Finite Group Databasebeta

← #14575396

Subgroups — #14575396

Order 2432.

464 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927355C211yesmaximal, characteristic, complemented
2#11927354C211yesmaximal, characteristic, complemented
3#11927348C211yesmaximal, characteristic, complemented
4#11927347C211yesmaximal, characteristic, complemented
5#11926931C211yesmaximal, characteristic, complemented
6#11926813C211yesmaximal, characteristic, complemented
7#11926812C211yesmaximal, characteristic, complemented
8#11926806C211yesmaximal, characteristic, complemented
9#11926805C211yesmaximal, characteristic, complemented
10#11926723C211yesmaximal, characteristic, complemented
11#11926718C211yesmaximal, characteristic, complemented
12#11926711C211yesmaximal, characteristic, complemented
13#11926663C211yesmaximal, characteristic, complemented
14#11926663C211yesmaximal, characteristic, complemented
15C19×#453C211yesmaximal, characteristic, complemented
16C19×H(5,𝔽2)C2211yescharacteristic, complemented
17#10597436C2211yescharacteristic, complemented
18#10597435C2211yescharacteristic
19#10597430C2211yescharacteristic, complemented
20C19×AGL(1,ℤ/8)C2211yescharacteristic
21C19×AGL(1,ℤ/8)C2211yescharacteristic, complemented
22C19×#127C2211yescharacteristic, complemented
23#10597397—21no—
24#10597397C2211yescharacteristic, complemented
25#10597396—21no—
26#10597396—21no—
27#10597396C2211yescharacteristic
28#10597396C2211yescharacteristic
29#10597395—21no—
30#10597395C2211yescharacteristic, complemented
31#10597394C2211yescharacteristic, complemented
32#10597394C2211yescharacteristic, complemented
33C2×#64526—21no—
34C2×#64526C2211yescharacteristic, complemented
35C2×#64526C2211yescharacteristic, complemented
36#10597378—21no—
37#10597378—21no—
38#10597378C2211yescharacteristic
39#10597378C2211yescharacteristic, complemented
40C2×#64525—21no—
41C2×#64525C2211yescharacteristic, complemented
42C2×#64525C2211yescharacteristic, complemented
43#10597362—21no—
44#10597361—21no—
45#10597360—21no—
46SD16×D19—21no—
47#10597358—21no—
48#10597357—21no—
49#10597357—21no—
50D8×D19—21no—
51#10597355C2211yescharacteristic, complemented
52#10597354C2211yescharacteristic, complemented
53#10597353C2211yescharacteristic, complemented
54#10597353C2211yescharacteristic, complemented
55#10597321C2211yescharacteristic, complemented
56C19×#104C2211yescharacteristic, complemented
57C19×#104C2211yescharacteristic, complemented
58C19×#100C2211yescharacteristic, complemented
59#10597290C2211yescharacteristic, complemented
60#10597281C2211yescharacteristic, complemented
61#10597280C2211yescharacteristic, complemented
62#10597279C2211yescharacteristic, complemented
63#10597279C2211yescharacteristic, complemented
64#10597262C2211yescharacteristic, complemented
65#10597262C2211yescharacteristic, complemented
66#10597260C2211yescharacteristic, complemented
67#41×C19—21no—
68#41×C19—21no—
69#41×C19C2311yescharacteristic
70#41×C19C2311yescharacteristic
71C2×D4×C19—21no—
72C2×D4×C19—21no—
73C2×D4×C19—41no—
74C2×D4×C19—41no—
75C2×D4×C19C2311yescharacteristic
