Finite Group Databasebeta

← #2846×D89 #36760251

Subgroups — #2846×D89 #36760251

Order 22784.

32890 conjugacy classes of subgroups; only the 1123 normal subgroups are shown.

normal subgroups only

This group has 32890 conjugacy classes of subgroups — too many to draw. Only its 1123 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
2C2×#120×D89C217yesmaximal, complemented
3#26028530C217yesmaximal, complemented
4#26028529C211yesmaximal, characteristic, complemented
5#26028528C217yesmaximal, complemented
6#379×D89C217yesmaximal, complemented
7C89×#2846C211yesmaximal, characteristic, complemented
8C25×D89—256no—
9C25×D89C2217yes—
10C25×D89C2217yescomplemented
11C22×D4×D89C2217yescomplemented
12C2×#15667982C22121yescomplemented
13C2×#15667981C2217yescomplemented
14C2×#15667980C22121yescomplemented
15#120×D89—256no—
16C2×C22⋊C4×D89C22121yescomplemented
17#19151454C2217yescomplemented
18#19151453C22142yescomplemented
19C26×C89C2211yescharacteristic, complemented
20C2×#120×C89C2217yescomplemented
21#379×C89C2217yescomplemented
22C24×D89—2896no—
23C24×D89—2168no—
24C24×D89—2168no—
25C24×D89—228no—
26C24×D89D4156yescomplemented
27C24×D89C23121yes—
28C24×D89C2317yes—
29C24×D89C2311yescharacteristic, complemented
30C22×D356C2317yescomplemented
31C22×C22⋊D89C2317yescomplemented
32C22×C22⋊D89C2317yescomplemented
33C2×D4×D89—284no—
34C22×C4×D89C2317yescomplemented
35#15667982—284no—
36#15667981—228no—
37#15667980—284no—
38C2×C22⋊Dic89C23121yescomplemented
39C2×#13083551C23142yescomplemented
40C22⋊C4×D89—284no—
41C25×C89—228no—
42C25×C89C2317yes—
43C22×D4×C89C2317yescomplemented
44#120×C89—228no—
45C2×C22⋊C4×C89C23121yescomplemented
46C23×D89—22048no—
47C23×D89—2672no—
48C23×D89—2896no—
49C23×D89—2896no—
50C23×D89—284no—
51C23×D89—2672no—
52C23×D89—2168no—
53C23×D89—256no—
54C23×D89—214no—
55C23×D89C2×D4184yes—
56C23×D89C2×D4184yescomplemented
57C23×D89C2417yes—
58C23×D89C2411yescharacteristic
59C23×D89C2411yescharacteristic, complemented
60C2×D356—242no—
61C2×C22⋊D89—242no—
62C2×C22⋊D89—242no—
63D4×D89—4112no—
64C22×Dic89C2417yescomplemented
65C2×C4×D89—242no—
66C22⋊Dic89—242no—
67#13083551—284no—
68C24×C89—2224no—
69C24×C89—284no—
70C24×C89C2×D4128yescomplemented
71C24×C89C2417yes—
72C24×C89C2411yescharacteristic, complemented
73C2×D4×C89—242no—
74C22×C4×C89C2417yescomplemented
75C22⋊C4×C89—242no—
76C23×C89—2256no—
77C23×C89—2224no—
78C23×C89—2168no—
79C23×C89—228no—
80C23×C89—27no—
81C23×C89C22×D4142yes—
82C23×C89C2511yescharacteristic
83C22×D89—21792no—
84C22×D89—2672no—
85C22×D89—21792no—
86C22×D89—2168no—
87C22×D89—228no—
88C22×D89—2336no—
89C22×D89—2336no—
90C22×D89—27no—
91C22×D89—428no—
92C22×D89#1201112yescomplemented
93C22×D89C22×D4142yes—
94C22×D89C22×D4114yes—
95D4×C89—428no—
96C2×C4×C89—221no—
97C22⋊D89—428no—
98C22⋊D89—428no—
99C2×Dic89—221no—
100D356—428no—
101C4×D89—428no—
102C22×C89—2224no—
103C22×C89—284no—
104C22×C89—47no—
105C22×C89C2×#120128yescomplemented
106C22×C89C23×D417yes—
107C2×D89—2672no—
108C2×D89—284no—
109C2×D89—2224no—
110C2×D89—47no—
111C2×D89—88no—
112C2×D89C2×#120128yes—
113C2×D89C2×#120128yescomplemented
114C4×C89—47no—
115Dic89—47no—
116C2×#2846—891nomaximal, Sylow
117C2×C89—228no—
118C2×C89—81no—
119C2×C89C22×#12017yes—
120D89—228no—
121D89—81no—
122D89#284618yesdirect product factor
123C27—891no—
124C22×#120—897no—
125#2846—897no—
126#2846—891no—
127#2846—897no—
128#2846D8911yescharacteristic, direct product factor
129C2×#379—897no—
130C89C2×#284611yescharacteristic, complemented, Sylow
131C26—897no—
132C26—897no—
133C26—17856no—
134C26C2×D8911yescharacteristic, complemented
135C23×D4—897no—
136C2×#120—897no—
137C2×#120—8921no—
138C2×#120—8921no—
139C2×#120—17856no—
140C2×#120C2×D8917yescomplemented
141C22×C22⋊C4—8921no—
142#379—897no—
143#379—8942no—
144#379C2×D8917yescomplemented
145C25—228no—
146C25—897no—
147C25—8956no—
148C25—8921no—
149C25—891no—
150C25—178168no—
151C25—178168no—
152C25—178896no—
153C25—17828no—
154C25C22×D8917yes—
155C22×D4—897no—
156C22×D4—897no—
157C22×D4—897no—
158C22×D4—17884no—
159C22×D4C22×D8917yescomplemented
160C23×C4—897no—
161#120—228no—
162#120—17884no—
163#120—17884no—
164#120—17828no—
165C2×C22⋊C4—8921no—
166C2×C22⋊C4—8942no—
167C2×C22⋊C4—17884no—
168C2×C22⋊C4C22×D89121yescomplemented
169C24—2224no—
170C24—284no—
171C24—891no—
172C24—8984no—
173C24—897no—
174C24—8984no—
175C24—891no—
176C24—17814no—
177C24—17856no—
178C24—178168no—
179C24—178672no—
180C24—178896no—
181C24—178896no—
182C24—1782048no—
183C24—178672no—
184C24—17884no—
185C24D4×D89128yescomplemented
186C24C23×D8917yes—
187C24C23×D8911yescharacteristic, complemented
188C2×D4—242no—
189C2×D4—356112no—
190C2×D4—17842no—
191C2×D4—17842no—
192C2×D4—17842no—
193C22×C4—897no—
194C22×C4—17842no—
195C22×C4C23×D8917yescomplemented
196C22⋊C4—242no—
197C22⋊C4—17884no—
198C22⋊C4—17842no—
199C23—2256no—
200C23—2224no—
201C23—228no—
202C23—2168no—
203C23—27no—
204C23—8914no—
205C23—8942no—
206C23—89112no—
207C23—35628no—
208C23—178336no—
209C23—178336no—
210C23—1781792no—
211C23—1781792no—
212C23—178672no—
213C23—1787no—
214C23—17828no—
215C23—178168no—
216C23C2×D4×D89142yes—
217C23C24×D8911yescharacteristic
218D4—428no—
219D4—35628no—
220D4—35628no—
221D4—35628no—
222C2×C4—221no—
223C2×C4—35628no—
224C2×C4—17821no—
225C22—2224no—
226C22—284no—
227C22—47no—
228C22—8928no—
229C22—8928no—
230C22—3567no—
231C22—178224no—
232C22—178672no—
233C22—17884no—
234C22—7128no—
235C22#120×D89128yescomplemented
236C22C22×D4×D8917yes—
237C4—47no—
238C4—3567no—
239C2—228no—
240C2—81no—
241C2—898no—
242C2—17828no—
243C2—7121no—
244C2C2×#120×D8917yes—
subgroupG/H
center, FrattiniC23C24×D89
commutator, socle, cosocleC23×C89C25
FittingC89×#2846C2
hypercenter#2846D89
hypocenterC89C2×#2846
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2846

