Finite Group Databasebeta

← #14573112

Subgroups — #14573112

Order 2432.

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

normal subgroups only

This group has 584 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#127×D19C211yesmaximal, characteristic, complemented
3C4×#64545C211yesmaximal, characteristic, complemented
4#11926744C211yesmaximal, characteristic, complemented
5#11926742C212yesmaximal, complemented
6#11926740C211yesmaximal, characteristic, complemented
7#11926738C212yesmaximal, complemented
8#11926736C211yesmaximal, characteristic, complemented
9#11926566C211yesmaximal, characteristic, complemented
10#11926547C212yesmaximal, complemented
11C19×#460C211yesmaximal, characteristic, complemented
12C2×#64545C2211yescharacteristic
13C2×D4×D19—21no—
14C2×D4×D19—21no—
15C2×D4×D19C2212yes—
16C2×SD16×C19C2212yescomplemented
17C19×#127C2211yescharacteristic
18C4×Q8×C19C2211yescharacteristic, complemented
19Q8×Dic19C2211yescharacteristic, complemented
20C2×#64527C2212yescomplemented
21#10597386—21no—
22#10597386—21no—
23#10597386C2212yes—
24C2×#64525C2212yescomplemented
25#10597360—28no—
26C2×D152C2212yescomplemented
27C2×#64515C2212yes—
28#10597339—21no—
29#10597339C2211yescharacteristic, complemented
30#10597338—21no—
31#10597338C2211yescharacteristic
32#10597320C2211yescharacteristic
33C4×D76—21no—
34C4×D76C2211yescharacteristic, complemented
35C42×D19—21no—
36C42×D19C2211yescharacteristic
37C19×C4⋊C8C2211yescharacteristic, complemented
38C19×#102C2212yescomplemented
39#10597289C2212yescomplemented
40#10597278C2212yescomplemented
41Dic19⋊C8C2212yescomplemented
42#10597266C2212yescomplemented
43C4⋊(C19⋊C8)C2211yescharacteristic, complemented
44C23×D19—22no—
45C2×Q8×C19C2311yescharacteristic
46C2×D4×C19—21no—
47C2×D4×C19—21no—
48C2×D4×C19C2312yes—
49C2×C22⋊D19—22no—
50C2×C22⋊D19—22no—
51C2×C22⋊D19—22no—
52#64545—22no—
53#64545D414yescomplemented
54D4×D19—24no—
55D4×D19—24no—
56D4×D19—44no—
57D4×D19—44no—
58C2×D76—21no—
59C2×D76—21no—
60C2×D76—21no—
61C2×D76C2312yes—
62C2×D76C2311yescharacteristic
63C2×C4×D19—21no—
64C2×C4×D19—21no—
65C2×C4×D19—21no—
66C2×C4×D19D411yescharacteristic
67C2×C4×D19D411yescharacteristic
68C2×C4×D19C2311yescharacteristic
69SD16×C19—24no—
70C2×C8×C19C2312yes—
71C4⋊C4×C19—21no—
72C4⋊C4×C19C2311yescharacteristic
73C42×C19—21no—
74C42×C19C2311yescharacteristic
75#64527—24no—
76#64525—24no—
77(C2×D19)⋊C4—21no—
78(C2×D19)⋊C4—21no—
79(C2×D19)⋊C4—21no—
80C4⋊Dic19—21no—
81C4⋊Dic19C2311yescharacteristic
82C4×Dic19—21no—
83C4×Dic19—21no—
84C4×Dic19D411yescharacteristic
85C4×Dic19D411yescharacteristic
86C4×Dic19C2311yescharacteristic
87C2×C19⋊C8C2312yes—
88D152—24no—
89#64515—24no—
90C23×C19—22no—
91C22×D19—21no—
92C22×D19—22no—
93C22×D19—44no—
94C22×D19—44no—
95C22×D19—44no—
96C22×D19C2×D411yescharacteristic
97Q8×C19—21no—
98Q8×C19C2×D412yescomplemented
