Finite Group Databasebeta

← #11771114

Subgroups — #11771114

Order 1152.

392 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 45 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#10593802C211yesmaximal, characteristic
2#10591152C212yesmaximal
3C22×C4×C3⋊D3C2211yescharacteristic
4C2×#3792C412yes—
5C2×#3710—22no—
6#63778—22no—
7C3×#830—22no—
8#63557C414yes—
9D3×C22⋊C8—62no—
10C23×C3⋊D3Q811yescharacteristic
11C22×C32×C4D411yescharacteristic
12C22×C3⋊Dic3C2×C411yescharacteristic
13C2×C4×C3⋊D3—42no—
14C2×C4×C3⋊D3C2×C412yes—
15C2×C4×C3⋊D3D412yes—
16#3792—42no—
17C2×#622—22no—
18C2×C3×C3⋊C8—24no—
19#3710—44no—
20#1298—91nomaximal, Sylow
21C22×C4×D3—62no—
22C2×D3×C8—64no—
23C3×C22⋊C8—62no—
24#830—22no—
25(C2×D3)⋊C8—64no—
26C23×C32C4⋊C411yescharacteristic
27C22×C3⋊D3—24no—
28C22×C3⋊D3—41no—
29C22×C3⋊D3C4⋊C412yes—
30C2×C32×C4—41no—
31C2×C32×C4C22⋊C412yes—
32C2×C3⋊Dic3—22no—
33C2×C3⋊Dic3C4211yescharacteristic
34C2×C3⋊Dic3C22⋊C411yescharacteristic
35C4×C3⋊D3—24no—
36C4×C3⋊D3—42no—
37#622—42no—
38C3×C3⋊C8—44no—
39#407—91no—
40C2×C22⋊C8—92no—
41C23×D3—62no—
42C22×C3×C4—22no—
43C22×Dic3—62no—
44C2×C4×D3—62no—
45C2×C4×D3—62no—
46C2×C4×D3—62no—
47C2×C4×D3—62no—
48C2×C4×D3—128no—
49C2×C3×C8—64no—
50C2×C3⋊C8—24no—
51D3×C8—128no—
52C22×C32—22no—
53C22×C32—21no—
54C22×C32#9511yescharacteristic
55C2×C3⋊D3—22no—
56C2×C3⋊D3—22no—
57C2×C3⋊D3—44no—
58C2×C3⋊D3#10814yes—
59C32×C4—22no—
60C3⋊Dic3—21no—
61C3⋊Dic3#9912yes—
62C23×C4—91no—
63C2×M16—92no—
64C22×C8—182no—
65C22⋊C8—62no—
66C22⋊C8—94no—
67C22⋊C8—182no—
68C23×C3—22no—
69C22×D3—62no—
70C22×D3—62no—
71C22×D3—68no—
72C22×D3—124no—
73C22×D3—124no—
74C2×C3×C4—22no—
75C2×C3×C4—22no—
76C2×C3×C4—44no—
77C2×Dic3—62no—
78C2×Dic3—62no—
79C2×Dic3—124no—
80C4×D3—68no—
81C4×D3—124no—
82C4×D3—124no—
83C4×D3—124no—
84C3×C8—124no—
85C3⋊C8—44no—
86C2×C32—41no—
87C2×C32#34112yes—
88C2×C32#34211yescharacteristic
89C3⋊D3—24no—
90C24—91no—
91C22×C4—91no—
92C22×C4—92no—
93C22×C4—92no—
94C22×C4—362no—
95C22×C4GO+(4,𝔽2)11yescharacteristic
96M16—362no—
97C2×C8—64no—
98C2×C8—182no—
99C2×C8—364no—
100C22×C3—24no—
101C22×C3—22no—
102C22×C3—42no—
103C22×C3—42no—
104C2×D3—64no—
105C2×D3—64no—
106C2×D3—64no—
107C2×D3—64no—
108C2×D3—122no—
109C2×D3—122no—
110C2×D3—1216no—
111C3×C4—24no—
112C3×C4—42no—
113Dic3—64no—
114Dic3—122no—
115C32#129811yescharacteristic, complemented, Sylow
116C23—92no—
117C23—184no—
118C23—361no—
119C23#377311yescharacteristic
120C2×C4—41no—
121C2×C4—91no—
122C2×C4—91no—
123C2×C4—184no—
124C2×C4—182no—
125C2×C4—362no—
126C2×C4D32⋊C412yes—
127C8—124no—
128C8—362no—
129C2×C3—22no—
130C2×C3—22no—
131C2×C3—22no—
132C2×C3—44no—
133D3—68no—
134D3—124no—
135C22—22no—
136C22—21no—
137C22—94no—
138C22—182no—
139C22—182no—
140C22—364no—
141C22#6373711yescharacteristic
142C4—22no—
143C4—92no—
144C4—181no—
145C3—22no—
146C2—41no—
147C2—184no—
148C2#1059005012yes—
149C2#1059007711yescharacteristic
subgroupG/H
centerC22#63737
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#95
prime radicalC23×C3⋊D3Q8
cosocleC22×C4×C3⋊D3C22
hypocenterC32#1298
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
115. C32#1298semidirect

Maximal subgroups

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

subgroupindex
#105938022
#105911522
#12989