Finite Group Databasebeta

← #14569417

Subgroups — #14569417

Order 2432.

526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C22×C4⋊Dic19C211yesmaximal, characteristic, complemented
2#11926483C212yesmaximal, complemented
3#11926480C212yesmaximal, complemented
4#11926474C212yesmaximal, complemented
5#11926469C212yesmaximal, complemented
6#11926424C212yesmaximal
7#11926416C212yesmaximal, complemented
8#11926407C211yesmaximal, characteristic, complemented
9C2×C19×#123C211yesmaximal, characteristic
10C22×D4×C19C2211yescharacteristic
11C23×C4×C19C2211yescharacteristic
12C23×Dic19C2212yes—
13C19×#123—24no—
14C2×C4⋊C4×C19C2211yescharacteristic
15C2×C4⋊C4×C19C2211yescharacteristic
16C2×C22⋊C4×C19C2211yescharacteristic
17C2×C22⋊C4×C19C2211yescharacteristic
18C2×C22⋊C4×C19C2211yescharacteristic
19C2×C22⋊Dic19C2212yes—
20C2×C22⋊Dic19C2214yes—
21C2×C4⋊Dic19—24no—
22C2×C4⋊Dic19C2212yes—
23C2×C4⋊Dic19C2212yes—
24C2×Dic19⋊C4C2214yes—
25C19⋊#95C2212yes—
26C19⋊#95C2212yes—
27C19⋊#95C2214yes—
28C19⋊#95C2214yes—
29C24×C19C2311yescharacteristic
30C24×C19C2311yescharacteristic
31C2×D4×C19—22no—
32C2×D4×C19—24no—
33C22×C4×C19—24no—
34C22×C4×C19D414yes—
35C22×C4×C19C2311yescharacteristic
36C22×C4×C19C2311yescharacteristic
37C22×C4×C19C2311yescharacteristic
38C22×C4×C19C2311yescharacteristic
39C22×C4×C19C2311yescharacteristic
40C22×Dic19—24no—
41C22×Dic19—44no—
42C22×Dic19C2314yes—
43C22×Dic19C2314yes—
44C4⋊C4×C19—22no—
45C4⋊C4×C19—22no—
46C22⋊C4×C19—22no—
47C22⋊C4×C19—22no—
48C22⋊C4×C19—22no—
49C22⋊Dic19—24no—
50C22⋊Dic19—44no—
51C4⋊Dic19—24no—
52C4⋊Dic19—24no—
53Dic19⋊C4—44no—
54C23×C19—22no—
55C23×C19—22no—
56C23×C19—21no—
57C23×C19—22no—
58C23×C19—22no—
59C23×C19—22no—
60C23×C19C2×D412yes—
61C23×C19#4114yes—
62C23×C19C2411yescharacteristic
63D4×C19—44no—
64C2×C4×C19—28no—
65C2×C4×C19—22no—
66C2×C4×C19—22no—
67C2×C4×C19—21no—
68C2×C4×C19—21no—
69C2×C4×C19—21no—
70C2×C4×C19—22no—
71C2×C4×C19—22no—
72C2×C4×C19—22no—
73C2×C4×C19C2×D412yes—
74C2×C4×C19C2×D412yes—
75C2×Dic19—24no—
76C2×Dic19—24no—
77C2×Dic19—24no—
78C2×Dic19—24no—
79C2×Dic19—24no—
80C2×Dic19—24no—
81C2×Dic19—48no—
82#2623—191nomaximal, Sylow
83C22×C19—22no—
84C22×C19—22no—
85C22×C19—28no—
86C22×C19—41no—
87C22×C19—41no—
88C22×C19—41no—
89C22×C19—44no—
90C22×C19#12314yes—
91C22×C19C22×D411yescharacteristic
92C22×C19C2×#4112yes—
93C22×C19H(5,𝔽2)12yes—
94C22×C192−1+412yes—
95C4×C19—22no—
96C4×C19—22no—
97C4×C19—41no—
98C4×C19—41no—
99C4×C19—41no—
100Dic19—44no—
101Dic19—44no—
102C2×#123D1911yescharacteristic
103C22×C4⋊C4—191no—
104#400—192no—
105#399—192no—
106#398—192no—
107#397—192no—
108#386—192no—
