Finite Group Databasebeta

← #14572864

Subgroups — #14572864

Order 2432.

994 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×D4×D19C211yesmaximal, characteristic, complemented
2C2×#10597354C211yesmaximal, characteristic, complemented
3C2×#10597378C211yesmaximal, characteristic, complemented
4#11927056C211yesmaximal, characteristic, complemented
5#11926696C214yesmaximal, complemented
6#11926679C214yesmaximal, complemented
7#11926548C211yesmaximal, characteristic, complemented
8#11926507C211yesmaximal, characteristic, complemented
9C19×#418C211yesmaximal, characteristic, complemented
10C24×D19—21no—
11C22×D4×C19C2211yescharacteristic
12C22×C22⋊D19—21no—
13C2×D4×D19—24no—
14C2×D4×D19—24no—
15C2×D4×D19—22no—
16C2×D4×D19C2214yes—
17C2×#64541C2211yescharacteristic, complemented
18C22×D76C2211yescharacteristic
19C22×C4×D19C2211yescharacteristic
20C2×M16×C19C2211yescharacteristic, complemented
21C19×#117C2211yescharacteristic, complemented
22C2×#64526C2212yescomplemented
23#10597378—24no—
24C2×#64525C2212yescomplemented
25C2×#64520C2211yescharacteristic, complemented
26#10597354—24no—
27C2×D152C2212yescomplemented
28C2×#64516C2212yescomplemented
29#10597343C2212yescomplemented
30#10597341C2212yescomplemented
31#10597332—21no—
32#10597328—21no—
33C4×D76—22no—
34C19×#102C2214yescomplemented
35(C2×D19)⋊C8C2214yescomplemented
36#10597266C2214yescomplemented
37C24×C19—21no—
38C23×D19—28no—
39C23×D19—21no—
40C23×D19—24no—
41C23×D19—48no—
42C23×D19D411yescharacteristic
43C2×D4×C19—21no—
44C2×D4×C19—22no—
45C2×D4×C19D414yescomplemented
46C2×D4×C19C2312yes—
47C22×C4×C19C2311yescharacteristic
48C2×C22⋊D19—28no—
49C2×C22⋊D19—21no—
50C2×C22⋊D19—24no—
51C22×Dic19D411yescharacteristic
52D4×D19—216no—
53D4×D19—28no—
54D4×D19—28no—
55#64541—22no—
56#64541—22no—
57C2×D76—22no—
58C2×D76—21no—
59C2×D76—22no—
60C2×D76D414yescomplemented
61C2×D76C2312yes—
62C2×D76C2311yescharacteristic, complemented
63C2×C4×D19—22no—
64C2×C4×D19—22no—
65C2×C4×D19—21no—
66C2×C4×D19D412yes—
67C2×C4×D19C2312yes—
68C2×Dic38C2311yescharacteristic, complemented
69M16×C19—22no—
70C2×C8×C19C2312yescomplemented
71C4⋊C4×C19C2312yescomplemented
72C22⋊C4×C19—21no—
73C42×C19—21no—
74#64526—24no—
75#64525—24no—
76(C2×D19)⋊C4—22no—
77(C2×D19)⋊C4—22no—
78C4⋊Dic19—22no—
79#64520—22no—
80C2×C19⋊C8C2312yescomplemented
81D152—24no—
82#64516—24no—
83C23×C19—24no—
84C23×C19—22no—
85C23×C19—44no—
86C23×C19C2×D411yescharacteristic
87C22×D19—22no—
88C22×D19—24no—
89C22×D19—216no—
90C22×D19—24no—
91C22×D19—22no—
92C22×D19—21no—
93C22×D19—432no—
94C22×D19—48no—
95C22×D19—44no—
96C22×D19—48no—