76C2×D4×C19C2311yescharacteristic
77C2×C22⋊D19—41no—
78#64545—21no—
79Q8×D19—21no—
80#64543—21no—
81#64543—21no—
82#64543—21no—
83#64543—41no—
84D4×D19—21no—
85D4×D19—21no—
86D4×D19—21no—
87D4×D19—41no—
88#64541—21no—
89#64541—21no—
90#64541C2311yescharacteristic
91#64541C2311yescharacteristic
92C2×D76—21no—
93C2×D76C2311yescharacteristic
94C2×Dic38—21no—
95C2×Dic38C2311yescharacteristic
96SD16×C19—21no—
97SD16×C19—21no—
98D8×C19—21no—
99D8×C19—21no—
100M16×C19C2311yescharacteristic
101M16×C19C2311yescharacteristic
102C42×C19C2311yescharacteristic
103#64528—21no—
104#64528D411yescharacteristic, complemented
105#64528D411yescharacteristic, complemented
106#64527—21no—
107#64527D411yescharacteristic, complemented
108#64527D411yescharacteristic, complemented
109#64526—21no—
110#64526—21no—
111#64526—21no—
112#64526—21no—
113#64526—21no—
114#64526—21no—
115#64526—21no—
116#64526D411yescharacteristic, complemented
117#64526D411yescharacteristic, complemented
118#64525—21no—
119#64525—21no—
120#64525—21no—
121#64525—21no—
122#64525—21no—
123#64525—21no—
124#64525—21no—
125#64525D411yescharacteristic, complemented
126#64525D411yescharacteristic, complemented
127(C2×D19)⋊C4—41no—
128#64520—21no—
129#64520—21no—
130#64520C2311yescharacteristic
131#64520C2311yescharacteristic
132C2×C19⋊C8—21no—
133C2×C19⋊C8—21no—
134C2×C19⋊C8C2311yescharacteristic
135C2×C19⋊C8C2311yescharacteristic
136Dic76—21no—
137D152—21no—
138#64516—21no—
139#64516—21no—
140#64515—21no—
141#64515—21no—
142C8×D19—21no—
143C8×D19—21no—
144C23×C19—21no—
145C23×C19—21no—
146C23×C19—41no—
147C22×D19—21no—
148C22×D19—41no—
149C22×D19—41no—
150Q8×C19C2×D411yescharacteristic
151Q8×C19C2×D411yescharacteristic
152D4×C19—21no—
153D4×C19—21no—
154D4×C19—21no—
155D4×C19—21no—
156D4×C19—21no—
157D4×C19—21no—
158D4×C19—41no—
159D4×C19—41no—
160D4×C19—82no—
161D4×C19C2×D411yescharacteristic
162D4×C19C2×D411yescharacteristic
163C2×C4×C19—21no—
164C2×C4×C19—21no—
165C2×C4×C19—21no—
166C2×C4×C19—41no—
167C2×C4×C19C2411yescharacteristic
168C22⋊D19—21no—
169C22⋊D19—21no—
170C22⋊D19—41no—
171C22⋊D19—41no—
172C22⋊D19—41no—
173C22⋊D19—41no—
174C2×Dic19—21no—
175C2×Dic19—41no—
176C2×Dic19—41no—
177D76—21no—
178D76—21no—
179D76—41no—
180D76C2×D411yescharacteristic
181D76C2×D411yescharacteristic
182C4×D19—21no—
183C4×D19—21no—
184C4×D19—41no—
185C4×D19—41no—
186Dic38—21no—
187Dic38—21no—
188Dic38—41no—
189Dic38C2×D411yescharacteristic
190Dic38C2×D411yescharacteristic
191C8×C19—21no—
192C8×C19—21no—
193C19⋊C8—21no—
194C19⋊C8—21no—
195C19⋊C8C2×D411yescharacteristic
196C19⋊C8C2×D411yescharacteristic
197C19⋊C8C2×D411yescharacteristic
198C19⋊C8C2×D411yescharacteristic
199#3288—191nomaximal, Sylow
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—41no—
203C22×C19—41no—
204C22×C19—81no—
205C22×C19—81no—
206C22×C19—161no—
207C22×C19H(5,𝔽2)11yescharacteristic
208C2×D19—21no—
209C2×D19—21no—
210C2×D19—41no—
211C2×D19—81no—
212C2×D19—161no—
213C2×D19—161no—
214C4×C19—21no—
215C4×C19—21no—
216C4×C19—41no—
217C4×C19C22×D411yescharacteristic
218C4×C19C22×D411yescharacteristic
