Finite Group Databasebeta

← C22×C19×#460 #18066365

Subgroups — C22×C19×#460 #18066365

Order 4864.

3478 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×SD16×C19C212yesmaximal, complemented
2C22×C19×#127C211yesmaximal, characteristic
3C22×C4×Q8×C19C211yesmaximal, characteristic, complemented
4C2×C19×#460C2124yesmaximal, direct product factor
5C22×C19×C4⋊C8C211yesmaximal, characteristic, complemented
6C22×C19×#102C212yesmaximal, complemented
7C23×Q8×C19C2211yescharacteristic
8C23×D4×C19—21no—
9C23×D4×C19—21no—
10C23×D4×C19C2212yes—
11C22×SD16×C19—216no—
12C22×SD16×C19C22124yescomplemented
13C23×C8×C19C2212yes—
14C2×C19×#127—26no—
15C2×C19×#127C22112yes—
16C2×C4×Q8×C19—26no—
17C2×C4×Q8×C19C22112yescomplemented
18C22×C4⋊C4×C19—21no—
19C22×C4⋊C4×C19C2211yescharacteristic
20C22×C42×C19—21no—
21C22×C42×C19C2211yescharacteristic
22C19×#460C22164yesdirect product factor
23C2×C19×C4⋊C8C22112yescomplemented
24C2×C19×#102C22124yescomplemented
25C25×C19—22no—
26C22×Q8×C19—23no—
27C22×Q8×C19—24no—
28C22×Q8×C19D418yescomplemented
29C22×Q8×C19C2316yes—
30C22×D4×C19—28no—
31C22×D4×C19—26no—
32C22×D4×C19—212no—
33C22×D4×C19—212no—
34C22×D4×C19—28no—
35C22×D4×C19—48no—
36C22×D4×C19—48no—
37C22×D4×C19C23112yes—
38C23×C4×C19—21no—
39C23×C4×C19—21no—
40C23×C4×C19D411yescharacteristic
41C23×C4×C19D411yescharacteristic
42C23×C4×C19C2311yescharacteristic
43C2×SD16×C19—296no—
44C2×SD16×C19C23132yescomplemented
45C22×C8×C19—28no—
46C22×C8×C19C23112yes—
47C19×#127—224no—
48C19×#127C23116yes—
49C4×Q8×C19—224no—
50C4×Q8×C19C23116yescomplemented
51C2×C4⋊C4×C19—212no—
52C2×C4⋊C4×C19—23no—
53C2×C4⋊C4×C19C2316yes—
54C2×C42×C19—212no—
55C2×C42×C19D416yes—
56C2×C42×C19C2316yes—
57C19×C4⋊C8C23116yescomplemented
58C19×#102C23132yescomplemented
59C24×C19—212no—
60C24×C19—48no—
61C24×C19—48no—
62C24×C19—48no—
63C24×C19C2×D411yescharacteristic
64C2×Q8×C19—224no—
65C2×Q8×C19—26no—
66C2×Q8×C19—212no—
67C2×Q8×C19C2×D4124yescomplemented
68C2×Q8×C19C2414yes—
69C2×D4×C19—224no—
70C2×D4×C19—212no—
71C2×D4×C19—216no—
72C2×D4×C19—216no—
73C2×D4×C19—224no—
74C2×D4×C19—448no—
75C2×D4×C19—424no—
76C2×D4×C19—448no—
77C2×D4×C19C2418yes—
78C22×C4×C19—28no—
79C22×C4×C19—24no—
80C22×C4×C19—26no—
81C22×C4×C19—26no—
82C22×C4×C19—44no—
83C22×C4×C19SD1618yescomplemented
84C22×C4×C19C2×D416yes—
85C22×C4×C19C2×D413yes—
86C22×C4×C19C2×D414yes—
87C22×C4×C19C2×D416yes—
88C22×C4×C19#4114yes—
89C22×C4×C19C2413yes—
90SD16×C19—264no—
91C2×C8×C19—224no—
92C2×C8×C19C2418yes—
93C4⋊C4×C19—216no—
94C4⋊C4×C19—26no—
95C4⋊C4×C19C2414yes—
96C42×C19—216no—
97C42×C19C2×D4112yes—
98C42×C19C2414yes—
99C22×#460C1911yesmaximal, characteristic, direct product factor, Sylow
100C23×C19—28no—
101C23×C19—424no—
102C23×C19—424no—
103C23×C19—424no—
104C23×C19—832no—
105C23×C19#12114yes—
106C23×C19C2×SD1614yes—
107C23×C19AGL(1,ℤ/8)14yes—
108C23×C19C22×D413yes—
109Q8×C19—224no—
110Q8×C19—24no—
111Q8×C19C22×D418yescomplemented
112D4×C19—28no—
113D4×C19—28no—
114D4×C19—432no—
115D4×C19—424no—
116D4×C19—432no—
117C2×C4×C19—224no—
118C2×C4×C19—212no—
119C2×C4×C19—24no—
120C2×C4×C19—24no—
