Finite Group Databasebeta

← C3×#2863⋊C3 #11919510

Subgroups — C3×#2863⋊C3 #11919510

Order 1152.

232 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 54 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×#383⋊C3C212yesmaximal
2C3×C4×C42⋊C3C211yesmaximal, characteristic
3C3×#2863C311yesmaximal, characteristic, complemented
4#2863⋊C3C313yesmaximal, direct product factor
5C3×Q8×A4—41nomaximal
6C2×C3×C42⋊C3C2211yescharacteristic
7C3×#391—31no—
8C3×#389—31no—
9C3×#387—32no—
10C3×#383C2×C312yes—
11C3×C43C2×C311yescharacteristic
12#383⋊C3C2×C316yes—
13C4×C42⋊C3C2×C313yes—
14C3×C4×A4—41no—
15C3×C4×A4—42no—
16C3×C42⋊C3Q811yescharacteristic, complemented
17#2863C3211yescharacteristic, complemented, Sylow
18C22×C3×Q8A411yescharacteristic
19Q8×A4—43no—
20C2×C3×C4⋊C4—32no—
21C2×C3×C4⋊C4—31no—
22C2×C3×C42—31no—
23C2×C3×C42—31no—
24C2×C3×C42C22×C311yescharacteristic
25C2×C42⋊C3C22×C313yes—
26C3×#95—32no—
27C3×#95—32no—
28C3×#95—32no—
29C2×C3×A4—41no—
30C32×Q8—161no—
31#391—31no—
32#389—31no—
33#387—32no—
34#383C2×C3212yes—
35C43C2×C3211yescharacteristic
36C2×C3×Q8—61no—
37C2×C3×Q8—61no—
38C22×C3×C4—31no—
39C22×C3×C4—31no—
40C22×C3×C4—32no—
41C22×C3×C4C2×A411yescharacteristic
42C22×C3×C4C2×A412yes—
43C4×A4—43no—
44C4×A4—46no—
45C3×C4⋊C4—61no—
46C3×C4⋊C4—61no—
47C3×C4⋊C4—64no—
48C3×C42—31no—
49C3×C42—61no—
50C3×C42—61no—
51C3×C42—62no—
52C3×C42C3×Q811yescharacteristic, complemented
53C42⋊C3C3×Q813yescomplemented
54C3×A4—41no—
55C32×C4—162no—
56C32×C4—161no—
57C22×Q8C3×A411yescharacteristic
58C2×C4⋊C4—32no—
59C2×C4⋊C4—31no—
60C2×C42—31no—
61C2×C42—31no—
62C2×C42C22×C3211yescharacteristic
63#95—32no—
64#95—32no—
65#95—32no—
66C23×C3C22×A411yescharacteristic
67C2×A4—43no—
68C3×Q8—41no—
69C3×Q8—121no—
70C3×Q8—163no—
71C2×C3×C4—31no—
72C2×C3×C4—31no—
73C2×C3×C4—32no—
74C2×C3×C4—31no—
75C2×C3×C4—31no—
76C2×C3×C4—62no—
77C2×C3×C4—61no—
78C2×C3×C4—61no—
79C2×C3×C4—61no—
80C2×C3×C4—61no—
81C2×C3×C4—64no—
82C2×C3×C4—62no—
83C2×C32—161no—
84C2×Q8—61no—
85C2×Q8—61no—
86C22×C4—31no—
87C22×C4—31no—
88C22×C4—32no—
89C22×C4C2×C3×A411yescharacteristic
90C22×C4C2×C3×A412yes—
91C4⋊C4—61no—
92C4⋊C4—61no—
93C4⋊C4—64no—
94C42—31no—
95C42—61no—
96C42—61no—
97C42—62no—
98C42C32×Q811yescharacteristic, complemented
99C22×C3—31no—
100C22×C3—31no—
101C22×C3Q8×A411yescharacteristic
102A4—43no—
103C3×C4—31no—
104C3×C4—42no—
105C3×C4—62no—
106C3×C4—61no—
107C3×C4—61no—
108C3×C4—122no—
109C3×C4—166no—
110C3×C4—163no—
111C3×C4#126⋊C311yescharacteristic
112C32—161noSylow
113C23C22×C3×A411yescharacteristic
114Q8—41no—
115Q8—121no—
116C2×C4—31no—
117C2×C4—31no—
118C2×C4—32no—
119C2×C4—31no—
120C2×C4—31no—
121C2×C4—62no—
122C2×C4—61no—
123C2×C4—61no—
124C2×C4—61no—
125C2×C4—61no—
126C2×C4—64no—
127C2×C4—62no—
128C2×C3—31no—
129C2×C3—31no—
130C2×C3—163no—
131C2×C3C2×#126⋊C311yescharacteristic
132C22—31no—
133C22—31no—
134C22C3×Q8×A411yescharacteristic
135C4—31no—
136C4—42no—
137C4—62no—
138C4—61no—
139C4—61no—
140C4—122no—
141C4C3×#126⋊C311yescharacteristic
142C3—163no—
143C3#2863⋊C311yescharacteristic, direct product factor
144C2—31no—
145C2—31no—
146C2C2×C3×#126⋊C311yescharacteristic
subgroupG/H
centerC2×C3C2×#126⋊C3
commutator, cosocleC2×C42C22×C32
FrattiniC23C22×C3×A4
FittingC3×#2863C3
socleC23×C3C22×A4
prime radicalC2×C3×C42⋊C3C22
hypercenterC3×C4#126⋊C3
hypocenterC42C32×Q8
LCSG ▷ C2×C42 ▷ C42
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
3. C3×#2863C3semidirect
4. #2863⋊C3C3direct (N × H)
16. C3×C42⋊C3Q8semidirect
17. #2863C32semidirect
52. C3×C42C3×Q8semidirect
53. C42⋊C3C3×Q8semidirect
98. C42C32×Q8semidirect
143. C3#2863⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#383⋊C32
C3×C4×C42⋊C32
C3×#28633
#2863⋊C33
C3×Q8×A44