Finite Group Databasebeta

← #11808063

Subgroups — #11808063

Order 1152.

981 conjugacy classes of subgroups; only the 284 normal subgroups are shown.

normal subgroups only

This group has 981 conjugacy classes of subgroups — too many to draw. Only its 284 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×#876C211yesmaximal, characteristic
2#10592636C211yesmaximal, characteristic, complemented
3C3×#4935C211yesmaximal, characteristic, complemented
4#10591377C213yesmaximal
5#10591307C213yesmaximal
6#10591265C213yesmaximal, complemented
7#10591262C213yesmaximal, complemented
8#83076—31nomaximal
9#74361—31nomaximal
10C22×D3×Dic3C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×C3×(C2×D3)⋊C4C2213yes—
13C2×C3×C4⋊Dic3C2213yes—
14C2×C3×C4⋊Dic3C2213yes—
15C2×C3×Dic3⋊C4C2213yes—
16C3×#876C418yescomplemented
17C2×Dic3⋊Dic3C2213yes—
18C2×(C2×D3)⋊Dic3C2213yes—
19C2×Dic32C2213yes—
20#63658C2213yes—
21#63658C2213yes—
22#63579C2213yes—
23#63579C2213yes—
24C2×C3×#126—31no—
25C2×#876D311yescharacteristic
26C3×#384—31no—
27#4990—33no—
28#4989—33no—
29#4984—33no—
30#4980—33no—
31#4978—33no—
32#4976—33no—
33#4951—33no—
34#4950—33no—
35#4937—31no—
36#4937—31no—
37#4937—61no—
38#4935D311yescharacteristic, complemented
39C23×C3×D3C2311yescharacteristic
40C22×C32×C4C2313yes—
41C22×C3⋊Dic3C2311yescharacteristic
42C22×C3⋊Dic3C2313yes—
43C22×C3×Dic3C2311yescharacteristic
44C22×C3×Dic3C2313yes—
45C22×C3×Dic3C2313yes—
46C2×D3×Dic3—43no—
47C32×C42C2×C414yescomplemented
48C3×(C2×D3)⋊C4C2×C4112yes—
49C3×C4⋊Dic3—43no—
50C3×C4⋊Dic3—43no—
51C3×Dic3⋊C4C2×C4112yescomplemented
52Dic3⋊Dic3—43no—
53(C2×D3)⋊Dic3—43no—
54Dic32—43no—
55#2383—91noSylow
56C23×Dic3—31no—
57C22×C4×D3—31no—
58C3×#126—38no—
59C2×C3×C4⋊C4—33no—
60C2×C3×C4⋊C4—33no—
61C2×C3×C4⋊C4—33no—
62C2×C3×C22⋊C4—33no—
63C2×C3×C42—21no—
64C2×C3×C42C2×D311yescharacteristic
65C2×C3×C42C2×D311yescharacteristic
66C2×#217—33no—
67C2×(C2×D3)⋊C4—33no—
68C2×(C2×D3)⋊C4C2×D313yes—
69C2×C4⋊Dic3—33no—
70C2×C4⋊Dic3C2×D313yes—
71C2×C4⋊Dic3C2×D313yes—
72C2×Dic3⋊C4—33no—
73C2×Dic3⋊C4C2×D313yes—
74C2×C4×Dic3—33no—
75C2×C4×Dic3—33no—
76#876Dic318yescomplemented
77C3⋊#95—33no—
78C3⋊#95—33no—
79C3⋊#95—33no—
80C3⋊#95—33no—
81C3⋊#95—33no—
82C3⋊#95—33no—
83C3⋊#95—33no—
84C3⋊#95—33no—
85C3⋊#95—63no—
86C3⋊#95—63no—
87C23×C32C2411yescharacteristic
88C22×C3×D3—23no—
89C22×C3×D3—23no—
90C22×C3×D3C22×C412yes—
91C2×C32×C4—23no—
92C2×C32×C4—23no—
93C2×C32×C4C22×C416yes—
94C2×C3⋊Dic3—23no—
