Finite Group Databasebeta

← #14565635

Subgroups — #14565635

Order 2432.

270 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 41 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#11927286C211yesmaximal, characteristic, complemented
2#11926731C212yesmaximal, complemented
3#11926339C211yesmaximal, characteristic, complemented
4#11926332C212yesmaximal, complemented
5C19×#455C211yesmaximal, characteristic, complemented
6C19×H(5,𝔽2)C2211yescharacteristic
7C19×#137—21no—
8C19×#124C2211yescharacteristic
9#10597393—21no—
10#10597383—22no—
11#10597383C2212yes—
12#10597331—22no—
13#10597328—22no—
14#10597321—21no—
15C19×#104—21no—
16C19×#100C2211yescharacteristic
17#10597291—22no—
18#10597291C2212yes—
19C23×D19D412yescomplemented
20#41×C19—21no—
21#41×C19—41no—
22C2×Q8×C19D411yescharacteristic, complemented
23C2×D4×C19—22no—
24C2×D4×C19—41no—
25C2×D4×C19C2311yescharacteristic
26C2×C22⋊D19—22no—
27C2×C22⋊D19—42no—
28C2×D76—21no—
29C2×D76—21no—
30C2×Dic38—21no—
31Q16×C19—41no—
32SD16×C19—41no—
33M16×C19—21no—
34C22⋊C4×C19—22no—
35C42×C19D411yescharacteristic, complemented
36C22⋊Dic19—22no—
37C22⋊Dic19D412yescomplemented
38(C2×D19)⋊C4—22no—
39(C2×D19)⋊C4—22no—
40(C2×D19)⋊C4—22no—
41(C2×D19)⋊C4—42no—
42C4×Dic19—21no—
43C23×C19—22no—
44C23×C19C2×D412yes—
45C22×D19—22no—
46C22×D19—42no—
47C22×D19—82no—
48Q8×C19—21no—
49Q8×C19—41no—
50D4×C19—21no—
51D4×C19—41no—
52D4×C19—42no—
53D4×C19—41no—
54C2×C4×C19—22no—
55C2×C4×C19—21no—
56C2×C4×C19—21no—
57C2×C4×C19—41no—
58C2×C4×C19C2×D411yescharacteristic
59C22⋊D19—82no—
60C22⋊D19—84no—
61C2×Dic19—22no—
62C2×Dic19—42no—
63D76—81no—
64D76—81no—
65Dic38—81no—
66C8×C19—41no—
67#2199—191nomaximal, Sylow
68C22×C19—22no—
69C22×C19—42no—
70C22×C19—41no—
71C22×C19—82no—
72C22×C19#12011yescharacteristic
73C2×D19—42no—
74C2×D19—42no—
75C2×D19—44no—
76C2×D19—42no—
77C2×D19—82no—
78C4×C19—21no—
79C4×C19—41no—
80C4×C19—41no—
81C4×C19—41no—
82Dic19—42no—
83Dic19—82no—
84H(3,𝔽4)—191no—
85B(4,𝔽2)—192no—
86#455D1911yescharacteristic, complemented
87#354—191no—
88AΣL(1,𝔽16)—192no—
89C2×C19—21no—
90C2×C19—42no—
91C2×C19—81no—
92C2×C19B(4,𝔽2)11yescharacteristic
93D19—82no—
94H(5,𝔽2)C2×D1911yescharacteristic
95#137—21no—
96#124—382no—
97#124—381no—
98#124—381no—
99#124C2×D1911yescharacteristic
100#120—192no—
101#120—382no—
102#120—382no—
103#104—21no—
104#100C2×D1911yescharacteristic
105#99—192no—
106#99—382no—
107C19#219911yescharacteristic, complemented, Sylow
108C24—192no—
109#41—21no—
110#41—41no—
111C2×Q8—381no—
112C2×Q8C22⋊D1911yescharacteristic, complemented
113C2×D4—22no—
114C2×D4—41no—
115C2×D4—381no—
116C2×D4—381no—
117C2×D4—382no—
118C2×D4—762no—
119C2×D4C22×D1911yescharacteristic
120Q16—41no—
121SD16—41no—
122M16—21no—
123C22⋊C4—22no—
124C22⋊C4—192no—
125C22⋊C4—382no—
126C22⋊C4—382no—
127C22⋊C4—382no—
128C22⋊C4—382no—
129C22⋊C4—762no—
130C42—381no—
131C42C22⋊D1911yescharacteristic, complemented
132C23—22no—
133C23—382no—
134C23—762no—
135C23—1522no—
136C23D4×D1912yes—
137Q8—21no—
138Q8—41no—
139Q8—1521no—
140D4—21no—
141D4—41no—
142D4—42no—
143D4—41no—
144D4—1521no—
145D4—1521no—
146D4—1522no—
147D4—1524no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—382no—
153C2×C4—762no—
154C2×C4C2×C22⋊D1911yescharacteristic
155C8—41no—
156C22—22no—
157C22—42no—
158C22—41no—
159C22—82no—
160C22—762no—
161C22—762no—
162C22—764no—
163C22—762no—
164C22—1522no—
165C22#1059738311yescharacteristic
166C4—21no—
167C4—41no—
168C4—41no—
169C4—41no—
170C4—762no—
171C4—1522no—
172C2—21no—
173C2—42no—
174C2—81no—
175C2—1522no—
176C2#1192673011yescharacteristic
subgroupG/H
centerC2#11926730
commutator, cosocleC2×D4×C19C23
FrattiniC2×D4C22×D19
FittingC19×#455C2
socleC2×C19B(4,𝔽2)
hypercenter#455D19
hypocenterC19#2199
LCSG ▷ C2×D4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #11927286C2semidirect
2. #11926731C2semidirect
3. #11926339C2semidirect
4. #11926332C2semidirect
5. C19×#455C2semidirect
19. C23×D19D4semidirect
22. C2×Q8×C19D4semidirect
35. C42×C19D4semidirect
37. C22⋊Dic19D4semidirect
86. #455D19semidirect
107. C19#2199semidirect
112. C2×Q8C22⋊D19semidirect
131. C42C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
#119272862
#119267312
#119263392
#119263322
C19×#4552
#219919