Finite Group Databasebeta

← #11771591

Subgroups — #11771591

Order 1152.

208 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 38 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#10592572C211yesmaximal, characteristic
2#10590174C211yesmaximal, characteristic
3#10590171C211yesmaximal, characteristic
4C2×#3746C411yescharacteristic
5#64096—21no—
6C4⋊#622—21no—
7C2×#3708—21no—
8C32×#107C411yescharacteristic
9C8×C3⋊Dic3C2211yescharacteristic
10#63637—21no—
11#4873—62no—
12C2×#634—21no—
13C2×#622—41no—
14C2×C32×C8C2×C411yescharacteristic
15C32×C4⋊C4—21no—
16#3750—41no—
17C4×C3⋊Dic3—41no—
18C4×C3⋊Dic3D411yescharacteristic
19C2×C3⋊(C3⋊C8)D411yescharacteristic
20#3746—21no—
21#3746C812yescomplemented
22#3708—22no—
23#1332—91nomaximal, Sylow
24C2×Dic12—62no—
25#887—64no—
26C3×#107—22no—
27C8×Dic3—62no—
28#810—64no—
29C2×C32×C4—41no—
30C2×C32×C4C22⋊C411yescharacteristic
31C2×C3⋊Dic3—41no—
32C2×C3⋊Dic3D811yescharacteristic
33C2×C3⋊Dic3SD1611yescharacteristic
34#634—22no—
35#634—41no—
36#622—81no—
37C32×C8C2×C811yescharacteristic
38C32×C8M1611yescharacteristic
39C3⋊(C3⋊C8)—21no—
40C4×Q16—91no—
41C4×C16—91no—
42#335—91no—
43C2×Dic6—64no—
44C2×C3×C8—22no—
45C3×C4⋊C4—24no—
46Dic3⋊C4—124no—
47C4×Dic3—62no—
48C4×Dic3—124no—
49C2×C3⋊C8—62no—
50Dic12—64no—
51Dic12—64no—
52C22×C32#10211yescharacteristic
53C32×C4—81no—
54C32×C4C22⋊C811yescharacteristic
55C32×C4#10411yescharacteristic
56C3⋊Dic3—21no—
57C3⋊Dic3—42no—
58C3⋊Dic3SD3211yescharacteristic
59C3⋊Dic3Q3211yescharacteristic
60C2×Q16—91no—
61C4×Q8—181no—
62C2×C16—181no—
63#107#15711yescharacteristic
64C4⋊C8—181no—
65#103—181no—
66C4×C8—91no—
67C2×C3×C4—22no—
68C2×C3×C4—44no—
69C2×Dic3—62no—
70C2×Dic3—62no—
71C2×Dic3—124no—
72Dic6—68no—
73Dic6—124no—
74C3×C8—22no—
75C3×C8—22no—
76C3⋊C8—122no—
77C2×C32D4⋊C811yescharacteristic
78C2×C32#35811yescharacteristic
79C2×C32#35911yescharacteristic
80C2×Q8—181no—
81Q16—92no—
82Q16—181no—
83C2×C8—91no—
84C2×C8—361no—
85C2×C8C2×#15711yescharacteristic
86C4⋊C4—21no—
87C4⋊C4—361no—
88C42—91no—
89C42—361no—
90C16—182no—
91C22×C3—22no—
92C3×C4—22no—
93C3×C4—22no—
94C3×C4—84no—
95Dic3—62no—
96Dic3—62no—
97Dic3—122no—
98Dic3—128no—
99C32#133211yescharacteristic, complemented, Sylow
100Q8—182no—
101Q8—361no—
102C2×C4—41no—
103C2×C4—91no—
104C2×C4—91no—
105C2×C4—361no—
106C2×C4C22⋊#15711yescharacteristic
107C8—181no—
108C8—721no—
109C8#378711yescharacteristic
110C8#378811yescharacteristic
111C2×C3—22no—
112C2×C3—22no—
113C2×C3—22no—
114C22#6378211yescharacteristic
115C4—81no—
116C4—91no—
117C4—91no—
118C4—181no—
119C4—362no—
120C4#6377811yescharacteristic
121C4#6378511yescharacteristic
122C3—22no—
123C2#1059016011yescharacteristic
124C2#1059019411yescharacteristic
125C2#1059019711yescharacteristic
subgroupG/H
centerC22#63782
commutatorC32×C8C2×C8
FrattiniC2×C8C2×#157
FittingC32×#107C4
socle, prime radicalC22×C32#102
cosocleC8×C3⋊Dic3C22
hypercenter#107#157
hypocenterC32#1332
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
21. #3746C8semidirect
99. C32#1332semidirect

Maximal subgroups

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

subgroupindex
#105925722
#105901742
#105901712
#13329