2#1059021411yescharacteristic
subgroupG/H
centerC2#10590214
commutatorC32×C42C2×C4
FrattiniC42C2×#157
FittingC32×C4⋊Q8C4
socleC2×C32#331
prime radical#64083C4
cosocleC4×C3⋊(C3⋊C8)C22
hypercenterC4⋊Q8#157
hypocenterC32#1359
LCSG ▷ C32×C42 ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10590150C2semidirect
80. C32#1359semidirect

Maximal subgroups

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

subgroupindex
#105927842
#105901502
#13599