Finite Group Databasebeta

← #14572886

Subgroups — #14572886

Order 2432.

806 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 141 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×#64545C211yesmaximal, characteristic, complemented
2C2×#10597360C212yesmaximal, complemented
3#121×D19C211yesmaximal, characteristic, complemented
4#11926692C212yesmaximal, complemented
5#11926688C212yesmaximal, complemented
6#11926683C211yesmaximal, characteristic, complemented
7#11926680C211yesmaximal, characteristic, complemented
8#11926677C211yesmaximal, characteristic, complemented
9#11926544C212yesmaximal, complemented
10#11926506C211yesmaximal, characteristic, complemented
11C19×#448C211yesmaximal, characteristic, complemented
12C22×Q8×C19C2211yescharacteristic, complemented
13C2×#64545—28no—
14C2×#64545—21no—
15C2×#64545—21no—
16C2×#64545C2212yes—
17C2×#64545C2212yescomplemented
18C2×D4×D19—21no—
19C2×D4×D19C2211yescharacteristic, complemented
20C22×D76—21no—
21C22×D76C2211yescharacteristic, complemented
22C22×C4×D19—21no—
23C22×C4×D19C2211yescharacteristic
24C2×SD16×C19C2212yescomplemented
25C19×#121C2211yescharacteristic
26C2×#64527C2212yescomplemented
27#10597385—21no—
28#10597384C2211yescharacteristic, complemented
29C2×#64525C2212yescomplemented
30#10597376C2211yescharacteristic
31#10597360—28no—
32C2×D152C2212yescomplemented
33C2×#64515C2212yescomplemented
34#10597341C2211yescharacteristic, complemented
35C4⋊C4×D19C2211yescharacteristic, complemented
36#10597330—21no—
37C22⋊C4×D19—21no—
38C19×#103C2212yescomplemented
39C19×C22⋊C8C2211yescharacteristic, complemented
40#10597292C2212yescomplemented
41C22⋊(C19⋊C8)C2211yescharacteristic, complemented
42#10597278C2212yescomplemented
43(C2×D19)⋊C8C2212yescomplemented
44#10597266C2212yescomplemented
45C23×D19—21no—
46C23×D19—21no—
47C23×D19D411yescharacteristic
48C2×Q8×C19—24no—
49C2×Q8×C19—21no—
50C2×Q8×C19C2312yes—
51C2×D4×C19—21no—
52C2×D4×C19C2311yescharacteristic
53C22×C4×C19—21no—
54C22×C4×C19C2311yescharacteristic
55C2×C22⋊D19—21no—
56C2×C22⋊D19—21no—
57C2×C22⋊D19—21no—
58C22×Dic19D411yescharacteristic
59#64545—28no—
60#64545—28no—
61#64545—24no—
62#64545—24no—
63#64545—24no—
64#64545D418yescomplemented
65D4×D19—24no—
66D4×D19—44no—
67C2×D76—28no—
68C2×D76—22no—
69C2×D76—22no—
70C2×D76—21no—
71C2×D76—24no—
72C2×D76—21no—
73C2×D76C2311yescharacteristic
74C2×D76C2312yes—
75C2×C4×D19—28no—
76C2×C4×D19—22no—
77C2×C4×D19—22no—
78C2×C4×D19—24no—
79C2×C4×D19—21no—
80C2×C4×D19D411yescharacteristic
81C2×C4×D19D411yescharacteristic
82C2×C4×D19C2311yescharacteristic
83C2×C4×D19C2311yescharacteristic
84SD16×C19—24no—
85C2×C8×C19C2312yes—
86C4⋊C4×C19C2311yescharacteristic
87C22⋊C4×C19—21no—
88C22⋊Dic19—21no—
89#64527—24no—
90#64525—24no—
91(C2×D19)⋊C4—21no—
92(C2×D19)⋊C4—21no—
93C4⋊Dic19C2311yescharacteristic
94Dic19⋊C4—21no—
95C2×C19⋊C8C2312yes—
96D152—24no—
97#64515—24no—
98C23×C19—21no—
99C23×C19C2×D411yescharacteristic
100C22×D19—24no—
101C22×D19—22no—
102C22×D19—22no—
103C22×D19—22no—
104C22×D19—21no—
105C22×D19—41no—
106C22×D19—42no—
107C22×D19—42no—
108C22×D19—42no—
109C22×D19—42no—
