Finite Group Databasebeta

← #11800785

Subgroups — #11800785

Order 1152.

1593 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C42×D3C211yesmaximal, characteristic
2C2×#63855C212yesmaximal
3#10592631C211yesmaximal, characteristic, complemented
4C3×#4932C211yesmaximal, characteristic, complemented
5#10591242C214yesmaximal, complemented
6C4×Dic32C212yesmaximal, complemented
7#10591237C214yesmaximal
8C4×#926—31nomaximal
9#73382—31nomaximal
10C22×C3×C4×D3C2212yes—
11C22×C3×C4×D3C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4×C3⋊Dic3C2212yes—
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2212yes—
16C2×C3×C4×Dic3C2212yes—
17C3×C42×D3C418yescomplemented
18C2×Dic3⋊Dic3C2214yes—
19C2×(C2×D3)⋊Dic3C2214yes—
20C2×Dic32C2218yes—
21#63855C4116yescomplemented
22#63658C2214yes—
23C3×C3⋊#95C2214yes—
24C22×C3×C42—31no—
25C2×#926—32no—
26C2×#872—32no—
27C2×C42×D3D311yescharacteristic
28C3×#376—31no—
29C4×#217—34no—
30C4×C4⋊Dic3—34no—
31#4932—31no—
32#4932—31no—
33#4932—61no—
34#4932D311yescharacteristic, complemented
35C42×Dic3—32no—
36C42×Dic3—32no—
37#4666—34no—
38#4649—34no—
39C23×C3×D3C2311yescharacteristic
40C22×C32×C4C2312yes—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3C2314yes—
43C22×C3×Dic3C2314yes—
44C22×C3×Dic3C2311yescharacteristic
45C22×C3×Dic3C2312yes—
46C2×C3×C4×D3—28no—
47C2×C3×C4×D3C2×C418yes—
48C2×C3×C4×D3C2×C418yes—
49C2×C3×C4×D3C2×C414yes—
50C32×C42C2×C414yes—
51C4×C3⋊Dic3C2×C418yescomplemented
52C3×C4×Dic3C2×C418yes—
53C3×C4×Dic3C2×C414yes—
54C3×C4×Dic3C2×C418yescomplemented
55Dic3⋊Dic3C2×C4116yescomplemented
56(C2×D3)⋊Dic3C2×C4116yes—
57Dic32—216no—
58C4×#117—91noSylow
59C23×C3×C4—31no—
60C23×C3×C4—32no—
61C22×C4×D3C2×D312yes—
62C22×C4×D3C2×D311yescharacteristic
63C2×C3×C42—21no—
64C2×C3×C42—31no—
65C2×C3×C42—32no—
66C2×C3×C42—32no—
67C2×C3×C42—38no—
68C2×C3×C42C2×D311yescharacteristic
69C2×C3×C42C2×D311yescharacteristic
70C2×#217—34no—
71C2×(C2×D3)⋊C4—34no—
72#926—316no—
73C2×C4⋊Dic3—34no—
74C2×Dic3⋊C4—34no—
75C2×C4×Dic3—32no—
76C2×C4×Dic3—32no—
77C2×C4×Dic3—38no—
78C2×C4×Dic3—38no—
79C2×C4×Dic3—62no—
80C2×C4×Dic3C2×D312yes—
81C2×C4×Dic3C2×D312yes—
82C2×C4×Dic3C2×D311yescharacteristic
83#872—316no—
84C42×D3Dic318yescomplemented
85C3×#95—34no—
86C3⋊#95—34no—
87C3⋊#95—34no—
88C3⋊#95—64no—
89C3⋊#95C2×D314yes—
90C23×C32C2411yescharacteristic
91C22×C3×D3—24no—
92C22×C3×D3C22×C414yes—
93C22×C3×D3C22×C412yes—
94C2×C32×C4—24no—
95C2×C32×C4C22×C414yes—
96C2×C32×C4C22×C414yes—
97C2×C32×C4C22×C412yes—
98C2×C3⋊Dic3—28no—
99C2×C3⋊Dic3C22×C418yes—
100C2×C3×Dic3—28no—
101C2×C3×Dic3C22×C418yes—
102C2×C3×Dic3C22×C414yes—
103C2×C3×Dic3C22×C412yes—
104C2×C3×Dic3C22×C414yes—
