Finite Group Databasebeta

← C2×C89×#2873 #36437902

Subgroups — C2×C89×#2873 #36437902

Order 22784.

3342 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×M16×C89C212yesmaximal
2C22×#117×C89C211yesmaximal, characteristic
3C89×#2873C2116yesmaximal, direct product factor
4C2×#405×C89C218yesmaximal, complemented
5C2×C4×M16×C89C214yesmaximal, complemented
6C24×C4×C89C2211yescharacteristic
7C22×M16×C89C4132yescomplemented
8C22×M16×C89C2214yes—
9C22×M16×C89C2214yes—
10C22×M16×C89C22116yes—
11C23×C8×C89C2214yes—
12C2×#117×C89C414yes—
13C2×#117×C89C418yes—
14C2×#117×C89C2214yes—
15C2×#117×C89C2218yes—
16C22×C4⋊C4×C89C412yes—
17C22×C22⋊C4×C89C412yes—
18C22×C42×C89C2212yes—
19#405×C89C22164yescomplemented
20C4×M16×C89C22132yescomplemented
21C2×#97×C89C2218yescomplemented
22C2×C4×C8×C89C2218yescomplemented
23C25×C89C2×C411yescharacteristic
24C23×C4×C89C2×C414yes—
25C23×C4×C89C2×C411yescharacteristic
26C23×C4×C89C2×C412yes—
27C23×C4×C89C2×C414yes—
28C23×C4×C89C2×C4116yes—
29C23×C4×C89C2314yes—
30C23×C4×C89C2311yescharacteristic
31C23×C4×C89C2312yes—
32C2×M16×C89C2×C4132yes—
33C2×M16×C89C2×C4132yescomplemented
34C2×M16×C89C2×C41128yescomplemented
35C2×M16×C89C23116yes—
36C2×M16×C89C23116yes—
37C22×C8×C89C2×C4132yescomplemented
38C22×C8×C89C2318yes—
39C22×C8×C89C23116yes—
40#117×C89C2×C4116yes—
41#117×C89C2×C4132yes—
42#117×C89C23116yes—
43C2×C4⋊C4×C89C2×C418yes—
44C2×C4⋊C4×C89C2×C4116yes—
45C2×C22⋊C4×C89C2×C418yes—
46C2×C22⋊C4×C89C2×C4116yes—
47C2×C42×C89C2×C414yes—
48C2×C42×C89C2×C418yes—
49C2×C42×C89C2318yes—
50C2×C42×C89C2314yes—
51#97×C89C23132yescomplemented
52C4×C8×C89C23132yescomplemented
53C24×C89—44no—
54C24×C89C4218yes—
55C24×C89C22×C412yes—
56C24×C89C22×C411yescharacteristic
57C24×C89C22×C414yes—
58C22×C4×C89—48no—
59C22×C4×C89C4218yes—
60C22×C4×C89C42116yes—
61C22×C4×C89C42132yes—
62C22×C4×C89C22×C418yes—
63C22×C4×C89C22×C4116yes—
64C22×C4×C89C22×C411yescharacteristic
65C22×C4×C89C22×C412yes—
66C22×C4×C89C22×C414yes—
67C22×C4×C89C22×C412yes—
68C22×C4×C89C22×C418yes—
69C22×C4×C89C22×C414yes—
70C22×C4×C89C22×C418yes—
71C22×C4×C89C22×C418yes—
72C22×C4×C89C22×C418yes—
73C22×C4×C89C22×C4132yes—
74C22×C4×C89C2412yes—
75C22×C4×C89C2414yes—
76C22×C4×C89C2411yescharacteristic
77M16×C89C22×C4164yes—
78M16×C89C22×C4164yescomplemented
79C2×C8×C89C22×C4132yes—
80C2×C8×C89C22×C4164yescomplemented
81C2×C8×C89C24116yes—
82C4⋊C4×C89C22×C4132yes—
83C22⋊C4×C89C22×C4132yes—
84C42×C89C22×C4116yes—
85C42×C89C22×C418yes—
86C42×C89C2418yes—
87C23×C89—24no—
88C23×C89—28no—
89C23×C89—416no—
90C23×C89—48no—
91C23×C89C2×C4218yes—
92C23×C89C2×C4214yes—
93C23×C89C2×C42116yes—
94C23×C89C23×C414yes—
95C23×C89C23×C412yes—
96C23×C89C23×C411yescharacteristic
97C2×C4×C89—216no—
98C2×C4×C89—416no—
99C2×C4×C89C2×C4218yes—
100C2×C4×C89C2×C42116yes—
101C2×C4×C89C2×C42116yes—
102C2×C4×C89C2×C42132yes—
103C2×C4×C89C2×C4214yes—
104C2×C4×C89C2×C4218yes—
105C2×C4×C89C23×C4116yes—
106C2×C4×C89C23×C414yes—
107C2×C4×C89C23×C418yes—
108C2×C4×C89C23×C418yes—
109C2×C4×C89C23×C418yes—
110C2×C4×C89C23×C412yes—
111C2×C4×C89C23×C411yescharacteristic
112C2×C4×C89C23×C414yes—
113C2×C4×C89C2511yescharacteristic
114C8×C89C23×C4132yes—
115C22×C89—28no—
116C22×C89—216no—
117C22×C89—24no—
118C22×C89—28no—
119C22×C89—416no—
120C22×C89C22×C4218yes—
121C22×C89C22×C4214yes—
122C22×C89C22×C4212yes—
123C22×C89#56814yes—
124C22×C89C24×C411yescharacteristic
125C4×C89—216no—
126C4×C89C22×C4212yes—
127C4×C89C22×C4218yes—
128C4×C89C22×C4214yes—
129C4×C89C24×C412yes—
130C2×#2873C8911yesmaximal, characteristic, direct product factor, Sylow
131C2×C89—24no—
132C2×C89—28no—
133C2×C89#287314yesdirect product factor
134C2×C89C23×C4211yescharacteristic
135C2×C89C2×#56812yes—
136C23×M16C2×C8912yes—
