Finite Group Databasebeta

← #14569306

Subgroups — #14569306

Order 2432.

540 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 137 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×#10597323C212yesmaximal, complemented
2#11926474C211yesmaximal, characteristic, complemented
3#11926467C212yesmaximal, complemented
4#11926437C212yesmaximal, complemented
5#11926426C212yesmaximal, complemented
6#11926424C212yesmaximal
7#11926416C212yesmaximal, complemented
8#11926409C211yesmaximal, characteristic, complemented
9C19×#394C211yesmaximal, characteristic
10C22×D4×C19C2211yescharacteristic
11C23×Dic19C2212yes—
12C2×C4⋊C4×C19C2211yescharacteristic
13C2×C22⋊C4×C19C2212yes—
14C2×C22⋊C4×C19C2212yes—
15C2×C22⋊Dic19C2212yes—
16C2×C22⋊Dic19C2212yes—
17C2×C22⋊Dic19C2212yes—
18C2×C4⋊Dic19C2211yescharacteristic
19C2×C4⋊Dic19C2211yescharacteristic
20C2×Dic19⋊C4C2212yes—
21C2×Dic19⋊C4C2212yes—
22C2×Dic19⋊C4C2212yes—
23C2×C4×Dic19C2212yes—
24C2×C4×Dic19C2211yescharacteristic
25#10597323—28no—
26C19×#95C2211yescharacteristic
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2211yescharacteristic
30C19⋊#95C2212yes—
31C19⋊#95C2212yes—
32C24×C19C2312yes—
33C2×D4×C19—24no—
34C2×D4×C19—41no—
35C22×C4×C19C2311yescharacteristic
36C22×C4×C19C2312yes—
37C22×C4×C19C2311yescharacteristic
38C22×C4×C19C2311yescharacteristic
39C22×Dic19—24no—
40C22×Dic19—24no—
41C22×Dic19—24no—
42C22×Dic19C2312yes—
43C22×Dic19C2312yes—
44C22×Dic19C2312yes—
45C22×Dic19C2312yes—
46C4⋊C4×C19—41no—
47C22⋊C4×C19—24no—
48C22⋊C4×C19—24no—
49C22⋊Dic19—24no—
50C22⋊Dic19—24no—
51C22⋊Dic19—42no—
52C4⋊Dic19—41no—
53C4⋊Dic19—41no—
54Dic19⋊C4—24no—
55Dic19⋊C4—24no—
56Dic19⋊C4—24no—
57C4×Dic19—24no—
58C4×Dic19D414yescomplemented
59C23×C19—22no—
60C23×C19—22no—
61C23×C19—22no—
62C23×C19—22no—
63C23×C19—22no—
64C23×C19—22no—
65C23×C19#4114yes—
66C23×C19C2411yescharacteristic
67D4×C19—44no—
68C2×C4×C19—21no—
69C2×C4×C19—21no—
70C2×C4×C19—22no—
71C2×C4×C19—22no—
72C2×C4×C19—22no—
73C2×C4×C19—22no—
74C2×C4×C19—22no—
75C2×C4×C19—21no—
76C2×C4×C19—21no—
77C2×C4×C19C2×D412yes—
78C2×Dic19—216no—
79C2×Dic19—22no—
80C2×Dic19—22no—
81C2×Dic19—22no—
82C2×Dic19—22no—
83C2×Dic19—22no—
84C2×Dic19—22no—
85C2×Dic19—22no—
86C2×Dic19—22no—
87C2×Dic19—22no—
88C2×Dic19—22no—
89C2×Dic19C2×D414yes—
90C2×Dic19#4114yes—
91#2609—191nomaximal, Sylow
92C22×C19—24no—
93C22×C19—24no—
94C22×C19—24no—
95C22×C19—42no—
96C22×C19—42no—
97C22×C19—42no—
98C22×C19—42no—
99C22×C19C22×D411yescharacteristic
100C22×C19C2×#4112yes—
101C22×C19C2×#4112yes—
102C22×C19H(5,𝔽2)11yescharacteristic
103C22×C192−1+411yescharacteristic
104C4×C19—22no—
105C4×C19—42no—
106C4×C19—41no—
107C4×C19—41no—
108Dic19—24no—
109Dic19—24no—
110Dic19—42no—
111Dic19—42no—
112C2×#117—192no—
113#398—191no—
114#396—192no—
