Finite Group Databasebeta

← C4×C19×#442 #18026459

Subgroups — C4×C19×#442 #18026459

Order 4864.

1326 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C19×#442C212yesmaximal
2C2×C4×D8×C19C211yesmaximal, characteristic
3C42×D4×C19C212yesmaximal, complemented
4C19×#1776C212yesmaximal, complemented
5C4×C19×#106C211yesmaximal, characteristic, complemented
6C19×#1762C214yesmaximal, complemented
7C4×C19×#102C212yesmaximal, complemented
8C4×C19×#97C211yesmaximal, characteristic, complemented
9C22×D8×C19C2211yescharacteristic
10C2×C4×D4×C19C2212yes—
11C2×C4×D4×C19C2214yes—
12C22×C42×C19—22no—
13C19×#442C4116yesdirect product factor
14C4×D8×C19C418yescomplemented
15C2×C19×#107C2211yescharacteristic
16C2×C19×#106C2212yes—
17C2×C19×#102C2212yes—
18C2×C19×#102C2214yes—
19C2×C19×#97C2212yes—
20C2×C19×#97C2212yes—
21C2×C4×C8×C19C2211yescharacteristic
22C2×C4×C8×C19C2211yescharacteristic
23C4×C4⋊C4×C19C2212yes—
24C4×C4⋊C4×C19C2214yes—
25C4×C22⋊C4×C19—24no—
26C4×C22⋊C4×C19—22no—
27C43×C19C2211yescharacteristic
28C19×#340C2214yes—
29C19×#340C2212yes—
30C22×D4×C19C2312yes—
31C23×C4×C19—24no—
32C23×C4×C19—22no—
33C2×D8×C19C2×C414yes—
34C2×D8×C19C2×C418yes—
35C22×C8×C19C2312yes—
36C22×C8×C19C2311yescharacteristic
37C22×C8×C19C2311yescharacteristic
38C4×D4×C19—24no—
39C4×D4×C19—28no—
40C4×D4×C19C2×C418yescomplemented
41C4×D4×C19C2×C4116yescomplemented
42C2×C4⋊C4×C19C2314yes—
43C2×C4⋊C4×C19C2312yes—
44C2×C22⋊C4×C19—24no—
45C2×C22⋊C4×C19—22no—
46C2×C42×C19—24no—
47C2×C42×C19—22no—
48C2×C42×C19—48no—
49C2×C42×C19D412yes—
50C2×C42×C19D412yes—
51C2×C42×C19C2312yes—
52C2×C42×C19C2311yescharacteristic
53C19×#107C2×C414yescomplemented
54C19×#106C2×C418yescomplemented
55C19×#102C2×C418yescomplemented
56C19×#102C2×C4116yescomplemented
57C19×#97—24no—
58C19×#97C2×C418yescomplemented
59C4×C8×C19—22no—
60C4×C8×C19C2×C414yescomplemented
61C19×#95—24no—
62C19×#95—22no—
63C24×C19—22no—
64C2×D4×C19—22no—
65C2×D4×C19—24no—
66C2×D4×C19C22×C414yes—
67C2×D4×C19C22×C418yes—
68C22×C4×C19—22no—
69C22×C4×C19—24no—
70C22×C4×C19—216no—
71C22×C4×C19—28no—
72C22×C4×C19—48no—
73C22×C4×C19—48no—
74C22×C4×C19—44no—
75C22×C4×C19—44no—
76C22×C4×C19C2×D414yes—
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2411yescharacteristic
80D8×C19C42116yescomplemented
81C2×C8×C19—22no—
82C2×C8×C19—22no—
83C2×C8×C19—22no—
84C2×C8×C19C22×C412yes—
85C2×C8×C19C22×C414yes—
86C2×C8×C19C22×C412yes—
87C2×C8×C19C22×C414yes—
88C4⋊C4×C19—24no—
89C4⋊C4×C19—22no—
90C4⋊C4×C19C22×C418yes—
91C4⋊C4×C19C22×C414yes—
92C22⋊C4×C19—28no—
93C22⋊C4×C19—216no—
94C42×C19—24no—
95C42×C19—42no—
96C42×C19—48no—
97C42×C19—44no—
98C42×C19C22×C412yes—
99C42×C19C22×C414yes—
100C42×C19#4112yes—
101C42×C19#4114yes—
102C4×#442C1911yesmaximal, characteristic, direct product factor, Sylow
103C23×C19—24no—
104C23×C19—28no—
105C23×C19—42no—
106C23×C19—42no—
107C23×C19—44no—
108C23×C19C22×D411yescharacteristic
109D4×C19—24no—
110D4×C19—28no—
111D4×C19C2×C4218yescomplemented
112C2×C4×C19—24no—
113C2×C4×C19—24no—
114C2×C4×C19—22no—
115C2×C4×C19—24no—
116C2×C4×C19—28no—
117C2×C4×C19—432no—
118C2×C4×C19—42no—
119C2×C4×C19—44no—
120C2×C4×C19—42no—
121C2×C4×C19—44no—
122C2×C4×C19—416no—
123C2×C4×C19C4×D412yes—
124C2×C4×C19C4×D418yes—
125C2×C4×C19C4×D412yes—
126C2×C4×C19AGL(1,ℤ/8)14yes—
127C2×C4×C19C23×C411yescharacteristic
128C2×C4×C19C23×C412yes—
129C2×C4×C19C2×#4111yescharacteristic
130C2×C4×C19C2×#4112yes—
131C8×C19—24no—
132C8×C19—22no—
133C8×C19C2×C4214yescomplemented
134C2×#442C2×C1912yes—
135C2×C4×D8C2×C1911yescharacteristic
136C42×D4C2×C1912yescomplemented
137#1776C2×C1912yescomplemented
138C4×#106C2×C1911yescharacteristic, complemented
139#1762C2×C1914yescomplemented
140C4×#102C2×C1912yescomplemented
141C4×#97C2×C1911yescharacteristic, complemented
142C22×C19—28no—
143C22×C19—44no—
144C22×C19—44no—
145C22×C19—48no—
146C22×C19—48no—
147C22×C19C2×C4×D411yescharacteristic
148C22×C19C2×C4×D412yes—
149C22×C19C2×AGL(1,ℤ/8)12yes—
150C22×C19#57512yes—