97C22×D19C2×D412yes—
98D4×C19—24no—
99D4×C19—22no—
100D4×C19C2×D414yes—
101C2×C4×C19—22no—
102C2×C4×C19C2×D412yes—
103C2×C4×C19C2×D411yescharacteristic
104C2×C4×C19C2×D412yes—
105C2×C4×C19C2411yescharacteristic
106C22⋊D19—216no—
107C22⋊D19—42no—
108C2×Dic19—22no—
109C2×Dic19—21no—
110C2×Dic19C2×D412yes—
111D76—24no—
112D76—22no—
113D76—21no—
114D76—21no—
115D76—44no—
116D76C2×D414yes—
117C4×D19—24no—
118C4×D19—22no—
119C4×D19—22no—
120C4×D19—42no—
121Dic38—21no—
122Dic38—21no—
123C8×C19—22no—
124C19⋊C8—22no—
125#3003—191nomaximal, Sylow
126C22×C19—22no—
127C22×C19—24no—
128C22×C19—48no—
129C22×C19—44no—
130C22×C19#12012yes—
131C22×C19C22×D411yescharacteristic
132C2×D19—28no—
133C2×D19—22no—
134C2×D19—22no—
135C2×D19—24no—
136C2×D19—432no—
137C2×D19—48no—
138C2×D19—44no—
139C2×D19—41no—
140C2×D19—42no—
141C2×D19AGL(1,ℤ/8)14yescomplemented
142C4×C19—42no—
143C4×C19#12012yes—
144C4×C19C22×D411yescharacteristic
145C4×C19C22×D411yescharacteristic
146Dic19—22no—
147Dic19—41no—
148C23×D4—191no—
149C2×AGL(1,ℤ/8)—191no—
150C2×AGL(1,ℤ/8)—191no—
151#525—191no—
152#450—194no—
153#447—194no—
154#418—191no—
155#418D1911yescharacteristic, complemented
156#407—191no—
157C2×C19—22no—
158C2×C19—44no—
159C2×C19C2×#12011yescharacteristic
160C2×C19C2×AGL(1,ℤ/8)12yes—
161D19—24no—
162D19—44no—
163D19—81no—
164C25—381no—
165C2×#41—191no—
166C22×D4—194no—
167C22×D4—191no—
168C22×D4—382no—
169C22×D4—381no—
170C22×D4—384no—
171C22×D4—384no—
172C22×D4C2×D1911yescharacteristic
173C23×C4—191no—
174AGL(1,ℤ/8)—384no—
175AGL(1,ℤ/8)—384no—
176C2×SD16—192no—
177C2×SD16—192no—
178C2×D8—192no—
179C2×D8—192no—
180C2×M16—191no—
181C2×M16C2×D1911yescharacteristic, complemented
182#123—381no—
183C22⋊Q8—192no—
184#121—192no—
185#120—381no—
186C4×D4—382no—
187#117C2×D1911yescharacteristic, complemented
188#102—194no—
189#102C2×D1914yescomplemented
190C22⋊C8—194no—
191C19#300311yescharacteristic, complemented, Sylow
192C24—21no—
193C24—191no—
194C24—384no—
195C24—388no—
196C24—381no—
197C24—768no—
198#41—382no—
199#41—382no—
200C2×Q8—191no—
201C2×D4—22no—
202C2×D4—21no—
203C2×D4—194no—
204C2×D4—192no—
205C2×D4—191no—
206C2×D4—382no—
207C2×D4—384no—
208C2×D4—388no—
209C2×D4—3816no—
210C2×D4—388no—
211C2×D4—388no—
212C2×D4—381no—
213C2×D4—382no—
214C2×D4—381no—
215C2×D4D7614yescomplemented
216C2×D4C22×D1912yes—
217C22×C4—191no—
218C22×C4—192no—
219C22×C4—192no—
220C22×C4—382no—
221C22×C4—382no—
222C22×C4—381no—
223C22×C4C22×D1911yescharacteristic
224SD16—384no—
225SD16—384no—
226D8—384no—
227D8—384no—
228M16—22no—
229M16—382no—
230C2×C8—192no—
231C2×C8C22×D1912yescomplemented
232C4⋊C4—382no—
