Finite Group Databasebeta

← #14576775

Subgroups — #14576775

Order 2432.

370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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#11927346C211yesmaximal, characteristic, complemented
2#11927345C211yesmaximal, characteristic, complemented
3#11926982C211yesmaximal, characteristic, complemented
4#11926981C212yesmaximal, complemented
5#11926978C212yesmaximal, complemented
6#11926975C212yesmaximal, complemented
7#11926974C211yesmaximal, characteristic, complemented
8C2×#10597283C211yesmaximal, characteristic, complemented
9D16×D19C212yesmaximal, complemented
10#11926962C211yesmaximal, characteristic, complemented
11C19×#509C211yesmaximal, characteristic, complemented
12#10597435—21no—
13#10597430—21no—
14C19×#135C2211yescharacteristic, complemented
15C2×D8×C19C2211yescharacteristic, complemented
16#10597395—21no—
17#10597378—21no—
18#10597365C2212yescomplemented
19#10597360—22no—
20#10597358C2212yescomplemented
21#10597357—22no—
22D8×D19C2212yescomplemented
23D8×D19C2212yescomplemented
24#10597350C2211yescharacteristic, complemented
25C2×D152C2211yescharacteristic, complemented
26#10597347C2211yescharacteristic
27C19×SD32C2212yescomplemented
28C19×D16C2212yescomplemented
29C19×M32C2211yescharacteristic, complemented
30#10597286C2211yescharacteristic, complemented
31#10597285C2211yescharacteristic, complemented
32#10597284C2211yescharacteristic, complemented
33#10597283C2211yescharacteristic, complemented
34#10597283C2212yescomplemented
35#10597283C2212yescomplemented
36C2×C19⋊C16C2211yescharacteristic, complemented
37#10597257C2212yescomplemented
38D304C2212yescomplemented
39#10597255C2212yescomplemented
40C16×D19C2212yescomplemented
41#41×C19—21no—
42C2×D4×C19—21no—
43C2×C22⋊D19—42no—
44#64545—22no—
45#64543—22no—
46#64543—41no—
47D4×D19—22no—
48D4×D19—22no—
49D4×D19—42no—
50D4×D19—41no—
51#64541—21no—
52#64541—41no—
53#64541D411yescharacteristic
54C2×D76—21no—
55C2×D76—41no—
56Q16×C19C2311yescharacteristic
57SD16×C19—21no—
58D8×C19—21no—
59D8×C19C2312yes—
60D8×C19C2311yescharacteristic
61C2×C8×C19C2311yescharacteristic
62#64527—22no—
63#64526—22no—
64#64525—22no—
65#64525—22no—
66#64520D411yescharacteristic
67Dic76C2311yescharacteristic
68D152—21no—
69D152C2311yescharacteristic
70D152C2312yes—
71#64516—21no—
72#64515D412yes—
73C8×D19C2312yes—
74C16×C19C2312yes—
75C19⋊C16C2311yescharacteristic
76C19⋊C16C2311yescharacteristic
77C23×C19—41no—
78C22×D19—41no—
79C22×D19—42no—
80C22×D19—42no—
81Q8×C19—21no—
82D4×C19—21no—
83D4×C19—22no—
84D4×C19—41no—
85D4×C19—41no—
86C2×C4×C19—41no—
87C2×C4×C19C2×D411yescharacteristic
88C22⋊D19—41no—
89C22⋊D19—42no—
90C22⋊D19—42no—
91C22⋊D19—42no—
92C22⋊D19D812yes—
93C2×Dic19—42no—
94D76—21no—
95D76—22no—
96D76—42no—
97D76—41no—
98D76D811yescharacteristic
99C4×D19—41no—
100C4×D19—42no—
101C4×D19C2×D412yes—
102Dic38—21no—
103Dic38D811yescharacteristic
104C8×C19C2×D411yescharacteristic
105C8×C19C2411yescharacteristic
106C19⋊C8C2×D412yes—
107#3415—191nomaximal, Sylow
108C22×C19—42no—
109C22×C19—41no—
110C22×C19—161no—
111C22×C19C2×D811yescharacteristic
112C2×D19—42no—
113C2×D19—41no—
114C2×D19—162no—
115C2×D19—162no—
116C2×D19—161no—
117C2×D19C2×D812yes—
118C4×C19—41no—
119C4×C19C2×D811yescharacteristic
120C4×C19C22×D411yescharacteristic
121Dic19—41no—
122Dic19C2×D812yes—
123#576—191no—
124#576—191no—
125#509—192no—
126#509—192no—
127#509—191no—
128#509D1911yescharacteristic, complemented
129#508—191no—
130#508—192no—
131C2×D16—191no—
132C2×D16—192no—
133#504—191no—
134C2×C19—21no—
135C2×C19—81no—
136C2×C19—82no—
