Finite Group Databasebeta

← #11808895

Subgroups — #11808895

Order 1152.

1296 conjugacy classes of subgroups; only the 255 normal subgroups are shown.

normal subgroups only

This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 255 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
1C32×#401C211yesmaximal, characteristic, complemented
2#10592375C211yesmaximal, characteristic
3#10592374C213yesmaximal
4#10592365C213yesmaximal
5#10592357C213yesmaximal, complemented
6#10592348C213yesmaximal, complemented
7#10592347C211yesmaximal, characteristic, complemented
8#78409—34nomaximal
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×#3752C2213yes—
11C2×#3752C2213yes—
12C2×#3750C2213yes—
13C2×#3750C2213yes—
14C2×C4×C3⋊Dic3C2213yes—
15C2×C4×C3⋊Dic3C2213yes—
16C32×#95C2211yescharacteristic
17C32×#95C2213yes—
18C32×#95C2213yes—
19#63658C2213yes—
20#63658C2213yes—
21#63658C2213yes—
22C3×#401D314yescomplemented
23#4676—34no—
24#4675—312no—
25#4666—312no—
26#4658—312no—
27#4649—312no—
28#4648—34no—
29C23×C3⋊D3C2311yescharacteristic
30C22×C32×C4C2311yescharacteristic
31C22×C32×C4C2313yes—
32C22×C32×C4C2313yes—
33C22×C3⋊Dic3C2313yes—
34C22×C3⋊Dic3C2313yes—
35C22×C3⋊Dic3C2311yescharacteristic
36C2×C4×C3⋊D3—26no—
37#3752—26no—
38#3752—26no—
39#3750—26no—
40#3750—26no—
41C4×C3⋊Dic3—26no—
42C4×C3⋊Dic3—26no—
43#2401—91noSylow
44C22×C4×D3—34no—
45C2×(C2×D3)⋊C4—312no—
46C2×(C2×D3)⋊C4—312no—
47C2×Dic3⋊C4—312no—
48C2×Dic3⋊C4—312no—
49C2×C4×Dic3—312no—
50C2×C4×Dic3—312no—
51C3×#95C2×D314yes—
52C3×#95C2×D3112yes—
53C3×#95C2×D3112yes—
54C3⋊#95—312no—
55C3⋊#95—312no—
56C3⋊#95—312no—
57C23×C32C2411yescharacteristic
58C22×C3⋊D3—23no—
59C22×C3⋊D3—23no—
60C22×C3⋊D3#4112yes—
61C2×C32×C4—23no—
62C2×C32×C4—23no—
63C2×C32×C4—23no—
64C2×C32×C4—23no—
65C2×C32×C4—23no—
66C2×C32×C4—23no—
67C2×C32×C4—23no—
68C2×C3⋊Dic3—23no—
69C2×C3⋊Dic3—23no—
70C2×C3⋊Dic3—23no—
71C2×C3⋊Dic3—23no—
72C2×C3⋊Dic3—23no—
73C2×C3⋊Dic3#4116yes—
74C2×C3⋊Dic3#4116yes—
75C4×C3⋊D3—44no—
76#401C3⋊D311yescharacteristic, complemented
77#400—93no—
78#397—93no—
79#396—91no—
80C4×C4⋊C4—93no—
81C4×C22⋊C4—93no—
82#376—91no—
83C23×D3—34no—
84C22×C3×C4C22×D314yes—
85C22×C3×C4C22×D3112yes—
86C22×C3×C4C22×D3112yes—
87C22×Dic3—34no—
88C22×Dic3—312no—
89C22×Dic3—312no—
90C2×C4×D3—624no—
91(C2×D3)⋊C4—624no—
92(C2×D3)⋊C4—624no—
93Dic3⋊C4—624no—
94Dic3⋊C4—624no—
95C4×Dic3—624no—
96C4×Dic3—624no—
97C22×C32C2×#4113yes—
98C22×C32C2×#4111yescharacteristic
99C22×C32C2×#4113yes—
100C2×C3⋊D3—26no—
101C2×C3⋊D3—41no—
102C2×C3⋊D3—43no—
103C32×C4—41no—
104C32×C4—43no—
105C32×C4—43no—
106C3⋊Dic3—26no—
