Finite Group Databasebeta

← #11920707

Subgroups — #11920707

Order 1152.

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

normal subgroups only

This group has 361 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×#986C211yesmaximal, characteristic
2C2×C3⋊(#131⋊C3)C211yesmaximal, characteristic, complemented
3#10593660C211yesmaximal, characteristic, complemented
4#73128—31nomaximal
5#72091—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7C3×#986—21no—
8C3×#986C412yescomplemented
9C2×C3×GL(2,𝔽3)—21no—
10C3⋊(#131⋊C3)—21no—
11C3⋊#859—21no—
12#63563—41nomaximal
13C2×#986D311yescharacteristic
14C2×C3×AGL(1,ℤ/8)—31no—
15C2×#948D311yescharacteristic, complemented
16C2×#131⋊C3—31no—
17#5426—31no—
18#5426—61no—
19#5232—31no—
20C2×#833—31no—
21C2×#832—31no—
22#4558—31no—
23#4554—31no—
24C2×C3×D12—41no—
25C3×#41⋊C3C2×C411yescharacteristic
26C3×#41⋊C3D411yescharacteristic
27C2×C3×SL(2,𝔽3)D411yescharacteristic
28C3×GL(2,𝔽3)—22no—
29C4⋊(C3⋊Dic3)—41no—
30C2×C3×C3⋊C8—41no—
31#1907—91noSylow
32C2×C3×#41C2×D311yescharacteristic
33C22×C3×D4—31no—
34C2×#41⋊C3—21no—
35C2×#41⋊C3C2×D311yescharacteristic
36#986—21no—
37#986Dic312yescomplemented
38C2×GL(2,𝔽3)—21no—
39C3×AGL(1,ℤ/8)—32no—
40C3×AGL(1,ℤ/8)—32no—
41C3×AGL(1,ℤ/8)—61no—
42C3×AGL(1,ℤ/8)—61no—
43C2×C3×SD16—61no—
44C2×C3×D8—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#835—61no—
56#833—62no—
57#832—61no—
58#832—61no—
59#832—61no—
60#821—121no—
61C22×C3×D3—81no—
62C2×C32×C4—41no—
63C2×C3⋊Dic3—81no—
64C3×D12—42no—
65C3×D12—81no—
66C3×SL(2,𝔽3)C22⋊C411yescharacteristic
67C3×C3⋊C8—81no—
68C2×AGL(1,ℤ/8)—31no—
69C2×#131—31no—
70#417—91no—
71C2×#102—91no—
72C2×#100—91no—
73#343—91no—
74#341—91no—
75C24×C3—61no—
76C3×#41—31no—
77C3×#41—31no—
78C3×#41C4×D311yescharacteristic
79C3×#41#6711yescharacteristic
80C2×C3×Q8D1211yescharacteristic
81C2×C3×D4—31no—
82C2×C3×D4—32no—
83C2×C3×D4—61no—
84C2×C3×D4—61no—
85C2×C3×D4—61no—
86C2×C3×D4—61no—
87C2×C3×D4—61no—
88C22×C3×C4—31no—
89C22×Dic3—61no—
90C2×D12—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
97GL(2,𝔽3)—22no—
98C3×SD16—62no—
99C3×SD16—62no—
100C3×D8—62no—
101C3×D8—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—
120C2×C3×D3—82no—
121C2×C3×D3—161no—
122C2×C3×D3—161no—
123C32×C4—41no—
124C32×C4—41no—
125C3⋊Dic3—161no—
126C2×#41D3211yescharacteristic
127C22×D4—31no—
128AGL(1,ℤ/8)—32no—
129AGL(1,ℤ/8)—32no—
130AGL(1,ℤ/8)—61no—
131AGL(1,ℤ/8)—61no—
132C2×SD16—61no—
133C2×D8—61no—
134#131—61no—
135#131—181no—
136C2×M16—31no—
137C2×M16—91no—
138C2×M16—91no—
139C22×C8—91no—
140C2×C4⋊C4—91no—
141#103—181no—
142#102—181no—
143#102—181no—
144#102—181no—
145#100—182no—
146C23×C3—31no—
147C23×C3—62no—
148C23×C3—121no—
149C23×C3—121no—
150C23×C3—241no—
151C23×C3—241no—
152C22×D3—81no—
153C3×Q8—31no—
154C3×Q8(C2×D3)⋊C411yescharacteristic
155C3×D4—31no—
156C3×D4—31no—
157C3×D4—61no—
158C3×D4—62no—
159C3×D4—62no—
160C3×D4—121no—
161C3×D4—121no—
162C2×C3×C4—31no—
163C2×C3×C4—31no—
164C2×C3×C4—31no—
165C2×C3×C4—31no—
