Finite Group Databasebeta

← #77233⋊C3 #11921183

Subgroups — #77233⋊C3 #11921183

Order 1152.

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

normal subgroups only

This group has 226 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, complemented
2C3⋊(#393⋊C3)C212yesmaximal, complemented
3#77233C311yesmaximal, characteristic, complemented
4#2785⋊C3—31nomaximal
5C3×C22⋊SL(2,𝔽3)C2211yescharacteristic
6A4×D12—41nomaximal
7C3×#395C2×C311yescharacteristic, complemented
8#5231C2×C312yescomplemented
9#4991—31no—
10#4977—31no—
11#4670—32no—
12#395⋊C3—21no—
13#395⋊C3D311yescharacteristic, complemented
14#393⋊C3—32no—
15C2×D3×A4—42no—
16C3×C4×A4—41no—
17#2785—31noSylow
18C22×C3×Q8C22×C311yescharacteristic
19C22×D12A411yescharacteristic
20C22⋊SL(2,𝔽3)—21no—
21C22⋊SL(2,𝔽3)C2×D311yescharacteristic
22D4×A4—121no—
23C2×C3×C4⋊C4—31no—
24C2×(C2×D3)⋊C4—32no—
25C2×(C2×D3)⋊C4—32no—
26C2×C4⋊Dic3—31no—
27C2×C4×Dic3—31no—
28C3×#95—31no—
29C3⋊#95—31no—
30C3⋊#95—32no—
31C2×C3×A4—41no—
32D3×A4—82no—
33C3×D12—161no—
34C3×SL(2,𝔽3)—161no—
35#395C3×D311yescharacteristic, complemented
36#394—91no—
37#393—32no—
38#388—92no—
39#382—91no—
40C23×D3C2×A412yes—
41C22×A4—122no—
42C2×C3×Q8—121no—
43C22×C3×C4—31no—
44C22×C3×C4—31no—
45C22×C3×C4C2×A411yescharacteristic
46C22×Dic3—32no—
47C2×D12—121no—
48C4×A4—41no—
49C4×A4—81no—
50C3×C4⋊C4—121no—
51(C2×D3)⋊C4—64no—
52(C2×D3)⋊C4—122no—
53C4⋊Dic3—121no—
54C4×Dic3—62no—
55C2×C3×D3—162no—
56C3×A4—41no—
57C32×C4—161no—
58C22×Q8C2×C3×D311yescharacteristic
59C22×D4—31no—
60C2×C4⋊C4—31no—
61C2×C4⋊C4—91no—
62C2×C22⋊C4—92no—
63C2×C22⋊C4—92no—
64C2×C42—91no—
65#95—31no—
66#95—92no—
67#95—91no—
68C23×C3C22×A411yescharacteristic
69C22×D3—22no—
70C22×D3—62no—
71C22×D3—62no—
72C2×A4—41no—
73C2×A4—81no—
74C2×A4—242no—
75C3×Q8—41no—
76C3×Q8—121no—
77C3×D4—481no—
78C2×C3×C4—32no—
79C2×C3×C4—61no—
80C2×C3×C4—61no—
81C2×C3×C4—61no—
82C2×C3×C4—62no—
83C2×C3×C4—61no—
84C2×Dic3—62no—
85C2×Dic3—62no—
86C2×Dic3—62no—
87D12—41no—
88D12—121no—
89SL(2,𝔽3)—161no—
90SL(2,𝔽3)—162no—
91C2×C32—161no—
92C3×D3—322no—
93C24—32no—
94C2×Q8—121no—
95C2×D4—361no—
96C22×C4—31no—
97C22×C4—31no—
98C22×C4—92no—
99C22×C4D3×A411yescharacteristic
100C4⋊C4—121no—
101C4⋊C4—361no—
102C22⋊C4—184no—
103C22⋊C4—362no—
104C42—182no—
105C22×C3—31no—
106C22×C3—31no—
107C22×C3—482no—
108C22×C32−1+4⋊C311yescharacteristic
109C2×D3—42no—
110C2×D3—122no—
111C2×D3—122no—
112A4—41no—
113A4—81no—
114C3×C4—41no—
115C3×C4—62no—
116C3×C4—121no—
117C3×C4—161no—
118C3×C4—321no—
119Dic3—122no—
120C32—161noSylow
121C23—62no—
122C23—182no—
123C23—182no—
124C23C2×D3×A411yescharacteristic
125Q8—41no—
126Q8—121no—
127D4—121no—
128D4—361no—
129C2×C4—32no—
130C2×C4—61no—
131C2×C4—61no—
132C2×C4—61no—
133C2×C4—62no—
134C2×C4—61no—
135C2×C4—182no—
136C2×C4—182no—
137C2×C4—182no—
138C2×C3—31no—
139C2×C3—31no—
140C2×C3—161no—
141C2×C3—321no—
142C2×C3—962no—
143C2×C3#545011yescharacteristic
144D3—82no—
145C22—31no—
146C22—31no—
147C22—122no—
148C22—362no—
149C22—362no—
150C22#1010⋊C311yescharacteristic
151C4—41no—
152C4—62no—
153C4—121no—
154C4—362no—
155C3—161no—
156C3—321no—
157C3#2785⋊C311yescharacteristic, complemented
158C2—31no—
159C2—31no—
160C2—242no—
161C2C3⋊#545011yescharacteristic
subgroupG/H
center, hypercenterC2C3⋊#5450
commutator, cosocle, hypocenterC22×C3×Q8C22×C3
FrattiniC23C2×D3×A4
FittingC3×#395C2×C3
socleC23×C3C22×A4
LCSG ▷ C22×C3×Q8
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3×#395⋊C3C2semidirect
2. C3⋊(#393⋊C3)C2semidirect
3. #77233C3semidirect
7. C3×#395C2×C3semidirect
8. #5231C2×C3semidirect
13. #395⋊C3D3semidirect
35. #395C3×D3semidirect
157. C3#2785⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#395⋊C32
C3⋊(#393⋊C3)2
#772333
#2785⋊C33
A4×D124