Finite Group Databasebeta

← C2×#20265983 #27185887

Subgroups — C2×#20265983 #27185887

Order 12928.

1460 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15692303C211yesmaximal, characteristic, complemented
2C2×#15692300C211yesmaximal, characteristic, complemented
3#20265983C2116yesmaximal, direct product factor
4C2×#15692286C211yesmaximal, characteristic, complemented
5C2×#15692284C212yesmaximal, complemented
6C2×#15692282C212yesmaximal, complemented
7C2×#15692281C211yesmaximal, characteristic, complemented
8C2×#15692277C211yesmaximal, characteristic, complemented
9C2×#15692276C212yesmaximal, complemented
10C2×SD16×D101C212yesmaximal, complemented
11C2×#15692261C211yesmaximal, characteristic, complemented
12C22×SD16×C101C211yesmaximal, characteristic, complemented
13#15692303—24no—
14#15692303C2218yescomplemented
15#15692300—24no—
16#15692300C2218yescomplemented
17C2×#13108075—21no—
18C2×#13108075C2212yescomplemented
19C2×#13108074—22no—
20C2×#13108074C2211yescharacteristic
21C2×#13108074C2211yescharacteristic
22C2×#13108074C2211yescharacteristic, complemented
23C2×#13108073—21no—
24C2×#13108073C2212yes—
25C2×Q8×D101—21no—
26C2×Q8×D101C2212yescomplemented
27C22×C22⋊D101—22no—
28C2×D4×D101—21no—
29C2×D4×D101C2212yes—
30#15692286C2218yescomplemented
31#15692284C22116yescomplemented
32#15692282C22116yescomplemented
33#15692281C2218yescomplemented
34#15692277C2218yescomplemented
35#15692276C22116yescomplemented
36C2×Dic404C2211yescharacteristic, complemented
37C2×#13108064C2212yescomplemented
38C2×#13108063C2211yescharacteristic, complemented
39C2×#13108063C2211yescharacteristic, complemented
40C2×#13108062C2212yescomplemented
41C2×#13108061C2212yescomplemented
42SD16×D101C22116yescomplemented
43C2×D808C2211yescharacteristic, complemented
44C2×#13108059C2212yescomplemented
45#15692261C2218yescomplemented
46C2×#13108058C2211yescharacteristic, complemented
47C2×#13108057C2212yescomplemented
48C2×C8×D101C2212yescomplemented
49C22×Q8×C101C2211yescharacteristic, complemented
50C22×D4×C101C2211yescharacteristic
51C2×SD16×C101C2212yescomplemented
52C2×SD16×C101C2212yescomplemented
53C2×SD16×C101C2218yescomplemented
54C22×C8×C101C2211yescharacteristic, complemented
55C23×D101—22no—
56#13108075—28no—
57#13108075—24no—
58#13108075C2318yescomplemented
59#13108074—22no—
60#13108074—22no—
61#13108074—216no—
62#13108074D414yes—
63#13108074C2314yes—
64#13108074C2314yes—
65#13108074C2314yescomplemented
66#13108073—24no—
67#13108073—28no—
68#13108073C2318yes—
69C2×Dic202—22no—
70C2×Dic202D411yescharacteristic
71C2×Dic202C2311yescharacteristic
72C2×Dic202C2311yescharacteristic
73Q8×D101—24no—
74Q8×D101—28no—
75Q8×D101C2318yescomplemented
76C2×D404—22no—
77C2×D404D411yescharacteristic
78C2×D404C2311yescharacteristic
79C2×D404C2311yescharacteristic
80C2×C22⋊D101—21no—
81C2×C22⋊D101—21no—
82C2×C22⋊D101—22no—
83C2×C22⋊D101—216no—
84C2×C22⋊D101—22no—
85C2×C22⋊D101D412yes—
86D4×D101—28no—
87D4×D101—24no—