105C2×C3×Dic3#4118yes—
106C3×C4×D3—216no—
107C3×C4×D3C42116yescomplemented
108C2×#117—92no—
109C22×C42—31no—
110C4×C4⋊C4—94no—
111C4×C22⋊C4—94no—
112#376—31no—
113#376—91no—
114C43—92no—
115C24×C3—31no—
116C23×D3C22×D311yescharacteristic
117C22×C3×C4—22no—
118C22×C3×C4—21no—
119C22×C3×C4—32no—
120C22×C3×C4—31no—
121C22×C3×C4—38no—
122C22×C3×C4—34no—
123C22×C3×C4—34no—
124C22×C3×C4—38no—
125C22×C3×C4—68no—
126C22×C3×C4C22×D312yes—
127C22×C3×C4C22×D312yes—
128C22×C3×C4C22×D311yescharacteristic
129C22×C3×C4C22×D311yescharacteristic
130C22×Dic3—34no—
131C22×Dic3—34no—
132C22×Dic3—64no—
133C22×Dic3C22×D314yes—
134C22×Dic3C22×D311yescharacteristic
135C22×Dic3C22×D312yes—
136C2×C4×D3—28no—
137C2×C4×D3C4×D318yes—
138C2×C4×D3C2×Dic318yes—
139C2×C4×D3C2×Dic314yes—
140C3×C42—24no—
141C3×C42—38no—
142C3×C42—38no—
143C3×C42—34no—
144C3×C42C4×D314yes—
145C3×C42C2×Dic314yes—
146#217—316no—
147(C2×D3)⋊C4—316no—
148C4⋊Dic3—316no—
149Dic3⋊C4—316no—
150C4×Dic3—38no—
151C4×Dic3—38no—
152C4×Dic3—68no—
153C4×Dic3—616no—
154C4×Dic3—616no—
155C4×Dic3C4×D318yescomplemented
156C4×Dic3C2×Dic318yes—
157C4×Dic3C2×Dic314yes—
158C22×C32C23×C412yes—
159C22×C32C23×C411yescharacteristic
160C22×C32C2×#4114yes—
161C2×C3×D3—24no—
162C2×C3×D3—28no—
163C2×C3×D3C2×C4214yes—
164C32×C4—24no—
165C32×C4C2×C4214yes—
166C3⋊Dic3—28no—
167C3×Dic3—28no—
168C3×Dic3C2×C4214yes—
169C3×Dic3#11718yescomplemented
170C23×C4—31no—
171C23×C4—32no—
172#117—916no—
173C2×C4⋊C4—94no—
174C2×C22⋊C4—94no—
175C2×C42—32no—
176C2×C42—32no—
177C2×C42—31no—
178C2×C42—38no—
179C2×C42—92no—
180C2×C42—98no—
181C2×C42D3211yescharacteristic
182#95—34no—
183#95—94no—
184C23×C3—21no—
185C23×C3—34no—
186C23×C3—32no—
187C23×C3—64no—
188C23×C3C23×D311yescharacteristic
189C23×C3C23×D311yescharacteristic
190C22×D3—24no—
191C22×D3C2×C4×D314yes—
192C22×D3C22×Dic312yes—
193C2×C3×C4—24no—
194C2×C3×C4—24no—
195C2×C3×C4—24no—
196C2×C3×C4—22no—
197C2×C3×C4—24no—
198C2×C3×C4—34no—
199C2×C3×C4—32no—
200C2×C3×C4—34no—
201C2×C3×C4—38no—
202C2×C3×C4—316no—
203C2×C3×C4—38no—
204C2×C3×C4—44no—
205C2×C3×C4—616no—
206C2×C3×C4—68no—
207C2×C3×C4C2×C4×D314yes—
208C2×C3×C4C2×C4×D314yes—
209C2×C3×C4C2×C4×D314yes—
210C2×C3×C4C2×C4×D312yes—
211C2×C3×C4C22×Dic314yes—
212C2×C3×C4C22×Dic312yes—
213C2×Dic3—28no—
214C2×Dic3—38no—
215C2×Dic3—38no—
216C2×Dic3—68no—
217C2×Dic3—68no—
218C2×Dic3—68no—
219C2×Dic3—128no—
220C2×Dic3C2×C4×D318yes—
221C2×Dic3C2×C4×D314yes—
222C2×Dic3#23518yes—
223C2×Dic3C22×Dic312yes—
224C2×Dic3C22×Dic314yes—
225C4×D3—216no—
226C4×D3C4×Dic3116yescomplemented
227C2×C32C22×C4211yescharacteristic
228C2×C32C2×#11712yes—
229C2×C32C4×#4114yes—
230C3×D3—24no—
231C24—31no—
232C22×C4—32no—
233C22×C4—31no—