107C3⋊Dic3—43no—
108C3⋊Dic3#12614yes—
109C23×C4—91no—
110C2×C4⋊C4—93no—
111C2×C4⋊C4—93no—
112C2×C22⋊C4—93no—
113C2×C22⋊C4—93no—
114C2×C42—93no—
115C2×C42—93no—
116#95—93no—
117#95—93no—
118#95—93no—
119#95C2×C3⋊D311yescharacteristic
120#95C2×C3⋊D313yes—
121#95C2×C3⋊D313yes—
122C23×C3C23×D314yes—
123C22×D3—38no—
124C22×D3—612no—
125C22×D3—612no—
126C2×C3×C4—212no—
127C2×C3×C4—212no—
128C2×C3×C4—212no—
129C2×C3×C4—212no—
130C2×C3×C4—212no—
131C2×C3×C4—212no—
132C2×C3×C4—212no—
133C2×Dic3—324no—
134C2×Dic3—324no—
135C2×Dic3—612no—
136C2×Dic3—612no—
137C2×Dic3—612no—
138C2×Dic3—612no—
139C2×Dic3—612no—
140C4×D3—1216no—
141C2×C32C2×#12611yescharacteristic
142C2×C32#52913yes—
143C2×C32#52913yes—
144C3⋊D3—42no—
145C24—91no—
146C22×C4—91no—
147C22×C4—93no—
148C22×C4—93no—
149C22×C4—186no—
150C22×C4C22×C3⋊D311yescharacteristic
151C22×C4C22×C3⋊D313yes—
152C22×C4C22×C3⋊D313yes—
153C4⋊C4—186no—
154C4⋊C4—186no—
155C22⋊C4—186no—
156C22⋊C4—186no—
157C42—186no—
158C42—186no—
159C22×C3D3×#41112yes—
160C22×C3D3×#41112yes—
161C22×C3D3×#4114yes—
162C2×D3—624no—
163C2×D3—124no—
164C2×D3—1212no—
165C3×C4—44no—
166C3×C4—412no—
167C3×C4—412no—
168Dic3—316no—
169Dic3—624no—
170Dic3—1212no—
171C32#240111yescharacteristic, complemented, Sylow
172C23—92no—
173C23—183no—
174C23—183no—
175C23C23×C3⋊D311yescharacteristic
176C2×C4—23no—
177C2×C4—23no—
178C2×C4—23no—
179C2×C4—23no—
180C2×C4—23no—
181C2×C4—23no—
182C2×C4—23no—
183C2×C4—96no—
184C2×C4—96no—
185C2×C4—183no—
186C2×C4—183no—
187C2×C4—183no—
188C2×C4—183no—
189C2×C4—183no—
190C2×C4—364no—
191C2×C3D3×#12614yes—
192C2×C3#5706112yes—
193C2×C3#5706112yes—
194D3—128no—
195C22—186no—
196C22—361no—
197C22—363no—
198C22#41×C3⋊D313yes—
199C22#41×C3⋊D313yes—
200C22#41×C3⋊D311yescharacteristic
201C4—41no—
202C4—43no—
203C4—43no—
204C4—94no—
205C4—186no—
206C4—363no—
207C3#7840914yescomplemented
208C2—362no—
209C2C3⋊D3×#12611yescharacteristic
210C2#1059617713yes—
211C2#1059617713yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#401C2
prime radicalC23×C3⋊D3C23
hypercenter#401C3⋊D3
hypocenterC32#2401
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #401

Complements

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

NH ≅ G/Ntype
1. C32×#401C2semidirect
5. #10592357C2semidirect
6. #10592348C2semidirect
7. #10592347C2semidirect
22. C3×#401D3semidirect
76. #401C3⋊D3semidirect
171. C32#2401semidirect
207. C3#78409semidirect

Maximal subgroups

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

subgroupindex
C32×#4012
#105923752
#105923742
#105923652
#105923572
#105923482
#105923472
#784093