Finite Group Databasebeta

← #77279⋊C3 #11921181

Subgroups — #77279⋊C3 #11921181

Order 1152.

210 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 29 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)C211yesmaximal, characteristic
3C3⋊(#395⋊C3)C211yesmaximal, characteristic, complemented
4#77279C311yesmaximal, characteristic, complemented
5#2835⋊C3—31nomaximal
6C3×C22⋊SL(2,𝔽3)C2211yescharacteristic
7C4×D3×A4—41nomaximal
8C3×#395C2×C311yescharacteristic, complemented
9#5231C2×C311yescharacteristic
10#5230C2×C311yescharacteristic, complemented
11#4989—31no—
12#4985—31no—
13#4675—31no—
14#4658—31no—
15#395⋊C3—21no—
16#395⋊C3—31no—
17#395⋊C3D311yescharacteristic, complemented
18#393⋊C3—31no—
19C2×D3×A4—41no—
20C3×C4×A4—41no—
21Dic3×A4—41no—
22#2835—31noSylow
23C22×C3×Q8C22×C311yescharacteristic
24C22×C4×D3A411yescharacteristic
25C22⋊SL(2,𝔽3)—21no—
26C22⋊SL(2,𝔽3)C2×D311yescharacteristic
27C2×C4×A4—121no—
28C2×C3×C4⋊C4—31no—
29C2×(C2×D3)⋊C4—31no—
30C2×(C2×D3)⋊C4—31no—
31C2×Dic3⋊C4—31no—
32C2×Dic3⋊C4—31no—
33C3×#95—31no—
34C3⋊#95—31no—
35C3⋊#95—31no—
36C3⋊#95—31no—
37C3⋊#95—31no—
38C3⋊#95—31no—
39C2×C3×A4—41no—
40D3×A4—42no—
41C3×C4×D3—161no—
42C3×SL(2,𝔽3)—161no—
43#400—91no—
44#400—91no—
45#397—91no—
46#395—31no—
47#395C3×D311yescharacteristic, complemented
48#393—31no—
49#385—91no—
50C23×D3C2×A411yescharacteristic
51C22×A4—121no—
52C2×C3×Q8—121no—
53C22×C3×C4—31no—
54C22×C3×C4—31no—
55C22×C3×C4C2×A411yescharacteristic
56C22×Dic3—31no—
57C22×Dic3—31no—
58C22×Dic3C2×A411yescharacteristic
59C2×C4×D3—121no—
60C4×A4—41no—
61C4×A4—81no—
62C4×A4—121no—
63C3×C4⋊C4—121no—
64(C2×D3)⋊C4—62no—
65(C2×D3)⋊C4—121no—
66Dic3⋊C4—121no—
67Dic3⋊C4—121no—
68C2×C3×D3—161no—
69C3×A4—41no—
70C32×C4—161no—
71C3×Dic3—161no—
72C22×Q8C2×C3×D311yescharacteristic
73C23×C4—31no—
74C2×C4⋊C4—31no—
75C2×C4⋊C4—91no—
76C2×C4⋊C4—91no—
77C2×C22⋊C4—91no—
78C2×C22⋊C4—91no—
79#95—31no—
80#95—91no—
81#95—91no—
82#95—91no—
83#95—91no—
84#95—91no—
85C23×C3C22×A411yescharacteristic
86C22×D3—61no—
87C22×D3—61no—
88C22×D3#41⋊C312yes—
89C2×A4—41no—
90C2×A4—81no—
91C2×A4—122no—
92C3×Q8—41no—
93C3×Q8—121no—
94C2×C3×C4—61no—
95C2×C3×C4—61no—
96C2×C3×C4—61no—
97C2×C3×C4—61no—
98C2×C3×C4—61no—
99C2×C3×C4—61no—
100C2×C3×C4—61no—
101C2×C3×C4—481no—
102C2×Dic3—61no—
103C2×Dic3—61no—
104C2×Dic3—61no—
105C2×Dic3—62no—
106C2×Dic3—61no—
107C2×Dic3—61no—
108C4×D3—41no—
109C4×D3—121no—
110SL(2,𝔽3)—161no—
111SL(2,𝔽3)—162no—
112C2×C32—161no—
113C3×D3—162no—
114C24—31no—
115C2×Q8—121no—
116C22×C4—31no—
117C22×C4—31no—
118C22×C4—31no—
119C22×C4—91no—
120C22×C4—91no—
121C22×C4—361no—
122C22×C4D3×A411yescharacteristic
123C4⋊C4—121no—
124C4⋊C4—361no—
125C4⋊C4—361no—
126C22⋊C4—182no—
127C22⋊C4—361no—
128C22×C3—31no—
129C22×C3—31no—
130C22×C3—481no—
131C22×C3C2×#41⋊C311yescharacteristic
132C2×D3—41no—
133C2×D3—62no—
134C2×D3—121no—
135A4—41no—
136A4—81no—
137C3×C4—41no—
138C3×C4—121no—
139C3×C4—121no—
140C3×C4—161no—
141C3×C4—321no—
142C3×C4—481no—
143Dic3—41no—
144Dic3—121no—
145Dic3—121no—
146C32—161noSylow
147C23—32no—
148C23—181no—
149C23—181no—
150C23C2×D3×A411yescharacteristic
151Q8—41no—
152Q8—121no—
153C2×C4—61no—
154C2×C4—61no—
155C2×C4—61no—
156C2×C4—61no—
157C2×C4—61no—
158C2×C4—61no—
159C2×C4—61no—
160C2×C4—121no—
161C2×C4—181no—
162C2×C4—181no—
163C2×C4—181no—
164C2×C4—182no—
165C2×C4—181no—
166C2×C4—181no—
167C2×C4—361no—
168C2×C3—31no—
169C2×C3—31no—
170C2×C3—161no—
171C2×C3—321no—
172C2×C3—482no—
173C2×C3#545011yescharacteristic
174D3—42no—
175C22—31no—
176C22—31no—
177C22—121no—
178C22—182no—
179C22—361no—
180C22D3×#41⋊C311yescharacteristic
181C4—41no—
182C4—121no—
183C4—121no—
184C4—121no—
185C4—361no—
186C4—361no—
187C3—161no—
188C3—321no—
189C3#2835⋊C311yescharacteristic, complemented
190C2—31no—
191C2—31no—
192C2—122no—
193C2C3⋊#545011yescharacteristic
subgroupG/H
center, hypercenterC2C3⋊#5450
commutator, cosocle, hypocenterC22×C3×Q8C22×C3
FrattiniC23C2×D3×A4
FittingC3×#395C2×C3
socleC23×C3C22×A4
prime radicalC3⋊(#393⋊C3)C2
LCSG ▷ C22×C3×Q8
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3×#395⋊C3C2semidirect
3. C3⋊(#395⋊C3)C2semidirect
4. #77279C3semidirect
8. C3×#395C2×C3semidirect
10. #5230C2×C3semidirect
17. #395⋊C3D3semidirect
47. #395C3×D3semidirect
189. C3#2835⋊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
C3⋊(#395⋊C3)2
#772793
#2835⋊C33
C4×D3×A44