234C22×C4—38no—
235C22×C4—34no—
236C22×C4—34no—
237C22×C4—38no—
238C22×C4—68no—
239C22×C4—94no—
240C22×C4C2×D3212yes—
241C22×C4C2×D3211yescharacteristic
242C4⋊C4—916no—
243C22⋊C4—916no—
244C42—38no—
245C42—38no—
246C42—34no—
247C42—98no—
248C42—1816no—
249C42D3×Dic314yes—
250C22×C3—22no—
251C22×C3—24no—
252C22×C3—21no—
253C22×C3—34no—
254C22×C3—64no—
255C22×C3—68no—
256C22×C3C22×C4×D312yes—
257C22×C3C22×C4×D312yes—
258C22×C3C22×C4×D311yescharacteristic
259C22×C3C2×#23514yes—
260C22×C3D3×#4114yes—
261C22×C3C23×Dic311yescharacteristic
262C2×D3—28no—
263C2×D3—24no—
264C2×D3C2×C4×Dic314yes—
265C3×C4—24no—
266C3×C4—24no—
267C3×C4—24no—
268C3×C4—34no—
269C3×C4—38no—
270C3×C4—44no—
271C3×C4—68no—
272C3×C4C42×D314yes—
273C3×C4C2×C4×Dic314yes—
274Dic3—28no—
275Dic3—68no—
276Dic3—68no—
277Dic3—128no—
278Dic3C2×C4×Dic314yes—
279Dic3#92618yescomplemented
280C32C4×#11711yescharacteristic, complemented, Sylow
281C23—34no—
282C23—32no—
283C23—64no—
284C23C22×D3211yescharacteristic
285C2×C4—24no—
286C2×C4—34no—
287C2×C4—38no—
288C2×C4—32no—
289C2×C4—34no—
290C2×C4—316no—
291C2×C4—38no—
292C2×C4—616no—
293C2×C4—68no—
294C2×C4—98no—
295C2×C4—188no—
296C2×C4C4×D3214yes—
297C2×C4C2×D3×Dic314yes—
298C2×C4C2×D3×Dic312yes—
299C2×C3—21no—
300C2×C3—22no—
301C2×C3—24no—
302C2×C3—64no—
303C2×C3C2×C42×D311yescharacteristic
304C2×C3C4×#23514yes—
305C2×C3D3×#11712yes—
306C2×C3#552214yes—
307C2×C3C22×C4×Dic311yescharacteristic
308C2×C3C2×#92612yes—
309D3—24no—
310C22—34no—
311C22—64no—
312C22—68no—
313C22C2×C4×D3212yes—
314C22D3×#23514yes—
315C22C22×D3×Dic311yescharacteristic
316C4—24no—
317C4—34no—
318C4—38no—
319C4—68no—
320C4—188no—
321C4C4×D3×Dic314yes—
322C3—21no—
323C3#7338211yescharacteristic, complemented
324C3C4×#92611yescharacteristic, complemented
325C2—64no—
326C2#1059396514yes—
327C2C2×C4×D3×Dic311yescharacteristic
328C2D3×#92612yes—
subgroupG/H
centerC22×C4C2×D32
commutatorC2×C32C22×C42
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32C4×#117
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. #10592631C2semidirect
4. C3×#4932C2semidirect
5. #10591242C2semidirect
6. C4×Dic32C2semidirect
17. C3×C42×D3C4semidirect
21. #63855C4semidirect
34. #4932D3semidirect
51. C4×C3⋊Dic3C2×C4semidirect
54. C3×C4×Dic3C2×C4semidirect
55. Dic3⋊Dic3C2×C4semidirect
84. C42×D3Dic3semidirect
107. C3×C4×D3C42semidirect
155. C4×Dic3C4×D3semidirect
169. C3×Dic3#117semidirect
226. C4×D3C4×Dic3semidirect
279. Dic3#926semidirect
280. C32C4×#117semidirect
323. C3#73382semidirect
324. C3C4×#926semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C42×D32
C2×#638552
#105926312
C3×#49322
#105912422
C4×Dic322
#105912372
C4×#9263
#733823