88D4×D101C2318yes—
89C22×Dic101—22no—
90C2×C4×D101—22no—
91C2×C4×D101—21no—
92C2×C4×D101—21no—
93C2×C4×D101—22no—
94C2×C4×D101C2312yes—
95Dic404C2314yescomplemented
96#13108064C2318yescomplemented
97#13108063C2314yescomplemented
98#13108063C2314yescomplemented
99#13108062C2318yescomplemented
100#13108061C2318yescomplemented
101D808C2314yescomplemented
102#13108059C2318yescomplemented
103#13108058C2314yescomplemented
104#13108057C2318yescomplemented
105C2×#11717579C2312yes—
106C8×D101C2318yescomplemented
107C24×C101—21no—
108C2×Q8×C101—21no—
109C2×Q8×C101—22no—
110C2×Q8×C101C2312yes—
111C2×Q8×C101C2314yescomplemented
112C2×D4×C101—21no—
113C2×D4×C101—22no—
114C2×D4×C101C2312yes—
115C2×D4×C101C2314yes—
116C22×C4×C101—21no—
117C22×C4×C101C2311yescharacteristic
118SD16×C101C2318yescomplemented
119SD16×C101C2318yescomplemented
120C2×C8×C101C2311yescharacteristic
121C2×C8×C101C2311yescharacteristic
122C2×C8×C101C2314yescomplemented
123C23×C101—22no—
124C23×C101—24no—
125C23×C101—82no—
126C23×C101C2×D411yescharacteristic
127C22×D101—21no—
128C22×D101—21no—
129C22×D101—28no—
130C22×D101—84no—
131C22×D101C2×D412yes—
132Q8×C101—22no—
133Q8×C101—24no—
134Q8×C101C2414yes—
135D4×C101—22no—
136D4×C101—24no—
137D4×C101C2414yes—
138C2×C4×C101—22no—
139C2×C4×C101—24no—
140C2×C4×C101C2×D411yescharacteristic
141C2×C4×C101C2×D412yes—
142C2×C4×C101C2411yescharacteristic
143C2×C4×C101C2412yes—
144C22⋊D101—24no—
145C22⋊D101—24no—
146C22⋊D101—28no—
147C22⋊D101—28no—
148C22⋊D101C2×D418yes—
149C2×Dic101—21no—
150C2×Dic101—21no—
151C2×Dic101—28no—
152C2×Dic101C2×D412yes—
153D404—28no—
154D404—21no—
155D404—21no—
156D404C2×D414yes—
157D404C2412yes—
158D404C2412yes—
159C4×D101—28no—
160C4×D101—24no—
161C4×D101—24no—
162C4×D101—28no—
163C4×D101C2×D414yes—
164C4×D101C2414yes—
165Dic202—21no—
166Dic202—21no—
167Dic202—28no—
168Dic202C2×D414yes—
169Dic202C2412yes—
170Dic202C2412yes—
171C8×C101C2412yes—
172C8×C101C2412yes—
173#11717579C2414yes—
174C22×C101—22no—
175C22×C101—24no—
176C22×C101—44no—
177C22×C101—84no—
178C22×C101C22×D412yes—
179C22×C101C22×D411yescharacteristic
180C2×D101—24no—
181C2×D101—22no—
182C2×D101—22no—
183C2×D101—42no—
184C2×D101—42no—
185C2×D101—88no—
186C2×D101C22×D414yes—
187C4×C101—24no—
188C4×C101C22×D411yescharacteristic
189C4×C101C22×D412yes—
190C4×C101C2511yescharacteristic
191Dic101—22no—
192Dic101—22no—
193Dic101C22×D414yes—
194C2×C101—22no—
195C2×C101—44no—
196C2×C101#57712yescomplemented
197C2×C101C23×D411yescharacteristic
198D101—24no—
199D101—42no—
200D101—42no—
201C2×#577—1011nomaximal, Sylow
202C101C2×#57711yescharacteristic, complemented, Sylow
203C2×2−1+4—1011no—
204C2×H(5,𝔽2)—1011no—
205#577—10116no—
206C2×#137—1011no—
207C2×#137—1012no—
208C2×AGL(1,ℤ/8)—1011no—
209C2×AGL(1,ℤ/8)—1012no—
210C2×#135—1012no—
211C2×#135—1011no—
212C22×SD16—1012no—
213C22×SD16D10111yescharacteristic, complemented
214C2×#131—1011no—
2152−1+4—1018no—
2162−1+4—2024no—
217H(5,𝔽2)—1018no—
