Finite Group Databasebeta

← #14576768

Subgroups — #14576768

Order 2432.

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

normal subgroups only

This group has 364 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#135×D19C212yesmaximal, complemented
2#11926986C212yesmaximal, complemented
3#11926983C212yesmaximal, complemented
4#11926981C212yesmaximal, complemented
5#11926978C212yesmaximal, complemented
6#11926976C211yesmaximal, characteristic, complemented
7#11926974C212yesmaximal, complemented
8C2×#10597255C211yesmaximal, characteristic, complemented
9C19×#508C211yesmaximal, characteristic, complemented
10#41×D19—22no—
11C19×#135C2212yescomplemented
12#10597396—22no—
13#10597365C2212yes—
14Q16×D19C2212yescomplemented
15#10597362—22no—
16SD16×D19—22no—
17#10597358C2212yes—
18D8×D19C2212yescomplemented
19#10597350C2212yescomplemented
20C2×C8×D19C2211yescharacteristic
21C19×Q32C2211yescharacteristic, complemented
22C19×SD32C2212yescomplemented
23C19×D16C2211yescharacteristic, complemented
24C2×C16×C19C2211yescharacteristic, complemented
25#10597286C2212yescomplemented
26#10597285C2212yescomplemented
27#10597284C2212yescomplemented
28#10597283C2212yescomplemented
29C2×C19⋊C16C2211yescharacteristic, complemented
30Dic152C2211yescharacteristic, complemented
31#10597257C2212yescomplemented
32D304C2211yescharacteristic, complemented
33#10597255C2212yescomplemented
34#10597255C2212yescomplemented
35#41×C19—22no—
36#64545—22no—
37Q8×D19—22no—
38#64543—22no—
39#64543—42no—
40D4×D19—22no—
41D4×D19—42no—
42#64541—22no—
43#64541—42no—
44C2×C4×D19—42no—
45C2×C4×D19D411yescharacteristic
46Q16×C19C2312yes—
47SD16×C19—22no—
48D8×C19C2312yes—
49C2×C8×C19C2311yescharacteristic
50#64528—22no—
51#64527—22no—
52#64526—22no—
53#64525—22no—
54C2×C19⋊C8D411yescharacteristic
55Dic76C2312yes—
56D152C2312yes—
57#64516—22no—
58C8×D19D412yes—
59C8×D19C2312yes—
60C16×C19C2311yescharacteristic
61C16×C19C2311yescharacteristic
62C19⋊C16C2312yes—
63C22×D19—42no—
64C22×D19D811yescharacteristic
65Q8×C19—22no—
66D4×C19—22no—
67D4×C19—42no—
68C2×C4×C19—42no—
69C2×C4×C19C2×D411yescharacteristic
70C22⋊D19—42no—
71C22⋊D19—42no—
72C22⋊D19—42no—
73C2×Dic19—42no—
74C2×Dic19D811yescharacteristic
75D76—22no—
76D76—42no—
77C4×D19—42no—
78C4×D19—42no—
79C4×D19—42no—
80C4×D19D812yes—
81C4×D19C2×D412yes—
82Dic38—22no—
83Dic38—42no—
84C8×C19C2×D411yescharacteristic
85C8×C19C2411yescharacteristic
86C19⋊C8C2×D412yes—
87#3414—191nomaximal, Sylow
88C22×C19—42no—
89C22×C19C2×D811yescharacteristic
90C2×D19—41no—
91C2×D19—42no—
92C2×D19—84no—
93C2×D19C2×D812yes—
94C4×C19—42no—
95C4×C19C2×D811yescharacteristic
96C4×C19C22×D411yescharacteristic
97Dic19—42no—
98Dic19C2×D812yes—
99C2×#135—192no—
100#510—192no—
101#510—192no—
102#509—192no—
103#509—192no—
104#508—192no—
105#508—191no—
106#508D1911yescharacteristic, complemented
107C2×M32—191no—
108C2×C19—21no—
109C2×C19—82no—
110C2×C19C22×D811yescharacteristic
111D19—22no—
112D19—82no—
113C2×#41—382no—
114#135—192no—
