Finite Group Databasebeta

← #11920700

Subgroups — #11920700

Order 1152.

333 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 333 conjugacy classes of subgroups — too many to draw. Only its 47 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×#984C211yesmaximal, characteristic
2C2×C3⋊(#131⋊C3)C211yesmaximal, characteristic
3#10593660C211yesmaximal, characteristic
4#73124—31nomaximal
5#72103—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7C3×#984—21no—
8C3×#984C412yescomplemented
9C2×C3×#226—21no—
10C3⋊(#131⋊C3)—21no—
11C3⋊#859—21no—
12#63566—41nomaximal
13C2×#984D311yescharacteristic
14C2×C3×#137—31no—
15C2×#948D311yescharacteristic
16C2×#131⋊C3—31no—
17#5426—31no—
18#5426—61no—
19#5232—31no—
20C2×#836—31no—
21C2×#835—31no—
22#4558—31no—
23#4554—31no—
24C2×C3×Dic6—41no—
25C3×#41⋊C3C2×C411yescharacteristic
26C3×#41⋊C3D411yescharacteristic
27C2×C3×SL(2,𝔽3)D411yescharacteristic
28C3×#226—22no—
29C4⋊(C3⋊Dic3)—41no—
30C2×C3×C3⋊C8—41no—
31#1908—91noSylow
32C2×C3×#41C2×D311yescharacteristic
33C22×C3×Q8—31no—
34C2×#41⋊C3—21no—
35C2×#41⋊C3C2×D311yescharacteristic
36#984—21no—
37#984Dic312yescomplemented
38C2×#226—21no—
39C3×#137—32no—
40C3×#137—32no—
41C3×#137—61no—
42C3×#137—61no—
43C2×C3×Q16—61no—
44C2×C3×SD16—61no—
45C2×C3×M16—31no—
46#948—21no—
47#948—61no—
48C2×C4⋊Dic3—31no—
49C2×#208—31no—
50C2×#208—31no—
51C22×C3⋊C8—31no—
52#131⋊C3—61no—
53#859—62no—
54#859—61no—
55#836—62no—
56#835—61no—
57#835—61no—
58#835—61no—
59#832—61no—
60#816—121no—
61C2×C32×C4—41no—
62C2×C3⋊Dic3—81no—
63C2×C3×Dic3—81no—
64C3×Dic6—42no—
65C3×Dic6—81no—
66C3×SL(2,𝔽3)C22⋊C411yescharacteristic
67C3×C3⋊C8—81no—
68C2×#137—31no—
69C2×#131—31no—
70#417—91no—
71C2×#103—91no—
72C2×#101—91no—
73#343—91no—
74#341—91no—
75C3×#41—31no—
76C3×#41—31no—
77C3×#41C4×D311yescharacteristic
78C3×#41#6711yescharacteristic
79C2×C3×Q8—32no—
80C2×C3×Q8—61no—
81C2×C3×Q8—61no—
82C2×C3×Q8—61no—
83C2×C3×Q8—61no—
84C2×C3×Q8—61no—
85C2×C3×Q8D1211yescharacteristic
86C2×C3×D4—31no—
87C22×C3×C4—31no—
88C22×C3×C4—61no—
89C22×Dic3—61no—
90C2×Dic6—41no—
91#41⋊C3—21no—
92#41⋊C3—21no—
93#41⋊C3C2×Dic311yescharacteristic
94#41⋊C3#6711yescharacteristic
95C2×SL(2,𝔽3)—21no—
96C2×SL(2,𝔽3)#6711yescharacteristic
97#226—22no—
98C3×Q16—62no—
99C3×Q16—62no—
100C3×SD16—62no—
101C3×SD16—62no—
102C3×M16—32no—
103C3×M16—61no—
104C2×C3×C8—61no—
105C2×C3×C8—121no—
106C4⋊Dic3—61no—
107C4⋊Dic3—61no—
108C4⋊Dic3—121no—
109C4⋊Dic3—241no—
110#208—32no—
111#208—61no—
112#208—61no—
113#208—61no—
114C2×C3⋊C8—31no—
115C2×C3⋊C8—61no—
116C2×C3⋊C8—61no—
117C2×C3⋊C8—61no—
118C2×C3⋊C8S411yescharacteristic
119C22×C32—41no—
120C32×C4—41no—
121C32×C4—41no—
122C3⋊Dic3—161no—
123C3×Dic3—82no—
124C2×#41D3211yescharacteristic
125C22×Q8—31no—
126#137—32no—
127#137—32no—
128#137—61no—
129#137—61no—
130C2×Q16—61no—
131C2×SD16—61no—
132#131—61no—
133#131—181no—
134C2×M16—31no—
135C2×M16—91no—
136C2×M16—91no—
137C22×C8—91no—
138C2×C4⋊C4—91no—
139#103—181no—
140#103—181no—
141#103—181no—
142#102—181no—
143#101—182no—
144C23×C3—31no—
