Finite Group Databasebeta

← #14573151

Subgroups — #14573151

Order 2432.

490 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597361C211yesmaximal, characteristic, complemented
2C2×SD16×D19C211yesmaximal, characteristic, complemented
3#11927107C211yesmaximal, characteristic
4#11927020C211yesmaximal, characteristic, complemented
5#11926767C211yesmaximal, characteristic, complemented
6#11926766C211yesmaximal, characteristic, complemented
7#11926765C211yesmaximal, characteristic, complemented
8#11926764C211yesmaximal, characteristic, complemented
9#11926743C211yesmaximal, characteristic, complemented
10#11926742C211yesmaximal, characteristic, complemented
11#11926741C211yesmaximal, characteristic, complemented
12#11926569C211yesmaximal, characteristic, complemented
13#11926547C211yesmaximal, characteristic, complemented
14#11926537C211yesmaximal, characteristic, complemented
15C19×#460C211yesmaximal, characteristic, complemented
16C2×Q8×D19C2211yescharacteristic
17C2×#64543C2211yescharacteristic
18C2×D4×D19C2211yescharacteristic
19C2×SD16×C19C2211yescharacteristic
20C2×SD16×C19C2211yescharacteristic, complemented
21C19×#127C2211yescharacteristic
22C4×Q8×C19C2211yescharacteristic, complemented
23Q8×Dic19C2211yescharacteristic, complemented
24C2×#64528C2211yescharacteristic, complemented
25C2×#64527C2211yescharacteristic
26#10597386C2211yescharacteristic
27#10597385—21no—
28#10597385—21no—
29#10597383—21no—
30#10597383—21no—
31#10597382C2211yescharacteristic
32C2×#64526C2211yescharacteristic
33C2×#64526C2211yescharacteristic, complemented
34#10597361—24no—
35SD16×D19—24no—
36C2×Dic76C2211yescharacteristic, complemented
37C2×#64516C2211yescharacteristic
38C2×#64515C2211yescharacteristic
39C2×C8×D19C2211yescharacteristic
40#10597338—21no—
41#10597338C2211yescharacteristic
42#10597333—21no—
43#10597333C2211yescharacteristic, complemented
44#10597321C2211yescharacteristic
45#10597318—21no—
46#10597318C2211yescharacteristic
47C4×Dic38—21no—
48C4×Dic38C2211yescharacteristic, complemented
49C19×C4⋊C8C2211yescharacteristic, complemented
50C19×#102C2211yescharacteristic
51C19×#102C2211yescharacteristic, complemented
52#10597289C2211yescharacteristic
53#10597289C2211yescharacteristic, complemented
54#10597278C2211yescharacteristic
55#10597273C2211yescharacteristic, complemented
56Dic19⋊C8C2211yescharacteristic, complemented
57Dic19⋊C8C2211yescharacteristic, complemented
58#10597267C2211yescharacteristic, complemented
59#10597266C2211yescharacteristic
60C4⋊(C19⋊C8)C2211yescharacteristic, complemented
61C23×D19—21no—
62C2×Q8×C19C2311yescharacteristic
63C2×D4×C19—21no—
64C2×D4×C19—21no—
65C2×D4×C19C2311yescharacteristic
66C2×D4×C19C2311yescharacteristic
67C2×C22⋊D19—21no—
68C2×C22⋊D19—21no—
69C2×C22⋊D19—21no—
70C2×C22⋊D19—21no—
71C22×Dic19—21no—
72Q8×D19—22no—
73Q8×D19D414yescomplemented
74#64543—22no—
75#64543—22no—
76D4×D19—22no—
77D4×D19—22no—
78C2×D76C2311yescharacteristic
79C2×C4×D19—21no—
80C2×C4×D19C2311yescharacteristic
81C2×Dic38—21no—
82C2×Dic38C2311yescharacteristic
83C2×Dic38C2311yescharacteristic
84SD16×C19—22no—
85SD16×C19—22no—
86C2×C8×C19C2311yescharacteristic
87C2×C8×C19C2311yescharacteristic
88C4⋊C4×C19—21no—
89C4⋊C4×C19C2311yescharacteristic
90C42×C19—21no—
91C42×C19C2311yescharacteristic
92C22⋊Dic19—21no—
93C22⋊Dic19—21no—
94#64528—22no—
95#64527—22no—
96#64526—22no—
97#64526—22no—
98(C2×D19)⋊C4—21no—
99(C2×D19)⋊C4—21no—
100(C2×D19)⋊C4—21no—
101(C2×D19)⋊C4D411yescharacteristic
