Finite Group Databasebeta

← C2×#26028530 #36760254

Subgroups — C2×#26028530 #36760254

Order 22784.

32890 conjugacy classes of subgroups; only the 1243 normal subgroups are shown.

normal subgroups only

This group has 32890 conjugacy classes of subgroups — too many to draw. Only its 1243 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
1C26×D89C211yesmaximal, characteristic, complemented
2C22×#15667982C216yesmaximal, complemented
3C22×#15667981C211yesmaximal, characteristic, complemented
4#26028530C2116yesmaximal, direct product factor
5C2×#19151453C216yesmaximal, complemented
6C2×#379×C89C211yesmaximal, characteristic, complemented
7C25×D89—28no—
8C25×D89—248no—
9C25×D89C2216yes—
10C25×D89C2218yescomplemented
11C23×D356C2214yescomplemented
12C23×C22⋊D89C2213yescomplemented
13C2×#15667982—248no—
14C2×#15667982C22148yescomplemented
15C2×#15667981—28no—
16C2×#15667981C2218yescomplemented
17C22×C22⋊Dic89C2213yescomplemented
18C22×#13083551C22112yescomplemented
19#19151453C22148yescomplemented
20C26×C89C2211yescharacteristic
21C22×C22⋊C4×C89C2216yescomplemented
22#379×C89C2218yescomplemented
23C24×D89—2512no—
24C24×D89—2384no—
25C24×D89—296no—
26C24×D89—2192no—
27C24×D89—224no—
28C24×D89—224no—
29C24×D89—232no—
30C24×D89D4148yescomplemented
31C24×D89C23124yes—
32C24×D89C2314yes—
33C24×D89C2311yescharacteristic, complemented
34C22×D356—248no—
35C22×D356C23116yescomplemented
36C22×C22⋊D89—212no—
37C22×C22⋊D89—224no—
38C22×C22⋊D89C23112yescomplemented
39C23×Dic89C2313yescomplemented
40#15667982—2192no—
41#15667981—232no—
42C2×C22⋊Dic89—212no—
43C2×C22⋊Dic89C23112yescomplemented
44C2×#13083551—248no—
45C2×#13083551C23148yescomplemented
46C25×C89—224no—
47C25×C89D418yescomplemented
48C25×C89C2314yes—
49C25×C89C2313yes—
50C23×C4×C89C2314yescomplemented
51C2×C22⋊C4×C89—224no—
52C2×C22⋊C4×C89C23124yescomplemented
53C23×D89—22048no—
54C23×D89—2384no—
55C23×D89—2384no—
56C23×D89—2768no—
57C23×D89—21024no—
58C23×D89—2192no—
59C23×D89—248no—
60C23×D89—248no—
61C23×D89—224no—
62C23×D89—28no—
63C23×D89—2384no—
64C23×D89—2192no—
65C23×D89—22no—
66C23×D89—212no—
67C23×D89C2×D4148yes—
68C23×D89C2×D4196yescomplemented
69C23×D89C2418yes—
70C23×D89C2412yescomplemented
71C2×D356—296no—
72C2×D356—464no—
73C2×C22⋊D89—224no—
74C2×C22⋊D89—248no—
75C2×C22⋊D89—448no—
76C22×Dic89—212no—
77C22×Dic89—26no—
78C22×Dic89C2416yescomplemented
79C22⋊Dic89—224no—
80#13083551—296no—
81C24×C89—2128no—
82C24×C89—296no—
83C24×C89—248no—
84C24×C89—224no—
85C24×C89C2×D4124yes—
86C24×C89C2×D4112yes—
87C24×C89C2×D4116yescomplemented
88C24×C89C2416yes—
89C24×C89C2411yescharacteristic
90C22×C4×C89—224no—
91C22×C4×C89C2418yescomplemented
92C22⋊C4×C89—248no—
93C23×C89—2256no—
94C23×C89—2128no—
95C23×C89—296no—
96C23×C89—248no—
97C23×C89—296no—
98C23×C89—224no—
99C23×C89#120148yescomplemented
100C23×C89C22×D4124yes—
101C23×C89C22×D4112yes—