219Dic19—21no—
220Dic19—21no—
221Dic19—41no—
222#577—191no—
223#577—191no—
224#576—191no—
225#576—191no—
226#496—191no—
227#472—191no—
228#472—191no—
229#471—191no—
230#471—191no—
231#455—191no—
232#454—191no—
233#453—191no—
234#453D1911yescharacteristic, complemented
235#444—191no—
236#444—191no—
237C2×C19—21no—
238C2×C19—41no—
239C2×C19—41no—
240C2×C19—81no—
241C2×C19—81no—
242C2×C19D4211yescharacteristic
243D19—41no—
244D19—41no—
245D19—81no—
2462−1+4—191no—
247H(5,𝔽2)—191no—
248H(5,𝔽2)—191no—
249H(5,𝔽2)C2×D1911yescharacteristic, complemented
250#137—191no—
251#137—191no—
252#137—381no—
253#137—381no—
254AGL(1,ℤ/8)—191no—
255AGL(1,ℤ/8)—191no—
256AGL(1,ℤ/8)—191no—
257AGL(1,ℤ/8)—191no—
258AGL(1,ℤ/8)—381no—
259AGL(1,ℤ/8)—381no—
260AGL(1,ℤ/8)—381no—
261AGL(1,ℤ/8)—381no—
262AGL(1,ℤ/8)—381no—
263AGL(1,ℤ/8)—381no—
264AGL(1,ℤ/8)C2×D1911yescharacteristic
265AGL(1,ℤ/8)C2×D1911yescharacteristic, complemented
266#135—191no—
267#135—191no—
268#135—381no—
269#135—381no—
270#135—381no—
271#135—381no—
272C2×SD16—191no—
273C2×SD16—191no—
274C2×SD16—381no—
275C2×SD16—381no—
276C2×D8—191no—
277C2×D8—191no—
278C2×D8—381no—
279C2×D8—381no—
280#131—191no—
281#131—191no—
282#131—191no—
283#131—191no—
284#127C2×D1911yescharacteristic, complemented
285#124—191no—
286#108—191no—
287#108—191no—
288#104—191no—
289#104—191no—
290#104C2×D1911yescharacteristic, complemented
291#104C2×D1911yescharacteristic, complemented
292#101—191no—
293#100—191no—
294#100—191no—
295#100C2×D1911yescharacteristic, complemented
296#97—191no—
297C19#328811yescharacteristic, complemented, Sylow
298#41—21no—
299#41—21no—
300#41—191no—
301#41—191no—
302#41—381no—
303#41—381no—
304#41—381no—
305#41—381no—
306#41—381no—
307#41—381no—
308#41—761no—
309#41C22×D1911yescharacteristic
310#41C22×D1911yescharacteristic
311C2×Q8—191no—
312C2×Q8—381no—
313C2×Q8—381no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—191no—
319C2×D4—381no—
320C2×D4—381no—
321C2×D4—381no—
322C2×D4—381no—
323C2×D4—761no—
324C2×D4—761no—
325C2×D4C22×D1911yescharacteristic
326C2×D4C22×D1911yescharacteristic
327Q16—191no—
328Q16—191no—
329Q16—381no—
330Q16—381no—
331SD16—21no—
332SD16—21no—
333SD16—191no—
334SD16—191no—
335SD16—191no—
336SD16—191no—
337SD16—381no—
338SD16—381no—
339SD16—381no—
340SD16—381no—
341SD16—381no—
342SD16—381no—
343SD16—381no—
344SD16—381no—
345SD16—381no—
346SD16—381no—
347D8—21no—
348D8—21no—
349D8—191no—
350D8—191no—
351D8—381no—
352D8—381no—
353D8—381no—
354D8—381no—
355D8—381no—
356D8—381no—
357D8—381no—
358D8—381no—
359M16—191no—
360M16—191no—
361M16—381no—
362M16—381no—
363M16—381no—
364M16—381no—
365M16C22×D1911yescharacteristic
366M16C22×D1911yescharacteristic
367C2×C8—191no—
368C2×C8—191no—
369C2×C8—381no—
370C2×C8—381no—
371C2×C8—381no—
372C2×C8—381no—
373C22⋊C4—761no—
374C42C22×D1911yescharacteristic
375C23—21no—
376C23—21no—
377C23—41no—
378C23—381no—
379C23—761no—
380C23—761no—
381Q8—191no—
382Q8—191no—
383Q8—381no—
384Q8—381no—
385Q8—761no—
386Q8D4×D1911yescharacteristic
387Q8D4×D1911yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—21no—
