Finite Group Databasebeta

← #77169⋊C3 #11921180

Subgroups — #77169⋊C3 #11921180

Order 1152.

408 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 30 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⋊#5948C211yesmaximal, characteristic, complemented
2C3×#395⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(#393⋊C3)C211yesmaximal, characteristic, complemented
4#77169C311yesmaximal, characteristic, complemented
5#2388⋊C3—31nomaximal
6C3×C22⋊SL(2,𝔽3)C2211yescharacteristic
7C4×D3×A4—41nomaximal
8C22×#239C2×C311yescharacteristic, complemented
9#5948—31no—
10C2×#893—31no—
11C3×#395C2×C311yescharacteristic, complemented
12#5231C2×C311yescharacteristic
13#4991—31no—
14#4671—31no—
15#4666—31no—
16#395⋊C3—21no—
17#395⋊C3D311yescharacteristic, complemented
18#393⋊C3—31no—
19C2×D3×A4—41no—
20C3×C4×A4—41no—
21Dic3×A4—41no—
22C3⋊(#41⋊C3)—82no—
23#2388—31noSylow
24C22×C3×Q8C22×C311yescharacteristic
25C2×#239—62no—
26C2×#239—62no—
27C22×D12—31no—
28C22×D12—31no—
29C22×C4×D3—31no—
30C22×C4×D3A411yescharacteristic
31C22⋊SL(2,𝔽3)—21no—
32C22⋊SL(2,𝔽3)C2×D311yescharacteristic
33C2×C4×A4—121no—
34C2×C3×C4⋊C4—31no—
35C2×(C2×D3)⋊C4—32no—
36C2×(C2×D3)⋊C4—31no—
37C2×(C2×D3)⋊C4—31no—
38C2×C4×Dic3—31no—
39#893—62no—
40#893—62no—
41C3×#95—31no—
42C3⋊#95—31no—
43C2×C3×A4—41no—
44D3×A4—42no—
45C3×C4×D3—161no—
46C3×SL(2,𝔽3)—82no—
47C22×#41—31no—
48C2×C4×D4—91no—
49#395C3×D311yescharacteristic, complemented
50#394—91no—
51#393—31no—
52#392—91no—
53C4×C22⋊C4—91no—
54C23×D3—31no—
55C23×D3C2×A411yescharacteristic
56C22×A4—121no—
57C2×C3×Q8—62no—
58C22×C3×C4—31no—
59C22×C3×C4—31no—
60C22×C3×C4C2×A411yescharacteristic
61C22×Dic3—31no—
62C22×Dic3C2×A411yescharacteristic
63#239—22no—
64#239—62no—
65#239—64no—
66#239—62no—
67#239—62no—
68C2×D12—62no—
69C2×D12—62no—
70C2×D12—62no—
71C2×D12—64no—
72C2×D12—62no—
73C2×C4×D3—32no—
74C2×C4×D3—32no—
75C2×C4×D3—61no—
76C2×C4×D3—62no—
77C2×C4×D3—62no—
78C2×C4×D3—61no—
79#41⋊C3—242no—
80C4×A4—41no—
81C4×A4—81no—
82C4×A4—121no—
83C3×C4⋊C4—62no—
84(C2×D3)⋊C4—62no—
85(C2×D3)⋊C4—64no—
86(C2×D3)⋊C4—62no—
87C4×Dic3—61no—
88C4×Dic3—61no—
89C2×C3×D3—161no—
90C3×A4—41no—
91C32×C4—161no—
92C3×Dic3—161no—
93C2×#41—182no—
94C2×#41—182no—
95C22×Q8C2×C3×D311yescharacteristic
96C22×D4—91no—
97C22×D4—91no—
98C23×C4—31no—
99C23×C4—91no—
100C4×D4—182no—
101C4×D4—182no—
102C2×C4⋊C4—31no—
103C2×C22⋊C4—91no—
104C2×C22⋊C4—92no—
105C2×C22⋊C4—91no—
106C2×C42—91no—
107#95—31no—
108#95—91no—
109C23×C3C22×A411yescharacteristic
110C22×D3—32no—
111C22×D3—61no—
112C22×D3—62no—
113C22×D3—62no—
114C22×D3—61no—
115C22×D3—61no—
116C22×D3—61no—
117C22×D3#41⋊C312yescomplemented
118C2×A4—41no—
119C2×A4—81no—
120C2×A4—122no—
121C3×Q8—22no—
122C3×Q8—62no—
123C2×C3×C4—32no—
124C2×C3×C4—32no—
