Finite Group Databasebeta

← #14565658

Subgroups — #14565658

Order 2432.

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

normal subgroups only

This group has 216 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#11927294C211yesmaximal, characteristic, complemented
2#11926729C212yesmaximal, complemented
3#11926716C211yesmaximal, characteristic
4#11926342C212yesmaximal, complemented
5C19×#355C211yesmaximal, characteristic, complemented
6#10597433C2211yescharacteristic
7C19×#124C2211yescharacteristic
8#10597390C2212yes—
9#10597381—21no—
10#10597378—21no—
11#10597355—22no—
12#10597325—22no—
13#10597324—22no—
14#10597316—21no—
15C19×#101C2212yes—
16#10597293C2211yescharacteristic
17#10597282—22no—
18#10597262—21no—
19C2×Q8×C19C2311yescharacteristic
20C2×D4×C19D411yescharacteristic
21C22×Dic19—21no—
22#64545—41no—
23Q8×D19—41no—
24#64541—21no—
25#64541—22no—
26C2×Dic38D412yes—
27M16×C19—22no—
28C22⋊C4×C19—22no—
29C42×C19D411yescharacteristic
30C22⋊Dic19—22no—
31C22⋊Dic19—21no—
32#64526—41no—
33#64525—41no—
34C4⋊Dic19—21no—
35C4⋊Dic19—21no—
36Dic19⋊C4—22no—
37Dic19⋊C4—22no—
38Dic19⋊C4—22no—
39C4×Dic19D412yes—
40#64520—21no—
41Dic76—42no—
42#64516—42no—
43C23×C19—21no—
44Q8×C19—41no—
45D4×C19—41no—
46C2×C4×C19—21no—
47C2×C4×C19C2×D411yescharacteristic
48C2×C4×C19C2×D412yes—
49C22⋊D19—41no—
50C2×Dic19—22no—
51C2×Dic19—22no—
52C2×Dic19—81no—
53D76—22no—
54D76—21no—
55C4×D19—41no—
56C4×D19—42no—
57Dic38—22no—
58Dic38—21no—
59Dic38—42no—
60C8×C19—42no—
61C19⋊C8—41no—
62#2203—191nomaximal, Sylow
63C22×C19—42no—
64C22×C19—41no—
65C22×C19#12011yescharacteristic
66C2×D19—41no—
67C4×C19—21no—
68C4×C19—22no—
69C4×C19—41no—
70Dic19—42no—
71Dic19—41no—
72Dic19—42no—
73#563—191no—
74#456—192no—
75#454—191no—
76#356—192no—
77#355D1911yescharacteristic, complemented
78C2×C19—21no—
79C2×C19—81no—
80C2×C19B(4,𝔽2)11yescharacteristic
81D19—81no—
822−1+4—191no—
83#137—382no—
84AGL(1,ℤ/8)—381no—
85C4⋊Q8—192no—
86#126—382no—
87#125—381no—
88#124C2×D1911yescharacteristic
89#123—381no—
90C22⋊Q8—382no—
91#104—382no—
92#104—381no—
93#101—191no—
94#101C2×D1912yes—
95C19#220311yescharacteristic, complemented, Sylow
96#41—381no—
97#41—382no—
98#41—761no—
99C2×Q8—192no—
100C2×Q8—761no—
101C2×Q8C22×D1911yescharacteristic
102C2×D4D7611yescharacteristic
103C22×C4—381no—
104Q16—762no—
105SD16—762no—
106SD16—761no—
107D8—761no—
108M16—22no—
109M16—381no—
110C4⋊C4—382no—
111C4⋊C4—381no—
112C4⋊C4—381no—
113C4⋊C4—382no—
114C4⋊C4—382no—
115C22⋊C4—22no—
116C22⋊C4—382no—
117C22⋊C4—381no—
118C42—192no—
119C42D7611yescharacteristic
120C23—21no—
121Q8—41no—
122Q8—381no—
123Q8—382no—
124Q8—762no—
125D4—41no—
126D4—381no—
127D4—382no—
128D4—761no—
129C2×C4—21no—
130C2×C4—382no—
131C2×C4—382no—
132C2×C4—762no—
133C2×C4—761no—
134C2×C4—1521no—
135C2×C4C2×D7611yescharacteristic
136C2×C4D4×D1912yes—
137C8—42no—
138C8—761no—
139C22—42no—
140C22—41no—
141C22—761no—
142C22#1059732811yescharacteristic
143C4—22no—
144C4—21no—
145C4—41no—
146C4—762no—
147C4—762no—
148C4—761no—
149C2—21no—
150C2—81no—
151C2—1521no—
152C2#1192673211yescharacteristic
subgroupG/H
centerC2#11926732
commutator, cosocleC2×Q8×C19C23
FrattiniC2×Q8C22×D19
FittingC19×#355C2
socleC2×C19B(4,𝔽2)
prime radical#11926716C2
hypercenter#355D19
hypocenterC19#2203
LCSG ▷ C2×Q8×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
1. #11927294C2semidirect
2. #11926729C2semidirect
4. #11926342C2semidirect
5. C19×#355C2semidirect
77. #355D19semidirect
95. C19#2203semidirect

Maximal subgroups

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

subgroupindex
#119272942
#119267292
#119267162
#119263422
C19×#3552
#220319