Finite Group Databasebeta

← #14565586

Subgroups — #14565586

Order 2432.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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#11926984C212yesmaximal, complemented
2#11926802C211yesmaximal, characteristic, complemented
3#11926354C212yesmaximal, complemented
4#11926326C211yesmaximal, characteristic, complemented
5C19×#575C211yesmaximal, characteristic
6C2×#41×C19—21no—
7C19×#137—22no—
8C19×AGL(1,ℤ/8)—22no—
9C19×#135—21no—
10C19×#135C2212yes—
11C2×M16×C19C2211yescharacteristic
12#10597370—21no—
13C2×Dic76C2211yescharacteristic, complemented
14#10597286—22no—
15#10597284—22no—
16#10597274C2211yescharacteristic, complemented
17#10597273—21no—
18#10597269C2212yescomplemented
19#41×C19—22no—
20#41×C19—22no—
21#41×C19—41no—
22#41×C19—41no—
23C2×Q8×C19—21no—
24C2×D4×C19—21no—
25C2×D4×C19—41no—
26C22×C4×C19—41no—
27C22×C4×C19D411yescharacteristic
28C2×Dic38—21no—
29Q16×C19—21no—
30Q16×C19D412yes—
31SD16×C19—22no—
32SD16×C19—22no—
33D8×C19—21no—
34D8×C19D412yes—
35M16×C19—22no—
36C2×C8×C19D411yescharacteristic
37C2×C8×C19C2311yescharacteristic
38C22⋊Dic19—41no—
39C4⋊Dic19—21no—
40Dic19⋊C4—41no—
41Dic76—22no—
42C19⋊C16—22no—
43C23×C19—41no—
44C23×C19D811yescharacteristic
45Q8×C19—22no—
46Q8×C19—41no—
47D4×C19—22no—
48D4×C19—41no—
49D4×C19—42no—
50D4×C19—42no—
51C2×C4×C19—21no—
52C2×C4×C19—21no—
53C2×C4×C19—42no—
54C2×C4×C19—41no—
55C2×C4×C19—42no—
56C2×C4×C19D811yescharacteristic
57C2×C4×C19C2×D411yescharacteristic
58C2×Dic19—41no—
59C2×Dic19—41no—
60Dic38—41no—
61Dic38—41no—
62C8×C19—21no—
63C8×C19C2×D412yes—
64#2191—191nomaximal, Sylow
65C22×C19—21no—
66C22×C19—41no—
67C22×C19—42no—
68C22×C19—82no—
69C22×C19C2×D811yescharacteristic
70C4×C19—21no—
71C4×C19—42no—
72C4×C19#12011yescharacteristic
73C4×C19AGL(1,ℤ/8)11yescharacteristic
74Dic19—81no—
75Dic19—81no—
76#575D1911yescharacteristic
77#510—192no—
78#470—191no—
79#360—192no—
80#349—191no—
81C2×C19—21no—
82C2×C19—41no—
83C2×C19—82no—
84C2×C19#44711yescharacteristic
85C2×#41—21no—
86#137—22no—
87AGL(1,ℤ/8)—22no—
88#135—21no—
89#135C2×D1912yes—
90C2×Q16—191no—
91C2×M16C2×D1911yescharacteristic
92C22⋊Q8—381no—
93Q32—382no—
94SD32—382no—
95M32—192no—
96#106—191no—
97#103—381no—
98C19#219111yescharacteristic, complemented, Sylow
99#41—22no—
100#41—22no—
101#41—41no—
102#41—41no—
103C2×Q8—21no—
104C2×Q8—381no—
105C2×D4—21no—
106C2×D4—41no—
107C22×C4—41no—
108C22×C4C22⋊D1911yescharacteristic
109Q16—21no—
110Q16—382no—
111Q16C22⋊D1912yes—
112SD16—22no—
113SD16—22no—
114D8—21no—
115D8C22⋊D1912yes—
116M16—22no—
117C2×C8C22⋊D1911yescharacteristic
118C2×C8C22×D1911yescharacteristic
119C4⋊C4—381no—
120C4⋊C4—761no—
121C22⋊C4—761no—
122C16—382no—
123C23—41no—
124C23#6452511yescharacteristic
125Q8—22no—
126Q8—41no—
127Q8—761no—
128Q8—761no—
129D4—22no—
130D4—41no—
131D4—42no—
132D4—42no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—42no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—761no—
139C2×C4—761no—
140C2×C4#6452511yescharacteristic
141C2×C4C2×C22⋊D1911yescharacteristic
142C8—21no—
143C8C2×C22⋊D1912yes—
144C22—21no—
145C22—41no—
146C22—42no—
147C22—82no—
148C22C2×#6452511yescharacteristic
149C4—21no—
150C4—42no—
151C4—1521no—
152C4—1521no—
153C4#1059737811yescharacteristic
154C4#1059739911yescharacteristic
155C2—21no—
156C2—41no—
157C2—82no—
158C2#1192667811yescharacteristic
subgroupG/H
centerC2#11926678
commutator, cosocleC2×C8×C19C23
FrattiniC2×C8C22×D19
Fitting, prime radicalC19×#575C2
socleC2×C19#447
hypercenter#575D19
hypocenterC19#2191
LCSG ▷ C2×C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #11926984C2semidirect
2. #11926802C2semidirect
3. #11926354C2semidirect
4. #11926326C2semidirect
13. C2×Dic76C22semidirect
16. #10597274C22semidirect
18. #10597269C22semidirect
98. C19#2191semidirect

Maximal subgroups

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

subgroupindex
#119269842
#119268022
#119263542
#119263262
C19×#5752
#219119