Finite Group Databasebeta

← #14565585

Subgroups — #14565585

Order 2432.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#11927344C211yesmaximal, characteristic
2#11926985C212yesmaximal, complemented
3#11926353C212yesmaximal, complemented
4#11926326C211yesmaximal, characteristic, complemented
5C19×#470C211yesmaximal, characteristic, complemented
6C2×#64541—21no—
7C2×Q16×C19C2211yescharacteristic, complemented
8C2×M16×C19C2211yescharacteristic
9C19×C22⋊Q8—21no—
10#10597355—22no—
11#10597354—22no—
12#10597350—21no—
13#10597350C2212yes—
14C19×#106C2211yescharacteristic, complemented
15C19×#103—21no—
16#10597286—22no—
17#10597285—22no—
18#10597269C2212yescomplemented
19C2×Q8×C19—21no—
20C22×C4×C19D411yescharacteristic
21C2×C22⋊D19—41no—
22#64541—22no—
23#64541—22no—
24#64541—41no—
25#64541—41no—
26C2×D76—21no—
27C2×C4×D19—41no—
28C2×Dic38—21no—
29Q16×C19—22no—
30M16×C19—22no—
31C2×C8×C19D411yescharacteristic
32C2×C8×C19C2311yescharacteristic
33C4⋊C4×C19—21no—
34C4⋊C4×C19—41no—
35C22⋊C4×C19—41no—
36Dic76—21no—
37Dic76D412yes—
38D152—21no—
39D152D412yes—
40#64516—22no—
41#64516—22no—
42C19⋊C16—22no—
43C23×C19D811yescharacteristic
44C22×D19—41no—
45Q8×C19—41no—
46Q8×C19—41no—
47C2×C4×C19—21no—
48C2×C4×C19—21no—
49C2×C4×C19—41no—
50C2×C4×C19—41no—
51C2×C4×C19D811yescharacteristic
52C2×C4×C19C2×D411yescharacteristic
53C22⋊D19—42no—
54C22⋊D19—42no—
55C2×Dic19—41no—
56D76—22no—
57D76—41no—
58C4×D19—42no—
59C4×D19—42no—
60Dic38—22no—
61Dic38—41no—
62C8×C19—21no—
63C8×C19C2×D412yes—
64#2191—191nomaximal, Sylow
65C22×C19—21no—
66C22×C19—41no—
67C22×C19C2×D811yescharacteristic
68C2×D19—42no—
69C2×D19—82no—
70C4×C19—21no—
71C4×C19—81no—
72C4×C19—81no—
73C4×C19#12011yescharacteristic
74C4×C19AGL(1,ℤ/8)11yescharacteristic
75Dic19—42no—
76#575—191no—
77#510—192no—
78#470D1911yescharacteristic, complemented
79#360—192no—
80#349—191no—
81C2×C19—21no—
82C2×C19—41no—
83C2×C19#44711yescharacteristic
84D19—82no—
85C2×#41—381no—
86#137—382no—
87AGL(1,ℤ/8)—382no—
88#135—192no—
89#135—381no—
90C2×Q16C2×D1911yescharacteristic, complemented
91C2×M16C2×D1911yescharacteristic
92C22⋊Q8—21no—
93Q32—382no—
94SD32—382no—
95M32—192no—
96#106C2×D1911yescharacteristic, complemented
97#103—21no—
98C19#219111yescharacteristic, complemented, Sylow
99#41—382no—
100#41—382no—
101#41—761no—
102#41—761no—
103C2×Q8—21no—
104C2×Q8—381no—
105C2×D4—381no—
106C2×D4—761no—
107C22×C4—761no—
108C22×C4C22⋊D1911yescharacteristic
109Q16—22no—
110Q16—192no—
111Q16—381no—
112SD16—382no—
113SD16—382no—
114D8—192no—
115D8—381no—
116M16—22no—
117C2×C8C22⋊D1911yescharacteristic
118C2×C8C22×D1911yescharacteristic
119C4⋊C4—21no—
120C4⋊C4—41no—
121C22⋊C4—41no—
122C16—382no—
123C23—761no—
124C23#6452511yescharacteristic
125Q8—41no—
126Q8—41no—
127Q8—382no—
128Q8—761no—
129D4—382no—
130D4—761no—
131D4—762no—
132D4—762no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—762no—
138C2×C4—761no—
139C2×C4—762no—
140C2×C4#6452511yescharacteristic
141C2×C4C2×C22⋊D1911yescharacteristic
142C8—21no—
143C8D4×D1912yes—
144C22—21no—
145C22—41no—
146C22—762no—
147C22—1522no—
148C22C2×#6452511yescharacteristic
149C4—21no—
150C4—81no—
151C4—81no—
152C4—762no—
153C4#1059738311yescharacteristic
154C4#1059739511yescharacteristic
155C2—21no—
156C2—41no—
157C2—1522no—
158C2#1192667711yescharacteristic
subgroupG/H
centerC2#11926677
commutator, cosocleC2×C8×C19C23
FrattiniC2×C8C22×D19
FittingC19×#470C2
socleC2×C19#447
prime radical#11927344C2
hypercenter#470D19
hypocenterC19#2191
LCSG ▷ C2×C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #11926985C2semidirect
3. #11926353C2semidirect
4. #11926326C2semidirect
5. C19×#470C2semidirect
7. C2×Q16×C19C22semidirect
14. C19×#106C22semidirect
18. #10597269C22semidirect
78. #470D19semidirect
90. C2×Q16C2×D19semidirect
96. #106C2×D19semidirect
98. C19#2191semidirect

Maximal subgroups

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

subgroupindex
#119273442
#119269852
#119263532
#119263262
C19×#4702
#219119