109#385—192no—
110#381—191no—
111C2×C19—24no—
112C2×C19—81no—
113C2×C19C2×#12311yescharacteristic
114C2×C19#53511yescharacteristic
115C2×C19#53611yescharacteristic
116C2×C19#53914yes—
117C22×D4C2×D1911yescharacteristic
118C23×C4—192no—
119C23×C4C2×D1911yescharacteristic
120#123—24no—
121C2×C4⋊C4—192no—
122C2×C4⋊C4—192no—
123C2×C4⋊C4—194no—
124C2×C4⋊C4—384no—
125C2×C4⋊C4C2×D1911yescharacteristic
126C2×C4⋊C4C2×D1911yescharacteristic
127C2×C22⋊C4—192no—
128C2×C22⋊C4—194no—
129C2×C22⋊C4C2×D1911yescharacteristic
130C2×C22⋊C4C2×D1911yescharacteristic
131C2×C22⋊C4C2×D1911yescharacteristic
132#95—192no—
133#95—192no—
134#95—194no—
135#95—194no—
136C19#262311yescharacteristic, complemented, Sylow
137C24C22×D1911yescharacteristic
138C24C22×D1911yescharacteristic
139C2×D4—24no—
140C2×D4—22no—
141C22×C4—24no—
142C22×C4—194no—
143C22×C4—194no—
144C22×C4—384no—
145C22×C4—764no—
146C22×C4C22⋊D1914yes—
147C22×C4C22×D1911yescharacteristic
148C22×C4C22×D1911yescharacteristic
149C22×C4C22×D1911yescharacteristic
150C22×C4C22×D1911yescharacteristic
151C22×C4C22×D1911yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—384no—
155C4⋊C4—384no—
156C4⋊C4—764no—
157C22⋊C4—22no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—384no—
161C22⋊C4—764no—
162C23—22no—
163C23—22no—
164C23—22no—
165C23—22no—
166C23—22no—
167C23—21no—
168C23#6454314yes—
169C23C2×C22⋊D1912yes—
170C23C23×D1911yescharacteristic
171D4—44no—
172C2×C4—28no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—384no—
182C2×C4—384no—
183C2×C4—384no—
184C2×C4—384no—
185C2×C4—384no—
186C2×C4—384no—
187C2×C4—768no—
188C2×C4C2×C22⋊D1912yes—
189C2×C4C2×C22⋊D1912yes—
190C22—22no—
191C22—22no—
192C22—28no—
193C22—41no—
194C22—41no—
195C22—41no—
196C22—44no—
197C22#1059738114yes—
198C22C2×#6454312yes—
199C22#1059743512yes—
200C22#1059743612yes—
201C22C22×C22⋊D1911yescharacteristic
202C4—22no—
203C4—22no—
204C4—41no—
205C4—41no—
206C4—41no—
207C4—764no—
208C4—764no—
209C2—24no—
210C2—81no—
211C2C2×#1059738111yescharacteristic
212C2#1192710811yescharacteristic
213C2#1192711511yescharacteristic
214C2#1192713814yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#123C2
prime radicalC22×D4×C19C22
hypercenterC2×#123D19
hypocenterC19#2623
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊Dic19C2semidirect
2. #11926483C2semidirect
3. #11926480C2semidirect
4. #11926474C2semidirect
5. #11926469C2semidirect
7. #11926416C2semidirect
8. #11926407C2semidirect
136. C19#2623semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊Dic192
#119264832
#119264802
#119264742
#119264692
#119264242
#119264162
#119264072
C2×C19×#1232
#262319