Finite Group Databasebeta

← C3×#2679⋊C3 #11919644

Subgroups — C3×#2679⋊C3 #11919644

Order 1152.

488 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 24 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, complemented
2#2679⋊C3C313yesmaximal, direct product factor
3C2×C3×C22⋊A4—42nomaximal
4C2×C3×C42⋊C3—41nomaximal
5C3×#95⋊C3—42nomaximal
6C2×C3×#120—32no—
7C3×#394—32no—
8C3×#390—31no—
9C3×C22⋊A4—42no—
10C3×C42⋊C3—41no—
11#2679C3211yescharacteristic, complemented, Sylow
12C25×C3A412yescomplemented
13C2×C22⋊A4—46no—
14C22×C3×D4—31no—
15C22×C3×D4—32no—
16C3×#120—68no—
17C2×C3×C4⋊C4—31no—
18C2×C3×C22⋊C4—34no—
19C2×C3×C22⋊C4—32no—
20C2×C3×C42A411yescharacteristic, complemented
21C2×C42⋊C3—43no—
22C3×#95A412yescomplemented
23#95⋊C3—46no—
24C2×C3×A4—168no—
25C2×C3×A4—161no—
26C2×#120—32no—
27#394—32no—
28#390—31no—
29C24×C3—32no—
30C24×C3—42no—
31C24×C3—64no—
32C24×C3—122no—
33C22⋊A4—46no—
34C2×C3×D4—34no—
35C2×C3×D4—68no—
36C2×C3×D4—121no—
37C2×C3×D4—121no—
38C2×C3×D4—122no—
39C22×C3×C4—31no—
40C22×C3×C4—32no—
41C3×C4⋊C4—121no—
42C3×C22⋊C4—68no—
43C3×C22⋊C4—64no—
44C3×C42—41no—
45C42⋊C3—43no—
46C3×A4—168no—
47C3×A4—161no—
48C25C3×A412yescomplemented
49C22×D4—31no—
50C22×D4—32no—
51#120—68no—
52C2×C4⋊C4—31no—
53C2×C22⋊C4—34no—
54C2×C22⋊C4—32no—
55C2×C42C3×A411yescharacteristic, complemented
56#95C3×A412yescomplemented
57C23×C3—34no—
58C23×C3—48no—
59C23×C3—64no—
60C23×C3—62no—
61C23×C3—64no—
62C23×C3—62no—
63C23×C3—124no—
64C23×C3—128no—
65C23×C3—124no—
66C23×C3C22⋊A411yescharacteristic
67C2×A4—1624no—
68C2×A4—163no—
69C3×D4—124no—
70C3×D4—128no—
71C2×C3×C4—32no—
72C2×C3×C4—61no—
73C2×C3×C4—61no—
74C2×C3×C4—64no—
75C2×C3×C4—62no—
76C2×C32—641no—
77C24—32no—
78C24—42no—
79C24—64no—
80C24—122no—
81C2×D4—34no—
82C2×D4—68no—
83C2×D4—121no—
84C2×D4—121no—
85C2×D4—122no—
86C22×C4—31no—
87C22×C4—32no—
88C4⋊C4—121no—
89C22⋊C4—68no—
90C22⋊C4—64no—
91C42—41no—
92C22×C3—31no—
93C22×C3—31no—
94C22×C3—48no—
95C22×C3—64no—
96C22×C3—68no—
97C22×C3—124no—
98C22×C3—122no—
99C22×C3—128no—
100C22×C3—122no—
101C22×C3#99711yescharacteristic
102A4—1624no—
103A4—163no—
104C3×C4—62no—
105C3×C4—122no—
106C32—641noSylow
107C23—34no—
108C23—48no—
109C23—64no—
110C23—62no—
111C23—64no—
112C23—62no—
113C23—124no—
114C23—128no—
115C23—124no—
116C23C3×C22⋊A411yescharacteristic
117D4—124no—
118D4—128no—
119C2×C4—32no—
120C2×C4—61no—
121C2×C4—61no—
122C2×C4—64no—
123C2×C4—62no—
124C2×C3—31no—
125C2×C3—31no—
126C2×C3—124no—
127C2×C3—643no—
128C2×C3#546411yescharacteristic
129C22—31no—
130C22—31no—
131C22—48no—
132C22—64no—
133C22—68no—
134C22—124no—
135C22—122no—
136C22—128no—
137C22—122no—
138C22C3×#99711yescharacteristic
139C4—62no—
140C4—122no—
141C3—643no—
142C3#2679⋊C311yescharacteristic, direct product factor
143C2—31no—
144C2—31no—
145C2—124no—
146C2C3×#546411yescharacteristic
subgroupG/H
center, hypercenterC2×C3#5464
commutator, cosocle, hypocenter#2679C32
FrattiniC23C3×C22⋊A4
FittingC3×#2679C3
socleC23×C3C22⋊A4
LCSG ▷ #2679
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C3×#2679C3semidirect
2. #2679⋊C3C3direct (N × H)
11. #2679C32semidirect
12. C25×C3A4semidirect
20. C2×C3×C42A4semidirect
22. C3×#95A4semidirect
48. C25C3×A4semidirect
55. C2×C42C3×A4semidirect
56. #95C3×A4semidirect
142. C3#2679⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#26793
#2679⋊C33
C2×C3×C22⋊A44
C2×C3×C42⋊C34
C3×#95⋊C34