Finite Group Databasebeta

← #125×C3⋊Dic3 #11802476

Subgroups — #125×C3⋊Dic3 #11802476

Order 1152.

1452 conjugacy classes of subgroups.

The subgroup lattice has 231 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#125C211yesmaximal, characteristic
2#10592683C212yesmaximal
3#10592679C214yesmaximal
4C4⋊C4×C3⋊Dic3C214yesmaximal
5C4⋊C4×C3⋊Dic3C212yesmaximal
6#10592635C211yesmaximal, characteristic
7C42×C3⋊Dic3C211yesmaximal, characteristic
8Dic3×#125—34nomaximal
9C32×#125C418yescomplemented
10C2×C32×C4⋊C4C2214yes—
11C2×C32×C4⋊C4C2212yes—
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2212yes—
14C2×C4⋊(C3⋊Dic3)C2214yes—
15C2×C4×C3⋊Dic3C2212yes—
16C2×C4×C3⋊Dic3C2212yes—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C4×C3⋊Dic3C2214yes—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20#63658C2214yes—
21#63658C2214yes—
22#63658C2214yes—
23C2×C3×#125D314yes—
24#4984—38no—
25#4980—316no—
26Dic3×C4⋊C4—316no—
27Dic3×C4⋊C4—38no—
28#4936—34no—
29C42×Dic3—34no—
30C22×C32×C4C2312yes—
31C22×C32×C4C2314yes—
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3C2314yes—
34C22×C3⋊Dic3C2311yescharacteristic
35C22×C3⋊Dic3C2312yes—
36C22×C3⋊Dic3C2311yescharacteristic
37C32×C4⋊C4C2×C4116yes—
38C32×C4⋊C4C2×C418yes—
39C32×C42C2×C414yes—
40C4⋊(C3⋊Dic3)—24no—
41C4⋊(C3⋊Dic3)—28no—
42C4×C3⋊Dic3—22no—
43C4×C3⋊Dic3—24no—
44C4×C3⋊Dic3—24no—
45C4×C3⋊Dic3—28no—
46C4×C3⋊Dic3Q814yes—
47C4×#125—91noSylow
48C3×#125Dic3132yescomplemented
49C2×C3×C4⋊C4C2×D3116yes—
50C2×C3×C4⋊C4C2×D318yes—
51C2×C3×C42C2×D314yes—
52C2×C4⋊Dic3—38no—
53C2×C4⋊Dic3—316no—
54C2×C4×Dic3—34no—
55C2×C4×Dic3—38no—
56C2×C4×Dic3—38no—
57C2×C4×Dic3—34no—
58C2×C4×Dic3—316no—
59C3⋊#95—316no—
60C3⋊#95—316no—
61C3⋊#95—316no—
62C23×C32C2411yescharacteristic
63C2×C32×C4—22no—
64C2×C32×C4—24no—
65C2×C32×C4—22no—
66C2×C32×C4—24no—
67C2×C32×C4C22×C414yes—
68C2×C32×C4C22×C418yes—
69C2×C32×C4C22×C412yes—
70C2×C32×C4C2×Q812yes—
71C2×C32×C4#4112yes—
72C2×C3⋊Dic3—22no—
73C2×C3⋊Dic3—22no—
74C2×C3⋊Dic3—22no—
75C2×C3⋊Dic3—24no—
76C2×C3⋊Dic3—24no—
77C2×C3⋊Dic3—24no—
78C2×C3⋊Dic3C2×Q812yes—
79C2×C3⋊Dic3C2×Q812yes—
80C2×C3⋊Dic3#4114yes—
81C2×C3⋊Dic3#4114yes—
82C2×#125C3⋊D311yescharacteristic
83#389—92no—
84#387—94no—
85#382—91no—
86C4×C4⋊C4—94no—
87C4×C4⋊C4—92no—
88C43—91no—
89C22×C3×C4C22×D318yes—
90C22×C3×C4C22×D3116yes—
91C22×C3×C4C22×D314yes—
92C22×Dic3—34no—
93C22×Dic3—34no—
94C22×Dic3—38no—
95C22×Dic3—316no—
96C3×C4⋊C4C2×Dic3164yes—
97C3×C4⋊C4C2×Dic3132yes—
98C3×C42C2×Dic3116yes—
99C4⋊Dic3—632no—
100C4⋊Dic3—616no—
101C4×Dic3—316no—
102C4×Dic3—616no—
103C4×Dic3—632no—
104C4×Dic3—616no—
105C4×Dic3—68no—
106C22×C32C23×C411yescharacteristic
107C22×C32C22×Q811yescharacteristic
108C22×C32C2×#4111yescharacteristic
109C22×C32C2×#4112yes—
110C22×C32C2×#4112yes—
111C32×C4—24no—
112C32×C4—28no—
113C32×C4C4×Q814yes—
114C3⋊Dic3—24no—
115C3⋊Dic3—22no—
116C3⋊Dic3—44no—