233C4⋊C4C22×D1912yescomplemented
234C22⋊C4—21no—
235C22⋊C4—382no—
236C22⋊C4—382no—
237C42—21no—
238C23—22no—
239C23—24no—
240C23—44no—
241C23—192no—
242C23—384no—
243C23—3816no—
244C23—382no—
245C23—382no—
246C23—384no—
247C23—381no—
248C23—764no—
249C23—768no—
250C23—7632no—
251C23—768no—
252C23D4×D1911yescharacteristic
253Q8—381no—
254Q8—381no—
255D4—22no—
256D4—24no—
257D4—194no—
258D4—3816no—
259D4—382no—
260D4—381no—
261D4—381no—
262D4—384no—
263D4—764no—
264D4—762no—
265D4C2×D7614yes—
266C2×C4—22no—
267C2×C4—192no—
268C2×C4—382no—
269C2×C4—382no—
270C2×C4—382no—
271C2×C4—384no—
272C2×C4—381no—
273C2×C4—762no—
274C2×C4C2×D7612yes—
275C2×C4D4×D1912yes—
276C2×C4D4×D1911yescharacteristic
277C2×C4C23×D1911yescharacteristic
278C8—22no—
279C8—382no—
280C22—22no—
281C22—24no—
282C22—48no—
283C22—44no—
284C22—194no—
285C22—388no—
286C22—382no—
287C22—382no—
288C22—384no—
289C22—768no—
290C22—7632no—
291C22—764no—
292C22—762no—
293C22—761no—
294C22#1059732812yes—
295C22C2×D4×D1911yescharacteristic
296C4—42no—
297C4—382no—
298C4—761no—
299C4#1059732812yes—
300C4C22×D7611yescharacteristic
301C4C2×D4×D1911yescharacteristic
302C2—22no—
303C2—44no—
304C2—384no—
305C2—764no—
306C2—1521no—
307C2C2×#1059732811yescharacteristic
308C2AGL(1,ℤ/8)×D1912yes—
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#418C2
socleC22×C19C22×D4
hypercenter#418D19
hypocenterC19#3003
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C22×D4×D19C2semidirect
2. C2×#10597354C2semidirect
3. C2×#10597378C2semidirect
4. #11927056C2semidirect
5. #11926696C2semidirect
6. #11926679C2semidirect
7. #11926548C2semidirect
8. #11926507C2semidirect
9. C19×#418C2semidirect
17. C2×#64541C22semidirect
20. C2×M16×C19C22semidirect
21. C19×#117C22semidirect
22. C2×#64526C22semidirect
24. C2×#64525C22semidirect
25. C2×#64520C22semidirect
27. C2×D152C22semidirect
28. C2×#64516C22semidirect
29. #10597343C22semidirect
30. #10597341C22semidirect
34. C19×#102C22semidirect
35. (C2×D19)⋊C8C22semidirect
36. #10597266C22semidirect
45. C2×D4×C19D4semidirect
60. C2×D76D4semidirect
62. C2×D76C23semidirect
68. C2×Dic38C23semidirect
70. C2×C8×C19C23semidirect
71. C4⋊C4×C19C23semidirect
80. C2×C19⋊C8C23semidirect
141. C2×D19AGL(1,ℤ/8)semidirect
155. #418D19semidirect
181. C2×M16C2×D19semidirect
187. #117C2×D19semidirect
189. #102C2×D19semidirect
191. C19#3003semidirect
215. C2×D4D76semidirect
231. C2×C8C22×D19semidirect
233. C4⋊C4C22×D19semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D192
C2×#105973542
C2×#105973782
#119270562
#119266962
#119266792
#119265482
#119265072
C19×#4182
#300319