Finite Group Databasebeta

← #2846×D83 #35610227

Subgroups — #2846×D83 #35610227

Order 21248.

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×D83C211yesmaximal, characteristic, complemented
2C2×#120×D83C217yesmaximal, complemented
3#24915741C217yesmaximal, complemented
4#24915740C211yesmaximal, characteristic, complemented
5#24915739C217yesmaximal, complemented
6#379×D83C217yesmaximal, complemented
7C83×#2846C211yesmaximal, characteristic, complemented
8C25×D83—256no—
9C25×D83C2217yes—
10C25×D83C2217yescomplemented
11C22×D4×D83C2217yescomplemented
12C2×#14581762C22121yescomplemented
13C2×#14581761C2217yescomplemented
14C2×#14581760C22121yescomplemented
15#120×D83—256no—
16C2×C22⋊C4×D83C22121yescomplemented
17#19127557C2217yescomplemented
18#19127556C22142yescomplemented
19C26×C83C2211yescharacteristic, complemented
20C2×#120×C83C2217yescomplemented
21#379×C83C2217yescomplemented
22C24×D83—2896no—
23C24×D83—2168no—
24C24×D83—2168no—
25C24×D83—228no—
26C24×D83D4156yescomplemented
27C24×D83C23121yes—
28C24×D83C2317yes—
29C24×D83C2311yescharacteristic, complemented
30C22×D332C2317yescomplemented
31C22×C22⋊D83C2317yescomplemented
32C22×C22⋊D83C2317yescomplemented
33C2×D4×D83—284no—
34C22×C4×D83C2317yescomplemented
35#14581762—284no—
36#14581761—228no—
37#14581760—284no—
38C2×C22⋊Dic83C23121yescomplemented
39C2×(C2×D83)⋊C4C23142yescomplemented
40C22⋊C4×D83—284no—
41C25×C83—228no—
42C25×C83C2317yes—
43C22×D4×C83C2317yescomplemented
44#120×C83—228no—
45C2×C22⋊C4×C83C23121yescomplemented
46C23×D83—22048no—
47C23×D83—2672no—
48C23×D83—2896no—
49C23×D83—2896no—
50C23×D83—284no—
51C23×D83—2672no—
52C23×D83—2168no—
53C23×D83—256no—
54C23×D83—214no—
55C23×D83C2×D4184yes—
56C23×D83C2×D4184yescomplemented
57C23×D83C2417yes—
58C23×D83C2411yescharacteristic
59C23×D83C2411yescharacteristic, complemented
60C2×D332—242no—
61C2×C22⋊D83—242no—
62C2×C22⋊D83—242no—
63D4×D83—4112no—
64C22×Dic83C2417yescomplemented
65C2×C4×D83—242no—
66C22⋊Dic83—242no—
67(C2×D83)⋊C4—284no—
68C24×C83—2224no—
69C24×C83—284no—
70C24×C83C2×D4128yescomplemented
71C24×C83C2417yes—
72C24×C83C2411yescharacteristic, complemented
73C2×D4×C83—242no—
74C22×C4×C83C2417yescomplemented
75C22⋊C4×C83—242no—
76C23×C83—2256no—
77C23×C83—2224no—
78C23×C83—2168no—
79C23×C83—228no—
80C23×C83—27no—
81C23×C83C22×D4142yes—
82C23×C83C2511yescharacteristic
83C22×D83—21792no—
84C22×D83—2672no—
85C22×D83—21792no—
86C22×D83—2168no—
87C22×D83—228no—
88C22×D83—2336no—
89C22×D83—2336no—
90C22×D83—27no—
91C22×D83—428no—
92C22×D83#1201112yescomplemented
93C22×D83C22×D4142yes—
94C22×D83C22×D4114yes—
95D4×C83—428no—
96C2×C4×C83—221no—
97C22⋊D83—428no—
98C22⋊D83—428no—
99C2×Dic83—221no—
100D332—428no—
101C4×D83—428no—
102C22×C83—2224no—
103C22×C83—284no—
104C22×C83—47no—
105C22×C83C2×#120128yescomplemented
106C22×C83C23×D417yes—
107C2×D83—2672no—
108C2×D83—284no—
109C2×D83—2224no—
110C2×D83—47no—
111C2×D83—88no—
112C2×D83C2×#120128yes—
113C2×D83C2×#120128yescomplemented
114C4×C83—47no—
115Dic83—47no—
116C2×#2846—831nomaximal, Sylow
117C2×C83—228no—
118C2×C83—81no—
119C2×C83C22×#12017yes—
120D83—228no—
121D83—81no—
122D83#284618yesdirect product factor
123C27—831no—
124C22×#120—837no—
125#2846—837no—
126#2846—831no—
127#2846—837no—
128#2846D8311yescharacteristic, direct product factor
129C2×#379—837no—
130C83C2×#284611yescharacteristic, complemented, Sylow
131C26—837no—
132C26—837no—
133C26—16656no—
134C26C2×D8311yescharacteristic, complemented
135C23×D4—837no—
136C2×#120—837no—
137C2×#120—8321no—
138C2×#120—8321no—
139C2×#120—16656no—
140C2×#120C2×D8317yescomplemented
141C22×C22⋊C4—8321no—
142#379—837no—
143#379—8342no—
144#379C2×D8317yescomplemented
145C25—228no—
146C25—837no—
147C25—8356no—
148C25—8321no—
149C25—831no—
150C25—166168no—
151C25—166168no—
152C25—166896no—
153C25—16628no—
154C25C22×D8317yes—
155C22×D4—837no—
156C22×D4—837no—
157C22×D4—837no—
158C22×D4—16684no—
159C22×D4C22×D8317yescomplemented
160C23×C4—837no—
161#120—228no—
162#120—16684no—
163#120—16684no—
164#120—16628no—
165C2×C22⋊C4—8321no—
166C2×C22⋊C4—8342no—
167C2×C22⋊C4—16684no—
168C2×C22⋊C4C22×D83121yescomplemented
169C24—2224no—
170C24—284no—
171C24—831no—
172C24—8384no—
173C24—837no—
174C24—8384no—
175C24—831no—
176C24—16614no—
177C24—166672no—
178C24—16656no—
179C24—166168no—
180C24—166896no—
181C24—166896no—
182C24—1662048no—
183C24—166672no—
184C24—16684no—
185C24D4×D83128yescomplemented
186C24C23×D8317yes—
187C24C23×D8311yescharacteristic, complemented
188C2×D4—242no—
189C2×D4—332112no—
190C2×D4—16642no—
191C2×D4—16642no—
192C2×D4—16642no—
193C22×C4—837no—
194C22×C4—16642no—
195C22×C4C23×D8317yescomplemented
196C22⋊C4—242no—
197C22⋊C4—16684no—
198C22⋊C4—16642no—
199C23—2256no—
200C23—2224no—
201C23—2168no—
202C23—228no—
203C23—27no—
204C23—33228no—
205C23—8314no—
206C23—83112no—
207C23—8342no—
208C23—166336no—
209C23—166336no—
210C23—1661792no—
211C23—1661792no—
212C23—166672no—
213C23—1667no—
214C23—166168no—
215C23—16628no—
216C23C2×D4×D83142yes—
217C23C24×D8311yescharacteristic
218D4—428no—
219D4—33228no—
220D4—33228no—
221D4—33228no—
222C2×C4—221no—
223C2×C4—33228no—
224C2×C4—16621no—
225C22—2224no—
226C22—284no—
227C22—47no—
228C22—3327no—
229C22—8328no—
230C22—8328no—
231C22—6648no—
232C22—166224no—
233C22—166672no—
234C22—16684no—
235C22#120×D83128yescomplemented
236C22C22×D4×D8317yes—
237C4—47no—
238C4—3327no—
239C2—228no—
240C2—81no—
241C2—838no—
242C2—6641no—
243C2—16628no—
244C2C2×#120×D8317yes—
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2846C2
hypercenter#2846D83
hypocenterC83C2×#2846
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2846

