Finite Group Databasebeta

← #76859⋊C3 #11921171

Subgroups — #76859⋊C3 #11921171

Order 1152.

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

normal subgroups only

This group has 214 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×#393⋊C3C211yesmaximal, characteristic
2C3⋊(#395⋊C3)C212yesmaximal, complemented
3#76859C311yesmaximal, characteristic, complemented
4#2835⋊C3—31nomaximal
5C3×C22⋊SL(2,𝔽3)C2211yescharacteristic
6C2×Dic3×A4—41nomaximal
7C3×#393C2×C311yescharacteristic
8#5230C2×C312yescomplemented
9#4953—31no—
10#4946—31no—
11#4660—32no—
12#395⋊C3—32no—
13#393⋊C3—21no—
14#393⋊C3D311yescharacteristic
15C22×C3×A4—41no—
16Dic3×A4—42no—
17#2835—31noSylow
18C22×C3×Q8C22×C311yescharacteristic
19C23×Dic3A411yescharacteristic
20C22⋊SL(2,𝔽3)—21no—
21C22⋊SL(2,𝔽3)C2×D311yescharacteristic
22C2×C4×A4—121no—
23C2×C3×C22⋊C4—31no—
24C2×#217—31no—
25C2×C4⋊Dic3—31no—
26C2×Dic3⋊C4—32no—
27C3×#95—31no—
28C3⋊#95—31no—
29C3⋊#95—32no—
30C3⋊#95—32no—
31C2×C3×A4—42no—
32C2×C3×A4—41no—
33C2×C3×Dic3—161no—
34C3×SL(2,𝔽3)—161no—
35#400—92no—
36#397—91no—
37#395—32no—
38#393C3×D311yescharacteristic
39#385—91no—
40C24×C3C2×A411yescharacteristic
41C22×A4—41no—
42C22×A4—81no—
43C2×C3×Q8—121no—
44C22×C3×C4—31no—
45C22×C3×C4—31no—
46C22×Dic3—32no—
47C22×Dic3—121no—
48C22×Dic3C2×A412yes—
49C4×A4—122no—
50C3×C22⋊C4—121no—
51#217—62no—
52C4⋊Dic3—121no—
53Dic3⋊C4—122no—
54C22×C32—161no—
55C3×A4—41no—
56C3×Dic3—162no—
57C22×Q8C2×C3×D311yescharacteristic
58C23×C4—31no—
59C2×C4⋊C4—92no—
60C2×C4⋊C4—91no—
61C2×C22⋊C4—31no—
62C2×C22⋊C4—91no—
63#95—31no—
64#95—92no—
65#95—92no—
66#95—91no—
67C23×C3—61no—
68C23×C3—61no—
69C23×C3#41⋊C312yes—
70C23×C3C22×A411yescharacteristic
71C2×A4—41no—
72C2×A4—42no—
73C2×A4—81no—
74C2×A4—82no—
75C3×Q8—41no—
76C3×Q8—121no—
77C2×C3×C4—62no—
78C2×C3×C4—61no—
79C2×C3×C4—61no—
80C2×C3×C4—62no—
81C2×C3×C4—481no—
82C2×Dic3—41no—
83C2×Dic3—62no—
84C2×Dic3—62no—
85C2×Dic3—62no—
86C2×Dic3—62no—
87C2×Dic3—121no—
88SL(2,𝔽3)—161no—
89SL(2,𝔽3)—162no—
90C2×C32—162no—
91C2×C32—161no—
92C24D3×A411yescharacteristic
93C2×Q8—121no—
94C22×C4—31no—
95C22×C4—31no—
96C22×C4—32no—
97C22×C4—92no—
98C22×C4—361no—
99C4⋊C4—362no—
100C4⋊C4—361no—
101C22⋊C4—121no—
102C22⋊C4—182no—
103C22×C3—31no—
104C22×C3—31no—
105C22×C3—41no—
106C22×C3—62no—
107C22×C3—121no—
108C22×C3—161no—
109C22×C3—321no—
110C22×C3C2×#41⋊C311yescharacteristic
111A4—41no—
112A4—81no—
113C3×C4—121no—
114C3×C4—121no—
115C3×C4—482no—
116Dic3—42no—
117Dic3—122no—
118C32—161noSylow
119C23—61no—
120C23—61no—
121C23C3⋊(#41⋊C3)12yes—
122C23C2×D3×A411yescharacteristic
123Q8—41no—
124Q8—121no—
125C2×C4—61no—
126C2×C4—61no—
127C2×C4—62no—
128C2×C4—62no—
129C2×C4—121no—
130C2×C4—182no—
131C2×C4—182no—
132C2×C4—182no—
133C2×C4—182no—
134C2×C4—361no—
135C2×C3—31no—
136C2×C3—31no—
137C2×C3—42no—
138C2×C3—162no—
139C2×C3—161no—
140C2×C3—322no—
141C2×C3—321no—
142C2×C3#545011yescharacteristic
143C22—31no—
144C22—31no—
145C22—41no—
146C22—62no—
147C22—121no—
148C22C2×C3⋊(#41⋊C3)11yescharacteristic
149C4—121no—
150C4—121no—
151C4—122no—
152C4—362no—
153C3—161no—
154C3—321no—
155C3#2835⋊C311yescharacteristic, complemented
156C2—31no—
157C2—31no—
158C2—42no—
159C2C3⋊#545011yescharacteristic
subgroupG/H
center, hypercenterC2C3⋊#5450
commutator, cosocle, hypocenterC22×C3×Q8C22×C3
FrattiniC23C2×D3×A4
FittingC3×#393C2×C3
socleC23×C3C22×A4
prime radicalC3×#393⋊C3C2
LCSG ▷ C22×C3×Q8
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊(#395⋊C3)C2semidirect
3. #76859C3semidirect
8. #5230C2×C3semidirect
155. C3#2835⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#393⋊C32
C3⋊(#395⋊C3)2
#768593
#2835⋊C33
C2×Dic3×A44