Finite Group Databasebeta

← C3×#67×C13⋊C3 #72241971

Subgroups — C3×#67×C13⋊C3 #72241971

Order 2808.

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

normal subgroups only

This group has 272 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×C32×C13⋊C3C211yesmaximal, characteristic, complemented
2C2×C3×D3×C13⋊C3C211yesmaximal, characteristic, complemented
3C3×Dic3×C13⋊C3C211yesmaximal, characteristic, complemented
4C3×C13×#67C311yesmaximal, characteristic, complemented
5C3×D4×C13⋊C3—31nomaximal
6#67×C13⋊C3C311yesmaximal, characteristic, direct product factor
7#67×C13⋊C3C311yesmaximal, characteristic, direct product factor
8#67×C13⋊C3C311yesmaximal, characteristic, direct product factor
9C2×C32×C13⋊C3—21no—
10C2×C32×C13⋊C3C2211yescharacteristic
11C3×D3×C13⋊C3—21no—
12C22×C32×C13C2×C311yescharacteristic, complemented
13C2×C3×D3×C13C2×C311yescharacteristic, complemented
14C22×C3×C13⋊C3—21no—
15C22×C3×C13⋊C3—21no—
16C22×C3×C13⋊C3—21no—
17C22×C3×C13⋊C3—21no—
18C22×C3×C13⋊C3—31no—
19C22×C3×C13⋊C3D311yescharacteristic, complemented
20C22×C3×C13⋊C3C2×C311yescharacteristic, complemented
21C22×C3×C13⋊C3C2×C311yescharacteristic, complemented
22C22×C3×C13⋊C3C2×C311yescharacteristic, complemented
23C2×D3×C13⋊C3C2×C311yescharacteristic, complemented
24C2×D3×C13⋊C3C2×C311yescharacteristic, complemented
25C2×D3×C13⋊C3C2×C311yescharacteristic, complemented
26C3×Dic3×C13C2×C311yescharacteristic, complemented
27C3×C4×C13⋊C3—31no—
28Dic3×C13⋊C3C2×C311yescharacteristic, complemented
29Dic3×C13⋊C3C2×C311yescharacteristic, complemented
30Dic3×C13⋊C3C2×C311yescharacteristic, complemented
31C32×C13⋊C3D411yescharacteristic, complemented, Hall
32C3×D4×C13—31no—
33C13×#67C3211yescharacteristic, complemented
34D4×C13⋊C3—31no—
35D4×C13⋊C3—31no—
36D4×C13⋊C3—31no—
37C2×C32×C13—21no—
38C2×C32×C13C22×C311yescharacteristic
39C3×D3×C13—21no—
40C2×C3×C13⋊C3—21no—
41C2×C3×C13⋊C3—21no—
42C2×C3×C13⋊C3—21no—
43C2×C3×C13⋊C3—21no—
44C2×C3×C13⋊C3—21no—
45C2×C3×C13⋊C3—21no—
46C2×C3×C13⋊C3—21no—
47C2×C3×C13⋊C3—21no—
48C2×C3×C13⋊C3—21no—
49C2×C3×C13⋊C3—21no—
50C2×C3×C13⋊C3—21no—
51C2×C3×C13⋊C3—21no—
52C2×C3×C13⋊C3—21no—
53C2×C3×C13⋊C3—21no—
54C2×C3×C13⋊C3—21no—
55C2×C3×C13⋊C3—21no—
56C2×C3×C13⋊C3—61no—
57C2×C3×C13⋊C3C2×D311yescharacteristic
58C2×C3×C13⋊C3C22×C311yescharacteristic
59C2×C3×C13⋊C3C22×C311yescharacteristic
60C2×C3×C13⋊C3C22×C311yescharacteristic
61D3×C13⋊C3—21no—
62D3×C13⋊C3—21no—
63D3×C13⋊C3—21no—
64C32×#67—131nomaximal, Hall
65C22×C3×C13—21no—
66C22×C3×C13—31no—
67C22×C3×C13C3×D311yescharacteristic, complemented
68C22×C3×C13C2×C3211yescharacteristic, complemented
69C2×D3×C13C2×C3211yescharacteristic, complemented
70C22×C13⋊C3—21no—
71C22×C13⋊C3—21no—
72C22×C13⋊C3—21no—
73C22×C13⋊C3—31no—
74C22×C13⋊C3—31no—
75C22×C13⋊C3—31no—
76C22×C13⋊C3C3×D311yescharacteristic, complemented
77C22×C13⋊C3C3×D311yescharacteristic, complemented
78C22×C13⋊C3C3×D311yescharacteristic, complemented
79C3×C4×C13—31no—
80Dic3×C13C2×C3211yescharacteristic, complemented
81C4×C13⋊C3—31no—
82C4×C13⋊C3—31no—
83C4×C13⋊C3—31no—
84C32×C13C3×D411yescharacteristic, complemented
85C3×C13⋊C3—21no—
86C3×C13⋊C3—21no—