166C2×C3×C4—31no—
167C2×C3×C4—41no—
168C2×C3×C4—81no—
169C2×C3×C4C2×S411yescharacteristic
170C2×Dic3—121no—
171C2×Dic3—241no—
172C2×Dic3—242no—
173C2×Dic3—241no—
174D12—42no—
175D12—81no—
176SL(2,𝔽3)—21no—
177SL(2,𝔽3)#21711yescharacteristic
178C3×C8—62no—
179C3×C8—241no—
180C3⋊C8—21no—
181C3⋊C8—61no—
182C3⋊C8—121no—
183C2×C32—41no—
184C2×C32—41no—
185C2×C32—41no—
186C3×D3—162no—
187C24—61no—
188#41—31no—
189#41—31no—
190#41D3×Dic311yescharacteristic
191#41#62511yescharacteristic
192C2×Q8#62611yescharacteristic
193C2×D4—31no—
194C2×D4—32no—
195C2×D4—61no—
196C2×D4—61no—
197C2×D4—61no—
198C2×D4—61no—
199C2×D4—61no—
200C22×C4—31no—
201C22×C4—181no—
202SD16—62no—
203SD16—62no—
204D8—62no—
205D8—62no—
206M16—32no—
207M16—61no—
208M16—92no—
209M16—181no—
210M16—181no—
211M16—181no—
212C2×C8—31no—
213C2×C8—61no—
214C2×C8—91no—
215C2×C8—181no—
216C2×C8—181no—
217C2×C8—181no—
218C4⋊C4—181no—
219C4⋊C4—181no—
220C22×C3—31no—
221C22×C3—31no—
222C22×C3—41no—
223C22×C3—61no—
224C22×C3—61no—
225C22×C3—81no—
226C22×C3—122no—
227C22×C3—242no—
228C22×C3—242no—
229C22×C3—241no—
230C22×C3—241no—
231C22×C3C4⋊S411yescharacteristic
232C2×D3—82no—
233C2×D3—161no—
234C2×D3—161no—
235C3×C4—31no—
236C3×C4—31no—
237C3×C4—41no—
238C3×C4—41no—
239C3×C4—81no—
240C3×C4—81no—
241C3×C4C4×S411yescharacteristic
242C3×C4GL(2,ℤ/4)11yescharacteristic
243Dic3—241no—
244Dic3—481no—
245Dic3—482no—
246C32—41noSylow
247C23—31no—
248C23—62no—
249C23—121no—
250C23—121no—
251C23—241no—
252C23—241no—
253Q8—31no—
254Q8(C2×D3)⋊Dic311yescharacteristic
255D4—31no—
256D4—31no—
257D4—61no—
258D4—62no—
259D4—62no—
260D4—121no—
261D4—121no—
262C2×C4—31no—
263C2×C4—31no—
264C2×C4—31no—
265C2×C4—31no—
266C2×C4—31no—
267C2×C4—361no—
268C2×C4—721no—
269C2×C4D3×S411yescharacteristic
270C8—62no—
271C8—61no—
272C8—181no—
273C8—361no—
274C2×C3—41no—
275C2×C3—41no—
276C2×C3—41no—
277C2×C3—61no—
278C2×C3—61no—
279C2×C3—81no—
280C2×C3—81no—
281C2×C3—81no—
282C2×C3—242no—
283C2×C3#540611yescharacteristic
284C2×C3#540711yescharacteristic
285C2×C3(C2×S4)⋊C411yescharacteristic
286D3—162no—
287C22—31no—
288C22—31no—
289C22—61no—
290C22—61no—
291C22—122no—
292C22—242no—
293C22—242no—
294C22—241no—
295C22—241no—
296C22#6420711yescharacteristic
297C4—31no—
298C4—31no—
299C4—721no—
300C4Dic3×S411yescharacteristic
301C4#6420911yescharacteristic
302C3—41no—
303C3—81no—
304C3#7312811yescharacteristic, complemented
305C2—61no—
306C2—61no—
307C2—242no—
308C2#1059322311yescharacteristic
309C2#1059322511yescharacteristic
310C2(C2×S4)⋊Dic311yescharacteristic
subgroupG/H
centerC22#64207
commutatorC3×#41⋊C3C2×C4
Frattini, hypercenterC2×C4D3×S4
FittingC2×C3×#41C2×D3
socleC22×C3C4⋊S4
prime radicalC2×C3×#986C2
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
2. C2×C3⋊(#131⋊C3)C2semidirect
3. #10593660C2semidirect
8. C3×#986C4semidirect
15. C2×#948D3semidirect
37. #986Dic3semidirect
304. C3#73128semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9862
C2×C3⋊(#131⋊C3)2
#105936602
#731283
#720913
#635634