Complements

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

NH ≅ G/Ntype
1. C26×D83C2semidirect
2. C2×#120×D83C2semidirect
3. #24915741C2semidirect
4. #24915740C2semidirect
5. #24915739C2semidirect
6. #379×D83C2semidirect
7. C83×#2846C2semidirect
10. C25×D83C22semidirect
11. C22×D4×D83C22semidirect
12. C2×#14581762C22semidirect
13. C2×#14581761C22semidirect
14. C2×#14581760C22semidirect
16. C2×C22⋊C4×D83C22semidirect
17. #19127557C22semidirect
18. #19127556C22semidirect
19. C26×C83C22semidirect
20. C2×#120×C83C22semidirect
21. #379×C83C22semidirect
26. C24×D83D4semidirect
29. C24×D83C23semidirect
30. C22×D332C23semidirect
31. C22×C22⋊D83C23semidirect
32. C22×C22⋊D83C23semidirect
34. C22×C4×D83C23semidirect
38. C2×C22⋊Dic83C23semidirect
39. C2×(C2×D83)⋊C4C23semidirect
43. C22×D4×C83C23semidirect
45. C2×C22⋊C4×C83C23semidirect
56. C23×D83C2×D4semidirect
59. C23×D83C24semidirect
64. C22×Dic83C24semidirect
70. C24×C83C2×D4semidirect
72. C24×C83C24semidirect
74. C22×C4×C83C24semidirect
92. C22×D83#120semidirect
105. C22×C83C2×#120semidirect
113. C2×D83C2×#120semidirect
122. D83#2846direct (N × H)
128. #2846D83direct (N × H)
130. C83C2×#2846semidirect
134. C26C2×D83semidirect
140. C2×#120C2×D83semidirect
144. #379C2×D83semidirect
159. C22×D4C22×D83semidirect
168. C2×C22⋊C4C22×D83semidirect
185. C24D4×D83semidirect
187. C24C23×D83semidirect
195. C22×C4C23×D83semidirect
235. C22#120×D83semidirect

Maximal subgroups

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

subgroupindex
C26×D832
C2×#120×D832
#249157412
#249157402
#249157392
#379×D832
C83×#28462
C2×#284683