Finite Group Databasebeta

← #11771645

Subgroups — #11771645

Order 1152.

206 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 32 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#10592594C211yesmaximal, characteristic
2#10590178C211yesmaximal, characteristic, complemented
3C8×#622C211yesmaximal, characteristic, complemented
4#64116—21no—
5#64113C411yescharacteristic
6C4×#622—21no—
7#63773—21no—
8C32×#108C411yescharacteristic
9#63652—21no—
10C8×C3⋊Dic3C2211yescharacteristic
11#4895—62no—
12#3828—21no—
13C2×#622—22no—
14C32×M16—21no—
15C2×C32×C8C2×C411yescharacteristic
16C4×C3⋊Dic3D411yescharacteristic
17C2×C3⋊(C3⋊C8)D411yescharacteristic
18#3746C811yescharacteristic, complemented
19#3745C811yescharacteristic, complemented
20#3744—21no—
21#3743—41no—
22C8×C3⋊D3—41no—
23#3708—41no—
24#1335—91nomaximal, Sylow
25#907—64no—
26#904—62no—
27C3×#108—22no—
28#825—64no—
29C8×Dic3—62no—
30C2×C32×C4C22⋊C411yescharacteristic
31#638—41no—
32C2×C3⋊Dic3—21no—
33C4⋊(C3⋊D3)—21no—
34C4×C3⋊D3—41no—
35#634—21no—
36#622—24no—
37C32×C8—41no—
38C32×C8C2×C811yescharacteristic
39C32×C8M1611yescharacteristic
40C3⋊(C3⋊C8)D811yescharacteristic
41C3⋊(C3⋊C8)SD1611yescharacteristic
42#443—91no—
43#364—91no—
44C82—91no—
45#235—64no—
46C3×M16—24no—
47C2×C3×C8—22no—
48C4×Dic3—62no—
49C2×C3⋊C8—62no—
50Dic12—62no—
51D24—62no—
52#204—64no—
53ΓL(1,𝔽25)—124no—
54D3×C8—124no—
55C22×C32#10411yescharacteristic
56C2×C3⋊D3—41no—
57C32×C4C22⋊C811yescharacteristic
58C32×C4#10211yescharacteristic
59C3⋊Dic3—22no—
60C3⋊Dic3—41no—
61#135—91no—
62#131—181no—
63M32—181no—
64#108#15711yescharacteristic
65#104—181no—
66C4×C8—91no—
67C4×C8—181no—
68C2×C3×C4—22no—
69#67—124no—
70C2×Dic3—122no—
71D12—64no—
72C4×D3—124no—
73Dic6—64no—
74C3×C8—22no—
75C3×C8—22no—
76C3×C8—44no—
77C3⋊C8—62no—
78C3⋊C8—62no—
79C2×C32—21no—
80C2×C32D4⋊C811yescharacteristic
81C3⋊D3—81no—
82#41—181no—
83Q16—91no—
84SD16—181no—
85D8—91no—
86M16—21no—
87M16—361no—
88C2×C8—91no—
89C2×C8—182no—
90C2×C8—361no—
91C2×C8C2×#15711yescharacteristic
92C42—91no—
93C16—361no—
94C22×C3—22no—
95C2×D3—124no—
96C3×C4—22no—
97C3×C4—22no—
98Dic3—124no—
99Dic3—124no—
100C32#133511yescharacteristic, complemented, Sylow
101Q8—181no—
102D4—181no—
103D4—361no—
104C2×C4—181no—
105C2×C4—361no—
106C2×C4C22⋊#15711yescharacteristic
107C8—41no—
108C8—91no—
109C8—91no—
110C8—184no—
111C8#378711yescharacteristic
112C8#378811yescharacteristic
113C2×C3—22no—
114C2×C3—42no—
115D3—244no—
116C22—361no—
117C22#6378511yescharacteristic
118C4—182no—
119C4—361no—
120C4#6377811yescharacteristic
121C4#6378211yescharacteristic
122C3—22no—
123C2—21no—
124C2—721no—
125C2#1059016011yescharacteristic
subgroupG/H
centerC4#63782
commutatorC32×C8C2×C8
FrattiniC2×C8C2×#157
FittingC32×#108C4
socleC2×C32D4⋊C8
prime radical#64113C4
cosocleC8×C3⋊Dic3C22
hypercenter#108#157
hypocenterC32#1335
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
2. #10590178C2semidirect
3. C8×#622C2semidirect
18. #3746C8semidirect
19. #3745C8semidirect
100. C32#1335semidirect

Maximal subgroups

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

subgroupindex
#105925942
#105901782
C8×#6222
#13359