Finite Group Databasebeta

← #11920958

Subgroups — #11920958

Order 1152.

290 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 25 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⋊#5931C211yesmaximal, characteristic
2C3⋊#5930C211yesmaximal, characteristic, complemented
3C3×#395⋊C3C211yesmaximal, characteristic, complemented
4#73002—33nomaximal
5#69705—31nomaximal
6C3×C22⋊SL(2,𝔽3)C2211yescharacteristic
7C4×C3⋊S4—41nomaximal
8#5931—33no—
9#5930—33no—
10#5515—31no—
11C3×#395D311yescharacteristic, complemented
12#5228—31no—
13#5227—31no—
14#395⋊C3D313yescomplemented
15#4528—31no—
16#4452—31no—
17#4451—31no—
18C2×C3⋊S4—41no—
19C3×C4×A4—41no—
20C3⋊SL(2,ℤ/4)—41no—
21C3⋊GL(2,𝔽3)—81no—
22C3⋊#226—81no—
23#1603—91noSylow
24C22×C3×Q8C2×D311yescharacteristic
25C22⋊SL(2,𝔽3)C2×D313yes—
26C4×S4—123no—
27C2×C3×C4⋊C4—31no—
28C2×#216—61no—
29C2×#215—61no—
30#930—31no—
31#929—61no—
32C4×#67—61no—
33#924—31no—
34#898—61no—
35#896—61no—
36#894—61no—
37#889—61no—
38C3×#95—31no—
39#835—61no—
40#835—61no—
41#830—31no—
42#830—31no—
43C2×C3×A4—41no—
44C3⋊S4—42no—
45C4×C3⋊D3—161no—
46C3×SL(2,𝔽3)—81no—
47C3×SL(2,𝔽3)—81no—
48#539—91no—
49#451—91no—
50#448—91no—
51#395C3⋊D311yescharacteristic, complemented
52#328—91no—
53#327—91no—
54#324—91no—
55C2×S4—123no—
56C2×C3×Q8—61no—
57C2×C3×Q8—61no—
58C22×C3×C4—31no—
59C22×C3×C4—31no—
60C22×C3×C4S411yescharacteristic
61C2×#67—61no—
62C2×D12—31no—
63C2×C4×D3—61no—
64C2×Dic6—31no—
65C4×A4—43no—
66SL(2,ℤ/4)—123no—
67GL(2,𝔽3)—243no—
68#226—243no—
69C3×C4⋊C4—61no—
70C3×C4⋊C4—61no—
71#217—61no—
72#216—121no—
73#216—121no—
74#215—121no—
75#215—121no—
76(C2×D3)⋊C4—61no—
77(C2×D3)⋊C4—61no—
78(C2×D3)⋊C4—61no—
79(C2×D3)⋊C4—61no—
80C4⋊Dic3—31no—
81C4⋊Dic3—31no—
82Dic3⋊C4—61no—
83Dic3⋊C4—61no—
84Dic3⋊C4—61no—
85Dic3⋊C4—61no—
86C4×Dic3—61no—
87C2×C3⋊C8—61no—
88C2×C3⋊C8—61no—
89C2×C3⋊D3—161no—
90C3×A4—41no—
91C32×C4—161no—
92C3⋊Dic3—161no—
93C22×Q8C2×C3⋊D311yescharacteristic
94C2×Q16—181no—
95C2×SD16—181no—
96#126—181no—
97#125—181no—
98#123—181no—
99#123—181no—
100C22⋊Q8—91no—
101C22⋊Q8—181no—
102#121—91no—
103C4×D4—181no—
104C2×C4⋊C4—31no—
105#103—181no—
106#103—181no—
107C22⋊C8—91no—
108C22⋊C8—91no—
109#95—31no—
110C23×C3C2×S411yescharacteristic
111C22×D3—61no—
112C2×A4—43no—
113S4—126no—
114C3×Q8—21no—
115C3×Q8—21no—
116C3×Q8—61no—
117C3×Q8—61no—
118C2×C3×C4—31no—
119C2×C3×C4—31no—
120C2×C3×C4—61no—
121C2×C3×C4—61no—