110C22×D19—42no—
111C22×D19C2×D411yescharacteristic
112C22×D19C2×D411yescharacteristic
113Q8×C19—24no—
114Q8×C19—22no—
115Q8×C19C2×D414yescomplemented
116D4×C19—22no—
117D4×C19—42no—
118C2×C4×C19—24no—
119C2×C4×C19—22no—
120C2×C4×C19—22no—
121C2×C4×C19—21no—
122C2×C4×C19C2×D411yescharacteristic
123C2×C4×C19C2411yescharacteristic
124C22⋊D19—42no—
125C22⋊D19—42no—
126C22⋊D19—42no—
127C2×Dic19—22no—
128C2×Dic19—21no—
129C2×Dic19C2×D411yescharacteristic
130C2×Dic19C2×D411yescharacteristic
131D76—28no—
132D76—24no—
133D76—28no—
134D76—22no—
135D76—22no—
136D76—42no—
137D76C2×D414yescomplemented
138C4×D19—28no—
139C4×D19—22no—
140C4×D19—22no—
141C4×D19—28no—
142C4×D19—22no—
143C4×D19—42no—
144C4×D19C2×D414yes—
145C8×C19—22no—
146C19⋊C8—22no—
147#3006—191nomaximal, Sylow
148C22×C19—21no—
149C22×C19—21no—
150C22×C19—41no—
151C22×C19—41no—
152C22×C19—41no—
153C22×C19AGL(1,ℤ/8)12yescomplemented
154C22×C19C22×D411yescharacteristic
155C2×D19—21no—
156C2×D19—21no—
157C2×D19—21no—
158C2×D19—24no—
159C2×D19—21no—
160C2×D19—21no—
161C2×D19—44no—
162C2×D19—48no—
163C2×D19—42no—
164C2×D19—42no—
165C2×D19—41no—
166C2×D19—41no—
167C2×D19—41no—
168C2×D19—84no—
169C2×D19#12012yes—
170C4×C19—24no—
171C4×C19—21no—
172C4×C19—41no—
173C4×C19C22×D412yes—
174Dic19—21no—
175Dic19—41no—
176Dic19#12012yes—
177C22×#41—191no—
178C2×AGL(1,ℤ/8)—192no—
179C2×#121—191no—
180#449—192no—
181#449—192no—
182#448—191no—
183#448D1911yescharacteristic, complemented
184#447—191no—
185#447—191no—
186#417—192no—
187#407—191no—
188C2×C19—22no—
189C2×C19—81no—
190C2×C19C2×#12011yescharacteristic
191C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C19#57511yescharacteristic
193D19—22no—
194D19—41no—
195D19—44no—
196D19—81no—
197C2×#41—192no—
198C2×#41—192no—
199C2×#41—381no—
200C2×#41—381no—
201C2×#41—388no—
202C22×Q8C2×D1911yescharacteristic, complemented
203C22×D4—191no—
204C22×D4—191no—
205C22×D4—381no—
206C22×D4—381no—
207C23×C4—191no—
208C23×C4—381no—
209AGL(1,ℤ/8)—388no—
210C2×SD16—192no—
211C2×SD16C2×D1912yescomplemented
212C2×D8—192no—
213C2×D8—192no—
214C2×M16—192no—
215#121—191no—
216#121—191no—
217#121—191no—
218#121—381no—
219#121—381no—
220#121C2×D1911yescharacteristic
221C2×C4⋊C4—191no—
222C2×C22⋊C4—381no—
223#103—192no—
224#103C2×D1912yescomplemented
225#102—192no—
226#102—192no—
227C22⋊C8—191no—
228C22⋊C8—192no—
229C22⋊C8C2×D1911yescharacteristic, complemented
230C19#300611yescharacteristic, complemented, Sylow
231C24—191no—
232C24—381no—
233C24—381no—
234#41—198no—
235#41—384no—
236#41—384no—
237#41—388no—
238#41—388no—
239#41—384no—
240C2×Q8—24no—
241C2×Q8—21no—
242C2×Q8C22×D1912yes—
243C2×D4—21no—
244C2×D4—192no—
245C2×D4—191no—
246C2×D4—384no—
247C2×D4—382no—
248C2×D4—382no—
249C2×D4—388no—
250C2×D4—381no—
251C2×D4—384no—
252C2×D4—381no—
253C2×D4—381no—
254C2×D4—381no—
255C2×D4—381no—
256C2×D4—764no—
257C2×D4C22×D1911yescharacteristic
258C22×C4—21no—
259C22×C4—191no—
260C22×C4—191no—
261C22×C4—191no—
262C22×C4—191no—
263C22×C4—191no—
264C22×C4—384no—
265C22×C4—382no—
266C22×C4—382no—
267C22×C4—388no—
268C22×C4—381no—
269C22×C4C22×D1911yescharacteristic
