Finite Group Databasebeta

← #14571673

Subgroups — #14571673

Order 2432.

444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×#10597324C212yesmaximal
2#11926486C212yesmaximal, complemented
3#11926485C212yesmaximal, complemented
4#11926472C212yesmaximal
5#11926469C211yesmaximal, characteristic
6#11926465C212yesmaximal, complemented
7#11926464C212yesmaximal, complemented
8#11926405C211yesmaximal, characteristic
9C19×#397C211yesmaximal, characteristic
10C23×Dic19C2211yescharacteristic
11C22×Dic38C2212yes—
12C2×C4⋊C4×C19C2211yescharacteristic
13C2×C22⋊C4×C19C2212yes—
14C2×C22⋊C4×C19C2211yescharacteristic
15C2×C22⋊Dic19C2212yes—
16C2×C22⋊Dic19C2211yescharacteristic
17C2×C4⋊Dic19C2212yes—
18C2×C4⋊Dic19C2211yescharacteristic
19C2×Dic19⋊C4C2212yes—
20C2×Dic19⋊C4C2212yes—
21C2×Dic19⋊C4C2212yes—
22#10597324—28no—
23C19×#95C2212yes—
24C19×#95C2211yescharacteristic
25C19⋊#95C2212yes—
26C19⋊#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2211yescharacteristic
31C19⋊#95C2212yes—
32C24×C19C2311yescharacteristic
33C22×C4×C19C2312yes—
34C22×C4×C19C2311yescharacteristic
35C22×C4×C19C2311yescharacteristic
36C22×C4×C19C2312yes—
37C22×Dic19—41no—
38C22×Dic19—41no—
39C22×Dic19D414yes—
40C22×Dic19C2312yes—
41C22×Dic19C2312yes—
42C22×Dic19C2312yes—
43C22×Dic19C2312yes—
44C2×Dic38—24no—
45C2×Dic38—42no—
46C2×Dic38—42no—
47C4⋊C4×C19—41no—
48C22⋊C4×C19—24no—
49C22⋊C4×C19—41no—
50C22⋊Dic19—24no—
51C22⋊Dic19—41no—
52C4⋊Dic19—24no—
53C4⋊Dic19—41no—
54Dic19⋊C4—24no—
55Dic19⋊C4—24no—
56Dic19⋊C4—42no—
57C23×C19—21no—
58C23×C19—21no—
59C23×C19—22no—
60C23×C19—22no—
61C23×C19C2×D412yes—
62C23×C19C2411yescharacteristic
63C2×C4×C19—22no—
64C2×C4×C19—22no—
65C2×C4×C19—22no—
66C2×C4×C19—21no—
67C2×C4×C19—21no—
68C2×C4×C19—22no—
69C2×C4×C19—22no—
70C2×C4×C19—22no—
71C2×C4×C19—22no—
72C2×C4×C19—22no—
73C2×Dic19—22no—
74C2×Dic19—22no—
75C2×Dic19—22no—
76C2×Dic19—22no—
77C2×Dic19—22no—
78C2×Dic19—22no—
79C2×Dic19—22no—
80C2×Dic19—22no—
81C2×Dic19—22no—
82C2×Dic19—22no—
83C2×Dic19—22no—
84C2×Dic19—44no—
85C2×Dic19C2×D414yes—
86Dic38—48no—
87#2817—191nomaximal, Sylow
88C22×C19—22no—
89C22×C19—24no—
90C22×C19—42no—
91C22×C19—41no—
92C22×C19—41no—
93C22×C19C22×D411yescharacteristic
94C22×C19H(5,𝔽2)11yescharacteristic
95C22×C19H(5,𝔽2)11yescharacteristic
96C22×C192−1+412yes—
97C22×C192−1+412yes—
98C4×C19—42no—
99C4×C19—42no—
100C4×C19—41no—
101C4×C19—41no—
102Dic19—24no—
103Dic19—42no—
104Dic19—42no—
105Dic19—42no—
106C2×C22⋊Q8—192no—
107#400—192no—
108#400—192no—
109#397—191no—
110#397—192no—
111#397D1911yescharacteristic
112#395—192no—
113#395—192no—
114#381—191no—
115C2×C19—42no—
116C2×C19#53411yescharacteristic
117C2×C19#53612yes—
118C2×C19#56312yes—
119C2×C19#56311yescharacteristic
120C2×C19#56311yescharacteristic
121C22×Q8—192no—
122C23×C4—191no—
123C22⋊Q8—388no—
124C2×C4⋊C4—192no—
125C2×C4⋊C4—192no—
126C2×C4⋊C4—192no—
127C2×C4⋊C4—192no—
128C2×C4⋊C4—191no—
129C2×C4⋊C4C2×D1911yescharacteristic
130C2×C22⋊C4—192no—
131C2×C22⋊C4—191no—
132C2×C22⋊C4C2×D1912yes—
133C2×C22⋊C4C2×D1911yescharacteristic
134#95—192no—
135#95—192no—
136#95—192no—
137#95—192no—
138#95—192no—
139#95—192no—
140#95—191no—
141#95C2×D1912yes—
142#95C2×D1911yescharacteristic
143C19#281711yescharacteristic, complemented, Sylow
144C24C22×D1911yescharacteristic
145C2×Q8—384no—
146C2×Q8—762no—
147C2×Q8—762no—
148C22×C4—192no—
149C22×C4—194no—
150C22×C4—192no—
151C22×C4—192no—
152C22×C4—192no—
153C22×C4—761no—
154C22×C4—761no—
155C22×C4C22×D1911yescharacteristic
156C22×C4C22×D1911yescharacteristic
157C22×C4C22×D1912yes—
158C22×C4C22×D1912yes—
159C4⋊C4—41no—
160C4⋊C4—384no—
161C4⋊C4—384no—
162C4⋊C4—384no—
163C4⋊C4—762no—
164C4⋊C4—761no—
165C22⋊C4—24no—
166C22⋊C4—41no—
167C22⋊C4—384no—
168C22⋊C4—761no—
169C23—21no—
170C23—21no—
171C23—22no—
172C23—22no—
173C23D4×D1912yes—
174C23C23×D1911yescharacteristic
175Q8—768no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—194no—
187C2×C4—382no—
188C2×C4—382no—
189C2×C4—382no—
190C2×C4—382no—
191C2×C4—382no—
192C2×C4—382no—
193C2×C4—382no—
194C2×C4—382no—
195C2×C4—382no—
196C2×C4—382no—
197C2×C4—382no—
198C2×C4—764no—
199C22—22no—
200C22—24no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22C2×D4×D1911yescharacteristic
205C22#1059743011yescharacteristic
206C22#1059743511yescharacteristic
207C22#1059743612yes—
208C22#1059743612yes—
209C4—41no—
210C4—42no—
211C4—42no—
212C4—41no—
213C4—384no—
214C4—762no—
215C4—762no—
216C4—762no—
217C2—42no—
218C2#1192710211yescharacteristic
219C2#1192711612yes—
220C2#1192729411yescharacteristic
221C2#1192729612yes—
222C2#1192729711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#397C2
prime radicalC24×C19C23
hypercenter#397D19
hypocenterC19#2817
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #11926486C2semidirect
3. #11926485C2semidirect
6. #11926465C2semidirect
7. #11926464C2semidirect
143. C19#2817semidirect

Maximal subgroups

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

subgroupindex
C2×#105973242
#119264862
#119264852
#119264722
#119264692
#119264652
#119264642
#119264052
C19×#3972
#281719