Finite Group Databasebeta

← #11772083

Subgroups — #11772083

Order 1152.

220 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 34 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#10592882C211yesmaximal, characteristic
2#10590177C211yesmaximal, characteristic
3#10590173C211yesmaximal, characteristic
4C2×C32×Q16C411yescharacteristic
5#64153—21no—
6C2×#3756—21no—
7C2×#3746C411yescharacteristic
8C4⋊#622—21no—
9C2×#3708—21no—
10C8×C3⋊Dic3C2211yescharacteristic
11#5183—62no—
12C2×C32×Q8—21no—
13C2×#634—21no—
14C2×#622—41no—
15C32×Q16—41no—
16C2×C32×C8C2×C411yescharacteristic
17#3756—41no—
18#3756—41no—
19#3750—41no—
20#3750—41no—
21C4×C3⋊Dic3D411yescharacteristic
22C2×C3⋊(C3⋊C8)D411yescharacteristic
23#3746—41no—
24#3708—41no—
25#1362—91nomaximal, Sylow
26C2×C3×Q16—22no—
27#944—64no—
28C2×#216—64no—
29C2×Dic12—62no—
30C8×Dic3—62no—
31C32×Q8—41no—
32C32×Q8—41no—
33C2×C32×C4—41no—
34C2×C32×C4C22⋊C411yescharacteristic
35C2×C3⋊Dic3—41no—
36C2×C3⋊Dic3D811yescharacteristic
37C2×C3⋊Dic3SD1611yescharacteristic
38#634—41no—
39#634—41no—
40#622—81no—
41C32×C8—21no—
42C3⋊(C3⋊C8)D811yescharacteristic
43C3⋊(C3⋊C8)SD1611yescharacteristic
44#494—91no—
45C4⋊C16—91no—
46#335—91no—
47C2×C3×Q8—24no—
48C2×Dic6—64no—
49C3×Q16—44no—
50C2×C3×C8—22no—
51#216—124no—
52#216—124no—
53Dic3⋊C4—124no—
54Dic3⋊C4—124no—
55C4×Dic3—62no—
56C2×C3⋊C8—62no—
57Dic12—124no—
58C22×C32#10211yescharacteristic
59C32×C4—81no—
60C32×C4#10011yescharacteristic
61C32×C4#10211yescharacteristic
62C3⋊Dic3—21no—
63C3⋊Dic3—81no—
64C3⋊Dic3SD3211yescharacteristic
65C3⋊Dic3Q3211yescharacteristic
66C2×Q16—91no—
67C2×Q16—181no—
68C2×Q16#15711yescharacteristic
69C4⋊Q8—181no—
70C2×C16—181no—
71C4⋊C8—181no—
72C4×C8—91no—
73C3×Q8—44no—
74C3×Q8—44no—
75C2×C3×C4—22no—
76C2×C3×C4—44no—
77C2×Dic3—62no—
78C2×Dic3—62no—
79C2×Dic3—124no—
80Dic6—124no—
81Dic6—124no—
82C3×C8—24no—
83C3⋊C8—62no—
84C3⋊C8—62no—
85C2×C32#33111yescharacteristic
86C2×C32#35811yescharacteristic
87C2×C32#36211yescharacteristic
88C2×Q8—21no—
89C2×Q8—181no—
90Q16—41no—
91Q16—361no—
92Q16—361no—
93Q16—361no—
94C2×C8—91no—
95C2×C8—361no—
96C2×C8C2×#15711yescharacteristic
97C4⋊C4—361no—
98C4⋊C4—361no—
99C42—91no—
100C16—361no—
101C22×C3—22no—
102C3×C4—22no—
103C3×C4—22no—
104C3×C4—84no—
105Dic3—62no—
106Dic3—62no—
107Dic3—64no—
108Dic3—244no—
109C32#136211yescharacteristic, complemented, Sylow
110Q8—41no—
111Q8—41no—
112Q8—361no—
113Q8—361no—
114C2×C4—41no—
115C2×C4—91no—
116C2×C4—91no—
117C2×C4—361no—
118C2×C4C22⋊#15711yescharacteristic
119C8—21no—
120C8—91no—
121C8—91no—
122C8—721no—
123C2×C3—22no—
124C2×C3—22no—
125C2×C3—22no—
126C22#6378211yescharacteristic
127C4—81no—
128C4—91no—
129C4—91no—
130C4—181no—
131C4—721no—
132C4#6378211yescharacteristic
133C4#6378811yescharacteristic
134C3—22no—
135C2#1059019711yescharacteristic
136C2#1059019911yescharacteristic
137C2#1059021411yescharacteristic
subgroupG/H
centerC22#63782
commutatorC2×C32×C8C2×C4
FrattiniC2×C8C2×#157
FittingC2×C32×Q16C4
socle, prime radicalC22×C32#102
cosocleC8×C3⋊Dic3C22
hypercenterC2×Q16#157
hypocenterC32#1362
LCSG ▷ C2×C32×C8 ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
109. C32#1362semidirect

Maximal subgroups

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

subgroupindex
#105928822
#105901772
#105901732
#13629