Finite Group Databasebeta

← #14578329

Subgroups — #14578329

Order 2432.

958 conjugacy classes of subgroups; only the 449 normal subgroups are shown.

normal subgroups only

This group has 958 conjugacy classes of subgroups — too many to draw. Only its 449 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#11927294C213yesmaximal, complemented
2#11927263C216yesmaximal, complemented
3#11927225C216yesmaximal, complemented
4#11927158C216yesmaximal, complemented
5#11927129C216yesmaximal, complemented
6#11927073C213yesmaximal, complemented
7C19×H(3,𝔽4)C211yesmaximal, characteristic, complemented
8C19×#124C2213yes—
9C19×#124C2216yes—
10C19×#120C2216yes—
11#10597399C2212yescomplemented
12C2×C22⋊Dic19C2216yescomplemented
13#10597392C2213yescomplemented
14Q8×Dic19C2213yescomplemented
15#10597390C2216yescomplemented
16#10597385C2216yes—
17#10597384C2213yes—
18#10597382C2216yes—
19#10597381C2216yes—
20#10597381C2216yes—
21D4×Dic19C2213yes—
22D4×Dic19C2216yes—
23#10597331C2216yescomplemented
24#10597329C2216yescomplemented
25(C22⋊D19)⋊C4C2216yescomplemented
26#10597325C2216yescomplemented
27#10597325C2216yescomplemented
28#10597325C2216yescomplemented
29#10597325C2216yescomplemented
30#10597324C2216yescomplemented
31#10597324C2216yescomplemented
32#10597324C2216yescomplemented
33#10597323C2216yescomplemented
34#10597323C2216yescomplemented
35#10597322C2212yescomplemented
36C42×D19C2211yescharacteristic, complemented
37#10597316C2213yescomplemented
38C4×Dic38C2216yescomplemented
39C24×C19C2312yes—
40C2×Q8×C19C2313yes—
41C2×D4×C19C2313yes—
42C2×D4×C19C2316yes—
43C2×C22⋊D19C2316yes—
44C22×Dic19C2316yes—
45C22×Dic19C2316yes—
46C2×C4×D19C2313yes—
47C2×Dic38C2316yes—
48C22⋊C4×C19C2316yes—
49C22⋊C4×C19C2316yes—
50C22⋊C4×C19C2316yes—
51C42×C19C2312yes—
52C42×C19C2311yescharacteristic
53C22⋊Dic19C2316yes—
54C22⋊Dic19C2316yes—
55C22⋊Dic19C2316yes—
56C22⋊Dic19C2316yes—
57C22⋊Dic19C2316yes—
58(C2×D19)⋊C4C2316yes—
59C4⋊Dic19C2316yes—
60C4⋊Dic19C2313yes—
61C4⋊Dic19C2313yes—
62Dic19⋊C4C2316yes—
63Dic19⋊C4C2316yes—
64Dic19⋊C4C2316yes—
65Dic19⋊C4C2316yes—
66Dic19⋊C4C2316yes—
67C4×Dic19C2316yes—
68C4×Dic19C2313yes—
69C4×Dic19C2316yes—
70C23×C19—46no—
71C23×C19C2416yes—
72C22×D19C2411yescharacteristic
73Q8×C19—43no—
74D4×C19—46no—
75D4×C19—43no—
76C2×C4×C19C2416yes—
77C2×C4×C19C2413yes—
78C22⋊D19—46no—
79C2×Dic19—46no—
80C2×Dic19—46no—
81C2×Dic19C2413yes—
82C2×Dic19C2416yes—
83C2×Dic19C2416yes—
84C4×D19—43no—
85Dic38—46no—
86#3568—191nomaximal, Sylow
87C22×C19—26no—
88C22×C19—26no—
89C22×C19—26no—
90C22×C19—84no—
91C22×C19C2511yescharacteristic
92C2×D19—23no—
93C4×C19—26no—
94C4×C19—23no—
95Dic19—26no—
96Dic19—26no—
97Dic19—23no—
98#563—193no—
99H(3,𝔽4)D1911yescharacteristic, complemented
100#556—196no—
101#551—196no—
102#542—196no—
103#538—196no—
