Finite Group Databasebeta

← #11800793

Subgroups — #11800793

Order 1152.

1753 conjugacy classes of subgroups.

The subgroup lattice has 271 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#926C212yesmaximal
3#10591705C214yesmaximal
4#10591274C214yesmaximal, complemented
5C4×Dic32C212yesmaximal, complemented
6#10591222C212yesmaximal, complemented
7Dic3×#117—32nomaximal
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2212yes—
10C2×C4×C3⋊Dic3C418yescomplemented
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C4×C3⋊Dic3C2212yes—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×#217C2214yes—
15C3×#926C4116yescomplemented
16C2×C3×C4⋊Dic3C2214yes—
17C2×C3×C4×Dic3C2214yes—
18C2×Dic32C2218yes—
19#63579C2218yes—
20C2×C3×#117—32no—
21C2×#926D312yes—
22C22×C4×Dic3—32no—
23C22×C4×Dic3—61no—
24Dic3×C4⋊C4—38no—
25Dic3×C22⋊C4—38no—
26#4932—34no—
27C42×Dic3—34no—
28C24×C32C2311yescharacteristic
29C22×C32×C4C2×C414yes—
30C22×C32×C4C2×C418yes—
31C22×C32×C4C2311yescharacteristic
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3—28no—
34C22×C3⋊Dic3C2×C418yes—
35C22×C3⋊Dic3C2312yes—
36C22×C3⋊Dic3C2312yes—
37C22×C3×Dic3C2318yes—
38C4×C3⋊Dic3C2×C414yes—
39C4×C3⋊Dic3C2×C418yes—
40C4×C3⋊Dic3C2×C414yes—
41C3×#217C2×C4116yes—
42C3×C4⋊Dic3C2×C4116yescomplemented
43C3×C4×Dic3C2×C4116yescomplemented
44Dic32—216no—
45C4×#117—91noSylow
46C23×C3×C4—21no—
47C23×C3×C4C2×D312yes—
48C23×Dic3—34no—
49C23×Dic3—62no—
50C3×#117—316no—
51C2×C3×C4⋊C4—34no—
52C2×C3×C22⋊C4—34no—
53C2×C3×C42—34no—
54C2×#217C2×D314yes—
55#926Dic3116yescomplemented
56C2×C4⋊Dic3C2×D314yes—
57C2×C4×Dic3—316no—
58C2×C4×Dic3—32no—
59C2×C4×Dic3—32no—
60C2×C4×Dic3—34no—
61C2×C4×Dic3—316no—
62C2×C4×Dic3—68no—
63C2×C4×Dic3—62no—
64C2×C4×Dic3—61no—
65C2×C4×Dic3—61no—
66C2×C4×Dic3C2×D314yes—
67C3⋊#95—316no—
68C23×C32—24no—
69C23×C32C22×C412yes—
70C23×C32C22×C414yes—
71C23×C32C2411yescharacteristic
72C2×C32×C4C42116yescomplemented
73C2×C32×C4C22×C412yes—
74C2×C32×C4C22×C412yes—
75C2×C32×C4C22×C414yes—
76C2×C32×C4C22×C414yes—
77C2×C3⋊Dic3—24no—
78C2×C3⋊Dic3—216no—
79C2×C3⋊Dic3C22×C414yes—
80C2×C3⋊Dic3C22×C414yes—
81C2×C3⋊Dic3#4118yes—
82C2×C3×Dic3—216no—
83C2×C3×Dic3C22×C4116yes—
84C2×#117—32no—
85C22×C42—91no—
86C4×C4⋊C4—94no—
87C4×C22⋊C4—94no—
88#376—92no—
89C43—92no—
90C24×C3—21no—
91C24×C3C22×D312yes—
92C22×C3×C4—28no—
93C22×C3×C4—24no—
94C22×C3×C4—21no—
95C22×C3×C4—21no—
96C22×C3×C4—38no—
97C22×C3×C4C4×D318yes—
98C22×C3×C4C4×D318yes—
99C22×C3×C4C2×Dic318yes—
100C22×C3×C4C22×D312yes—
101C22×C3×C4C22×D312yes—
102C22×Dic3—34no—
103C22×Dic3—316no—
104C22×Dic3—34no—
105C22×Dic3—68no—
106C22×Dic3—62no—
107C22×Dic3—62no—
108C22×Dic3—616no—
109C22×Dic3—616no—
110C22×Dic3C22×D318yes—
111C3×C4⋊C4—316no—
112C3×C22⋊C4—316no—
113C3×C42—316no—
114#217C2×Dic3116yes—
115C4⋊Dic3C2×Dic3116yescomplemented
116C4×Dic3—38no—
117C4×Dic3—316no—
118C4×Dic3—38no—
119C4×Dic3—64no—
120C4×Dic3—68no—
121C4×Dic3—64no—
122C4×Dic3—632no—
123C4×Dic3C2×Dic3116yescomplemented
124C22×C32—24no—
125C22×C32—28no—
126C22×C32C2×C4214yes—
127C22×C32C23×C411yescharacteristic
128C22×C32C23×C412yes—
129C22×C32C2×#4114yes—
130C32×C4C2×C4214yes—
131C32×C4C2×C4214yes—
132C3⋊Dic3—24no—
133C3⋊Dic3#11718yescomplemented
134C3×Dic3—216no—
135C23×C4—92no—
136C23×C4D3211yescharacteristic
137#117—316no—
138C2×C4⋊C4—34no—