122C2×C3×C4—61no—
123C2×C3×C4—61no—
124C2×C3×C4—121no—
125#67—121no—
126#67—121no—
127C2×Dic3—61no—
128C2×Dic3—61no—
129C2×Dic3—61no—
130D12—121no—
131C4×D3—241no—
132C4×D3—483no—
133Dic6—121no—
134SL(2,𝔽3)—83no—
135SL(2,𝔽3)—83no—
136C3⋊C8—121no—
137C3⋊C8—121no—
138C2×C32—161no—
139C3⋊D3—162no—
140C2×Q8—61no—
141C2×Q8—61no—
142C2×Q8—91no—
143C2×D4—91no—
144C2×D4—181no—
145C22×C4—31no—
146C22×C4—31no—
147C22×C4—181no—
148C22×C4C3⋊S411yescharacteristic
149Q16—361no—
150Q16—361no—
151SD16—361no—
152SD16—361no—
153C2×C8—181no—
154C2×C8—181no—
155C4⋊C4—61no—
156C4⋊C4—61no—
157C4⋊C4—91no—
158C4⋊C4—91no—
159C4⋊C4—181no—
160C4⋊C4—181no—
161C4⋊C4—181no—
162C4⋊C4—181no—
163C22⋊C4—181no—
164C22⋊C4—181no—
165C22⋊C4—181no—
166C22⋊C4—181no—
167C22⋊C4—181no—
168C42—181no—
169C22×C3—31no—
170C22×C3—31no—
171C22×C3#98511yescharacteristic
172C2×D3—121no—
173C2×D3—121no—
174C2×D3—121no—
175C2×D3—483no—
176A4—43no—
177C3×C4—41no—
178C3×C4—61no—
179C3×C4—61no—
180C3×C4—121no—
181C3×C4—163no—
182Dic3—121no—
183Dic3—121no—
184Dic3—121no—
185Dic3—483no—
186C32—161noSylow
187C23—181no—
188C23C2×C3⋊S411yescharacteristic
189Q8—21no—
190Q8—21no—
191Q8—61no—
192Q8—61no—
193Q8—361no—
194D4—361no—
195D4—361no—
196D4—361no—
197C2×C4—31no—
198C2×C4—31no—
199C2×C4—61no—
200C2×C4—61no—
201C2×C4—61no—
202C2×C4—61no—
203C2×C4—121no—
204C2×C4—181no—
205C2×C4—181no—
206C2×C4—181no—
207C2×C4—721no—
208C8—361no—
209C8—361no—
210C2×C3—31no—
211C2×C3—31no—
212C2×C3—163no—
213C2×C3#1020⋊C211yescharacteristic
214D3—241no—
215D3—486no—
216C22—31no—
217C22—31no—
218C22—361no—
219C22—361no—
220C22—361no—
221C22#6426611yescharacteristic
222C4—41no—
223C4—61no—
224C4—61no—
225C4—121no—
226C4—361no—
227C4—361no—
228C4—361no—
229C3—163no—
230C3#7300211yescharacteristic, complemented
231C2—31no—
232C2—31no—
233C2—721no—
234C2#1059363011yescharacteristic
subgroupG/H
center, hypercenterC2#10593630
commutator, cosocle, hypocenterC3×C22⋊SL(2,𝔽3)C22
FrattiniC23C2×C3⋊S4
FittingC3×#395D3
socleC23×C3C2×S4
prime radicalC3⋊#5931C2
LCSG ▷ C3×C22⋊SL(2,𝔽3)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊#5930C2semidirect
3. C3×#395⋊C3C2semidirect
11. C3×#395D3semidirect
14. #395⋊C3D3semidirect
51. #395C3⋊D3semidirect
230. C3#73002semidirect

Maximal subgroups

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

subgroupindex
C3⋊#59312
C3⋊#59302
C3×#395⋊C32
#730023
#697053
C4×C3⋊S44