Finite Group Databasebeta

← #14567511

Subgroups — #14567511

Order 2432.

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

normal subgroups only

This group has 660 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
1C2×#10597381C212yesmaximal, complemented
2C2×D4×Dic19C212yesmaximal, complemented
3#11926480C211yesmaximal, characteristic, complemented
4#11926458C212yesmaximal, complemented
5#11926441C212yesmaximal, complemented
6#11926438C212yesmaximal, complemented
7#11926419C212yesmaximal, complemented
8#11926416C211yesmaximal, characteristic, complemented
9C19×#392C211yesmaximal, characteristic
10C22×D4×C19C2212yes—
11C22×D4×C19C2211yescharacteristic
12C23×Dic19C2212yes—
13C23×Dic19C2211yescharacteristic
14C2×C22⋊C4×C19C2212yes—
15C2×C22⋊C4×C19C2211yescharacteristic
16C2×C22⋊Dic19C2212yes—
17C2×C22⋊Dic19C2212yes—
18C2×C22⋊Dic19C2211yescharacteristic
19C2×C22⋊Dic19C2212yes—
20C2×C22⋊Dic19C2212yes—
21#10597381—28no—
22D4×Dic19—28no—
23C2×C4⋊Dic19C2212yes—
24C2×C4⋊Dic19C2211yescharacteristic
25C2×Dic19⋊C4C2212yes—
26C2×Dic19⋊C4C2212yes—
27C2×Dic19⋊C4C2212yes—
28C2×C4×Dic19C2212yes—
29C19×#95C2211yescharacteristic
30C19⋊#95C2212yes—
31C19⋊#95C2212yes—
32C19⋊#95C2211yescharacteristic
33C24×C19C2312yes—
34C24×C19C2311yescharacteristic
35C2×D4×C19—24no—
36C2×D4×C19—24no—
37C2×D4×C19—24no—
38C2×D4×C19—24no—
39C2×D4×C19—41no—
40C22×C4×C19C2311yescharacteristic
41C22×C4×C19C2311yescharacteristic
42C22×C4×C19C2312yes—
43C22×Dic19—24no—
44C22×Dic19—24no—
45C22×Dic19—24no—
46C22×Dic19—41no—
47C22×Dic19—42no—
48C22×Dic19C2312yes—
49C22×Dic19C2312yes—
50C22×Dic19C2312yes—
51C22×Dic19C2312yes—
52C22⋊C4×C19—24no—
53C22⋊C4×C19—41no—
54C22⋊Dic19—24no—
55C22⋊Dic19—22no—
56C22⋊Dic19—24no—
57C22⋊Dic19—24no—
58C22⋊Dic19D418yescomplemented
59C4⋊Dic19—24no—
60C4⋊Dic19—41no—
61Dic19⋊C4—24no—
62Dic19⋊C4—24no—
63Dic19⋊C4—24no—
64C4×Dic19—24no—
65C23×C19—22no—
66C23×C19—22no—
67C23×C19—22no—
68C23×C19—22no—
69C23×C19—22no—
70C23×C19—22no—
71C23×C19—21no—
72C23×C19—22no—
73C23×C19—21no—
74C23×C19—22no—
75C23×C19C2×D414yes—
76C23×C19#4112yes—
77C23×C19C2411yescharacteristic
78D4×C19—216no—
79D4×C19—44no—
80C2×C4×C19—22no—
81C2×C4×C19—22no—
82C2×C4×C19—22no—
83C2×C4×C19—22no—
84C2×C4×C19—21no—
85C2×C4×C19—21no—
86C2×C4×C19#4114yes—
87C2×Dic19—22no—
88C2×Dic19—22no—
89C2×Dic19—22no—
90C2×Dic19—22no—
91C2×Dic19—22no—
92C2×Dic19—22no—
93C2×Dic19—22no—
94C2×Dic19—22no—
95C2×Dic19—22no—
96C2×Dic19—22no—
97C2×Dic19—44no—
98C2×Dic19—48no—
99C2×Dic19C2×D414yes—
100C2×Dic19C2×D414yes—
101#2455—191nomaximal, Sylow
102C22×C19—24no—
103C22×C19—24no—
104C22×C19—22no—
105C22×C19—24no—
106C22×C19—24no—
107C22×C19—42no—
108C22×C19—42no—
109C22×C19—41no—
110C22×C19—42no—
111C22×C19—42no—
112C22×C19—42no—
113C22×C19—41no—
114C22×C19C22×D412yes—
115C22×C19C2×#4111yescharacteristic
116C22×C19C2×#4112yes—
117C22×C19H(5,𝔽2)11yescharacteristic
118C22×C192−1+411yescharacteristic
119C4×C19—24no—
120C4×C19—41no—
121C4×C19—41no—
122Dic19—24no—
123Dic19—24no—
124Dic19—42no—
125Dic19—42no—
126C2×#123—192no—
127C2×C4×D4—192no—
128#399—191no—
129#394—192no—
