Finite Group Databasebeta

← #14574431

Subgroups — #14574431

Order 2432.

514 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#121×D19C212yesmaximal, complemented
2#11926864C212yesmaximal, complemented
3#11926861C212yesmaximal, complemented
4#11926797C211yesmaximal, characteristic, complemented
5#11926795C212yesmaximal, complemented
6#11926679C212yesmaximal, complemented
7#11926676C212yesmaximal, complemented
8#11926507C211yesmaximal, characteristic, complemented
9C19×#469C211yesmaximal, characteristic, complemented
10C2×D4×D19—22no—
11C2×D4×D19C2212yescomplemented
12C22×C4×D19C2211yescharacteristic
13C2×D8×C19C2211yescharacteristic, complemented
14C2×M16×C19C2211yescharacteristic, complemented
15C19×#121C2212yescomplemented
16#10597385—22no—
17#10597384C2212yes—
18C2×#64525C2212yescomplemented
19#10597376C2212yescomplemented
20C2×#64520C2211yescharacteristic, complemented
21C2×D152C2211yescharacteristic, complemented
22#10597341C2212yes—
23C4⋊C4×D19C2212yescomplemented
24#10597330—22no—
25C22⋊C4×D19—22no—
26C19×#106C2211yescharacteristic, complemented
27C19×#102C2212yescomplemented
28#10597289C2212yescomplemented
29#10597278C2212yescomplemented
30(C2×D19)⋊C8C2212yescomplemented
31(C2×D19)⋊C8C2212yescomplemented
32#10597274C2211yescharacteristic, complemented
33#10597266C2212yescomplemented
34#10597265C2212yescomplemented
35C23×D19—22no—
36C23×D19D411yescharacteristic
37C2×D4×C19—22no—
38C2×D4×C19C2312yes—
39C22×C4×C19C2311yescharacteristic
40C2×C22⋊D19—22no—
41C2×C22⋊D19—22no—
42C2×C22⋊D19—22no—
43C22×Dic19D411yescharacteristic
44D4×D19—42no—
45D4×D19—42no—
46D4×D19—48no—
47C2×D76—22no—
48C2×D76C2312yes—
49C2×C4×D19—22no—
50C2×C4×D19—41no—
51C2×C4×D19—41no—
52C2×C4×D19D412yes—
53C2×C4×D19C2312yes—
54D8×C19—41no—
55M16×C19—41no—
56C2×C8×C19C2311yescharacteristic
57C2×C8×C19C2311yescharacteristic
58C4⋊C4×C19C2312yes—
59C22⋊C4×C19—22no—
60C22⋊Dic19—22no—
61#64525—42no—
62(C2×D19)⋊C4—22no—
63(C2×D19)⋊C4—22no—
64C4⋊Dic19C2312yes—
65Dic19⋊C4—22no—
66#64520—41no—
67C2×C19⋊C8C2312yes—
68D152—41no—
69C23×C19—22no—
70C23×C19C2×D411yescharacteristic
71C22×D19—24no—
72C22×D19—22no—
73C22×D19—41no—
74C22×D19—44no—
75C22×D19—44no—
76C22×D19—44no—
77C22×D19C2×D412yes—
78D4×C19—22no—
79D4×C19—22no—
80D4×C19—44no—
81C2×C4×C19—21no—
82C2×C4×C19—21no—
83C2×C4×C19—22no—
84C2×C4×C19C2×D411yescharacteristic
85C2×C4×C19C2411yescharacteristic
86C22⋊D19—44no—
87C22⋊D19—44no—
88C22⋊D19—44no—
89C2×Dic19—22no—
90C2×Dic19—41no—
91C2×Dic19C2×D412yes—
92D76—22no—
93D76—22no—
94D76—44no—
95C4×D19—22no—
96C4×D19—22no—
97C4×D19—42no—
98C4×D19—44no—
99C8×C19—21no—
100C8×C19—21no—
101C19⋊C8—22no—
102#3192—191nomaximal, Sylow
103C22×C19—21no—
104C22×C19—22no—
105C22×C19—42no—
106C22×C19—42no—
107C22×C19—42no—
108C22×C19C22×D411yescharacteristic
109C2×D19—22no—
110C2×D19—22no—
111C2×D19—44no—
112C2×D19—42no—
113C2×D19—42no—
114C2×D19—42no—
115C2×D19—88no—
116C2×D19AGL(1,ℤ/8)14yes—
117C4×C19—21no—
118C4×C19—42no—
119C4×C19H(5,𝔽2)11yescharacteristic
120C4×C19H(5,𝔽2)11yescharacteristic
121Dic19—22no—
122Dic19—42no—
123C2×#121—192no—
124#481—192no—
125#481—192no—
126#469—191no—
127#469—192no—
128#469D1911yescharacteristic, complemented
129#447—192no—
130#447—192no—
131#407—191no—
132C2×C19—41no—
133C2×C19—82no—
134C2×C19#53411yescharacteristic
135C2×C19C2×AGL(1,ℤ/8)12yes—
136D19—24no—
137D19—82no—
138C22×D4—192no—
139C22×D4—382no—
