Finite Group Databasebeta

← #77201⋊C3 #11921177

Subgroups — #77201⋊C3 #11921177

Order 1152.

352 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 28 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
2C3×#395⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(#395⋊C3)C211yesmaximal, characteristic, complemented
4#77201C311yesmaximal, characteristic, complemented
5#2616⋊C3—31nomaximal
6C3×C22⋊SL(2,𝔽3)C2211yescharacteristic
7A4×Dic6—41nomaximal
8C22×#239C2×C311yescharacteristic
9#5948—31no—
10C2×#896—31no—
11C3×#395C2×C311yescharacteristic
12#5230C2×C311yescharacteristic
13#4991—31no—
14#4672—31no—
15#4667—31no—
16#395⋊C3—21no—
17#395⋊C3—31no—
18#395⋊C3D311yescharacteristic, complemented
19C3×C4×A4—41no—
20Dic3×A4—41no—
21Dic3×A4—41no—
22C3⋊(#41⋊C3)—82no—
23#2616—31noSylow
24C22×C3×Q8C22×C311yescharacteristic
25C2×#239—62no—
26C2×#239—62no—
27C22×D12—31no—
28C22×C4×D3—31no—
29C22×Dic6A411yescharacteristic
30C22⋊SL(2,𝔽3)—21no—
31C22⋊SL(2,𝔽3)C2×D311yescharacteristic
32Q8×A4—121no—
33C2×C3×C4⋊C4—31no—
34C2×(C2×D3)⋊C4—31no—
35C2×(C2×D3)⋊C4—31no—
36C2×(C2×D3)⋊C4—32no—
37C2×Dic3⋊C4—31no—
38C2×Dic3⋊C4—31no—
39#896—62no—
40#896—62no—
41C3×#95—31no—
42C3⋊#95—31no—
43C2×C3×A4—41no—
44C3×Dic6—161no—
45C3×SL(2,𝔽3)—82no—
46C22×#41—31no—
47C2×C22⋊Q8—91no—
48#395—31no—
49#395C3×D311yescharacteristic
50#394—91no—
51#394—91no—
52#380—91no—
53C23×D3—31no—
54C2×C3×Q8—62no—
55C22×C3×C4—31no—
56C22×C3×C4—31no—
57C22×C3×C4C2×A411yescharacteristic
58C22×Dic3—31no—
59C22×Dic3C2×A411yescharacteristic
60C22×Dic3C2×A411yescharacteristic
61#239—22no—
62#239—62no—
63#239—64no—
64#239—62no—
65#239—62no—
66C2×D12—62no—
67C2×D12—64no—
68C2×C4×D3—32no—
69C2×C4×D3—32no—
70C2×C4×D3—62no—
71C2×C4×D3—62no—
72C2×Dic6—61no—
73C2×Dic6—61no—
74#41⋊C3—242no—
75C4×A4—41no—
76C4×A4—81no—
77C4×A4—121no—
78C4×A4—121no—
79C3×C4⋊C4—62no—
80(C2×D3)⋊C4—62no—
81(C2×D3)⋊C4—62no—
82(C2×D3)⋊C4—122no—
83Dic3⋊C4—61no—
84Dic3⋊C4—61no—
85Dic3⋊C4—62no—
86C3×A4—41no—
87C32×C4—161no—
88C3×Dic3—161no—
89C3×Dic3—161no—
90C2×#41—182no—
91C2×#41—182no—
92C22×Q8—31no—
93C22×Q8C2×C3×D311yescharacteristic
94C22×D4—91no—
95C23×C4—91no—
96C22⋊Q8—182no—
97C22⋊Q8—182no—
98C2×C4⋊C4—31no—
99C2×C4⋊C4—91no—
100C2×C4⋊C4—91no—
101C2×C22⋊C4—91no—
102C2×C22⋊C4—91no—
103C2×C22⋊C4—92no—
104#95—31no—
105#95—91no—
106C23×C3C22×A411yescharacteristic
107C22×D3—32no—
108C22×D3—62no—
109C22×D3—61no—
110C22×D3—62no—
111C22×D3—61no—
112C2×A4—41no—
113C2×A4—81no—
114C3×Q8—22no—
115C3×Q8—62no—
116C3×Q8—481no—
117C2×C3×C4—32no—
118C2×C3×C4—61no—
