Finite Group Databasebeta

← #14562676

Subgroups — #14562676

Order 2432.

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

normal subgroups only

This group has 202 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#11927175C211yesmaximal, characteristic
2#11926879C212yesmaximal
3#11926280C212yesmaximal
4#11926270C211yesmaximal, characteristic
5C19×#400C211yesmaximal, characteristic
6C2×C4⋊C4×C19C2211yescharacteristic
7C2×C4⋊C4×C19C2211yescharacteristic
8#10597372—21no—
9#10597370—21no—
10#10597370C2212yes—
11#10597336—22no—
12#10597334—22no—
13C19×#95—21no—
14C19×#95—21no—
15C19×#95C2211yescharacteristic
16C22⋊(C19⋊C8)C2212yes—
17#10597267—22no—
18#10597264—22no—
19C22×C4×C19—21no—
20C22×C4×C19—21no—
21C22×C4×C19D411yescharacteristic
22C22×C4×C19D411yescharacteristic
23C22×C4×C19C2311yescharacteristic
24C2×Dic38—21no—
25C2×Dic38D412yes—
26C4⋊C4×C19—22no—
27C4⋊C4×C19—22no—
28C22⋊Dic19—22no—
29C4⋊Dic19—21no—
30C4⋊Dic19—21no—
31C4⋊Dic19—21no—
32C4⋊Dic19D412yes—
33Dic19⋊C4—22no—
34Dic19⋊C4—22no—
35C4×Dic19—22no—
36C2×C19⋊C8—22no—
37C23×C19C2×D411yescharacteristic
38C2×C4×C19—21no—
39C2×C4×C19—21no—
40C2×C4×C19—21no—
41C2×C4×C19—41no—
42C2×C4×C19—41no—
43C2×C4×C19—41no—
44C2×C4×C19—41no—
45C2×C4×C19—42no—
46C2×C4×C19—41no—
47C2×C4×C19—41no—
48C2×C4×C19Q1612yes—
49C2×C4×C19C2×D412yes—
50C2×Dic19—22no—
51C2×Dic19—22no—
52Dic38—42no—
53Dic38—81no—
54C19⋊C8—42no—
55#1617—191nomaximal, Sylow
56C22×C19—21no—
57C22×C19—21no—
58C22×C19#12011yescharacteristic
59C22×C19C2×Q1611yescharacteristic
60C22×C19#13711yescharacteristic
61C4×C19—22no—
62C4×C19—22no—
63C4×C19—41no—
64C4×C19—81no—
65C4×C19—81no—
66Dic19—42no—
67Dic19—42no—
68#544—191no—
69#484—192no—
70#400D1911yescharacteristic
71#328—192no—
72#324—191no—
73C2×C19—21no—
74C2×C19—21no—
75C2×C19#45111yescharacteristic
76C2×C19#45411yescharacteristic
77C2×C19#45811yescharacteristic
78C4⋊Q8—382no—
79#125—382no—
80C22⋊Q8—192no—
81C22⋊Q8—381no—
82#117—381no—
83C2×C4⋊C4C2×D1911yescharacteristic
84C2×C4⋊C4C2×D1911yescharacteristic
85#107—382no—
86#103—382no—
87C22⋊C8—192no—
88#95—21no—
89#95—21no—
90#95C2×D1911yescharacteristic
91C19#161711yescharacteristic, complemented, Sylow
92C2×Q8—192no—
93C2×Q8—381no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4C22⋊D1911yescharacteristic
97C22×C4C22⋊D1911yescharacteristic
98C22×C4C22×D1911yescharacteristic
99C2×C8—382no—
100C4⋊C4—22no—
101C4⋊C4—22no—
102C4⋊C4—192no—
103C4⋊C4—382no—
104C4⋊C4—381no—
105C4⋊C4—381no—
106C4⋊C4—381no—
107C4⋊C4—382no—
108C22⋊C4—382no—
109C42—382no—
110C23C2×C22⋊D1911yescharacteristic
111Q8—762no—
112Q8—1521no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—42no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—382no—
124C2×C4—382no—
125C2×C4#6452812yes—
126C2×C4D4×D1912yes—
127C8—762no—
128C22—21no—
129C22—21no—
130C22#1059738311yescharacteristic
131C22C2×#6452811yescharacteristic
132C22#1059739711yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—81no—
137C4—81no—
138C4—762no—
139C4—762no—
140C2—21no—
141C2—21no—
142C2#1192669911yescharacteristic
143C2#1192671611yescharacteristic
144C2#1192673311yescharacteristic
subgroupG/H
centerC22#10597383
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC19×#400C2
socleC22×C19#120
prime radicalC23×C19C2×D4
hypercenter#400D19
hypocenterC19#1617
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
91. C19#1617semidirect

Maximal subgroups

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

subgroupindex
#119271752
#119268792
#119262802
#119262702
C19×#4002
#161719