Finite Group Databasebeta

← #72253000

Subgroups — #72253000

Order 2592.

303 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 303 conjugacy classes of subgroups — too many to draw. Only its 56 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
1C3×#88691C211yesmaximal, characteristic
2C32×#948C311yesmaximal, characteristic
3#11721359—31nomaximal
4C3⋊(#131⋊C9)C313yesmaximal, complemented
5C3×#6204C411yescharacteristic
6C3⋊C8×3−1+2—41nomaximal
7C33×#41C2×C311yescharacteristic
8C32×#208—31no—
9C2×C32×C3⋊C8—31no—
10#88691—21no—
11#88691—23no—
12#88691D311yescharacteristic
13C3×#41⋊C9C2×C313yes—
14C3×C4×3−1+2—41no—
15C32×#131—31no—
16C3×#948—31no—
17C3×#948C3211yescharacteristic
18#131⋊C9—33no—
19C33×Q8C3×C411yescharacteristic
20C33×D4—31no—
21C2×C33×C4—31no—
22C32×C3⋊C8—31no—
23C32×C3⋊C8A411yescharacteristic
24#6204—21no—
25#6204—23no—
26#6204Dic311yescharacteristic
27C3×Q8⋊C9C3×C413yes—
28C8×3−1+2—121no—
29C9×C3⋊C8—43no—
30C2×C3×3−1+2—41no—
31C32×#41—21no—
32C32×#41—31no—
33C32×#41—61no—
34C32×#41C3×D311yescharacteristic
35C32×#41C2×C3211yescharacteristic
36C32×M16—91no—
37C2×C32×C8—91no—
38C3×#208—33no—
39C3×#208—31no—
40C2×C3×C3⋊C8—33no—
41C2×C3×C3⋊C8—31no—
42#41⋊C9—23no—
43#41⋊C9C3×D313yes—
44C22×C33—31no—
45C33×C4—31no—
46C33×C4C2×A411yescharacteristic
47C4×3−1+2—41no—
48C4×3−1+2—83no—
49C4×3−1+2—81no—
50C3×C4×C9—43no—
51C3×#131—31no—
52C3×#131—91no—
53#9483−1+211yescharacteristic, complemented
54C3×3−1+2—41noSylow
55C32×Q8—21no—
56C32×Q8—31no—
57C32×Q8—61no—
58C32×Q8C3×Dic311yescharacteristic
59C32×Q8C32×C411yescharacteristic
60C32×D4—31no—
61C32×D4—31no—
62C32×D4—33no—
63C32×D4—61no—
64C32×D4—63no—
65C2×C32×C4—31no—
66C2×C32×C4—33no—
67C2×C32×C4—31no—
68C2×C32×C4—61no—
69C2×C32×C4—63no—
70C32×C8—31no—
71C32×C8—91no—
72C3×C3⋊C8—33no—
73C3×C3⋊C8—31no—
74C3×C3⋊C8—31no—
75C3×C3⋊C8C3×A411yescharacteristic
76Q8⋊C9—23no—
77Q8⋊C9C3×Dic313yes—
78C8×C9—123no—
79C2×C33—61no—
80C2×C33C4×A411yescharacteristic
81C2×3−1+2—41no—
82C2×3−1+2—83no—
83C2×3−1+2—81no—
84C2×C3×C9—43no—
85C3×#41—21no—
86C3×#41—31no—
87C3×#41—61no—
88C3×#41C2×3−1+211yescharacteristic
89C3×#41C32×D311yescharacteristic
90C3×M16—93no—
91C3×M16—91no—
92C2×C3×C8—91no—
93C2×C3×C8—93no—
94#208—31no—
95C2×C3⋊C8—31no—
96C22×C32—31no—
97C22×C32—33no—
98C22×C32—31no—
99C22×C32—61no—
100C22×C32—63no—
101C32×C4—21no—
102C32×C4—31no—
103C32×C4—33no—
104C32×C4—31no—
105C32×C4—31no—
106C32×C4—61no—
