Finite Group Databasebeta

← #14569351

Subgroups — #14569351

Order 2432.

1134 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C23×D76C211yesmaximal, characteristic, complemented
2C2×#10597383C212yesmaximal, complemented
3#11926461C214yesmaximal, complemented
4#11926453C214yesmaximal, complemented
5#11926407C211yesmaximal, characteristic, complemented
6#11926399C212yesmaximal, complemented
7C2×C19×#123C211yesmaximal, characteristic, complemented
8C24×D19C2212yes—
9C22×D4×C19C2211yescharacteristic
10C23×C4×C19C2211yescharacteristic
11C22×C22⋊D19C2214yescomplemented
12C22×D76—28no—
13C22×D76—24no—
14C22×D76C2214yes—
15C19×#123—24no—
16C2×C4⋊C4×C19C2212yescomplemented
17C2×C22⋊C4×C19C2211yescharacteristic
18C2×C22⋊C4×C19C2212yescomplemented
19C2×C22⋊Dic19C2212yes—
20#10597383—28no—
21C2×(C2×D19)⋊C4C2214yescomplemented
22C2×(C2×D19)⋊C4C2218yescomplemented
23C19⋊#95C2214yescomplemented
24C24×C19C2311yescharacteristic
25C24×C19C2311yescharacteristic
26C23×D19—24no—
27C23×D19—24no—
28C23×D19—48no—
29C23×D19D418yescomplemented
30C23×D19C2314yes—
31C2×D4×C19—24no—
32C2×D4×C19—22no—
33C22×C4×C19—24no—
34C22×C4×C19D414yescomplemented
35C22×C4×C19C2312yes—
36C22×C4×C19C2311yescharacteristic
37C22×C4×C19C2312yes—
38C2×C22⋊D19—28no—
39C2×C22⋊D19—48no—
40C22×Dic19C2314yes—
41C2×D76—232no—
42C2×D76—216no—
43C2×D76—28no—
44C4⋊C4×C19—24no—
45C22⋊C4×C19—22no—
46C22⋊C4×C19—24no—
47C22⋊Dic19—24no—
48(C2×D19)⋊C4—28no—
49(C2×D19)⋊C4—48no—
50C23×C19—24no—
51C23×C19—21no—
52C23×C19—22no—
53C23×C19—24no—
54C23×C19C2×D414yes—
55C23×C19C2×D412yes—
56C23×C19C2411yescharacteristic
57C22×D19—216no—
58C22×D19—24no—
59C22×D19—24no—
60C22×D19—28no—
61C22×D19—28no—
62C22×D19—416no—
63C22×D19—416no—
64C22×D19—416no—
65C22×D19C2×D418yes—
66D4×C19—44no—
67C2×C4×C19—28no—
68C2×C4×C19—24no—
69C2×C4×C19—22no—
70C2×C4×C19—22no—
71C2×C4×C19—21no—
72C2×C4×C19—24no—
73C2×C4×C19C2×D414yes—
74C22⋊D19—416no—
75C2×Dic19—24no—
76C2×Dic19—28no—
77D76—232no—
78#2613—191nomaximal, Sylow
79C22×C19—28no—
80C22×C19—24no—
81C22×C19—41no—
82C22×C19—44no—
83C22×C19—42no—
84C22×C19#12014yes—
85C22×C19C22×D412yes—
86C22×C19C22×D411yescharacteristic
87C22×C19H(5,𝔽2)14yes—
88C2×D19—28no—
89C2×D19—28no—
90C2×D19—28no—
91C2×D19—432no—
92C2×D19—48no—
93C2×D19—48no—
94C4×C19—24no—
95C4×C19—41no—
96C4×C19—42no—
97Dic19—44no—
98C23×D4—191no—
99C2×#123D1911yescharacteristic, complemented
100C2×#120—192no—
101#394—194no—
102#392—194no—
103#381—191no—
104#379—192no—
105C2×C19—24no—
106C2×C19—81no—
107C2×C19C2×#12011yescharacteristic
108C2×C19#53414yes—
109C2×C19#53512yes—
110D19—48no—
