Finite Group Databasebeta

← D19×#509 #14576755

Subgroups — D19×#509 #14576755

Order 2432.

400 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#135×D19C211yesmaximal, characteristic, complemented
2C2×D8×D19C211yesmaximal, characteristic, complemented
3#11926982C211yesmaximal, characteristic, complemented
4#11926981C212yesmaximal, complemented
5#11926980C211yesmaximal, characteristic, complemented
6#11926979C211yesmaximal, characteristic, complemented
7#11926978C212yesmaximal, complemented
8SD32×D19C212yesmaximal, complemented
9D16×D19C212yesmaximal, complemented
10M32×D19C211yesmaximal, characteristic, complemented
11C19×#509C211yesmaximal, characteristic, complemented
12#41×D19—21no—
13C2×D4×D19—21no—
14C19×#135C2211yescharacteristic, complemented
15C2×D8×C19C2211yescharacteristic, complemented
16#10597396—21no—
17C2×#64525—21no—
18#10597365C2211yescharacteristic, complemented
19Q16×D19C2211yescharacteristic, complemented
20#10597362—21no—
21SD16×D19—21no—
22#10597358C2211yescharacteristic, complemented
23D8×D19—21no—
24D8×D19—21no—
25D8×D19C2212yes—
26D8×D19C2212yescomplemented
27D8×D19C2211yescharacteristic, complemented
28#10597350C2211yescharacteristic, complemented
29C2×D152C2211yescharacteristic, complemented
30C2×C8×D19C2211yescharacteristic
31C19×SD32C2212yescomplemented
32C19×D16C2212yescomplemented
33C19×M32C2211yescharacteristic, complemented
34#10597285C2212yescomplemented
35#10597284C2212yescomplemented
36#10597283C2212yescomplemented
37#10597283C2212yescomplemented
38#10597269C2211yescharacteristic, complemented
39#10597257C2212yescomplemented
40D304C2212yescomplemented
41#10597255C2212yescomplemented
42C16×D19C2212yescomplemented
43C23×D19—41no—
44#41×C19—21no—
45C2×D4×C19—21no—
46C2×C22⋊D19—41no—
47#64545—21no—
48Q8×D19—21no—
49#64543—21no—
50#64543—41no—
51D4×D19—22no—
52D4×D19—22no—
53D4×D19—21no—
54D4×D19—41no—
55D4×D19—41no—
56D4×D19—41no—
57#64541—21no—
58#64541—41no—
59C2×D76—21no—
60C2×C4×D19—41no—
61C2×C4×D19D411yescharacteristic
62Q16×C19C2311yescharacteristic, complemented
63SD16×C19—21no—
64D8×C19—21no—
65D8×C19C2312yes—
66D8×C19C2311yescharacteristic, complemented
67C2×C8×C19C2311yescharacteristic
68#64528—21no—
69#64527—21no—
70#64526—21no—
71#64525—22no—
72#64525—22no—
73#64525—21no—
74C2×C19⋊C8D411yescharacteristic
75Dic76C2311yescharacteristic, complemented
76D152—21no—
77D152C2312yes—
78D152C2311yescharacteristic, complemented
79#64516—21no—
80C8×D19D411yescharacteristic
81C8×D19D411yescharacteristic
82C8×D19C2311yescharacteristic
83C8×D19C2311yescharacteristic
84C16×C19C2312yescomplemented
85C19⋊C16C2312yescomplemented
86C23×C19—41no—
87C22×D19—41no—
88C22×D19—41no—
89C22×D19—42no—
90C22×D19—42no—
91C22×D19—84no—
92C22×D19D811yescharacteristic
93Q8×C19—21no—
94D4×C19—22no—
95D4×C19—21no—
