Finite Group Databasebeta

← C2×#13127984 #16769439

Subgroups — C2×#13127984 #16769439

Order 3328.

2074 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719458C211yesmaximal, characteristic, complemented
2C2×#11719457C211yesmaximal, characteristic, complemented
3#13127984C2116yesmaximal, direct product factor
4C2×#11718570C213yesmaximal, complemented
5C2×#11718569C213yesmaximal, complemented
6C2×#11718565C213yesmaximal, complemented
7C22×#88040C213yesmaximal, complemented
8C2×C13×#504C211yesmaximal, characteristic, complemented
9C2×#88257—21no—
10C2×#88256—21no—
11C2×C13×#131C2211yescharacteristic
12#11719458—24no—
13#11719458C2218yescomplemented
14#11719457—24no—
15#11719457C2218yescomplemented
16C2×#88163—23no—
17C2×#88162—23no—
18C22×Dic52C2213yescomplemented
19C2×#88158C2213yes—
20C2×#88158C2213yescomplemented
21C22×D104C2213yes—
22C13×#504C2218yescomplemented
23C2×C13×M32C2213yescomplemented
24C22×C13×C16C2213yescomplemented
25#11718570C22124yescomplemented
26#11718569C22124yescomplemented
27C2×Dic104C2213yescomplemented
28#11718565C22124yescomplemented
29C2×#88040C2213yescomplemented
30C2×#88040C2216yescomplemented
31C2×#88040C2211yescharacteristic, complemented
32C2×#88040C22124yescomplemented
33C2×D208C2213yescomplemented
34C2×C13×#41D411yescharacteristic
35#88257—28no—
36#88257—44no—
37#88256—28no—
38#88256—44no—
39C2×#6131—41no—
40C2×Q8×D13—41no—
41C2×#6129—43no—
42C2×D4×D13—43no—
43C2×#6127—23no—
44C2×#6127—23no—
45C22×D52—23no—
46C22×Dic26—23no—
47C13×#131D414yes—
48C13×#131C2314yes—
49C2×C13×M16D413yes—
50C22×C8×C13C2313yes—
51#88163—224no—
52#88162—224no—
53C2×Dic52—23no—
54C2×Dic52—26no—
55C2×Dic52C2311yescharacteristic
56C2×Dic52C2313yes—
57C2×Dic52C23112yescomplemented
58#88158—26no—
59#88158—26no—
60#88158C23112yes—
61#88158C23112yescomplemented
62C2×D104—23no—
63C2×D104—26no—
64C2×D104C2313yes—
65C2×D104C23112yes—
66C2×D104C2311yescharacteristic
67C2×#6095—23no—
68C2×#6095—23no—
69C13×M32C23112yescomplemented
70C2×C13×C16C2311yescharacteristic
71C2×C13×C16C2313yes—
72C2×C13×C16C23112yescomplemented
73Dic104C23112yescomplemented
74#88040C23112yescomplemented
75#88040C23124yescomplemented
76#88040C2314yescomplemented
77D208C23112yescomplemented
78C2×#3416—131nomaximal, Sylow
79C23×D13—43no—
80C13×#41D814yes—
81C13×#41C2×D414yes—
82C2×Q8×C13D811yescharacteristic
83C2×D4×C13D813yes—
84C22×C4×C13C2×D413yes—
85C2×C22⋊D13—43no—
86C2×C22⋊D13—43no—
87C22×Dic13—43no—
88#6131—48no—
89Q8×D13—48no—
90#6129—424no—
91D4×D13—424no—
92#6127—212no—
93#6127—212no—
94#6127—46no—
95#6127—46no—
96C2×D52—21no—
97C2×D52—23no—
98C2×D52—212no—
99C2×D52—43no—
100C2×D52—46no—
101C2×C4×D13—43no—
102C2×C4×D13—43no—
103C2×Dic26—21no—
104C2×Dic26—23no—
105C2×Dic26—212no—
106C2×Dic26—43no—
107C2×Dic26—46no—
108C13×M16C2×D4112yes—
109C2×C8×C13C2×D413yes—
110C2×C8×C13C2×D416yes—
111C2×C8×C13C2411yescharacteristic
112C2×C8×C13C2416yes—
113Dic52—21no—
114Dic52—23no—
115Dic52—212no—
116Dic52C2412yes—
117Dic52C2416yes—
118D104—23no—
119D104—212no—
120D104—21no—
121D104C2416yes—
122D104C2412yes—
123#6095—212no—
124#6095—212no—
125C13×C16C2412yes—
126C13×C16C2416yes—
127C2×#578—131no—
128C2×#576—131no—
129#3416—1316no—
130C2×#510—133no—
131C2×#509—133no—
132C2×#508—133no—
133C22×SD32—133no—
134C2×#504D1311yescharacteristic, complemented
135C23×C13C2×D813yes—
136C22×D13—41no—
137C22×D13—43no—
138C22×D13—412no—
139C22×D13—166no—
140Q8×C13C2×D814yes—
141D4×C13C2×D8112yes—
142C2×C4×C13C2×D813yes—
143C2×C4×C13C2×D816yes—
144C2×C4×C13C22×D411yescharacteristic
145C2×C4×C13C22×D416yes—
146C22⋊D13—412no—
147C22⋊D13—412no—
148C2×Dic13—43no—
149C2×Dic13—412no—
150C2×Dic13—41no—
151D52—22no—
152D52—26no—
153D52—43no—
154D52—412no—
155D52—41no—
156C4×D13—412no—
157C4×D13—412no—
158Dic26—22no—
159Dic26—26no—
160Dic26—43no—
161Dic26—412no—
162Dic26—41no—