104#529—193no—
105C2×C19—46no—
106C2×C19#58513yes—
107D19—41no—
108C4⋊Q8—196no—
109#126—196no—
110#126—196no—
111#126—196no—
112#126—196no—
113#126—192no—
114#125—193no—
115#124—196no—
116#124—196no—
117#124C2×D1913yes—
118#124C2×D1916yes—
119#123—196no—
120#123—196no—
121#123—196no—
122C22⋊Q8—193no—
123C22⋊Q8—196no—
124C22⋊Q8—196no—
125C22⋊Q8—196no—
126#121—193no—
127#121—196no—
128#120—192no—
129#120C2×D1916yes—
130C4×Q8—193no—
131C4×Q8—196no—
132C4×D4—193no—
133C4×D4—196no—
134C4×D4—196no—
135#117—196no—
136#117—196no—
137C2×C22⋊C4—196no—
138C2×C42—191no—
139C19#356811yescharacteristic, complemented, Sylow
140C24C22×D1912yes—
141C2×Q8—196no—
142C2×Q8C22×D1913yes—
143C2×D4—196no—
144C2×D4C22×D1913yes—
145C2×D4C22×D1916yes—
146C22×C4—196no—
147C22×C4—196no—
148C22×C4—193no—
149C4⋊C4—196no—
150C4⋊C4—196no—
151C4⋊C4—196no—
152C4⋊C4—196no—
153C4⋊C4—196no—
154C4⋊C4—196no—
155C4⋊C4—193no—
156C4⋊C4—193no—
157C22⋊C4—196no—
158C22⋊C4—196no—
159C22⋊C4—196no—
160C22⋊C4—196no—
161C22⋊C4—196no—
162C22⋊C4—196no—
163C22⋊C4C22×D1916yes—
164C22⋊C4C22×D1916yes—
165C22⋊C4C22×D1916yes—
166C42—193no—
167C42—196no—
168C42—196no—
169C42C22×D1911yescharacteristic
170C42C22×D1912yes—
171C23—46no—
172C23—191no—
173C23C23×D1916yes—
174Q8—43no—
175Q8—766no—
176D4—43no—
177D4—46no—
178D4—766no—
179C2×C4—193no—
180C2×C4—196no—
181C2×C4—196no—
182C2×C4—763no—
183C2×C4—766no—
184C2×C4—766no—
185C2×C4C23×D1916yes—
186C2×C4C23×D1913yes—
187C22—26no—
188C22—26no—
189C22—26no—
190C22—84no—
191C22—383no—
192C22C24×D1911yescharacteristic
193C4—23no—
194C4—26no—
195C4—383no—
196C4—386no—
197C4—386no—
198C2—46no—
199C2—761no—
200C2#1192737913yes—
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×H(3,𝔽4)C2
hypercenterH(3,𝔽4)D19
hypocenterC19#3568
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #11927294C2semidirect
2. #11927263C2semidirect
3. #11927225C2semidirect
4. #11927158C2semidirect
5. #11927129C2semidirect
6. #11927073C2semidirect
7. C19×H(3,𝔽4)C2semidirect
11. #10597399C22semidirect
12. C2×C22⋊Dic19C22semidirect
13. #10597392C22semidirect
14. Q8×Dic19C22semidirect
15. #10597390C22semidirect
23. #10597331C22semidirect
24. #10597329C22semidirect
25. (C22⋊D19)⋊C4C22semidirect
26. #10597325C22semidirect
27. #10597325C22semidirect
28. #10597325C22semidirect
29. #10597325C22semidirect
30. #10597324C22semidirect
31. #10597324C22semidirect
32. #10597324C22semidirect
33. #10597323C22semidirect
34. #10597323C22semidirect
35. #10597322C22semidirect
36. C42×D19C22semidirect
37. #10597316C22semidirect
38. C4×Dic38C22semidirect
99. H(3,𝔽4)D19semidirect
139. C19#3568semidirect

Maximal subgroups

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

subgroupindex
#119272942
#119272632
#119272252
#119271582
#119271292
#119270732
C19×H(3,𝔽4)2
#356819