139C2×C22⋊C4—34no—
140C2×C42—34no—
141C2×C42—98no—
142C2×C42—92no—
143C2×C42—91no—
144C2×C42—91no—
145C2×C42—98no—
146#95—98no—
147C23×C3—28no—
148C23×C3—28no—
149C23×C3—21no—
150C23×C3—24no—
151C23×C3—22no—
152C23×C3C2×C4×D314yes—
153C23×C3C2×C4×D314yes—
154C23×C3C22×Dic314yes—
155C23×C3C23×D312yes—
156C2×C3×C4—216no—
157C2×C3×C4—24no—
158C2×C3×C4—24no—
159C2×C3×C4—22no—
160C2×C3×C4—22no—
161C2×C3×C4—316no—
162C2×C3×C4—616no—
163C2×C3×C4C4×Dic3132yescomplemented
164C2×C3×C4C2×C4×D314yes—
165C2×C3×C4C2×C4×D314yes—
166C2×C3×C4C2×C4×D314yes—
167C2×C3×C4C2×C4×D314yes—
168C2×C3×C4C22×Dic314yes—
169C2×C3×C4C22×Dic314yes—
170C2×Dic3—216no—
171C2×Dic3—38no—
172C2×Dic3—316no—
173C2×Dic3—38no—
174C2×Dic3—64no—
175C2×Dic3—64no—
176C2×Dic3—68no—
177C2×Dic3—632no—
178C2×Dic3—632no—
179C2×Dic3—68no—
180C2×Dic3—68no—
181C2×Dic3C22×Dic3116yes—
182C2×C32—24no—
183C2×C32C22×C4211yescharacteristic
184C2×C32C2×#11712yes—
185C2×C32C4×#4114yes—
186C24C2×D3211yescharacteristic
187C22×C4—38no—
188C22×C4—92no—
189C22×C4—92no—
190C22×C4—98no—
191C22×C4—188no—
192C22×C4D3×Dic318yes—
193C22×C4#62414yes—
194C22×C4C2×D3211yescharacteristic
195C22×C4C2×D3211yescharacteristic
196C4⋊C4—316no—
197C22⋊C4—316no—
198C42—316no—
199C42—94no—
200C42—98no—
201C42—94no—
202C42—1816no—
203C22×C3—28no—
204C22×C3—216no—
205C22×C3—28no—
206C22×C3—28no—
207C22×C3—28no—
208C22×C3—24no—
209C22×C3—22no—
210C22×C3—21no—
211C22×C3—24no—
212C22×C3C2×C4×Dic318yes—
213C22×C3C22×C4×D312yes—
214C22×C3C22×C4×D312yes—
215C22×C3D3×#4118yes—
216C22×C3C23×Dic312yes—
217C3×C4—24no—
218C3×C4—24no—
219C3×C4—616no—
220C3×C4C2×C4×Dic318yes—
221C3×C4C2×C4×Dic318yes—
222Dic3—216no—
223Dic3—316no—
224Dic3—68no—
225Dic3—68no—
226Dic3—68no—
227C32C4×#11711yescharacteristic, complemented, Sylow
228C23—24no—
229C23C2×D3×Dic314yes—
230C23C2×#62412yes—
231C23C22×D3211yescharacteristic
232C2×C4—316no—
233C2×C4—616no—
234C2×C4—98no—
235C2×C4—94no—
236C2×C4—94no—
237C2×C4—1816no—
238C2×C4—184no—
239C2×C4Dic32116yescomplemented
240C2×C4C2×D3×Dic314yes—
241C2×C4C2×D3×Dic314yes—
242C2×C4C2×#62412yes—
243C2×C4C2×#62412yes—
244C2×C3—28no—
245C2×C3—28no—
246C2×C3—24no—
247C2×C3—21no—
248C2×C3—22no—
249C2×C3D3×#11714yes—
250C2×C3#552214yes—
251C2×C3C22×C4×Dic312yes—
252C2×C3Dic3×#4114yes—
253C22—28no—
254C22—24no—
255C22C2×Dic3214yes—
256C22#6430614yes—
257C22C22×D3×Dic312yes—
258C22C22×#62411yescharacteristic
259C4—616no—
260C4—98no—
261C4—184no—
262C4C2×Dic3214yes—
263C4C2×Dic3214yes—
264C3—21no—
265C3Dic3×#11712yescomplemented
266C2—24no—
267C2#1059495814yes—
268C2#1059496912yes—
269C2C22×Dic3211yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC2×C32C22×C42
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32C4×#117
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. #10591274C2semidirect
5. C4×Dic32C2semidirect
6. #10591222C2semidirect
10. C2×C4×C3⋊Dic3C4semidirect
15. C3×#926C4semidirect
42. C3×C4⋊Dic3C2×C4semidirect
43. C3×C4×Dic3C2×C4semidirect
55. #926Dic3semidirect
72. C2×C32×C4C42semidirect
115. C4⋊Dic3C2×Dic3semidirect
123. C4×Dic3C2×Dic3semidirect
133. C3⋊Dic3#117semidirect
163. C2×C3×C4C4×Dic3semidirect
227. C32C4×#117semidirect
239. C2×C4Dic32semidirect
265. C3Dic3×#117semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊Dic32
C2×C3×#9262
#105917052
#105912742
C4×Dic322
#105912222
Dic3×#1173