Finite Group Databasebeta

← #14568567

Subgroups — #14568567

Order 2432.

900 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 900 conjugacy classes of subgroups — too many to draw. Only its 169 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×#10597383C212yesmaximal, complemented
3C22×(C2×D19)⋊C4C211yesmaximal, characteristic, complemented
4#11926479C212yesmaximal, complemented
5#11926452C212yesmaximal, complemented
6#11926444C214yesmaximal, complemented
7C4×C22⋊Dic19C211yesmaximal, characteristic, complemented
8C2×C19×#121C211yesmaximal, characteristic, complemented
9C24×D19C2211yescharacteristic
10C22×D4×C19C2212yes—
11C22×D4×C19C2211yescharacteristic, complemented
12C23×C4×C19C2211yescharacteristic
13C22×C22⋊D19C2214yes—
14C23×Dic19C2211yescharacteristic
15C19×#121—24no—
16C2×C4⋊C4×C19C2211yescharacteristic, complemented
17C2×C22⋊C4×C19C2212yescomplemented
18C2×C22⋊Dic19C2212yes—
19C2×C22⋊Dic19C2214yescomplemented
20#10597383—28no—
21#10597381—28no—
22C2×(C2×D19)⋊C4—24no—
23C2×(C2×D19)⋊C4C2212yes—
24C2×(C2×D19)⋊C4C2214yes—
25C2×(C2×D19)⋊C4C2212yes—
26C2×Dic19⋊C4C2214yescomplemented
27C2×C4×Dic19C2212yescomplemented
28C19⋊#95C2212yescomplemented
29C24×C19C2312yes—
30C24×C19C2311yescharacteristic
31C23×D19—22no—
32C23×D19—24no—
33C23×D19—24no—
34C23×D19—42no—
35C23×D19C2312yes—
36C2×D4×C19—24no—
37C2×D4×C19—24no—
38C2×D4×C19—24no—
39C2×D4×C19—22no—
40C2×D4×C19—42no—
41C22×C4×C19—42no—
42C22×C4×C19D414yescomplemented
43C22×C4×C19C2312yes—
44C22×C4×C19C2311yescharacteristic
45C22×C4×C19C2311yescharacteristic
46C2×C22⋊D19—28no—
47C2×C22⋊D19—28no—
48C2×C22⋊D19—44no—
49C22×Dic19—24no—
50C22×Dic19—22no—
51C22×Dic19C2312yes—
52C22×Dic19C2314yes—
53C4⋊C4×C19—22no—
54C22⋊C4×C19—24no—
55C22⋊Dic19—28no—
56C22⋊Dic19D418yescomplemented
57(C2×D19)⋊C4—24no—
58(C2×D19)⋊C4—24no—
59(C2×D19)⋊C4—28no—
60Dic19⋊C4—28no—
61C4×Dic19—42no—
62C23×C19—22no—
63C23×C19—22no—
64C23×C19—22no—
65C23×C19—22no—
66C23×C19—22no—
67C23×C19—24no—
68C23×C19—24no—
69C23×C19C2×D414yes—
70C23×C19C2×D412yes—
71C23×C19C2411yescharacteristic
72C22×D19—28no—
73C22×D19—22no—
74C22×D19—24no—
75C22×D19—22no—
76C22×D19—24no—
77C22×D19—416no—
78C22×D19—44no—
79C22×D19—44no—
80C22×D19#4114yes—
81D4×C19—44no—
82D4×C19—48no—
83C2×C4×C19—22no—
84C2×C4×C19—22no—
85C2×C4×C19—22no—
86C2×C4×C19—22no—
87C2×C4×C19—22no—
88C2×C4×C19—44no—
89C2×C4×C19C2×D412yes—
90C2×C4×C19C2×D412yes—
91C22⋊D19—416no—
92C2×Dic19—24no—
93C2×Dic19—24no—
94C2×Dic19—24no—
95C2×Dic19—22no—
96C2×Dic19—44no—
97C2×Dic19C2×D418yes—
98#2539—191nomaximal, Sylow
99C22×C19—22no—
100C22×C19—22no—
101C22×C19—28no—
102C22×C19—42no—
103C22×C19—42no—
104C22×C19—42no—
105C22×C19—44no—
106C22×C19—44no—
107C22×C19#12714yes—
108C22×C19C22×D412yes—
109C22×C19C22×D411yescharacteristic
110C22×C19C2×#4112yes—
111C22×C19H(5,𝔽2)12yes—
112C2×D19—24no—
113C2×D19—28no—
114C2×D19—416no—
115C2×D19—42no—
116C2×D19—42no—
117C2×D19—44no—
118C4×C19—22no—
119C4×C19—22no—
120C4×C19—42no—
121Dic19—28no—
122Dic19—42no—
123C2×#123—192no—
124C2×#121D1911yescharacteristic, complemented
125C2×#120—192no—
126C22×C22⋊C4—191no—
127#399—192no—
128#392—192no—
129#390—194no—
130C4×C22⋊C4—191no—
131C2×C19—24no—
132C2×C19—82no—
133C2×C19#52511yescharacteristic
