Finite Group Databasebeta

← #14578415

Subgroups — #14578415

Order 2432.

1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.

normal subgroups only

This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 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#11927380C211yesmaximal, characteristic, complemented
2#11927355C218yesmaximal, complemented
3#11927347C218yesmaximal, complemented
4#11927342C216yesmaximal, complemented
5C2×#10597378C216yesmaximal, complemented
6#11927311C211yesmaximal, characteristic, complemented
7C2×C19×H(5,𝔽2)C211yesmaximal, characteristic, complemented
8C19×H(5,𝔽2)—24no—
9C19×H(5,𝔽2)C2218yescomplemented
10C2×#41×C19—21no—
11C2×#41×C19C2211yescharacteristic
12C2×#41×C19C2213yescomplemented
13C22×D4×C19—23no—
14C22×D4×C19C2213yescomplemented
15#10597436C2214yescomplemented
16#10597435C2214yescomplemented
17#41×D19—24no—
18#10597433—21no—
19#10597430—23no—
20C2×#64541C2216yescomplemented
21#10597397C22112yescomplemented
22#10597396C22124yescomplemented
23#10597395C22112yescomplemented
24#10597394C2218yescomplemented
25#10597388C2214yescomplemented
26C2×#64526C22112yescomplemented
27#10597378C22112yescomplemented
28#10597378C22124yescomplemented
29C2×#64525C22112yescomplemented
30C2×#64520C2216yescomplemented
31C24×C19—23no—
32#41×C19—28no—
33#41×C19—26no—
34#41×C19D414yes—
35#41×C19C23112yes—
36#41×C19C2314yes—
37C2×Q8×C19D411yescharacteristic
38C2×Q8×C19C2311yescharacteristic
39C2×D4×C19—23no—
40C2×D4×C19—224no—
41C2×D4×C19—23no—
42C2×D4×C19—26no—
43C2×D4×C19D413yes—
44C2×D4×C19C23112yes—
45C2×D4×C19C2313yes—
46C22×C4×C19—23no—
47C22×C4×C19C2313yes—
48C2×C22⋊D19—26no—
49#64545—24no—
50Q8×D19—24no—
51#64543—212no—
52D4×D19—212no—
53#64541—26no—
54#64541—26no—
55#64541C2314yes—
56#64541C23112yescomplemented
57C2×D76C2316yescomplemented
58C2×C4×D19—26no—
59C2×Dic38C2316yescomplemented
60#64528C2318yescomplemented
61#64527C2318yescomplemented
62#64526C23124yescomplemented
63#64525C23124yescomplemented
64#64520C2314yes—
65#64520C23112yescomplemented
66C2×C19⋊C8C23112yescomplemented
67C23×C19—23no—
68C23×C19—212no—
69C23×C19—86no—
70C23×C19C2×D413yes—
71C22×D19—26no—
72Q8×C19—21no—
73Q8×C19C2×D414yes—
74Q8×C19C2412yes—
75D4×C19—212no—
76D4×C19—212no—
77D4×C19—23no—
78D4×C19C2×D4112yes—
79D4×C19C2416yes—
80C2×C4×C19—21no—
81C2×C4×C19—212no—
82C2×C4×C19C2×D416yes—
83C2×C4×C19C2×D413yes—
84C2×C4×C19C2416yes—
85C2×C4×C19C2411yescharacteristic
86C22⋊D19—24no—
87C22⋊D19—212no—
88C2×Dic19—26no—
89D76—26no—
90D76C2414yes—
91C4×D19—24no—
92C4×D19—212no—
93Dic38—26no—
94Dic38C2414yes—
95C19⋊C8C2418yes—
96#3585—191nomaximal, Sylow
97C22×C19—26no—
98C22×C19—43no—
99C22×C19—46no—
100C22×C19—812no—
101C22×C19C22×D416yes—
102C22×C19C22×D411yescharacteristic
103C2×D19—24no—
104C2×D19—86no—
105C4×C19—22no—
106C4×C19C22×D416yes—
107C4×C19C22×D411yescharacteristic
108C4×C19C2511yescharacteristic
109Dic19—24no—
110#585—191no—
111C2×H(5,𝔽2)D1911yescharacteristic, complemented
112#577—198no—
113#576—198no—
114#575—196no—
115C2×AGL(1,ℤ/8)—196no—
116#568—191no—
117C2×C19—26no—
118C2×C19—21no—
119C2×C19—46no—
120C2×C19C23×D411yescharacteristic
121D19—44no—
1222−1+4—194no—
1232−1+4—381no—
124H(5,𝔽2)—24no—
125H(5,𝔽2)—194no—
126H(5,𝔽2)—383no—
127H(5,𝔽2)C2×D1918yescomplemented
128C2×#41—21no—
129C2×#41—196no—