99D4×C19—22no—
100D4×C19—22no—
101D4×C19—42no—
102D4×C19—42no—
103C2×C4×C19—21no—
104C2×C4×C19—21no—
105C2×C4×C19C2×D411yescharacteristic
106C2×C4×C19C2×D411yescharacteristic
107C2×C4×C19C2411yescharacteristic
108C22⋊D19—44no—
109C22⋊D19—44no—
110C22⋊D19—44no—
111C2×Dic19—21no—
112C2×Dic19C2×D411yescharacteristic
113C2×Dic19C2×D411yescharacteristic
114C2×Dic19C2×D411yescharacteristic
115D76—24no—
116D76—22no—
117D76—21no—
118D76—22no—
119D76—42no—
120D76—42no—
121D76C2×D412yescomplemented
122C4×D19—22no—
123C4×D19—24no—
124C4×D19—22no—
125C4×D19—42no—
126C4×D19—42no—
127C4×D19C2×D412yes—
128C4×D19#4112yes—
129C8×C19—22no—
130C19⋊C8—22no—
131#3038—191nomaximal, Sylow
132C22×C19—42no—
133C22×C19—42no—
134C22×C19—42no—
135C22×C19C22×D411yescharacteristic
136C2×D19—21no—
137C2×D19—21no—
138C2×D19—22no—
139C2×D19—41no—
140C2×D19—41no—
141C2×D19—42no—
142C2×D19—42no—
143C2×D19—42no—
144C2×D19—88no—
145C2×D19#12112yes—
146C4×C19—22no—
147C4×C19—21no—
148C4×C19—41no—
149C4×C19AGL(1,ℤ/8)12yescomplemented
150C4×C19C22×D411yescharacteristic
151C4×C19C2×#4111yescharacteristic
152Dic19—21no—
153Dic19—41no—
154Dic19#12112yes—
155Dic19AGL(1,ℤ/8)12yescomplemented
156C2×AGL(1,ℤ/8)—192no—
157C2×#127—191no—
158C4×#41—191no—
159#460—192no—
160#460—191no—
161#460D1911yescharacteristic, complemented
162#459—191no—
163#459—191no—
164#459—192no—
165#423—191no—
166#418—192no—
167C2×C19—82no—
168C2×C19C2×#12111yescharacteristic
169C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
170C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
171D19—22no—
172D19—42no—
173D19—82no—
174C2×#41—191no—
175C22×D4—192no—
176C22×D4—381no—
177C22×D4—381no—
178AGL(1,ℤ/8)—388no—
179C2×SD16—192no—
180C2×SD16C2×D1912yescomplemented
181C2×D8—192no—
182C2×D8—192no—
183C2×M16—192no—
184#127—192no—
185#127—191no—
186#127—381no—
187#127—381no—
188#127C2×D1911yescharacteristic
189C4×Q8—191no—
190C4×Q8C2×D1911yescharacteristic, complemented
191C4×D4—191no—
192C4×D4—191no—
193C4×D4—381no—
194C4×D4—381no—
195#117—191no—
196#117—381no—
197C2×C42—191no—
198C2×C42—381no—
199C4⋊C8—192no—
200C4⋊C8—191no—
201C4⋊C8C2×D1911yescharacteristic, complemented
202#102—192no—
203#102—192no—
204#102—192no—
205#102C2×D1912yescomplemented
206C19#303811yescharacteristic, complemented, Sylow
207C24—382no—
208#41—194no—
209#41—382no—
210C2×Q8C22×D1911yescharacteristic
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—191no—
214C2×D4—192no—
215C2×D4—381no—
216C2×D4—384no—
217C2×D4—384no—
218C2×D4—382no—
219C2×D4—382no—
220C2×D4—382no—
221C2×D4—381no—
222C2×D4—381no—
223C2×D4—764no—
224C2×D4—764no—
225C2×D4C22×D1912yes—
226C22×C4—191no—
227C22×C4—191no—
228C22×C4—191no—
229C22×C4—381no—
230C22×C4—381no—
231C22×C4—381no—
232SD16—24no—
233SD16—384no—
234D8—384no—
235D8—384no—
236M16—384no—
237C2×C8—192no—
238C2×C8C22×D1912yes—
239C4⋊C4—21no—
240C4⋊C4—191no—
