Finite Group Databasebeta

← C2×#13122833 #16069037

Subgroups — C2×#13122833 #16069037

Order 3328.

4438 conjugacy classes of subgroups; only the 667 normal subgroups are shown.

normal subgroups only

This group has 4438 conjugacy classes of subgroups — too many to draw. Only its 667 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×#88207C212yesmaximal, complemented
2#13122833C2116yesmaximal, direct product factor
3C2×#11718614C213yesmaximal, complemented
4C2×#11718622C216yesmaximal, complemented
5C2×#11718621C213yesmaximal, complemented
6C2×C13×#379C211yesmaximal, characteristic, complemented
7C26×C13C2211yescharacteristic
8C23×C22⋊D13C2216yes—
9C23×D52C2211yescharacteristic, complemented
10C22×C13×C22⋊C4C2213yes—
11C22×C13×C22⋊C4C2213yes—
12C2×#88207—216no—
13C2×#88207C22116yescomplemented
14C22×C22⋊Dic13C2216yes—
15C22×#6103C2216yescomplemented
16C22×C4⋊Dic13C2213yescomplemented
17C13×#379C2218yescomplemented
18C2×#88071C2213yescomplemented
19C2×#88071C2213yescomplemented
20#11718622C22148yescomplemented
21#11718621C22124yescomplemented
22#11718614C22124yescomplemented
23C25×C13—46no—
24C25×C13—46no—
25C25×C13D418yescomplemented
26C25×C13C2313yes—
27C25×C13C2314yes—
28C24×D13C2312yes—
29C23×C4×C13C2313yes—
30C23×C4×C13C2311yescharacteristic
31C22×C22⋊D13—224no—
32C22×C22⋊D13—412no—
33C22×C22⋊D13—412no—
34C22×C22⋊D13C23124yes—
35C23×Dic13C2316yes—
36C22×D52—46no—
37C22×D52C2314yescomplemented
38C2×C13×C22⋊C4—46no—
39C2×C13×C22⋊C4—46no—
40C2×C13×C22⋊C4C23112yes—
41C2×C13×C22⋊C4C23112yes—
42#88207—264no—
43C2×C22⋊Dic13—224no—
44C2×C22⋊Dic13C23124yes—
45C2×#6103—412no—
46C2×#6103C23124yescomplemented
47C2×C4⋊Dic13—46no—
48C2×C4⋊Dic13C23112yescomplemented
49#88071C23112yescomplemented
50#88071C23112yescomplemented
51C2×#2812—131nomaximal, Sylow
52C24×C13—26no—
53C24×C13—26no—
54C24×C13—212no—
55C24×C13—212no—
56C24×C13—448no—
57C24×C13—412no—
58C24×C13—412no—
59C24×C13—448no—
60C24×C13—416no—
61C24×C13C2×D4112yes—
62C24×C13C2×D4116yescomplemented
63C24×C13C2416yes—
64C24×C13C2411yescharacteristic
65C23×D13—24no—
66C23×D13—212no—
67C23×D13—212no—
68C23×D13C2414yes—
69C22×C4×C13—26no—
70C22×C4×C13—212no—
71C22×C4×C13—26no—
72C22×C4×C13C2412yes—
73C22×C4×C13C2416yes—
74C2×C22⋊D13—248no—
75C2×C22⋊D13—424no—
76C2×C22⋊D13—424no—
77C2×C22⋊D13—496no—
78C22×Dic13—212no—
79C22×Dic13—212no—
80C22×Dic13—212no—
81C22×Dic13C24112yes—
82C2×D52—412no—
83C2×D52—416no—
84C13×C22⋊C4—412no—
85C13×C22⋊C4—412no—
86C22⋊Dic13—248no—
87#6103—424no—
88C4⋊Dic13—412no—
89C22×#120—132no—
90#2812—1316no—
91C2×#397—133no—
92C2×#394—136no—
93C2×#392—133no—
94C2×#379D1311yescharacteristic, complemented
95C23×C13—248no—
96C23×C13—224no—
97C23×C13—26no—
98C23×C13—26no—
99C23×C13—212no—
100C23×C13—212no—
101C23×C13—448no—
102C23×C13—448no—
103C23×C13—416no—
104C23×C13—4128no—
105C23×C13—424no—
106C23×C13—412no—
107C23×C13—412no—
108C23×C13C22×D4112yes—
109C23×C13C22×D412yes—
110C23×C13H(5,𝔽2)16yes—
111C23×C13H(5,𝔽2)16yes—
112C23×C13C2511yescharacteristic
113C22×D13—24no—
114C22×D13—212no—
115C22×D13—212no—
116C22×D13—424no—
117C22×D13—424no—
118C22×D13—48no—
119C2×C4×C13—26no—
120C2×C4×C13—212no—
121C2×C4×C13—26no—
122C2×C4×C13—412no—
123C2×C4×C13—44no—
124C22⋊D13—496no—
125C2×Dic13—212no—
126C2×Dic13—212no—
127C2×Dic13—212no—
128C2×Dic13—424no—
129D52—416no—
130C26C2×D1311yescharacteristic
131C23×D4—136no—
132C23×D4—131no—
133C2×#120—1316no—
134C2×#120—2616no—
135C22×C4⋊C4—133no—
136C22×C22⋊C4—136no—
137C22×C22⋊C4—136no—
138C22×C22⋊C4C2×D1313yes—
139C22×C22⋊C4C2×D1313yes—
140#397—1324no—
141#394—1348no—
142#392—1324no—
143#379C2×D1318yescomplemented
144C2×#95—133no—
145C2×#95—133no—
146C22×C13—224no—
147C22×C13—212no—
148C22×C13—464no—
149C22×C13—412no—
150C22×C13—46no—
151C22×C13—46no—
152C22×C13—448no—
153C22×C13#534112yes—
