Finite Group Databasebeta

← C2×C23×#2873 #19207680

Subgroups — C2×C23×#2873 #19207680

Order 5888.

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×C23C212yesmaximal
2C22×C23×#117C211yesmaximal, characteristic
3C23×#2873C2116yesmaximal, direct product factor
4C2×C23×#405C218yesmaximal, complemented
5C2×C4×M16×C23C214yesmaximal, complemented
6C24×C4×C23C2211yescharacteristic
7C22×M16×C23C4132yescomplemented
8C22×M16×C23C2214yes—
9C22×M16×C23C2214yes—
10C22×M16×C23C22116yes—
11C23×C8×C23C2214yes—
12C2×C23×#117C414yes—
13C2×C23×#117C418yes—
14C2×C23×#117C2214yes—
15C2×C23×#117C2218yes—
16C22×C4⋊C4×C23C412yes—
17C22×C22⋊C4×C23C412yes—
18C22×C42×C23C2212yes—
19C23×#405C22164yescomplemented
20C4×M16×C23C22132yescomplemented
21C2×C23×#97C2218yescomplemented
22C2×C4×C8×C23C2218yescomplemented
23C25×C23C2×C411yescharacteristic
24C23×C4×C23C2×C414yes—
25C23×C4×C23C2×C411yescharacteristic
26C23×C4×C23C2×C412yes—
27C23×C4×C23C2×C414yes—
28C23×C4×C23C2×C4116yes—
29C23×C4×C23C2314yes—
30C23×C4×C23C2312yes—
31C23×C4×C23C2311yescharacteristic
32C2×M16×C23C2×C4132yes—
33C2×M16×C23C2×C4132yescomplemented
34C2×M16×C23C2×C41128yescomplemented
35C2×M16×C23C23116yes—
36C2×M16×C23C23116yes—
37C22×C8×C23C2×C4132yescomplemented
38C22×C8×C23C2318yes—
39C22×C8×C23C23116yes—
40C23×#117C2×C4116yes—
41C23×#117C2×C4132yes—
42C23×#117C23116yes—
43C2×C4⋊C4×C23C2×C418yes—
44C2×C4⋊C4×C23C2×C4116yes—
45C2×C22⋊C4×C23C2×C418yes—
46C2×C22⋊C4×C23C2×C4116yes—
47C2×C42×C23C2×C414yes—
48C2×C42×C23C2×C418yes—
49C2×C42×C23C2318yes—
50C2×C42×C23C2314yes—
51C23×#97C23132yescomplemented
52C4×C8×C23C23132yescomplemented
53C24×C23—44no—
54C24×C23C4218yes—
55C24×C23C22×C412yes—
56C24×C23C22×C411yescharacteristic
57C24×C23C22×C414yes—
58C22×C4×C23—48no—
59C22×C4×C23C4218yes—
60C22×C4×C23C42116yes—
61C22×C4×C23C42132yes—
62C22×C4×C23C22×C418yes—
63C22×C4×C23C22×C4116yes—
64C22×C4×C23C22×C411yescharacteristic
65C22×C4×C23C22×C412yes—
66C22×C4×C23C22×C414yes—
67C22×C4×C23C22×C412yes—
68C22×C4×C23C22×C418yes—
69C22×C4×C23C22×C414yes—
70C22×C4×C23C22×C418yes—
71C22×C4×C23C22×C418yes—
72C22×C4×C23C22×C418yes—
73C22×C4×C23C22×C4132yes—
74C22×C4×C23C2412yes—
75C22×C4×C23C2414yes—
76C22×C4×C23C2411yescharacteristic
77M16×C23C22×C4164yes—
78M16×C23C22×C4164yescomplemented
79C2×C8×C23C22×C4132yes—
80C2×C8×C23C22×C4164yescomplemented
81C2×C8×C23C24116yes—
82C4⋊C4×C23C22×C4132yes—
83C22⋊C4×C23C22×C4132yes—
84C42×C23C22×C4116yes—
85C42×C23C22×C418yes—
86C42×C23C2418yes—
87C2×#2873C2311yesmaximal, characteristic, direct product factor, Sylow
88C23×C23—24no—
89C23×C23—28no—
90C23×C23—416no—
91C23×C23—48no—
92C23×C23C2×C4218yes—
93C23×C23C2×C4214yes—
94C23×C23C2×C42116yes—
95C23×C23C23×C414yes—
96C23×C23C23×C412yes—
97C23×C23C23×C411yescharacteristic
98C2×C4×C23—216no—
99C2×C4×C23—416no—
100C2×C4×C23C2×C4218yes—
