Finite Group Databasebeta

← #14567913

Subgroups — #14567913

Order 2432.

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

normal subgroups only

This group has 700 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
1C22×C22⋊Dic19C211yesmaximal, characteristic
2#11926472C214yesmaximal, complemented
3#11926417C212yesmaximal, complemented
4#11926416C212yesmaximal, complemented
5#11926407C212yesmaximal, complemented
6#11926405C212yesmaximal, complemented
7#11926400C211yesmaximal, characteristic
8C22×C22⋊C4×C19C211yesmaximal, characteristic
9C25×C19C2211yescharacteristic
10C23×C4×C19C2211yescharacteristic
11C23×C4×C19C2211yescharacteristic
12C23×Dic19C2211yescharacteristic
13C23×Dic19C2211yescharacteristic
14C2×C22⋊C4×C19—24no—
15C2×C22⋊C4×C19C2212yes—
16C2×C22⋊C4×C19C2212yes—
17C2×C22⋊Dic19—24no—
18C2×C22⋊Dic19C2212yes—
19C2×C22⋊Dic19C2212yes—
20C2×C22⋊Dic19C2212yes—
21C2×C22⋊Dic19C2212yes—
22C2×C22⋊Dic19C2212yes—
23C2×Dic19⋊C4C2214yescomplemented
24C19⋊#95C2214yescomplemented
25C19⋊#95C2214yescomplemented
26C19⋊#95C2214yescomplemented
27C24×C19—24no—
28C24×C19—24no—
29C24×C19—42no—
30C24×C19D414yes—
31C24×C19C2311yescharacteristic
32C24×C19C2311yescharacteristic
33C24×C19C2311yescharacteristic
34C22×C4×C19—22no—
35C22×C4×C19—22no—
36C22×C4×C19—24no—
37C22×C4×C19—42no—
38C22×C4×C19C2312yes—
39C22×C4×C19C2312yes—
40C22×Dic19—22no—
41C22×Dic19—22no—
42C22×Dic19—24no—
43C22×Dic19—42no—
44C22×Dic19C2314yes—
45C22×Dic19C2312yes—
46C22×Dic19C2312yes—
47C22⋊C4×C19—24no—
48C22⋊C4×C19—24no—
49C22⋊Dic19—24no—
50C22⋊Dic19—24no—
51C22⋊Dic19—24no—
52C22⋊Dic19—24no—
53C22⋊Dic19—42no—
54Dic19⋊C4—44no—
55C23×C19—22no—
56C23×C19—22no—
57C23×C19—22no—
58C23×C19—22no—
59C23×C19—28no—
60C23×C19—28no—
61C23×C19—22no—
62C23×C19—22no—
63C23×C19—22no—
64C23×C19—44no—
65C23×C19—416no—
66C23×C19C2×D412yes—
67C23×C19C2×D412yes—
68C23×C19C2×D412yes—
69C23×C19#4114yes—
70C23×C19#4114yes—
71C23×C19C2411yescharacteristic
72C2×C4×C19—22no—
73C2×C4×C19—22no—
74C2×C4×C19—24no—
75C2×C4×C19—24no—
76C2×C4×C19—44no—
77C2×C4×C19—44no—
78C2×Dic19—22no—
79C2×Dic19—22no—
80C2×Dic19—24no—
81C2×Dic19—24no—
82C2×Dic19—24no—
83C2×Dic19—24no—
84C2×Dic19—24no—
85C2×Dic19—44no—
86C2×Dic19—44no—
87#2483—191nomaximal, Sylow
88C22×C19—22no—
89C22×C19—22no—
90C22×C19—22no—
91C22×C19—22no—
92C22×C19—28no—
93C22×C19—28no—
94C22×C19—22no—
95C22×C19—22no—
96C22×C19—22no—
97C22×C19—416no—
98C22×C19—44no—
99C22×C19#12314yes—
100C22×C19#12314yes—
101C22×C19C22×D411yescharacteristic
102C22×C19C2×#4112yes—
103C22×C19C2×#4112yes—
104C22×C19H(5,𝔽2)12yes—
105C4×C19—42no—
106C4×C19—42no—
107Dic19—42no—
108Dic19—42no—
109Dic19—44no—
110C22×C22⋊C4—191no—
111C22×C22⋊C4D1911yescharacteristic
112#397—194no—
113#385—192no—
114#385—192no—
115#381—192no—
116#381—192no—
117#379—191no—
118C2×C19—24no—
