Finite Group Databasebeta

← C3×#10619530 #14516739

Subgroups — C3×#10619530 #14516739

Order 1944.

290 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 52 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×C3×C9⋊D9C211yesmaximal, characteristic, complemented
2C2×C3×C9×D9C211yesmaximal, characteristic, complemented
3C3×C9×Dic9C211yesmaximal, characteristic, complemented
4C3×#6195—31nomaximal
5C3×#6192—31nomaximal
6#10619530C311yesmaximal, characteristic, direct product factor
7C2×C3×C92C2211yescharacteristic
8C3×C9⋊D9—21no—
9C3×C9×D9—21no—
10C2×C3×C3⋊D9—31no—
11C2×C3×C3⋊D9—31no—
12C2×C3×C3⋊D9—61no—
13C2×C3×D3×C9—31no—
14C2×C32×D9D311yescharacteristic
15C3×C9×Dic3—31no—
16C32×Dic9D311yescharacteristic
17C2×C9⋊D9C2×C311yescharacteristic, complemented
18C2×C9×D9—21no—
19C2×C9×D9C2×C311yescharacteristic, complemented
20C9×Dic9—21no—
21C9×Dic9C2×C311yescharacteristic, complemented
22C3×C92D411yescharacteristic, complemented, Sylow
23C3×#626—91no—
24C3×#611—91no—
25C3×D36—91no—
26#6195—31no—
27#6192—31no—
28C2×C32×C9—21no—
29C2×C32×C9C2×D311yescharacteristic
30C2×C32×C9C2×D311yescharacteristic
31C3×C3⋊D9—62no—
32C3×C3⋊D9—61no—
33C3×C3⋊D9—61no—
34C3×D3×C9—61no—
35C32×D9—21no—
36C2×C92—21no—
37C2×C92—21no—
38C2×C92—41no—
39C2×C92C22×C311yescharacteristic
40C9⋊D9—21no—
41C9×D9—22no—
42C9×D9—21no—
43C2×C3×C3⋊D3—91no—
44C2×C32×D3—31no—
45C32×Dic3—31no—
46C22×C3×C9—91no—
47C2×C3⋊D9—31no—
48C2×C3⋊D9—31no—
49C2×C3⋊D9—61no—
50C2×D3×C9—31no—
51C2×D3×C9—61no—
52C2×C3×D9—21no—
53C2×C3×D9—91no—
54C2×C3×D9—91no—
55C2×C3×D9—181no—
56C2×C3×D9—181no—
57C2×C3×D9—183no—
58C2×C3×D9D911yescharacteristic, complemented
59C2×C3×D9C3×D311yescharacteristic
60C3×C4×C9—91no—
61C9×Dic3—31no—
62C9×Dic3—61no—
63C3×Dic9—21no—
64C3×Dic9D911yescharacteristic, complemented
65C3×Dic9C3×D311yescharacteristic
66C32×C9—21no—
67C32×C9D1211yescharacteristic
68C32×C9#6711yescharacteristic
69C92—21no—
70C92—21no—
71C92—41no—
72C92C3×D411yescharacteristic, complemented
73C3×#67—271no—
74C3×D12—271no—
75#626—91no—
76#611—91no—
77D36—91no—
78C2×C33D3211yescharacteristic
79C3×C3⋊D3—181no—
80C32×D3—61no—
81C2×C3×C9—21no—
82C2×C3×C9—23no—
83C2×C3×C9—21no—
84C2×C3×C9—21no—
85C2×C3×C9—21no—
86C2×C3×C9—21no—
87C2×C3×C9—21no—
88C2×C3×C9—21no—
89C2×C3×C9—41no—
90C2×C3×C9—41no—
91C2×C3×C9—43no—
92C2×C3×C9—41no—
93C2×C3×C9—181no—
94C2×C3×C9C2×D911yescharacteristic
95C2×C3×C9C2×D911yescharacteristic
96C2×C3×C9C2×C3×D311yescharacteristic
97C2×C3×C9C2×C3×D311yescharacteristic
98C3⋊D9—62no—
99C3⋊D9—61no—
100C3⋊D9—61no—
101D3×C9—62no—
102D3×C9—61no—
103C3×D9—22no—
104C3×D9—21no—
105C3×D9—21no—
106C3×D9—186no—
107C3×D9—182no—
108C3×D9—182no—
109C3×D9—181no—
110C3×D9—181no—
111C22×C32—91no—
112C2×C3⋊D3—91no—
113C2×C3×D3—31no—
114C2×C3×D3—31no—
115C2×C3×D3—61no—
116C2×C3×D3—271no—
117C2×C3×D3—271no—
118C2×C3×D3—541no—
119C32×C4—91no—
120C3×Dic3—31no—
121C3×Dic3—31no—
122C3×Dic3—61no—
123C22×C9—91no—
124C22×C9—181no—
125C2×D9—91no—
126C2×D9—91no—
127C2×D9—181no—
128C2×D9—181no—
129C2×D9—183no—