101C2×C4×C23C2×C42116yes—
102C2×C4×C23C2×C42116yes—
103C2×C4×C23C2×C42132yes—
104C2×C4×C23C2×C4214yes—
105C2×C4×C23C2×C4218yes—
106C2×C4×C23C23×C4116yes—
107C2×C4×C23C23×C414yes—
108C2×C4×C23C23×C418yes—
109C2×C4×C23C23×C418yes—
110C2×C4×C23C23×C418yes—
111C2×C4×C23C23×C412yes—
112C2×C4×C23C23×C411yescharacteristic
113C2×C4×C23C23×C414yes—
114C2×C4×C23C2511yescharacteristic
115C8×C23C23×C4132yes—
116C23×M16C2×C2312yes—
117C22×#117C2×C2311yescharacteristic
118#2873C2×C23116yesdirect product factor
119C2×#405C2×C2318yescomplemented
120C2×C4×M16C2×C2314yescomplemented
121C22×C23—28no—
122C22×C23—216no—
123C22×C23—24no—
124C22×C23—28no—
125C22×C23—416no—
126C22×C23C22×C4218yes—
127C22×C23C22×C4214yes—
128C22×C23C22×C4212yes—
129C22×C23#56814yes—
130C22×C23C24×C411yescharacteristic
131C4×C23—216no—
132C4×C23C22×C4212yes—
133C4×C23C22×C4218yes—
134C4×C23C22×C4214yes—
135C4×C23C24×C412yes—
136C24×C4C22×C2311yescharacteristic
137C22×M16C4×C23132yescomplemented
138C22×M16C22×C2314yes—
139C22×M16C22×C2314yes—
140C22×M16C22×C23116yes—
141C23×C8C22×C2314yes—
142C2×#117C4×C2314yes—
143C2×#117C4×C2318yes—
144C2×#117C22×C2314yes—
145C2×#117C22×C2318yes—
146C22×C4⋊C4C4×C2312yes—
147C22×C22⋊C4C4×C2312yes—
148C22×C42C22×C2312yes—
149#405C22×C23164yescomplemented
150C4×M16C22×C23132yescomplemented
151C2×#97C22×C2318yescomplemented
152C2×C4×C8C22×C2318yescomplemented
153C2×C23—24no—
154C2×C23—28no—
155C2×C23#287314yesdirect product factor
156C2×C23C23×C4211yescharacteristic
157C2×C23C2×#56812yes—
158C25C2×C4×C2311yescharacteristic
159C23×C4C2×C4×C2314yes—
160C23×C4C2×C4×C2311yescharacteristic
161C23×C4C2×C4×C2312yes—
162C23×C4C2×C4×C2314yes—
163C23×C4C2×C4×C23116yes—
164C23×C4C23×C2312yes—
165C23×C4C23×C2314yes—
166C23×C4C23×C2311yescharacteristic
167C2×M16C2×C4×C23132yes—
168C2×M16C2×C4×C23132yescomplemented
169C2×M16C2×C4×C231128yescomplemented
170C2×M16C23×C23116yes—
171C2×M16C23×C23116yes—
172C22×C8C2×C4×C23132yescomplemented
173C22×C8C23×C2318yes—
174C22×C8C23×C23116yes—
175#117C2×C4×C23116yes—
176#117C2×C4×C23132yes—
177#117C23×C23116yes—
178C2×C4⋊C4C2×C4×C2318yes—
179C2×C4⋊C4C2×C4×C23116yes—
180C2×C22⋊C4C2×C4×C2318yes—
181C2×C22⋊C4C2×C4×C23116yes—
182C2×C42C2×C4×C2314yes—
183C2×C42C2×C4×C2318yes—
184C2×C42C23×C2314yes—
185C2×C42C23×C2318yes—
186#97C23×C23132yescomplemented
187C4×C8C23×C23132yescomplemented
188C23C2×#287311yescharacteristic, direct product factor, Sylow
189C24—44no—
190C24C42×C2318yes—
191C24C22×C4×C2312yes—
192C24C22×C4×C2311yescharacteristic
193C24C22×C4×C2314yes—
194C22×C4—48no—
195C22×C4C42×C2318yes—
196C22×C4C42×C23116yes—
197C22×C4C42×C23132yes—
198C22×C4C22×C4×C2318yes—
199C22×C4C22×C4×C23116yes—
200C22×C4C22×C4×C2312yes—
201C22×C4C22×C4×C2311yescharacteristic
202C22×C4C22×C4×C2314yes—
203C22×C4C22×C4×C2312yes—
204C22×C4C22×C4×C2314yes—
205C22×C4C22×C4×C2318yes—