107C32×C4—61no—
108C32×C4—63no—
109C32×C4D3×A411yescharacteristic
110C32×C4C2×C3×A411yescharacteristic
111C4×C9—43no—
112C4×C9—83no—
113#131—31noSylow
114C33#131⋊C311yescharacteristic
1153−1+2—41no—
1163−1+2—83no—
1173−1+2—81no—
118C3×C9—43no—
119C3×Q8—21no—
120C3×Q8—31no—
121C3×Q8—61no—
122C3×Q8C4×3−1+211yescharacteristic
123C3×Q8C32×Dic311yescharacteristic
124C3×D4—31no—
125C3×D4—31no—
126C3×D4—33no—
127C3×D4—61no—
128C3×D4—63no—
129C2×C3×C4—33no—
130C2×C3×C4—31no—
131C2×C3×C4—31no—
132C2×C3×C4—61no—
133C2×C3×C4—63no—
134C3×C8—31no—
135C3×C8—91no—
136C3×C8—93no—
137C3×C8—91no—
138C3⋊C8—31no—
139C3⋊C8#109411yescharacteristic
140C2×C32—21no—
141C2×C32—31no—
142C2×C32—61no—
143C2×C32—61no—
144C2×C32—63no—
145C2×C32—61no—
146C2×C32—121no—
147C2×C32—123no—
148C2×C32Dic3×A411yescharacteristic
149C2×C32C3×C4×A411yescharacteristic
150C2×C9—43no—
151C2×C9—83no—
152#41D3×3−1+211yescharacteristic
153M16—91no—
154C2×C8—91no—
155C22×C3—33no—
156C22×C3—31no—
157C22×C3—31no—
158C22×C3—61no—
159C22×C3—63no—
160C3×C4—21no—
161C3×C4—33no—
162C3×C4—31no—
163C3×C4—31no—
164C3×C4—31no—
165C3×C4—61no—
166C3×C4—63no—
167C3×C4—61no—
168C3×C4C2×#109411yescharacteristic
169C3×C4C3×D3×A411yescharacteristic
170C32—21no—
171C32—31no—
172C32—61no—
173C32C3⋊(#131⋊C3)11yescharacteristic
174C32C3×#131⋊C311yescharacteristic
175C9—43no—
176C9—83no—
177Q8Dic3×3−1+211yescharacteristic
178D4—31no—
179C2×C4—31no—
180C8—31no—
181C8—91no—
182C2×C3—21no—
183C2×C3—31no—
184C2×C3—63no—
185C2×C3—61no—
186C2×C3—61no—
187C2×C3—61no—
188C2×C3—121no—
189C2×C3—123no—
190C2×C3C4×#109411yescharacteristic
191C2×C3C3×Dic3×A411yescharacteristic
192C22—31no—
193C4—31no—
194C4D3×#109411yescharacteristic
195C3—21no—
196C3—31no—
197C3—61no—
198C3#1172135911yescharacteristic, complemented
199C3C3×C3⋊(#131⋊C3)11yescharacteristic
200C2—61no—
201C2Dic3×#109411yescharacteristic
subgroupG/H
center, FrattiniC3×C4C3×D3×A4
commutatorC32×Q8C32×C4
Fitting, prime radicalC33×#41C2×C3
socleC2×C32C3×C4×A4
cosocleC32×#41C2×C32
hypercenterC32×C4D3×A4
hypocenterC3×Q8C4×3−1+2
LCSG ▷ C32×Q8 ▷ C3×Q8
UCSC1 ◁ C3×C4 ◁ C32×C4

Complements

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

NH ≅ G/Ntype
4. C3⋊(#131⋊C9)C3semidirect
53. #9483−1+2semidirect
198. C3#11721359semidirect

Maximal subgroups

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

subgroupindex
C3×#886912
C32×#9483
#117213593
C3⋊(#131⋊C9)3
C3⋊C8×3−1+24