163C8×C13C22×D416yes—
164C8×C13C22×D411yescharacteristic
165C8×C13C2511yescharacteristic
166C2×2−1+4—261no—
167C2×H(5,𝔽2)—261no—
168#578—138no—
169#578—264no—
170#576—138no—
171#576—264no—
172C2×#137—263no—
173C2×AGL(1,ℤ/8)—263no—
174C2×#135—133no—
175C2×#135—133no—
176C22×Q16—133no—
177C22×D8—133no—
178C2×#131C2×D1311yescharacteristic
179#510—1324no—
180#509—1324no—
181#508—1324no—
182C2×Q32—133no—
183C2×SD32—133no—
184C2×SD32—136no—
185C2×SD32—131no—
186C2×SD32—1324no—
187C2×D16—133no—
188#504C2×D1318yescomplemented
189C2×M32C2×D1313yescomplemented
190C22×C16C2×D1313yescomplemented
191C22×C13—26no—
192C22×C13C22×D816yes—
193C22×C13C22×D811yescharacteristic
194C2×D13—42no—
195C2×D13—46no—
196C2×D13—82no—
197C2×D13—86no—
198C2×D13—1612no—
199C4×C13C22×D811yescharacteristic
200C4×C13C22×D816yes—
201C4×C13C23×D411yescharacteristic
202Dic13—46no—
203Dic13—42no—
2042−1+4—268no—
2052−1+4—524no—
206H(5,𝔽2)—268no—
207H(5,𝔽2)—524no—
208C2×#41—263no—
209C2×#41—263no—
210C2×#41—521no—
211C2×#41—523no—
212C2×#41D5211yescharacteristic
213C22×Q8—263no—
214C22×Q8—521no—
215C22×D4—263no—
216C22×D4—523no—
217#137—2624no—
218AGL(1,ℤ/8)—2624no—
219#135—1312no—
220#135—1312no—
221#135—266no—
222#135—266no—
223C2×Q16—133no—
224C2×Q16—1312no—
225C2×Q16—131no—
226C2×Q16—263no—
227C2×Q16—266no—
228C2×SD16—263no—
229C2×SD16—263no—
230C2×D8—133no—
231C2×D8—1312no—
232C2×D8—131no—
233C2×D8—263no—
234C2×D8—266no—
235#131D5214yes—
236#131C22×D1314yes—
237C2×M16D5213yes—
238C22×C8C22×D1313yes—
239Q32—1312no—
240SD32—1312no—
241SD32—1324no—
242SD32—134no—
243D16—1312no—
244M32C22×D13112yescomplemented
245C2×C16C22×D1311yescharacteristic
246C2×C16C22×D1313yes—
247C2×C16C22×D13112yescomplemented
248C2×C13—26no—
249C2×C13#341612yescomplemented
250C2×C13C23×D811yescharacteristic
251D13—82no—
252D13—86no—
253C24—523no—
254#41—2612no—
255#41—2612no—
256#41—528no—
257#41—5224no—
258#41—526no—
259#41—526no—
260#41D10414yes—
261#41C2×D5214yes—
262C2×Q8—261no—
263C2×Q8—263no—
264C2×Q8—2612no—
265C2×Q8—528no—
266C2×Q8—523no—
267C2×Q8—526no—
268C2×Q8D10411yescharacteristic
269C2×D4—263no—
270C2×D4—2612no—
271C2×D4—261no—
272C2×D4—523no—
273C2×D4—523no—
274C2×D4—5224no—
275C2×D4—523no—
276C2×D4—526no—
277C2×D4D10413yes—
278C22×C4—523no—
279C22×C4—523no—
280C22×C4—523no—
281C22×C4C2×D5213yes—
282Q16—136no—
283Q16—132no—
284Q16—263no—
285Q16—2612no—
286Q16—261no—
287SD16—2612no—
288SD16—2612no—
289D8—132no—
290D8—136no—
291D8—263no—
292D8—2612no—
293D8—261no—
294M16C2×D52112yes—
295C2×C8C2×D5213yes—
296C2×C8C2×D5216yes—
297C2×C8C23×D1311yescharacteristic
298C2×C8C23×D1316yes—
299C16C23×D1312yes—
300C16C23×D1316yes—
301C13C2×#341611yescharacteristic, complemented, Sylow
302C23—521no—
303C23—523no—
304C23—5212no—
305C23—2086no—
306C23C2×D10413yes—
307Q8—262no—
308Q8—266no—
309Q8—5212no—
310Q8—523no—
311Q8—521no—
312Q8C2×D10414yes—
313D4—266no—
314D4—262no—
315D4—5212no—
316D4—5212no—
317D4—5212no—
318D4—523no—
319D4—521no—
320D4C2×D104112yes—
321C2×C4—5212no—
322C2×C4—521no—
323C2×C4—523no—
324C2×C4—5212no—
325C2×C4—5212no—
326C2×C4C2×D10416yes—
327C2×C4C2×D10413yes—
328C2×C4C22×D5216yes—
329C2×C4C22×D5211yescharacteristic
330C8C22×D5211yescharacteristic
331C8C22×D5216yes—
332C8C24×D1311yescharacteristic
333C22—26no—
334C22—522no—
335C22—526no—
336C22—1042no—
337C22—1046no—
338C22—20812no—
339C22C22×D10416yes—
340C22C22×D10411yescharacteristic
341C4—522no—
342C4—526no—
343C4C22×D10416yes—
344C4C22×D10411yescharacteristic
345C4C23×D5211yescharacteristic
346C2—26no—
347C2—1046no—
348C2—1042no—
349C2#1312798412yesdirect product factor
350C2C23×D10411yescharacteristic
subgroupG/H
centerC22C22×D104
commutator, cosocleC8×C13C25
FrattiniC8C24×D13
FittingC2×C13×#504C2
socleC22×C13C22×D8
hypercenterC2×#504D13
hypocenterC13C2×#3416
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ C2×#504

