Finite Group Databasebeta

← #14517433

Subgroups — #14517433

Order 1944.

356 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C22×C9⋊H(3,𝔽3)C211yesmaximal, characteristic, complemented
2C2×#92262C211yesmaximal, characteristic, complemented
3#11757566C211yesmaximal, characteristic, complemented
4C9×#638C311yesmaximal, characteristic, complemented
5#67×3−1+2—31nomaximal
6C3×#638⋊C3C311yesmaximal, characteristic
7#638⋊C9C312yesmaximal, complemented
8C2×C9⋊H(3,𝔽3)—21no—
9C2×C9⋊H(3,𝔽3)C2211yescharacteristic
10#92262—21no—
11C22×C3×3−1+2—21no—
12C22×C3×3−1+2D311yescharacteristic, complemented
13C22×C3×H(3,𝔽3)C2×C311yescharacteristic
14C22×C32×C9C2×C311yescharacteristic, complemented
15C2×C9×C3⋊D3C2×C311yescharacteristic, complemented
16C2×D3×3−1+2—31no—
17C2×C3×(C3⋊D3)⋊C3C2×C311yescharacteristic
18C9×C3⋊Dic3C2×C311yescharacteristic, complemented
19Dic3×3−1+2—31no—
20C3×(C3⋊Dic3)⋊C3C2×C311yescharacteristic
21C22×C32⋊C9—21no—
22C22×C32⋊C9—22no—
23C22×C32⋊C9C2×C312yescomplemented
24C2×(C3⋊D3)⋊C9C2×C312yescomplemented
25(C3⋊Dic3)⋊C9C2×C312yescomplemented
26C9⋊H(3,𝔽3)D411yescharacteristic, complemented, Sylow
27C3×#638C3211yescharacteristic
28C32×#67—31no—
29D4×3−1+2—91no—
30#638⋊C3—31no—
31C9×#67—31no—
32C9×#67—32no—
33C9×#67—91no—
34C2×C3×3−1+2—22no—
35C2×C3×3−1+2—21no—
36C2×C3×3−1+2—21no—
37C2×C3×3−1+2C2×D311yescharacteristic
38C2×C3×H(3,𝔽3)—21no—
39C2×C3×H(3,𝔽3)C22×C311yescharacteristic
40C2×C32×C9—21no—
41C2×C32×C9C22×C311yescharacteristic
42C9×C3⋊D3—21no—
43D3×3−1+2—61no—
44C3×(C3⋊D3)⋊C3—21no—
45C2×C32⋊C9—22no—
46C2×C32⋊C9—24no—
47C2×C32⋊C9—22no—
48C2×C32⋊C9—21no—
49C2×C32⋊C9—22no—
50C2×C32⋊C9C22×C312yes—
51(C3⋊D3)⋊C9—22no—
52C22×C33—21no—
53C22×C33C3×D311yescharacteristic
54C22×C33C2×C3211yescharacteristic
55C2×C3×C3⋊D3C2×C3211yescharacteristic
56C2×C32×D3—31no—
57C3×C3⋊Dic3C2×C3211yescharacteristic
58C32×Dic3—31no—
59C22×3−1+2—31no—
60C22×3−1+2—61no—
61C22×3−1+2—62no—
62C22×3−1+2—61no—
63C22×3−1+2—91no—
64C22×H(3,𝔽3)—31no—
65C22×H(3,𝔽3)—61no—
66C22×C3×C9—21no—
67C22×C3×C9—22no—
68C22×C3×C9—31no—
69C22×C3×C9—61no—
70C22×C3×C9C3×D311yescharacteristic
71C22×C3×C9C3×D312yes—
72C2×(C3⋊D3)⋊C3—31no—
73C2×D3×C9—32no—
74C2×D3×C9—31no—
75C2×D3×C9—91no—
76C4×3−1+2—91no—
77(C3⋊Dic3)⋊C3—31no—
78C9×Dic3—32no—
79C9×Dic3—31no—
80C9×Dic3—91no—
81C3×3−1+2—21no—
82C3×3−1+2#6711yescharacteristic, complemented
83C3×H(3,𝔽3)C3×D411yescharacteristic
84C32×C9C3×D411yescharacteristic, complemented
85C32⋊C9—21no—
86C32⋊C9—22no—
87C32⋊C9C3×D412yescomplemented
88C32×D4—91no—
89#6383−1+211yescharacteristic, complemented
90C3×#67—31no—
91C3×#67—91no—
92C3×#67—91no—
93D4×C9—92no—
94D4×C9—91no—
95C2×C33—21no—
96C2×C33—22no—
97C2×C33—21no—
98C2×C33—21no—
99C2×C33C2×C3×D311yescharacteristic
100C2×C33C22×C3211yescharacteristic
101C3×C3⋊D3—21no—
102C32×D3—61no—
103C2×3−1+2—31no—
104C2×3−1+2—61no—
105C2×3−1+2—61no—
106C2×3−1+2—62no—
107C2×3−1+2—64no—
108C2×3−1+2—62no—
109C2×3−1+2—62no—
110C2×3−1+2—61no—
111C2×3−1+2—181no—
112C2×H(3,𝔽3)—31no—
113C2×H(3,𝔽3)—61no—
114C2×H(3,𝔽3)—61no—
115C2×H(3,𝔽3)—62no—
116C2×C3×C9—21no—
117C2×C3×C9—22no—
118C2×C3×C9—24no—
119C2×C3×C9—22no—
120C2×C3×C9—21no—
121C2×C3×C9—22no—
122C2×C3×C9—31no—
123C2×C3×C9—61no—
124C2×C3×C9—62no—
125C2×C3×C9—61no—
126C2×C3×C9C2×C3×D311yescharacteristic