102(C2×D19)⋊C4D411yescharacteristic
103C4⋊Dic19—21no—
104C4⋊Dic19C2311yescharacteristic
105Dic19⋊C4—21no—
106Dic19⋊C4—21no—
107Dic19⋊C4D411yescharacteristic
108Dic19⋊C4D411yescharacteristic
109C4×Dic19—21no—
110C4×Dic19—21no—
111C4×Dic19—21no—
112C4×Dic19—21no—
113C4×Dic19C2311yescharacteristic
114C2×C19⋊C8C2311yescharacteristic
115C2×C19⋊C8C2311yescharacteristic
116Dic76—22no—
117#64516—22no—
118#64515—22no—
119C8×D19—22no—
120C23×C19—21no—
121C23×C19—21no—
122C22×D19—21no—
123C22×D19—42no—
124C22×D19—81no—
125C22×D19—81no—
126C22×D19C2×D411yescharacteristic
127Q8×C19—21no—
128Q8×C19C2×D412yes—
129D4×C19—21no—
130D4×C19—21no—
131D4×C19—21no—
132D4×C19—21no—
133D4×C19—81no—
134D4×C19—81no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19C2×D411yescharacteristic
138C2×C4×C19C2×D411yescharacteristic
139C2×C4×C19C2411yescharacteristic
140C22⋊D19—42no—
141C22⋊D19—42no—
142C22⋊D19—81no—
143C22⋊D19—81no—
144C2×Dic19—21no—
145C2×Dic19—21no—
146C2×Dic19—21no—
147C2×Dic19—42no—
148C2×Dic19C2×D411yescharacteristic
149C2×Dic19C2×D411yescharacteristic
150C2×Dic19C2×D411yescharacteristic
151D76—21no—
152D76—21no—
153C4×D19—24no—
154C4×D19C2×D412yes—
155C4×D19#4112yes—
156Dic38—21no—
157Dic38—24no—
158Dic38—21no—
159Dic38—21no—
160Dic38C2×D412yes—
161C8×C19—21no—
162C8×C19—21no—
163C19⋊C8—21no—
164C19⋊C8—21no—
165#3043—191nomaximal, Sylow
166C22×C19—41no—
167C22×C19—41no—
168C22×C19—41no—
169C22×C19—41no—
170C22×C19—41no—
171C22×C19—41no—
172C22×C19C22×D411yescharacteristic
173C2×D19—21no—
174C2×D19—21no—
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—41no—
178C2×D19—84no—
179C2×D19#12112yes—
180C4×C19—22no—
181C4×C19—21no—
182C4×C19—21no—
183C4×C19—41no—
184C4×C19C22×D411yescharacteristic
185C4×C19C2×#4111yescharacteristic
186Dic19—22no—
187Dic19—21no—
188Dic19—21no—
189Dic19—41no—
190Dic19—41no—
191Dic19#12112yes—
192C2×#137—191no—
193C22×SD16—191no—
194#535—191no—
195#519—191no—
196#464—191no—
197#464—191no—
198#464—191no—
199#464—191no—
200#460—191no—
201#460—191no—
202#460—191no—
203#460D1911yescharacteristic, complemented
204#424—191no—
205#418—191no—
206#416—191no—
207C2×C19—81no—
208C2×C19—81no—
209C2×C19C2×#12111yescharacteristic
210C2×C19#57711yescharacteristic
211C2×C19#57711yescharacteristic
212D19—22no—
213D19—81no—
214C2×#41—191no—
215C22×Q8—191no—
216C22×D4—191no—
217#137—384no—
218C2×Q16—191no—
219C2×Q16—191no—
220C2×SD16—191no—
221C2×SD16—191no—
222C2×SD16—191no—
223C2×SD16—191no—
224C2×SD16—384no—
225C2×SD16C2×D1911yescharacteristic
226C2×SD16C2×D1911yescharacteristic, complemented
227C2×M16—191no—
228C22×C8—191no—
229#127—191no—
230#127C2×D1911yescharacteristic
231#124—191no—
232#124—191no—
233#121—381no—
234#121—381no—
235#120—381no—
236#120—381no—
237C4×Q8—191no—
238C4×Q8—191no—
239C4×Q8—191no—
240C4×Q8—381no—
241C4×Q8—381no—
242C4×Q8C2×D1911yescharacteristic, complemented
243#117—191no—
244#117—191no—
245#117—381no—
246#117—381no—
247C4⋊C8—191no—
248C4⋊C8—191no—
249C4⋊C8—191no—
250C4⋊C8C2×D1911yescharacteristic, complemented
251#103—191no—
252#103—191no—
253#102—191no—
254#102—191no—
255#102—191no—
256#102—191no—
257#102C2×D1911yescharacteristic
258#102C2×D1911yescharacteristic, complemented
259C19#304311yescharacteristic, complemented, Sylow
260C24—381no—
261#41—382no—
262#41—382no—
263C2×Q8—194no—
264C2×Q8—191no—
265C2×Q8—191no—
266C2×Q8—381no—
267C2×Q8—382no—
268C2×Q8C22×D1911yescharacteristic
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—191no—
272C2×D4—382no—
273C2×D4—382no—
