Finite Group Databasebeta

← #14575256

Subgroups — #14575256

Order 2432.

556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10597360C212yesmaximal, complemented
2#11927216C211yesmaximal, characteristic, complemented
3D4×D76C211yesmaximal, characteristic, complemented
4#11926921C211yesmaximal, characteristic, complemented
5#11926798C212yesmaximal, complemented
6#11926744C211yesmaximal, characteristic, complemented
7#11926739C211yesmaximal, characteristic, complemented
8#11926692C212yesmaximal, complemented
9#11926679C212yesmaximal, complemented
10#11926623C211yesmaximal, characteristic, complemented
11C4×SD16×C19C211yesmaximal, characteristic, complemented
12C2×#64545C2212yescomplemented
13C2×D4×D19C2212yes—
14C22×D76—21no—
15C2×SD16×C19C2211yescharacteristic
16C4×Q8×C19C2211yescharacteristic, complemented
17C4×D4×C19C2211yescharacteristic
18C2×#64527C2212yescomplemented
19C2×#64525C2212yes—
20#10597376—21no—
21#10597360—28no—
22C2×D152C2212yescomplemented
23C2×D152C2212yescomplemented
24C2×#64515C2212yescomplemented
25#10597341—22no—
26#10597341C2212yes—
27#10597341C2212yescomplemented
28#10597328—22no—
29#10597320—21no—
30#10597320C2211yescharacteristic
31#10597320C2211yescharacteristic, complemented
32C4×D76—21no—
33C4×D76C2211yescharacteristic
34C19×#106C2211yescharacteristic, complemented
35C19×#103C2211yescharacteristic, complemented
36C19×#102C2211yescharacteristic
37C4×C8×C19C2211yescharacteristic, complemented
38(C2×D19)⋊C8C2212yescomplemented
39#10597266C2212yescomplemented
40#10597266C2212yescomplemented
41C4⋊(C19⋊C8)C2211yescharacteristic, complemented
42C23×D19—22no—
43C2×Q8×C19C2311yescharacteristic
44C2×D4×C19C2311yescharacteristic
45C22×C4×C19—21no—
46C2×C22⋊D19—22no—
47#64545—24no—
48#64545—42no—
49D4×D19—24no—
50D4×D19—42no—
51C2×D76—22no—
52C2×D76—22no—
53C2×D76—21no—
54C2×D76—21no—
55C2×D76—22no—
56C2×D76—21no—
57C2×D76—21no—
58C2×D76—44no—
59C2×D76D411yescharacteristic
60C2×D76C2312yes—
61C2×D76C2312yes—
62C2×C4×D19—22no—
63C2×C4×D19C2312yes—
64SD16×C19D414yescomplemented
65C2×C8×C19C2311yescharacteristic
66C2×C8×C19C2311yescharacteristic
67C4⋊C4×C19—21no—
68C4⋊C4×C19C2311yescharacteristic
69C4⋊C4×C19C2311yescharacteristic
70C22⋊C4×C19—21no—
71C42×C19—21no—
72C42×C19C2311yescharacteristic
73#64527—24no—
74#64525—24no—
75(C2×D19)⋊C4—22no—
76(C2×D19)⋊C4—22no—
77(C2×D19)⋊C4D412yes—
78C4⋊Dic19D411yescharacteristic
79C2×C19⋊C8C2312yes—
80D152—24no—
81D152—42no—
82#64515—24no—
83C23×C19—21no—
84C22×D19—22no—
85C22×D19—22no—
86C22×D19—44no—
87C22×D19—44no—
88C22×D19—82no—
89C22×D19C2×D412yes—
90Q8×C19—21no—
91Q8×C19C2×D412yescomplemented
92D4×C19—21no—
93D4×C19C2×D412yes—
94C2×C4×C19—21no—
95C2×C4×C19—21no—
96C2×C4×C19—21no—
97C2×C4×C19—42no—
98C2×C4×C19C2×D411yescharacteristic
99C2×C4×C19C2×D411yescharacteristic
100C2×C4×C19C2411yescharacteristic
101C22⋊D19—44no—
102C2×Dic19C2×D412yes—
103D76—22no—
104D76—22no—
105D76—22no—
106D76—22no—
107D76—22no—
108D76—44no—
109D76—44no—
110D76—42no—
111D76—42no—
112D76—81no—
113D76—81no—
114D76—82no—
115C4×D19—22no—
116C4×D19—22no—
117C4×D19—44no—
118C8×C19—21no—
119C8×C19C2×D412yescomplemented
120C19⋊C8—22no—
121#3274—191nomaximal, Sylow
122C22×C19—22no—
123C22×C19—41no—
124C22×C19—41no—
125C22×C19C22×D411yescharacteristic
126C2×D19—22no—
127C2×D19—22no—
128C2×D19—22no—
129C2×D19—42no—
130C2×D19—42no—
131C2×D19—42no—
132C2×D19—42no—
133C2×D19—42no—
134C2×D19—42no—
135C2×D19—88no—
136C4×C19—22no—
137C4×C19—21no—
138C4×C19—41no—
139C4×C19—41no—
140C4×C19AGL(1,ℤ/8)12yescomplemented
141C4×C19C22×D411yescharacteristic
142C4×C19H(5,𝔽2)11yescharacteristic
143Dic19—22no—
144C2×AGL(1,ℤ/8)—192no—
145#550—191no—
146D42—191no—
147#493—191no—
148#469—192no—
149#460—191no—
150#459—191no—
151#449—192no—
152#447—192no—
153C4×SD16D1911yescharacteristic, complemented
154#436—191no—
155C2×C19—42no—
156C2×C19D4211yescharacteristic
157C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
158C2×C19#57611yescharacteristic
159D19—42no—
160D19—82no—
161D19—82no—
162C2×#41—192no—
163C22×D4—192no—
164C22×D4—381no—
