Finite Group Databasebeta

← #14565660

Subgroups — #14565660

Order 2432.

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

normal subgroups only

This group has 236 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#11927260C211yesmaximal, characteristic, complemented
2#11926717C212yesmaximal, complemented
3#11926343C211yesmaximal, characteristic, complemented
4#11926340C212yesmaximal, complemented
5C19×#456C211yesmaximal, characteristic, complemented
6C19×2−1+4C2211yescharacteristic
7C19×#137—21no—
8C19×C4⋊Q8C2211yescharacteristic
9#10597395—22no—
10#10597393—21no—
11#10597393C2212yes—
12#10597341—22no—
13#10597338—22no—
14C4×D76—21no—
15C19×#104—21no—
16C19×#101C2211yescharacteristic
17#10597294—22no—
18#10597293C2212yes—
19#41×C19—22no—
20#41×C19—21no—
21#41×C19—41no—
22C2×Q8×C19—41no—
23C2×Q8×C19D411yescharacteristic
24C2×Q8×C19C2311yescharacteristic
25C2×D76—21no—
26C2×D76—21no—
27C2×D76D412yes—
28C2×C4×D19—22no—
29Q16×C19—41no—
30SD16×C19—41no—
31M16×C19—21no—
32C4⋊C4×C19—22no—
33C42×C19D411yescharacteristic
34#64527—42no—
35#64525—42no—
36(C2×D19)⋊C4—22no—
37(C2×D19)⋊C4—22no—
38(C2×D19)⋊C4—22no—
39C4⋊Dic19—21no—
40C4×Dic19—21no—
41C4×Dic19D412yes—
42#64520—22no—
43C22×D19—22no—
44Q8×C19—22no—
45Q8×C19—21no—
46Q8×C19—41no—
47Q8×C19—41no—
48D4×C19—22no—
49D4×C19—21no—
50D4×C19—41no—
51C2×C4×C19—21no—
52C2×C4×C19—21no—
53C2×C4×C19—42no—
54C2×C4×C19—41no—
55C2×C4×C19C2×D412yes—
56C2×C4×C19C2×D411yescharacteristic
57C2×Dic19—22no—
58D76—42no—
59D76—42no—
60D76—81no—
61C4×D19—44no—
62C8×C19—41no—
63C19⋊C8—42no—
64#2204—191nomaximal, Sylow
65C22×C19—41no—
66C22×C19#12011yescharacteristic
67C2×D19—42no—
68C2×D19—42no—
69C2×D19—42no—
70C4×C19—22no—
71C4×C19—22no—
72C4×C19—21no—
73C4×C19—41no—
74C4×C19—41no—
75Dic19—42no—
76#555—191no—
77#456D1911yescharacteristic, complemented
78#454—192no—
79#356—191no—
80#355—192no—
81C2×C19—21no—
82C2×C19—81no—
83C2×C19B(4,𝔽2)11yescharacteristic
84D19—82no—
852−1+4C2×D1911yescharacteristic
86#137—21no—
87AGL(1,ℤ/8)—382no—
88C4⋊Q8C2×D1911yescharacteristic
89#124—192no—
90#124—381no—
91#121—382no—
92C4×D4—381no—
93#117—382no—
94#104—21no—
95#104—382no—
96#101—192no—
97#101C2×D1911yescharacteristic
98C19#220411yescharacteristic, complemented, Sylow
99#41—22no—
100#41—21no—
101#41—41no—
102C2×Q8—41no—
103C2×Q8C22⋊D1911yescharacteristic
104C2×Q8C22×D1911yescharacteristic
105C2×D4—192no—
106C2×D4—381no—
107C2×D4—381no—
108C22×C4—382no—
109Q16—41no—
110SD16—41no—
111SD16—762no—
112D8—762no—
113M16—21no—
114M16—382no—
115C4⋊C4—22no—
116C4⋊C4—381no—
117C22⋊C4—382no—
118C22⋊C4—382no—
119C22⋊C4—382no—
120C42—192no—
121C42—381no—
122C42C22⋊D1911yescharacteristic
123C23—382no—
124Q8—22no—
125Q8—21no—
126Q8—41no—
127Q8—41no—
128D4—22no—
129D4—21no—
130D4—41no—
131D4—762no—
132D4—762no—
133D4—1521no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—382no—
139C2×C4—764no—
140C2×C4D4×D1912yes—
141C2×C4C2×C22⋊D1911yescharacteristic
142C8—41no—
143C8—762no—
144C22—41no—
145C22—762no—
146C22—762no—
147C22—762no—
148C22#1059738311yescharacteristic
149C4—22no—
150C4—21no—
151C4—22no—
152C4—41no—
153C4—41no—
154C4—762no—
155C2—21no—
156C2—81no—
157C2—1522no—
158C2#1192673011yescharacteristic
subgroupG/H
centerC2#11926730
commutator, cosocleC2×Q8×C19C23
FrattiniC2×Q8C22×D19
FittingC19×#456C2
socleC2×C19B(4,𝔽2)
hypercenter#456D19
hypocenterC19#2204
LCSG ▷ C2×Q8×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #11927260C2semidirect
2. #11926717C2semidirect
3. #11926343C2semidirect
4. #11926340C2semidirect
5. C19×#456C2semidirect
77. #456D19semidirect
98. C19#2204semidirect

Maximal subgroups

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

subgroupindex
#119272602
#119267172
#119263432
#119263402
C19×#4562
#220419