115#394D1911yescharacteristic
116#388—192no—
117#387—192no—
118#386—192no—
119#385—192no—
120#382—191no—
121C2×C19—44no—
122C2×C19#52512yes—
123C2×C19#53711yescharacteristic
124C2×C19#55111yescharacteristic
125C2×C19#55212yes—
126C2×C19#55511yescharacteristic
127C22×D4C2×D1911yescharacteristic
128C23×C4—192no—
129#117—388no—
130C2×C4⋊C4—192no—
131C2×C4⋊C4—192no—
132C2×C4⋊C4—192no—
133C2×C4⋊C4—191no—
134C2×C4⋊C4—191no—
135C2×C4⋊C4C2×D1911yescharacteristic
136C2×C22⋊C4—192no—
137C2×C22⋊C4—192no—
138C2×C22⋊C4—192no—
139C2×C22⋊C4C2×D1912yes—
140C2×C22⋊C4C2×D1912yes—
141C2×C42—191no—
142C2×C42—192no—
143#95—192no—
144#95—192no—
145#95—191no—
146#95—192no—
147#95—192no—
148#95C2×D1911yescharacteristic
149C19#260911yescharacteristic, complemented, Sylow
150C24C22×D1912yes—
151C2×D4—24no—
152C2×D4—41no—
153C22×C4—192no—
154C22×C4—192no—
155C22×C4—192no—
156C22×C4—192no—
157C22×C4—384no—
158C22×C4—384no—
159C22×C4—384no—
160C22×C4C22×D1911yescharacteristic
161C22×C4C22×D1911yescharacteristic
162C22×C4C22×D1912yes—
163C22×C4C22×D1911yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—384no—
166C4⋊C4—384no—
167C4⋊C4—384no—
168C4⋊C4—761no—
169C4⋊C4—761no—
170C22⋊C4—24no—
171C22⋊C4—24no—
172C22⋊C4—384no—
173C22⋊C4—384no—
174C22⋊C4—762no—
175C42—194no—
176C42—384no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23#6454314yes—
184C23C23×D1911yescharacteristic
185D4—44no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—194no—
196C2×C4—194no—
197C2×C4—3816no—
198C2×C4—382no—
199C2×C4—382no—
200C2×C4—382no—
201C2×C4—382no—
202C2×C4—382no—
203C2×C4—382no—
204C2×C4—382no—
205C2×C4—382no—
206C2×C4—382no—
207C2×C4—382no—
208C2×C4D4×D1912yes—
209C22—24no—
210C22—24no—
211C22—24no—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—42no—
216C22C2×D4×D1911yescharacteristic
217C22C2×#6454312yes—
218C22#1059743011yescharacteristic
219C22#41×D1912yes—
220C22#1059743611yescharacteristic
221C4—22no—
222C4—42no—
223C4—41no—
224C4—41no—
225C4—384no—
226C4—384no—
227C4—762no—
228C4—762no—
229C2—44no—
230C2#1192705412yes—
231C2#1192712111yescharacteristic
232C2#1192722511yescharacteristic
233C2#1192723112yes—
234C2#1192725611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#394C2
prime radicalC22×D4×C19C22
hypercenter#394D19
hypocenterC19#2609
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#10597323C2semidirect
2. #11926474C2semidirect
3. #11926467C2semidirect
4. #11926437C2semidirect
5. #11926426C2semidirect
7. #11926416C2semidirect
8. #11926409C2semidirect
58. C4×Dic19D4semidirect
149. C19#2609semidirect

Maximal subgroups

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

subgroupindex
C2×#105973232
#119264742
#119264672
#119264372
#119264262
#119264242
#119264162
#119264092
C19×#3942
#260919