Finite Group Databasebeta

← #73309⋊C3 #11921116

Subgroups — #73309⋊C3 #11921116

Order 1152.

205 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 205 conjugacy classes of subgroups — too many to draw. Only its 33 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×C4×C42⋊C3C211yesmaximal, characteristic
2C3⋊(#383⋊C3)C212yesmaximal
3#73309C311yesmaximal, characteristic, complemented
4#2863⋊C3—31nomaximal
5A4×Dic6—41nomaximal
6C2×C3×C42⋊C3C2211yescharacteristic
7C3×C43C2×C311yescharacteristic
8#4937C2×C312yes—
9#4933—32no—
10#4929—31no—
11#4928—31no—
12#383⋊C3—32no—
13C4×C42⋊C3—21no—
14C4×C42⋊C3D311yescharacteristic
15C3×C4×A4—41no—
16Dic3×A4—42no—
17C3×C42⋊C3Q811yescharacteristic, complemented
18#2863—31noSylow
19C22×Dic6A411yescharacteristic
20Q8×A4—121no—
21C2×C3×C42—31no—
22C2×C3×C42—31no—
23C2×C3×C42C22×C311yescharacteristic
24C2×C4⋊Dic3—31no—
25C2×Dic3⋊C4—32no—
26C2×C42⋊C3—21no—
27C2×C42⋊C3C2×D311yescharacteristic
28C3⋊#95—32no—
29C3⋊#95—32no—
30C3⋊#95—32no—
31C2×C3×A4—41no—
32C3×Dic6—161no—
33#391—91no—
34#389—91no—
35#387—92no—
36#383—32no—
37C43C3×D311yescharacteristic
38C22×C3×C4—31no—
39C22×C3×C4—31no—
40C22×C3×C4C2×A411yescharacteristic
41C22×Dic3—32no—
42C22×Dic3C2×A412yes—
43C2×Dic6—61no—
44C2×Dic6—61no—
45C4×A4—41no—
46C4×A4—81no—
47C4×A4—122no—
48C3×C42—31no—
49C3×C42—61no—
50C3×C42—61no—
51C3×C42—62no—
52C3×C42C3×Q811yescharacteristic, complemented
53C4⋊Dic3—61no—
54C4⋊Dic3—61no—
55Dic3⋊C4—64no—
56C42⋊C3—21no—
57C42⋊C3Dic611yescharacteristic, complemented
58C3×A4—41no—
59C32×C4—161no—
60C3×Dic3—162no—
61C22×Q8—31no—
62C2×C4⋊C4—92no—
63C2×C4⋊C4—91no—
64C2×C42—31no—
65C2×C42—31no—
66C2×C42C2×C3×D311yescharacteristic
67#95—92no—
68#95—92no—
69#95—92no—
70C23×C3C22×A411yescharacteristic
71C2×A4—41no—
72C2×A4—81no—
73C3×Q8—481no—
74C2×C3×C4—31no—
75C2×C3×C4—31no—
76C2×C3×C4—32no—
77C2×C3×C4—31no—
78C2×C3×C4—31no—
79C2×C3×C4—61no—
80C2×C3×C4—61no—
81C2×C3×C4—61no—
82C2×C3×C4—61no—
83C2×Dic3—62no—
84C2×Dic3—64no—
85C2×Dic3—62no—
86Dic6—41no—
87Dic6—121no—
88C2×C32—161no—
89C2×Q8—181no—
90C2×Q8—181no—
91C22×C4—31no—
92C22×C4—31no—
93C22×C4—32no—
94C22×C4—92no—
95C22×C4D3×A411yescharacteristic
96C4⋊C4—184no—
97C4⋊C4—181no—
98C4⋊C4—181no—
99C42—31no—
100C42—61no—
101C42—61no—
102C42—62no—
103C42C3×Dic611yescharacteristic, complemented
104C22×C3—31no—
105C22×C3—31no—
106C22×C3Q8×A411yescharacteristic
107A4—41no—
108A4—81no—
109C3×C4—31no—
110C3×C4—62no—
111C3×C4—61no—
112C3×C4—61no—
113C3×C4—161no—
114C3×C4—321no—
115C3×C4—482no—
116C3×C4#126⋊C311yescharacteristic
117Dic3—42no—
118Dic3—122no—
119C32—161noSylow
120C23C2×D3×A411yescharacteristic
121Q8—121no—
122Q8—361no—
123C2×C4—31no—
124C2×C4—31no—
125C2×C4—32no—
126C2×C4—31no—
127C2×C4—31no—
128C2×C4—61no—
129C2×C4—61no—
130C2×C4—61no—
131C2×C4—61no—
132C2×C4—182no—
133C2×C4—184no—
134C2×C4—182no—
135C2×C3—31no—
136C2×C3—31no—
137C2×C3—161no—
138C2×C3—321no—
139C2×C3C2×#126⋊C311yescharacteristic
140C22—31no—
141C22—31no—
142C22A4×Dic611yescharacteristic
143C4—31no—
144C4—62no—
145C4—61no—
146C4—61no—
147C4—122no—
148C4—362no—
149C4C3⋊(#126⋊C3)11yescharacteristic
150C3—161no—
151C3—321no—
152C3#2863⋊C311yescharacteristic, complemented
153C2—31no—
154C2—31no—
155C2C2×C3⋊(#126⋊C3)11yescharacteristic
subgroupG/H
centerC2C2×C3⋊(#126⋊C3)
commutator, cosocleC2×C3×C42C22×C3
FrattiniC23C2×D3×A4
FittingC3×C43C2×C3
socleC23×C3C22×A4
prime radicalC2×C3×C42⋊C3C22
hypercenterC4C3⋊(#126⋊C3)
hypocenterC3×C42C3×Q8
LCSG ▷ C2×C3×C42 ▷ C3×C42
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
3. #73309C3semidirect
17. C3×C42⋊C3Q8semidirect
52. C3×C42C3×Q8semidirect
57. C42⋊C3Dic6semidirect
103. C42C3×Dic6semidirect
152. C3#2863⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×C4×C42⋊C32
C3⋊(#383⋊C3)2
#733093
#2863⋊C33
A4×Dic64