119C2×C19—24no—
120C2×C19—42no—
121C2×C19C2×#12311yescharacteristic
122C2×C19C2×#12311yescharacteristic
123C2×C19#53411yescharacteristic
124C2×C19#55114yes—
125C25C2×D1911yescharacteristic
126C23×C4—191no—
127C23×C4—191no—
128C23×C4C2×D1911yescharacteristic
129C23×C4C2×D1911yescharacteristic
130C2×C4⋊C4—194no—
131C2×C22⋊C4—24no—
132C2×C22⋊C4—192no—
133C2×C22⋊C4—192no—
134C2×C22⋊C4—192no—
135C2×C22⋊C4—192no—
136C2×C22⋊C4—192no—
137C2×C22⋊C4—384no—
138C2×C22⋊C4C2×D1912yes—
139C2×C22⋊C4C2×D1912yes—
140#95—194no—
141#95—194no—
142#95—194no—
143C19#248311yescharacteristic, complemented, Sylow
144C24—24no—
145C24—24no—
146C24—42no—
147C24C22⋊D1914yes—
148C24C22×D1911yescharacteristic
149C24C22×D1911yescharacteristic
150C24C22×D1911yescharacteristic
151C22×C4—24no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—42no—
155C22×C4—192no—
156C22×C4—194no—
157C22×C4—192no—
158C22×C4—384no—
159C22×C4—382no—
160C22×C4—382no—
161C22×C4—762no—
162C22×C4C22×D1912yes—
163C22×C4C22×D1912yes—
164C4⋊C4—764no—
165C22⋊C4—24no—
166C22⋊C4—24no—
167C22⋊C4—384no—
168C22⋊C4—384no—
169C22⋊C4—384no—
170C22⋊C4—384no—
171C22⋊C4—762no—
172C23—22no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—28no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23—28no—
181C23—44no—
182C23—416no—
183C23#6454114yes—
184C23#6454314yes—
185C23C2×C22⋊D1912yes—
186C23C2×C22⋊D1912yes—
187C23C2×C22⋊D1912yes—
188C23C23×D1911yescharacteristic
189C2×C4—24no—
190C2×C4—24no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—44no—
194C2×C4—44no—
195C2×C4—384no—
196C2×C4—384no—
197C2×C4—384no—
198C2×C4—384no—
199C2×C4—384no—
200C2×C4—382no—
201C2×C4—382no—
202C2×C4—764no—
203C2×C4—764no—
204C22—22no—
205C22—22no—
206C22—22no—
207C22—22no—
208C22—28no—
209C22—28no—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—416no—
214C22—44no—
215C22#1059737514yes—
216C22#1059738114yes—
217C22C2×#6454112yes—
218C22C2×#6454312yes—
219C22#1059743012yes—
220C22C22×C22⋊D1911yescharacteristic
221C4—42no—
222C4—42no—
223C4—762no—
224C4—762no—
225C4—764no—
226C2—24no—
227C2—24no—
228C2—42no—
229C2C2×#1059738111yescharacteristic
230C2C2×#1059737511yescharacteristic
231C2#1192710311yescharacteristic
232C2#1192722014yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC22×C22⋊C4×C19C2
prime radicalC25×C19C22
hypercenterC22×C22⋊C4D19
hypocenterC19#2483
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #11926472C2semidirect
3. #11926417C2semidirect
4. #11926416C2semidirect
5. #11926407C2semidirect
6. #11926405C2semidirect
23. C2×Dic19⋊C4C22semidirect
24. C19⋊#95C22semidirect
25. C19⋊#95C22semidirect
26. C19⋊#95C22semidirect
143. C19#2483semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Dic192
#119264722
#119264172
#119264162
#119264072
#119264052
#119264002
C22×C22⋊C4×C192
#248319