Finite Group Databasebeta

← #14572860

Subgroups — #14572860

Order 2432.

994 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×D4×D19C211yesmaximal, characteristic, complemented
2C2×#10597395C211yesmaximal, characteristic, complemented
3#11927051C211yesmaximal, characteristic, complemented
4#11926693C214yesmaximal, complemented
5#11926676C214yesmaximal, complemented
6#11926550C211yesmaximal, characteristic, complemented
7#11926549C211yesmaximal, characteristic, complemented
8#11926507C211yesmaximal, characteristic, complemented
9C2×C19×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
10C24×D19—21no—
11C2×#41×C19C2211yescharacteristic, complemented
12C22×D4×C19C2211yescharacteristic
13C22×C22⋊D19—21no—
14C2×D4×D19—24no—
15C2×D4×D19—24no—
16C2×D4×D19—22no—
17C2×D4×D19C2214yes—
18C22×D76C2211yescharacteristic
19C22×C4×D19C2211yescharacteristic
20C19×AGL(1,ℤ/8)—24no—
21C2×SD16×C19C2212yescomplemented
22C2×D8×C19C2212yescomplemented
23C2×M16×C19C2211yescharacteristic, complemented
24#10597395—24no—
25#10597392C2212yescomplemented
26C2×#64527C2212yescomplemented
27#10597384C2212yescomplemented
28#10597383—21no—
29#10597381—21no—
30C2×#64525C2212yescomplemented
31C4×C22⋊D19—22no—
32#10597372C2211yescharacteristic, complemented
33C2×#64520C2211yescharacteristic, complemented
34#10597289C2214yescomplemented
35#10597278C2214yescomplemented
36(C2×D19)⋊C8C2214yescomplemented
37C24×C19—21no—
38C23×D19—28no—
39C23×D19—21no—
40C23×D19—24no—
41C23×D19—48no—
42C23×D19D411yescharacteristic
43#41×C19—22no—
44#41×C19—22no—
45C2×Q8×C19C2311yescharacteristic, complemented
46C2×D4×C19—21no—
47C2×D4×C19—21no—
48C2×D4×C19—22no—
49C2×D4×C19D414yescomplemented
50C2×D4×C19C2312yes—
51C2×D4×C19C2311yescharacteristic, complemented
52C22×C4×C19—21no—
53C22×C4×C19C2311yescharacteristic
54C2×C22⋊D19—28no—
55C2×C22⋊D19—22no—
56C2×C22⋊D19—24no—
57C22×Dic19D411yescharacteristic
58D4×D19—216no—
59D4×D19—28no—
60D4×D19—28no—
61C2×D76—21no—
62C2×D76—22no—
63C2×D76D414yescomplemented
64C2×D76C2312yes—
65C2×C4×D19—22no—
66C2×C4×D19—22no—
67C2×C4×D19D412yes—
68C2×C4×D19C2312yes—
69SD16×C19—24no—
70D8×C19—24no—
71M16×C19—22no—
72C2×C8×C19C2312yescomplemented
73C22⋊Dic19—21no—
74C22⋊Dic19—22no—
75#64527—24no—
76#64525—24no—
77(C2×D19)⋊C4—22no—
78C4⋊Dic19C2312yescomplemented
79Dic19⋊C4—22no—
80C4×Dic19—21no—
81#64520—22no—
82C2×C19⋊C8C2312yescomplemented
83C23×C19—24no—
84C23×C19—22no—
85C23×C19—21no—
86C23×C19—44no—
87C23×C19C2×D411yescharacteristic
88C22×D19—22no—
89C22×D19—24no—
90C22×D19—216no—
91C22×D19—24no—
92C22×D19—22no—
93C22×D19—432no—
94C22×D19—48no—
95C22×D19—44no—
96C22×D19—48no—
97C22×D19C2×D412yes—
98Q8×C19—21no—
99Q8×C19—21no—
