Finite Group Databasebeta

← #11921031

Subgroups — #11921031

Order 1152.

326 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 59 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×#520⋊C3C211yesmaximal, characteristic
2#10593660C211yesmaximal, characteristic
3C2×C3⋊GU(2,𝔽3)C211yesmaximal, characteristic
4#73075—33nomaximal
5#71665—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7C3×C4×SL(2,𝔽3)—21no—
8C3⋊GU(2,𝔽3)C412yescomplemented
9C3⋊#859—21no—
10#63634—41nomaximal
11C3×#520D311yescharacteristic
12#520⋊C3D313yes—
13#5426—33no—
14C2×GU(2,𝔽3)—33no—
15C2×#837—31no—
16#5232—31no—
17#4995—31no—
18#4977—31no—
19#4532—31no—
20#4530—31no—
21C3×#41⋊C3C2×C411yescharacteristic
22C3×#41⋊C3Q811yescharacteristic
23C2×C3×SL(2,𝔽3)D411yescharacteristic
24C32×C4⋊C4—41no—
25C4⋊(C3⋊Dic3)—41no—
26C2×C3⋊(C3⋊C8)—41no—
27#1860—91noSylow
28C2×C3×#41C2×D311yescharacteristic
29C2×#41⋊C3C2×D313yes—
30C3×C4×Q8—21no—
31C3×C4×D4—61no—
32C3×#117—31no—
33C2×C3×C4⋊C4—31no—
34C2×C4⋊Dic3—31no—
35C2×C4×Dic3—31no—
36C2×#208—31no—
37C2×#208—31no—
38C4×SL(2,𝔽3)—23no—
39GU(2,𝔽3)—36no—
40#859—63no—
41#837—32no—
42#837—32no—
43#835—61no—
44#832—61no—
45C3⋊#95—62no—
46#808—61no—
47#807—61no—
48#807—123no—
49C2×C32×C4—41no—
50C2×C32×C4—81no—
51C2×C3⋊Dic3—81no—
52C3×SL(2,𝔽3)C4⋊C411yescharacteristic
53C3⋊(C3⋊C8)—42no—
54#520C3⋊D311yescharacteristic
55#428—91no—
56C2×#104—91no—
57#417—91no—
58#382—91no—
59#343—91no—
60#339—91no—
61C3×#41—31no—
62C3×#41—31no—
63C3×#41Dic611yescharacteristic
64C3×#41C4×D311yescharacteristic
65C2×C3×Q8#6711yescharacteristic
66C2×C3×D4—31no—
67C22×C3×C4—31no—
68C22×C3×C4—32no—
69C22×Dic3—61no—
70C22×Dic3—61no—
71#41⋊C3Dic613yes—
72#41⋊C3C4×D313yes—
73C2×SL(2,𝔽3)#6713yes—
74C3×C4⋊C4—31no—
75C3×C4⋊C4—43no—
76C3×C4⋊C4—61no—
77C3×C4⋊C4S411yescharacteristic
78C3×C22⋊C4—61no—
79C3×C42—61no—
80C4⋊Dic3—61no—
81C4⋊Dic3—61no—
82C4⋊Dic3—123no—
83C4×Dic3—32no—
84C4×Dic3—61no—
85#208—32no—
86#208—61no—
87#208—61no—
88#208—61no—
89C2×C3⋊C8—61no—
90C2×C3⋊C8—61no—
91C2×C3⋊C8—123no—
92C22×C32—41no—
93C32×C4—41no—
94C32×C4—41no—
95C32×C4—161no—
96C3⋊Dic3—161no—
97C2×#41C2×C3⋊D311yescharacteristic
98C2×M16—91no—
99C2×M16—91no—
100C4×Q8—21no—
101C4×D4—61no—
102#117—31no—
103C2×C4⋊C4—31no—
104C2×C4⋊C4—91no—
105C2×C42—91no—
106#107—181no—
107#106—181no—
108#104—92no—
109#104—92no—
110#103—181no—
111#102—181no—
112#95—182no—
113C23×C3—31no—
114C3×Q8—31no—
115C3×Q8Dic3⋊C411yescharacteristic
116C3×D4—31no—
117C3×D4—31no—
118C3×D4—61no—
119C2×C3×C4—21no—
120C2×C3×C4—31no—
121C2×C3×C4—31no—
122C2×C3×C4—31no—
123C2×C3×C4—31no—