130C2×#41—384no—
131C2×#41C2×D1911yescharacteristic
132C2×#41C2×D1913yescomplemented
133C22×D4—23no—
134C22×D4C2×D1913yescomplemented
135#137—1912no—
136#137—194no—
137AGL(1,ℤ/8)—1912no—
138AGL(1,ℤ/8)—1912no—
139AGL(1,ℤ/8)—1924no—
140#135—1924no—
141C2×SD16—1912no—
142C2×D8—1912no—
143#131—198no—
144C2×M16—196no—
145C19#358511yescharacteristic, complemented, Sylow
146C24—23no—
147#41—28no—
148#41—26no—
149#41—194no—
150#41—1912no—
151#41—384no—
152#41—3812no—
153#41—386no—
154#41—386no—
155#41C22⋊D1914yes—
156#41C22×D19112yes—
157#41C22×D1914yes—
158C2×Q8—196no—
159C2×Q8—384no—
160C2×Q8C22⋊D1911yescharacteristic
161C2×Q8C22×D1911yescharacteristic
162C2×D4—23no—
163C2×D4—224no—
164C2×D4—23no—
165C2×D4—26no—
166C2×D4—196no—
167C2×D4—386no—
168C2×D4—3812no—
169C2×D4C22⋊D1913yes—
170C2×D4C22×D19112yes—
171C2×D4C22×D1913yes—
172C22×C4—23no—
173C22×C4—386no—
174C22×C4C22×D1913yes—
175Q16—198no—
176SD16—198no—
177SD16—1924no—
178D8—1924no—
179M16—194no—
180M16—1912no—
181C2×C8—1912no—
182C23—23no—
183C23—212no—
184C23—86no—
185C23—386no—
186C23C2×C22⋊D1913yes—
187Q8—21no—
188Q8—194no—
189Q8—386no—
190Q8C2×C22⋊D1914yes—
191Q8C23×D1912yes—
192D4—212no—
193D4—212no—
194D4—23no—
195D4—194no—
196D4—384no—
197D4—3812no—
198D4—386no—
199D4C2×C22⋊D19112yes—
200D4C23×D1916yes—
201C2×C4—21no—
202C2×C4—212no—
203C2×C4—386no—
204C2×C4—384no—
205C2×C4—3812no—
206C2×C4C2×C22⋊D1913yes—
207C2×C4C2×C22⋊D1916yes—
208C2×C4C23×D1916yes—
209C2×C4C23×D1911yescharacteristic
210C8—198no—
211C22—26no—
212C22—43no—
213C22—46no—
214C22—812no—
215C22—384no—
216C22—1526no—
217C22C22×C22⋊D1911yescharacteristic
218C22C22×C22⋊D1916yes—
219C4—22no—
220C4—384no—
221C4C22×C22⋊D1916yes—
222C4C22×C22⋊D1911yescharacteristic
223C4C24×D1911yescharacteristic
224C2—21no—
225C2—26no—
226C2—46no—
227C2—764no—
228C2C23×C22⋊D1911yescharacteristic
subgroupG/H
centerC2C23×C22⋊D19
commutator, cosocleC4×C19C25
FrattiniC4C24×D19
FittingC2×C19×H(5,𝔽2)C2
socleC2×C19C23×D4
hypercenterC2×H(5,𝔽2)D19
hypocenterC19#3585
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×#41 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #11927380C2semidirect
2. #11927355C2semidirect
3. #11927347C2semidirect
4. #11927342C2semidirect
5. C2×#10597378C2semidirect
6. #11927311C2semidirect
7. C2×C19×H(5,𝔽2)C2semidirect
9. C19×H(5,𝔽2)C22semidirect
12. C2×#41×C19C22semidirect
14. C22×D4×C19C22semidirect
15. #10597436C22semidirect
16. #10597435C22semidirect
20. C2×#64541C22semidirect
21. #10597397C22semidirect
22. #10597396C22semidirect
23. #10597395C22semidirect
24. #10597394C22semidirect
25. #10597388C22semidirect
26. C2×#64526C22semidirect
27. #10597378C22semidirect
28. #10597378C22semidirect
29. C2×#64525C22semidirect
30. C2×#64520C22semidirect
56. #64541C23semidirect
57. C2×D76C23semidirect
59. C2×Dic38C23semidirect
60. #64528C23semidirect
61. #64527C23semidirect
62. #64526C23semidirect
63. #64525C23semidirect
65. #64520C23semidirect
66. C2×C19⋊C8C23semidirect
111. C2×H(5,𝔽2)D19semidirect
127. H(5,𝔽2)C2×D19semidirect
132. C2×#41C2×D19semidirect
134. C22×D4C2×D19semidirect
145. C19#3585semidirect

Maximal subgroups

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

subgroupindex
#119273802
#119273552
#119273472
#119273422
C2×#105973782
#119273112
C2×C19×H(5,𝔽2)2
#358519