100D4×C19—24no—
101D4×C19—22no—
102D4×C19—21no—
103D4×C19—21no—
104D4×C19—42no—
105D4×C19C2×D414yes—
106C2×C4×C19—21no—
107C2×C4×C19—42no—
108C2×C4×C19C2×D411yescharacteristic
109C2×C4×C19C2×D412yes—
110C2×C4×C19C2×D412yes—
111C2×C4×C19C2411yescharacteristic
112C22⋊D19—216no—
113C22⋊D19—44no—
114C2×Dic19—22no—
115C2×Dic19—22no—
116C2×Dic19C2×D412yes—
117D76—24no—
118D76—22no—
119D76C2×D414yes—
120C4×D19—24no—
121C4×D19—22no—
122C4×D19—22no—
123C8×C19—22no—
124C19⋊C8—22no—
125#3003—191nomaximal, Sylow
126C22×C19—22no—
127C22×C19—24no—
128C22×C19—48no—
129C22×C19—44no—
130C22×C19—41no—
131C22×C19—42no—
132C22×C19#12012yes—
133C22×C19C22×D411yescharacteristic
134C2×D19—28no—
135C2×D19—22no—
136C2×D19—22no—
137C2×D19—24no—
138C2×D19—432no—
139C2×D19—48no—
140C2×D19—44no—
141C2×D19AGL(1,ℤ/8)14yescomplemented
142C4×C19—41no—
143C4×C19#12012yes—
144C4×C19C22×D411yescharacteristic
145C4×C19C22×D411yescharacteristic
146Dic19—22no—
147Dic19—42no—
148C23×D4—191no—
149C2×AGL(1,ℤ/8)—191no—
150C2×AGL(1,ℤ/8)D1911yescharacteristic, complemented
151#525—191no—
152#450—194no—
153#447—194no—
154#418—191no—
155#418—191no—
156#407—191no—
157C2×C19—22no—
158C2×C19—44no—
159C2×C19—81no—
160C2×C19C2×#12011yescharacteristic
161C2×C19C2×AGL(1,ℤ/8)12yes—
162D19—24no—
163D19—44no—
164C25—381no—
165C2×#41C2×D1911yescharacteristic, complemented
166C22×D4—194no—
167C22×D4—191no—
168C22×D4—382no—
169C22×D4—381no—
170C22×D4—384no—
171C22×D4—384no—
172C22×D4C2×D1911yescharacteristic
173C23×C4—191no—
174AGL(1,ℤ/8)—24no—
175AGL(1,ℤ/8)—384no—
176C2×SD16—192no—
177C2×SD16C2×D1912yescomplemented
178C2×D8—192no—
179C2×D8C2×D1912yescomplemented
180C2×M16—191no—
181C2×M16C2×D1911yescharacteristic, complemented
182#123—381no—
183C22⋊Q8—192no—
184#121—192no—
185#120—381no—
186C4×D4—382no—
187#117—191no—
188#102—194no—
189#102—194no—
190C22⋊C8—194no—
191C19#300311yescharacteristic, complemented, Sylow
192C24—21no—
193C24—191no—
194C24—384no—
195C24—388no—
196C24—381no—
197C24—768no—
198#41—22no—
199#41—22no—
200C2×Q8C22×D1911yescharacteristic, complemented
201C2×D4—21no—
202C2×D4—21no—
203C2×D4—22no—
204C2×D4—194no—
205C2×D4—192no—
206C2×D4—384no—
207C2×D4—388no—
208C2×D4—3816no—
209C2×D4—388no—
210C2×D4—388no—
211C2×D4—382no—
212C2×D4—381no—
213C2×D4—382no—
214C2×D4C22⋊D1914yescomplemented
215C2×D4C22×D1912yes—
216C2×D4C22×D1911yescharacteristic, complemented
217C22×C4—21no—
218C22×C4—191no—
219C22×C4—192no—
220C22×C4—192no—
221C22×C4—382no—
222C22×C4—382no—
223C22×C4C22×D1911yescharacteristic
224SD16—24no—
225SD16—384no—
226D8—24no—
227D8—384no—
228M16—22no—
229M16—382no—
230C2×C8—192no—
231C2×C8C22×D1912yescomplemented
232C4⋊C4—192no—
233C4⋊C4—382no—