137C22×#117C2×C8911yescharacteristic
138#2873C2×C89116yesdirect product factor
139C2×#405C2×C8918yescomplemented
140C2×C4×M16C2×C8914yescomplemented
141C89C2×#287311yescharacteristic, direct product factor, Sylow
142C24×C4C22×C8911yescharacteristic
143C22×M16C4×C89132yescomplemented
144C22×M16C22×C8914yes—
145C22×M16C22×C8914yes—
146C22×M16C22×C89116yes—
147C23×C8C22×C8914yes—
148C2×#117C4×C8914yes—
149C2×#117C4×C8918yes—
150C2×#117C22×C8914yes—
151C2×#117C22×C8918yes—
152C22×C4⋊C4C4×C8912yes—
153C22×C22⋊C4C4×C8912yes—
154C22×C42C22×C8912yes—
155#405C22×C89164yescomplemented
156C4×M16C22×C89132yescomplemented
157C2×#97C22×C8918yescomplemented
158C2×C4×C8C22×C8918yescomplemented
159C25C2×C4×C8911yescharacteristic
160C23×C4C2×C4×C8914yes—
161C23×C4C2×C4×C8911yescharacteristic
162C23×C4C2×C4×C8912yes—
163C23×C4C2×C4×C8914yes—
164C23×C4C2×C4×C89116yes—
165C23×C4C23×C8912yes—
166C23×C4C23×C8914yes—
167C23×C4C23×C8911yescharacteristic
168C2×M16C2×C4×C89132yes—
169C2×M16C2×C4×C89132yescomplemented
170C2×M16C2×C4×C891128yescomplemented
171C2×M16C23×C89116yes—
172C2×M16C23×C89116yes—
173C22×C8C2×C4×C89132yescomplemented
174C22×C8C23×C8918yes—
175C22×C8C23×C89116yes—
176#117C2×C4×C89116yes—
177#117C2×C4×C89132yes—
178#117C23×C89116yes—
179C2×C4⋊C4C2×C4×C8918yes—
180C2×C4⋊C4C2×C4×C89116yes—
181C2×C22⋊C4C2×C4×C8918yes—
182C2×C22⋊C4C2×C4×C89116yes—
183C2×C42C2×C4×C8914yes—
184C2×C42C2×C4×C8918yes—
185C2×C42C23×C8914yes—
186C2×C42C23×C8918yes—
187#97C23×C89132yescomplemented
188C4×C8C23×C89132yescomplemented
189C24—44no—
190C24C42×C8918yes—
191C24C22×C4×C8912yes—
192C24C22×C4×C8911yescharacteristic
193C24C22×C4×C8914yes—
194C22×C4—48no—
195C22×C4C42×C8918yes—
196C22×C4C42×C89116yes—
197C22×C4C42×C89132yes—
198C22×C4C22×C4×C8918yes—
199C22×C4C22×C4×C89116yes—
200C22×C4C22×C4×C8912yes—
201C22×C4C22×C4×C8911yescharacteristic
202C22×C4C22×C4×C8914yes—
203C22×C4C22×C4×C8912yes—
204C22×C4C22×C4×C8914yes—
205C22×C4C22×C4×C8918yes—
206C22×C4C22×C4×C8918yes—
207C22×C4C22×C4×C8918yes—
208C22×C4C22×C4×C8918yes—
209C22×C4C22×C4×C89132yes—
210C22×C4C24×C8911yescharacteristic
211C22×C4C24×C8912yes—
212C22×C4C24×C8914yes—
213M16C22×C4×C89164yes—
214M16C22×C4×C89164yescomplemented
215C2×C8C22×C4×C89132yes—
216C2×C8C22×C4×C89164yescomplemented
217C2×C8C24×C89116yes—
218C4⋊C4C22×C4×C89132yes—
219C22⋊C4C22×C4×C89132yes—
220C42C22×C4×C8918yes—
221C42C22×C4×C89116yes—
222C42C24×C8918yes—
223C23—24no—
224C23—28no—
225C23—416no—
226C23—48no—
227C23C2×C42×C8918yes—
228C23C2×C42×C8914yes—
229C23C2×C42×C89116yes—
230C23C23×C4×C8914yes—
231C23C23×C4×C8912yes—
232C23C23×C4×C8911yescharacteristic
233C2×C4—216no—
234C2×C4—416no—
235C2×C4C2×C42×C8918yes—
236C2×C4C2×C42×C89116yes—
237C2×C4C2×C42×C89116yes—
238C2×C4C2×C42×C89132yes—
239C2×C4C2×C42×C8914yes—
240C2×C4C2×C42×C8918yes—
241C2×C4C23×C4×C89116yes—
242C2×C4C23×C4×C8912yes—
243C2×C4C23×C4×C8911yescharacteristic
244C2×C4C23×C4×C8914yes—
245C2×C4C23×C4×C8914yes—
246C2×C4C23×C4×C8918yes—
247C2×C4C23×C4×C8918yes—
248C2×C4C23×C4×C8918yes—
249C2×C4C25×C8911yescharacteristic
250C8C23×C4×C89132yes—
251C22—28no—
252C22—216no—
253C22—24no—
254C22—28no—
255C22—416no—
256C22C22×C42×C8918yes—
257C22C22×C42×C8914yes—
258C22C22×C42×C8912yes—
259C22#568×C8914yes—
260C22C24×C4×C8911yescharacteristic
261C4—216no—
262C4C22×C42×C8912yes—
263C4C22×C42×C8914yes—
264C4C22×C42×C8918yes—
265C4C24×C4×C8912yes—
266C2—24no—
267C2—28no—
268C2C89×#287314yesdirect product factor
269C2C23×C42×C8911yescharacteristic
270C2C2×#568×C8912yes—
subgroupG/H
centerC22×C4×C89C24
commutatorC2C23×C42×C89
Frattini, cosocleC2×C4C25×C89
socleC23×C89C23×C4
prime radicalC25×C89C2×C4
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C89 ◁ G