151C4×C19—22no—
152C4×C19—28no—
153C4×C19—44no—
154C4×C19—48no—
155C4×C19#44214yesdirect product factor
156C4×C19C22×C4211yescharacteristic
157C4×C19C4×#4112yes—
158C4×C19C4×#4111yescharacteristic
159C22×D8C22×C1911yescharacteristic
160C2×C4×D4C22×C1912yes—
161C2×C4×D4C22×C1914yes—
162C22×C42—22no—
163#442C4×C19116yesdirect product factor
164C4×D8C4×C1918yescomplemented
165C2×#107C22×C1911yescharacteristic
166C2×#106C22×C1912yes—
167C2×#102C22×C1912yes—
168C2×#102C22×C1914yes—
169C2×#97C22×C1912yes—
170C2×#97C22×C1912yes—
171C2×C4×C8C22×C1911yescharacteristic
172C2×C4×C8C22×C1911yescharacteristic
173C4×C4⋊C4C22×C1912yes—
174C4×C4⋊C4C22×C1914yes—
175C4×C22⋊C4—22no—
176C4×C22⋊C4—24no—
177C43C22×C1911yescharacteristic
178#340C22×C1914yes—
179#340C22×C1912yes—
180C2×C19—48no—
181C2×C19C42×D411yescharacteristic
182C2×C19C2×#44211yescharacteristic
183C2×C19#294311yescharacteristic
184C2×C19C4×AGL(1,ℤ/8)14yes—
185C22×D4C23×C1912yes—
186C23×C4—24no—
187C23×C4—22no—
188C2×D8C2×C4×C1914yes—
189C2×D8C2×C4×C1918yes—
190C22×C8C23×C1912yes—
191C22×C8C23×C1911yescharacteristic
192C22×C8C23×C1911yescharacteristic
193C4×D4—24no—
194C4×D4—28no—
195C4×D4C2×C4×C1918yescomplemented
196C4×D4C2×C4×C19116yescomplemented
197C2×C4⋊C4C23×C1914yes—
198C2×C4⋊C4C23×C1912yes—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—24no—
201C2×C42—24no—
202C2×C42—22no—
203C2×C42—48no—
204C2×C42D4×C1912yes—
205C2×C42D4×C1912yes—
206C2×C42C23×C1911yescharacteristic
207C2×C42C23×C1912yes—
208#107C2×C4×C1914yescomplemented
209#106C2×C4×C1918yescomplemented
210#102C2×C4×C1918yescomplemented
211#102C2×C4×C19116yescomplemented
212#97—24no—
213#97C2×C4×C1918yescomplemented
214C4×C8—22no—
215C4×C8C2×C4×C1914yescomplemented
216#95—22no—
217#95—24no—
218C19C4×#44211yescharacteristic, direct product factor, Sylow
219C24—22no—
220C2×D4—22no—
221C2×D4—24no—
222C2×D4C22×C4×C1914yes—
223C2×D4C22×C4×C1918yes—
224C22×C4—22no—
225C22×C4—24no—
226C22×C4—216no—
227C22×C4—28no—
228C22×C4—48no—
229C22×C4—48no—
230C22×C4—44no—
231C22×C4—44no—
232C22×C4C2×D4×C1911yescharacteristic
233C22×C4C2×D4×C1914yes—
234C22×C4C2×D4×C1911yescharacteristic
235C22×C4C24×C1911yescharacteristic
236D8C42×C19116yescomplemented
237C2×C8—22no—
238C2×C8—22no—
239C2×C8—22no—
240C2×C8C22×C4×C1912yes—
241C2×C8C22×C4×C1914yes—
242C2×C8C22×C4×C1912yes—
243C2×C8C22×C4×C1914yes—
244C4⋊C4—24no—
245C4⋊C4—22no—
246C4⋊C4C22×C4×C1918yes—
247C4⋊C4C22×C4×C1914yes—
248C22⋊C4—28no—
249C22⋊C4—216no—
250C42—24no—
251C42—42no—
252C42—48no—
253C42—44no—
254C42C22×C4×C1912yes—
255C42C22×C4×C1914yes—
256C42#41×C1912yes—
257C42#41×C1914yes—
258C23—24no—
259C23—28no—
260C23—42no—
261C23—42no—
262C23—44no—
263C23C22×D4×C1911yescharacteristic
264D4—24no—
265D4—28no—
266D4C2×C42×C1918yescomplemented
267C2×C4—24no—
268C2×C4—24no—
269C2×C4—22no—
270C2×C4—24no—
271C2×C4—28no—
272C2×C4—432no—
273C2×C4—42no—
274C2×C4—44no—
275C2×C4—42no—
276C2×C4—44no—
277C2×C4—416no—
278C2×C4C4×D4×C1912yes—
279C2×C4C4×D4×C1918yes—
280C2×C4C4×D4×C1912yes—
281C2×C4C19×AGL(1,ℤ/8)14yes—
282C2×C4C23×C4×C1911yescharacteristic
283C2×C4C23×C4×C1912yes—
284C2×C4C2×#41×C1911yescharacteristic
285C2×C4C2×#41×C1912yes—
286C8—24no—
287C8—22no—
288C8C2×C42×C1914yescomplemented
289C22—28no—
290C22—44no—
291C22—44no—
292C22—48no—
293C22—48no—
294C22C2×C4×D4×C1911yescharacteristic
295C22C2×C4×D4×C1912yes—
296C22C2×C19×AGL(1,ℤ/8)12yes—
297C22C19×#57512yes—
298C4—22no—
299C4—28no—
300C4—44no—
301C4—48no—
302C4C19×#44214yesdirect product factor
303C4C22×C42×C1911yescharacteristic
304C4C4×#41×C1912yes—
305C4C4×#41×C1911yescharacteristic
306C2—48no—
307C2C42×D4×C1911yescharacteristic
308C2C2×C19×#44211yescharacteristic
309C2C19×#294311yescharacteristic
310C2C4×C19×AGL(1,ℤ/8)14yes—
subgroupG/H
centerC22×C4×C19C2×D4
commutatorC4C22×C42×C19
Frattini, cosocleC22×C4C24×C19
socleC23×C19C22×D4
prime radicalC22×D8×C19C22
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C19 ◁ C43×C19 ◁ G

