Finite Group Databasebeta

← C2×#72220635 #72241946

Subgroups — C2×#72220635 #72241946

Order 5616.

580 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 107 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×C3⋊AGL(1,𝔽13)C212yesmaximal, complemented
2C2×C3⋊D3×D13⋊C3C211yesmaximal, characteristic
3#72220635C214yesmaximal, direct product factor
4C2×(C3⋊#261)⋊D3C311yesmaximal, characteristic, complemented
5C2×D3×AGL(1,𝔽13)—32nomaximal
6C2×C3⋊(C3⋊(D13⋊C3))C411yescharacteristic, complemented
7C2×C3⋊D3×C13⋊C3C411yescharacteristic, complemented
8C2×C32×D13⋊C3C2211yescharacteristic
9C3⋊D3×D13⋊C3C412yescomplemented
10C3⋊D3×D13⋊C3C2212yes—
11C3×C3⋊AGL(1,𝔽13)C2214yescomplemented
12C2×C3⋊D3×D13C2×C311yescharacteristic
13C2×C3×C3⋊#261C2×C312yescomplemented
14(C3⋊#261)⋊D3C2×C314yescomplemented
15C2×D3×D13⋊C3—32no—
16C2×D3×D13⋊C3—61no—
17C2×C3⋊AGL(1,𝔽13)—22no—
18C2×C3⋊AGL(1,𝔽13)D312yescomplemented
19C2×C3×AGL(1,𝔽13)—32no—
20D3×AGL(1,𝔽13)—38no—
21C2×C32×C13⋊C3C2×C411yescharacteristic, complemented
22C3⋊(C3⋊(D13⋊C3))C2×C412yescomplemented
23C3⋊D3×C13⋊C3C2×C412yescomplemented
24C32×D13⋊C3C2×C411yescharacteristic, complemented
25C32×D13⋊C3C2311yescharacteristic
26C2×D3×#261—32no—
27C22×AGL(1,𝔽13)—91no—
28C2×C3⋊D39C3×C411yescharacteristic, complemented
29C2×C13×C3⋊D3C3×C411yescharacteristic, complemented
30C2×C32×D13C22×C311yescharacteristic
31C3⋊D3×D13C3×C412yescomplemented
32C3⋊D3×D13C22×C312yes—
33C3×C3⋊#261C22×C314yescomplemented
34C2×C3⋊(D13⋊C3)—32no—
35C2×C3⋊(D13⋊C3)—61no—
36C2×D3×C13⋊C3—32no—
37C2×D3×C13⋊C3—61no—
38C2×C3×D13⋊C3—22no—
39C2×C3×D13⋊C3—21no—
40C2×C3×D13⋊C3—41no—
41C2×C3×D13⋊C3C2×D312yes—
42D3×D13⋊C3—34no—
43D3×D13⋊C3—34no—
44D3×D13⋊C3—62no—
45D3×D13⋊C3—62no—
46C3⋊AGL(1,𝔽13)—24no—
47C3⋊AGL(1,𝔽13)C2×D314yescomplemented
48C3×AGL(1,𝔽13)—34no—
49C2×C3×#624—131nomaximal, Hall
50C32×C13⋊C3C22×C411yescharacteristic, complemented, Hall
51C2×D3×D13—32no—
52C2×D3×D13—61no—
53C2×C3⋊#261C3×D312yescomplemented
54C2×C3×#261—32no—
55C22×D13⋊C3—91no—
56D3×#261—38no—
57C2×AGL(1,𝔽13)—32no—
58C2×AGL(1,𝔽13)—62no—
59C2×AGL(1,𝔽13)—94no—
60C2×C32×C13C2×C3×C411yescharacteristic, complemented
61C3⋊D39C2×C3×C412yescomplemented
62C13×C3⋊D3C2×C3×C412yescomplemented
63C32×D13C2×C3×C411yescharacteristic, complemented
64C32×D13C23×C311yescharacteristic
65C2×C3×C13⋊C3—21no—
66C2×C3×C13⋊C3—22no—
67C2×C3×C13⋊C3—41no—
68C2×C3×C13⋊C3C4×D312yescomplemented
69C3⋊(D13⋊C3)—34no—
70C3⋊(D13⋊C3)—62no—
71D3×C13⋊C3—34no—
72D3×C13⋊C3—62no—
73C3×D13⋊C3—22no—
74C3×D13⋊C3—22no—
75C3×D13⋊C3—21no—
76C3×D13⋊C3—21no—
77C3×D13⋊C3—41no—
78C3×D13⋊C3—41no—
79C3×D13⋊C3C4×D312yescomplemented
80C3×D13⋊C3C22×D312yes—
81C22×C3×C3⋊D3—131no—
82C2×C32×Dic3—132no—
83C3×#624—134no—
84C22×#261—91noHall
85C2×D39—32no—
86C2×D39—61no—
87C2×D3×C13—32no—
88C2×D3×C13—61no—
89C2×C3×D13—21no—
90C2×C3×D13C2×C3×D312yes—
91C22×C13⋊C3—91no—
92D3×D13—34no—
93D3×D13—34no—
94D3×D13—62no—
95D3×D13—62no—
