Finite Group Databasebeta

← #76777⋊C3 #11921170

Subgroups — #76777⋊C3 #11921170

Order 1152.

412 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 32 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×#393⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(#395⋊C3)C211yesmaximal, characteristic, complemented
4#76777C311yesmaximal, characteristic, complemented
5#2388⋊C3—31nomaximal
6C3×C22⋊SL(2,𝔽3)C2211yescharacteristic
7C2×Dic3×A4—41nomaximal
8C22×#239C2×C311yescharacteristic, complemented
9#5948—31no—
10C2×#67⋊C4—31no—
11C3×#393C2×C311yescharacteristic
12#5230C2×C311yescharacteristic, complemented
13#4960—31no—
14#4672—31no—
15#4666—31no—
16#395⋊C3—31no—
17#393⋊C3—21no—
18#393⋊C3D311yescharacteristic, complemented
19C22×C3×A4—41no—
20Dic3×A4—41no—
21Dic3×A4—41no—
22C3⋊(#41⋊C3)—82no—
23#2388—31noSylow
24C22×C3×Q8C22×C311yescharacteristic
25C22×#67—31no—
26C23×Dic3A411yescharacteristic
27C2×#239—62no—
28C2×#239—62no—
29C22×D12—31no—
30C22×C4×D3—31no—
31C22⋊SL(2,𝔽3)—21no—
32C22⋊SL(2,𝔽3)C2×D311yescharacteristic
33C2×C4×A4—121no—
34C2×C3×C22⋊C4—31no—
35C2×(C2×D3)⋊C4—32no—
36C2×(C2×D3)⋊C4—31no—
37C2×Dic3⋊C4—31no—
38C2×C4×Dic3—31no—
39#67⋊C4—62no—
40#67⋊C4—62no—
41C3×#95—31no—
42C3⋊#95—31no—
43C2×C3×A4—42no—
44C2×C3×A4—41no—
45C2×C3×Dic3—161no—
46C3×SL(2,𝔽3)—82no—
47C22×#41—31no—
48C2×C4×D4—91no—
49#395—31no—
50#394—91no—
51#393C3×D311yescharacteristic
52#392—91no—
53C4×C22⋊C4—91no—
54C24×C3C2×A411yescharacteristic
55C23×D3—31no—
56C22×A4—41no—
57C22×A4—81no—
58C2×C3×Q8—62no—
59C22×C3×C4—31no—
60C22×C3×C4—31no—
61C2×#67—62no—
62C2×#67—62no—
63C2×#67—62no—
64C22×Dic3—31no—
65C22×Dic3—61no—
66C22×Dic3—61no—
67C22×Dic3C2×A411yescharacteristic
68C22×Dic3C2×A411yescharacteristic
69#239—22no—
70#239—62no—
71#239—64no—
72#239—62no—
73#239—62no—
74C2×D12—62no—
75C2×D12—64no—
76C2×C4×D3—32no—
77C2×C4×D3—32no—
78C2×C4×D3—62no—
79C2×C4×D3—62no—
80#41⋊C3—242no—
81C4×A4—121no—
82C4×A4—121no—
83C3×C22⋊C4—62no—
84(C2×D3)⋊C4—64no—
85(C2×D3)⋊C4—62no—
86Dic3⋊C4—62no—
87C4×Dic3—61no—
88C4×Dic3—61no—
89C22×C32—161no—
90C3×A4—41no—
91C3×Dic3—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—91no—
103C2×C22⋊C4—31no—
104C2×C22⋊C4—91no—
105C2×C22⋊C4—92no—
106C2×C42—91no—
107#95—31no—
108#95—91no—
109C23×C3—61no—
110C23×C3—61no—
111C23×C3#41⋊C312yescomplemented
112C23×C3C22×A411yescharacteristic
113C22×D3—32no—
114C22×D3—62no—
115C22×D3—62no—
116C22×D3—61no—
117C22×D3—61no—
118C2×A4—41no—
119C2×A4—42no—
120C2×A4—81no—
121C2×A4—82no—
122C3×Q8—22no—
123C3×Q8—62no—
124C2×C3×C4—32no—
125C2×C3×C4—62no—
126C2×C3×C4—61no—
127C2×C3×C4—62no—
128C2×C3×C4—481no—
129#67—68no—
130C2×Dic3—31no—
131C2×Dic3—31no—
132C2×Dic3—32no—
133C2×Dic3—41no—
