Finite Group Databasebeta

← #14571919

Subgroups — #14571919

Order 2432.

1068 conjugacy classes of subgroups; only the 201 normal subgroups are shown.

normal subgroups only

This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 201 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
1C23×C4×D19C211yesmaximal, characteristic
2C2×#10597392C212yesmaximal, complemented
3#11926416C212yesmaximal, complemented
4#11926415C214yesmaximal, complemented
5#11926404C211yesmaximal, characteristic, complemented
6#11926401C212yesmaximal, complemented
7#11926399C212yesmaximal
8C2×C19×C22⋊Q8C211yesmaximal, characteristic, complemented
9C24×D19C2211yescharacteristic
10C22×Q8×C19C2211yescharacteristic, complemented
11C23×C4×C19C2211yescharacteristic
12C23×Dic19C2211yescharacteristic
13C22×C4×D19—24no—
14C22×C4×D19—28no—
15C22×C4×D19C2212yes—
16C22×C4×D19C2212yes—
17C19×C22⋊Q8—24no—
18C2×C4⋊C4×C19C2211yescharacteristic, complemented
19C2×C4⋊C4×C19C2212yescomplemented
20C2×C22⋊C4×C19C2212yes—
21C2×C22⋊Dic19C2212yes—
22#10597392—28no—
23C2×(C2×D19)⋊C4C2214yes—
24C2×(C2×D19)⋊C4C2214yes—
25C2×C4⋊Dic19C2212yescomplemented
26C2×Dic19⋊C4C2214yescomplemented
27C19⋊#95C2214yescomplemented
28C19⋊#95C2212yescomplemented
29C24×C19C2311yescharacteristic
30C23×D19—22no—
31C23×D19—22no—
32C23×D19—24no—
33C23×D19—24no—
34C23×D19Q814yescomplemented
35C23×D19C2312yes—
36C2×Q8×C19—24no—
37C2×Q8×C19—22no—
38C22×C4×C19—24no—
39C22×C4×C19D414yes—
40C22×C4×C19C2312yes—
41C22×C4×C19C2312yes—
42C22×C4×C19C2311yescharacteristic
43C22×C4×C19C2311yescharacteristic
44C22×Dic19—22no—
45C22×Dic19—24no—
46C22×Dic19C2314yes—
47C22×Dic19C2312yes—
48C2×C4×D19—232no—
49C2×C4×D19—24no—
50C2×C4×D19—24no—
51C2×C4×D19—24no—
52C2×C4×D19—24no—
53C2×C4×D19—24no—
54C2×C4×D19D418yes—
55C4⋊C4×C19—22no—
56C4⋊C4×C19—24no—
57C22⋊C4×C19—24no—
58C22⋊Dic19—24no—
59(C2×D19)⋊C4—28no—
60(C2×D19)⋊C4—28no—
61C4⋊Dic19—24no—
62Dic19⋊C4—28no—
63C23×C19—22no—
64C23×C19—22no—
65C23×C19C2×D412yes—
66C23×C19C2×Q812yes—
67C23×C19#4112yes—
68C23×C19C2411yescharacteristic
69C22×D19—28no—
70C22×D19—216no—
71C22×D19—28no—
72C22×D19—28no—
73C22×D19—22no—
74C22×D19—22no—
75C22×D19—22no—
76C22×D19—22no—
77C22×D19—216no—
78C22×D19C2×D414yes—
79C22×D19C2×Q814yes—
80C22×D19#4114yes—
81Q8×C19—44no—
82C2×C4×C19—22no—
83C2×C4×C19—28no—
84C2×C4×C19—24no—
85C2×C4×C19—22no—
86C2×C4×C19—22no—
87C2×C4×C19—24no—
88C2×C4×C19C2×D414yes—
89C2×C4×C19C2×D412yes—
90C2×C4×C19C2×D412yes—
91C2×Dic19—28no—
92C2×Dic19—22no—
93C2×Dic19—22no—
94C2×Dic19—24no—
95C2×Dic19—24no—
96C2×Dic19—24no—
97C2×Dic19C2×D414yes—
98C4×D19—216no—
99C4×D19—216no—
100#2848—191nomaximal, Sylow
101C22×C19—22no—
102C22×C19—24no—
103C22×C19—22no—
104C22×C19—24no—
105C22×C19C22⋊Q814yescomplemented
106C22×C19C22×D412yes—
107C22×C19C22×D411yescharacteristic
108C22×C19C22×Q811yescharacteristic
109C22×C19C2×#4111yescharacteristic
110C22×C19C2×#4112yes—
111C2×D19—232no—
112C2×D19—24no—
113C2×D19—24no—
114C2×D19—24no—
115C2×D19—24no—
116C2×D19—24no—
117C2×D19—24no—
118C2×D19C22⋊Q818yescomplemented
119C4×C19—22no—
120C4×C19—42no—
121C4×C19—42no—
122C4×C19#12014yes—
123Dic19—24no—
124Dic19—44no—
125C24×C4—191no—
126C2×C22⋊Q8—192no—
127C2×C22⋊Q8D1911yescharacteristic, complemented
128#385—194no—
129#385—192no—
130#380—191no—
131#380—192no—
132#379—192no—
133C2×C19—24no—
134C2×C19C2×#12011yescharacteristic
135C2×C19C2×C22⋊Q812yes—
