Finite Group Databasebeta

← #2679⋊C9 #11919645

Subgroups — #2679⋊C9 #11919645

Order 1152.

401 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 401 conjugacy classes of subgroups — too many to draw. Only its 21 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
1C3×#2679C311yesmaximal, characteristic
2C2×C22⋊(C22⋊C9)—42nomaximal
3C2×C42⋊C9—41nomaximal
4#95⋊C9—42nomaximal
5C2×C3×#120—32no—
6C3×#394—32no—
7C3×#390—31no—
8C22⋊(C22⋊C9)—42no—
9C42⋊C9—41no—
10#2679C911yescharacteristic, complemented, Sylow
11C25×C3A412yes—
12C22×C3×D4—31no—
13C22×C3×D4—32no—
14C3×#120—68no—
15C2×C3×C4⋊C4—31no—
16C2×C3×C22⋊C4—34no—
17C2×C3×C22⋊C4—32no—
18C2×C3×C42A411yescharacteristic
19C3×#95A412yes—
20C2×C22⋊C9—168no—
21C2×C22⋊C9—161no—
22C2×#120—32no—
23#394—32no—
24#390—31no—
25C24×C3—32no—
26C24×C3—42no—
27C24×C3—64no—
28C24×C3—122no—
29C2×C3×D4—34no—
30C2×C3×D4—68no—
31C2×C3×D4—121no—
32C2×C3×D4—121no—
33C2×C3×D4—122no—
34C22×C3×C4—31no—
35C22×C3×C4—32no—
36C3×C4⋊C4—121no—
37C3×C22⋊C4—68no—
38C3×C22⋊C4—64no—
39C3×C42—41no—
40C22⋊C9—168no—
41C22⋊C9—161no—
42C25C22⋊C912yescomplemented
43C22×D4—31no—
44C22×D4—32no—
45#120—68no—
46C2×C4⋊C4—31no—
47C2×C22⋊C4—34no—
48C2×C22⋊C4—32no—
49C2×C42C22⋊C911yescharacteristic, complemented
50#95C22⋊C912yescomplemented
51C23×C3—34no—
52C23×C3—48no—
53C23×C3—64no—
54C23×C3—62no—
55C23×C3—64no—
56C23×C3—62no—
57C23×C3—124no—
58C23×C3—128no—
59C23×C3—124no—
60C23×C3C22⋊A411yescharacteristic
61C3×D4—124no—
62C3×D4—128no—
63C2×C3×C4—32no—
64C2×C3×C4—61no—
65C2×C3×C4—61no—
66C2×C3×C4—64no—
67C2×C3×C4—62no—
68C2×C9—641no—
69C24—32no—
70C24—42no—
71C24—64no—
72C24—122no—
73C2×D4—34no—
74C2×D4—68no—
75C2×D4—121no—
76C2×D4—121no—
77C2×D4—122no—
78C22×C4—31no—
79C22×C4—32no—
80C4⋊C4—121no—
81C22⋊C4—68no—
82C22⋊C4—64no—
83C42—41no—
84C22×C3—31no—
85C22×C3—31no—
86C22×C3—48no—
87C22×C3—64no—
88C22×C3—68no—
89C22×C3—124no—
90C22×C3—122no—
91C22×C3—128no—
92C22×C3—122no—
93C22×C3#99711yescharacteristic
94C3×C4—62no—
95C3×C4—122no—
96C9—641noSylow
97C23—34no—
98C23—48no—
99C23—64no—
100C23—62no—
101C23—64no—
102C23—62no—
103C23—124no—
104C23—128no—
105C23—124no—
106C23C22⋊(C22⋊C9)11yescharacteristic
107D4—124no—
108D4—128no—
109C2×C4—32no—
110C2×C4—61no—
111C2×C4—61no—
112C2×C4—64no—
113C2×C4—62no—
114C2×C3—31no—
115C2×C3—31no—
116C2×C3—124no—
117C2×C3#546411yescharacteristic
118C22—31no—
119C22—31no—
120C22—48no—
121C22—64no—
122C22—68no—
123C22—124no—
124C22—122no—
125C22—128no—
126C22—122no—
127C22#6370311yescharacteristic
128C4—62no—
129C4—122no—
130C3#2679⋊C311yescharacteristic
131C2—31no—
132C2—31no—
133C2—124no—
134C2#1058956611yescharacteristic
subgroupG/H
center, hypercenterC2×C3#5464
commutator, hypocenter#2679C9
Frattini, socleC23×C3C22⋊A4
Fitting, prime radical, cosocleC3×#2679C3
LCSG ▷ #2679
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
10. #2679C9semidirect
42. C25C22⋊C9semidirect
49. C2×C42C22⋊C9semidirect
50. #95C22⋊C9semidirect

Maximal subgroups

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

subgroupindex
C3×#26793
C2×C22⋊(C22⋊C9)4
C2×C42⋊C94
#95⋊C94