96C3⋊#261C2×C3×D314yescomplemented
97C3×#261—34no—
98C2×D13⋊C3—22no—
99C2×D13⋊C3—41no—
100C2×D13⋊C3—91no—
101C2×D13⋊C3—92no—
102C2×D13⋊C3—92no—
103C2×D13⋊C3D3211yescharacteristic
104AGL(1,𝔽13)—34no—
105AGL(1,𝔽13)—64no—
106C2×C3×C4×D3—392no—
107C2×#624—131no—
108C32×C13C22×C3×C411yescharacteristic, complemented
109C3×C13⋊C3—21no—
110C3×C13⋊C3—22no—
111C3×C13⋊C3—41no—
112C3×C13⋊C3C2×C4×D312yescomplemented
113C22×C33—131no—
114C2×C3×C3⋊D3—131no—
115C2×C3×C3⋊D3—132no—
116C2×C3×C3⋊D3—132no—
117C2×C3×C3⋊D3—521no—
118C32×Dic3—134no—
119C22×D13—91no—
120C2×#261—32no—
121C2×#261—94no—
122C2×C3×C13—21no—
123C2×C3×C13C3×C4×D312yescomplemented
124D39—34no—
125D39—62no—
126C3×D13—21no—
127C3×D13—21no—
128C3×D13C3×C4×D312yescomplemented
129C3×D13C22×C3×D312yes—
130D3×C13—34no—
131D3×C13—62no—
132C2×C13⋊C3—22no—
133C2×C13⋊C3—41no—
134C2×C13⋊C3—92no—
135C2×C13⋊C3#62411yescharacteristic, complemented
136D13⋊C3—22no—
137D13⋊C3—22no—
138D13⋊C3—41no—
139D13⋊C3—41no—
140D13⋊C3—92no—
141D13⋊C3#62411yescharacteristic, complemented
142D13⋊C3C2×D3211yescharacteristic
143C22×C3⋊D3—131no—
144C22×C3×D3—392no—
145C22×C3×D3—781no—
146C2×C32×C4—392no—
147C2×C3×Dic3—132no—
148C2×C3×Dic3—132no—
149C2×C3×Dic3—262no—
150C3×C4×D3—398no—
151#624—134no—
152C2×C33—131no—
153C2×C33—131no—
154C2×C33—521no—
155C3×C3⋊D3—132no—
156C3×C3⋊D3—522no—
157C22×C13—91no—
158C2×D13—91no—
159C2×D13—92no—
160C2×D13—92no—
161C2×D13C3×D3211yescharacteristic
162#261—34no—
163C22×C3×C4—1171no—
164C2×C4×D3—392no—
165C3×C13—21no—
166C3×C13C2×C3×C4×D312yescomplemented
167C13⋊C3—22no—
168C13⋊C3—41no—
169C13⋊C3C2×#62411yescharacteristic, complemented
170C22×C32—132no—
171C22×C32—131no—
172C22×C32—261no—
173C22×C32—262no—
174C22×C32—521no—
175C2×C3⋊D3—131no—
176C2×C3⋊D3—132no—
177C2×C3⋊D3—132no—
178C2×C3⋊D3AGL(1,𝔽13)11yescharacteristic, complemented
179C2×C3×D3—392no—
180C2×C3×D3—394no—
181C2×C3×D3—394no—
182C2×C3×D3—781no—
183C2×C3×D3—782no—
184C2×C3×D3—782no—
185C2×C3×D3—1562no—
186C2×C3×D3—1561no—
187C32×C4—394no—
188C3×Dic3—134no—
189C3×Dic3—134no—
190C3×Dic3—264no—
191C33—521noSylow
192C2×C13—92no—
193C2×C13C3×#62411yescharacteristic, complemented
194D13—92no—
195D13C3×#62411yescharacteristic, complemented
196D13C2×C3×D3211yescharacteristic
197C23×C3—1171no—
198C22×D3—392no—
199C22×D3—781no—
200C2×C3×C4—392no—
201C2×C3×C4—392no—
202C2×C3×C4—782no—
203C2×C3×C4—1174no—
204C2×Dic3—132no—
205C4×D3—398no—
206C2×C32—132no—
207C2×C32—132no—
208C2×C32—131no—
209C2×C32—131no—
210C2×C32—261no—
211C2×C32—261no—
212C2×C32—262no—
213C2×C32—262no—
214C2×C32—521no—
215C2×C32—521no—
216C2×C32—521no—
217C2×C32—522no—
218C2×C32—1041no—
219C2×C32—1042no—
220C2×C32C2×AGL(1,𝔽13)11yescharacteristic, complemented
221C3⋊D3—132no—
222C3⋊D3C2×AGL(1,𝔽13)12yescomplemented
223C3×D3—394no—
224C3×D3—782no—
225C3×D3—1564no—
226C3×D3—1562no—
227C22×C4—1171noSylow
228C13C2×C3×#62411yescharacteristic, complemented, Sylow
229C22×C3—131no—
230C22×C3—132no—