Complements

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

NH ≅ G/Ntype
3. C89×#2873C2direct (N × H)
4. C2×#405×C89C2semidirect
5. C2×C4×M16×C89C2semidirect
7. C22×M16×C89C4semidirect
19. #405×C89C22semidirect
20. C4×M16×C89C22semidirect
21. C2×#97×C89C22semidirect
22. C2×C4×C8×C89C22semidirect
33. C2×M16×C89C2×C4semidirect
34. C2×M16×C89C2×C4semidirect
37. C22×C8×C89C2×C4semidirect
51. #97×C89C23semidirect
52. C4×C8×C89C23semidirect
78. M16×C89C22×C4semidirect
80. C2×C8×C89C22×C4semidirect
130. C2×#2873C89direct (N × H)
133. C2×C89#2873direct (N × H)
138. #2873C2×C89direct (N × H)
139. C2×#405C2×C89semidirect
140. C2×C4×M16C2×C89semidirect
141. C89C2×#2873direct (N × H)
143. C22×M16C4×C89semidirect
155. #405C22×C89semidirect
156. C4×M16C22×C89semidirect
157. C2×#97C22×C89semidirect
158. C2×C4×C8C22×C89semidirect
169. C2×M16C2×C4×C89semidirect
170. C2×M16C2×C4×C89semidirect
173. C22×C8C2×C4×C89semidirect
187. #97C23×C89semidirect
188. C4×C8C23×C89semidirect
214. M16C22×C4×C89semidirect
216. C2×C8C22×C4×C89semidirect
268. C2C89×#2873direct (N × H)

Maximal subgroups

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

subgroupindex
C23×M16×C892
C22×#117×C892
C89×#28732
C2×#405×C892
C2×C4×M16×C892
C2×#287389