127C2×C3×C9C2×C3×D312yes—
128(C3⋊D3)⋊C3—61no—
129D3×C9—62no—
130D3×C9—61no—
131D3×C9—181no—
132C22×C32—21no—
133C22×C32—31no—
134C22×C32—31no—
135C22×C32—31no—
136C22×C32—61no—
137C22×C32—61no—
138C22×C32—62no—
139C22×C32—61no—
140C22×C32—61no—
141C22×C32—91no—
142C22×C32C2×3−1+211yescharacteristic, complemented
143C22×C32C32×D311yescharacteristic
144C2×C3⋊D3C2×3−1+211yescharacteristic, complemented
145C2×C3×D3—31no—
146C2×C3×D3—91no—
147C2×C3×D3—91no—
148C32×C4—91no—
149C3⋊Dic3C2×3−1+211yescharacteristic, complemented
150C3×Dic3—31no—
151C3×Dic3—91no—
152C3×Dic3—91no—
153C22×C9—21no—
154C22×C9—32no—
155C22×C9—61no—
156C22×C9—62no—
157C22×C9—92no—
158C22×C9—91no—
159C22×C9(C3⋊D3)⋊C311yescharacteristic, complemented
160C4×C9—92no—
161C4×C9—91no—
162C33—21no—
163C33C3×#6711yescharacteristic
164C33C32×D411yescharacteristic
1653−1+2—31no—
1663−1+2—61no—
1673−1+2—62no—
1683−1+2—61no—
169H(3,𝔽3)—31no—
170H(3,𝔽3)—61no—
171C3×C9—21no—
172C3×C9—22no—
173C3×C9—31no—
174C3×C9—61no—
175C3×C9C3×#6711yescharacteristic
176C3×C9C3×#6712yes—
177C3×D4—91no—
178C3×D4—271no—
179#67—31no—
180#67—91no—
181C2×C32—21no—
182C2×C32—22no—
183C2×C32—21no—
184C2×C32—21no—
185C2×C32—31no—
186C2×C32—31no—
187C2×C32—31no—
188C2×C32—61no—
189C2×C32—61no—
190C2×C32—62no—
191C2×C32—61no—
192C2×C32—61no—
193C2×C32—61no—
194C2×C32—62no—
195C2×C32—62no—
196C2×C32—62no—
197C2×C32—64no—
198C2×C32—62no—
199C2×C32—61no—
200C2×C32—61no—
201C2×C32—181no—
202C2×C32C22×3−1+211yescharacteristic
203C2×C32C2×C32×D311yescharacteristic
204C3⋊D3—21no—
205C3×D3—61no—
206C3×D3—181no—
207C3×D3—181no—
208C2×C9—22no—
209C2×C9—21no—
210C2×C9—21no—
211C2×C9—32no—
212C2×C9—62no—
213C2×C9—62no—
214C2×C9—64no—
215C2×C9—61no—
216C2×C9—62no—
217C2×C9—182no—
218C2×C9—181no—
219C2×C9C2×(C3⋊D3)⋊C311yescharacteristic
220C22×C3—21no—
221C22×C3—31no—
222C22×C3—61no—
223C22×C3—91no—
224C22×C3—91no—
225C22×C3—181no—
226C22×C3—271no—
227C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
228C22×C3D3×3−1+211yescharacteristic
229C2×D3—31no—
230C2×D3—91no—
231C3×C4—91no—
232C3×C4—271no—
233Dic3—31no—
234Dic3—91no—
235C32—21no—
236C32—31no—
237C32—31no—
238C32—31no—
239C32—61no—
240C32—61no—
241C32—62no—
242C32—61no—
243C32—61no—
244C32D4×3−1+211yescharacteristic, complemented
245C32C32×#6711yescharacteristic
246C9—21no—
247C9—32no—
248C9—61no—
249C9—62no—
250C9#638⋊C311yescharacteristic, complemented
251D4—91noSylow
252C2×C3—22no—
253C2×C3—21no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—31no—
257C2×C3—61no—
258C2×C3—62no—
259C2×C3—61no—
260C2×C3—91no—
261C2×C3—181no—
262C2×C3—182no—
263C2×C3—181no—
264C2×C3—181no—
265C2×C3—541no—
266C2×C3C2×C3×(C3⋊D3)⋊C311yescharacteristic
267C2×C3C2×D3×3−1+211yescharacteristic
268D3—61no—
269D3—181no—
270C22—91no—
271C22#9226211yescharacteristic, complemented
272C4—91no—
273C3—21no—
274C3—31no—
275C3—61no—
276C3—91no—
277C3—181no—
278C3C3×#638⋊C311yescharacteristic
279C3#67×3−1+211yescharacteristic
280C2—21no—
281C2—181no—
282C2C2×#9226211yescharacteristic
subgroupG/H
centerC2×C3C2×C3×(C3⋊D3)⋊C3
commutator, cosocleC2×C33C22×C32
Frattini, socleC2×C32C2×C32×D3
FittingC22×C9⋊H(3,𝔽3)C2
prime radicalC3×#638⋊C3C3
hypercenterC22×C9(C3⋊D3)⋊C3
hypocenterC32D4×3−1+2
LCSG ▷ C2×C33 ▷ C32
UCSC1 ◁ C2×C3 ◁ C22×C9

