Finite Group Databasebeta

← #11920696

Subgroups — #11920696

Order 1152.

281 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 281 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C2×C3⋊(#131⋊C3)C211yesmaximal, characteristic
2#10593658C211yesmaximal, characteristic
3C2×C3×GU(2,𝔽3)C211yesmaximal, characteristic
4#73122—31nomaximal
5#70376—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7C3⋊(#131⋊C3)—21no—
8C3⋊#859C411yescharacteristic, complemented
9C3⋊#859C411yescharacteristic, complemented
10C3×GU(2,𝔽3)—21no—
11#63572—41nomaximal
12C2×#948D311yescharacteristic
13C2×#131⋊C3—31no—
14#5424—31no—
15#5424—61no—
16C2×GU(2,𝔽3)D311yescharacteristic
17C2×C3×#104—31no—
18#5233—31no—
19C2×#822—31no—
20#5119—31no—
21#4524—31no—
22#4523—31no—
23C3×#41⋊C3D411yescharacteristic
24C3×#41⋊C3Q811yescharacteristic
25C2×C3×SL(2,𝔽3)C2×C411yescharacteristic
26C4×C3⋊Dic3—41no—
27C2×C3×C3⋊C8—41no—
28C2×C3×C3⋊C8—41no—
29#1866—91noSylow
30C2×C3×#41C2×D311yescharacteristic
31C2×#41⋊C3—21no—
32C2×#41⋊C3C2×D311yescharacteristic
33C2×C3×M16—31no—
34C2×C3×C42—31no—
35#948—21no—
36#948—61no—
37#926—31no—
38C2×#208—31no—
39C22×C3⋊C8—31no—
40C22×C3⋊C8—31no—
41#131⋊C3—61no—
42GU(2,𝔽3)—21no—
43#859—31no—
44#859—31no—
45#859—61no—
46#859—61no—
47C3×#104—61no—
48C3×#104—61no—
49#835—31no—
50#835—31no—
51#832—31no—
52#832—31no—
53#822—62no—
54Dic3⋊C8—61no—
55Dic3⋊C8—61no—
56Dic3⋊C8—121no—
57C2×C32×C4—41no—
58C2×C3⋊Dic3—41no—
59C2×C3⋊Dic3—41no—
60C3×SL(2,𝔽3)C4⋊C411yescharacteristic
61C3×C3⋊C8—81no—
62C3×C3⋊C8—81no—
63C2×#131—31no—
64C2×#108—91no—
65#424—91no—
66C2×#104—31no—
67#416—91no—
68#339—91no—
69#336—91no—
70C3×#41—31no—
71C3×#41—31no—
72C3×#41Dic611yescharacteristic
73C3×#41#6711yescharacteristic
74C2×C3×Q8C4×D311yescharacteristic
75C2×C3×D4—31no—
76C22×C3×C4—31no—
77C22×C3×C4—61no—
78#41⋊C3—21no—
79#41⋊C3—21no—
80#41⋊C3Dic611yescharacteristic
81#41⋊C3#6711yescharacteristic
82C2×SL(2,𝔽3)—21no—
83C2×SL(2,𝔽3)C4×D311yescharacteristic
84C3×M16—61no—
85C3×M16—61no—
86C2×C3×C8—61no—
87C2×C3×C8—121no—
88C3×C42—61no—
89C3×C42—61no—
90#217—61no—
91C4⋊Dic3—31no—
92C4⋊Dic3—31no—
93C4×Dic3—61no—
94C4×Dic3—121no—
95C4×Dic3—241no—
96#208—32no—
97#208—61no—
98C2×C3⋊C8—31no—
99C2×C3⋊C8—31no—
100C2×C3⋊C8—31no—
101C2×C3⋊C8—41no—
102C2×C3⋊C8—61no—
103C2×C3⋊C8—61no—
104C2×C3⋊C8—61no—
105C2×C3⋊C8—61no—
106C2×C3⋊C8S411yescharacteristic
107C22×C32—41no—
108C32×C4—41no—
109C32×C4—41no—
110C3⋊Dic3—42no—
111C3⋊Dic3—81no—
112C2×#41D3211yescharacteristic
113#131—61no—
114#131—181no—
115C2×M16—31no—
116C2×M16—91no—
117C22×C8—91no—
118C22×C8—91no—
119#117—91no—
120C2×C42—31no—
121#108—182no—
122C4⋊C8—181no—
123C4⋊C8—181no—
124#104—61no—
125#104—61no—
126#103—91no—
127#103—91no—
128#102—91no—
129#102—91no—
130C23×C3—31no—
131C3×Q8—31no—
132C3×Q8Dic3⋊C411yescharacteristic
133C3×D4—31no—
134C3×D4—31no—