Complements

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

NH ≅ G/Ntype
1. C26×D89C2semidirect
2. C2×#120×D89C2semidirect
3. #26028530C2semidirect
4. #26028529C2semidirect
5. #26028528C2semidirect
6. #379×D89C2semidirect
7. C89×#2846C2semidirect
10. C25×D89C22semidirect
11. C22×D4×D89C22semidirect
12. C2×#15667982C22semidirect
13. C2×#15667981C22semidirect
14. C2×#15667980C22semidirect
16. C2×C22⋊C4×D89C22semidirect
17. #19151454C22semidirect
18. #19151453C22semidirect
19. C26×C89C22semidirect
20. C2×#120×C89C22semidirect
21. #379×C89C22semidirect
26. C24×D89D4semidirect
29. C24×D89C23semidirect
30. C22×D356C23semidirect
31. C22×C22⋊D89C23semidirect
32. C22×C22⋊D89C23semidirect
34. C22×C4×D89C23semidirect
38. C2×C22⋊Dic89C23semidirect
39. C2×#13083551C23semidirect
43. C22×D4×C89C23semidirect
45. C2×C22⋊C4×C89C23semidirect
56. C23×D89C2×D4semidirect
59. C23×D89C24semidirect
64. C22×Dic89C24semidirect
70. C24×C89C2×D4semidirect
72. C24×C89C24semidirect
74. C22×C4×C89C24semidirect
92. C22×D89#120semidirect
105. C22×C89C2×#120semidirect
113. C2×D89C2×#120semidirect
122. D89#2846direct (N × H)
128. #2846D89direct (N × H)
130. C89C2×#2846semidirect
134. C26C2×D89semidirect
140. C2×#120C2×D89semidirect
144. #379C2×D89semidirect
159. C22×D4C22×D89semidirect
168. C2×C22⋊C4C22×D89semidirect
185. C24D4×D89semidirect
187. C24C23×D89semidirect
195. C22×C4C23×D89semidirect
235. C22#120×D89semidirect

Maximal subgroups

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

subgroupindex
C26×D892
C2×#120×D892
#260285302
#260285292
#260285282
#379×D892
C89×#28462
C2×#284689