Finite Group Databasebeta

← #11808892

Subgroups — #11808892

Order 1152.

1296 conjugacy classes of subgroups; only the 295 normal subgroups are shown.

normal subgroups only

This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 295 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×#396C211yesmaximal, characteristic
2#10592685C213yesmaximal, complemented
3C4⋊C4×C3⋊Dic3C213yesmaximal, complemented
4#10592652C213yesmaximal
5C22⋊C4×C3⋊Dic3C213yesmaximal
6#10592361C211yesmaximal, characteristic, complemented
7#10592347C211yesmaximal, characteristic, complemented
8#77283—34nomaximal
9C23×C3⋊Dic3C2211yescharacteristic
10C2×C32×C4⋊C4C2213yes—
11C2×C32×C22⋊C4C2213yes—
12C2×#3757C2213yes—
13C2×C4⋊(C3⋊Dic3)C2213yes—
14C2×C4×C3⋊Dic3C2213yes—
15C2×C4×C3⋊Dic3C2213yes—
16C32×#95C2211yescharacteristic
17#63658C2213yes—
18#63658C2213yes—
19#63658C2213yes—
20#63658C2213yes—
21#63658C2213yes—
22C3×#396D314yes—
23#4986—312no—
24Dic3×C4⋊C4—312no—
25#4953—312no—
26Dic3×C22⋊C4—312no—
27C3⋊#401—34no—
28#4648—34no—
29C24×C32C2311yescharacteristic
30C22×C32×C4C2313yes—
31C22×C32×C4C2313yes—
32C22×C3⋊Dic3—26no—
33C22×C3⋊Dic3C2311yescharacteristic
34C22×C3⋊Dic3C2313yes—
35C22×C3⋊Dic3C2313yes—
36C22×C3⋊Dic3C2311yescharacteristic
37C32×C4⋊C4—26no—
38C32×C22⋊C4—26no—
39#3757—26no—
40C4⋊(C3⋊Dic3)—26no—
41C4×C3⋊Dic3—26no—
42C4×C3⋊Dic3—26no—
43#2401—91noSylow
44C23×Dic3—34no—
45C2×C3×C4⋊C4C2×D3112yes—
46C2×C3×C22⋊C4C2×D3112yes—
47C2×#217—312no—
48C2×C4⋊Dic3—312no—
49C2×C4×Dic3—312no—
50C2×C4×Dic3—312no—
51C3×#95C2×D314yes—
52C3⋊#95—312no—
53C3⋊#95—312no—
54C3⋊#95—312no—
55C3⋊#95—312no—
56C3⋊#95—312no—
57C23×C32—23no—
58C23×C32—23no—
59C23×C32#4112yes—
60C23×C32C2411yescharacteristic
61C2×C32×C4—23no—
62C2×C32×C4—23no—
63C2×C32×C4—23no—
64C2×C32×C4—23no—
65C2×C32×C4—23no—
66C2×C32×C4#4116yes—
67C2×C3⋊Dic3—23no—
68C2×C3⋊Dic3—23no—
69C2×C3⋊Dic3—23no—
70C2×C3⋊Dic3—23no—
71C2×C3⋊Dic3—23no—
72C2×C3⋊Dic3—23no—
73C2×C3⋊Dic3—23no—
74C2×C3⋊Dic3—44no—
75C2×C3⋊Dic3#4116yes—
76#401—91no—
77#400—93no—
78#397—93no—
79#396C3⋊D311yescharacteristic
80C4×C4⋊C4—93no—
81C4×C22⋊C4—93no—
82#376—91no—
83C24×C3C22×D314yes—
84C22×C3×C4C22×D3112yes—
85C22×C3×C4C22×D3112yes—
86C22×Dic3—34no—
87C22×Dic3—34no—
88C22×Dic3—312no—
89C22×Dic3—312no—
90C22×Dic3—624no—
91C3×C4⋊C4—224no—
92C3×C22⋊C4—224no—
93#217—624no—
94C4⋊Dic3—624no—
95C4×Dic3—624no—
96C4×Dic3—624no—
97C22×C32—26no—
98C22×C32—41no—
99C22×C32—43no—
100C22×C32C2×#4113yes—
101C22×C32C2×#4111yescharacteristic
102C22×C32C2×#4113yes—
103C32×C4—26no—
