Finite Group Databasebeta

← #72243331

Subgroups — #72243331

Order 2916.

232 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 44 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
1#13090629C211yesmaximal, characteristic, complemented
2#13090628C211yesmaximal, characteristic, complemented
3#13090628C211yesmaximal, characteristic, complemented
4D3×D9⋊C9—31nomaximal
5D3×D9⋊C9—31nomaximal
6C3×D92C311yesmaximal, characteristic
7#10624550C2211yescharacteristic, complemented, Sylow
8C3⋊(D9⋊C9)—31no—
9C3⋊(D9⋊C9)—31no—
10C3×C9⋊D9C2×C311yescharacteristic
11D3×C9⋊C9—31no—
12D3×C9⋊C9—31no—
13C3×D9⋊C9—21no—
14C3×D9⋊C9—21no—
15C3×D9⋊C9D311yescharacteristic
16C3×D9⋊C9D311yescharacteristic
17C3×C9×D9C2×C311yescharacteristic
18C3×C9×D9C2×C311yescharacteristic
19#92158—61no—
20D32×C9—91no—
21C3×D3×D9—31no—
22C3×D3×D9—31no—
23C2×D9⋊C9—91no—
24C2×D9⋊C9—91no—
25D92C911yescharacteristic, complemented
26C3×C9⋊C9—21no—
27C3×C9⋊C9—21no—
28C3×C9⋊C9C2×D311yescharacteristic
29C3×C9⋊C9C2×D311yescharacteristic
30C3×C92C22×C311yescharacteristic
31#6855—21no—
32#6855—41no—
33C9×C3⋊D3—91no—
34C3×C3⋊D9—31no—
35C3×C3⋊D9—31no—
36C3×C3⋊D9—61no—
37C3×D3×C9—31no—
38C3×D3×C9—31no—
39C3×D3×C9—31no—
40C3×D3×C9—31no—
41C3×D3×C9—61no—
42C3×D3×C9—61no—
43C32×D9C3×D311yescharacteristic
44C32×D9C3×D311yescharacteristic
45C2×C9⋊C9—91no—
46C2×C9⋊C9—91no—
47C9⋊D9C2×C911yescharacteristic, complemented
48D9⋊C9—31no—
49D9⋊C9—61no—
50D9⋊C9—61no—
51D9⋊C9—61no—
52D9⋊C9—91no—
53D9⋊C9—91no—
54D9⋊C9—181no—
55D9⋊C9—181no—
56C9×D9—21no—
57C9×D9—21no—
58C9×D9C2×C911yescharacteristic, complemented
59C9×D9C2×C911yescharacteristic, complemented
60C3×D32—91no—
61C2×D3×C9—271no—
62C2×D3×C9—271no—
63C2×C3×D9—91no—
64C2×C3×D9—91no—
65D3×D9—31no—
66D3×D9—31no—
67C32×C9—21no—
68C32×C9—21no—
69C32×C9—21no—
70C32×C9—41no—
71C32×C9D3211yescharacteristic
72C32×C9C2×C3×D311yescharacteristic
73C32×C9C2×C3×D311yescharacteristic
74C9⋊C9—31no—
75C9⋊C9—61no—
76C9⋊C9—61no—
77C9⋊C9—61no—
78C9⋊C9—61no—
79C9⋊C9—121no—
80C9⋊C9—121no—
81C9⋊C9—121no—
82C92—21no—
83C92—21no—
84C92—41no—
85C92C22×C911yescharacteristic, complemented
86C3×C3⋊D3—91no—
87C32×D3—31no—
88C32×D3—31no—
89C2×C3×C9—91no—
90C2×C3×C9—91no—
91C2×C3×C9—91no—
92C2×C3×C9—91no—
93C2×C3×C9—181no—
94C2×C3×C9—181no—
95C3⋊D9—31no—
96C3⋊D9—31no—
97C3⋊D9—61no—
98D3×C9—31no—
99D3×C9—31no—
100D3×C9—61no—
101D3×C9—61no—
102D3×C9—91no—
103D3×C9—181no—
104D3×C9—181no—
105D3×C9—181no—
106D3×C9—271no—
107D3×C9—271no—
108D3×C9—541no—
109C3×D9—21no—
110C3×D9—21no—
111C3×D9—91no—
112C3×D9—91no—
113C3×D9—181no—
114C3×D9—181no—
115C3×D9—541no—
116C3×D9D3×C911yescharacteristic
117C3×D9D3×C911yescharacteristic
118C3×D9AGL(1,ℤ/9)11yescharacteristic