102C23×C89C22×D4112yes—
103C23×C89C22×D412yes—
104C23×C89C2511yescharacteristic
105C22×D89—22048no—
106C22×D89—21536no—
107C22×D89—2384no—
108C22×D89—2384no—
109C22×D89—296no—
110C22×D89—296no—
111C22×D89—2192no—
112C22×D89—224no—
113C22×D89—28no—
114C22×D89—2384no—
115C22×D89—22no—
116C22×D89—212no—
117C22×D89—412no—
118C22×D89—416no—
119C22×D89#120164yescomplemented
120C22×D89C22×D4148yes—
121C2×C4×C89—224no—
122C2×C4×C89—416no—
123C22⋊D89—448no—
124C2×Dic89—212no—
125C2×Dic89—26no—
126C2×Dic89—412no—
127D356—464no—
128C22×C89—2128no—
129C22×C89—296no—
130C22×C89—248no—
131C22×C89—224no—
132C22×C89C2×#120116yes—
133C22×C89C2×#120112yes—
134C22×C89C2×#120124yescomplemented
135C22×C89C23×D416yes—
136C22×C89C23×D411yescharacteristic
137C2×D89—2768no—
138C2×D89—2128no—
139C2×D89—248no—
140C2×D89—248no—
141C2×D89—48no—
142C2×D89—46no—
143C2×D89—88no—
144C2×D89C2×#120132yescomplemented
145C4×C89—48no—
146Dic89—46no—
147C2×#2846—891nomaximal, Sylow
148C2×C89—224no—
149C2×C89#284618yescomplemented
150C2×C89C22×#12014yes—
151C2×C89C22×#12013yes—
152D89—232no—
153D89—82no—
154C27—891no—
155C22×#120—891no—
156C22×#120—896no—
157#2846—8916no—
158C2×#379—896no—
159C2×#379D8911yescharacteristic, complemented
160C89C2×#284611yescharacteristic, complemented, Sylow
161C26—896no—
162C26—898no—
163C26—17848no—
164C26—1788no—
165C26C2×D8911yescharacteristic
166C23×D4—893no—
167C23×D4—894no—
168C2×#120—898no—
169C2×#120—8948no—
170C2×#120—17848no—
171C2×#120—1788no—
172C22×C22⋊C4—893no—
173C22×C22⋊C4—8912no—
174C22×C22⋊C4C2×D8916yescomplemented
175#379—8948no—
176#379C2×D8918yescomplemented
177C25—224no—
178C25—894no—
179C25—8948no—
180C25—8924no—
181C25—891no—
182C25—17896no—
183C25—178192no—
184C25—178512no—
185C25—178384no—
186C25—17824no—
187C25—17824no—
188C25—17832no—
189C25D35618yescomplemented
190C25C22×D8914yes—
191C25C22×D8913yes—
192C22×D4—8912no—
193C22×D4—8916no—
194C22×D4—17848no—
195C22×D4—17824no—
196C22×D4—17812no—
197C23×C4—893no—
198C23×C4C22×D8914yescomplemented
199#120—178192no—
200#120—17832no—
201C2×C22⋊C4—224no—
202C2×C22⋊C4—8912no—
203C2×C22⋊C4—8948no—
204C2×C22⋊C4—17848no—
205C2×C22⋊C4—17812no—
206C2×C22⋊C4C22×D89124yescomplemented
207C24—2128no—
208C24—296no—
209C24—248no—
210C24—224no—
211C24—8948no—
212C24—898no—
213C24—8996no—
214C24—892no—
215C24—178192no—
216C24—178384no—
217C24—1781024no—
218C24—1782048no—
219C24—178384no—
220C24—178384no—
221C24—178768no—
222C24—17812no—
223C24—1782no—
224C24—178192no—
225C24—17848no—
226C24—17824no—
227C24—17848no—
228C24—1788no—
229C24D4×D89124yes—
230C24C2×D356112yes—
231C24C2×D356116yescomplemented
232C24C23×D8916yes—
233C24C23×D8911yescharacteristic
234C2×D4—35664no—
235C2×D4—35648no—
236C2×D4—17896no—
237C2×D4—17848no—
238C2×D4—17824no—
239C22×C4—224no—
240C22×C4—896no—
241C22×C4—17812no—
242C22×C4—1786no—
243C22×C4C23×D8918yescomplemented
244C22⋊C4—248no—