135C3×D4—61no—
136C2×C3×C4—31no—
137C2×C3×C4—31no—
138C2×C3×C4—31no—
139C2×C3×C4—31no—
140C2×C3×C4—31no—
141C2×C3×C4—41no—
142C2×C3×C4—62no—
143C2×C3×C4—81no—
144C2×C3×C4—121no—
145C2×C3×C4—121no—
146C2×C3×C4C2×S411yescharacteristic
147C2×Dic3—61no—
148C2×Dic3—61no—
149C2×Dic3—121no—
150C2×Dic3—121no—
151C2×Dic3—241no—
152C2×Dic3—241no—
153SL(2,𝔽3)—21no—
154SL(2,𝔽3)Dic3⋊C411yescharacteristic
155C3×C8—121no—
156C3×C8—241no—
157C3⋊C8—21no—
158C3⋊C8—61no—
159C3⋊C8—61no—
160C3⋊C8—61no—
161C3⋊C8—81no—
162C2×C32—41no—
163C2×C32—41no—
164C2×C32—41no—
165#41—31no—
166#41—31no—
167#41#62511yescharacteristic
168#41#62711yescharacteristic
169C2×Q8#62411yescharacteristic
170C2×D4—31no—
171C22×C4—31no—
172C22×C4—61no—
173M16—61no—
174M16—61no—
175M16—92no—
176M16—181no—
177C2×C8—31no—
178C2×C8—61no—
179C2×C8—91no—
180C2×C8—91no—
181C2×C8—91no—
182C2×C8—181no—
183C2×C8—181no—
184C2×C8—181no—
185C2×C8—181no—
186C4⋊C4—91no—
187C4⋊C4—91no—
188C22⋊C4—181no—
189C42—61no—
190C42—61no—
191C42—181no—
192C22×C3—31no—
193C22×C3—31no—
194C22×C3—41no—
195C22×C3—61no—
196C22×C3—61no—
197C22×C3—81no—
198C22×C3C4×S411yescharacteristic
199C3×C4—31no—
200C3×C4—31no—
201C3×C4—41no—
202C3×C4—41no—
203C3×C4—81no—
204C3×C4—81no—
205C3×C4—122no—
206C3×C4A4⋊Q811yescharacteristic
207C3×C4GL(2,ℤ/4)11yescharacteristic
208Dic3—122no—
209Dic3—121no—
210Dic3—121no—
211Dic3—241no—
212Dic3—242no—
213Dic3—242no—
214C32—41noSylow
215C23—31no—
216Q8—31no—
217Q8#372411yescharacteristic
218D4—31no—
219D4—31no—
220D4—61no—
221C2×C4—31no—
222C2×C4—31no—
223C2×C4—31no—
224C2×C4—31no—
225C2×C4—31no—
226C2×C4—62no—
227C2×C4—121no—
228C2×C4—121no—
229C2×C4—181no—
230C2×C4—181no—
231C2×C4D3×S411yescharacteristic
232C8—61no—
233C8—121no—
234C8—181no—
235C8—181no—
236C8—181no—
237C2×C3—41no—
238C2×C3—41no—
239C2×C3—41no—
240C2×C3—61no—
241C2×C3—61no—
242C2×C3—81no—
243C2×C3—81no—
244C2×C3—81no—
245C2×C3#540411yescharacteristic
246C2×C3#540511yescharacteristic
247C2×C3SL(2,ℤ/4)⋊C411yescharacteristic
248C22—31no—
249C22—31no—
250C22—61no—
251C22—61no—
252C22(C3⋊S4)⋊C411yescharacteristic
253C4—31no—
254C4—31no—
255C4—122no—
256C4—361no—
257C4—361no—
258C4#6420411yescharacteristic
259C4#6420911yescharacteristic
260C3—41no—
261C3—81no—
262C3#7312211yescharacteristic, complemented
263C2—61no—
264C2—61no—
265C2#1059322011yescharacteristic
266C2#1059322211yescharacteristic
267C2#1059323811yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2×C4D3×S4
commutatorC2×C3×SL(2,𝔽3)C2×C4
FittingC2×C3×#41C2×D3
socleC22×C3C4×S4
prime radical, cosocleC2×C3×#41⋊C3C22
hypocenterC3×SL(2,𝔽3)C4⋊C4
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
8. C3⋊#859C4semidirect
9. C3⋊#859C4semidirect
262. C3#73122semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊(#131⋊C3)2
#105936582
C2×C3×GU(2,𝔽3)2
#731223
#703763
#635724