Finite Group Databasebeta

← #14565286

Subgroups — #14565286

Order 2432.

266 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 65 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#11927108C211yesmaximal, characteristic
2#11926518C211yesmaximal, characteristic, complemented
3#11926332C214yesmaximal, complemented
4C19×#413C211yesmaximal, characteristic, complemented
5C2×#41×C19C2211yescharacteristic
6C22×D76C411yescharacteristic, complemented
7C2×M16×C19—21no—
8#10597393—21no—
9#10597386—21no—
10#10597383C412yescomplemented
11#10597383C2212yes—
12#10597376—21no—
13#10597376—21no—
14#10597372—21no—
15#10597372C411yescharacteristic, complemented
16C19×#101—21no—
17C19×#100C2212yes—
18#10597291—21no—
19#10597291C2212yes—
20C23×D19C2×C412yes—
21#41×C19—41no—
22#41×C19—41no—
23C2×Q8×C19D411yescharacteristic
24C2×D4×C19C2×C411yescharacteristic
25C2×D4×C19D411yescharacteristic
26C2×D4×C19C2311yescharacteristic
27C22×C4×C19C2×C411yescharacteristic
28C22×C4×C19D411yescharacteristic
29C22×C4×C19D411yescharacteristic
30C2×C22⋊D19—22no—
31C2×C22⋊D19—22no—
32C2×D76—21no—
33C2×D76—21no—
34C2×D76—41no—
35C2×D76—41no—
36M16×C19—22no—
37M16×C19—41no—
38C2×C8×C19—41no—
39C22⋊Dic19—22no—
40C22⋊Dic19C2×C412yes—
41(C2×D19)⋊C4—22no—
42(C2×D19)⋊C4—22no—
43C4⋊Dic19—21no—
44C4⋊Dic19—41no—
45C4×Dic19—21no—
46C4×Dic19—41no—
47C23×C19C22⋊C411yescharacteristic
48C23×C19C22×C411yescharacteristic
49C23×C19C2×D411yescharacteristic
50C22×D19—22no—
51C22×D19—42no—
52C22×D19—82no—
53Q8×C19—41no—
54D4×C19—41no—
55D4×C19—41no—
56D4×C19—41no—
57C2×C4×C19—21no—
58C2×C4×C19—21no—
59C2×C4×C19—21no—
60C2×C4×C19—21no—
61C2×C4×C19—21no—
62C2×C4×C19—21no—
63C2×C4×C19C22⋊C411yescharacteristic
64C2×C4×C19C22⋊C411yescharacteristic
65C2×C4×C19C22⋊C411yescharacteristic
66C2×C4×C19C2×D411yescharacteristic
67C22⋊D19—82no—
68C22⋊D19—82no—
69C2×Dic19—22no—
70C2×Dic19—42no—
71D76—42no—
72D76—41no—
73D76—41no—
74C8×C19—42no—
75#2122—191nomaximal, Sylow
76C22×C19—21no—
77C22×C19—21no—
78C22×C19—21no—
79C22×C19—41no—
80C22×C19—41no—
81C22×C19—41no—
82C22×C19C2×C22⋊C411yescharacteristic
83C2×D19—42no—
84C2×D19—42no—
85C2×D19—42no—
86C2×D19—84no—
87C4×C19—21no—
88C4×C19—21no—
89C4×C19—21no—
90C4×C19#9911yescharacteristic
91C4×C19#9911yescharacteristic
92Dic19—42no—
93Dic19—82no—
94#535—191no—
95#413D1911yescharacteristic, complemented
96#410—191no—
97AΣL(1,𝔽16)—194no—
98C2×C19—21no—
99C2×C19—41no—
100C2×C19—41no—
101C2×C19—41no—
102C2×C19C2×#9911yescharacteristic
103D19—82no—
104C2×#41C2×D1911yescharacteristic
105C22×D4—191no—
106C2×M16—21no—
107#127—381no—
108#124—381no—
109#121—381no—
110#121—381no—
111#120—192no—
112#120—192no—
113#117—191no—
114#117—381no—
115#101—21no—
116#100C2×D1912yes—
117#99—192no—
118#99—381no—
119C19#212211yescharacteristic, complemented, Sylow
120C24—192no—
121#41—41no—
122#41—41no—
123C2×Q8C22⋊D1911yescharacteristic
124C2×D4—382no—
125C2×D4—382no—
126C2×D4—381no—
127C2×D4—381no—
128C2×D4—761no—
129C2×D4—761no—
130C2×D4C4×D1911yescharacteristic
131C2×D4D7611yescharacteristic
132C2×D4C22×D1911yescharacteristic
133C22×C4C4×D1911yescharacteristic
134C22×C4D7611yescharacteristic
135C22×C4C22⋊D1911yescharacteristic
136M16—22no—
137M16—41no—
138C2×C8—41no—
139C4⋊C4—381no—
140C4⋊C4—761no—
141C22⋊C4—192no—
142C22⋊C4—382no—
143C22⋊C4—382no—
144C22⋊C4—382no—
145C42—381no—
146C42—761no—
147C23—382no—
148C23—762no—
149C23—1522no—
150C23(C2×D19)⋊C411yescharacteristic
151C23C2×C4×D1911yescharacteristic
152C23C2×D7611yescharacteristic
153Q8—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—762no—
158D4—761no—
159D4—761no—
160D4—1522no—
161D4—1522no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—382no—
169C2×C4—762no—
170C2×C4(C2×D19)⋊C411yescharacteristic
171C2×C4(C2×D19)⋊C411yescharacteristic
172C2×C4(C2×D19)⋊C411yescharacteristic
173C2×C4C2×C22⋊D1911yescharacteristic
174C8—42no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—762no—
182C22—762no—
183C22—762no—
184C22—1524no—
185C22C2×(C2×D19)⋊C411yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—762no—
190C4—1522no—
191C4#1059726311yescharacteristic
192C4#1059726311yescharacteristic
193C2—21no—
194C2—41no—
195C2—41no—
196C2—41no—
197C2—1522no—
198C2C2×#1059726311yescharacteristic
subgroupG/H
centerC2C2×#10597263
commutatorC23×C19C22×C4
FrattiniC2×D4C22×D19
FittingC19×#413C2
socleC2×C19C2×#99
prime radical#11927108C2
cosocleC2×D4×C19C23
hypercenter#413D19
hypocenterC19#2122
LCSG ▷ C23×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #11926518C2semidirect
3. #11926332C2semidirect
4. C19×#413C2semidirect
6. C22×D76C4semidirect
10. #10597383C4semidirect
15. #10597372C4semidirect
95. #413D19semidirect
119. C19#2122semidirect

Maximal subgroups

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

subgroupindex
#119271082
#119265182
#119263322
C19×#4132
#212219