Finite Group Databasebeta

← #63460⋊C3 #11721484

Subgroups — #63460⋊C3 #11721484

Order 864.

193 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 193 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C4⋊C4×3−1+2C211yesmaximal, characteristic, complemented
2(C2×AGL(1,ℤ/9))⋊C4C211yesmaximal, characteristic
3(C2×AGL(1,ℤ/9))⋊C4C211yesmaximal, characteristic
4(C2×AGL(1,ℤ/9))⋊C4C211yesmaximal, characteristic
5C4⋊(3−1+2⋊C4)C211yesmaximal, characteristic, complemented
6(3−1+2⋊C4)⋊C4C211yesmaximal, characteristic, complemented
7C4×3−1+2⋊C4C211yesmaximal, characteristic, complemented
8C3×#898—31nomaximal
9#63460C311yesmaximal, characteristic, complemented
10C22×AGL(1,ℤ/9)C2211yescharacteristic
11C2×C4×3−1+2C2211yescharacteristic
12C2×C4×3−1+2C2211yescharacteristic
13C2×C4×3−1+2C2211yescharacteristic
14C2×3−1+2⋊C4C2211yescharacteristic
15C2×3−1+2⋊C4C2211yescharacteristic
16C2×3−1+2⋊C4C2211yescharacteristic
17C32×C4⋊C4D311yescharacteristic
18C3×(C2×D3)⋊C4—31no—
19C3×(C2×D3)⋊C4—31no—
20C3×(C2×D3)⋊C4—31no—
21C3×C4⋊Dic3—31no—
22C3×Dic3⋊C4—31no—
23C3×C4×Dic3—31no—
24C9×C4⋊C4—21no—
25C9×C4⋊C4C2×C311yescharacteristic, complemented
26(C2×D9)⋊C4C2×C311yescharacteristic
27(C2×D9)⋊C4C2×C311yescharacteristic
28(C2×D9)⋊C4C2×C311yescharacteristic
29C4⋊Dic9C2×C311yescharacteristic, complemented
30Dic9⋊C4C2×C311yescharacteristic, complemented
31C4×Dic9C2×C311yescharacteristic, complemented
32C22×3−1+2C2311yescharacteristic
33C2×AGL(1,ℤ/9)—21no—
34C2×AGL(1,ℤ/9)—21no—
35C2×AGL(1,ℤ/9)—21no—
36C4×3−1+2—21no—
37C4×3−1+2—21no—
38C4×3−1+2—21no—
393−1+2⋊C4—21no—
403−1+2⋊C4—21no—
413−1+2⋊C4—21no—
42C3×#126—91no—
43#898—31no—
44C22×C3×D3—31no—
45C2×C32×C4C2×D311yescharacteristic
46C2×C32×C4C2×D311yescharacteristic
47C2×C32×C4C2×D311yescharacteristic
48C2×C3×Dic3—31no—
49C2×C3×Dic3—31no—
50C2×C3×Dic3—31no—
51C22×D9C22×C311yescharacteristic
52C2×C4×C9—21no—
53C2×C4×C9—21no—
54C2×C4×C9—21no—
55C2×C4×C9C22×C311yescharacteristic
56C2×C4×C9C22×C311yescharacteristic
57C2×C4×C9C22×C311yescharacteristic
58C2×Dic9C22×C311yescharacteristic
59C2×Dic9C22×C311yescharacteristic
60C2×Dic9C22×C311yescharacteristic
61C2×3−1+2#4111yescharacteristic
62C2×3−1+2#4111yescharacteristic
63C2×3−1+2#4111yescharacteristic
64AGL(1,ℤ/9)—41no—
65C3×C4⋊C4—61no—
66C3×C4⋊C4—91no—
67C3×C4⋊C4—91no—
68C3×C4⋊C4C3×D311yescharacteristic
69C3×C22⋊C4—91no—
70C3×C22⋊C4—91no—
71C3×C22⋊C4—91no—
72C3×C42—91no—
73(C2×D3)⋊C4—31no—
74(C2×D3)⋊C4—31no—
75(C2×D3)⋊C4—31no—
76C4⋊Dic3—31no—
77Dic3⋊C4—31no—
78C4×Dic3—31no—
79C22×C32C22×D311yescharacteristic
80C2×C3×D3—61no—
81C2×C3×D3—61no—
82C2×C3×D3—61no—
83C32×C4—21no—
84C32×C4—21no—
85C32×C4—21no—
86C3×Dic3—61no—
87C3×Dic3—61no—
88C3×Dic3—61no—
89C22×C9—21no—
90C22×C9C23×C311yescharacteristic
91C2×D9—21no—
92C2×D9—21no—