95C2×C3⋊Dic3—23no—
96C2×C3⋊Dic3—26no—
97C2×C3×Dic3—23no—
98C2×C3×Dic3—23no—
99C2×C3×Dic3—23no—
100C2×C3×Dic3—23no—
101C2×C3×Dic3—23no—
102C2×C3×Dic3—23no—
103C2×C3×Dic3C22×C416yes—
104D3×Dic3—44no—
105C2×#126—31no—
106#389—93no—
107#388—93no—
108#387—93no—
109#385—93no—
110#384—31no—
111#383—91no—
112C24×C3—31no—
113C23×D3C22×D311yescharacteristic
114C22×C3×C4—23no—
115C22×C3×C4—33no—
116C22×C3×C4—31no—
117C22×C3×C4—33no—
118C22×C3×C4C22×D313yes—
119C22×C3×C4C22×D313yes—
120C22×Dic3—33no—
121C22×Dic3—33no—
122C22×Dic3—31no—
123C22×Dic3—31no—
124C22×Dic3—63no—
125C22×Dic3—61no—
126C22×Dic3—123no—
127C22×Dic3C22×D311yescharacteristic
128C22×Dic3C22×D313yes—
129C22×Dic3C22×D313yes—
130C2×C4×D3—123no—
131C3×C4⋊C4—312no—
132C3×C4⋊C4—123no—
133C3×C4⋊C4—123no—
134C3×C22⋊C4—312no—
135C3×C42—24no—
136C3×C42C4×D314yescomplemented
137C3×C42C2×Dic314yescomplemented
138#217—123no—
139(C2×D3)⋊C4—123no—
140(C2×D3)⋊C4C2×Dic3112yes—
141C4⋊Dic3—43no—
142C4⋊Dic3—43no—
143C4⋊Dic3—123no—
144Dic3⋊C4—123no—
145Dic3⋊C4C2×Dic3112yescomplemented
146C4×Dic3—123no—
147C4×Dic3—123no—
148C22×C32C23×C411yescharacteristic
149C22×C32H(5,𝔽2)13yes—
150C22×C322−1+413yes—
151C2×C3×D3—26no—
152C2×C3×D3—41no—
153C2×C3×D3—43no—
154C32×C4—26no—
155C3⋊Dic3—41no—
156C3⋊Dic3—43no—
157C3×Dic3—26no—
158C3×Dic3—41no—
159C3×Dic3—43no—
160C23×C4—91no—
161#126—38no—
162C2×C4⋊C4—33no—
163C2×C4⋊C4—33no—
164C2×C4⋊C4—33no—
165C2×C4⋊C4—93no—
166C2×C22⋊C4—33no—
167C2×C22⋊C4—93no—
168C2×C42—93no—
169C2×C42D3211yescharacteristic
170#95—93no—
171#95—93no—
172#95—93no—
173#95—93no—
174C23×C3—21no—
175C23×C3—32no—
176C23×C3—63no—
177C23×C3—63no—
178C23×C3C23×D311yescharacteristic
179C23×C3C23×D311yescharacteristic
180C22×D3—23no—
181C22×D3—23no—
182C22×D3C22×Dic312yes—
183C2×C3×C4—23no—
184C2×C3×C4—23no—
185C2×C3×C4—23no—
186C2×C3×C4—23no—
187C2×C3×C4—26no—
188C2×C3×C4—36no—
189C2×C3×C4—43no—
190C2×C3×C4—43no—
191C2×C3×C4—63no—
192C2×C3×C4—63no—
193C2×C3×C4—63no—
194C2×C3×C4—63no—
195C2×C3×C4—63no—
196C2×C3×C4—63no—
197C2×C3×C4C2×C4×D316yes—
198C2×C3×C4C22×Dic316yes—
199C2×Dic3—23no—
200C2×Dic3—23no—
201C2×Dic3—23no—
202C2×Dic3—23no—
203C2×Dic3—23no—
204C2×Dic3—23no—
205C2×Dic3—63no—
206C2×Dic3—63no—
207C2×Dic3—66no—
208C2×Dic3—63no—
209C2×Dic3—63no—
210C2×Dic3—66no—
211C2×Dic3—126no—
212C2×Dic3—123no—
213C2×Dic3—123no—
214C2×Dic3—124no—
215C2×Dic3C22×Dic316yes—
216C4×D3—124no—
217C2×C32#52013yes—
218C2×C32#56011yescharacteristic
