Finite Group Databasebeta

← #13048742

Subgroups — #13048742

Order 1296.

340 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 62 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×C9×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×C4×C3⋊D9C212yesmaximal, complemented
3#10619899C212yesmaximal, complemented
4#10619897C211yesmaximal, characteristic, complemented
5#10619895C211yesmaximal, characteristic, complemented
6#89042—31nomaximal
7#88640—32nomaximal
8C2×C9×C3⋊D3C2211yescharacteristic
9C2×C3×C3⋊D9C2212yes—
10C32×C4×C9C2211yescharacteristic
11C9×C3⋊Dic3C2211yescharacteristic
12C3×C3⋊Dic9C2212yes—
13C3×C4×C3⋊D3—32no—
14C3×C4×C3⋊D3D311yescharacteristic
15#6296—31no—
16#6295—32no—
17#6295—31no—
18C4×C3⋊D9D312yescomplemented
19C4×D3×C9—32no—
20C4×D3×C9—61no—
21C3×C4×D9—32no—
22C3×C4×D9—62no—
23#6195—32no—
24#6194—32no—
25#6192—32no—
26#6189—32no—
27C2×C32×C9C2311yescharacteristic
28C9×C3⋊D3—21no—
29C3×C3⋊D9—22no—
30#3798—92no—
31#3798—91no—
32#3697—91no—
33C2×C3×C3⋊D3—32no—
34C2×C3×C3⋊D3C2×D311yescharacteristic
35C33×C4C2×D311yescharacteristic
36C3×C3⋊Dic3—32no—
37C3×C3⋊Dic3C2×D311yescharacteristic
38C2×C3⋊D9C2×D312yes—
39C2×D3×C9—32no—
40C2×D3×C9—61no—
41C2×C3×D9—32no—
42C2×C3×D9—62no—
43C3×C4×C9—22no—
44C3×C4×C9—21no—
45C3×C4×C9—41no—
46C3×C4×C9C2×D312yes—
47C3⋊Dic9C2×D312yes—
48C9×Dic3—32no—
49C9×Dic3—61no—
50C3×Dic9—32no—
51C3×Dic9—62no—
52C32×C9#4111yescharacteristic, complemented, Sylow
53C4×C3⋊D3—32no—
54C4×C3⋊D3D911yescharacteristic, complemented
55C3×C4×D3—32no—
56C3×C4×D3—61no—
57C3×C4×D3—92no—
58C3×C4×D3—92no—
59C3×C4×D3—182no—
60#627—92no—
61#627—91no—
62#626—92no—
63#626—92no—
64#626—92no—
65#625—92no—
66#625—91no—
67C2×C4×C9—91no—
68#611—92no—
69D36—91no—
70C4×D9—32no—
71C4×D9—62no—
72Dic18—91no—
73C2×C33C22×D311yescharacteristic
74C3×C3⋊D3—21no—
75C3×C3⋊D3—62no—
76C2×C3×C9—22no—
77C2×C3×C9—21no—
78C2×C3×C9—41no—
79C2×C3×C9C22×D312yes—
80C3⋊D9—22no—
81D3×C9—62no—
82D3×C9—62no—
83C3×D9—64no—
84C3×D9—62no—
85#235—272no—
86#235—271no—
87C2×C3⋊D3—32no—
88C2×C3⋊D3C2×D911yescharacteristic
89C2×C3×D3—32no—
90C2×C3×D3—61no—
91C2×C3×D3—92no—
92C2×C3×D3—92no—
93C2×C3×D3—182no—
94C32×C4—22no—
95C32×C4—21no—
96C32×C4—41no—
97C32×C4C2×D911yescharacteristic
98C32×C4D3212yes—
99C3⋊Dic3—32no—
100C3⋊Dic3C2×D911yescharacteristic
101C3×Dic3—32no—
102C3×Dic3—61no—
103C3×Dic3—92no—
104C3×Dic3—92no—
105C3×Dic3—182no—
106C22×C9—91no—
107C2×D9—32no—
108C2×D9—62no—
109C4×C9—22no—
110C4×C9—41no—
111C4×C9—91no—
112C4×C9D3211yescharacteristic
113Dic9—32no—
114Dic9—62no—
115C33#23511yescharacteristic
116C3×C9—22no—
117C3×C9—21no—
118C3×C9—41no—
119C3×C9#23512yescomplemented
120C2×C3×C4—91no—
121C2×C3×C4—272no—
122#67—272no—
123#67—272no—
124#67—272no—
125D12—271no—
126D12—272no—
127C4×D3—32no—
128C4×D3—61no—
129C4×D3—92no—
130C4×D3—92no—
131C4×D3—182no—
132Dic6—272no—
133Dic6—271no—
134C2×C32—22no—
135C2×C32—21no—
136C2×C32—41no—
137C2×C32C22×D911yescharacteristic
138C2×C32C2×D3212yes—
139C3⋊D3—21no—
140C3⋊D3—62no—
141C3×D3—62no—
142C3×D3—62no—
143C3×D3—184no—
144C3×D3—182no—
145C3×D3—182no—
146C2×C9—22no—
147C2×C9—41no—
148C2×C9—181no—
149C2×C9C2×D3211yescharacteristic
150D9—64no—
151D9—62no—
152#41—811noSylow
153C22×C3—91no—
154C22×C3—272no—
155C2×D3—32no—
156C2×D3—61no—
157C2×D3—92no—
158C2×D3—92no—
159C2×D3—182no—
160C3×C4—21no—
161C3×C4—22no—
162C3×C4—41no—
163C3×C4—91no—
164C3×C4—272no—
165C3×C4D3×D912yes—
166C3×C4#111311yescharacteristic
167Dic3—32no—
168Dic3—61no—
169Dic3—92no—
170Dic3—92no—
171Dic3—182no—
172C32—22no—
173C32—21no—
174C32—41no—
175C32#369711yescharacteristic, complemented
176C32#379812yes—
177C9—22no—
178C9—41no—
179C9#379811yescharacteristic, complemented
180Q8—811no—
181D4—811no—
182D4—812no—
183C2×C4—91no—
184C2×C4—272no—
185C2×C3—21no—
186C2×C3—22no—
187C2×C3—41no—
188C2×C3—181no—
189C2×C3—542no—
190C2×C3C2×D3×D912yes—
191C2×C3C2×#111311yescharacteristic
192D3—62no—
193D3—62no—
194D3—184no—
195D3—182no—
196D3—182no—
197C22—91no—
198C22—272no—
199C4—91no—
200C4—272no—
201C4#6643111yescharacteristic
202C3—21no—
203C3—22no—
204C3—41no—
205C3#8864012yescomplemented
206C3#8904211yescharacteristic
207C2—181no—
208C2—542no—
209C2C2×#6643111yescharacteristic
subgroupG/H
center, hypercenterC4#66431
commutator, cosocleC2×C32×C9C23
FrattiniC2×C3C2×#1113
FittingC32×C4×C9C22
socleC2×C33C22×D3
hypocenterC32×C9#41
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C4×C9×C3⋊D3C2semidirect
2. C3×C4×C3⋊D9C2semidirect
3. #10619899C2semidirect
4. #10619897C2semidirect
5. #10619895C2semidirect
18. C4×C3⋊D9D3semidirect
52. C32×C9#41semidirect
54. C4×C3⋊D3D9semidirect
119. C3×C9#235semidirect
175. C32#3697semidirect
179. C9#3798semidirect
205. C3#88640semidirect

Maximal subgroups

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

subgroupindex
C4×C9×C3⋊D32
C3×C4×C3⋊D92
#106198992
#106198972
#106198952
#890423
#886403