134C2×C19C2×#12711yescharacteristic
135C2×C19#53411yescharacteristic
136C2×C19#54614yes—
137D19—44no—
138C25—191no—
139C22×D4—194no—
140C22×D4C2×D1912yes—
141C22×D4C2×D1911yescharacteristic, complemented
142C23×C4—191no—
143C23×C4C2×D1911yescharacteristic
144#123—388no—
145#121—24no—
146#120—388no—
147C2×C4⋊C4—194no—
148C2×C4⋊C4C2×D1911yescharacteristic, complemented
149C2×C22⋊C4—192no—
150C2×C22⋊C4—194no—
151C2×C22⋊C4—192no—
152C2×C22⋊C4—192no—
153C2×C22⋊C4—194no—
154C2×C22⋊C4—384no—
155C2×C22⋊C4C2×D1912yescomplemented
156C2×C42—192no—
157#95—192no—
158C19#253911yescharacteristic, complemented, Sylow
159C24—192no—
160C24—384no—
161C24—382no—
162C24—384no—
163C24—762no—
164C24C22×D1912yes—
165C24C22×D1911yescharacteristic
166C2×D4—24no—
167C2×D4—24no—
168C2×D4—24no—
169C2×D4—22no—
170C2×D4—42no—
171C2×D4—388no—
172C2×D4—388no—
173C2×D4—764no—
174C22×C4—42no—
175C22×C4—194no—
176C22×C4—192no—
177C22×C4—384no—
178C22×C4—382no—
179C22×C4C22⋊D1914yescomplemented
180C22×C4C22×D1912yes—
181C22×C4C22×D1911yescharacteristic
182C22×C4C22×D1911yescharacteristic
183C4⋊C4—22no—
184C4⋊C4—388no—
185C22⋊C4—24no—
186C22⋊C4—198no—
187C22⋊C4—388no—
188C22⋊C4—388no—
189C22⋊C4—384no—
190C22⋊C4—384no—
191C42—762no—
192C23—22no—
193C23—22no—
194C23—22no—
195C23—22no—
196C23—24no—
197C23—24no—
198C23—22no—
199C23—194no—
200C23—388no—
201C23—384no—
202C23—384no—
203C23—382no—
204C23—382no—
205C23—7616no—
206C23—764no—
207C23—764no—
208C23D4×D1914yes—
209C23C2×C22⋊D1912yes—
210C23C23×D1911yescharacteristic
211D4—44no—
212D4—48no—
213D4—7616no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—44no—
220C2×C4—198no—
221C2×C4—384no—
222C2×C4—384no—
223C2×C4—384no—
224C2×C4—382no—
225C2×C4—764no—
226C2×C4C2×C22⋊D1912yes—
227C2×C4C2×C22⋊D1912yes—
228C22—22no—
229C22—22no—
230C22—28no—
231C22—42no—
232C22—42no—
233C22—42no—
234C22—44no—
235C22—44no—
236C22—384no—
237C22—388no—
238C22—7616no—
239C22—762no—
240C22—762no—
241C22—764no—
242C22#1059738614yes—
243C22C2×D4×D1912yes—
244C22#1059743012yes—
245C22#41×D1912yes—
246C22C22×C22⋊D1911yescharacteristic
247C4—22no—
248C4—22no—
249C4—42no—
250C4—388no—
251C4—762no—
252C2—24no—
253C2—82no—
254C2—764no—
255C2#1192705111yescharacteristic
256C2C2×#1059738611yescharacteristic
257C2#1192710311yescharacteristic
258C2#1192718314yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#121C2
hypercenterC2×#121D19
hypocenterC19#2539
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10597381C2semidirect
2. C2×#10597383C2semidirect
3. C22×(C2×D19)⋊C4C2semidirect
4. #11926479C2semidirect
5. #11926452C2semidirect
6. #11926444C2semidirect
7. C4×C22⋊Dic19C2semidirect
8. C2×C19×#121C2semidirect
11. C22×D4×C19C22semidirect
16. C2×C4⋊C4×C19C22semidirect
17. C2×C22⋊C4×C19C22semidirect
19. C2×C22⋊Dic19C22semidirect
26. C2×Dic19⋊C4C22semidirect
27. C2×C4×Dic19C22semidirect
28. C19⋊#95C22semidirect
42. C22×C4×C19D4semidirect
56. C22⋊Dic19D4semidirect
124. C2×#121D19semidirect
141. C22×D4C2×D19semidirect
148. C2×C4⋊C4C2×D19semidirect
155. C2×C22⋊C4C2×D19semidirect
158. C19#2539semidirect
179. C22×C4C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973812
C2×#105973832
C22×(C2×D19)⋊C42
#119264792
#119264522
#119264442
C4×C22⋊Dic192
C2×C19×#1212
#253919