Finite Group Databasebeta

← #14565661

Subgroups — #14565661

Order 2432.

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

normal subgroups only

This group has 236 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#11926726C211yesmaximal, characteristic, complemented
2#11926716C212yesmaximal, complemented
3#11926343C211yesmaximal, characteristic, complemented
4#11926341C212yesmaximal, complemented
5C19×#555C211yesmaximal, characteristic, complemented
6#10597433C2211yescharacteristic
7C19×C4⋊Q8C2211yescharacteristic
8C19×#124—21no—
9C19×#124C2212yes—
10C19×#121—22no—
11C4×D4×C19—21no—
12C19×#117—22no—
13#10597388—21no—
14#10597378—22no—
15#10597293C2211yescharacteristic
16#10597293C2212yes—
17#10597262—22no—
18#10597262—21no—
19C2×Q8×C19D411yescharacteristic
20C2×Q8×C19C2311yescharacteristic
21C2×D4×C19—21no—
22C2×D4×C19—21no—
23C2×D4×C19D412yes—
24C22×C4×C19—22no—
25#64545—41no—
26Q8×D19—41no—
27#64541—22no—
28#64541—21no—
29C4⋊C4×C19—21no—
30C4⋊C4×C19—22no—
31C22⋊C4×C19—22no—
32C22⋊C4×C19—22no—
33C22⋊C4×C19—22no—
34C42×C19—21no—
35C42×C19D412yes—
36C42×C19D411yescharacteristic
37#64528—41no—
38#64527—41no—
39#64526—42no—
40#64525—42no—
41#64520—22no—
42#64520—21no—
43C23×C19—22no—
44Q8×C19—41no—
45Q8×C19—41no—
46D4×C19—42no—
47D4×C19—42no—
48D4×C19—81no—
49C2×C4×C19—21no—
50C2×C4×C19—22no—
51C2×C4×C19—21no—
52C2×C4×C19—44no—
53C2×C4×C19C2×D411yescharacteristic
54C2×C4×C19C2×D412yes—
55C22⋊D19—41no—
56D76—22no—
57D76—21no—
58C4×D19—42no—
59C4×D19—41no—
60Dic38—22no—
61Dic38—21no—
62C19⋊C8—42no—
63C19⋊C8—41no—
64#2204—191nomaximal, Sylow
65C22×C19—42no—
66C22×C19—42no—
67C22×C19—42no—
68C22×C19#12011yescharacteristic
69C2×D19—41no—
70C4×C19—22no—
71C4×C19—22no—
72C4×C19—21no—
73C4×C19—42no—
74C4×C19—41no—
75Dic19—41no—
76#555D1911yescharacteristic, complemented
77#456—191no—
78#454—192no—
79#356—191no—
80#355—192no—
81C2×C19—21no—
82C2×C19—82no—
83C2×C19B(4,𝔽2)11yescharacteristic
84D19—81no—
852−1+4—191no—
86#137—381no—
87AGL(1,ℤ/8)—382no—
88C4⋊Q8C2×D1911yescharacteristic
89#124—21no—
90#124C2×D1912yes—
91#121—22no—
92C4×D4—21no—
93#117—22no—
94#104—382no—
95#104—381no—
96#101—191no—
97#101—192no—
98C19#220411yescharacteristic, complemented, Sylow
99#41—382no—
100#41—381no—
101#41—761no—
102C2×Q8—761no—
103C2×Q8C22⋊D1911yescharacteristic
104C2×Q8C22×D1911yescharacteristic
105C2×D4—21no—
106C2×D4—21no—
107C2×D4C22⋊D1912yes—
108C22×C4—22no—
109Q16—761no—
110SD16—762no—
111SD16—761no—
112D8—762no—
113M16—382no—
114M16—381no—
115C4⋊C4—21no—
116C4⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—22no—
119C22⋊C4—22no—
120C42—21no—
121C42C22⋊D1912yes—
122C42C22⋊D1911yescharacteristic
123C23—22no—
124Q8—41no—
125Q8—41no—
126Q8—382no—
127Q8—381no—
128D4—42no—
129D4—42no—
130D4—81no—
131D4—382no—
132D4—381no—
133D4—761no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—44no—
138C2×C4—762no—
139C2×C4—761no—
140C2×C4C2×C22⋊D1911yescharacteristic
141C2×C4C2×C22⋊D1912yes—
142C8—762no—
143C8—761no—
144C22—42no—
145C22—42no—
146C22—42no—
147C22—761no—
148C22#1059739911yescharacteristic
149C4—22no—
150C4—22no—
151C4—21no—
152C4—42no—
153C4—41no—
154C4—761no—
155C2—21no—
156C2—82no—
157C2—1521no—
158C2#1192673111yescharacteristic
subgroupG/H
centerC2#11926731
commutator, cosocleC2×Q8×C19C23
FrattiniC2×Q8C22×D19
FittingC19×#555C2
socleC2×C19B(4,𝔽2)
hypercenter#555D19
hypocenterC19#2204
LCSG ▷ C2×Q8×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #11926726C2semidirect
2. #11926716C2semidirect
3. #11926343C2semidirect
4. #11926341C2semidirect
5. C19×#555C2semidirect
76. #555D19semidirect
98. C19#2204semidirect

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×#5552
#220419