394D4—41no—
395D4—41no—
396D4—82no—
397D4—191no—
398D4—191no—
399D4—381no—
400D4—381no—
401D4—381no—
402D4—381no—
403D4—761no—
404D4—761no—
405D4—761no—
406D4—761no—
407D4—761no—
408D4D4×D1911yescharacteristic
409D4D4×D1911yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—381no—
415C2×C4—381no—
416C2×C4—381no—
417C2×C4—761no—
418C2×C4—761no—
419C2×C4—761no—
420C2×C4—761no—
421C2×C4C23×D1911yescharacteristic
422C8—21no—
423C8—21no—
424C8—191no—
425C8—191no—
426C8—191no—
427C8—191no—
428C8—381no—
429C8—381no—
430C22—21no—
431C22—21no—
432C22—41no—
433C22—41no—
434C22—81no—
435C22—81no—
436C22—161no—
437C22—381no—
438C22—381no—
439C22—3041no—
440C22—3041no—
441C22—761no—
442C22—1521no—
443C22#1059743011yescharacteristic
444C4—21no—
445C4—21no—
446C4—41no—
447C4—381no—
448C4—381no—
449C4—761no—
450C4C2×D4×D1911yescharacteristic
451C4C2×D4×D1911yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—81no—
456C2—81no—
457C2—761no—
458C2—761no—
459C2—1521no—
460C2#1192717611yescharacteristic
subgroupG/H
centerC2#11927176
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#453C2
socleC2×C19D42
hypercenter#453D19
hypocenterC19#3288
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #11927355C2semidirect
2. #11927354C2semidirect
3. #11927348C2semidirect
4. #11927347C2semidirect
5. #11926931C2semidirect
6. #11926813C2semidirect
7. #11926812C2semidirect
8. #11926806C2semidirect
9. #11926805C2semidirect
10. #11926723C2semidirect
11. #11926718C2semidirect
12. #11926711C2semidirect
13. #11926663C2semidirect
14. #11926663C2semidirect
15. C19×#453C2semidirect
16. C19×H(5,𝔽2)C22semidirect
17. #10597436C22semidirect
19. #10597430C22semidirect
21. C19×AGL(1,ℤ/8)C22semidirect
22. C19×#127C22semidirect
24. #10597397C22semidirect
30. #10597395C22semidirect
31. #10597394C22semidirect
32. #10597394C22semidirect
34. C2×#64526C22semidirect
35. C2×#64526C22semidirect
39. #10597378C22semidirect
41. C2×#64525C22semidirect
42. C2×#64525C22semidirect
51. #10597355C22semidirect
52. #10597354C22semidirect
53. #10597353C22semidirect
54. #10597353C22semidirect
55. #10597321C22semidirect
56. C19×#104C22semidirect
57. C19×#104C22semidirect
58. C19×#100C22semidirect
59. #10597290C22semidirect
60. #10597281C22semidirect
61. #10597280C22semidirect
62. #10597279C22semidirect
63. #10597279C22semidirect
64. #10597262C22semidirect
65. #10597262C22semidirect
66. #10597260C22semidirect
104. #64528D4semidirect
105. #64528D4semidirect
107. #64527D4semidirect
108. #64527D4semidirect
116. #64526D4semidirect
117. #64526D4semidirect
125. #64525D4semidirect
126. #64525D4semidirect
234. #453D19semidirect
249. H(5,𝔽2)C2×D19semidirect
265. AGL(1,ℤ/8)C2×D19semidirect
284. #127C2×D19semidirect
290. #104C2×D19semidirect
291. #104C2×D19semidirect
295. #100C2×D19semidirect
297. C19#3288semidirect

Maximal subgroups

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

subgroupindex
#119273552
#119273542
#119273482
#119273472
#119269312
#119268132
#119268122
#119268062
#119268052
#119267232
#119267182
#119267112
#119266632
C19×#4532
#328819