Finite Group Databasebeta

← #11771721

Subgroups — #11771721

Order 1152.

244 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 26 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#10592564C211yesmaximal, characteristic
2#10590184C211yesmaximal, characteristic, complemented
3#10590180C211yesmaximal, characteristic, complemented
4#64286—21no—
5C2×#3745C411yescharacteristic, complemented
6C2×#3743C2211yescharacteristic
7#64104—21no—
8#63773—21no—
9C32×#106C411yescharacteristic, complemented
10#63636—21no—
11#4865—62no—
12C2×C4⋊(C3⋊D3)—21no—
13C2×C4⋊(C3⋊D3)—41no—
14C2×C4×C3⋊D3D411yescharacteristic
15C22⋊#157—41no—
16C4⋊#157—41no—
17C4×#157—22no—
18C2×C32×C8C2×C411yescharacteristic
19C32×C4⋊C4—21no—
20#3752—41no—
21C2×C3⋊(C3⋊C8)D411yescharacteristic
22#3745—41no—
23#3743—41no—
24#3708—41no—
25#1339—91nomaximal, Sylow
26C2×D24—62no—
27C2×ΓL(1,𝔽25)—62no—
28#895—64no—
29C3×#106—22no—
30#809—64no—
31C22×C3⋊D3—41no—
32C22×C3⋊D3D811yescharacteristic
33C2×#157—42no—
34C2×C32×C4—41no—
35C2×C32×C4C22⋊C411yescharacteristic
36C2×C3⋊Dic3SD1611yescharacteristic
37C4⋊(C3⋊D3)—41no—
38C4⋊(C3⋊D3)—41no—
39C4⋊(C3⋊D3)—82no—
40C4×C3⋊D3—21no—
41C4×C3⋊D3—21no—
42C32×C8—21no—
43C3⋊(C3⋊C8)—21no—
44#469—91no—
45#349—91no—
46H(3,ℤ/4)—91no—
47C2×D12—64no—
48C2×D12—124no—
49C2×C4×D3—62no—
50C2×C3×C8—22no—
51C3×C4⋊C4—24no—
52(C2×D3)⋊C4—124no—
53C2×C3⋊C8—62no—
54D24—124no—
55ΓL(1,𝔽25)—124no—
56C22×C32#10211yescharacteristic
57C2×C3⋊D3—21no—
58C2×C3⋊D3—41no—
59C2×C3⋊D3—81no—
60C2×C3⋊D3—81no—
61C2×C3⋊D3—81no—
62#157—82no—
63C32×C4—81no—
64C32×C4#9911yescharacteristic
65C32×C4#10411yescharacteristic
66C3⋊Dic3—21no—
67C2×D8—91no—
68C2×M16—91no—
69#121—181no—
70#117—181no—
71M32—181no—
72#106#15711yescharacteristic, complemented
73#102—181no—
74C22×D3—62no—
75C22×D3—124no—
76C2×C3×C4—22no—
77C2×C3×C4—44no—
78C2×Dic3—62no—
79D12—124no—
80D12—124no—
81D12—248no—
82C4×D3—122no—
83C4×D3—122no—
84C3×C8—24no—
85C3⋊C8—122no—
86C2×C32—21no—
87C2×C32#32711yescharacteristic
88C3⋊D3—41no—
89C3⋊D3—161no—
90C2×D4—181no—
91C2×D4—361no—
92C22×C4—91no—
93D8—361no—
94M16—361no—
95C2×C8—91no—
96C2×C8C2×#15711yescharacteristic
97C4⋊C4—21no—
98C4⋊C4—361no—
99C22⋊C4—361no—
100C22⋊C4—361no—
101C42—182no—
102C16—361no—
103C22×C3—22no—
104C2×D3—122no—
105C2×D3—124no—
106C2×D3—244no—
107C2×D3—244no—
108C2×D3—244no—
109C3×C4—22no—
110C3×C4—22no—
111C3×C4—84no—
112Dic3—122no—
113C32#133911yescharacteristic, complemented, Sylow
114C23—91no—
115C23—361no—
116D4—361no—
117D4—361no—
118D4—722no—
119C2×C4—41no—
120C2×C4—91no—
121C2×C4—181no—
122C2×C4—181no—
123C2×C4—362no—
124C2×C4C22⋊#15711yescharacteristic
125C8—21no—
126C8—181no—
127C2×C3—24no—
128C2×C3—22no—
129D3—242no—
130D3—484no—
131C22—181no—
132C22—361no—
133C22—721no—
134C22—721no—
135C22—721no—
136C22#6378211yescharacteristic
137C4—81no—
138C4—181no—
139C4—722no—
140C4#6377411yescharacteristic
141C4#6378511yescharacteristic
142C3—22no—
143C2—21no—
144C2—361no—
145C2—1441no—
146C2#1059015711yescharacteristic
subgroupG/H
centerC2#10590157
commutatorC2×C32×C8C2×C4
FrattiniC2×C8C2×#157
FittingC32×#106C4
socleC2×C32#327
prime radical#10592564C2
cosocleC2×#3743C22
hypercenter#106#157
hypocenterC32#1339
LCSG ▷ C2×C32×C8 ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10590184C2semidirect
3. #10590180C2semidirect
5. C2×#3745C4semidirect
9. C32×#106C4semidirect
72. #106#157semidirect
113. C32#1339semidirect

Maximal subgroups

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

subgroupindex
#105925642
#105901842
#105901802
#13399