136C2×C19C2×C22⋊Q811yescharacteristic
137C2×C19#52511yescharacteristic
138C2×C19#52512yes—
139D19—28no—
140C25—191no—
141C22×Q8C2×D1911yescharacteristic, complemented
142C23×C4—192no—
143C23×C4—191no—
144C23×C4—192no—
145C23×C4—388no—
146C23×C4—384no—
147C23×C4C2×D1911yescharacteristic
148C22⋊Q8—24no—
149C22⋊Q8—388no—
150C2×C4⋊C4—192no—
151C2×C4⋊C4—194no—
152C2×C4⋊C4C2×D1911yescharacteristic, complemented
153C2×C4⋊C4C2×D1912yescomplemented
154C2×C22⋊C4—192no—
155C2×C22⋊C4—194no—
156C2×C22⋊C4—194no—
157C2×C22⋊C4C2×D1912yes—
158#95—194no—
159#95—192no—
160C19#284811yescharacteristic, complemented, Sylow
161C24—192no—
162C24—194no—
163C24—384no—
164C24—384no—
165C24—382no—
166C24—382no—
167C24C22×D1911yescharacteristic
168C2×Q8—24no—
169C2×Q8—22no—
170C22×C4—24no—
171C22×C4—192no—
172C22×C4—198no—
173C22×C4—194no—
174C22×C4—384no—
175C22×C4—384no—
176C22×C4—3832no—
177C22×C4—384no—
178C22×C4—382no—
179C22×C4—384no—
180C22×C4—384no—
181C22×C4—384no—
182C22×C4C22⋊D1914yes—
183C22×C4C22×D1912yes—
184C22×C4C22×D1912yes—
185C22×C4C22×D1911yescharacteristic
186C22×C4C22×D1911yescharacteristic
187C4⋊C4—22no—
188C4⋊C4—24no—
189C4⋊C4—388no—
190C4⋊C4—384no—
191C22⋊C4—24no—
192C22⋊C4—388no—
193C22⋊C4—388no—
194C22⋊C4—384no—
195C23—22no—
196C23—22no—
197C23—194no—
198C23—194no—
199C23—194no—
200C23—3816no—
201C23—388no—
202C23—388no—
203C23—3816no—
204C23—388no—
205C23—382no—
206C23—382no—
207C23—382no—
208C23—382no—
209C23Q8×D1912yes—
210C23#6454512yes—
211C23C2×C22⋊D1912yes—
212C23C23×D1911yescharacteristic
213Q8—44no—
214C2×C4—22no—
215C2×C4—28no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—194no—
221C2×C4—3816no—
222C2×C4—388no—
223C2×C4—382no—
224C2×C4—382no—
225C2×C4—3816no—
226C2×C4—384no—
227C2×C4—384no—
228C2×C4—384no—
229C2×C4D4×D1914yes—
230C2×C4C2×C22⋊D1912yes—
231C2×C4C2×C22⋊D1912yes—
232C22—22no—
233C22—24no—
234C22—22no—
235C22—24no—
236C22—198no—
237C22—3832no—
238C22—384no—
239C22—384no—
240C22—384no—
241C22—384no—
242C22—384no—
243C22—384no—
244C22#1059739214yescomplemented
245C22C2×D4×D1912yes—
246C22C2×Q8×D1911yescharacteristic
247C22C2×#6454511yescharacteristic
248C22#41×D1912yes—
249C22C22×C22⋊D1911yescharacteristic
250C4—22no—
251C4—42no—
252C4—42no—
253C4—384no—
254C4—764no—
255C4#1059738314yes—
256C2—24no—
257C2—388no—
258C2C2×#1059738311yescharacteristic
259C2C22⋊Q8×D1912yes—
260C2C2×#1059739211yescharacteristic
261C2#1192705111yescharacteristic
262C2#1192705712yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×C22⋊Q8C2
prime radicalC24×D19C22
hypercenterC2×C22⋊Q8D19
hypocenterC19#2848
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#10597392C2semidirect
3. #11926416C2semidirect
4. #11926415C2semidirect
5. #11926404C2semidirect
6. #11926401C2semidirect
8. C2×C19×C22⋊Q8C2semidirect
10. C22×Q8×C19C22semidirect
18. C2×C4⋊C4×C19C22semidirect
19. C2×C4⋊C4×C19C22semidirect
25. C2×C4⋊Dic19C22semidirect
26. C2×Dic19⋊C4C22semidirect
27. C19⋊#95C22semidirect
28. C19⋊#95C22semidirect
34. C23×D19Q8semidirect
105. C22×C19C22⋊Q8semidirect
118. C2×D19C22⋊Q8semidirect
127. C2×C22⋊Q8D19semidirect
141. C22×Q8C2×D19semidirect
152. C2×C4⋊C4C2×D19semidirect
153. C2×C4⋊C4C2×D19semidirect
160. C19#2848semidirect
244. C22#10597392semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D192
C2×#105973922
#119264162
#119264152
#119264042
#119264012
#119263992
C2×C19×C22⋊Q82
#284819