218H(5,𝔽2)—2024no—
219C2×#41—1011no—
220C2×#41—1012no—
221C2×#41—1012no—
222C2×#41—1011no—
223C2×#41—1011no—
224C2×#41—2022no—
225C2×#41—2021no—
226C2×#41—2021no—
227C22×Q8—1012no—
228C22×Q8—2021no—
229C22×Q8C2×D10111yescharacteristic, complemented
230C22×D4—1012no—
231C22×D4—2021no—
232C22×D4—2022no—
233C22×D4C2×D10111yescharacteristic
234#137—1018no—
235#137—10116no—
236AGL(1,ℤ/8)—1018no—
237AGL(1,ℤ/8)—10116no—
238#135—10116no—
239#135—1018no—
240C2×Q16—1012no—
241C2×Q16—1011no—
242C2×SD16—1012no—
243C2×SD16—1012no—
244C2×SD16—10116no—
245C2×SD16—1011no—
246C2×SD16—1011no—
247C2×SD16C2×D10112yescomplemented
248C2×SD16C2×D10112yescomplemented
249C2×SD16C2×D10118yescomplemented
250C2×D8—1012no—
251C2×D8—1011no—
252#131—1018no—
253C2×M16—1011no—
254C2×M16—1012no—
255C22×C8—1012no—
256C22×C8C2×D10111yescharacteristic, complemented
257C24—21no—
258C24—2022no—
259#41—1014no—
260#41—1014no—
261#41—1018no—
262#41—1018no—
263#41—1014no—
264#41—1014no—
265#41—20216no—
266#41—2024no—
267#41—2024no—
268#41—2028no—
269#41—2028no—
270#41—2022no—
271#41—2022no—
272C2×Q8—21no—
273C2×Q8—22no—
274C2×Q8—1011no—
275C2×Q8—1018no—
276C2×Q8—1011no—
277C2×Q8—1011no—
278C2×Q8—2022no—
279C2×Q8—2024no—
280C2×Q8—2028no—
281C2×Q8C22×D10112yes—
282C2×Q8C22×D10114yescomplemented
283C2×D4—21no—
284C2×D4—22no—
285C2×D4—1012no—
286C2×D4—1018no—
287C2×D4—1011no—
288C2×D4—1011no—
289C2×D4—1011no—
290C2×D4—2022no—
291C2×D4—2024no—
292C2×D4—2022no—
293C2×D4—2028no—
294C2×D4—20216no—
295C2×D4—2022no—
296C2×D4—2021no—
297C2×D4—2021no—
298C2×D4C22×D10112yes—
299C2×D4C22×D10114yes—
300C22×C4—21no—
301C22×C4—1012no—
302C22×C4—2022no—
303C22×C4—2022no—
304C22×C4—2022no—
305C22×C4—2021no—
306C22×C4—2021no—
307C22×C4C22×D10111yescharacteristic
308Q16—1018no—
309Q16—1014no—
310SD16—1018no—
311SD16—1018no—
312SD16—1014no—
313SD16—1014no—
314SD16C22×D10118yescomplemented
315SD16C22×D10118yescomplemented
316D8—1018no—
317D8—1014no—
318M16—1014no—
319M16—1018no—
320C2×C8—1012no—
321C2×C8—1018no—
322C2×C8C22×D10111yescharacteristic
323C2×C8C22×D10111yescharacteristic
324C2×C8C22×D10114yescomplemented
325C23—22no—
326C23—24no—
327C23—82no—
328C23—8084no—
329C23—1012no—
330C23—2028no—
331C23—2021no—
332C23—2021no—
333C23D4×D10111yescharacteristic
334Q8—22no—
335Q8—24no—
336Q8—1014no—
337Q8—1012no—
338Q8—1012no—
339Q8—2028no—
340Q8—2021no—
341Q8—2021no—
342Q8C23×D10114yes—
343D4—22no—
344D4—24no—
345D4—1018no—
346D4—1014no—
347D4—1012no—
348D4—1012no—
349D4—2028no—
350D4—2028no—
351D4—2028no—
352D4—2024no—
353D4—2024no—
354D4—2021no—
355D4—2021no—
356D4C23×D10114yes—
357C2×C4—24no—
358C2×C4—22no—
359C2×C4—1012no—
360C2×C4—1014no—
361C2×C4—1014no—
362C2×C4—2028no—
363C2×C4—2028no—
364C2×C4—2028no—
365C2×C4—2021no—
366C2×C4—2021no—
367C2×C4—2024no—
368C2×C4—2024no—
369C2×C4D4×D10112yes—
370C2×C4D4×D10111yescharacteristic
371C2×C4C23×D10112yes—
372C2×C4C23×D10111yescharacteristic
373C8—1014no—
374C8C23×D10112yes—
375C8C23×D10112yes—
376C22—22no—