140C23×C4—191no—
141C2×D8—192no—
142C2×D8—191no—
143C2×D8C2×D1911yescharacteristic, complemented
144C2×M16—191no—
145C2×M16C2×D1911yescharacteristic, complemented
146#121—192no—
147#121—192no—
148#121—192no—
149#121—382no—
150#121—382no—
151#121C2×D1912yescomplemented
152C2×C4⋊C4—192no—
153C2×C22⋊C4—382no—
154#106—191no—
155#106—192no—
156#106C2×D1911yescharacteristic, complemented
157#102—192no—
158#102—192no—
159#102—192no—
160#102C2×D1912yescomplemented
161C22⋊C8—192no—
162C22⋊C8—192no—
163C19#319211yescharacteristic, complemented, Sylow
164C24—191no—
165C24—382no—
166C2×D4—22no—
167C2×D4—192no—
168C2×D4—382no—
169C2×D4—382no—
170C2×D4—382no—
171C2×D4—382no—
172C2×D4—762no—
173C2×D4—762no—
174C2×D4—768no—
175C2×D4C22×D1912yes—
176C22×C4—191no—
177C22×C4—192no—
178C22×C4—192no—
179C22×C4—382no—
180C22×C4—761no—
181C22×C4—761no—
182C22×C4C22×D1911yescharacteristic
183D8—41no—
184D8—761no—
185D8—762no—
186M16—41no—
187M16—761no—
188C2×C8—192no—
189C2×C8C22×D1911yescharacteristic
190C2×C8C22×D1911yescharacteristic
191C4⋊C4—192no—
192C4⋊C4—382no—
193C4⋊C4C22×D1912yes—
194C22⋊C4—22no—
195C22⋊C4—382no—
196C22⋊C4—382no—
197C22⋊C4—382no—
198C23—22no—
199C23—192no—
200C23—384no—
201C23—382no—
202C23—761no—
203C23—764no—
204C23—764no—
205C23—764no—
206C23D4×D1911yescharacteristic
207D4—22no—
208D4—22no—
209D4—44no—
210D4—382no—
211D4—382no—
212D4—764no—
213D4—764no—
214D4—764no—
215D4—764no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—192no—
220C2×C4—382no—
221C2×C4—382no—
222C2×C4—382no—
223C2×C4—762no—
224C2×C4—764no—
225C2×C4—761no—
226C2×C4D4×D1911yescharacteristic
227C2×C4C23×D1911yescharacteristic
228C8—21no—
229C8—21no—
230C8—382no—
231C22—22no—
232C22—21no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—194no—
237C22—382no—
238C22—382no—
239C22—764no—
240C22—762no—
241C22—762no—
242C22—762no—
243C22—1528no—
244C22C2×D4×D1911yescharacteristic
245C4—21no—
246C4—42no—
247C4—382no—
248C4—762no—
249C4#1059743011yescharacteristic
250C4#1059743511yescharacteristic
251C2—41no—
252C2—82no—
253C2—384no—
254C2—1522no—
255C2#1192710211yescharacteristic
256C2AGL(1,ℤ/8)×D1912yes—
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#469C2
socleC22×C19C22×D4
hypercenter#469D19
hypocenterC19#3192
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #121×D19C2semidirect
2. #11926864C2semidirect
3. #11926861C2semidirect
4. #11926797C2semidirect
5. #11926795C2semidirect
6. #11926679C2semidirect
7. #11926676C2semidirect
8. #11926507C2semidirect
9. C19×#469C2semidirect
11. C2×D4×D19C22semidirect
13. C2×D8×C19C22semidirect
14. C2×M16×C19C22semidirect
15. C19×#121C22semidirect
18. C2×#64525C22semidirect
19. #10597376C22semidirect
20. C2×#64520C22semidirect
21. C2×D152C22semidirect
23. C4⋊C4×D19C22semidirect
26. C19×#106C22semidirect
27. C19×#102C22semidirect
28. #10597289C22semidirect
29. #10597278C22semidirect
30. (C2×D19)⋊C8C22semidirect
31. (C2×D19)⋊C8C22semidirect
32. #10597274C22semidirect
33. #10597266C22semidirect
34. #10597265C22semidirect
128. #469D19semidirect
143. C2×D8C2×D19semidirect
145. C2×M16C2×D19semidirect
151. #121C2×D19semidirect
156. #106C2×D19semidirect
160. #102C2×D19semidirect
163. C19#3192semidirect

Maximal subgroups

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

subgroupindex
#121×D192
#119268642
#119268612
#119267972
#119267952
#119266792
#119266762
#119265072
C19×#4692
#319219