Finite Group Databasebeta

← #14565664

Subgroups — #14565664

Order 2432.

224 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 41 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#11927274C211yesmaximal, characteristic, complemented
2#11926727C212yesmaximal
3#11926343C211yesmaximal, characteristic, complemented
4#11926342C212yesmaximal, complemented
5C19×#456C211yesmaximal, characteristic
6C19×2−1+4C2211yescharacteristic
7C19×#137—21no—
8C19×C4⋊Q8C2211yescharacteristic
9#10597397—22no—
10#10597390—21no—
11#10597390C2212yes—
12#10597334—22no—
13#10597333—22no—
14C4×Dic38—21no—
15C19×#104—21no—
16C19×#101C2211yescharacteristic
17#10597294—22no—
18#10597293C2212yes—
19#41×C19—22no—
20#41×C19—21no—
21#41×C19—41no—
22C2×Q8×C19—41no—
23C2×Q8×C19D411yescharacteristic
24C2×Q8×C19C2311yescharacteristic
25C2×Dic38—21no—
26C2×Dic38—21no—
27C2×Dic38D412yes—
28Q16×C19—41no—
29SD16×C19—41no—
30M16×C19—21no—
31C4⋊C4×C19—22no—
32C42×C19D411yescharacteristic
33#64528—42no—
34#64526—42no—
35C4⋊Dic19—21no—
36Dic19⋊C4—22no—
37Dic19⋊C4—22no—
38Dic19⋊C4—22no—
39C4×Dic19—21no—
40C4×Dic19—22no—
41C4×Dic19D412yes—
42#64520—22no—
43Q8×C19—22no—
44Q8×C19—21no—
45Q8×C19—41no—
46Q8×C19—41no—
47D4×C19—22no—
48D4×C19—21no—
49D4×C19—41no—
50C2×C4×C19—21no—
51C2×C4×C19—21no—
52C2×C4×C19—42no—
53C2×C4×C19—41no—
54C2×C4×C19C2×D412yes—
55C2×C4×C19C2×D411yescharacteristic
56C2×Dic19—22no—
57C2×Dic19—22no—
58Dic38—24no—
59Dic38—42no—
60Dic38—81no—
61C8×C19—41no—
62C19⋊C8—42no—
63#2205—191nomaximal, Sylow
64C22×C19—41no—
65C22×C19#12011yescharacteristic
66C4×C19—22no—
67C4×C19—22no—
68C4×C19—21no—
69C4×C19—41no—
70C4×C19—41no—
71Dic19—24no—
72Dic19—42no—
73Q82—191no—
74#456—192no—
75#456D1911yescharacteristic
76#356—191no—
77#356—192no—
78C2×C19—21no—
79C2×C19—81no—
80C2×C19B(4,𝔽2)11yescharacteristic
812−1+4C2×D1911yescharacteristic
82#137—21no—
83#137—382no—
84C4⋊Q8—192no—
85C4⋊Q8—382no—
86C4⋊Q8—381no—
87C4⋊Q8C2×D1911yescharacteristic
88C4×Q8—382no—
89C4×Q8—381no—
90#104—21no—
91#104—382no—
92#101—192no—
93#101C2×D1911yescharacteristic
94C19#220511yescharacteristic, complemented, Sylow
95#41—22no—
96#41—21no—
97#41—41no—
98C2×Q8—41no—
99C2×Q8—192no—
100C2×Q8—381no—
101C2×Q8—381no—
102C2×Q8C22⋊D1911yescharacteristic
103C2×Q8C22×D1911yescharacteristic
104Q16—41no—
105Q16—762no—
106SD16—41no—
107SD16—762no—
108M16—21no—
109M16—382no—
110C4⋊C4—22no—
111C4⋊C4—382no—
112C4⋊C4—381no—
113C4⋊C4—382no—
114C4⋊C4—382no—
115C42—192no—
116C42—382no—
117C42—381no—
118C42C22⋊D1911yescharacteristic
119Q8—21no—
120Q8—22no—
121Q8—41no—
122Q8—41no—
123Q8—384no—
124Q8—762no—
125Q8—1521no—
126D4—21no—
127D4—22no—
128D4—41no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—42no—
133C2×C4—382no—
134C2×C4—382no—
135C2×C4D4×D1912yes—
136C2×C4C2×C22⋊D1911yescharacteristic
137C8—41no—
138C8—762no—
139C22—41no—
140C22#1059738311yescharacteristic
141C4—22no—
142C4—21no—
143C4—22no—
144C4—41no—
145C4—41no—
146C4—384no—
147C4—762no—
148C2—21no—
149C2—81no—
150C2#1192673011yescharacteristic
subgroupG/H
centerC2#11926730
commutator, cosocleC2×Q8×C19C23
FrattiniC2×Q8C22×D19
FittingC19×#456C2
socleC2×C19B(4,𝔽2)
prime radicalC19×2−1+4C22
hypercenter#456D19
hypocenterC19#2205
LCSG ▷ C2×Q8×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #11927274C2semidirect
3. #11926343C2semidirect
4. #11926342C2semidirect
94. C19#2205semidirect

Maximal subgroups

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

subgroupindex
#119272742
#119267272
#119263432
#119263422
C19×#4562
#220519