Finite Group Databasebeta

← C2×#14541928 #17940840

Subgroups — C2×#14541928 #17940840

Order 4352.

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×#11763614C211yesmaximal, characteristic, complemented
2#14541928C2116yesmaximal, direct product factor
3C2×#11763250C213yesmaximal, complemented
4C2×#11763244C213yesmaximal, complemented
5C2×#11763239C213yesmaximal, complemented
6C22×#10587499C213yesmaximal, complemented
7C2×#11763226C211yesmaximal, characteristic, complemented
8C2×C17×#578C211yesmaximal, characteristic, complemented
9C2×#10587696—21no—
10#11763614—24no—
11#11763614C2218yescomplemented
12C2×#10587594—23no—
13C2×#10587590C2213yes—
14C22×D136C2213yes—
15#11763250C22124yescomplemented
16#11763244C22124yescomplemented
17#11763239C22124yescomplemented
18C2×#10587500C2213yescomplemented
19C2×#10587498C2211yescharacteristic, complemented
20C2×#10587499C2213yescomplemented
21C2×#10587499C2216yescomplemented
22C2×#10587499C22124yescomplemented
23C2×#10587497C2213yescomplemented
24#11763226C2218yescomplemented
25C2×#10587483C2213yescomplemented
26C22×#63214C2213yescomplemented
27C2×C17×2−1+4—21no—
28C17×#578—24no—
29C17×#578C2218yescomplemented
30C2×C17×#137—23no—
31C2×C17×#135C2213yescomplemented
32C22×Q16×C17C2213yescomplemented
33C2×C17×#131C2211yescharacteristic
34C17×2−1+4—28no—
35C17×2−1+4—44no—
36C2×#41×C17—23no—
37C2×#41×C17—43no—
38C2×#41×C17D411yescharacteristic
39C22×Q8×C17—23no—
40C22×Q8×C17—41no—
41#10587696—28no—
42#10587696—44no—
43C2×#63256—41no—
44C2×D4×D17—43no—
45C2×#63252—23no—
46C22×D68—23no—
47C17×#137—224no—
48C17×#135—26no—
49C17×#135C23112yescomplemented
50C2×Q16×C17—23no—
51C2×Q16×C17—26no—
52C2×Q16×C17C2313yes—
53C2×Q16×C17C23112yescomplemented
54C2×SD16×C17—23no—
55C2×D8×C17C2311yescharacteristic
56C17×#131D414yes—
57C17×#131C2314yes—
58C2×M16×C17D413yes—
59C22×C8×C17C2313yes—
60#10587594—224no—
61C2×Dic68C2311yescharacteristic
62#10587590—26no—
63#10587590C23112yes—
64C2×D136—23no—
65C2×D136—26no—
66C2×D136C2313yes—
67C2×D136C23112yes—
68C2×#63219—23no—
69#10587500C23112yescomplemented
70#10587499C23112yescomplemented
71#10587499C23124yescomplemented
72#10587498C2314yescomplemented
73#10587497C23112yescomplemented
74#10587483C23112yescomplemented
75C2×#63214C2311yescharacteristic
76C2×#63214C2313yes—
77C2×#63214C23112yescomplemented
78C23×D17—43no—
79#41×C17—212no—
80#41×C17—424no—
81#41×C17—46no—
82#41×C17D814yes—
83#41×C17C2×D414yes—
84C2×Q8×C17—23no—
85C2×Q8×C17—212no—
86C2×Q8×C17—48no—
87C2×Q8×C17—43no—
88C2×Q8×C17—46no—
89C2×Q8×C17D811yescharacteristic
90C2×D4×C17—21no—
91C2×D4×C17—43no—
92C2×D4×C17D813yes—
93C22×C4×C17—43no—
94C22×C4×C17—43no—
95C22×C4×C17C2×D413yes—
96C2×C22⋊D17—43no—
97#63256—48no—
98D4×D17—424no—
99#63252—212no—
100#63252—46no—
101C2×D68—23no—
102C2×D68—212no—
103C2×D68—43no—
104C2×D68—46no—
105C2×C4×D17—43no—
106C2×Dic34—21no—
107Q16×C17—23no—
108Q16×C17—212no—
109Q16×C17C2416yes—
110SD16×C17—212no—
111D8×C17—21no—
112D8×C17C2412yes—
113M16×C17C2×D4112yes—
114C2×C8×C17C2×D413yes—
115C2×C8×C17C2×D416yes—
116C2×C8×C17C2411yescharacteristic
117C2×C8×C17C2416yes—
118Dic68—21no—
119Dic68C2412yes—
120D136—23no—
121D136—212no—
122D136C2416yes—
123#63219—212no—
124#63214C2412yes—
125#63214C2416yes—
126C2×#3416—171nomaximal, Sylow
127C23×C17—41no—
128C23×C17C2×D813yes—
129C22×D17—43no—
130C22×D17—412no—
131C22×D17—166no—
132Q8×C17—26no—
133Q8×C17—43no—
134Q8×C17—412no—
135Q8×C17C2×D814yes—
136D4×C17—22no—
137D4×C17—412no—
138D4×C17—41no—
139D4×C17C2×D8112yes—
140C2×C4×C17—43no—
141C2×C4×C17—412no—
142C2×C4×C17—412no—
143C2×C4×C17C2×D813yes—
144C2×C4×C17C2×D816yes—
145C2×C4×C17C22×D411yescharacteristic
146C2×C4×C17C22×D416yes—
147C22⋊D17—412no—
148C2×Dic17—41no—
149D68—26no—
150D68—43no—
151D68—412no—
152C4×D17—412no—
153Dic34—22no—
154Dic34—41no—
155C8×C17C22×D411yescharacteristic
156C8×C17C22×D416yes—
157C8×C17C2511yescharacteristic
158C2×#578D1711yescharacteristic, complemented