117C3⋊Dic3#12514yesdirect product factor
118#125C3⋊Dic318yesdirect product factor
119C2×C4⋊C4—92no—
120C2×C4⋊C4—94no—
121C2×C4⋊C4C2×C3⋊D314yes—
122C2×C4⋊C4C2×C3⋊D312yes—
123C2×C42—91no—
124C2×C42—92no—
125C2×C42—92no—
126C2×C42—91no—
127C2×C42—94no—
128C2×C42C2×C3⋊D311yescharacteristic
129#95—94no—
130#95—94no—
131#95—94no—
132C23×C3C23×D314yes—
133C2×C3×C4—28no—
134C2×C3×C4—216no—
135C2×C3×C4—28no—
136C2×C3×C4—216no—
137C2×C3×C4D3×Q818yes—
138C2×C3×C4#23918yes—
139C2×C3×C4C22×Dic3116yes—
140C2×C3×C4C22×Dic3132yes—
141C2×C3×C4C22×Dic318yes—
142C2×Dic3—38no—
143C2×Dic3—316no—
144C2×Dic3—38no—
145C2×Dic3—316no—
146C2×Dic3—68no—
147C2×Dic3—68no—
148C2×Dic3—68no—
149C2×Dic3—616no—
150C2×Dic3—616no—
151C2×Dic3—616no—
152C2×C32C2×C4×Q811yescharacteristic
153C2×C32C4×#4112yes—
154C2×C32C2×#12511yescharacteristic
155C2×C32#52912yes—
156C2×C32#53311yescharacteristic
157C22×C4—91no—
158C22×C4—91no—
159C22×C4—92no—
160C22×C4—94no—
161C22×C4C22×C3⋊D312yes—
162C22×C4C22×C3⋊D314yes—
163C22×C4C22×C3⋊D311yescharacteristic
164C4⋊C4—188no—
165C4⋊C4—184no—
166C4⋊C4C2×C3⋊Dic3116yes—
167C4⋊C4C2×C3⋊Dic318yes—
168C42—94no—
169C42—184no—
170C42—188no—
171C42—184no—
172C42—182no—
173C42C2×C3⋊Dic314yes—
174C22×C3C2×D3×Q814yes—
175C22×C3C2×#23914yes—
176C22×C3D3×#4118yes—
177C22×C3D3×#4118yes—
178C22×C3C23×Dic314yes—
179C3×C4—216no—
180C3×C4—232no—
181C3×C4Q8×Dic3116yes—
182Dic3—316no—
183Dic3—68no—
184Dic3—616no—
185Dic3—1216no—
186C32C4×#12511yescharacteristic, complemented, Sylow
187C23C23×C3⋊D311yescharacteristic
188C2×C4—22no—
189C2×C4—24no—
190C2×C4—22no—
191C2×C4—24no—
192C2×C4—92no—
193C2×C4—94no—
194C2×C4—92no—
195C2×C4—94no—
196C2×C4—182no—
197C2×C4—182no—
198C2×C4—182no—
199C2×C4—184no—
200C2×C4—184no—
201C2×C4—184no—
202C2×C4Q8×C3⋊D312yes—
203C2×C4#383212yes—
204C2×C4C22×C3⋊Dic314yes—
205C2×C4C22×C3⋊Dic318yes—
206C2×C4C22×C3⋊Dic312yes—
207C2×C3D3×#12514yes—
208C2×C3#568814yes—
209C2×C3#569118yes—
210C2×C3C2×Q8×Dic314yes—
211C2×C3Dic3×#4118yes—
212C22C2×Q8×C3⋊D311yescharacteristic
213C22C2×#383211yescharacteristic
214C22#41×C3⋊D312yes—
215C22#41×C3⋊D312yes—
216C22C23×C3⋊Dic311yescharacteristic
217C4—24no—
218C4—28no—
219C4—94no—
220C4—182no—
221C4—184no—
222C4—364no—
223C4Q8×C3⋊Dic314yes—
224C3Dic3×#12514yescomplemented
225C2C3⋊D3×#12511yescharacteristic
226C2#1059615911yescharacteristic
227C2#1059616212yes—
228C2C2×Q8×C3⋊Dic311yescharacteristic
229C2#41×C3⋊Dic312yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC2×C32×#125C2
socle, prime radical, cosocleC23×C32C24
hypercenterC2×#125C3⋊D3
hypocenterC32C4×#125
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
9. C32×#125C4semidirect
48. C3×#125Dic3semidirect
117. C3⋊Dic3#125direct (N × H)
118. #125C3⋊Dic3direct (N × H)
186. C32C4×#125semidirect
224. C3Dic3×#125semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1252
#105926832
#105926792
C4⋊C4×C3⋊Dic32
#105926352
C42×C3⋊Dic32
Dic3×#1253