Finite Group Databasebeta

← C2×#10620045 #13049277

Subgroups — C2×#10620045 #13049277

Order 1296.

272 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 42 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
1C2×#66436C211yesmaximal, characteristic, complemented
2#10620045C212yesmaximal, direct product factor
3C2×C9⋊S4C311yesmaximal, characteristic, complemented
4C2×(C3⋊S4)⋊C3—31nomaximal
5C2×((C22⋊C9)⋊C2)⋊C3—32nomaximal
6C2×C3×#611—31nomaximal
7C2×#4207—41nomaximal
8#66436C2211yescharacteristic, complemented
9C23×C3×C9D311yescharacteristic, complemented
10C22×C3×D9—31no—
11C2×C22⋊H(3,𝔽3)D311yescharacteristic
12C2×#1094D312yescomplemented
13C2×C9⋊A4—21no—
14C2×C9⋊A4—22no—
15C2×C9×A4—21no—
16C2×C9×A4C2×C311yescharacteristic, complemented
17C9⋊S4C2×C312yescomplemented
18(C3⋊S4)⋊C3—32no—
19((C22⋊C9)⋊C2)⋊C3—34no—
20C3×#611—32no—
21C3×#611—32no—
22C2×C3×Dic9—31no—
23C2×#737—41no—
24#4207—42no—
25C2×C3⋊S4—31no—
26C2×C3×#67—91no—
27C2×(C22⋊C9)⋊C2—32no—
28C2×#611—31no—
29C22×C3×C9—31no—
30C22×C3×C9—31no—
31C22×C3×C9C2×D311yescharacteristic, complemented
32C2×C3⋊D9—41no—
33C2×AGL(1,ℤ/9)—122no—
34C2×(C3⋊D3)⋊C3—121no—
35C2×C3×D9—32no—
36C2×C3×D9—61no—
37C2×C3×D9—61no—
38C22⋊H(3,𝔽3)C2×D311yescharacteristic
39#1094C2×D312yescomplemented
40C9⋊A4—21no—
41C9⋊A4—22no—
42C9×A4—21no—
43C9×A4C22×C311yescharacteristic, complemented
44C3×Dic9—32no—
45#737—41noSylow
46C23×C32C3⋊D311yescharacteristic
47C22×C3×D3—91no—
48C2×C3×A4—21no—
49C2×C3×A4C3×D311yescharacteristic
50C3⋊S4—32no—
51C3×#67—92no—
52C3×#67—92no—
53C2×C3×Dic3—91no—
54C23×C9—21no—
55C23×C9C3×D311yescharacteristic
56C22×D9—31no—
57C2×C22⋊C9—22no—
58C2×C22⋊C9C3×D312yes—
59(C22⋊C9)⋊C2—34no—
60#611—32no—
61#611—32no—
62C2×Dic9—31no—
63C2×3−1+2—42no—
64C2×3−1+2—82no—
65C2×3−1+2—81no—
66C2×H(3,𝔽3)—41no—
67C2×C3×C9—31no—
68C2×C3×C9—31no—
69C2×C3×C9—41no—
70C2×C3×C9—81no—
71C2×C3×C9S411yescharacteristic, complemented
72C3⋊D9—42no—
73AGL(1,ℤ/9)—124no—
74(C3⋊D3)⋊C3—122no—
75C3×D9—62no—
76C2×S4—271no—
77C2×C3×D4—271no—
78C2×#67—91no—
79C22×C32—31no—
80C22×C32—31no—
81C22×C32C2×C3⋊D311yescharacteristic
82C2×C3⋊D3—121no—
83C2×C3×D3—92no—
84C2×C3×D3—181no—
85C2×C3×D3—181no—
86C3×A4—21no—
87C3×A4C2×C3×D311yescharacteristic
88C3×Dic3—92no—
89C22×C9—21no—
90C22×C9—31no—
91C22×C9—31no—
92C22×C9—61no—
93C22×C9—61no—
94C22×C9C2×C3×D311yescharacteristic
95C2×D9—32no—
96C2×D9—61no—
97C2×D9—61no—
98C2×D9—122no—
99C22⋊C9—22no—
100C22⋊C9C2×C3×D312yes—
101Dic9—32no—
1023−1+2—42no—