121C2×C4×C19—412no—
122C2×C4×C19#121112yes—
123C2×C4×C19C2×SD16124yescomplemented
124C2×C4×C19C22×D414yes—
125C2×C4×C19C22×D413yes—
126C2×C4×C19C22×D416yes—
127C2×C4×C19C22×D414yes—
128C2×C4×C19C2×#4116yes—
129C2×C4×C19C2511yescharacteristic
130C8×C19—28no—
131C23×SD16C2×C1912yescomplemented
132C22×#127C2×C1911yescharacteristic
133C22×C4×Q8C2×C1911yescharacteristic, complemented
134C2×#460C2×C19124yesdirect product factor
135C22×C4⋊C8C2×C1911yescharacteristic, complemented
136C22×#102C2×C1912yescomplemented
137C22×C19—48no—
138C22×C19—48no—
139C22×C19—48no—
140C22×C19—848no—
141C22×C19#460116yesdirect product factor
142C22×C19C2×#12116yes—
143C22×C19C22×SD1616yes—
144C22×C19C2×AGL(1,ℤ/8)16yes—
145C22×C19C23×D411yescharacteristic
146C4×C19—28no—
147C4×C19—24no—
148C4×C19—44no—
149C4×C19C2×#12116yes—
150C4×C19C22×SD1618yescomplemented
151C4×C19C23×D411yescharacteristic
152C4×C19C22×#4111yescharacteristic
153C23×Q8C22×C1911yescharacteristic
154C23×D4—21no—
155C23×D4—21no—
156C23×D4C22×C1912yes—
157C22×SD16—216no—
158C22×SD16C22×C19124yescomplemented
159C23×C8C22×C1912yes—
160C2×#127—26no—
161C2×#127C22×C19112yes—
162C2×C4×Q8—26no—
163C2×C4×Q8C22×C19112yescomplemented
164C22×C4⋊C4—21no—
165C22×C4⋊C4C22×C1911yescharacteristic
166C22×C42—21no—
167C22×C42C22×C1911yescharacteristic
168#460C22×C19164yesdirect product factor
169C2×C4⋊C8C22×C19112yescomplemented
170C2×#102C22×C19124yescomplemented
171C2×C19—88no—
172C2×C19C2×#460112yesdirect product factor
173C2×C19C22×#12111yescharacteristic
174C2×C19C23×SD1611yescharacteristic
175C2×C19C22×AGL(1,ℤ/8)11yescharacteristic
176C25—22no—
177C22×Q8—23no—
178C22×Q8—24no—
179C22×Q8D4×C1918yescomplemented
180C22×Q8C23×C1916yes—
181C22×D4—28no—
182C22×D4—26no—
183C22×D4—212no—
184C22×D4—212no—
185C22×D4—28no—
186C22×D4—48no—
187C22×D4—48no—
188C22×D4C23×C19112yes—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4D4×C1911yescharacteristic
192C23×C4D4×C1911yescharacteristic
193C23×C4C23×C1911yescharacteristic
194C2×SD16—296no—
195C2×SD16C23×C19132yescomplemented
196C22×C8—28no—
197C22×C8C23×C19112yes—
198#127—224no—
199#127C23×C19116yes—
200C4×Q8—224no—
201C4×Q8C23×C19116yescomplemented
202C2×C4⋊C4—212no—
203C2×C4⋊C4—23no—
204C2×C4⋊C4C23×C1916yes—
205C2×C42—212no—
206C2×C42D4×C1916yes—
207C2×C42C23×C1916yes—
208C4⋊C8C23×C19116yescomplemented
209#102C23×C19132yescomplemented
210C19C22×#46011yescharacteristic, direct product factor, Sylow
211C24—212no—
212C24—48no—
213C24—48no—
214C24—48no—
215C24C2×D4×C1911yescharacteristic
216C2×Q8—224no—
217C2×Q8—26no—
218C2×Q8—212no—
219C2×Q8C2×D4×C19124yescomplemented
220C2×Q8C24×C1914yes—
221C2×D4—224no—
222C2×D4—212no—
223C2×D4—216no—
224C2×D4—216no—
225C2×D4—224no—
226C2×D4—448no—
227C2×D4—424no—
228C2×D4—448no—
229C2×D4C24×C1918yes—
230C22×C4—28no—
231C22×C4—24no—
232C22×C4—26no—
233C22×C4—26no—
234C22×C4—44no—
235C22×C4SD16×C1918yescomplemented
236C22×C4C2×D4×C1916yes—
237C22×C4C2×D4×C1913yes—
238C22×C4C2×D4×C1914yes—
239C22×C4C2×D4×C1916yes—
240C22×C4#41×C1914yes—
241C22×C4C24×C1913yes—
242SD16—264no—
243C2×C8—224no—