96D4×C19—41no—
97D4×C19—41no—
98C2×C4×C19—41no—
99C2×C4×C19C2×D411yescharacteristic
100C22⋊D19—41no—
101C22⋊D19—41no—
102C22⋊D19—41no—
103C22⋊D19—42no—
104C22⋊D19—42no—
105C2×Dic19—41no—
106C2×Dic19D811yescharacteristic
107D76—21no—
108D76—22no—
109D76—41no—
110D76—41no—
111C4×D19—41no—
112C4×D19—41no—
113C4×D19—41no—
114C4×D19D811yescharacteristic
115C4×D19D811yescharacteristic
116C4×D19C2×D411yescharacteristic
117C4×D19C2×D411yescharacteristic
118Dic38—21no—
119Dic38—41no—
120C8×C19C2×D411yescharacteristic
121C8×C19C2411yescharacteristic
122C19⋊C8C2×D411yescharacteristic
123C19⋊C8C2×D411yescharacteristic
124C2×#509—191nomaximal, Sylow
125C22×C19—41no—
126C22×C19—42no—
127C22×C19—82no—
128C22×C19C2×D811yescharacteristic
129C2×D19—22no—
130C2×D19—41no—
131C2×D19—42no—
132C2×D19—84no—
133C2×D19—82no—
134C2×D19—82no—
135C2×D19—84no—
136C2×D19C2×D811yescharacteristic
137C2×D19C2×D811yescharacteristic
138C4×C19—41no—
139C4×C19C2×D811yescharacteristic
140C4×C19C22×D411yescharacteristic
141Dic19—41no—
142Dic19C2×D811yescharacteristic
143Dic19C2×D811yescharacteristic
144C2×#135—191no—
145C22×D8—191no—
146#509—191no—
147#509—191no—
148#509—192no—
149#509—192no—
150#509—191no—
151#509D1911yescharacteristic, direct product factor
152C2×SD32—192no—
153C2×D16—192no—
154C2×M32—191no—
155C2×C19—21no—
156C2×C19—82no—
157C2×C19—81no—
158C2×C19C22×D811yescharacteristic
159D19—21no—
160D19—81no—
161D19—82no—
162D19#50912yesdirect product factor
163C2×#41—381no—
164C22×D4—381no—
165#135—191no—
166#135—191no—
167#135—191no—
168#135—381no—
169#135—381no—
170#135C2×D1911yescharacteristic, complemented
171C2×Q16—191no—
172C2×SD16—381no—
173C2×D8—192no—
174C2×D8—192no—
175C2×D8—191no—
176C2×D8—191no—
177C2×D8—381no—
178C2×D8—381no—
179C2×D8—381no—
180C2×D8C2×D1911yescharacteristic, complemented
181C22×C8—191no—
182SD32—192no—
183SD32—192no—
184SD32—192no—
185SD32C2×D1912yescomplemented
186D16—192no—
187D16—192no—
188D16—192no—
189D16C2×D1912yescomplemented
190M32—191no—
191M32—192no—
192M32C2×D1911yescharacteristic, complemented
193C2×C16—192no—
194C19C2×#50911yescharacteristic, complemented, Sylow
195C24—761no—
196#41—21no—
197#41—381no—
198#41—381no—
199#41—381no—
200#41—761no—
201#41—761no—
202C2×Q8—381no—
203C2×D4—21no—
204C2×D4—382no—
205C2×D4—382no—
206C2×D4—381no—
207C2×D4—381no—
208C2×D4—761no—
209C2×D4—761no—
210C2×D4—761no—
211C2×D4—761no—
212C22×C4—191no—
213C22×C4—761no—
214Q16—191no—
215Q16—381no—
216Q16C22×D1911yescharacteristic, complemented
217SD16—21no—
218SD16—381no—
219SD16—381no—
220SD16—381no—
221D8—21no—
222D8—192no—
223D8—191no—
224D8—382no—
225D8—382no—
226D8—381no—
227D8—381no—
228D8C22×D1912yes—
229D8C22×D1911yescharacteristic, complemented
230C2×C8—191no—
231C2×C8—191no—
232C2×C8—191no—
233C2×C8—191no—
234C2×C8—191no—