234C22⋊C4—382no—
235C22⋊C4—382no—
236C22⋊C4—381no—
237C42—381no—
238C23—24no—
239C23—22no—
240C23—21no—
241C23—44no—
242C23—192no—
243C23—384no—
244C23—3816no—
245C23—382no—
246C23—384no—
247C23—382no—
248C23—764no—
249C23—768no—
250C23—7632no—
251C23—768no—
252C23D4×D1911yescharacteristic
253Q8—21no—
254Q8—21no—
255D4—24no—
256D4—22no—
257D4—21no—
258D4—21no—
259D4—42no—
260D4—194no—
261D4—3816no—
262D4—384no—
263D4—382no—
264D4—764no—
265D4C2×C22⋊D1914yes—
266C2×C4—21no—
267C2×C4—42no—
268C2×C4—192no—
269C2×C4—382no—
270C2×C4—384no—
271C2×C4—382no—
272C2×C4—382no—
273C2×C4—382no—
274C2×C4D4×D1911yescharacteristic
275C2×C4D4×D1912yes—
276C2×C4C2×C22⋊D1912yes—
277C2×C4C23×D1911yescharacteristic
278C8—22no—
279C8—382no—
280C22—22no—
281C22—24no—
282C22—48no—
283C22—44no—
284C22—42no—
285C22—41no—
286C22—194no—
287C22—388no—
288C22—382no—
289C22—382no—
290C22—384no—
291C22—768no—
292C22—7632no—
293C22—764no—
294C22#1059738312yes—
295C22C2×D4×D1911yescharacteristic
296C4—41no—
297C4—382no—
298C4—762no—
299C4#1059738312yes—
300C4C2×D4×D1911yescharacteristic
301C4C22×C22⋊D1911yescharacteristic
302C2—22no—
303C2—44no—
304C2—81no—
305C2—384no—
306C2—764no—
307C2C2×#1059738311yescharacteristic
308C2AGL(1,ℤ/8)×D1912yes—
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC2×C19×AGL(1,ℤ/8)C2
socleC22×C19C22×D4
hypercenterC2×AGL(1,ℤ/8)D19
hypocenterC19#3003
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C22×D4×D19C2semidirect
2. C2×#10597395C2semidirect
3. #11927051C2semidirect
4. #11926693C2semidirect
5. #11926676C2semidirect
6. #11926550C2semidirect
7. #11926549C2semidirect
8. #11926507C2semidirect
9. C2×C19×AGL(1,ℤ/8)C2semidirect
11. C2×#41×C19C22semidirect
21. C2×SD16×C19C22semidirect
22. C2×D8×C19C22semidirect
23. C2×M16×C19C22semidirect
25. #10597392C22semidirect
26. C2×#64527C22semidirect
27. #10597384C22semidirect
30. C2×#64525C22semidirect
32. #10597372C22semidirect
33. C2×#64520C22semidirect
34. #10597289C22semidirect
35. #10597278C22semidirect
36. (C2×D19)⋊C8C22semidirect
45. C2×Q8×C19C23semidirect
49. C2×D4×C19D4semidirect
51. C2×D4×C19C23semidirect
63. C2×D76D4semidirect
72. C2×C8×C19C23semidirect
78. C4⋊Dic19C23semidirect
82. C2×C19⋊C8C23semidirect
141. C2×D19AGL(1,ℤ/8)semidirect
150. C2×AGL(1,ℤ/8)D19semidirect
165. C2×#41C2×D19semidirect
177. C2×SD16C2×D19semidirect
179. C2×D8C2×D19semidirect
181. C2×M16C2×D19semidirect
191. C19#3003semidirect
200. C2×Q8C22×D19semidirect
214. C2×D4C22⋊D19semidirect
216. C2×D4C22×D19semidirect
231. C2×C8C22×D19semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D192
C2×#105973952
#119270512
#119266932
#119266762
#119265502
#119265492
#119265072
C2×C19×AGL(1,ℤ/8)2
#300319