Finite Group Databasebeta

← #11800895

Subgroups — #11800895

Order 1152.

1601 conjugacy classes of subgroups.

The subgroup lattice has 247 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
2C2×C3×#926C212yesmaximal
3#10591705C214yesmaximal
4Dic3×C4⋊Dic3C218yesmaximal, complemented
5#82223—32nomaximal
6C23×C32×C4C2211yescharacteristic
7C23×C3⋊Dic3C2212yes—
8C2×C4⋊(C3⋊Dic3)C418yescomplemented
9C2×C4⋊(C3⋊Dic3)C2214yes—
10C2×C3×#217C2214yes—
11C3×#926C4116yescomplemented
12C2×C3×C4⋊Dic3C2214yes—
13C2×C3×C4×Dic3C2214yes—
14C2×Dic32C2218yes—
15#63579C2218yes—
16C2×C3×#117—32no—
17C2×#926D312yes—
18C22×C4⋊Dic3—32no—
19C22×C4⋊Dic3—61no—
20Dic3×C4⋊C4—38no—
21Dic3×C22⋊C4—38no—
22C4×C4⋊Dic3—38no—
23C24×C32C2311yescharacteristic
24C22×C32×C4C2×C414yes—
25C22×C32×C4C2×C418yes—
26C22×C32×C4C2312yes—
27C22×C3⋊Dic3—44no—
28C22×C3⋊Dic3C2×C418yes—
29C22×C3⋊Dic3C2314yes—
30C22×C3×Dic3C2318yes—
31C4⋊(C3⋊Dic3)C2×C4116yes—
32C3×#217C2×C4116yes—
33C3×C4⋊Dic3C2×C4116yescomplemented
34C3×C4×Dic3C2×C4116yescomplemented
35Dic32—48no—
36#2274—91noSylow
37C23×C3×C4—21no—
38C23×C3×C4C2×D312yes—
39C23×Dic3—34no—
40C23×Dic3—62no—
41C3×#117—316no—
42C2×C3×C4⋊C4—34no—
43C2×C3×C22⋊C4—34no—
44C2×C3×C42—34no—
45C2×#217C2×D314yes—
46#926Dic3116yescomplemented
47C2×C4⋊Dic3—316no—
48C2×C4⋊Dic3—34no—
49C2×C4⋊Dic3—34no—
50C2×C4⋊Dic3—68no—
51C2×C4⋊Dic3—64no—
52C2×C4⋊Dic3C2×D314yes—
53C2×C4×Dic3—316no—
54C2×C4×Dic3C2×D314yes—
55C3⋊#95—316no—
56C23×C32—22no—
57C23×C32—22no—
58C23×C32C22×C412yes—
59C23×C32C22×C414yes—
60C23×C32C2411yescharacteristic
61C2×C32×C4C42116yescomplemented
62C2×C32×C4C22×C414yes—
63C2×C32×C4C22×C414yes—
64C2×C32×C4C22×C414yes—
65C2×C3⋊Dic3—28no—
66C2×C3⋊Dic3—48no—
67C2×C3⋊Dic3C22×C418yes—
68C2×C3×Dic3—28no—
69C2×C3×Dic3—28no—
70C2×C3×Dic3C22×C4116yes—
71C2×#117—32no—
72C22×C4⋊C4—91no—
73C4×C4⋊C4—98no—
74C4×C22⋊C4—94no—
75C24×C3—21no—
76C24×C3C22×D312yes—
77C22×C3×C4—28no—
78C22×C3×C4—24no—
79C22×C3×C4—22no—
80C22×C3×C4—38no—
81C22×C3×C4C4×D318yes—
82C22×C3×C4C4×D318yes—
83C22×C3×C4C2×Dic318yes—
84C22×C3×C4C22×D312yes—
85C22×C3×C4C22×D312yes—
86C22×Dic3—38no—
87C22×Dic3—316no—
88C22×Dic3—68no—
89C22×Dic3—64no—
90C22×Dic3—128no—
91C22×Dic3—128no—
92C22×Dic3C22×D318yes—
93C3×C4⋊C4—316no—
94C3×C22⋊C4—316no—
95C3×C42—316no—
96#217C2×Dic3116yes—
97C4⋊Dic3—316no—
98C4⋊Dic3—316no—
99C4⋊Dic3—616no—
100C4⋊Dic3C2×Dic3116yescomplemented
101C4×Dic3—1216no—
102C4×Dic3C2×Dic3116yescomplemented
103C22×C32—22no—
104C22×C32—22no—
105C22×C32—28no—
106C22×C32C2×C4214yes—
107C22×C32C23×C411yescharacteristic
108C22×C32C23×C412yes—
109C22×C32H(5,𝔽2)12yes—
110C22×C322−1+412yes—
111C32×C4C2×C4218yes—
112C3⋊Dic3—28no—
113C3×Dic3—216no—
114C23×C4—92no—
115C23×C4D3211yescharacteristic
116#117—316no—
117C2×C4⋊C4—34no—
118C2×C4⋊C4—98no—
119C2×C4⋊C4—94no—
120C2×C22⋊C4—34no—
121C2×C42—34no—
122C2×C42—98no—
123#95—98no—
124C23×C3—24no—
125C23×C3—24no—
126C23×C3—24no—
127C23×C3—24no—
128C23×C3—21no—
129C23×C3—24no—
130C23×C3—22no—
131C23×C3C2×C4×D314yes—
