Finite Group Databasebeta

← C3⋊#73203 #11921178

Subgroups — C3⋊#73203 #11921178

Order 1152.

214 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 27 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×#395⋊C3C211yesmaximal, characteristic
2C3⋊(#395⋊C3)C212yesmaximal
3#77240C311yesmaximal, characteristic, complemented
4#73203—31nomaximal
5C3×C22⋊SL(2,𝔽3)C2211yescharacteristic
6A4×Dic6—41nomaximal
7C3×#395C2×C311yescharacteristic
8#5230C2×C312yes—
9#4979—31no—
10#4973—31no—
11#4646—32no—
12#395⋊C3—21no—
13#395⋊C3—32no—
14#395⋊C3D311yescharacteristic
15C3×C4×A4—41no—
16Dic3×A4—42no—
17#2811—31noSylow
18C22×C3×Q8C22×C311yescharacteristic
19C22×Dic6—31no—
20C22×Dic6A411yescharacteristic
21C22⋊SL(2,𝔽3)—21no—
22C22⋊SL(2,𝔽3)C2×D311yescharacteristic
23Q8×A4—121no—
24C2×C3×C4⋊C4—31no—
25C2×Dic3⋊C4—32no—
26C2×C4×Dic3—31no—
27C3×#95—31no—
28C3⋊#95—31no—
29C3⋊#95—32no—
30C3⋊#95—32no—
31C2×C3×A4—41no—
32C3×Dic6—161no—
33C3×SL(2,𝔽3)—161no—
34#395—32no—
35#395—91no—
36#395C3×D311yescharacteristic
37#391—92no—
38#391—91no—
39C2×C3×Q8—121no—
40C22×C3×C4—31no—
41C22×C3×C4—31no—
42C22×C3×C4C2×A411yescharacteristic
43C22×Dic3—32no—
44C22×Dic3C2×A412yes—
45C2×Dic6—34no—
46C2×Dic6—121no—
47C2×Dic6—121no—
48C2×Dic6—121no—
49C4×A4—41no—
50C4×A4—81no—
51C4×A4—122no—
52C3×C4⋊C4—121no—
53Dic3⋊C4—122no—
54C4×Dic3—121no—
55C3×A4—41no—
56C32×C4—161no—
57C3×Dic3—162no—
58C22×Q8—31no—
59C22×Q8—91no—
60C22×Q8C2×C3×D311yescharacteristic
61C2×C4⋊C4—31no—
62C2×C4⋊C4—92no—
63C2×C42—91no—
64#95—31no—
65#95—92no—
66#95—92no—
67#95—91no—
68C23×C3C22×A411yescharacteristic
69C2×A4—41no—
70C2×A4—81no—
71C3×Q8—41no—
72C3×Q8—121no—
73C3×Q8—481no—
74C2×C3×C4—32no—
75C2×C3×C4—61no—
76C2×C3×C4—61no—
77C2×C3×C4—61no—
78C2×C3×C4—62no—
79C2×C3×C4—61no—
80C2×Dic3—34no—
81C2×Dic3—62no—
82C2×Dic3—62no—
83C2×Dic3—62no—
84Dic6—41no—
85Dic6—121no—
86Dic6—124no—
87SL(2,𝔽3)—161no—
88SL(2,𝔽3)—162no—
89C2×C32—161no—
90C2×Q8—94no—
91C2×Q8—121no—
92C2×Q8—361no—
93C2×Q8—361no—
94C2×Q8—361no—
95C22×C4—31no—
96C22×C4—31no—
97C22×C4—32no—
98C22×C4—92no—
99C22×C4D3×A411yescharacteristic
100C4⋊C4—121no—
101C4⋊C4—362no—
102C42—361no—
103C22×C3—31no—
104C22×C3—31no—
105C22×C3#99411yescharacteristic
106A4—41no—
107A4—81no—
108C3×C4—41no—
109C3×C4—62no—
110C3×C4—121no—
111C3×C4—161no—
112C3×C4—321no—
113C3×C4—482no—
114Dic3—42no—
115Dic3—64no—
116C32—161noSylow
117C23C2×D3×A411yescharacteristic
118Q8—41no—
119Q8—121no—
120Q8—121no—
121Q8—361no—
122Q8—364no—
123C2×C4—32no—
124C2×C4—61no—
125C2×C4—61no—
126C2×C4—61no—
127C2×C4—61no—
128C2×C4—62no—
129C2×C4—94no—
130C2×C4—182no—
131C2×C4—182no—
132C2×C4—182no—
133C2×C3—31no—
134C2×C3—31no—
135C2×C3—161no—
136C2×C3—321no—
137C2×C3#545011yescharacteristic
138C22—31no—
139C22—31no—
140C22C3⋊#99411yescharacteristic
141C4—41no—
142C4—62no—
143C4—121no—
144C4—122no—
145C4—184no—
146C3—161no—
147C3—321no—
148C3#7320311yescharacteristic, complemented
149C2—31no—
150C2—31no—
151C2C3⋊#545011yescharacteristic
subgroupG/H
center, hypercenterC2C3⋊#5450
commutator, cosocle, hypocenterC22×C3×Q8C22×C3
FrattiniC23C2×D3×A4
FittingC3×#395C2×C3
socleC23×C3C22×A4
prime radicalC3×C22⋊SL(2,𝔽3)C22
LCSG ▷ C22×C3×Q8
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
3. #77240C3semidirect
148. C3#73203semidirect

Maximal subgroups

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

subgroupindex
C3×#395⋊C32
C3⋊(#395⋊C3)2
#772403
#732033
A4×Dic64