270SD16—24no—
271SD16—384no—
272D8—384no—
273D8—384no—
274M16—384no—
275C2×C8—192no—
276C2×C8C22×D1912yes—
277C4⋊C4—191no—
278C4⋊C4—381no—
279C4⋊C4C22×D1911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—381no—
282C22⋊C4—381no—
283C22⋊C4—381no—
284C23—21no—
285C23—191no—
286C23—191no—
287C23—382no—
288C23—384no—
289C23—382no—
290C23—382no—
291C23—381no—
292C23—761no—
293C23—762no—
294C23—762no—
295C23—762no—
296C23—762no—
297C23—762no—
298C23D4×D1911yescharacteristic
299Q8—24no—
300Q8—22no—
301Q8D4×D1914yescomplemented
302D4—22no—
303D4—42no—
304D4—194no—
305D4—388no—
306D4—388no—
307D4—384no—
308D4—382no—
309D4—382no—
310D4—762no—
311D4—762no—
312D4—762no—
313D4—762no—
314C2×C4—24no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—191no—
319C2×C4—194no—
320C2×C4—191no—
321C2×C4—382no—
322C2×C4—388no—
323C2×C4—382no—
324C2×C4—388no—
325C2×C4—382no—
326C2×C4—382no—
327C2×C4—381no—
328C2×C4—762no—
329C2×C4D4×D1911yescharacteristic
330C2×C4C23×D1911yescharacteristic
331C8—22no—
332C8—382no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—192no—
339C22—381no—
340C22—381no—
341C22—381no—
342C22—381no—
343C22—384no—
344C22—381no—
345C22—764no—
346C22—768no—
347C22—762no—
348C22—762no—
349C22—761no—
350C22—761no—
351C22—761no—
352C22—1524no—
353C22#1059736012yescomplemented
354C22C2×D4×D1911yescharacteristic
355C4—24no—
356C4—21no—
357C4—41no—
358C4—192no—
359C4—381no—
360C4—761no—
361C4C2×D4×D1912yes—
362C2—22no—
363C2—81no—
364C2—382no—
365C2—761no—
366C2—764no—
367C2—1521no—
368C2#120×D1911yescharacteristic
369C2C2×#1059736011yescharacteristic
370C2#1192734311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#448C2
socleC22×C19C22×D4
hypercenter#448D19
hypocenterC19#3006
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C22×#64545C2semidirect
2. C2×#10597360C2semidirect
3. #121×D19C2semidirect
4. #11926692C2semidirect
5. #11926688C2semidirect
6. #11926683C2semidirect
7. #11926680C2semidirect
8. #11926677C2semidirect
9. #11926544C2semidirect
10. #11926506C2semidirect
11. C19×#448C2semidirect
12. C22×Q8×C19C22semidirect
17. C2×#64545C22semidirect
19. C2×D4×D19C22semidirect
21. C22×D76C22semidirect
24. C2×SD16×C19C22semidirect
26. C2×#64527C22semidirect
28. #10597384C22semidirect
29. C2×#64525C22semidirect
32. C2×D152C22semidirect
33. C2×#64515C22semidirect
34. #10597341C22semidirect
35. C4⋊C4×D19C22semidirect
38. C19×#103C22semidirect
39. C19×C22⋊C8C22semidirect
40. #10597292C22semidirect
41. C22⋊(C19⋊C8)C22semidirect
42. #10597278C22semidirect
43. (C2×D19)⋊C8C22semidirect
44. #10597266C22semidirect
64. #64545D4semidirect
115. Q8×C19C2×D4semidirect
137. D76C2×D4semidirect
153. C22×C19AGL(1,ℤ/8)semidirect
183. #448D19semidirect
202. C22×Q8C2×D19semidirect
211. C2×SD16C2×D19semidirect
224. #103C2×D19semidirect
229. C22⋊C8C2×D19semidirect
230. C19#3006semidirect
301. Q8D4×D19semidirect
353. C22#10597360semidirect

Maximal subgroups

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

subgroupindex
C22×#645452
C2×#105973602
#121×D192
#119266922
#119266882
#119266832
#119266802
#119266772
#119265442
#119265062
C19×#4482
#300619