Finite Group Databasebeta

← C2×#10619769 #13048131

Subgroups — C2×#10619769 #13048131

Order 1296.

298 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 29 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×#66357C211yesmaximal, characteristic, complemented
2#10619769C212yesmaximal, direct product factor
3C23×C3⋊D9C311yesmaximal, characteristic, complemented
4C2×(C3⋊D3)⋊A4—31nomaximal
5C2×#4177—41nomaximal
6#66357C2211yescharacteristic, complemented
7C23×C3×C9C2×C311yescharacteristic, complemented
8C22×C3⋊D9—31no—
9C22×C3⋊D9—31no—
10C22×C3⋊D9—32no—
11C22×C3⋊D9C2×C312yescomplemented
12C2×C22⋊H(3,𝔽3)D311yescharacteristic
13C2×#1094—21no—
14(C3⋊D3)⋊A4—32no—
15C2×#731—41no—
16#4177—42no—
17C23×C3⋊D3—31no—
18C2×D3×A4—91no—
19C23×D9—91no—
20C22×C3×C9—31no—
21C22×C3×C9—31no—
22C22×C3×C9C22×C311yescharacteristic, complemented
23C2×C3⋊D9—32no—
24C2×C3⋊D9—31no—
25C2×C3⋊D9—32no—
26C2×C3⋊D9—32no—
27C2×C3⋊D9—32no—
28C2×C3⋊D9A411yescharacteristic, complemented
29C2×(C3⋊D3)⋊C3—121no—
30C22⋊H(3,𝔽3)C2×D311yescharacteristic
31#1094—21no—
32#731—41noSylow
33C23×C32C3×D311yescharacteristic
34C22×C3⋊D3—32no—
35C22×C3⋊D3—91no—
36C22×C3⋊D3—92no—
37C22×C3⋊D3—91no—
38C2×C3×A4—31no—
39D3×A4—92no—
40C23×C9—31no—
41C22×D9—92no—
42C22×D9—93no—
43C22×D9—96no—
44C22×D9—93no—
45C2×C22⋊C9—61no—
46C2×3−1+2—81no—
47C2×H(3,𝔽3)—41no—
48C2×C3×C9—31no—
49C2×C3×C9—31no—
50C2×C3×C9C2×A411yescharacteristic, complemented
51C3⋊D9—32no—
52C3⋊D9C2×A412yescomplemented
53(C3⋊D3)⋊C3—122no—
54C23×D3—91no—
55C23×D3—271no—
56C22×A4—271no—
57C22×C32—31no—
58C22×C32—31no—
59C22×C32C2×C3×D311yescharacteristic
60C2×C3⋊D3—31no—
61C2×C3⋊D3—92no—
62C2×C3⋊D3—92no—
63C2×C3⋊D3—92no—
64C2×C3⋊D3—91no—
65C2×C3⋊D3—92no—
66C2×C3×D3—361no—
67C3×A4—31no—
68C22×C9—33no—
69C22×C9—33no—
70C22×C9—31no—
71C2×D9—91no—
72C2×D9—96no—
73C2×D9—96no—
74C2×D9—96no—
75C2×D9—93no—
76C2×D9—96no—
77C22⋊C9—61no—
783−1+2—81no—
79H(3,𝔽3)—41no—
80C3×C9C22×A411yescharacteristic, complemented
81C23×C3—31no—
82C23×C3(C3⋊D3)⋊C311yescharacteristic
83C22×D3—92no—
84C22×D3—272no—
85C22×D3—271no—
86C22×D3—273no—
87C22×D3—276no—
88C22×D3—273no—
89C22×D3—272no—
90C22×D3—271no—
91C2×A4—91no—
92C2×A4—272no—
93C2×C32—31no—
94C2×C32—31no—
95C2×C32—121no—
96C2×C32D3×A411yescharacteristic
97C3⋊D3—32no—
98C3⋊D3—92no—
99C3×D3—362no—
100C2×C9—33no—
101C2×C9—33no—
102C2×C9—31no—
103C2×C9—241no—
104D9—92no—
105D9—96no—
106C24—271noSylow
107C22×C3—31no—
108C22×C3—33no—
109C22×C3—33no—
110C22×C3—31no—
111C22×C3—31no—
112C22×C3—1081no—
113C22×C3C2×(C3⋊D3)⋊C311yescharacteristic
114C2×D3—91no—
115C2×D3—271no—
116C2×D3—272no—
117C2×D3—272no—
118C2×D3—272no—
119C2×D3—276no—
120C2×D3—276no—
121C2×D3—276no—
122C2×D3—276no—
123C2×D3—273no—
124C2×D3—271no—
125C2×D3—272no—
126A4—91no—
127C32—121no—
128C32C2×D3×A411yescharacteristic
129C9—31no—
130C9—241no—
131C23—272no—
132C23—811no—
133C23—812no—
134C23—811no—
135C23#417711yescharacteristic, complemented
136C2×C3—33no—
137C2×C3—33no—
138C2×C3—31no—
139C2×C3—31no—
140C2×C3—31no—
141C2×C3—361no—
142C2×C3—1082no—
143C2×C3(C3⋊D3)⋊A411yescharacteristic
144D3—92no—
145D3—272no—
146D3—276no—
147D3—272no—
148C22—31no—
149C22—31no—
150C22—271no—
151C22—812no—
152C22—812no—
153C22—812no—
154C22—812no—
155C22—811no—
156C22C2×#417711yescharacteristic, complemented
157C3—31no—
158C3—361no—
159C3C2×(C3⋊D3)⋊A411yescharacteristic
160C2—31no—
161C2—31no—
162C2—272no—
163C2—812no—
164C2#1061976911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#10619769
commutator, cosocle, hypocenterC22×C3×C9C22×C3
FrattiniC32C2×D3×A4
FittingC23×C3×C9C2×C3
socleC23×C3(C3⋊D3)⋊C3
LCSG ▷ C22×C3×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#66357C2semidirect
2. #10619769C2direct (N × H)
3. C23×C3⋊D9C3semidirect
6. #66357C22semidirect
7. C23×C3×C9C2×C3semidirect
11. C22×C3⋊D9C2×C3semidirect
22. C22×C3×C9C22×C3semidirect
28. C2×C3⋊D9A4semidirect
50. C2×C3×C9C2×A4semidirect
52. C3⋊D9C2×A4semidirect
80. C3×C9C22×A4semidirect
135. C23#4177semidirect
156. C22C2×#4177semidirect
164. C2#10619769direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#663572
#106197692
C23×C3⋊D93
C2×(C3⋊D3)⋊A43
C2×#41774