124C2×C3×C4—31no—
125C2×C3×C4—43no—
126C2×C3×C4—61no—
127C2×C3×C4—83no—
128C2×C3×C4—122no—
129C2×C3×C4C2×S411yescharacteristic
130C2×Dic3—62no—
131C2×Dic3—121no—
132C2×Dic3—121no—
133C2×Dic3—122no—
134C2×Dic3—121no—
135C2×Dic3—243no—
136SL(2,𝔽3)Dic3⋊C413yes—
137C3⋊C8—62no—
138C3⋊C8—126no—
139C3⋊C8—121no—
140C2×C32—41no—
141C2×C32—41no—
142C2×C32—41no—
143#41—31no—
144#41—31no—
145#41#63411yescharacteristic
146#41C4×C3⋊D311yescharacteristic
147C2×Q8#63811yescharacteristic
148C2×D4—31no—
149C22×C4—31no—
150C22×C4—32no—
151C22×C4—181no—
152C22×C4—181no—
153M16—92no—
154M16—181no—
155M16—181no—
156M16—181no—
157C2×C8—181no—
158C2×C8—181no—
159C4⋊C4—31no—
160C4⋊C4—61no—
161C4⋊C4—181no—
162C4⋊C4—181no—
163C4⋊C4C3⋊S411yescharacteristic
164C22⋊C4—61no—
165C42—61no—
166C42—92no—
167C42—181no—
168C22×C3—31no—
169C22×C3—31no—
170C22×C3—43no—
171C22×C3—61no—
172C22×C3—61no—
173C22×C3GL(2,ℤ/4)11yescharacteristic
174C3×C4—31no—
175C3×C4—31no—
176C3×C4—41no—
177C3×C4—43no—
178C3×C4—43no—
179C3×C4—121no—
180C3×C4—163no—
181C3×C4A4⋊Q811yescharacteristic
182C3×C4C4×S411yescharacteristic
183Dic3—122no—
184Dic3—241no—
185Dic3—483no—
186C32—41noSylow
187C23—31no—
188Q8—31no—
189Q8#375011yescharacteristic
190D4—31no—
191D4—31no—
192D4—61no—
193C2×C4—21no—
194C2×C4—31no—
195C2×C4—31no—
196C2×C4—31no—
197C2×C4—31no—
198C2×C4—31no—
199C2×C4—61no—
200C2×C4—122no—
201C2×C4—182no—
202C2×C4—361no—
203C2×C4—361no—
204C2×C4—362no—
205C2×C4—361no—
206C2×C4C2×C3⋊S411yescharacteristic
207C8—182no—
208C8—361no—
209C2×C3—43no—
210C2×C3—43no—
211C2×C3—43no—
212C2×C3—61no—
213C2×C3—61no—
214C2×C3SL(2,ℤ/4)⋊C411yescharacteristic
215C2×C3#542811yescharacteristic
216C2×C3#543111yescharacteristic
217C22—31no—
218C22—31no—
219C22—61no—
220C22—61no—
221C22#6426911yescharacteristic
222C4—31no—
223C4—31no—
224C4—41no—
225C4—121no—
226C4—362no—
227C4—721no—
228C4#6425911yescharacteristic
229C4C4×C3⋊S411yescharacteristic
230C3—43no—
231C3#7307511yescharacteristic, complemented
232C2—61no—
233C2—61no—
234C2#1059364511yescharacteristic
235C2#1059366211yescharacteristic
236C2#1059366511yescharacteristic
subgroupG/H
centerC22#64269
commutatorC3×#41⋊C3C2×C4
FrattiniC2×C4C2×C3⋊S4
FittingC3×#520D3
socleC22×C3GL(2,ℤ/4)
prime radical, cosocleC2×C3×#41⋊C3C22
hypercenterC4⋊C4C3⋊S4
hypocenterC3×SL(2,𝔽3)C4⋊C4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
8. C3⋊GU(2,𝔽3)C4semidirect
231. C3#73075semidirect

Maximal subgroups

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

subgroupindex
C3×#520⋊C32
#105936602
C2×C3⋊GU(2,𝔽3)2
#730753
#716653
#636344