Finite Group Databasebeta

← #14562645

Subgroups — #14562645

Order 2432.

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

normal subgroups only

This group has 210 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#11926875C212yesmaximal
3#11926474C211yesmaximal, characteristic
4#11926282C212yesmaximal
5C19×#324C211yesmaximal, characteristic
6C2×C4⋊C4×C19C2211yescharacteristic
7#10597372—21no—
8C2×C4⋊Dic19C2211yescharacteristic
9#10597370—21no—
10#10597370C2212yes—
11C2×Dic19⋊C4—21no—
12#10597336—22no—
13#10597334—22no—
14C19×C22⋊C8C2212yes—
15C19⋊#95—21no—
16C19⋊#95C2211yescharacteristic
17#10597274—22no—
18#10597273—22no—
19C22×C4×C19D411yescharacteristic
20C22×C4×C19D411yescharacteristic
21C22×C4×C19C2311yescharacteristic
22C22×Dic19—21no—
23C22×Dic19—21no—
24C2×Dic38—21no—
25C2×Dic38D412yes—
26C2×C8×C19—22no—
27C4⋊C4×C19—22no—
28C22⋊Dic19—22no—
29C4⋊Dic19—21no—
30C4⋊Dic19—21no—
31C4⋊Dic19—21no—
32C4⋊Dic19—22no—
33C4⋊Dic19D412yes—
34Dic19⋊C4—22no—
35Dic19⋊C4—22no—
36Dic19⋊C4—42no—
37C4×Dic19—22no—
38C23×C19C2×D411yescharacteristic
39C2×C4×C19—21no—
40C2×C4×C19—21no—
41C2×C4×C19—21no—
42C2×C4×C19—41no—
43C2×C4×C19—41no—
44C2×C4×C19SD1612yes—
45C2×C4×C19C2×D412yes—
46C2×Dic19—22no—
47C2×Dic19—22no—
48C2×Dic19—22no—
49C2×Dic19—41no—
50C2×Dic19—41no—
51C2×Dic19—41no—
52C2×Dic19—41no—
53C2×Dic19—41no—
54Dic38—42no—
55Dic38—81no—
56C8×C19—42no—
57#1611—191nomaximal, Sylow
58C22×C19—21no—
59C22×C19—21no—
60C22×C19#12011yescharacteristic
61C22×C19C2×SD1611yescharacteristic
62C22×C19#13711yescharacteristic
63C4×C19—22no—
64C4×C19—22no—
65C4×C19—41no—
66Dic19—42no—
67Dic19—42no—
68Dic19—42no—
69Dic19—81no—
70#544—191no—
71#483—192no—
72#398—191no—
73#328—192no—
74#324D1911yescharacteristic
75C2×C19—21no—
76C2×C19—21no—
77C2×C19#44811yescharacteristic
78C2×C19#45611yescharacteristic
79C2×C19#45811yescharacteristic
80C4⋊Q8—382no—
81#125—382no—
82C22⋊Q8—192no—
83C22⋊Q8—381no—
84#117—381no—
85C2×C4⋊C4—191no—
86C2×C4⋊C4—381no—
87C2×C4⋊C4C2×D1911yescharacteristic
88#106—382no—
89#103—382no—
90C22⋊C8C2×D1912yes—
91#95—191no—
92#95—381no—
93C19#161111yescharacteristic, complemented, Sylow
94C2×Q8—192no—
95C2×Q8—381no—
96C22×C4—381no—
97C22×C4—381no—
98C22×C4D7611yescharacteristic
99C22×C4D7611yescharacteristic
100C22×C4C22×D1911yescharacteristic
101C2×C8—22no—
102C4⋊C4—22no—
103C4⋊C4—192no—
104C4⋊C4—382no—
105C4⋊C4—381no—
106C4⋊C4—381no—
107C4⋊C4—381no—
108C4⋊C4—382no—
109C4⋊C4—382no—
110C4⋊C4—762no—
111C22⋊C4—382no—
112C42—382no—
113C23C2×D7611yescharacteristic
114Q8—762no—
115Q8—1521no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—382no—
122C2×C4—382no—
123C2×C4—382no—
124C2×C4—761no—
125C2×C4—761no—
126C2×C4—761no—
127C2×C4—761no—
128C2×C4—761no—
129C2×C4#6451612yes—
130C2×C4D4×D1912yes—
131C8—42no—
132C22—21no—
133C22—21no—
134C22#1059732811yescharacteristic
135C22C2×#6451611yescharacteristic
136C22#1059735511yescharacteristic
137C4—22no—
138C4—22no—
139C4—41no—
140C4—762no—
141C4—762no—
142C4—762no—
143C4—1521no—
144C2—21no—
145C2—21no—
146C2#1192668511yescharacteristic
147C2#1192672911yescharacteristic
148C2#1192673511yescharacteristic
subgroupG/H
centerC22#10597328
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC19×#324C2
socleC22×C19#120
prime radicalC23×C19C2×D4
hypercenter#324D19
hypocenterC19#1611
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
93. C19#1611semidirect

Maximal subgroups

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

subgroupindex
#119271752
#119268752
#119264742
#119262822
C19×#3242
#161119