119C3×D9AGL(1,ℤ/9)11yescharacteristic
120C2×C3×D3—271no—
121C2×C3×D3—271no—
122D32—91no—
123C22×C9—811no—
124C2×D9—91no—
125C2×D9—91no—
126C33C3×D3211yescharacteristic
127C3×C9—21no—
128C3×C9—21no—
129C3×C9—21no—
130C3×C9—21no—
131C3×C9—21no—
132C3×C9—21no—
133C3×C9—21no—
134C3×C9—31no—
135C3×C9—41no—
136C3×C9—41no—
137C3×C9—41no—
138C3×C9—61no—
139C3×C9—61no—
140C3×C9—61no—
141C3×C9—61no—
142C3×C9—121no—
143C3×C9—121no—
144C3×C9—121no—
145C3×C9—121no—
146C3×C9—121no—
147C3×C9—121no—
148C3×C9—121no—
149C3×C9—121no—
150C3×C9—121no—
151C3×C9—121no—
152C3×C9C2×D3×C911yescharacteristic
153C3×C9C2×D3×C911yescharacteristic
154C3×C9C2×AGL(1,ℤ/9)11yescharacteristic
155C3×C9C2×AGL(1,ℤ/9)11yescharacteristic
156C2×C32—91no—
157C2×C32—91no—
158C3⋊D3—91no—
159C3×D3—31no—
160C3×D3—31no—
161C3×D3—31no—
162C3×D3—31no—
163C3×D3—61no—
164C3×D3—61no—
165C3×D3—271no—
166C3×D3—271no—
167C3×D3—541no—
168C2×C9—91no—
169C2×C9—91no—
170C2×C9—181no—
171C2×C9—181no—
172C2×C9—271no—
173C2×C9—541no—
174C2×C9—541no—
175C2×C9—541no—
176C2×C9—811no—
177D9—91no—
178D9—91no—
179D9—181no—
180D9—181no—
181D9—541no—
182D9D9⋊C911yescharacteristic, complemented
183D9D9⋊C911yescharacteristic, complemented
184C22×C3—811no—
185C2×D3—271no—
186C2×D3—271no—
187C32—21no—
188C32—21no—
189C32—21no—
190C32—41no—
191C32D32×C911yescharacteristic
192C32D3×AGL(1,ℤ/9)11yescharacteristic
193C32D3×AGL(1,ℤ/9)11yescharacteristic
194C9—21no—
195C9—21no—
196C9—21no—
197C9—21no—
198C9—41no—
199C9—41no—
200C9—61no—
201C9—121no—
202C9—181no—
203C9—181no—
204C9—361no—
205C9—361no—
206C9C2×D9⋊C911yescharacteristic, complemented
207C9C2×D9⋊C911yescharacteristic, complemented
208C2×C3—91no—
209C2×C3—91no—
210C2×C3—91no—
211C2×C3—91no—
212C2×C3—181no—
213C2×C3—181no—
214C2×C3—811no—
215D3—31no—
216D3—31no—
217D3—271no—
218D3—271no—
219D3—541no—
220C22—811noSylow
221C3—21no—
222C3—21no—
223C3—21no—
224C3—41no—
225C3D3×D9⋊C911yescharacteristic
226C3D3×D9⋊C911yescharacteristic
227C3#92264⋊C211yescharacteristic
228C2—91no—
229C2—91no—
230C2—811no—
subgroupG/H
center, hypercenterC3#92264⋊C2
commutator, hypocenterC92C22×C9
Frattini, socleC33C3×D32
Fitting#10624550C22
prime radicalC3×D92C3
cosocleC3×C92C22×C3
LCSG ▷ C92
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. #13090629C2semidirect
2. #13090628C2semidirect
3. #13090628C2semidirect
7. #10624550C22semidirect
25. D92C9semidirect
47. C9⋊D9C2×C9semidirect
58. C9×D9C2×C9semidirect
59. C9×D9C2×C9semidirect
85. C92C22×C9semidirect
182. D9D9⋊C9semidirect
183. D9D9⋊C9semidirect
206. C9C2×D9⋊C9semidirect
207. C9C2×D9⋊C9semidirect

Maximal subgroups

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

subgroupindex
#130906292
#130906282
D3×D9⋊C93
C3×D923