274C2×D4—381no—
275C2×D4—381no—
276C2×D4—381no—
277C2×D4—381no—
278C2×D4C22×D1911yescharacteristic
279C2×D4C22×D1911yescharacteristic
280C22×C4—191no—
281C22×C4—381no—
282C22×C4—381no—
283Q16—382no—
284Q16—382no—
285SD16—22no—
286SD16—22no—
287SD16—382no—
288SD16—382no—
289SD16—382no—
290SD16—382no—
291M16—382no—
292C2×C8—191no—
293C2×C8—191no—
294C2×C8—382no—
295C2×C8C22×D1911yescharacteristic
296C2×C8C22×D1911yescharacteristic
297C4⋊C4—21no—
298C4⋊C4—191no—
299C4⋊C4—191no—
300C4⋊C4—191no—
301C4⋊C4—381no—
302C4⋊C4—381no—
303C4⋊C4—381no—
304C4⋊C4C22×D1911yescharacteristic
305C22⋊C4—191no—
306C22⋊C4—191no—
307C22⋊C4—381no—
308C22⋊C4—381no—
309C22⋊C4—381no—
310C22⋊C4—381no—
311C22⋊C4—381no—
312C42—21no—
313C42—191no—
314C42—381no—
315C42—381no—
316C42—381no—
317C42—381no—
318C42C22×D1911yescharacteristic
319C23—21no—
320C23—21no—
321C23—191no—
322C23—381no—
323C23—762no—
324C23—1521no—
325C23—1521no—
326Q8—21no—
327Q8—192no—
328Q8—384no—
329Q8—381no—
330Q8—381no—
331Q8—381no—
332Q8D4×D1912yes—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—21no—
337D4—81no—
338D4—81no—
339D4—381no—
340D4—381no—
341D4—762no—
342D4—762no—
343D4—1521no—
344D4—1521no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—191no—
348C2×C4—192no—
349C2×C4—192no—
350C2×C4—191no—
351C2×C4—191no—
352C2×C4—384no—
353C2×C4—381no—
354C2×C4—381no—
355C2×C4—381no—
356C2×C4—762no—
357C2×C4D4×D1911yescharacteristic
358C2×C4D4×D1911yescharacteristic
359C2×C4C23×D1911yescharacteristic
360C8—21no—
361C8—21no—
362C8—381no—
363C8—381no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—192no—
371C22—381no—
372C22—381no—
373C22—761no—
374C22—761no—
375C22—761no—
376C22—1524no—
377C22C2×D4×D1911yescharacteristic
378C4—21no—
379C4—21no—
380C4—22no—
381C4—41no—
382C4—192no—
383C4—381no—
384C4—381no—
385C4—382no—
386C4—761no—
387C4—761no—
388C4C2×D4×D1911yescharacteristic
389C4#41×D1911yescharacteristic
390C2—81no—
391C2—81no—
392C2—382no—
393C2—1521no—
394C2#121×D1911yescharacteristic
395C2#1192735011yescharacteristic
396C2#1192735411yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#460C2
socleC22×C19C22×D4
prime radical#11927107C2
hypercenter#460D19
hypocenterC19#3043
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×#10597361C2semidirect
2. C2×SD16×D19C2semidirect
4. #11927020C2semidirect
5. #11926767C2semidirect
6. #11926766C2semidirect
7. #11926765C2semidirect
8. #11926764C2semidirect
9. #11926743C2semidirect
10. #11926742C2semidirect
11. #11926741C2semidirect
12. #11926569C2semidirect
13. #11926547C2semidirect
14. #11926537C2semidirect
15. C19×#460C2semidirect
20. C2×SD16×C19C22semidirect
22. C4×Q8×C19C22semidirect
23. Q8×Dic19C22semidirect
24. C2×#64528C22semidirect
33. C2×#64526C22semidirect
36. C2×Dic76C22semidirect
43. #10597333C22semidirect
48. C4×Dic38C22semidirect
49. C19×C4⋊C8C22semidirect
51. C19×#102C22semidirect
53. #10597289C22semidirect
55. #10597273C22semidirect
56. Dic19⋊C8C22semidirect
57. Dic19⋊C8C22semidirect
58. #10597267C22semidirect
60. C4⋊(C19⋊C8)C22semidirect
73. Q8×D19D4semidirect
203. #460D19semidirect
226. C2×SD16C2×D19semidirect
242. C4×Q8C2×D19semidirect
250. C4⋊C8C2×D19semidirect
258. #102C2×D19semidirect
259. C19#3043semidirect

Maximal subgroups

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

subgroupindex
C2×#105973612
C2×SD16×D192
#119271072
#119270202
#119267672
#119267662
#119267652
#119267642
#119267432
#119267422
#119267412
#119265692
#119265472
#119265372
C19×#4602
#304319