Complements

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

NH ≅ G/Ntype
1. C2×#11719458C2semidirect
2. C2×#11719457C2semidirect
3. #13127984C2direct (N × H)
4. C2×#11718570C2semidirect
5. C2×#11718569C2semidirect
6. C2×#11718565C2semidirect
7. C22×#88040C2semidirect
8. C2×C13×#504C2semidirect
13. #11719458C22semidirect
15. #11719457C22semidirect
18. C22×Dic52C22semidirect
20. C2×#88158C22semidirect
22. C13×#504C22semidirect
23. C2×C13×M32C22semidirect
24. C22×C13×C16C22semidirect
25. #11718570C22semidirect
26. #11718569C22semidirect
27. C2×Dic104C22semidirect
28. #11718565C22semidirect
29. C2×#88040C22semidirect
30. C2×#88040C22semidirect
31. C2×#88040C22semidirect
32. C2×#88040C22semidirect
33. C2×D208C22semidirect
57. C2×Dic52C23semidirect
61. #88158C23semidirect
69. C13×M32C23semidirect
72. C2×C13×C16C23semidirect
73. Dic104C23semidirect
74. #88040C23semidirect
75. #88040C23semidirect
76. #88040C23semidirect
77. D208C23semidirect
134. C2×#504D13semidirect
188. #504C2×D13semidirect
189. C2×M32C2×D13semidirect
190. C22×C16C2×D13semidirect
244. M32C22×D13semidirect
247. C2×C16C22×D13semidirect
249. C2×C13#3416semidirect
301. C13C2×#3416semidirect
349. C2#13127984direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117194582
C2×#117194572
#131279842
C2×#117185702
C2×#117185692
C2×#117185652
C22×#880402
C2×C13×#5042
C2×#341613