115#135—192no—
116#135—192no—
117#135—382no—
118#135—382no—
119#135C2×D1912yescomplemented
120C2×Q16—192no—
121C2×SD16—382no—
122C2×D8—192no—
123C22×C8—191no—
124Q32—192no—
125Q32—191no—
126Q32C2×D1911yescharacteristic, complemented
127SD32—192no—
128SD32—192no—
129SD32—192no—
130SD32C2×D1912yescomplemented
131D16—192no—
132D16—191no—
133D16C2×D1911yescharacteristic, complemented
134M32—192no—
135M32—192no—
136C2×C16—191no—
137C2×C16C2×D1911yescharacteristic, complemented
138C19#341411yescharacteristic, complemented, Sylow
139#41—22no—
140#41—382no—
141#41—382no—
142#41—382no—
143#41—762no—
144#41—762no—
145C2×Q8—382no—
146C2×D4—382no—
147C2×D4—762no—
148C22×C4—191no—
149C22×C4—762no—
150Q16—192no—
151Q16—382no—
152Q16C22×D1912yes—
153SD16—22no—
154SD16—382no—
155SD16—382no—
156SD16—382no—
157D8—192no—
158D8—382no—
159D8C22×D1912yes—
160C2×C8—191no—
161C2×C8—192no—
162C2×C8—192no—
163C2×C8C22×D1911yescharacteristic
164C16—192no—
165C16C22×D1911yescharacteristic
166C16C22×D1911yescharacteristic
167C23—191no—
168C23—762no—
169Q8—22no—
170Q8—382no—
171Q8—762no—
172D4—22no—
173D4—42no—
174D4—382no—
175D4—762no—
176D4—762no—
177D4—762no—
178D4—762no—
179C2×C4—42no—
180C2×C4—191no—
181C2×C4—192no—
182C2×C4—192no—
183C2×C4—762no—
184C2×C4—762no—
185C2×C4—762no—
186C2×C4—762no—
187C2×C4D4×D1911yescharacteristic
188C8—192no—
189C8D4×D1911yescharacteristic
190C8C23×D1911yescharacteristic
191C22—42no—
192C22—192no—
193C22—761no—
194C22—762no—
195C22—1524no—
196C22D8×D1911yescharacteristic
197C4—42no—
198C4—192no—
199C4—762no—
200C4D8×D1911yescharacteristic
201C4C2×D4×D1911yescharacteristic
202C2—21no—
203C2—82no—
204C2—382no—
205C2—1522no—
206C2C2×D8×D1911yescharacteristic
subgroupG/H
centerC4D8×D19
commutator, cosocleC8×C19C24
FrattiniC8C23×D19
FittingC19×#508C2
socleC2×C19C22×D8
hypercenter#508D19
hypocenterC19#3414
LCSG ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #135×D19C2semidirect
2. #11926986C2semidirect
3. #11926983C2semidirect
4. #11926981C2semidirect
5. #11926978C2semidirect
6. #11926976C2semidirect
7. #11926974C2semidirect
8. C2×#10597255C2semidirect
9. C19×#508C2semidirect
11. C19×#135C22semidirect
14. Q16×D19C22semidirect
18. D8×D19C22semidirect
19. #10597350C22semidirect
21. C19×Q32C22semidirect
22. C19×SD32C22semidirect
23. C19×D16C22semidirect
24. C2×C16×C19C22semidirect
25. #10597286C22semidirect
26. #10597285C22semidirect
27. #10597284C22semidirect
28. #10597283C22semidirect
29. C2×C19⋊C16C22semidirect
30. Dic152C22semidirect
31. #10597257C22semidirect
32. D304C22semidirect
33. #10597255C22semidirect
34. #10597255C22semidirect
106. #508D19semidirect
119. #135C2×D19semidirect
126. Q32C2×D19semidirect
130. SD32C2×D19semidirect
133. D16C2×D19semidirect
137. C2×C16C2×D19semidirect
138. C19#3414semidirect

Maximal subgroups

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

subgroupindex
#135×D192
#119269862
#119269832
#119269812
#119269782
#119269762
#119269742
C2×#105972552
C19×#5082
#341419