Finite Group Databasebeta

← #3556⋊C9 #11919849

Subgroups — #3556⋊C9 #11919849

Order 1152.

334 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 32 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#564⋊C9C211yesmaximal, characteristic, complemented
2C3×#3556C311yesmaximal, characteristic
3#126⋊C9—44nomaximal
4C2×C42⋊C9—41nomaximal
5C3×#564—31no—
6C3×#564C2×C311yescharacteristic
7C3×#557—34no—
8C3×#541—34no—
9C3×#533—31no—
10C42⋊C9—41no—
11C42⋊C9—44no—
12#3556C911yescharacteristic, complemented, Sylow
13C3×C4⋊Q8—32no—
14C3×C4⋊Q8—34no—
15C3×#126—34no—
16C3×#126A414yes—
17C3×#125—38no—
18C3×#125—34no—
19C3×#125—34no—
20C3×#125—31no—
21C3×#125—31no—
22C3×#125—34no—
23C3×C22⋊Q8—34no—
24C3×C4×Q8—34no—
25C3×C4×Q8—34no—
26C3×C4×Q8—34no—
27C3×#117—32no—
28C2×C3×C42A411yescharacteristic
29C2×C22⋊C9—161no—
30#564—31no—
31#564C2×C911yescharacteristic, complemented
32#557—34no—
33#541—34no—
34#533—31no—
35C2×C3×Q8—34no—
36C22×C3×C4—31no—
37C3×C4⋊C4—34no—
38C3×C4⋊C4—32no—
39C3×C4⋊C4—32no—
40C3×C4⋊C4—34no—
41C3×C4⋊C4—34no—
42C3×C4⋊C4—34no—
43C3×C4⋊C4—38no—
44C3×C4⋊C4—34no—
45C3×C22⋊C4—34no—
46C3×C42—31no—
47C3×C42—34no—
48C3×C42—34no—
49C3×C42C2×A411yescharacteristic
50C3×C42C2×A414yes—
51C22⋊C9—161no—
52C4⋊Q8—32no—
53C4⋊Q8—34no—
54#126—34no—
55#126C22⋊C914yes—
56#125—34no—
57#125—38no—
58#125—34no—
59#125—31no—
60#125—31no—
61#125—34no—
62C22⋊Q8—34no—
63C4×Q8—34no—
64C4×Q8—34no—
65C4×Q8—34no—
66#117—32no—
67C2×C42C22⋊C911yescharacteristic
68C23×C3C22⋊A411yescharacteristic
69C3×Q8—68no—
70C2×C3×C4—31no—
71C2×C3×C4—34no—
72C2×C3×C4—34no—
73C2×C3×C4—31no—
74C2×C3×C4—62no—
75C2×C9—641no—
76C2×Q8—34no—
77C22×C4—31no—
78C4⋊C4—34no—
79C4⋊C4—32no—
80C4⋊C4—32no—
81C4⋊C4—34no—
82C4⋊C4—34no—
83C4⋊C4—34no—
84C4⋊C4—38no—
85C4⋊C4—34no—
86C22⋊C4—34no—
87C42—31no—
88C42—34no—
89C42—34no—
90C42C2×C22⋊C911yescharacteristic
91C42C2×C22⋊C914yes—
92C22×C3—61no—
93C22×C3C2×C22⋊A411yescharacteristic
94C3×C4—32no—
95C3×C4—61no—
96C3×C4—64no—
97C3×C4—64no—
98C9—641noSylow
99C23C22⋊(C22⋊C9)11yescharacteristic
100Q8—68no—
101C2×C4—31no—
102C2×C4—34no—
103C2×C4—34no—
104C2×C4—31no—
105C2×C4—62no—
106C2×C3—31no—
107C2×C3—41no—
108C22—61no—
109C22C2×C22⋊(C22⋊C9)11yescharacteristic
110C4—32no—
111C4—61no—
112C4—64no—
113C4—64no—
114C3#3556⋊C311yescharacteristic
115C2—31no—
116C2—41no—
subgroupG/H
center, hypercenterC3#3556⋊C3
commutator, hypocenter#564C2×C9
Frattini, socleC22×C3C2×C22⋊A4
FittingC3×#3556C3
prime radicalC23×C3C22⋊A4
cosocleC3×#564C2×C3
LCSG ▷ #564
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. #564⋊C9C2semidirect
12. #3556C9semidirect
31. #564C2×C9semidirect

Maximal subgroups

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

subgroupindex
#564⋊C92
C3×#35563
#126⋊C94
C2×C42⋊C94