206C22×C4C22×C4×C2318yes—
207C22×C4C22×C4×C2318yes—
208C22×C4C22×C4×C2318yes—
209C22×C4C22×C4×C23132yes—
210C22×C4C24×C2311yescharacteristic
211C22×C4C24×C2312yes—
212C22×C4C24×C2314yes—
213M16C22×C4×C23164yes—
214M16C22×C4×C23164yescomplemented
215C2×C8C22×C4×C23132yes—
216C2×C8C22×C4×C23164yescomplemented
217C2×C8C24×C23116yes—
218C4⋊C4C22×C4×C23132yes—
219C22⋊C4C22×C4×C23132yes—
220C42C22×C4×C2318yes—
221C42C22×C4×C23116yes—
222C42C24×C2318yes—
223C23—24no—
224C23—28no—
225C23—416no—
226C23—48no—
227C23C2×C42×C2318yes—
228C23C2×C42×C2314yes—
229C23C2×C42×C23116yes—
230C23C23×C4×C2314yes—
231C23C23×C4×C2312yes—
232C23C23×C4×C2311yescharacteristic
233C2×C4—216no—
234C2×C4—416no—
235C2×C4C2×C42×C2318yes—
236C2×C4C2×C42×C23116yes—
237C2×C4C2×C42×C23116yes—
238C2×C4C2×C42×C23132yes—
239C2×C4C2×C42×C2314yes—
240C2×C4C2×C42×C2318yes—
241C2×C4C23×C4×C23116yes—
242C2×C4C23×C4×C2314yes—
243C2×C4C23×C4×C2318yes—
244C2×C4C23×C4×C2318yes—
245C2×C4C23×C4×C2318yes—
246C2×C4C23×C4×C2311yescharacteristic
247C2×C4C23×C4×C2312yes—
248C2×C4C23×C4×C2314yes—
249C2×C4C25×C2311yescharacteristic
250C8C23×C4×C23132yes—
251C22—24no—
252C22—28no—
253C22—28no—
254C22—216no—
255C22—416no—
256C22C22×C42×C2318yes—
257C22C22×C42×C2314yes—
258C22C22×C42×C2312yes—
259C22C23×#56814yes—
260C22C24×C4×C2311yescharacteristic
261C4—216no—
262C4C22×C42×C2312yes—
263C4C22×C42×C2318yes—
264C4C22×C42×C2314yes—
265C4C24×C4×C2312yes—
266C2—24no—
267C2—28no—
268C2C23×#287314yesdirect product factor
269C2C23×C42×C2311yescharacteristic
270C2C2×C23×#56812yes—
subgroupG/H
centerC22×C4×C23C24
commutatorC2C23×C42×C23
Frattini, cosocleC2×C4C25×C23
socleC23×C23C23×C4
prime radicalC25×C23C2×C4
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
3. C23×#2873C2direct (N × H)
4. C2×C23×#405C2semidirect
5. C2×C4×M16×C23C2semidirect
7. C22×M16×C23C4semidirect
19. C23×#405C22semidirect
20. C4×M16×C23C22semidirect
21. C2×C23×#97C22semidirect
22. C2×C4×C8×C23C22semidirect
33. C2×M16×C23C2×C4semidirect
34. C2×M16×C23C2×C4semidirect
37. C22×C8×C23C2×C4semidirect
51. C23×#97C23semidirect
52. C4×C8×C23C23semidirect
78. M16×C23C22×C4semidirect
80. C2×C8×C23C22×C4semidirect
87. C2×#2873C23direct (N × H)
118. #2873C2×C23direct (N × H)
119. C2×#405C2×C23semidirect
120. C2×C4×M16C2×C23semidirect
137. C22×M16C4×C23semidirect
149. #405C22×C23semidirect
150. C4×M16C22×C23semidirect
151. C2×#97C22×C23semidirect
152. C2×C4×C8C22×C23semidirect
155. C2×C23#2873direct (N × H)
168. C2×M16C2×C4×C23semidirect
169. C2×M16C2×C4×C23semidirect
172. C22×C8C2×C4×C23semidirect
186. #97C23×C23semidirect
187. C4×C8C23×C23semidirect
188. C23C2×#2873direct (N × H)
214. M16C22×C4×C23semidirect
216. C2×C8C22×C4×C23semidirect
268. C2C23×#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×C232
C22×C23×#1172
C23×#28732
C2×C23×#4052
C2×C4×M16×C232
C2×#287323