377C22—24no—
378C22—44no—
379C22—84no—
380C22—8088no—
381C22—1014no—
382C22—4042no—
383C22—4042no—
384C22—2022no—
385C22—2022no—
386C22—2024no—
387C22C2×D4×D10112yes—
388C22C2×D4×D10111yescharacteristic
389C4—24no—
390C4—1014no—
391C4—2022no—
392C4—2022no—
393C4C2×D4×D10111yescharacteristic
394C4C2×D4×D10112yes—
395C4C24×D10111yescharacteristic
396C2—22no—
397C2—44no—
398C2—4042no—
399C2—4042no—
400C2—2024no—
401C2#2026598312yesdirect product factor
402C2C22×D4×D10111yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC4×C101C25
FrattiniC4C24×D101
FittingC22×SD16×C101C2
socleC22×C101C22×D4
hypercenterC22×SD16D101
hypocenterC101C2×#577
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#15692303C2semidirect
2. C2×#15692300C2semidirect
3. #20265983C2direct (N × H)
4. C2×#15692286C2semidirect
5. C2×#15692284C2semidirect
6. C2×#15692282C2semidirect
7. C2×#15692281C2semidirect
8. C2×#15692277C2semidirect
9. C2×#15692276C2semidirect
10. C2×SD16×D101C2semidirect
11. C2×#15692261C2semidirect
12. C22×SD16×C101C2semidirect
14. #15692303C22semidirect
16. #15692300C22semidirect
18. C2×#13108075C22semidirect
22. C2×#13108074C22semidirect
26. C2×Q8×D101C22semidirect
30. #15692286C22semidirect
31. #15692284C22semidirect
32. #15692282C22semidirect
33. #15692281C22semidirect
34. #15692277C22semidirect
35. #15692276C22semidirect
36. C2×Dic404C22semidirect
37. C2×#13108064C22semidirect
38. C2×#13108063C22semidirect
39. C2×#13108063C22semidirect
40. C2×#13108062C22semidirect
41. C2×#13108061C22semidirect
42. SD16×D101C22semidirect
43. C2×D808C22semidirect
44. C2×#13108059C22semidirect
45. #15692261C22semidirect
46. C2×#13108058C22semidirect
47. C2×#13108057C22semidirect
48. C2×C8×D101C22semidirect
49. C22×Q8×C101C22semidirect
51. C2×SD16×C101C22semidirect
52. C2×SD16×C101C22semidirect
53. C2×SD16×C101C22semidirect
54. C22×C8×C101C22semidirect
58. #13108075C23semidirect
65. #13108074C23semidirect
75. Q8×D101C23semidirect
95. Dic404C23semidirect
96. #13108064C23semidirect
97. #13108063C23semidirect
98. #13108063C23semidirect
99. #13108062C23semidirect
100. #13108061C23semidirect
101. D808C23semidirect
102. #13108059C23semidirect
103. #13108058C23semidirect
104. #13108057C23semidirect
106. C8×D101C23semidirect
111. C2×Q8×C101C23semidirect
118. SD16×C101C23semidirect
119. SD16×C101C23semidirect
122. C2×C8×C101C23semidirect
196. C2×C101#577semidirect
202. C101C2×#577semidirect
213. C22×SD16D101semidirect
229. C22×Q8C2×D101semidirect
247. C2×SD16C2×D101semidirect
248. C2×SD16C2×D101semidirect
249. C2×SD16C2×D101semidirect
256. C22×C8C2×D101semidirect
282. C2×Q8C22×D101semidirect
314. SD16C22×D101semidirect
315. SD16C22×D101semidirect
324. C2×C8C22×D101semidirect
401. C2#20265983direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156923032
C2×#156923002
#202659832
C2×#156922862
C2×#156922842
C2×#156922822
C2×#156922812
C2×#156922772
C2×#156922762
C2×SD16×D1012
C2×#156922612
C22×SD16×C1012
C2×#577101