154C22×C13#560112yes—
155C22×C13H(3,𝔽4)14yes—
156C22×C13C23×D411yescharacteristic
157C22×C13C2×H(5,𝔽2)13yes—
158C22×C13C2×H(5,𝔽2)13yes—
159C2×D13—412no—
160C2×D13—412no—
161C2×D13—44no—
162C2×D13—816no—
163C4×C13—46no—
164C4×C13—42no—
165Dic13—412no—
166C25—46no—
167C25—46no—
168C25—132no—
169C25D5218yescomplemented
170C25C22×D1313yes—
171C25C22×D1314yes—
172C22×D4—1324no—
173C22×D4—134no—
174C22×D4—2624no—
175C22×D4—526no—
176C22×D4—5212no—
177C22×D4—5212no—
178C23×C4—136no—
179C23×C4C22×D1313yes—
180C23×C4C22×D1311yescharacteristic
181#120—2664no—
182C2×C4⋊C4—1312no—
183C2×C4⋊C4—526no—
184C2×C22⋊C4—46no—
185C2×C22⋊C4—46no—
186C2×C22⋊C4—1324no—
187C2×C22⋊C4—1324no—
188C2×C22⋊C4—2624no—
189C2×C22⋊C4—5212no—
190C2×C22⋊C4C22×D13112yes—
191C2×C22⋊C4C22×D13112yes—
192#95—1312no—
193#95—1312no—
194C2×C13—412no—
195C2×C13#281218yescomplemented
196C2×C13C2×#53413yes—
197C2×C13C2×#56013yes—
198C2×C13C2×H(3,𝔽4)11yescharacteristic
199D13—84no—
200C24—26no—
201C24—26no—
202C24—212no—
203C24—212no—
204C24—448no—
205C24—412no—
206C24—412no—
207C24—416no—
208C24—448no—
209C24—134no—
210C24—264no—
211C24—2612no—
212C24—2612no—
213C24C2×D52112yes—
214C24C2×D52116yescomplemented
215C24C23×D1316yes—
216C24C23×D1311yescharacteristic
217C2×D4—2648no—
218C2×D4—5212no—
219C2×D4—5216no—
220C2×D4—5224no—
221C2×D4—5224no—
222C2×D4—5296no—
223C22×C4—212no—
224C22×C4—26no—
225C22×C4—26no—
226C22×C4—1312no—
227C22×C4—2612no—
228C22×C4—2612no—
229C22×C4—2612no—
230C22×C4C23×D1312yes—
231C22×C4C23×D1316yes—
232C4⋊C4—5212no—
233C22⋊C4—412no—
234C22⋊C4—412no—
235C22⋊C4—2648no—
236C22⋊C4—5224no—
237C13C2×#281211yescharacteristic, complemented, Sylow
238C23—248no—
239C23—224no—
240C23—26no—
241C23—26no—
242C23—212no—
243C23—212no—
244C23—448no—
245C23—4128no—
246C23—448no—
247C23—416no—
248C23—412no—
249C23—412no—
250C23—424no—
251C23—264no—
252C23—2612no—
253C23—2612no—
254C23—5224no—
255C23—528no—
256C23—5224no—
257C23C22×D52112yes—
258C23C22×D5212yes—
259C23#8825116yes—
260C23#8825116yes—
261C23C24×D1311yescharacteristic
262D4—5216no—
263D4—5296no—
264C2×C4—212no—
265C2×C4—26no—
266C2×C4—26no—
267C2×C4—44no—
268C2×C4—412no—
269C2×C4—2612no—
270C2×C4—2612no—
271C2×C4—2612no—
272C2×C4—5224no—
273C22—224no—
274C22—212no—
275C22—464no—
276C22—448no—
277C22—412no—
278C22—46no—
279C22—46no—
280C22—5212no—
281C22—5212no—
282C22—524no—
283C22—10416no—
284C22#11719198112yes—
285C22#1171929914yes—
286C22#11719300112yes—
287C22C23×D5211yescharacteristic
288C22C2×#8825113yes—
289C22C2×#8825113yes—
290C4—46no—
291C4—42no—
292C4—5212no—
293C2—412no—
294C2—1044no—
295C2#1312283318yesdirect product factor
296C2C2×#1171919813yes—
297C2C2×#1171930013yes—
298C2C2×#1171929911yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#379C2
socleC24×C13C24
hypercenterC2×#379D13
hypocenterC13C2×#2812
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C22×#88207C2semidirect
2. #13122833C2direct (N × H)
3. C2×#11718614C2semidirect
4. C2×#11718622C2semidirect
5. C2×#11718621C2semidirect
6. C2×C13×#379C2semidirect
9. C23×D52C22semidirect
13. C2×#88207C22semidirect
15. C22×#6103C22semidirect
16. C22×C4⋊Dic13C22semidirect
17. C13×#379C22semidirect
18. C2×#88071C22semidirect
19. C2×#88071C22semidirect
20. #11718622C22semidirect
21. #11718621C22semidirect
22. #11718614C22semidirect
25. C25×C13D4semidirect
37. C22×D52C23semidirect
46. C2×#6103C23semidirect
48. C2×C4⋊Dic13C23semidirect
49. #88071C23semidirect
50. #88071C23semidirect
62. C24×C13C2×D4semidirect
94. C2×#379D13semidirect
143. #379C2×D13semidirect
169. C25D52semidirect
195. C2×C13#2812semidirect
214. C24C2×D52semidirect
237. C13C2×#2812semidirect
295. C2#13122833direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882072
#131228332
C2×#117186142
C2×#117186222
C2×#117186212
C2×C13×#3792
C2×#281213