Finite Group Databasebeta

← #11771522

Subgroups — #11771522

Order 1152.

237 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 237 conjugacy classes of subgroups — too many to draw. Only its 58 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#10592818C211yesmaximal, characteristic
2C3×#4553C212yesmaximal
3#67533—32nomaximal
4C2×C32×M16C2211yescharacteristic
5#64135C411yescharacteristic
6C22×C3⋊(C3⋊C8)C411yescharacteristic
7#63641—22no—
8C3×#812—22no—
9#5119—32no—
10#5119—61no—
11C3×#349—32no—
12#4553D312yes—
13C22×C32×C4C2×C411yescharacteristic
14C32×M16—41no—
15C2×C32×C8D412yes—
16#3757C812yes—
17C4⋊(C3⋊Dic3)—21no—
18C4×C3⋊Dic3—21no—
19C2×C3⋊(C3⋊C8)—21no—
20C2×C3⋊(C3⋊C8)—41no—
21C3×C3⋊C16—42no—
22#1328—91noSylow
23C2×C3×M16—21no—
24C2×C3×M16C2×D312yes—
25#926—32no—
26#926—61no—
27C22×C3⋊C8—32no—
28C22×C3⋊C8—61no—
29C3×M32—62no—
30Dic3⋊C8—64no—
31Dic3⋊C8—62no—
32Dic3⋊C8—62no—
33#812—22no—
34C23×C32C2×C811yescharacteristic
35C2×C32×C4—21no—
36C2×C32×C4—21no—
37C2×C32×C4C22⋊C411yescharacteristic
38C2×C32×C4M1611yescharacteristic
39C2×C3⋊Dic3—22no—
40C32×C8—22no—
41C3⋊(C3⋊C8)—41no—
42#424—91no—
43#349—32no—
44C22×C3×C4—21no—
45C22×C3×C4C4×D312yes—
46C3×M16—42no—
47C3×M16—42no—
48C2×C3×C8—22no—
49C2×C3×C8D1212yes—
50C2×C3×C8#6712yes—
51#217—34no—
52#217—62no—
53C4⋊Dic3—62no—
54C4⋊Dic3—62no—
55C4×Dic3—62no—
56C4×Dic3—62no—
57C2×C3⋊C8—62no—
58C2×C3⋊C8—62no—
59C2×C3⋊C8—122no—
60C2×C3⋊C8—122no—
61C3×C16—122no—
62C3⋊C16—42no—
63C22×C32—21no—
64C22×C32—41no—
65C22×C32C22⋊C811yescharacteristic
66C32×C4—21no—
67C32×C4#9911yescharacteristic
68C32×C4#10111yescharacteristic
69C3⋊Dic3—42no—
70C2×M16D3211yescharacteristic
71C22×C8—91no—
72#117—91no—
73M32—62no—
74C4⋊C8—182no—
75C23×C3—21no—
76C23×C3D3×C812yes—
77C2×C3×C4—22no—
78C2×C3×C4—22no—
79C2×C3×C4—22no—
80C2×C3×C4—22no—
81C2×C3×C4—21no—
82C2×C3×C4—21no—
83C2×C3×C4ΓL(1,𝔽25)12yes—
84C2×C3×C4(C2×D3)⋊C412yes—
85C2×Dic3—64no—
86C2×Dic3—64no—
87C3×C8—22no—
88C3×C8—22no—
89C3×C8—42no—
90C3⋊C8—122no—
91C3⋊C8—122no—
92C2×C32—21no—
93C2×C32—41no—
94C2×C32#32411yescharacteristic
95C22×C4#62411yescharacteristic
96M16—41no—
97C2×C8—181no—
98C2×C8—361no—
99C2×C8#62612yes—
100C4⋊C4—181no—
101C22⋊C4—92no—
102C42—181no—
103C16—122no—
104C22×C3—22no—
105C22×C3—22no—
106C22×C3—21no—
107C22×C3—42no—
108C22×C3—42no—
109C22×C3(C2×D3)⋊C812yes—
110C3×C4—22no—
111C3×C4—22no—
112C3×C4—21no—
113C3×C4—21no—
114C3×C4#80612yes—
115C3×C4#82412yes—
116Dic3—124no—
117Dic3—124no—
118C32#132811yescharacteristic, complemented, Sylow
119C23#371011yescharacteristic
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—182no—
123C2×C4#371211yescharacteristic
124C2×C4#372211yescharacteristic
125C8—22no—
126C8—361no—
127C2×C3—22no—
128C2×C3—22no—
129C2×C3—21no—
130C2×C3—42no—
131C2×C3—42no—
132C2×C3#446912yes—
133C22—21no—
134C22—41no—
135C22#6355711yescharacteristic
136C4—21no—
137C4—362no—
138C4#6356111yescharacteristic
139C4#6358111yescharacteristic
140C3—21no—
141C3#6753312yescomplemented
142C2—21no—
143C2—41no—
144C2#1058914811yescharacteristic
subgroupG/H
centerC4#63581
commutator, prime radicalC23×C32C2×C8
Frattini, hypercenterC2×M16D32
Fitting, cosocleC2×C32×M16C22
socleC2×C32#324
hypocenterC32#1328
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
118. C32#1328semidirect
141. C3#67533semidirect

Maximal subgroups

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

subgroupindex
#105928182
C3×#45532
#675333