231C22×C3—261no—
232C22×C3—262no—
233C22×C3—521no—
234C22×C3—1172no—
235C22×C3—1172no—
236C22×C3—1171no—
237C22×C3—4681no—
238C2×D3—32no—
239C2×D3—61no—
240C2×D3—394no—
241C2×D3—394no—
242C2×D3—392no—
243C2×D3—782no—
244C2×D3—782no—
245C2×D3—781no—
246C3×C4—394no—
247C3×C4—394no—
248C3×C4—784no—
249Dic3—134no—
250C32—521no—
251C32—522no—
252C32—1041no—
253C32—1042no—
254C32C22×AGL(1,𝔽13)11yescharacteristic, complemented
255C23—1171no—
256C2×C4—392no—
257C2×C4—1174no—
258C2×C3—21no—
259C2×C3—131no—
260C2×C3—131no—
261C2×C3—132no—
262C2×C3—132no—
263C2×C3—261no—
264C2×C3—261no—
265C2×C3—262no—
266C2×C3—262no—
267C2×C3—521no—
268C2×C3—521no—
269C2×C3—521no—
270C2×C3—1042no—
271C2×C3—1041no—
272C2×C3—1172no—
273C2×C3—4682no—
274C2×C3D3×AGL(1,𝔽13)12yescomplemented
275D3—34no—
276D3—62no—
277D3—394no—
278D3—782no—
279C22—91no—
280C22—131no—
281C22—1172no—
282C22—1172no—
283C22—1171no—
284C4—394no—
285C3—21no—
286C3—521no—
287C3—1042no—
288C3—1041no—
289C3C2×D3×AGL(1,𝔽13)12yescomplemented
290C2—92no—
291C2—131no—
292C2—131no—
293C2—1172no—
294C2#7222063511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#72220635
commutator, hypocenterC32×C13C22×C3×C4
FrattiniC1G
Fitting, socleC2×C32×C13C2×C3×C4
prime radicalC2×C3⋊D3×D13⋊C3C2
cosocleC32×D13C23×C3
LCSG ▷ C32×C13
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×C3⋊AGL(1,𝔽13)C2semidirect
3. #72220635C2direct (N × H)
4. C2×(C3⋊#261)⋊D3C3semidirect
6. C2×C3⋊(C3⋊(D13⋊C3))C4semidirect
7. C2×C3⋊D3×C13⋊C3C4semidirect
9. C3⋊D3×D13⋊C3C4semidirect
11. C3×C3⋊AGL(1,𝔽13)C22semidirect
13. C2×C3×C3⋊#261C2×C3semidirect
14. (C3⋊#261)⋊D3C2×C3semidirect
18. C2×C3⋊AGL(1,𝔽13)D3semidirect
21. C2×C32×C13⋊C3C2×C4semidirect
22. C3⋊(C3⋊(D13⋊C3))C2×C4semidirect
23. C3⋊D3×C13⋊C3C2×C4semidirect
24. C32×D13⋊C3C2×C4semidirect
28. C2×C3⋊D39C3×C4semidirect
29. C2×C13×C3⋊D3C3×C4semidirect
31. C3⋊D3×D13C3×C4semidirect
33. C3×C3⋊#261C22×C3semidirect
47. C3⋊AGL(1,𝔽13)C2×D3semidirect
50. C32×C13⋊C3C22×C4semidirect
53. C2×C3⋊#261C3×D3semidirect
60. C2×C32×C13C2×C3×C4semidirect
61. C3⋊D39C2×C3×C4semidirect
62. C13×C3⋊D3C2×C3×C4semidirect
63. C32×D13C2×C3×C4semidirect
68. C2×C3×C13⋊C3C4×D3semidirect
79. C3×D13⋊C3C4×D3semidirect
96. C3⋊#261C2×C3×D3semidirect
108. C32×C13C22×C3×C4semidirect
112. C3×C13⋊C3C2×C4×D3semidirect
123. C2×C3×C13C3×C4×D3semidirect
128. C3×D13C3×C4×D3semidirect
135. C2×C13⋊C3#624semidirect
141. D13⋊C3#624semidirect
166. C3×C13C2×C3×C4×D3semidirect
169. C13⋊C3C2×#624semidirect
178. C2×C3⋊D3AGL(1,𝔽13)semidirect
193. C2×C13C3×#624semidirect
195. D13C3×#624semidirect
220. C2×C32C2×AGL(1,𝔽13)semidirect
222. C3⋊D3C2×AGL(1,𝔽13)semidirect
228. C13C2×C3×#624semidirect
254. C32C22×AGL(1,𝔽13)semidirect
274. C2×C3D3×AGL(1,𝔽13)semidirect
289. C3C2×D3×AGL(1,𝔽13)semidirect
294. C2#72220635direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C3⋊AGL(1,𝔽13)2
C2×C3⋊D3×D13⋊C32
#722206352
C2×(C3⋊#261)⋊D33
C2×D3×AGL(1,𝔽13)3
C2×C3×#62413