Finite Group Databasebeta

← #14565656

Subgroups — #14565656

Order 2432.

216 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 45 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#11926726C212yesmaximal, complemented
2#11926716C211yesmaximal, characteristic
3#11926343C212yesmaximal, complemented
4#11926341C211yesmaximal, characteristic, complemented
5C19×#563C211yesmaximal, characteristic, complemented
6#10597433C2211yescharacteristic
7C19×C4⋊Q8C2212yes—
8C19×#126—22no—
9C19×#125—21no—
10C19×#124C2211yescharacteristic
11C19×#123—21no—
12C19×C22⋊Q8—22no—
13#10597388—22no—
14#10597378—21no—
15#10597293C2212yes—
16#10597293C2211yescharacteristic
17#10597262—21no—
18#10597262—22no—
19C2×Q8×C19D412yes—
20C2×Q8×C19C2311yescharacteristic
21C2×D4×C19D411yescharacteristic
22C22×C4×C19—21no—
23#64545—41no—
24Q8×D19—41no—
25#64541—21no—
26#64541—22no—
27C4⋊C4×C19—21no—
28C4⋊C4×C19—22no—
29C4⋊C4×C19—21no—
30C4⋊C4×C19—22no—
31C4⋊C4×C19—22no—
32C22⋊C4×C19—22no—
33C22⋊C4×C19—21no—
34C22⋊C4×C19—22no—
35C42×C19D411yescharacteristic
36C42×C19D412yes—
37#64528—42no—
38#64527—42no—
39#64526—41no—
40#64525—41no—
41#64520—21no—
42#64520—22no—
43C23×C19—21no—
44Q8×C19—41no—
45Q8×C19—42no—
46D4×C19—41no—
47C2×C4×C19—21no—
48C2×C4×C19—22no—
49C2×C4×C19—22no—
50C2×C4×C19—81no—
51C2×C4×C19C2×D412yes—
52C2×C4×C19C2×D411yescharacteristic
53C22⋊D19—41no—
54D76—21no—
55D76—22no—
56C4×D19—41no—
57C4×D19—42no—
58Dic38—21no—
59Dic38—22no—
60C19⋊C8—41no—
61C19⋊C8—42no—
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—
70C4×C19—42no—
71C4×C19—42no—
72Dic19—41no—
73#563D1911yescharacteristic, complemented
74#456—192no—
75#454—191no—
76#356—192no—
77#355—191no—
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⋊Q8C2×D1912yes—
86#126—22no—
87#125—21no—
88#124C2×D1911yescharacteristic
89#123—21no—
90C22⋊Q8—22no—
91#104—381no—
92#104—382no—
93#101—192no—
94#101—191no—
95C19#220311yescharacteristic, complemented, Sylow
96#41—381no—
97#41—382no—
98#41—761no—
99C2×Q8—761no—
100C2×Q8C22⋊D1912yes—
101C2×Q8C22×D1911yescharacteristic
102C2×D4C22⋊D1911yescharacteristic
103C22×C4—21no—
104Q16—762no—
105SD16—761no—
106SD16—762no—
107D8—761no—
108M16—381no—
109M16—382no—
110C4⋊C4—21no—
111C4⋊C4—22no—
112C4⋊C4—21no—
113C4⋊C4—22no—
114C4⋊C4—22no—
115C22⋊C4—22no—
116C22⋊C4—21no—
117C22⋊C4—22no—
118C42C22⋊D1911yescharacteristic
119C42C22⋊D1912yes—
120C23—21no—
121Q8—41no—
122Q8—42no—
123Q8—381no—
124Q8—382no—
125D4—41no—
126D4—381no—
127D4—382no—
128D4—761no—
129C2×C4—21no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—81no—
133C2×C4—761no—
134C2×C4—762no—
135C2×C4C2×C22⋊D1912yes—
136C2×C4C2×C22⋊D1911yescharacteristic
137C8—761no—
138C8—762no—
139C22—42no—
140C22—41no—
141C22—761no—
142C22#1059739911yescharacteristic
143C4—21no—
144C4—22no—
145C4—41no—
146C4—42no—
147C4—42no—
148C4—761no—
149C2—21no—
150C2—81no—
151C2—1521no—
152C2#1192673111yescharacteristic
subgroupG/H
centerC2#11926731
commutator, cosocleC2×Q8×C19C23
FrattiniC2×Q8C22×D19
FittingC19×#563C2
socleC2×C19B(4,𝔽2)
prime radical#11926716C2
hypercenter#563D19
hypocenterC19#2203
LCSG ▷ C2×Q8×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #11926726C2semidirect
3. #11926343C2semidirect
4. #11926341C2semidirect
5. C19×#563C2semidirect
73. #563D19semidirect
95. C19#2203semidirect

Maximal subgroups

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

subgroupindex
#119267262
#119267162
#119263432
#119263412
C19×#5632
#220319