Finite Group Databasebeta

← #14564800

Subgroups — #14564800

Order 2432.

466 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 67 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#11927170C211yesmaximal, characteristic, complemented
2#11926399C211yesmaximal, characteristic
3#11926399C212yesmaximal
4#11926310C212yesmaximal, complemented
5C19×#342C211yesmaximal, characteristic, complemented
6C24×D19C2211yescharacteristic
7C2×C22⋊C4×C19C2212yes—
8C2×C22⋊C4×C19C2211yescharacteristic
9C2×C22⋊Dic19C2211yescharacteristic
10C2×C22⋊Dic19C2212yes—
11C2×(C2×D19)⋊C4—22no—
12C2×(C2×D19)⋊C4—24no—
13#10597370—22no—
14#10597324—24no—
15C24×C19C2311yescharacteristic
16C23×D19—21no—
17C23×D19—22no—
18C23×D19—22no—
19C23×D19—21no—
20C23×D19—44no—
21C23×D19Q812yescomplemented
22C22×C4×C19—22no—
23C22×C4×C19D412yes—
24C22×Dic19—21no—
25C22×Dic19D414yes—
26C2×Dic38—22no—
27C22⋊C4×C19—22no—
28C22⋊C4×C19—22no—
29C22⋊C4×C19—22no—
30C22⋊Dic19—22no—
31C22⋊Dic19—22no—
32C22⋊Dic19—22no—
33(C2×D19)⋊C4—48no—
34(C2×D19)⋊C4—44no—
35C4⋊Dic19—22no—
36Dic19⋊C4—24no—
37C23×C19—42no—
38C23×C19C2×D411yescharacteristic
39C23×C19C2×D412yes—
40C23×C19C2×Q811yescharacteristic
41C23×C19#4112yes—
42C23×C19#4111yescharacteristic
43C22×D19—24no—
44C22×D19—28no—
45C22×D19—24no—
46C22×D19—22no—
47C22×D19—44no—
48C22×D19—48no—
49C22×D19—44no—
50C22×D19—42no—
51C22×D19—44no—
52C22×D19—41no—
53C22×D19—41no—
54C22×D19—42no—
55C2×C4×C19—22no—
56C2×C4×C19—42no—
57C2×C4×C19—44no—
58C2×C4×C19—42no—
59C2×Dic19—24no—
60C2×Dic19—44no—
61C2×Dic19—42no—
62C2×Dic19—41no—
63Dic38—82no—
64#2029—191nomaximal, Sylow
65C22×C19—22no—
66C22×C19—24no—
67C22×C19—41no—
68C22×C19—42no—
69C22×C19—41no—
70C22×C19#12011yescharacteristic
71C22×C19C22⋊Q812yes—
72C22×C19C22⋊Q811yescharacteristic
73C22×C19#12411yescharacteristic
74C22×C19#12412yes—
75C2×D19—28no—
76C2×D19—24no—
77C2×D19—44no—
78C2×D19—48no—
79C2×D19—44no—
80C2×D19—42no—
81C2×D19—42no—
82C2×D19—44no—
83C4×C19—42no—
84C4×C19—82no—
85Dic19—44no—
86Dic19—81no—
87#543—191no—
88#379—192no—
89#379—191no—
90#342—192no—
91#342D1911yescharacteristic, complemented
92C2×C19—21no—
93C2×C19—22no—
94C2×C19—22no—
95C2×C19—21no—
96C2×C19#39311yescharacteristic
97C2×C19B(4,𝔽2)12yes—
98D19—44no—
99C25—191no—
100C22⋊Q8—384no—
101C22⋊Q8—382no—
102C2×C22⋊C4—192no—
103C2×C22⋊C4—191no—
104C2×C22⋊C4—384no—
105C2×C22⋊C4—382no—
106C2×C22⋊C4C2×D1912yes—
107C2×C22⋊C4C2×D1911yescharacteristic
108C19#202911yescharacteristic, complemented, Sylow
109C24—192no—
110C24—381no—
111C24—382no—
112C24—382no—
113C24—381no—
114C24—764no—
115C24C22×D1911yescharacteristic
116C2×Q8—382no—
117C22×C4—22no—
118C22×C4—194no—
119C22×C4—381no—
120C22×C4D7612yes—
121C4⋊C4—384no—
122C4⋊C4—382no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—382no—
127C22⋊C4—382no—
128C22⋊C4—382no—
129C22⋊C4—764no—
130C22⋊C4—768no—
131C23—42no—
132C23—384no—
133C23—388no—
134C23—384no—
135C23—382no—
136C23—762no—
137C23—764no—
138C23—764no—
139C23—768no—
140C23—764no—
141C23—761no—
142C23—761no—
143C23—762no—
144C23C2×D7611yescharacteristic
145C23#6454112yes—
146C23D4×D1912yes—
147C23#6454311yescharacteristic
148C23Q8×D1911yescharacteristic
149Q8—1522no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—42no—
154C2×C4—384no—
155C2×C4—764no—
156C2×C4—762no—
157C2×C4—761no—
158C22—22no—
159C22—24no—
160C22—42no—
161C22—41no—
162C22—41no—
163C22—388no—
164C22—384no—
165C22—768no—
166C22—764no—
167C22—764no—
168C22—762no—
169C22—762no—
170C22—764no—
171C22#1059732111yescharacteristic
172C22#1059732811yescharacteristic
173C22#1059733112yes—
174C22#1059734212yes—
175C22#1059734311yescharacteristic
176C4—42no—
177C4—82no—
178C4—764no—
179C4—1521no—
180C2—22no—
181C2—21no—
182C2—22no—
183C2—21no—
184C2—764no—
185C2#1192645711yescharacteristic
186C2#1192673212yes—
subgroupG/H
centerC22#10597328
commutator, cosocleC24×C19C23
FrattiniC24C22×D19
FittingC19×#342C2
socleC22×C19#120
prime radicalC24×D19C22
hypercenter#342D19
hypocenterC19#2029
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #11927170C2semidirect
4. #11926310C2semidirect
5. C19×#342C2semidirect
21. C23×D19Q8semidirect
91. #342D19semidirect
108. C19#2029semidirect

Maximal subgroups

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

subgroupindex
#119271702
#119263992
#119263102
C19×#3422
#202919