219C2×C32#56313yes—
220C3×D3—42no—
221C24—31no—
222C22×C4—33no—
223C22×C4—31no—
224C22×C4—33no—
225C22×C4—93no—
226C22×C4—91no—
227C22×C4—363no—
228C22×C4C2×D3213yes—
229C4⋊C4—312no—
230C4⋊C4—123no—
231C4⋊C4—123no—
232C4⋊C4—363no—
233C22⋊C4—312no—
234C22⋊C4—363no—
235C42—363no—
236C42D3×Dic314yescomplemented
237C22×C3—23no—
238C22×C3—23no—
239C22×C3—21no—
240C22×C3—66no—
241C22×C3—121no—
242C22×C3—123no—
243C22×C3C22×C4×D311yescharacteristic
244C22×C3#100413yes—
245C22×C3#100713yes—
246C22×C3#100913yes—
247C22×C3#101013yes—
248C22×C3C23×Dic311yescharacteristic
249C2×D3—26no—
250C2×D3—41no—
251C2×D3—43no—
252C3×C4—26no—
253C3×C4—26no—
254C3×C4—46no—
255C3×C4—66no—
256C3×C4—121no—
257C3×C4—123no—
258Dic3—26no—
259Dic3—41no—
260Dic3—43no—
261Dic3—121no—
262Dic3—123no—
263Dic3—121no—
264Dic3—123no—
265Dic3—243no—
266Dic3—241no—
267C32#238311yescharacteristic, complemented, Sylow
268C23—32no—
269C23—63no—
270C23—63no—
271C23C22×D3211yescharacteristic
272C2×C4—23no—
273C2×C4—23no—
274C2×C4—36no—
275C2×C4—63no—
276C2×C4—63no—
277C2×C4—63no—
278C2×C4—63no—
279C2×C4—63no—
280C2×C4—63no—
281C2×C4—186no—
282C2×C4—183no—
283C2×C4—183no—
284C2×C4—364no—
285C2×C4C2×D3×Dic316yes—
286C2×C3—23no—
287C2×C3—23no—
288C2×C3—21no—
289C2×C3—122no—
290C2×C3#550413yes—
291C2×C3#571111yescharacteristic
292C2×C3#571213yes—
293C2×C3#572011yescharacteristic
294C2×C3#573513yes—
295C2×C3#582713yes—
296D3—42no—
297C22—66no—
298C22—123no—
299C22—121no—
300C22#6429713yes—
301C22#6430713yes—
302C22C22×D3×Dic311yescharacteristic
303C4—26no—
304C4—66no—
305C4—121no—
306C4—123no—
307C4—363no—
308C4—361no—
309C3—21no—
310C3#7436111yescharacteristic, complemented
311C3#8307611yescharacteristic, complemented
312C2—122no—
313C2#1059395713yes—
314C2#1059402211yescharacteristic
315C2#1059498613yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2383
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10592636C2semidirect
3. C3×#4935C2semidirect
6. #10591265C2semidirect
7. #10591262C2semidirect
16. C3×#876C4semidirect
38. #4935D3semidirect
47. C32×C42C2×C4semidirect
51. C3×Dic3⋊C4C2×C4semidirect
76. #876Dic3semidirect
136. C3×C42C4×D3semidirect
137. C3×C42C2×Dic3semidirect
145. Dic3⋊C4C2×Dic3semidirect
236. C42D3×Dic3semidirect
267. C32#2383semidirect
310. C3#74361semidirect
311. C3#83076semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8762
#105926362
C3×#49352
#105913772
#105913072
#105912652
#105912622
#830763
#743613