93C2×D9—21no—
94C4×C9—22no—
95C4×C9—21no—
96C4×C9—21no—
97C4×C9—21no—
98C4×C9—41no—
99C4×C9—41no—
100Dic9—21no—
101Dic9—21no—
102Dic9—21no—
103#126—91noSylow
1043−1+2#12611yescharacteristic, complemented, Sylow
105C23×C3—91no—
106C22×D3—31no—
107C2×C3×C4—61no—
108C2×C3×C4—61no—
109C2×C3×C4—61no—
110C2×C3×C4—91no—
111C2×C3×C4—91no—
112C2×C3×C4—91no—
113C2×C3×C4C2×C3×D311yescharacteristic
114C2×C3×C4C2×C3×D311yescharacteristic
115C2×C3×C4C2×C3×D311yescharacteristic
116C2×Dic3—31no—
117C2×Dic3—31no—
118C2×Dic3—31no—
119C2×C32#23511yescharacteristic
120C2×C32#23711yescharacteristic
121C2×C32#23911yescharacteristic
122C3×D3—121no—
123C2×C9—21no—
124C2×C9—21no—
125C2×C9—21no—
126C2×C9C3×#4111yescharacteristic
127C2×C9C3×#4111yescharacteristic
128C2×C9C3×#4111yescharacteristic
129D9—41no—
130C4⋊C4—91no—
131C4⋊C4—91no—
132C4⋊C4AGL(1,ℤ/9)11yescharacteristic, complemented
133C22⋊C4—91no—
134C22⋊C4—91no—
135C22⋊C4—91no—
136C42—91no—
137C22×C3—61no—
138C22×C3—181no—
139C22×C3—181no—
140C22×C3—181no—
141C22×C3C22×C3×D311yescharacteristic
142C2×D3—61no—
143C2×D3—61no—
144C2×D3—61no—
145C3×C4—21no—
146C3×C4—21no—
147C3×C4—21no—
148C3×C4—61no—
149C3×C4—121no—
150C3×C4—121no—
151C3×C4—181no—
152C3×C4—181no—
153C3×C4—181no—
154Dic3—61no—
155Dic3—61no—
156Dic3—61no—
157C32#89811yescharacteristic
158C9—21no—
159C9C3×#12611yescharacteristic, complemented
160C23—91no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—91no—
164C2×C4C2×AGL(1,ℤ/9)11yescharacteristic
165C2×C4C2×AGL(1,ℤ/9)11yescharacteristic
166C2×C4C2×AGL(1,ℤ/9)11yescharacteristic
167C2×C3—61no—
168C2×C3—61no—
169C2×C3—61no—
170C2×C3—361no—
171C2×C3C3×#23511yescharacteristic
172C2×C3C3×#23711yescharacteristic
173C2×C3C3×#23911yescharacteristic
174D3—121no—
175C22—181no—
176C22—181no—
177C22—181no—
178C22C22×AGL(1,ℤ/9)11yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—181no—
183C4—181no—
184C4—181no—
185C3—61no—
186C3C3×#89811yescharacteristic
187C2—361no—
188C2#3697⋊C311yescharacteristic
189C2#3699⋊C311yescharacteristic
190C2#8872411yescharacteristic
subgroupG/H
centerC22C22×AGL(1,ℤ/9)
commutator, cosocleC22×C9C23×C3
Frattini, socleC22×C3C22×C3×D3
FittingC4⋊C4×3−1+2C2
prime radicalC22×AGL(1,ℤ/9)C22
hypercenterC4⋊C4AGL(1,ℤ/9)
hypocenterC9C3×#126
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C4⋊C4×3−1+2C2semidirect
5. C4⋊(3−1+2⋊C4)C2semidirect
6. (3−1+2⋊C4)⋊C4C2semidirect
7. C4×3−1+2⋊C4C2semidirect
9. #63460C3semidirect
25. C9×C4⋊C4C2×C3semidirect
29. C4⋊Dic9C2×C3semidirect
30. Dic9⋊C4C2×C3semidirect
31. C4×Dic9C2×C3semidirect
104. 3−1+2#126semidirect
132. C4⋊C4AGL(1,ℤ/9)semidirect
159. C9C3×#126semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×3−1+22
(C2×AGL(1,ℤ/9))⋊C42
C4⋊(3−1+2⋊C4)2
(3−1+2⋊C4)⋊C42
C4×3−1+2⋊C42
C3×#8983
#634603