134C2×Dic3—61no—
135C2×Dic3—61no—
136C2×Dic3—61no—
137C2×Dic3—121no—
138D12—62no—
139D12—62no—
140D12—64no—
141C4×D3—64no—
142C4×D3—62no—
143C4×D3—62no—
144SL(2,𝔽3)—82no—
145SL(2,𝔽3)—162no—
146C2×C32—162no—
147C2×C32—161no—
148C24—91no—
149C24D3×A411yescharacteristic
150#41—62no—
151#41—182no—
152#41—184no—
153#41—182no—
154#41—182no—
155C2×Q8—62no—
156C2×D4—182no—
157C2×D4—184no—
158C2×D4—182no—
159C2×D4—182no—
160C2×D4—182no—
161C22×C4—31no—
162C22×C4—31no—
163C22×C4—31no—
164C22×C4—31no—
165C22×C4—92no—
166C22×C4—92no—
167C22×C4—91no—
168C22×C4—182no—
169C22×C4—182no—
170C22×C4—181no—
171C22×C4—181no—
172C4⋊C4—182no—
173C22⋊C4—62no—
174C22⋊C4—184no—
175C22⋊C4—182no—
176C42—181no—
177C42—181no—
178C22×C3—31no—
179C22×C3—31no—
180C22×C3—41no—
181C22×C3—62no—
182C22×C3—121no—
183C22×C3—161no—
184C22×C3—321no—
185C22×C3C2×#41⋊C311yescharacteristic
186C2×D3—62no—
187C2×D3—62no—
188C2×D3—62no—
189C2×D3—122no—
190C2×D3—122no—
191A4—41no—
192A4—81no—
193C3×C4—62no—
194C3×C4—121no—
195C3×C4—481no—
196C3×C4—481no—
197Dic3—31no—
198Dic3—41no—
199Dic3—62no—
200Dic3#120⋊C311yescharacteristic
201C32—161noSylow
202C23—61no—
203C23—61no—
204C23—92no—
205C23—182no—
206C23—182no—
207C23—181no—
208C23—181no—
209C23C3⋊(#41⋊C3)12yescomplemented
210C23C2×D3×A411yescharacteristic
211Q8—22no—
212Q8—62no—
213D4—182no—
214D4—182no—
215D4—184no—
216D4—188no—
217C2×C4—32no—
218C2×C4—62no—
219C2×C4—61no—
220C2×C4—62no—
221C2×C4—91no—
222C2×C4—91no—
223C2×C4—92no—
224C2×C4—121no—
225C2×C4—182no—
226C2×C4—182no—
227C2×C4—184no—
228C2×C4—181no—
229C2×C4—181no—
230C2×C4—181no—
231C2×C4—361no—
232C2×C3—31no—
233C2×C3—31no—
234C2×C3—42no—
235C2×C3—162no—
236C2×C3—161no—
237C2×C3—322no—
238C2×C3—321no—
239C2×C3C2×#120⋊C311yescharacteristic
240D3—122no—
241C22—31no—
242C22—31no—
243C22—41no—
244C22—62no—
245C22—121no—
246C22—182no—
247C22—182no—
248C22—182no—
249C22—362no—
250C22—362no—
251C22C2×C3⋊(#41⋊C3)11yescharacteristic
252C4—31no—
253C4—62no—
254C4—91no—
255C4—121no—
256C4—121no—
257C4—182no—
258C3—161no—
259C3—321no—
260C3#2388⋊C311yescharacteristic, complemented
261C2—31no—
262C2—31no—
263C2—42no—
264C2—362no—
265C2D3×#120⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#120⋊C3
commutator, cosocle, hypocenterC22×C3×Q8C22×C3
FrattiniC23C2×D3×A4
FittingC3×#393C2×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×#393⋊C3C2semidirect
3. C3⋊(#395⋊C3)C2semidirect
4. #76777C3semidirect
8. C22×#239C2×C3semidirect
12. #5230C2×C3semidirect
18. #393⋊C3D3semidirect
111. C23×C3#41⋊C3semidirect
209. C23C3⋊(#41⋊C3)semidirect
260. 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×#393⋊C32
C3⋊(#395⋊C3)2
#767773
#2388⋊C33
C2×Dic3×A44