Complements

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

NH ≅ G/Ntype
1. C22×C9⋊H(3,𝔽3)C2semidirect
2. C2×#92262C2semidirect
3. #11757566C2semidirect
4. C9×#638C3semidirect
7. #638⋊C9C3semidirect
12. C22×C3×3−1+2D3semidirect
14. C22×C32×C9C2×C3semidirect
15. C2×C9×C3⋊D3C2×C3semidirect
18. C9×C3⋊Dic3C2×C3semidirect
23. C22×C32⋊C9C2×C3semidirect
24. C2×(C3⋊D3)⋊C9C2×C3semidirect
25. (C3⋊Dic3)⋊C9C2×C3semidirect
26. C9⋊H(3,𝔽3)D4semidirect
82. C3×3−1+2#67semidirect
84. C32×C9C3×D4semidirect
87. C32⋊C9C3×D4semidirect
89. #6383−1+2semidirect
142. C22×C32C2×3−1+2semidirect
144. C2×C3⋊D3C2×3−1+2semidirect
149. C3⋊Dic3C2×3−1+2semidirect
159. C22×C9(C3⋊D3)⋊C3semidirect
244. C32D4×3−1+2semidirect
250. C9#638⋊C3semidirect
271. C22#92262semidirect

Maximal subgroups

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

subgroupindex
C22×C9⋊H(3,𝔽3)2
C2×#922622
#117575662
C9×#6383
#67×3−1+23
C3×#638⋊C33
#638⋊C93