159C2×#576—171no—
160#3416—1716no—
161C2×#510—173no—
162C2×#509—173no—
163C2×#508—173no—
164C22×SD32—173no—
165C2×#504—171no—
166C22×C17—26no—
167C22×C17—42no—
168C22×C17—82no—
169C22×C17C22×D816yes—
170C22×C17C22×D811yescharacteristic
171C2×D17—46no—
172C2×D17—86no—
173C2×D17—1612no—
174C4×C17—46no—
175C4×C17C22×D811yescharacteristic
176C4×C17C22×D816yes—
177C4×C17C23×D411yescharacteristic
178Dic17—42no—
179C2×2−1+4—21no—
180C2×H(5,𝔽2)—341no—
181#578—24no—
182#578C2×D1718yescomplemented
183#576—178no—
184#576—344no—
185C2×#137—23no—
186C2×AGL(1,ℤ/8)—343no—
187C2×#135—173no—
188C2×#135C2×D1713yescomplemented
189C22×Q16C2×D1713yescomplemented
190C22×D8—173no—
191C2×#131C2×D1711yescharacteristic
192#510—1724no—
193#509—1724no—
194#508—1724no—
195C2×Q32—173no—
196C2×SD32—173no—
197C2×SD32—176no—
198C2×SD32—1724no—
199C2×SD32—171no—
200C2×D16—173no—
201#504—178no—
202C2×M32—173no—
203C22×C16—173no—
204C2×C17—26no—
205C2×C17—82no—
206C2×C17#341612yescomplemented
207C2×C17C23×D811yescharacteristic
208D17—86no—
2092−1+4—28no—
2102−1+4—44no—
211H(5,𝔽2)—348no—
212H(5,𝔽2)—684no—
213C2×#41—23no—
214C2×#41—43no—
215C2×#41—343no—
216C2×#41—681no—
217C2×#41C22⋊D1711yescharacteristic
218C22×Q8—23no—
219C22×Q8—41no—
220C22×D4—343no—
221C22×D4—683no—
222#137—224no—
223AGL(1,ℤ/8)—3424no—
224#135—26no—
225#135—1712no—
226#135—346no—
227#135C22×D17112yescomplemented
228C2×Q16—23no—
229C2×Q16—26no—
230C2×Q16—171no—
231C2×Q16C22×D1713yes—
232C2×Q16C22×D17112yescomplemented
233C2×SD16—23no—
234C2×SD16—343no—
235C2×D8—173no—
236C2×D8—1712no—
237C2×D8—343no—
238C2×D8—346no—
239C2×D8C22×D1711yescharacteristic
240#131C22⋊D1714yes—
241#131C22×D1714yes—
242C2×M16C22⋊D1713yes—
243C22×C8C22×D1713yes—
244Q32—1712no—
245SD32—1712no—
246SD32—1724no—
247SD32—174no—
248D16—1712no—
249M32—1712no—
250C2×C16—171no—
251C2×C16—173no—
252C2×C16—1712no—
253C17C2×#341611yescharacteristic, complemented, Sylow
254C24—683no—
255#41—212no—
256#41—424no—
257#41—46no—
258#41—3412no—
259#41—688no—
260#41—686no—
261#41#6322814yes—
262#41C2×C22⋊D1714yes—
263C2×Q8—23no—
264C2×Q8—212no—
265C2×Q8—48no—
266C2×Q8—43no—
267C2×Q8—46no—
268C2×Q8—341no—
269C2×Q8#6322811yescharacteristic
270C2×D4—21no—
271C2×D4—43no—
272C2×D4—343no—
273C2×D4—3412no—
274C2×D4—683no—
275C2×D4—6824no—
276C2×D4—683no—
277C2×D4—686no—
278C2×D4#6322813yes—
279C22×C4—43no—
280C22×C4—43no—
281C22×C4—683no—
282C22×C4C2×C22⋊D1713yes—
283Q16—23no—
284Q16—212no—
285Q16—172no—
286Q16—341no—
287Q16C23×D1716yes—
288SD16—212no—
289SD16—3412no—
290D8—21no—
291D8—176no—
292D8—343no—
293D8—3412no—
294D8C23×D1712yes—
295M16C2×C22⋊D17112yes—
296C2×C8C2×C22⋊D1713yes—
297C2×C8C2×C22⋊D1716yes—
298C2×C8C23×D1711yescharacteristic
299C2×C8C23×D1716yes—
300C16—172no—
301C16—176no—
302C23—41no—
303C23—2726no—
304C23—6812no—
305C23—683no—
306C23C2×#6322813yes—
307Q8—26no—
308Q8—412no—
309Q8—43no—
310Q8—342no—
311Q8—681no—
312Q8C2×#6322814yes—
313D4—22no—
314D4—412no—
315D4—41no—
316D4—346no—
317D4—6812no—
318D4—6812no—
319D4—683no—
320D4C2×#63228112yes—
321C2×C4—412no—
322C2×C4—43no—
323C2×C4—412no—
324C2×C4—681no—
325C2×C4—6812no—
326C2×C4C2×#6322816yes—
327C2×C4C2×#6322813yes—
328C2×C4C22×C22⋊D1716yes—
329C2×C4C22×C22⋊D1711yescharacteristic
330C8C22×C22⋊D1711yescharacteristic
331C8C22×C22⋊D1716yes—
332C8C24×D1711yescharacteristic
333C22—26no—
334C22—42no—
335C22—82no—
336C22—27212no—
337C22—686no—
338C22—1366no—
339C22C22×#6322816yes—
340C22C22×#6322811yescharacteristic
341C4—46no—
342C4—682no—
343C4C22×#6322816yes—
344C4C22×#6322811yescharacteristic
345C4C23×C22⋊D1711yescharacteristic
346C2—26no—
347C2—82no—
348C2—1366no—
349C2#1454192812yesdirect product factor
350C2C23×#6322811yescharacteristic
subgroupG/H
centerC22C22×#63228
commutator, cosocleC8×C17C25
FrattiniC8C24×D17
FittingC2×C17×#578C2
socleC22×C17C22×D8
hypercenterC2×#578D17
hypocenterC17C2×#3416
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ C2×#578