132C23×C3C2×C4×D314yes—
133C23×C3C22×Dic314yes—
134C23×C3C23×D312yes—
135C2×C3×C4—216no—
136C2×C3×C4—24no—
137C2×C3×C4—24no—
138C2×C3×C4—24no—
139C2×C3×C4—316no—
140C2×C3×C4—68no—
141C2×C3×C4—68no—
142C2×C3×C4C4×Dic3132yescomplemented
143C2×C3×C4C2×C4×D314yes—
144C2×C3×C4C2×C4×D314yes—
145C2×C3×C4C2×C4×D314yes—
146C2×C3×C4C2×C4×D314yes—
147C2×C3×C4C22×Dic314yes—
148C2×C3×C4C22×Dic314yes—
149C2×Dic3—28no—
150C2×Dic3—28no—
151C2×Dic3—316no—
152C2×Dic3—68no—
153C2×Dic3—616no—
154C2×Dic3—128no—
155C2×Dic3—1216no—
156C2×Dic3—1216no—
157C2×Dic3C22×Dic3116yes—
158C2×C32—24no—
159C2×C32C22×C4211yescharacteristic
160C2×C32#51811yescharacteristic
161C2×C32#51911yescharacteristic
162C2×C32#52014yes—
163C24C2×D3211yescharacteristic
164C22×C4—38no—
165C22×C4—94no—
166C22×C4—98no—
167C22×C4—364no—
168C22×C4D3×Dic318yes—
169C22×C4#62414yes—
170C22×C4C2×D3212yes—
171C4⋊C4—316no—
172C4⋊C4—916no—
173C22⋊C4—316no—
174C42—316no—
175C42—368no—
176C22×C3—24no—
177C22×C3—24no—
178C22×C3—216no—
179C22×C3—24no—
180C22×C3—24no—
181C22×C3—28no—
182C22×C3—28no—
183C22×C3—22no—
184C22×C3—22no—
185C22×C3—22no—
186C22×C3—21no—
187C22×C3—24no—
188C22×C3C2×C4×Dic318yes—
189C22×C3C22×C4×D312yes—
190C22×C3C22×C4×D312yes—
191C22×C3#100914yes—
192C22×C3#101014yes—
193C22×C3C23×Dic312yes—
194C3×C4—28no—
195C3×C4—616no—
196C3×C4C2×C4×Dic318yes—
197C3×C4C2×C4×Dic318yes—
198Dic3—216no—
199Dic3—616no—
200Dic3—128no—
201C32#227411yescharacteristic, complemented, Sylow
202C23—22no—
203C23—22no—
204C23C2×D3×Dic314yes—
205C23C2×#62412yes—
206C23C22×D3211yescharacteristic
207C2×C4—316no—
208C2×C4—68no—
209C2×C4—68no—
210C2×C4—98no—
211C2×C4—188no—
212C2×C4—368no—
213C2×C4Dic32116yescomplemented
214C2×C4C2×D3×Dic314yes—
215C2×C4C2×D3×Dic314yes—
216C2×C4C2×#62414yes—
217C2×C3—28no—
218C2×C3—28no—
219C2×C3—21no—
220C2×C3—21no—
221C2×C3—24no—
222C2×C3—21no—
223C2×C3#551612yes—
224C2×C3#552112yes—
225C2×C3#552314yes—
226C2×C3C22×C4×Dic312yes—
227C2×C3#582714yes—
228C22—22no—
229C22—28no—
230C22—22no—
231C22C2×Dic3214yes—
232C22#6429812yes—
233C22#6430812yes—
234C22C22×D3×Dic312yes—
235C22C22×#62411yescharacteristic
236C4—616no—
237C4—188no—
238C4C2×Dic3218yes—
239C3—21no—
240C3#8222312yescomplemented
241C2—24no—
242C2#1059482811yescharacteristic
243C2#1059499214yes—
244C2#1059499611yescharacteristic
245C2C22×Dic3211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC2×C32C22×C42
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2274
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. Dic3×C4⋊Dic3C2semidirect
8. C2×C4⋊(C3⋊Dic3)C4semidirect
11. C3×#926C4semidirect
33. C3×C4⋊Dic3C2×C4semidirect
34. C3×C4×Dic3C2×C4semidirect
46. #926Dic3semidirect
61. C2×C32×C4C42semidirect
100. C4⋊Dic3C2×Dic3semidirect
102. C4×Dic3C2×Dic3semidirect
142. C2×C3×C4C4×Dic3semidirect
201. C32#2274semidirect
213. C2×C4Dic32semidirect
240. C3#82223semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊(C3⋊Dic3)2
C2×C3×#9262
#105917052
Dic3×C4⋊Dic32
#822233