130#392D1911yescharacteristic
131#389—192no—
132#388—192no—
133#385—191no—
134#385—192no—
135C2×C19—44no—
136C2×C19—42no—
137C2×C19#52512yes—
138C2×C19#53911yescharacteristic
139C2×C19D4211yescharacteristic
140C2×C19#54712yes—
141C2×C19#55911yescharacteristic
142C22×D4C2×D1912yes—
143C22×D4C2×D1911yescharacteristic
144C23×C4—191no—
145C23×C4—192no—
146#123—388no—
147C4×D4—388no—
148C2×C4⋊C4—192no—
149C2×C4⋊C4—192no—
150C2×C4⋊C4—192no—
151C2×C4⋊C4—192no—
152C2×C4⋊C4—191no—
153C2×C22⋊C4—192no—
154C2×C22⋊C4—192no—
155C2×C22⋊C4—192no—
156C2×C22⋊C4—192no—
157C2×C22⋊C4—191no—
158C2×C22⋊C4C2×D1912yes—
159C2×C22⋊C4C2×D1911yescharacteristic
160C2×C42—192no—
161#95—192no—
162#95—192no—
163#95—191no—
164#95C2×D1911yescharacteristic
165C19#245511yescharacteristic, complemented, Sylow
166C24C22×D1912yes—
167C24C22×D1911yescharacteristic
168C2×D4—24no—
169C2×D4—24no—
170C2×D4—24no—
171C2×D4—24no—
172C2×D4—41no—
173C22×C4—192no—
174C22×C4—192no—
175C22×C4—192no—
176C22×C4—192no—
177C22×C4—384no—
178C22×C4—384no—
179C22×C4—384no—
180C22×C4—761no—
181C22×C4—762no—
182C22×C4C22×D1911yescharacteristic
183C22×C4C22×D1911yescharacteristic
184C22×C4C22×D1912yes—
185C4⋊C4—384no—
186C4⋊C4—384no—
187C4⋊C4—384no—
188C4⋊C4—384no—
189C4⋊C4—761no—
190C22⋊C4—24no—
191C22⋊C4—41no—
192C22⋊C4—198no—
193C22⋊C4—384no—
194C22⋊C4—384no—
195C22⋊C4—384no—
196C22⋊C4—382no—
197C42—384no—
198C23—22no—
199C23—22no—
200C23—22no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—21no—
205C23—22no—
206C23—21no—
207C23—22no—
208C23D4×D1914yes—
209C23#6454312yes—
210C23C23×D1911yescharacteristic
211D4—216no—
212D4—44no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—194no—
220C2×C4—194no—
221C2×C4—382no—
222C2×C4—382no—
223C2×C4—382no—
224C2×C4—382no—
225C2×C4—382no—
226C2×C4—382no—
227C2×C4—382no—
228C2×C4—382no—
229C2×C4—382no—
230C2×C4—382no—
231C2×C4—764no—
232C2×C4—768no—
233C2×C4#6454314yes—
234C22—24no—
235C22—24no—
236C22—22no—
237C22—24no—
238C22—24no—
239C22—42no—
240C22—42no—
241C22—41no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—41no—
246C22C2×D4×D1912yes—
247C22C2×#6454311yescharacteristic
248C22C2×#6454312yes—
249C22#1059743011yescharacteristic
250C22#1059743611yescharacteristic
251C4—24no—
252C4—41no—
253C4—41no—
254C4—384no—
255C4—384no—
256C4—762no—
257C4—762no—
258C2—44no—
259C2—42no—
260C2#1192705012yes—
261C2#1192713911yescharacteristic
262C2#1192717611yescharacteristic
263C2#1192719412yes—
264C2#1192728011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
Fitting, prime radicalC19×#392C2
hypercenter#392D19
hypocenterC19#2455
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#10597381C2semidirect
2. C2×D4×Dic19C2semidirect
3. #11926480C2semidirect
4. #11926458C2semidirect
5. #11926441C2semidirect
6. #11926438C2semidirect
7. #11926419C2semidirect
8. #11926416C2semidirect
58. C22⋊Dic19D4semidirect
165. C19#2455semidirect

Maximal subgroups

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

subgroupindex
C2×#105973812
C2×D4×Dic192
#119264802
#119264582
#119264412
#119264382
#119264192
#119264162
C19×#3922
#245519