Finite Group Databasebeta

← #74354⋊C3 #11921157

Subgroups — #74354⋊C3 #11921157

Order 1152.

185 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 185 conjugacy classes of subgroups — too many to draw. Only its 31 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×#384⋊C3C211yesmaximal, characteristic
2C3⋊(#383⋊C3)C212yesmaximal
3#74354C311yesmaximal, characteristic, complemented
4#2843⋊C3—31nomaximal
5A4×Dic6—41nomaximal
6C2×C3×C42⋊C3C2211yescharacteristic
7C3×#384C2×C311yescharacteristic
8#4986—31no—
9#4982—32no—
10#4979—31no—
11#4937C2×C312yes—
12#384⋊C3—21no—
13#384⋊C3D311yescharacteristic
14#383⋊C3—32no—
15C3×C4×A4—41no—
16Dic3×A4—42no—
17C3×C42⋊C3Q811yescharacteristic, complemented
18#2843—31noSylow
19C22×Dic6A411yescharacteristic
20Q8×A4—121no—
21C2×C3×C4⋊C4—31no—
22C2×C3×C4⋊C4—31no—
23C2×C3×C42C22×C311yescharacteristic
24C2×C4⋊Dic3—31no—
25C2×Dic3⋊C4—32no—
26C2×C42⋊C3—21no—
27C2×C42⋊C3C2×D311yescharacteristic
28C3⋊#95—31no—
29C3⋊#95—31no—
30C3⋊#95—32no—
31C3⋊#95—32no—
32C2×C3×A4—41no—
33C3×Dic6—161no—
34#400—91no—
35#398—92no—
36#395—91no—
37#384C3×D311yescharacteristic
38#383—32no—
39C22×C3×C4—31no—
40C22×C3×C4—31no—
41C22×C3×C4C2×A411yescharacteristic
42C22×Dic3—32no—
43C22×Dic3C2×A412yes—
44C2×Dic6—121no—
45C4×A4—41no—
46C4×A4—81no—
47C4×A4—122no—
48C3×C4⋊C4—121no—
49C3×C4⋊C4—121no—
50C3×C42—31no—
51C3×C42C3×Q811yescharacteristic, complemented
52C4⋊Dic3—121no—
53Dic3⋊C4—122no—
54C42⋊C3—21no—
55C42⋊C3Dic611yescharacteristic, complemented
56C3×A4—41no—
57C32×C4—161no—
58C3×Dic3—162no—
59C22×Q8—31no—
60C2×C4⋊C4—31no—
61C2×C4⋊C4—31no—
62C2×C4⋊C4—92no—
63C2×C4⋊C4—91no—
64C2×C42C2×C3×D311yescharacteristic
65#95—92no—
66#95—92no—
67#95—91no—
68#95—91no—
69C23×C3C22×A411yescharacteristic
70C2×A4—41no—
71C2×A4—81no—
72C3×Q8—481no—
73C2×C3×C4—31no—
74C2×C3×C4—31no—
75C2×C3×C4—61no—
76C2×C3×C4—61no—
77C2×C3×C4—61no—
78C2×C3×C4—62no—
79C2×C3×C4—61no—
80C2×Dic3—62no—
81C2×Dic3—62no—
82C2×Dic3—64no—
83Dic6—41no—
84Dic6—121no—
85C2×C32—161no—
86C2×Q8—361no—
87C22×C4—31no—
88C22×C4—31no—
89C22×C4—32no—
90C22×C4—92no—
91C22×C4D3×A411yescharacteristic
92C4⋊C4—121no—
93C4⋊C4—121no—
94C4⋊C4—362no—
95C4⋊C4—361no—
96C42—31no—
97C42C3×Dic611yescharacteristic, complemented
98C22×C3—31no—
99C22×C3—31no—
100C22×C3Q8×A411yescharacteristic
101A4—41no—
102A4—81no—
103C3×C4—41no—
104C3×C4—61no—
105C3×C4—61no—
106C3×C4—121no—
107C3×C4—161no—
108C3×C4—321no—
109C3×C4—482no—
110Dic3—42no—
111Dic3—122no—
112C32—161noSylow
113C23C2×D3×A411yescharacteristic
114Q8—121no—
115Q8—361no—
116C2×C4—31no—
117C2×C4—31no—
118C2×C4—61no—
119C2×C4—61no—
120C2×C4—61no—
121C2×C4—62no—
122C2×C4—61no—
123C2×C4—182no—
124C2×C4—182no—
125C2×C4—184no—
126C2×C3—31no—
127C2×C3—31no—
128C2×C3—161no—
129C2×C3—321no—
130C2×C3#560⋊C311yescharacteristic
131C22—31no—
132C22—31no—
133C22A4×Dic611yescharacteristic
134C4—41no—
135C4—61no—
136C4—61no—
137C4—121no—
138C4—122no—
139C4—362no—
140C3—161no—
141C3—321no—
142C3#2843⋊C311yescharacteristic, complemented
143C2—31no—
144C2—31no—
145C2#5720⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#5720⋊C3
commutator, cosocleC2×C3×C42C22×C3
FrattiniC23C2×D3×A4
FittingC3×#384C2×C3
socleC23×C3C22×A4
prime radicalC2×C3×C42⋊C3C22
hypocenterC3×C42C3×Q8
LCSG ▷ C2×C3×C42 ▷ C3×C42
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
3. #74354C3semidirect
17. C3×C42⋊C3Q8semidirect
51. C3×C42C3×Q8semidirect
55. C42⋊C3Dic6semidirect
97. C42C3×Dic6semidirect
142. C3#2843⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#384⋊C32
C3⋊(#383⋊C3)2
#743543
#2843⋊C33
A4×Dic64