125C2×C3×C4—61no—
126C2×C3×C4—61no—
127C2×C3×C4—62no—
128C2×C3×C4—61no—
129C2×C3×C4—481no—
130C2×Dic3—31no—
131C2×Dic3—31no—
132C2×Dic3—61no—
133C2×Dic3—62no—
134D12—62no—
135D12—62no—
136D12—68no—
137D12—64no—
138C4×D3—41no—
139C4×D3—64no—
140C4×D3—62no—
141C4×D3—62no—
142C4×D3—121no—
143SL(2,𝔽3)—82no—
144SL(2,𝔽3)—162no—
145C2×C32—161no—
146C3×D3—162no—
147C24—31no—
148C24—91no—
149#41—62no—
150#41—182no—
151#41—184no—
152#41—182no—
153#41—182no—
154C2×Q8—62no—
155C2×D4—182no—
156C2×D4—182no—
157C2×D4—182no—
158C2×D4—182no—
159C2×D4—184no—
160C22×C4—31no—
161C22×C4—31no—
162C22×C4—31no—
163C22×C4—92no—
164C22×C4—92no—
165C22×C4—91no—
166C22×C4—181no—
167C22×C4—182no—
168C22×C4—182no—
169C22×C4—181no—
170C22×C4D3×A411yescharacteristic
171C4⋊C4—62no—
172C22⋊C4—182no—
173C22⋊C4—184no—
174C22⋊C4—182no—
175C42—181no—
176C42—181no—
177C22×C3—31no—
178C22×C3—31no—
179C22×C3—481no—
180C22×C3C2×#41⋊C311yescharacteristic
181C2×D3—41no—
182C2×D3—62no—
183C2×D3—62no—
184C2×D3—62no—
185C2×D3—62no—
186C2×D3—121no—
187C2×D3—122no—
188C2×D3—122no—
189A4—41no—
190A4—81no—
191C3×C4—41no—
192C3×C4—62no—
193C3×C4—62no—
194C3×C4—161no—
195C3×C4—321no—
196C3×C4—481no—
197Dic3—31no—
198Dic3—121no—
199Dic3#120⋊C311yescharacteristic
200C32—161noSylow
201C23—32no—
202C23—92no—
203C23—181no—
204C23—181no—
205C23—182no—
206C23—182no—
207C23—181no—
208C23—181no—
209C23C2×D3×A411yescharacteristic
210Q8—22no—
211Q8—62no—
212D4—182no—
213D4—182no—
214D4—184no—
215D4—188no—
216C2×C4—32no—
217C2×C4—32no—
218C2×C4—61no—
219C2×C4—61no—
220C2×C4—62no—
221C2×C4—61no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4—121no—
225C2×C4—182no—
226C2×C4—182no—
227C2×C4—184no—
228C2×C4—181no—
229C2×C4—182no—
230C2×C4—361no—
231C2×C3—31no—
232C2×C3—31no—
233C2×C3—161no—
234C2×C3—321no—
235C2×C3—482no—
236C2×C3C2×#120⋊C311yescharacteristic
237D3—42no—
238D3—122no—
239C22—31no—
240C22—31no—
241C22—121no—
242C22—182no—
243C22—182no—
244C22—182no—
245C22—182no—
246C22—361no—
247C22—362no—
248C22—362no—
249C22D3×#41⋊C311yescharacteristic
250C4—31no—
251C4—41no—
252C4—62no—
253C4—62no—
254C4—91no—
255C4—361no—
256C3—161no—
257C3—321no—
258C3#2388⋊C311yescharacteristic, complemented
259C2—31no—
260C2—31no—
261C2—122no—
262C2—362no—
263C2D3×#120⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#120⋊C3
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⋊#5948C2semidirect
2. C3×#395⋊C3C2semidirect
3. C3⋊(#393⋊C3)C2semidirect
4. #77169C3semidirect
8. C22×#239C2×C3semidirect
11. C3×#395C2×C3semidirect
17. #395⋊C3D3semidirect
49. #395C3×D3semidirect
117. C22×D3#41⋊C3semidirect
258. C3#2388⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3⋊#59482
C3×#395⋊C32
C3⋊(#393⋊C3)2
#771693
#2388⋊C33
C4×D3×A44