130C2×D9C3×D911yescharacteristic, complemented
131C4×C9—91no—
132C4×C9—181no—
133Dic9C3×D911yescharacteristic, complemented
134C33#62611yescharacteristic
135C3×C9—21no—
136C3×C9—23no—
137C3×C9—21no—
138C3×C9—21no—
139C3×C9—21no—
140C3×C9—21no—
141C3×C9—21no—
142C3×C9—21no—
143C3×C9—41no—
144C3×C9—41no—
145C3×C9—43no—
146C3×C9—41no—
147C3×C9D3611yescharacteristic, complemented
148C3×C9#61111yescharacteristic, complemented
149C3×C9C3×D1211yescharacteristic
150C3×C9C3×#6711yescharacteristic
151C3×D4—811no—
152#67—271no—
153D12—271no—
154C2×C32—21no—
155C2×C32—21no—
156C2×C32—21no—
157C2×C32—41no—
158C2×C32—181no—
159C2×C32D3×D911yescharacteristic
160C2×C32D3×D911yescharacteristic
161C2×C32C3×D3211yescharacteristic
162C3⋊D3—181no—
163C3×D3—62no—
164C3×D3—61no—
165C3×D3—61no—
166C3×D3—542no—
167C3×D3—541no—
168C3×D3—541no—
169C2×C9—23no—
170C2×C9—21no—
171C2×C9—21no—
172C2×C9—21no—
173C2×C9—21no—
174C2×C9—43no—
175C2×C9—41no—
176C2×C9—41no—
177C2×C9—182no—
178C2×C9—181no—
179C2×C9C2×C3×D911yescharacteristic
180C2×C9C2×C3×D911yescharacteristic
181D9—21no—
182D9—186no—
183D9—182no—
184D9—182no—
185D9—181no—
186D9—181no—
187C22×C3—91no—
188C22×C3—91no—
189C22×C3—181no—
190C22×C3—811no—
191C2×D3—31no—
192C2×D3—271no—
193C2×D3—271no—
194C2×D3—541no—
195C3×C4—91no—
196C3×C4—91no—
197C3×C4—181no—
198Dic3—31no—
199C32—21no—
200C32—21no—
201C32—21no—
202C32—41no—
203C32#619211yescharacteristic
204C32#619511yescharacteristic
205C32C3×#62611yescharacteristic
206C9—23no—
207C9—21no—
208C9—21no—
209C9—21no—
210C9—21no—
211C9—43no—
212C9—41no—
213C9—41no—
214C9C3×D3611yescharacteristic, complemented
215C9C3×#61111yescharacteristic, complemented
216D4—811noSylow
217C2×C3—21no—
218C2×C3—21no—
219C2×C3—21no—
220C2×C3—41no—
221C2×C3—182no—
222C2×C3—181no—
223C2×C3—181no—
224C2×C3—1621no—
225C2×C3D9211yescharacteristic
226C2×C3C3×D3×D911yescharacteristic
227C2×C3C3×D3×D911yescharacteristic
228D3—61no—
229D3—542no—
230D3—541no—
231D3—541no—
232C22—91no—
233C22—811no—
234C4—91no—
235C3—21no—
236C3—21no—
237C3—21no—
238C3—41no—
239C3#1061953011yescharacteristic, direct product factor
240C3C3×#619211yescharacteristic
241C3C3×#619511yescharacteristic
242C2—181no—
243C2—1621no—
244C2C3×D9211yescharacteristic
subgroupG/H
center, hypercenterC2×C3D92
commutator, cosocleC2×C92C22×C3
FrattiniC2×C32C3×D32
FittingC2×C3×C92C22
socleC2×C33D32
hypocenterC92C3×D4
LCSG ▷ C2×C92 ▷ C92
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×C9⋊D9C2semidirect
2. C2×C3×C9×D9C2semidirect
3. C3×C9×Dic9C2semidirect
6. #10619530C3direct (N × H)
17. C2×C9⋊D9C2×C3semidirect
19. C2×C9×D9C2×C3semidirect
21. C9×Dic9C2×C3semidirect
22. C3×C92D4semidirect
58. C2×C3×D9D9semidirect
64. C3×Dic9D9semidirect
72. C92C3×D4semidirect
130. C2×D9C3×D9semidirect
133. Dic9C3×D9semidirect
147. C3×C9D36semidirect
148. C3×C9#611semidirect
214. C9C3×D36semidirect
215. C9C3×#611semidirect
239. C3#10619530direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C9⋊D92
C2×C3×C9×D92
C3×C9×Dic92
C3×#61953
C3×#61923
#106195303