Finite Group Databasebeta

← #2863⋊C9 #11919511

Subgroups — #2863⋊C9 #11919511

Order 1152.

178 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 36 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#383⋊C9C212yesmaximal
2C4×C42⋊C9C211yesmaximal, characteristic
3C3×#2863C311yesmaximal, characteristic
4Q8×C22⋊C9—41nomaximal
5C2×C42⋊C9C2211yescharacteristic
6C3×#391—31no—
7C3×#389—31no—
8C3×#387—32no—
9C3×#383C2×C312yes—
10C3×C43C2×C311yescharacteristic
11C4×C22⋊C9—41no—
12C4×C22⋊C9—42no—
13C42⋊C9Q811yescharacteristic, complemented
14#2863C911yescharacteristic, complemented, Sylow
15C22×C3×Q8A411yescharacteristic
16C2×C3×C4⋊C4—32no—
17C2×C3×C4⋊C4—31no—
18C2×C3×C42—31no—
19C2×C3×C42—31no—
20C2×C3×C42C22×C311yescharacteristic
21C3×#95—32no—
22C3×#95—32no—
23C3×#95—32no—
24C2×C22⋊C9—41no—
25Q8×C9—161no—
26#391—31no—
27#389—31no—
28#387—32no—
29#383C2×C912yes—
30C43C2×C911yescharacteristic
31C2×C3×Q8—61no—
32C2×C3×Q8—61no—
33C22×C3×C4—31no—
34C22×C3×C4—31no—
35C22×C3×C4—32no—
36C22×C3×C4C2×A411yescharacteristic
37C22×C3×C4C2×A412yes—
38C3×C4⋊C4—61no—
39C3×C4⋊C4—61no—
40C3×C4⋊C4—64no—
41C3×C42—31no—
42C3×C42—61no—
43C3×C42—61no—
44C3×C42—62no—
45C3×C42C3×Q811yescharacteristic
46C22⋊C9—41no—
47C4×C9—162no—
48C4×C9—161no—
49C22×Q8C22⋊C911yescharacteristic
50C2×C4⋊C4—32no—
51C2×C4⋊C4—31no—
52C2×C42—31no—
53C2×C42—31no—
54C2×C42C22×C911yescharacteristic
55#95—32no—
56#95—32no—
57#95—32no—
58C23×C3C22×A411yescharacteristic
59C3×Q8—41no—
60C3×Q8—121no—
61C2×C3×C4—31no—
62C2×C3×C4—31no—
63C2×C3×C4—32no—
64C2×C3×C4—31no—
65C2×C3×C4—31no—
66C2×C3×C4—62no—
67C2×C3×C4—61no—
68C2×C3×C4—61no—
69C2×C3×C4—61no—
70C2×C3×C4—61no—
71C2×C3×C4—64no—
72C2×C3×C4—62no—
73C2×C9—161no—
74C2×Q8—61no—
75C2×Q8—61no—
76C22×C4—31no—
77C22×C4—31no—
78C22×C4—32no—
79C22×C4C2×C22⋊C911yescharacteristic
80C22×C4C2×C22⋊C912yes—
81C4⋊C4—61no—
82C4⋊C4—61no—
83C4⋊C4—64no—
84C42—31no—
85C42—61no—
86C42—61no—
87C42—62no—
88C42Q8×C911yescharacteristic, complemented
89C22×C3—31no—
90C22×C3—31no—
91C22×C3Q8×A411yescharacteristic
92C3×C4—31no—
93C3×C4—42no—
94C3×C4—62no—
95C3×C4—61no—
96C3×C4—61no—
97C3×C4—122no—
98C3×C4#126⋊C311yescharacteristic
99C9—161noSylow
100C23C22×C22⋊C911yescharacteristic
101Q8—41no—
102Q8—121no—
103C2×C4—31no—
104C2×C4—31no—
105C2×C4—32no—
106C2×C4—31no—
107C2×C4—31no—
108C2×C4—62no—
109C2×C4—61no—
110C2×C4—61no—
111C2×C4—61no—
112C2×C4—61no—
113C2×C4—64no—
114C2×C4—62no—
115C2×C3—31no—
116C2×C3—31no—
117C2×C3C2×#126⋊C311yescharacteristic
118C22—31no—
119C22—31no—
120C22Q8×C22⋊C911yescharacteristic
121C4—31no—
122C4—42no—
123C4—62no—
124C4—61no—
125C4—61no—
126C4—122no—
127C4#126⋊C911yescharacteristic
128C3#2863⋊C311yescharacteristic
129C2—31no—
130C2—31no—
131C2C2×#126⋊C911yescharacteristic
subgroupG/H
centerC2×C3C2×#126⋊C3
commutatorC2×C42C22×C9
Frattini, socle, prime radicalC23×C3C22×A4
FittingC3×#2863C3
cosocleC2×C3×C42C22×C3
hypercenterC3×C4#126⋊C3
hypocenterC42Q8×C9
LCSG ▷ C2×C42 ▷ C42
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
13. C42⋊C9Q8semidirect
14. #2863C9semidirect
88. C42Q8×C9semidirect

Maximal subgroups

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

subgroupindex
#383⋊C92
C4×C42⋊C92
C3×#28633
Q8×C22⋊C94