244C2×C8C24×C1918yes—
245C4⋊C4—216no—
246C4⋊C4—26no—
247C4⋊C4C24×C1914yes—
248C42—216no—
249C42C2×D4×C19112yes—
250C42C24×C1914yes—
251C23—28no—
252C23—424no—
253C23—424no—
254C23—424no—
255C23—832no—
256C23C19×#12114yes—
257C23C2×SD16×C1914yes—
258C23C19×AGL(1,ℤ/8)14yes—
259C23C22×D4×C1913yes—
260Q8—224no—
261Q8—24no—
262Q8C22×D4×C1918yescomplemented
263D4—28no—
264D4—28no—
265D4—432no—
266D4—424no—
267D4—432no—
268C2×C4—224no—
269C2×C4—212no—
270C2×C4—24no—
271C2×C4—24no—
272C2×C4—412no—
273C2×C4C19×#121112yes—
274C2×C4C2×SD16×C19124yescomplemented
275C2×C4C22×D4×C1914yes—
276C2×C4C22×D4×C1913yes—
277C2×C4C22×D4×C1916yes—
278C2×C4C22×D4×C1914yes—
279C2×C4C2×#41×C1916yes—
280C2×C4C25×C1911yescharacteristic
281C8—28no—
282C22—48no—
283C22—48no—
284C22—48no—
285C22—848no—
286C22C19×#460116yesdirect product factor
287C22C2×C19×#12116yes—
288C22C22×SD16×C1916yes—
289C22C2×C19×AGL(1,ℤ/8)16yes—
290C22C23×D4×C1911yescharacteristic
291C4—28no—
292C4—24no—
293C4—44no—
294C4C2×C19×#12116yes—
295C4C22×SD16×C1918yescomplemented
296C4C23×D4×C1911yescharacteristic
297C4C22×#41×C1911yescharacteristic
298C2—88no—
299C2C2×C19×#460112yesdirect product factor
300C2C22×C19×#12111yescharacteristic
301C2C23×SD16×C1911yescharacteristic
302C2C22×C19×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
center, socleC24×C19C2×D4
commutator, Frattini, cosocleC2×C4C25×C19
prime radicalC22×C19×#127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C19 ◁ C22×C42×C19 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×SD16×C19C2semidirect
3. C22×C4×Q8×C19C2semidirect
4. C2×C19×#460C2direct (N × H)
5. C22×C19×C4⋊C8C2semidirect
6. C22×C19×#102C2semidirect
12. C22×SD16×C19C22semidirect
17. C2×C4×Q8×C19C22semidirect
22. C19×#460C22direct (N × H)
23. C2×C19×C4⋊C8C22semidirect
24. C2×C19×#102C22semidirect
28. C22×Q8×C19D4semidirect
44. C2×SD16×C19C23semidirect
50. C4×Q8×C19C23semidirect
57. C19×C4⋊C8C23semidirect
58. C19×#102C23semidirect
67. C2×Q8×C19C2×D4semidirect
83. C22×C4×C19SD16semidirect
99. C22×#460C19direct (N × H)
111. Q8×C19C22×D4semidirect
123. C2×C4×C19C2×SD16semidirect
131. C23×SD16C2×C19semidirect
133. C22×C4×Q8C2×C19semidirect
134. C2×#460C2×C19direct (N × H)
135. C22×C4⋊C8C2×C19semidirect
136. C22×#102C2×C19semidirect
141. C22×C19#460direct (N × H)
150. C4×C19C22×SD16semidirect
158. C22×SD16C22×C19semidirect
163. C2×C4×Q8C22×C19semidirect
168. #460C22×C19direct (N × H)
169. C2×C4⋊C8C22×C19semidirect
170. C2×#102C22×C19semidirect
172. C2×C19C2×#460direct (N × H)
179. C22×Q8D4×C19semidirect
195. C2×SD16C23×C19semidirect
201. C4×Q8C23×C19semidirect
208. C4⋊C8C23×C19semidirect
209. #102C23×C19semidirect
210. C19C22×#460direct (N × H)
219. C2×Q8C2×D4×C19semidirect
235. C22×C4SD16×C19semidirect
262. Q8C22×D4×C19semidirect
274. C2×C4C2×SD16×C19semidirect
286. C22C19×#460direct (N × H)
295. C4C22×SD16×C19semidirect
299. C2C2×C19×#460direct (N × H)

Maximal subgroups

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

subgroupindex
C23×SD16×C192
C22×C19×#1272
C22×C4×Q8×C192
C2×C19×#4602
C22×C19×C4⋊C82
C22×C19×#1022
C22×#46019