87C3×C13⋊C3—21no—
88C3×C13⋊C3—21no—
89C3×C13⋊C3#6711yescharacteristic, direct product factor
90C3×C13⋊C3C3×D411yescharacteristic, complemented
91C3×C13⋊C3C3×D411yescharacteristic, complemented
92C3×C13⋊C3C3×D411yescharacteristic, complemented
93C22×C33—131no—
94C2×C32×D3—131no—
95C32×Dic3—131no—
96D4×C13—31noHall
97C2×C3×C13—21no—
98C2×C3×C13—21no—
99C2×C3×C13—21no—
100C2×C3×C13—21no—
101C2×C3×C13—21no—
102C2×C3×C13—61no—
103C2×C3×C13C2×C3×D311yescharacteristic
104C2×C3×C13C22×C3211yescharacteristic
105D3×C13—21no—
106C2×C13⋊C3—21no—
107C2×C13⋊C3—21no—
108C2×C13⋊C3—21no—
109C2×C13⋊C3—21no—
110C2×C13⋊C3—21no—
111C2×C13⋊C3—21no—
112C2×C13⋊C3—21no—
113C2×C13⋊C3—21no—
114C2×C13⋊C3—21no—
115C2×C13⋊C3—21no—
116C2×C13⋊C3—21no—
117C2×C13⋊C3—21no—
118C2×C13⋊C3—61no—
119C2×C13⋊C3—61no—
120C2×C13⋊C3—61no—
121C2×C13⋊C3C2×C3×D311yescharacteristic
122C2×C13⋊C3C2×C3×D311yescharacteristic
123C2×C13⋊C3C2×C3×D311yescharacteristic
124C32×D4—391no—
125C3×#67—131no—
126C3×#67—131no—
127C3×#67—131no—
128C3×#67C13⋊C311yescharacteristic, direct product factor
129C2×C33—131no—
130C2×C33—261no—
131C32×D3—261no—
132C22×C13—31no—
133C22×C13C32×D311yescharacteristic, complemented
134C4×C13—31no—
135C3×C13—21no—
136C3×C13C3×#6711yescharacteristic, complemented
137C3×C13C32×D411yescharacteristic, complemented
138C13⋊C3—21no—
139C13⋊C3—21no—
140C13⋊C3—21no—
141C13⋊C3C3×#6711yescharacteristic, direct product factor
142C13⋊C3C3×#6711yescharacteristic, direct product factor
143C13⋊C3C3×#6711yescharacteristic, direct product factor
144C22×C32—131no—
145C22×C32—131no—
146C22×C32—131no—
147C22×C32—131no—
148C22×C32—261no—
149C22×C32—261no—
150C22×C32—261no—
151C22×C32—261no—
152C22×C32—391no—
153C22×C32C2×C13⋊C311yescharacteristic, complemented
154C2×C3×D3—131no—
155C2×C3×D3—131no—
156C2×C3×D3—131no—
157C2×C3×D3C2×C13⋊C311yescharacteristic, complemented
158C32×C4—391no—
159C3×Dic3—131no—
160C3×Dic3—131no—
161C3×Dic3—131no—
162C3×Dic3C2×C13⋊C311yescharacteristic, complemented
163C33—131noSylow
164C2×C13—21no—
165C2×C13—61no—
166C2×C13C2×C32×D311yescharacteristic
167C3×D4—31no—
168C3×D4—391no—
169C3×D4—391no—
170C3×D4—391no—
171#67C3×C13⋊C311yescharacteristic, direct product factor
172C2×C32—21no—
173C2×C32—131no—
174C2×C32—131no—
175C2×C32—131no—
176C2×C32—131no—
177C2×C32—261no—
178C2×C32—261no—
179C2×C32—261no—
180C2×C32—261no—
181C2×C32—261no—
182C2×C32—261no—
183C2×C32—261no—
184C2×C32—261no—
185C2×C32—261no—
186C2×C32—261no—
187C2×C32—261no—
188C2×C32—261no—
189C2×C32—261no—
190C2×C32—261no—
191C2×C32—261no—
192C2×C32—261no—
193C2×C32—781no—
194C2×C32C22×C13⋊C311yescharacteristic
195C3×D3—21no—
196C3×D3—261no—
197C3×D3—261no—
198C3×D3—261no—
199C13C32×#6711yescharacteristic, complemented, Sylow
200C22×C3—21no—
201C22×C3—31no—
202C22×C3—131no—
203C22×C3—131no—
204C22×C3—131no—
205C22×C3—261no—
206C22×C3—261no—
207C22×C3—261no—
208C22×C3—391no—
209C22×C3—391no—
210C22×C3—391no—
211C22×C3D3×C13⋊C311yescharacteristic, complemented
212C22×C3C2×C3×C13⋊C311yescharacteristic, complemented
213C2×D3C2×C3×C13⋊C311yescharacteristic, complemented
214C3×C4—31no—
215C3×C4—391no—
216C3×C4—391no—
217C3×C4—391no—
