Finite Group Databasebeta

← #14565580

Subgroups — #14565580

Order 2432.

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

normal subgroups only

This group has 226 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, complemented
2#11926980C212yesmaximal, complemented
3#11926353C212yesmaximal, complemented
4#11926326C211yesmaximal, characteristic, complemented
5C19×#469C211yesmaximal, characteristic, complemented
6C2×#64541—21no—
7C2×D8×C19C2211yescharacteristic, complemented
8C2×M16×C19C2211yescharacteristic
9C19×#121—21no—
10#10597355—22no—
11#10597354—22no—
12#10597350—21no—
13#10597350C2212yes—
14C19×#106C2211yescharacteristic, complemented
15C19×#102—21no—
16#10597284—22no—
17#10597283—22no—
18#10597269C2212yescomplemented
19C2×D4×C19—21no—
20C2×D4×C19—41no—
21C22×C4×C19D411yescharacteristic
22C2×C22⋊D19—41no—
23#64541—22no—
24#64541—22no—
25#64541—41no—
26#64541—41no—
27C2×D76—21no—
28C2×C4×D19—41no—
29C2×Dic38—21no—
30D8×C19—22no—
31M16×C19—22no—
32C2×C8×C19D411yescharacteristic
33C2×C8×C19C2311yescharacteristic
34C4⋊C4×C19—21no—
35C22⋊C4×C19—41no—
36Dic76—21no—
37Dic76D412yescomplemented
38D152—21no—
39D152D412yescomplemented
40#64516—22no—
41#64516—22no—
42C19⋊C16—22no—
43C23×C19—41no—
44C23×C19D811yescharacteristic
45C22×D19—41no—
46D4×C19—41no—
47D4×C19—41no—
48D4×C19—82no—
49C2×C4×C19—21no—
50C2×C4×C19—21no—
51C2×C4×C19—41no—
52C2×C4×C19D811yescharacteristic
53C2×C4×C19C2×D411yescharacteristic
54C22⋊D19—42no—
55C22⋊D19—42no—
56C2×Dic19—41no—
57D76—22no—
58D76—41no—
59C4×D19—42no—
60C4×D19—42no—
61Dic38—22no—
62Dic38—41no—
63C8×C19—21no—
64C8×C19C2×D412yes—
65#2190—191nomaximal, Sylow
66C22×C19—21no—
67C22×C19—41no—
68C22×C19—81no—
69C22×C19—81no—
70C22×C19—81no—
71C22×C19C2×D811yescharacteristic
72C2×D19—42no—
73C2×D19—82no—
74C4×C19—21no—
75C4×C19—81no—
76C4×C19#12011yescharacteristic
77C4×C19AGL(1,ℤ/8)11yescharacteristic
78Dic19—42no—
79#575—191no—
80#509—192no—
81#469D1911yescharacteristic, complemented
82#360—192no—
83#349—191no—
84C2×C19—21no—
85C2×C19—41no—
86C2×C19—161no—
87C2×C19#44711yescharacteristic
88D19—82no—
89C2×#41—381no—
90#137—382no—
91AGL(1,ℤ/8)—382no—
92#135—192no—
93#135—381no—
94C2×D8C2×D1911yescharacteristic, complemented
95C2×M16C2×D1911yescharacteristic
96#121—21no—
97SD32—382no—
98D16—382no—
99M32—192no—
100#106C2×D1911yescharacteristic, complemented
101#102—21no—
102C19#219011yescharacteristic, complemented, Sylow
103#41—382no—
104#41—382no—
105#41—761no—
106#41—761no—
107C2×Q8—381no—
108C2×D4—21no—
109C2×D4—41no—
110C2×D4—381no—
111C2×D4—761no—
112C22×C4—761no—
113C22×C4C22⋊D1911yescharacteristic
114Q16—192no—
115Q16—381no—
116SD16—382no—
117SD16—382no—
118D8—22no—
119D8—192no—
120D8—381no—
121M16—22no—
122C2×C8C22⋊D1911yescharacteristic
123C2×C8C22×D1911yescharacteristic
124C4⋊C4—21no—
125C22⋊C4—41no—
126C16—382no—
127C23—41no—
128C23—761no—
129C23#6452511yescharacteristic
130Q8—382no—
131Q8—761no—
132D4—41no—
133D4—41no—
134D4—82no—
135D4—382no—
136D4—761no—
137D4—762no—
138D4—762no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—41no—
142C2×C4—762no—
143C2×C4—761no—
144C2×C4—762no—
145C2×C4#6452511yescharacteristic
146C2×C4C2×C22⋊D1911yescharacteristic
147C8—21no—
148C8D4×D1912yes—
149C22—21no—
150C22—41no—
151C22—81no—
152C22—81no—
153C22—81no—
154C22—762no—
155C22—1522no—
156C22C2×#6452511yescharacteristic
157C4—21no—
158C4—81no—
159C4—762no—
160C4#1059738311yescharacteristic
161C4#1059739511yescharacteristic
162C2—21no—
163C2—41no—
164C2—161no—
165C2—1522no—
166C2#1192667711yescharacteristic
subgroupG/H
centerC2#11926677
commutator, cosocleC2×C8×C19C23
FrattiniC2×C8C22×D19
FittingC19×#469C2
socleC2×C19#447
hypercenter#469D19
hypocenterC19#2190
LCSG ▷ C2×C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #11927344C2semidirect
2. #11926980C2semidirect
3. #11926353C2semidirect
4. #11926326C2semidirect
5. C19×#469C2semidirect
7. C2×D8×C19C22semidirect
14. C19×#106C22semidirect
18. #10597269C22semidirect
37. Dic76D4semidirect
39. D152D4semidirect
81. #469D19semidirect
94. C2×D8C2×D19semidirect
100. #106C2×D19semidirect
102. C19#2190semidirect

Maximal subgroups

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

subgroupindex
#119273442
#119269802
#119263532
#119263262
C19×#4692
#219019