119C2×C3×C4—62no—
120C2×C3×C4—61no—
121C2×C3×C4—61no—
122C2×C3×C4—61no—
123C2×Dic3—31no—
124C2×Dic3—31no—
125C2×Dic3—61no—
126C2×Dic3—61no—
127C2×Dic3—61no—
128C2×Dic3—61no—
129D12—62no—
130D12—62no—
131D12—64no—
132C4×D3—64no—
133C4×D3—62no—
134C4×D3—62no—
135Dic6—41no—
136Dic6—121no—
137SL(2,𝔽3)—82no—
138SL(2,𝔽3)—162no—
139C2×C32—161no—
140C24—91no—
141#41—62no—
142#41—182no—
143#41—184no—
144#41—182no—
145#41—182no—
146C2×Q8—62no—
147C2×Q8—181no—
148C2×Q8—181no—
149C2×D4—182no—
150C2×D4—184no—
151C22×C4—31no—
152C22×C4—31no—
153C22×C4—31no—
154C22×C4—31no—
155C22×C4—92no—
156C22×C4—92no—
157C22×C4—91no—
158C22×C4—182no—
159C22×C4—182no—
160C22×C4D3×A411yescharacteristic
161C4⋊C4—62no—
162C4⋊C4—182no—
163C4⋊C4—181no—
164C4⋊C4—181no—
165C22⋊C4—182no—
166C22⋊C4—182no—
167C22⋊C4—362no—
168C22×C3—31no—
169C22×C3—31no—
170C22×C3#99411yescharacteristic
171C2×D3—62no—
172C2×D3—62no—
173C2×D3—62no—
174C2×D3—122no—
175C2×D3—122no—
176A4—41no—
177A4—81no—
178C3×C4—41no—
179C3×C4—62no—
180C3×C4—121no—
181C3×C4—161no—
182C3×C4—321no—
183C3×C4—481no—
184C3×C4—481no—
185Dic3—31no—
186Dic3—41no—
187Dic3—121no—
188Dic3#120⋊C311yescharacteristic
189C32—161noSylow
190C23—92no—
191C23—182no—
192C23—181no—
193C23—182no—
194C23—181no—
195C23C2×D3×A411yescharacteristic
196Q8—22no—
197Q8—62no—
198Q8—121no—
199Q8—361no—
200D4—182no—
201D4—182no—
202D4—184no—
203C2×C4—32no—
204C2×C4—61no—
205C2×C4—62no—
206C2×C4—61no—
207C2×C4—61no—
208C2×C4—61no—
209C2×C4—91no—
210C2×C4—91no—
211C2×C4—182no—
212C2×C4—182no—
213C2×C4—184no—
214C2×C4—181no—
215C2×C4—181no—
216C2×C4—181no—
217C2×C4—181no—
218C2×C3—31no—
219C2×C3—31no—
220C2×C3—161no—
221C2×C3—321no—
222C2×C3C2×#120⋊C311yescharacteristic
223D3—122no—
224C22—31no—
225C22—31no—
226C22—182no—
227C22—182no—
228C22—182no—
229C22—362no—
230C22—362no—
231C22C3⋊#99411yescharacteristic
232C4—31no—
233C4—41no—
234C4—62no—
235C4—91no—
236C4—121no—
237C4—121no—
238C4—361no—
239C3—161no—
240C3—321no—
241C3#2616⋊C311yescharacteristic, complemented
242C2—31no—
243C2—31no—
244C2—362no—
245C2D3×#120⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#120⋊C3
commutator, cosocle, hypocenterC22×C3×Q8C22×C3
FrattiniC23C2×D3×A4
FittingC3×#395C2×C3
socleC23×C3C22×A4
prime radicalC3⋊#5948C2
LCSG ▷ C22×C3×Q8
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3×#395⋊C3C2semidirect
3. C3⋊(#395⋊C3)C2semidirect
4. #77201C3semidirect
18. #395⋊C3D3semidirect
241. C3#2616⋊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⋊(#395⋊C3)2
#772013
#2616⋊C33
A4×Dic64