218Dic3C2×C3×C13⋊C311yescharacteristic, complemented
219C32—131no—
220C32—131no—
221C32—131no—
222C32—131no—
223C32—261no—
224C32—261no—
225C32—261no—
226C32—261no—
227C32D4×C13⋊C311yescharacteristic, complemented
228D4—31noSylow
229C2×C3—21no—
230C2×C3—21no—
231C2×C3—21no—
232C2×C3—21no—
233C2×C3—21no—
234C2×C3—61no—
235C2×C3—131no—
236C2×C3—131no—
237C2×C3—131no—
238C2×C3—261no—
239C2×C3—261no—
240C2×C3—261no—
241C2×C3—261no—
242C2×C3—261no—
243C2×C3—261no—
244C2×C3—261no—
245C2×C3—261no—
246C2×C3—261no—
247C2×C3—261no—
248C2×C3—261no—
249C2×C3—261no—
250C2×C3—781no—
251C2×C3—781no—
252C2×C3—781no—
253C2×C3C2×D3×C13⋊C311yescharacteristic
254C2×C3C22×C3×C13⋊C311yescharacteristic
255D3—21no—
256C22—31no—
257C22C3×D3×C13⋊C311yescharacteristic, complemented
258C4—31no—
259C3—21no—
260C3—131no—
261C3—131no—
262C3—131no—
263C3—261no—
264C3—261no—
265C3—261no—
266C3#67×C13⋊C311yescharacteristic, direct product factor
267C3C3×D4×C13⋊C311yescharacteristic, complemented
268C2—21no—
269C2—61no—
270C2C2×C3×D3×C13⋊C311yescharacteristic
subgroupG/H
centerC2×C3C2×D3×C13⋊C3
commutator, cosocleC2×C3×C13C22×C32
FrattiniC2C2×C3×D3×C13⋊C3
FittingC22×C32×C13C2×C3
socleC2×C32×C13C22×C3
hypercenterC22×C3D3×C13⋊C3
hypocenterC3×C13C32×D4
LCSG ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C2×C3 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C22×C32×C13⋊C3C2semidirect
2. C2×C3×D3×C13⋊C3C2semidirect
3. C3×Dic3×C13⋊C3C2semidirect
4. C3×C13×#67C3semidirect
6. #67×C13⋊C3C3direct (N × H)
7. #67×C13⋊C3C3direct (N × H)
8. #67×C13⋊C3C3direct (N × H)
12. C22×C32×C13C2×C3semidirect
13. C2×C3×D3×C13C2×C3semidirect
19. C22×C3×C13⋊C3D3semidirect
20. C22×C3×C13⋊C3C2×C3semidirect
21. C22×C3×C13⋊C3C2×C3semidirect
22. C22×C3×C13⋊C3C2×C3semidirect
23. C2×D3×C13⋊C3C2×C3semidirect
24. C2×D3×C13⋊C3C2×C3semidirect
25. C2×D3×C13⋊C3C2×C3semidirect
26. C3×Dic3×C13C2×C3semidirect
28. Dic3×C13⋊C3C2×C3semidirect
29. Dic3×C13⋊C3C2×C3semidirect
30. Dic3×C13⋊C3C2×C3semidirect
31. C32×C13⋊C3D4semidirect
33. C13×#67C32semidirect
67. C22×C3×C13C3×D3semidirect
68. C22×C3×C13C2×C32semidirect
69. C2×D3×C13C2×C32semidirect
76. C22×C13⋊C3C3×D3semidirect
77. C22×C13⋊C3C3×D3semidirect
78. C22×C13⋊C3C3×D3semidirect
80. Dic3×C13C2×C32semidirect
84. C32×C13C3×D4semidirect
89. C3×C13⋊C3#67direct (N × H)
90. C3×C13⋊C3C3×D4semidirect
91. C3×C13⋊C3C3×D4semidirect
92. C3×C13⋊C3C3×D4semidirect
128. C3×#67C13⋊C3direct (N × H)
133. C22×C13C32×D3semidirect
136. C3×C13C3×#67semidirect
137. C3×C13C32×D4semidirect
141. C13⋊C3C3×#67direct (N × H)
142. C13⋊C3C3×#67direct (N × H)
143. C13⋊C3C3×#67direct (N × H)
153. C22×C32C2×C13⋊C3semidirect
157. C2×C3×D3C2×C13⋊C3semidirect
162. C3×Dic3C2×C13⋊C3semidirect
171. #67C3×C13⋊C3direct (N × H)
199. C13C32×#67semidirect
211. C22×C3D3×C13⋊C3semidirect
212. C22×C3C2×C3×C13⋊C3semidirect
213. C2×D3C2×C3×C13⋊C3semidirect
218. Dic3C2×C3×C13⋊C3semidirect
227. C32D4×C13⋊C3semidirect
257. C22C3×D3×C13⋊C3semidirect
266. C3#67×C13⋊C3direct (N × H)
267. C3C3×D4×C13⋊C3semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C13⋊C32
C2×C3×D3×C13⋊C32
C3×Dic3×C13⋊C32
C3×C13×#673
C3×D4×C13⋊C33
#67×C13⋊C33
C32×#6713