245C22⋊C4—17896no—
246C22⋊C4—17824no—
247C23—2128no—
248C23—2256no—
249C23—224no—
250C23—296no—
251C23—248no—
252C23—296no—
253C23—8948no—
254C23—8964no—
255C23—35616no—
256C23—35612no—
257C23—178384no—
258C23—1782048no—
259C23—178384no—
260C23—178384no—
261C23—1781536no—
262C23—17812no—
263C23—1782no—
264C23—17824no—
265C23—1788no—
266C23—17896no—
267C23—17896no—
268C23—178192no—
269C23#15667982148yescomplemented
270C23C2×D4×D89124yes—
271C23C2×D4×D89112yes—
272C23C22×D356112yes—
273C23C22×D35612yes—
274C23C24×D8911yescharacteristic
275D4—35664no—
276D4—35648no—
277C2×C4—224no—
278C2×C4—416no—
279C2×C4—35612no—
280C2×C4—17812no—
281C2×C4—1786no—
282C22—2128no—
283C22—248no—
284C22—224no—
285C22—296no—
286C22—8932no—
287C22—3568no—
288C22—3566no—
289C22—178768no—
290C22—17848no—
291C22—17848no—
292C22—178128no—
293C22—7128no—
294C22#120×D89116yes—
295C22C2×#15667982112yes—
296C22C2×#15667982124yescomplemented
297C22C22×D4×D8916yes—
298C22C23×D35611yescharacteristic
299C4—48no—
300C4—3566no—
301C2—224no—
302C2—17832no—
303C2—7122no—
304C2#2602853018yesdirect product factor
305C2C2×#120×D8914yes—
306C2C22×#1566798213yes—
subgroupG/H
centerC24C23×D89
commutator, cosocleC23×C89C25
FrattiniC23C24×D89
FittingC2×#379×C89C2
socleC24×C89C24
hypercenterC2×#379D89
hypocenterC89C2×#2846
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C26×D89C2semidirect
2. C22×#15667982C2semidirect
3. C22×#15667981C2semidirect
4. #26028530C2direct (N × H)
5. C2×#19151453C2semidirect
6. C2×#379×C89C2semidirect
10. C25×D89C22semidirect
11. C23×D356C22semidirect
12. C23×C22⋊D89C22semidirect
14. C2×#15667982C22semidirect
16. C2×#15667981C22semidirect
17. C22×C22⋊Dic89C22semidirect
18. C22×#13083551C22semidirect
19. #19151453C22semidirect
21. C22×C22⋊C4×C89C22semidirect
22. #379×C89C22semidirect
30. C24×D89D4semidirect
33. C24×D89C23semidirect
35. C22×D356C23semidirect
38. C22×C22⋊D89C23semidirect
39. C23×Dic89C23semidirect
43. C2×C22⋊Dic89C23semidirect
45. C2×#13083551C23semidirect
47. C25×C89D4semidirect
50. C23×C4×C89C23semidirect
52. C2×C22⋊C4×C89C23semidirect
68. C23×D89C2×D4semidirect
70. C23×D89C24semidirect
78. C22×Dic89C24semidirect
87. C24×C89C2×D4semidirect
91. C22×C4×C89C24semidirect
99. C23×C89#120semidirect
119. C22×D89#120semidirect
134. C22×C89C2×#120semidirect
144. C2×D89C2×#120semidirect
149. C2×C89#2846semidirect
159. C2×#379D89semidirect
160. C89C2×#2846semidirect
174. C22×C22⋊C4C2×D89semidirect
176. #379C2×D89semidirect
189. C25D356semidirect
198. C23×C4C22×D89semidirect
206. C2×C22⋊C4C22×D89semidirect
231. C24C2×D356semidirect
243. C22×C4C23×D89semidirect
269. C23#15667982semidirect
296. C22C2×#15667982semidirect
304. C2#26028530direct (N × H)

Maximal subgroups

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

subgroupindex
C26×D892
C22×#156679822
C22×#156679812
#260285302
C2×#191514532
C2×#379×C892
C2×#284689