137C2×C19C22×D811yescharacteristic
138D19—22no—
139D19—82no—
140D19—81no—
141H(5,𝔽2)—381no—
142H(5,𝔽2)—381no—
143AGL(1,ℤ/8)—382no—
144AGL(1,ℤ/8)—382no—
145AGL(1,ℤ/8)—381no—
146AGL(1,ℤ/8)—381no—
147#135—192no—
148#135—192no—
149#135—191no—
150#135C2×D1911yescharacteristic, complemented
151C2×D8—192no—
152C2×D8—192no—
153C2×D8—191no—
154C2×D8C2×D1911yescharacteristic, complemented
155#131—191no—
156Q32—191no—
157SD32—191no—
158SD32—191no—
159SD32—192no—
160SD32C2×D1912yescomplemented
161D16—192no—
162D16—191no—
163D16—192no—
164D16—192no—
165D16C2×D1912yescomplemented
166M32—192no—
167M32C2×D1911yescharacteristic, complemented
168C2×C16—191no—
169C2×C16—192no—
170C19#341511yescharacteristic, complemented, Sylow
171#41—21no—
172#41—191no—
173#41—382no—
174#41—382no—
175#41—381no—
176#41—761no—
177#41—761no—
178C2×D4—21no—
179C2×D4—382no—
180C2×D4—382no—
181C2×D4—381no—
182C2×D4—761no—
183C2×D4—762no—
184C2×D4—761no—
185C2×D4—762no—
186Q16—191no—
187Q16C22×D1911yescharacteristic
188SD16—21no—
189SD16—382no—
190SD16—382no—
191SD16—381no—
192D8—21no—
193D8—191no—
194D8—192no—
195D8—382no—
196D8—382no—
197D8—381no—
198D8C22×D1912yes—
199D8C22×D1911yescharacteristic
200M16—191no—
201M16—192no—
202C2×C8—192no—
203C2×C8C22×D1911yescharacteristic
204C16—191no—
205C16—191no—
206C16C22×D1912yes—
207C23—41no—
208C23—762no—
209C23—762no—
210C23—761no—
211Q8—21no—
212Q8—191no—
213Q8—381no—
214D4—22no—
215D4—21no—
216D4—41no—
217D4—41no—
218D4—192no—
219D4—191no—
220D4—381no—
221D4—382no—
222D4—762no—
223D4—762no—
224D4—762no—
225D4—762no—
226D4—761no—
227D4—761no—
228C2×C4—41no—
229C2×C4—192no—
230C2×C4—762no—
231C2×C4—762no—
232C2×C4—761no—
233C2×C4D4×D1911yescharacteristic
234C8—192no—
235C8D4×D1911yescharacteristic
236C8C23×D1911yescharacteristic
237C22—41no—
238C22—42no—
239C22—161no—
240C22—192no—
241C22—3041no—
242C22—3042no—
243C22—3042no—
244C22—762no—
245C22—761no—
246C22D8×D1911yescharacteristic
247C4—41no—
248C4—192no—
249C4—761no—
250C4D8×D1911yescharacteristic
251C4C2×D4×D1911yescharacteristic
252C2—21no—
253C2—82no—
254C2—81no—
255C2—382no—
256C2—1522no—
257C2—1521no—
258C2C2×D8×D1911yescharacteristic
subgroupG/H
centerC2C2×D8×D19
commutator, cosocleC8×C19C24
FrattiniC8C23×D19
FittingC19×#509C2
socleC2×C19C22×D8
hypercenter#509D19
hypocenterC19#3415
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. #11927346C2semidirect
2. #11927345C2semidirect
3. #11926982C2semidirect
4. #11926981C2semidirect
5. #11926978C2semidirect
6. #11926975C2semidirect
7. #11926974C2semidirect
8. C2×#10597283C2semidirect
9. D16×D19C2semidirect
10. #11926962C2semidirect
11. C19×#509C2semidirect
14. C19×#135C22semidirect
15. C2×D8×C19C22semidirect
18. #10597365C22semidirect
20. #10597358C22semidirect
22. D8×D19C22semidirect
23. D8×D19C22semidirect
24. #10597350C22semidirect
25. C2×D152C22semidirect
27. C19×SD32C22semidirect
28. C19×D16C22semidirect
29. C19×M32C22semidirect
30. #10597286C22semidirect
31. #10597285C22semidirect
32. #10597284C22semidirect
33. #10597283C22semidirect
34. #10597283C22semidirect
35. #10597283C22semidirect
36. C2×C19⋊C16C22semidirect
37. #10597257C22semidirect
38. D304C22semidirect
39. #10597255C22semidirect
40. C16×D19C22semidirect
128. #509D19semidirect
150. #135C2×D19semidirect
154. C2×D8C2×D19semidirect
160. SD32C2×D19semidirect
165. D16C2×D19semidirect
167. M32C2×D19semidirect
170. C19#3415semidirect

Maximal subgroups

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

subgroupindex
#119273462
#119273452
#119269822
#119269812
#119269782
#119269752
#119269742
C2×#105972832
D16×D192
#119269622
C19×#5092
#341519