Complements

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

NH ≅ G/Ntype
1. C2×#11763614C2semidirect
2. #14541928C2direct (N × H)
3. C2×#11763250C2semidirect
4. C2×#11763244C2semidirect
5. C2×#11763239C2semidirect
6. C22×#10587499C2semidirect
7. C2×#11763226C2semidirect
8. C2×C17×#578C2semidirect
11. #11763614C22semidirect
15. #11763250C22semidirect
16. #11763244C22semidirect
17. #11763239C22semidirect
18. C2×#10587500C22semidirect
19. C2×#10587498C22semidirect
20. C2×#10587499C22semidirect
21. C2×#10587499C22semidirect
22. C2×#10587499C22semidirect
23. C2×#10587497C22semidirect
24. #11763226C22semidirect
25. C2×#10587483C22semidirect
26. C22×#63214C22semidirect
29. C17×#578C22semidirect
31. C2×C17×#135C22semidirect
32. C22×Q16×C17C22semidirect
49. C17×#135C23semidirect
53. C2×Q16×C17C23semidirect
69. #10587500C23semidirect
70. #10587499C23semidirect
71. #10587499C23semidirect
72. #10587498C23semidirect
73. #10587497C23semidirect
74. #10587483C23semidirect
77. C2×#63214C23semidirect
158. C2×#578D17semidirect
182. #578C2×D17semidirect
188. C2×#135C2×D17semidirect
189. C22×Q16C2×D17semidirect
206. C2×C17#3416semidirect
227. #135C22×D17semidirect
232. C2×Q16C22×D17semidirect
253. C17C2×#3416semidirect
349. C2#14541928direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117636142
#145419282
C2×#117632502
C2×#117632442
C2×#117632392
C22×#105874992
C2×#117632262
C2×C17×#5782
C2×#341617