145C3×Q8—31no—
146C3×Q8—62no—
147C3×Q8—62no—
148C3×Q8—121no—
149C3×Q8—121no—
150C3×Q8(C2×D3)⋊C411yescharacteristic
151C3×D4—31no—
152C3×D4—31no—
153C3×D4—61no—
154C2×C3×C4—31no—
155C2×C3×C4—31no—
156C2×C3×C4—31no—
157C2×C3×C4—31no—
158C2×C3×C4—31no—
159C2×C3×C4—41no—
160C2×C3×C4—62no—
161C2×C3×C4—81no—
162C2×C3×C4—121no—
163C2×C3×C4—121no—
164C2×C3×C4C2×S411yescharacteristic
165C2×Dic3—81no—
166C2×Dic3—121no—
167C2×Dic3—241no—
168C2×Dic3—242no—
169C2×Dic3—241no—
170Dic6—42no—
171Dic6—81no—
172SL(2,𝔽3)—21no—
173SL(2,𝔽3)#21711yescharacteristic
174C3×C8—62no—
175C3×C8—241no—
176C3⋊C8—21no—
177C3⋊C8—61no—
178C3⋊C8—121no—
179C2×C32—41no—
180C2×C32—41no—
181C2×C32—41no—
182#41—31no—
183#41—31no—
184#41D3×Dic311yescharacteristic
185#41#62511yescharacteristic
186C2×Q8—32no—
187C2×Q8—61no—
188C2×Q8—61no—
189C2×Q8—61no—
190C2×Q8—61no—
191C2×Q8—61no—
192C2×Q8#62611yescharacteristic
193C2×D4—31no—
194C22×C4—31no—
195C22×C4—61no—
196C22×C4—181no—
197Q16—62no—
198Q16—62no—
199SD16—62no—
200SD16—62no—
201M16—32no—
202M16—61no—
203M16—92no—
204M16—181no—
205M16—181no—
206M16—181no—
207C2×C8—31no—
208C2×C8—61no—
209C2×C8—91no—
210C2×C8—181no—
211C2×C8—181no—
212C2×C8—181no—
213C4⋊C4—181no—
214C4⋊C4—181no—
215C22×C3—31no—
216C22×C3—31no—
217C22×C3—41no—
218C22×C3—61no—
219C22×C3—61no—
220C22×C3—81no—
221C22×C3C4⋊S411yescharacteristic
222C3×C4—31no—
223C3×C4—31no—
224C3×C4—41no—
225C3×C4—41no—
226C3×C4—81no—
227C3×C4—81no—
228C3×C4—122no—
229C3×C4C4×S411yescharacteristic
230C3×C4GL(2,ℤ/4)11yescharacteristic
231Dic3—82no—
232Dic3—241no—
233Dic3—481no—
234Dic3—482no—
235C32—41noSylow
236C23—31no—
237Q8—31no—
238Q8—62no—
239Q8—62no—
240Q8—121no—
241Q8—121no—
242Q8(C2×D3)⋊Dic311yescharacteristic
243D4—31no—
244D4—31no—
245D4—61no—
246C2×C4—31no—
247C2×C4—31no—
248C2×C4—31no—
249C2×C4—31no—
250C2×C4—31no—
251C2×C4—62no—
252C2×C4—121no—
253C2×C4—121no—
254C2×C4—361no—
255C2×C4—721no—
256C2×C4D3×S411yescharacteristic
257C8—62no—
258C8—61no—
259C8—181no—
260C8—361no—
261C2×C3—41no—
262C2×C3—41no—
263C2×C3—41no—
264C2×C3—61no—
265C2×C3—61no—
266C2×C3—81no—
267C2×C3—81no—
268C2×C3—81no—
269C2×C3#540311yescharacteristic
270C2×C3#540611yescharacteristic
271C2×C3(C2×S4)⋊C411yescharacteristic
272C22—31no—
273C22—31no—
274C22—61no—
275C22—61no—
276C22#6420711yescharacteristic
277C4—31no—
278C4—31no—
279C4—122no—
280C4—721no—
281C4Dic3×S411yescharacteristic
282C4#6420911yescharacteristic
283C3—41no—
284C3—81no—
285C3#7312411yescharacteristic, complemented
286C2—61no—
287C2—61no—
288C2#1059322411yescharacteristic
289C2#1059322611yescharacteristic
290C2(C2×S4)⋊Dic311yescharacteristic
subgroupG/H
centerC22#64207
commutatorC3×#41⋊C3C2×C4
Frattini, hypercenterC2×C4D3×S4
FittingC2×C3×#41C2×D3
socleC22×C3C4⋊S4
prime radical, cosocleC2×C3×#41⋊C3C22
hypocenterC3×SL(2,𝔽3)C22⋊C4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
8. C3×#984C4semidirect
37. #984Dic3semidirect
285. C3#73124semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9842
C2×C3⋊(#131⋊C3)2
#105936602
#731243
#721033
#635664