Complements

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

NH ≅ G/Ntype
3. C42×D4×C19C2semidirect
4. C19×#1776C2semidirect
5. C4×C19×#106C2semidirect
6. C19×#1762C2semidirect
7. C4×C19×#102C2semidirect
8. C4×C19×#97C2semidirect
13. C19×#442C4direct (N × H)
14. C4×D8×C19C4semidirect
40. C4×D4×C19C2×C4semidirect
41. C4×D4×C19C2×C4semidirect
53. C19×#107C2×C4semidirect
54. C19×#106C2×C4semidirect
55. C19×#102C2×C4semidirect
56. C19×#102C2×C4semidirect
58. C19×#97C2×C4semidirect
60. C4×C8×C19C2×C4semidirect
80. D8×C19C42semidirect
102. C4×#442C19direct (N × H)
111. D4×C19C2×C42semidirect
133. C8×C19C2×C42semidirect
136. C42×D4C2×C19semidirect
137. #1776C2×C19semidirect
138. C4×#106C2×C19semidirect
139. #1762C2×C19semidirect
140. C4×#102C2×C19semidirect
141. C4×#97C2×C19semidirect
155. C4×C19#442direct (N × H)
163. #442C4×C19direct (N × H)
164. C4×D8C4×C19semidirect
195. C4×D4C2×C4×C19semidirect
196. C4×D4C2×C4×C19semidirect
208. #107C2×C4×C19semidirect
209. #106C2×C4×C19semidirect
210. #102C2×C4×C19semidirect
211. #102C2×C4×C19semidirect
213. #97C2×C4×C19semidirect
215. C4×C8C2×C4×C19semidirect
218. C19C4×#442direct (N × H)
236. D8C42×C19semidirect
266. D4C2×C42×C19semidirect
288. C8C2×C42×C19semidirect
302. C4C19×#442direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C19×#4422
C2×C4×D8×C192
C42×D4×C192
C19×#17762
C4×C19×#1062
C19×#17622
C4×C19×#1022
C4×C19×#972
C4×#44219