235C2×C8C22×D1911yescharacteristic
236C16—192no—
237C16C22×D1912yescomplemented
238C23—41no—
239C23—191no—
240C23—761no—
241C23—762no—
242C23—762no—
243C23—761no—
244C23—1524no—
245Q8—21no—
246Q8—381no—
247Q8—761no—
248D4—22no—
249D4—21no—
250D4—41no—
251D4—41no—
252D4—382no—
253D4—381no—
254D4—761no—
255D4—762no—
256D4—762no—
257D4—761no—
258D4—761no—
259D4—761no—
260D4—761no—
261C2×C4—41no—
262C2×C4—191no—
263C2×C4—191no—
264C2×C4—191no—
265C2×C4—191no—
266C2×C4—191no—
267C2×C4—761no—
268C2×C4—761no—
269C2×C4—761no—
270C2×C4—761no—
271C2×C4D4×D1911yescharacteristic
272C8—191no—
273C8—191no—
274C8D4×D1911yescharacteristic
275C8C23×D1911yescharacteristic
276C22—41no—
277C22—42no—
278C22—82no—
279C22—191no—
280C22—191no—
281C22—382no—
282C22—761no—
283C22—762no—
284C22—1522no—
285C22—1524no—
286C22—1522no—
287C22—1524no—
288C22D8×D1911yescharacteristic
289C4—41no—
290C4—191no—
291C4—191no—
292C4—761no—
293C4D8×D1911yescharacteristic
294C4C2×D4×D1911yescharacteristic
295C2—21no—
296C2—82no—
297C2—81no—
298C2—192no—
299C2—381no—
300C2—1522no—
301C2—1521no—
302C2C2×D8×D1911yescharacteristic
subgroupG/H
centerC2C2×D8×D19
commutator, cosocleC8×C19C24
FrattiniC8C23×D19
FittingC19×#509C2
socleC2×C19C22×D8
hypercenter#509D19
hypocenterC19C2×#509
LCSG ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #135×D19C2semidirect
2. C2×D8×D19C2semidirect
3. #11926982C2semidirect
4. #11926981C2semidirect
5. #11926980C2semidirect
6. #11926979C2semidirect
7. #11926978C2semidirect
8. SD32×D19C2semidirect
9. D16×D19C2semidirect
10. M32×D19C2semidirect
11. C19×#509C2semidirect
14. C19×#135C22semidirect
15. C2×D8×C19C22semidirect
18. #10597365C22semidirect
19. Q16×D19C22semidirect
22. #10597358C22semidirect
26. D8×D19C22semidirect
27. D8×D19C22semidirect
28. #10597350C22semidirect
29. C2×D152C22semidirect
31. C19×SD32C22semidirect
32. C19×D16C22semidirect
33. C19×M32C22semidirect
34. #10597285C22semidirect
35. #10597284C22semidirect
36. #10597283C22semidirect
37. #10597283C22semidirect
38. #10597269C22semidirect
39. #10597257C22semidirect
40. D304C22semidirect
41. #10597255C22semidirect
42. C16×D19C22semidirect
62. Q16×C19C23semidirect
66. D8×C19C23semidirect
75. Dic76C23semidirect
78. D152C23semidirect
84. C16×C19C23semidirect
85. C19⋊C16C23semidirect
151. #509D19direct (N × H)
162. D19#509direct (N × H)
170. #135C2×D19semidirect
180. C2×D8C2×D19semidirect
185. SD32C2×D19semidirect
189. D16C2×D19semidirect
192. M32C2×D19semidirect
194. C19C2×#509semidirect
216. Q16C22×D19semidirect
229. D8C22×D19semidirect
237. C16C22×D19semidirect

Maximal subgroups

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

subgroupindex
#135×D192
C2×D8×D192
#119269822
#119269812
#119269802
#119269792
#119269782
SD32×D192
D16×D192
M32×D192
C19×#5092
C2×#50919