1033−1+2—82no—
1043−1+2—81no—
105H(3,𝔽3)—41no—
106C3×C9—41no—
107C3×C9—81no—
108C3×C9C2×S411yescharacteristic, complemented
109C23×C3—31no—
110C23×C3—271no—
111C23×C3C3×C3⋊D311yescharacteristic
112C22×D3—91no—
113C2×A4—31no—
114C2×A4—61no—
115S4—272no—
116C3×D4—272no—
117C3×D4—272no—
118C2×C3×C4—271no—
119#67—92no—
120#67—92no—
121C2×Dic3—91no—
122C2×C32—31no—
123C2×C32—31no—
124C2×C32—41no—
125C2×C32—81no—
126C2×C32C3⋊S411yescharacteristic
127C3⋊D3—122no—
128C3×D3—182no—
129C2×C9—21no—
130C2×C9—31no—
131C2×C9—31no—
132C2×C9—42no—
133C2×C9—61no—
134C2×C9—61no—
135C2×C9—82no—
136C2×C9C3×S411yescharacteristic
137D9—62no—
138D9—124no—
139C2×D4—271noSylow
140C22×C3—31no—
141C22×C3—31no—
142C22×C3—31no—
143C22×C3—31no—
144C22×C3—31no—
145C22×C3—61no—
146C22×C3—61no—
147C22×C3—272no—
148C22×C3—541no—
149C22×C3—541no—
150C22×C3C2×C3×C3⋊D311yescharacteristic
151C2×D3—92no—
152C2×D3—181no—
153C2×D3—181no—
154C2×D3—1081no—
155A4—31no—
156A4—61no—
157C3×C4—272no—
158Dic3—92no—
159C32—41no—
160C32—81no—
161C32C2×C3⋊S411yescharacteristic
162C9—21no—
163C9—42no—
164C9—82no—
165C9C2×C3×S411yescharacteristic
166C23—271no—
167C23#420711yescharacteristic, complemented
168D4—272no—
169D4—272no—
170C2×C4—271no—
171C2×C3—31no—
172C2×C3—31no—
173C2×C3—31no—
174C2×C3—31no—
175C2×C3—31no—
176C2×C3—61no—
177C2×C3—61no—
178C2×C3—121no—
179C2×C3—241no—
180C2×C3—542no—
181C2×C3C3×C3⋊S411yescharacteristic
182D3—182no—
183D3—1082no—
184C22—31no—
185C22—31no—
186C22—272no—
187C22—541no—
188C22—541no—
189C22C2×#420711yescharacteristic, complemented
190C4—272no—
191C3—31no—
192C3—121no—
193C3—241no—
194C3C2×C3×C3⋊S411yescharacteristic
195C2—31no—
196C2—31no—
197C2—542no—
198C2#1062004511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#10620045
commutator, cosocle, hypocenterC9×A4C22×C3
FrattiniC3C2×C3×C3⋊S4
FittingC23×C3×C9D3
socleC23×C3C3×C3⋊D3
LCSG ▷ C9×A4
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#66436C2semidirect
2. #10620045C2direct (N × H)
3. C2×C9⋊S4C3semidirect
8. #66436C22semidirect
9. C23×C3×C9D3semidirect
12. C2×#1094D3semidirect
16. C2×C9×A4C2×C3semidirect
17. C9⋊S4C2×C3semidirect
31. C22×C3×C9C2×D3semidirect
39. #1094C2×D3semidirect
43. C9×A4C22×C3semidirect
71. C2×C3×C9S4semidirect
108. C3×C9C2×S4semidirect
167. C23#4207semidirect
189. C22C2×#4207semidirect
198. C2#10620045direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#664362
#106200452
C2×C9⋊S43
C2×(C3⋊S4)⋊C33
C2×((C22⋊C9)⋊C2)⋊C33
C2×C3×#6113
C2×#42074