104C32×C4—43no—
105C3⋊Dic3—41no—
106C3⋊Dic3—43no—
107C3⋊Dic3—43no—
108C3⋊Dic3#12614yes—
109C23×C4—91no—
110C2×C4⋊C4—93no—
111C2×C4⋊C4C2×C3⋊D313yes—
112C2×C22⋊C4—93no—
113C2×C22⋊C4C2×C3⋊D313yes—
114C2×C42—93no—
115C2×C42—93no—
116#95—93no—
117#95—93no—
118#95—93no—
119#95—93no—
120#95—93no—
121#95C2×C3⋊D311yescharacteristic
122C23×C3—212no—
123C23×C3—212no—
124C23×C3#23918yes—
125C23×C3C23×D314yes—
126C2×C3×C4—212no—
127C2×C3×C4—212no—
128C2×C3×C4—212no—
129C2×C3×C4—212no—
130C2×C3×C4—212no—
131C2×C3×C4#237124yes—
132C2×Dic3—324no—
133C2×Dic3—612no—
134C2×Dic3—612no—
135C2×Dic3—612no—
136C2×Dic3—612no—
137C2×Dic3—612no—
138C2×Dic3—612no—
139C2×Dic3—612no—
140C2×Dic3—1216no—
141C2×C32—42no—
142C2×C32C2×#12611yescharacteristic
143C2×C32#52913yes—
144C2×C32#52913yes—
145C24C22×C3⋊D311yescharacteristic
146C22×C4—91no—
147C22×C4—91no—
148C22×C4—93no—
149C22×C4—93no—
150C22×C4—186no—
151C22×C4C22×C3⋊D313yes—
152C22×C4C22×C3⋊D313yes—
153C4⋊C4—26no—
154C4⋊C4—186no—
155C22⋊C4—26no—
156C22⋊C4—186no—
157C42—186no—
158C42—186no—
159C22×C3—224no—
160C22×C3—44no—
161C22×C3—412no—
162C22×C3C2×#237112yes—
163C22×C3C2×#23914yes—
164C22×C3D3×#41112yes—
165C3×C4—224no—
166C3×C4—412no—
167Dic3—316no—
168Dic3—124no—
169Dic3—1212no—
170Dic3—1212no—
171C32#240111yescharacteristic, complemented, Sylow
172C23—23no—
173C23—23no—
174C23#383212yes—
175C23C23×C3⋊D311yescharacteristic
176C2×C4—23no—
177C2×C4—23no—
178C2×C4—23no—
179C2×C4—23no—
180C2×C4—23no—
181C2×C4—96no—
182C2×C4—183no—
183C2×C4—183no—
184C2×C4—183no—
185C2×C4—183no—
186C2×C4—183no—
187C2×C4—183no—
188C2×C4—183no—
189C2×C4—364no—
190C2×C4#383016yes—
191C2×C3—48no—
192C2×C3#5600112yes—
193C2×C3#5624112yes—
194C2×C3D3×#12614yes—
195C22—26no—
196C22—41no—
197C22—43no—
198C22C2×#383013yes—
199C22C2×#383211yescharacteristic
200C22#41×C3⋊D313yes—
201C4—26no—
202C4—43no—
203C4—94no—
204C4—361no—
205C4—363no—
206C4—363no—
207C3#7728314yescomplemented
208C2—42no—
209C2#1059607113yes—
210C2#1059609513yes—
211C2C3⋊D3×#12611yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#396C2
prime radicalC24×C32C23
hypercenter#396C3⋊D3
hypocenterC32#2401
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
2. #10592685C2semidirect
3. C4⋊C4×C3⋊Dic3C2semidirect
6. #10592361C2semidirect
7. #10592347C2semidirect
171. C32#2401semidirect
207. C3#77283semidirect

Maximal subgroups

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

subgroupindex
C32×#3962
#105926852
C4⋊C4×C3⋊Dic32
#105926522
C22⋊C4×C3⋊Dic32
#105923612
#105923472
#772833