Finite Group Databasebeta

← #14565648

Subgroups — #14565648

Order 2432.

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

normal subgroups only

This group has 226 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#11926733C212yesmaximal
2#11926721C211yesmaximal, characteristic
3#11926339C211yesmaximal, characteristic, complemented
4#11926334C212yesmaximal, complemented
5C19×#563C211yesmaximal, characteristic, complemented
6#10597430C2211yescharacteristic
7C19×C4⋊Q8—21no—
8C19×#126—22no—
9C19×#125—21no—
10C19×#124C2211yescharacteristic
11C19×#123C2212yes—
12C19×C22⋊Q8—22no—
13#10597388—21no—
14#10597375—22no—
15#10597291C2212yes—
16#10597290C2211yescharacteristic
17#10597263—22no—
18#10597262—21no—
19C2×Q8×C19—21no—
20C2×Q8×C19D411yescharacteristic
21C2×D4×C19C2311yescharacteristic
22C22×C4×C19D412yes—
23C2×C22⋊D19—22no—
24#64543—41no—
25D4×D19—41no—
26#64541—21no—
27C4⋊C4×C19—21no—
28C4⋊C4×C19—22no—
29C4⋊C4×C19—22no—
30C4⋊C4×C19—21no—
31C4⋊C4×C19—22no—
32C22⋊C4×C19—22no—
33C22⋊C4×C19—22no—
34C22⋊C4×C19D412yes—
35C42×C19—21no—
36C42×C19D411yescharacteristic
37C22⋊Dic19—22no—
38#64528—41no—
39#64527—41no—
40(C2×D19)⋊C4—42no—
41Dic19⋊C4—42no—
42#64520—21no—
43C23×C19C2×D412yes—
44C22×D19—22no—
45Q8×C19—41no—
46Q8×C19—81no—
47D4×C19—41no—
48C2×C4×C19—21no—
49C2×C4×C19—22no—
50C2×C4×C19—21no—
51C2×C4×C19—22no—
52C2×C4×C19—42no—
53C2×C4×C19C2×D411yescharacteristic
54C22⋊D19—42no—
55C22⋊D19—41no—
56C2×Dic19—22no—
57C2×Dic19—42no—
58D76—21no—
59C4×D19—41no—
60Dic38—21no—
61C19⋊C8—41no—
62#2201—191nomaximal, Sylow
63C22×C19—22no—
64C22×C19—42no—
65C22×C19#12011yescharacteristic
66C2×D19—41no—
67C2×D19—82no—
68C4×C19—21no—
69C4×C19—42no—
70C4×C19—41no—
71C4×C19—42no—
72C4×C19—41no—
73Dic19—41no—
74Dic19—82no—
75#563D1911yescharacteristic, complemented
76#458—192no—
77#455—191no—
78#354—191no—
79#352—192no—
80C2×C19—21no—
81C2×C19—42no—
82C2×C19B(4,𝔽2)11yescharacteristic
83D19—81no—
84H(5,𝔽2)—191no—
85#137—381no—
86C4⋊Q8—21no—
87#126—22no—
88#125—21no—
89#124C2×D1911yescharacteristic
90#123—382no—
91#123C2×D1912yes—
92C22⋊Q8—22no—
93#104—381no—
94#100—191no—
95#99—192no—
96#99—382no—
97C19#220111yescharacteristic, complemented, Sylow
98#41—381no—
99#41—761no—
100C2×Q8—21no—
101C2×Q8C22⋊D1911yescharacteristic
102C2×D4—382no—
103C2×D4—761no—
104C2×D4C22×D1911yescharacteristic
105C22×C4C22⋊D1912yes—
106Q16—761no—
107SD16—761no—
108M16—381no—
109C4⋊C4—21no—
110C4⋊C4—22no—
111C4⋊C4—22no—
112C4⋊C4—21no—
113C4⋊C4—22no—
114C4⋊C4—762no—
115C22⋊C4—22no—
116C22⋊C4—22no—
117C22⋊C4—382no—
118C22⋊C4—762no—
119C22⋊C4C22⋊D1912yes—
120C42—21no—
121C42C22⋊D1911yescharacteristic
122C23—382no—
123C23C2×C22⋊D1912yes—
124Q8—41no—
125Q8—81no—
126Q8—381no—
127D4—41no—
128D4—381no—
129D4—762no—
130D4—761no—
131C2×C4—21no—
132C2×C4—22no—
133C2×C4—21no—
134C2×C4—22no—
135C2×C4—42no—
136C2×C4—382no—
137C2×C4—761no—
138C2×C4—762no—
139C2×C4C2×C22⋊D1911yescharacteristic
140C8—761no—
141C22—22no—
142C22—42no—
143C22—761no—
144C22—1522no—
145C22#1059739911yescharacteristic
146C4—21no—
147C4—42no—
148C4—41no—
149C4—42no—
150C4—41no—
151C4—761no—
152C4—1522no—
153C2—21no—
154C2—42no—
155C2—1521no—
156C2#1192673111yescharacteristic
subgroupG/H
centerC2#11926731
commutator, cosocleC2×D4×C19C23
FrattiniC2×D4C22×D19
FittingC19×#563C2
socleC2×C19B(4,𝔽2)
prime radical#10597430C22
hypercenter#563D19
hypocenterC19#2201
LCSG ▷ C2×D4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #563

Complements

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

NH ≅ G/Ntype
3. #11926339C2semidirect
4. #11926334C2semidirect
5. C19×#563C2semidirect
75. #563D19semidirect
97. C19#2201semidirect

Maximal subgroups

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

subgroupindex
#119267332
#119267212
#119263392
#119263342
C19×#5632
#220119