165AGL(1,ℤ/8)—388no—
166C2×SD16—192no—
167C2×SD16C2×D1911yescharacteristic
168C2×D8—192no—
169C2×D8—192no—
170C2×D8—192no—
171C2×M16—192no—
172#127—191no—
173#127—191no—
174#127—381no—
175#121—192no—
176#121—192no—
177#121—382no—
178#121—381no—
179#120—382no—
180C4×Q8C2×D1911yescharacteristic, complemented
181C4×D4—191no—
182C4×D4—381no—
183C4×D4C2×D1911yescharacteristic
184#106C2×D1911yescharacteristic, complemented
185C4⋊C8—191no—
186#103C2×D1911yescharacteristic, complemented
187#102—192no—
188#102—192no—
189#102C2×D1911yescharacteristic
190C22⋊C8—192no—
191C4×C8C2×D1911yescharacteristic, complemented
192C19#327411yescharacteristic, complemented, Sylow
193C24—382no—
194#41—384no—
195#41—762no—
196C2×Q8C22×D1911yescharacteristic
197C2×D4—191no—
198C2×D4—192no—
199C2×D4—192no—
200C2×D4—382no—
201C2×D4—382no—
202C2×D4—382no—
203C2×D4—382no—
204C2×D4—384no—
205C2×D4—381no—
206C2×D4—381no—
207C2×D4—381no—
208C2×D4—381no—
209C2×D4—764no—
210C2×D4—762no—
211C2×D4C22×D1911yescharacteristic
212C22×C4—21no—
213C22×C4—192no—
214C22×C4—382no—
215SD16—384no—
216SD16D7614yescomplemented
217D8—384no—
218D8—384no—
219D8—762no—
220M16—384no—
221C2×C8—192no—
222C2×C8C22×D1911yescharacteristic
223C2×C8C22×D1911yescharacteristic
224C4⋊C4—21no—
225C4⋊C4—191no—
226C4⋊C4C22×D1911yescharacteristic
227C4⋊C4C22×D1911yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—192no—
230C22⋊C4—382no—
231C22⋊C4—382no—
232C42—21no—
233C42C22×D1911yescharacteristic
234C23—21no—
235C23—192no—
236C23—382no—
237C23—382no—
238C23—764no—
239C23—764no—
240C23—1522no—
241Q8—21no—
242Q8C2×D7612yescomplemented
243D4—21no—
244D4—382no—
245D4—382no—
246D4—382no—
247D4—382no—
248D4—382no—
249D4—764no—
250D4—764no—
251D4—764no—
252D4—762no—
253D4—762no—
254D4—1521no—
255D4—1521no—
256D4—1522no—
257D4C2×D7612yes—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—192no—
263C2×C4—382no—
264C2×C4—382no—
265C2×C4—764no—
266C2×C4D4×D1911yescharacteristic
267C2×C4D4×D1911yescharacteristic
268C2×C4C23×D1911yescharacteristic
269C8—21no—
270C8—382no—
271C8C2×D7612yescomplemented
272C22—22no—
273C22—41no—
274C22—41no—
275C22—382no—
276C22—382no—
277C22—382no—
278C22—762no—
279C22—762no—
280C22—762no—
281C22—762no—
282C22—762no—
283C22—762no—
284C22—1528no—
285C22C2×D4×D1911yescharacteristic
286C4—21no—
287C4—22no—
288C4—41no—
289C4—41no—
290C4—382no—
291C4#1059736012yescomplemented
292C4C22×D7611yescharacteristic
293C4#1059743511yescharacteristic
294C2—42no—
295C2—762no—
296C2—1522no—
297C2—1522no—
298C2D4×D7611yescharacteristic
299C2C2×#1059736011yescharacteristic
300C2#1192734611yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC4×SD16×C19C2
socleC22×C19C22×D4
hypercenterC4×SD16D19
hypocenterC19#3274
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10597360C2semidirect
2. #11927216C2semidirect
3. D4×D76C2semidirect
4. #11926921C2semidirect
5. #11926798C2semidirect
6. #11926744C2semidirect
7. #11926739C2semidirect
8. #11926692C2semidirect
9. #11926679C2semidirect
10. #11926623C2semidirect
11. C4×SD16×C19C2semidirect
12. C2×#64545C22semidirect
16. C4×Q8×C19C22semidirect
18. C2×#64527C22semidirect
22. C2×D152C22semidirect
23. C2×D152C22semidirect
24. C2×#64515C22semidirect
27. #10597341C22semidirect
31. #10597320C22semidirect
34. C19×#106C22semidirect
35. C19×#103C22semidirect
37. C4×C8×C19C22semidirect
38. (C2×D19)⋊C8C22semidirect
39. #10597266C22semidirect
40. #10597266C22semidirect
41. C4⋊(C19⋊C8)C22semidirect
64. SD16×C19D4semidirect
91. Q8×C19C2×D4semidirect
119. C8×C19C2×D4semidirect
140. C4×C19AGL(1,ℤ/8)semidirect
153. C4×SD16D19semidirect
180. C4×Q8C2×D19semidirect
184. #106C2×D19semidirect
186. #103C2×D19semidirect
191. C4×C8C2×D19semidirect
192. C19#3274semidirect
216. SD16D76semidirect
242. Q8C2×D76semidirect
271. C8C2×D76semidirect
291. C4#10597360semidirect

Maximal subgroups

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

subgroupindex
C2×#105973602
#119272162
D4×D762
#119269212
#119267982
#119267442
#119267392
#119266922
#119266792
#119266232
C4×SD16×C192
#327419