111C25—192no—
112C22×D4—194no—
113C22×D4—194no—
114C22×D4—388no—
115C22×D4—384no—
116C22×D4C2×D1911yescharacteristic
117C23×C4C2×D1911yescharacteristic
118#123—24no—
119#120—388no—
120C2×C4⋊C4C2×D1912yescomplemented
121C2×C22⋊C4—192no—
122C2×C22⋊C4—194no—
123C2×C22⋊C4—198no—
124C2×C22⋊C4C2×D1911yescharacteristic
125C2×C22⋊C4C2×D1912yescomplemented
126#95—194no—
127C19#261311yescharacteristic, complemented, Sylow
128C24—194no—
129C24—198no—
130C24—384no—
131C24—384no—
132C24—768no—
133C24C22×D1911yescharacteristic
134C24C22×D1911yescharacteristic
135C2×D4—24no—
136C2×D4—22no—
137C2×D4—3816no—
138C2×D4—3832no—
139C2×D4—388no—
140C2×D4—388no—
141C2×D4—768no—
142C22×C4—24no—
143C22×C4—194no—
144C22×C4C22⋊D1914yescomplemented
145C22×C4C22×D1912yes—
146C22×C4C22×D1911yescharacteristic
147C22×C4C22×D1912yes—
148C4⋊C4—24no—
149C22⋊C4—22no—
150C22⋊C4—24no—
151C22⋊C4—388no—
152C22⋊C4—384no—
153C22⋊C4—768no—
154C23—24no—
155C23—22no—
156C23—24no—
157C23—21no—
158C23—198no—
159C23—3816no—
160C23—384no—
161C23—388no—
162C23—388no—
163C23—384no—
164C23—7616no—
165C23—7616no—
166C23—7616no—
167C23D4×D1914yes—
168C23C2×C22⋊D1912yes—
169C23C23×D1911yescharacteristic
170D4—44no—
171D4—3832no—
172D4—7616no—
173C2×C4—28no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—384no—
180C2×C4—388no—
181C2×C4C2×C22⋊D1914yes—
182C22—28no—
183C22—24no—
184C22—44no—
185C22—42no—
186C22—41no—
187C22—388no—
188C22—388no—
189C22—388no—
190C22—7632no—
191C22—768no—
192C22—768no—
193C22#1059738314yes—
194C22C2×D4×D1912yes—
195C22#1059743514yes—
196C22C22×C22⋊D1911yescharacteristic
197C4—24no—
198C4—42no—
199C4—41no—
200C4—764no—
201C2—24no—
202C2—81no—
203C2—768no—
204C2C2×#1059738311yescharacteristic
205C2#1192710514yes—
206C2#1192710812yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#123C2
hypercenterC2×#123D19
hypocenterC19#2613
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C23×D76C2semidirect
2. C2×#10597383C2semidirect
3. #11926461C2semidirect
4. #11926453C2semidirect
5. #11926407C2semidirect
6. #11926399C2semidirect
7. C2×C19×#123C2semidirect
11. C22×C22⋊D19C22semidirect
16. C2×C4⋊C4×C19C22semidirect
18. C2×C22⋊C4×C19C22semidirect
21. C2×(C2×D19)⋊C4C22semidirect
22. C2×(C2×D19)⋊C4C22semidirect
23. C19⋊#95C22semidirect
29. C23×D19D4semidirect
34. C22×C4×C19D4semidirect
99. C2×#123D19semidirect
120. C2×C4⋊C4C2×D19semidirect
125. C2×C22⋊C4C2×D19semidirect
127. C19#2613semidirect
144. C22×C4C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C23×D762
C2×#105973832
#119264612
#119264532
#119264072
#119263992
C2×C19×#1232
#261319