241C4⋊C4—381no—
242C4⋊C4C22×D1911yescharacteristic
243C22⋊C4—381no—
244C22⋊C4—381no—
245C22⋊C4—381no—
246C42—21no—
247C42—191no—
248C42—191no—
249C42—191no—
250C42—381no—
251C42—381no—
252C42C22×D1911yescharacteristic
253C23—22no—
254C23—191no—
255C23—381no—
256C23—382no—
257C23—764no—
258C23—764no—
259C23—764no—
260Q8—21no—
261Q8D4×D1912yescomplemented
262D4—22no—
263D4—22no—
264D4—42no—
265D4—42no—
266D4—192no—
267D4—384no—
268D4—382no—
269D4—381no—
270D4—382no—
271D4—762no—
272D4—764no—
273D4—764no—
274D4—764no—
275D4—762no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—191no—
279C2×C4—191no—
280C2×C4—192no—
281C2×C4—192no—
282C2×C4—191no—
283C2×C4—382no—
284C2×C4—384no—
285C2×C4—382no—
286C2×C4—381no—
287C2×C4—762no—
288C2×C4—762no—
289C2×C4D4×D1911yescharacteristic
290C2×C4D4×D1911yescharacteristic
291C2×C4C23×D1911yescharacteristic
292C8—22no—
293C8—382no—
294C22—42no—
295C22—42no—
296C22—42no—
297C22—192no—
298C22—381no—
299C22—381no—
300C22—382no—
301C22—761no—
302C22—761no—
303C22—762no—
304C22—762no—
305C22—762no—
306C22—1528no—
307C22C2×D4×D1911yescharacteristic
308C4—21no—
309C4—22no—
310C4—41no—
311C4—192no—
312C4—192no—
313C4—381no—
314C4—761no—
315C4#1059736012yescomplemented
316C4C2×D4×D1911yescharacteristic
317C4#41×D1911yescharacteristic
318C2—82no—
319C2—382no—
320C2—762no—
321C2—1522no—
322C2#121×D1911yescharacteristic
323C2AGL(1,ℤ/8)×D1911yescharacteristic
324C2C2×#1059736011yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#460C2
socleC22×C19C22×D4
hypercenter#460D19
hypocenterC19#3038
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#10597360C2semidirect
2. #127×D19C2semidirect
3. C4×#64545C2semidirect
4. #11926744C2semidirect
5. #11926742C2semidirect
6. #11926740C2semidirect
7. #11926738C2semidirect
8. #11926736C2semidirect
9. #11926566C2semidirect
10. #11926547C2semidirect
11. C19×#460C2semidirect
16. C2×SD16×C19C22semidirect
18. C4×Q8×C19C22semidirect
19. Q8×Dic19C22semidirect
20. C2×#64527C22semidirect
24. C2×#64525C22semidirect
26. C2×D152C22semidirect
29. #10597339C22semidirect
34. C4×D76C22semidirect
37. C19×C4⋊C8C22semidirect
38. C19×#102C22semidirect
39. #10597289C22semidirect
40. #10597278C22semidirect
41. Dic19⋊C8C22semidirect
42. #10597266C22semidirect
43. C4⋊(C19⋊C8)C22semidirect
53. #64545D4semidirect
98. Q8×C19C2×D4semidirect
121. D76C2×D4semidirect
149. C4×C19AGL(1,ℤ/8)semidirect
155. Dic19AGL(1,ℤ/8)semidirect
161. #460D19semidirect
180. C2×SD16C2×D19semidirect
190. C4×Q8C2×D19semidirect
201. C4⋊C8C2×D19semidirect
205. #102C2×D19semidirect
206. C19#3038semidirect
261. Q8D4×D19semidirect
315. C4#10597360semidirect

Maximal subgroups

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

subgroupindex
C2×#105973602
#127×D192
C4×#645452
#119267442
#119267422
#119267402
#119267382
#119267362
#119265662
#119265472
C19×#4602
#303819