Finite Group Databasebeta

← #11771279

Subgroups — #11771279

Order 1152.

272 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 49 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#10593728C211yesmaximal, characteristic
2#10590340C212yesmaximal
3C2×#3788C412yes—
4C42×C3⋊D3C2211yescharacteristic
5C2×#3712C414yes—
6C4⋊#622—22no—
7C3×C4⋊(C3⋊C8)—22no—
8#63572—22no—
9#4837—62no—
10C2×C4×C3⋊D3C2×C411yescharacteristic
11C2×C4×C3⋊D3C2×C412yes—
12C2×#622—22no—
13#3788—42no—
14C32×C42D411yescharacteristic
15C4×C3⋊Dic3D412yes—
16C4×C3⋊Dic3Q811yescharacteristic
17C2×C3×C3⋊C8—24no—
18#3712—44no—
19#1309—91nomaximal, Sylow
20C2×ΓL(1,𝔽25)—64no—
21C42×D3—62no—
22C3×C4⋊C8—62no—
23Dic3⋊C8—64no—
24C4⋊(C3⋊C8)—22no—
25C22×C3⋊D3C4211yescharacteristic
26C2×C32×C4C22⋊C412yes—
27C2×C32×C4C4⋊C411yescharacteristic
28C2×C3⋊Dic3C22⋊C411yescharacteristic
29C2×C3⋊Dic3C4⋊C412yes—
30C4×C3⋊D3—22no—
31C4×C3⋊D3—22no—
32C4×C3⋊D3—21no—
33C4×C3⋊D3—21no—
34#622—42no—
35C3×C3⋊C8—44no—
36#423—92no—
37#423—91no—
38C2×C4×D3—62no—
39C2×C4×D3—62no—
40C2×C4×D3—62no—
41C2×C3×C8—64no—
42C3×C42—22no—
43C4×Dic3—62no—
44C4×Dic3—62no—
45C4×Dic3—62no—
46C2×C3⋊C8—24no—
47ΓL(1,𝔽25)—128no—
48C22×C32#9511yescharacteristic
49C2×C3⋊D3—22no—
50C2×C3⋊D3—21no—
51C32×C4—21no—
52C32×C4#10012yes—
53C32×C4#10112yes—
54C3⋊Dic3—22no—
55C3⋊Dic3#10011yescharacteristic
56C3⋊Dic3#10111yescharacteristic
57C2×M16—94no—
58C2×M16—92no—
59C2×C42—91no—
60C4⋊C8—62no—
61C4⋊C8—182no—
62C4⋊C8—182no—
63C22×D3—62no—
64C2×C3×C4—22no—
65C2×C3×C4—22no—
66C2×C3×C4—22no—
67C2×Dic3—62no—
68C2×Dic3—62no—
69C2×Dic3—62no—
70C4×D3—64no—
71C4×D3—64no—
72C4×D3—122no—
73C4×D3—122no—
74C4×D3—122no—
75C4×D3—122no—
76C3×C8—124no—
77C3⋊C8—44no—
78C2×C32#34312yes—
79C2×C32#34311yescharacteristic
80C3⋊D3—41no—
81C22×C4—92no—
82C22×C4—91no—
83M16—364no—
84M16—362no—
85C2×C8—64no—
86C2×C8—182no—
87C42—92no—
88C42—91no—
89C42GO+(4,𝔽2)11yescharacteristic
90C22×C3—22no—
91C2×D3—64no—
92C2×D3—122no—
93C2×D3—122no—
94C3×C4—22no—
95C3×C4—22no—
96C3×C4—22no—
97C3×C4—22no—
98C3×C4—42no—
99Dic3—62no—
100Dic3—62no—
101Dic3—64no—
102Dic3—122no—
103C32#130911yescharacteristic, complemented, Sylow
104C23—91no—
105C2×C4—91no—
106C2×C4—92no—
107C2×C4—181no—
108C2×C4—181no—
109C2×C4—182no—
110C2×C4—182no—
111C2×C4D32⋊C412yes—
112C2×C4#377311yescharacteristic
113C8—124no—
114C8—362no—
115C2×C3—22no—
116C2×C3—22no—
117C2×C3—22no—
118D3—124no—
119C22—182no—
120C22—181no—
121C22#6373711yescharacteristic
122C4—21no—
123C4—91no—
124C4—91no—
125C4—182no—
126C4#6372712yes—
127C4#6372812yes—
128C3—22no—
129C2—361no—
130C2#1059005212yes—
131C2#1059005311yescharacteristic
subgroupG/H
centerC22#63737
commutator, prime radicalC22×C3⋊D3C42
Frattini, hypercenterC42GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32#95
cosocleC42×C3⋊D3C22
hypocenterC32#1309
LCSG ▷ C22×C3⋊D3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
103. C32#1309semidirect

Maximal subgroups

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

subgroupindex
#105937282
#105903402
#13099