Finite Group Databasebeta

← #14575397

Subgroups — #14575397

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#11927352C211yesmaximal, characteristic, complemented
2#11927347C211yesmaximal, characteristic, complemented
3#11927346C211yesmaximal, characteristic, complemented
4#11926930C211yesmaximal, characteristic, complemented
5#11926814C211yesmaximal, characteristic, complemented
6#11926812C211yesmaximal, characteristic, complemented
7#11926809C211yesmaximal, characteristic, complemented
8#11926804C211yesmaximal, characteristic, complemented
9#11926720C211yesmaximal, characteristic, complemented
10#11926717C211yesmaximal, characteristic, complemented
11#11926712C211yesmaximal, characteristic, complemented
12#11926710C211yesmaximal, characteristic, complemented
13#11926666C211yesmaximal, characteristic, complemented
14#11926664C211yesmaximal, characteristic, complemented
15C19×#577C211yesmaximal, characteristic, complemented
16C19×2−1+4C2211yescharacteristic, complemented
17C19×H(5,𝔽2)C2211yescharacteristic, complemented
18#10597435C2211yescharacteristic
19#10597435C2211yescharacteristic, complemented
20C19×#137—21no—
21C19×#137C2211yescharacteristic, complemented
22C19×AGL(1,ℤ/8)—21no—
23C19×AGL(1,ℤ/8)C2211yescharacteristic, complemented
24C19×#135—21no—
25C19×#135C2211yescharacteristic
26C2×SD16×C19—21no—
27C2×SD16×C19C2211yescharacteristic, complemented
28C19×#131C2211yescharacteristic, complemented
29#10597396—21no—
30#10597396—21no—
31#10597396C2211yescharacteristic
32#10597395—21no—
33#10597395—21no—
34#10597395C2211yescharacteristic
35#10597395C2211yescharacteristic, complemented
36#10597395C2211yescharacteristic, complemented
37#10597395C2211yescharacteristic, complemented
38#10597394C2211yescharacteristic, complemented
39#10597394C2211yescharacteristic, complemented
40#10597393C2211yescharacteristic, complemented
41#10597388—21no—
42#10597388C2211yescharacteristic, complemented
43C2×#64527—21no—
44C2×#64527C2211yescharacteristic, complemented
45#10597386C2211yescharacteristic, complemented
46#10597378—21no—
47#10597378C2211yescharacteristic
48C2×#64525—21no—
49C2×#64525C2211yescharacteristic, complemented
50#10597365—21no—
51#10597360—21no—
52#10597360—21no—
53D8×D19—21no—
54C2×D152C2211yescharacteristic, complemented
55#10597347C2211yescharacteristic, complemented
56#10597294C2211yescharacteristic, complemented
57#10597294C2211yescharacteristic, complemented
58#10597294C2211yescharacteristic, complemented
59#10597293C2211yescharacteristic, complemented
60#10597290C2211yescharacteristic, complemented
61#10597282C2211yescharacteristic, complemented
62#10597280C2211yescharacteristic, complemented
63#10597280C2211yescharacteristic, complemented
64#10597279C2211yescharacteristic, complemented
65#10597276C2211yescharacteristic, complemented
66#10597272C2211yescharacteristic, complemented
67#41×C19—21no—
68#41×C19—21no—
69#41×C19—21no—
70#41×C19—21no—
71#41×C19—41no—
72#41×C19C2311yescharacteristic
73#41×C19C2311yescharacteristic
74#41×C19C2311yescharacteristic
75C2×Q8×C19—21no—
76C2×Q8×C19—21no—
77C2×Q8×C19C2311yescharacteristic
78C2×D4×C19—21no—
79C2×D4×C19—21no—
80C2×D4×C19—41no—
81C2×D4×C19C2311yescharacteristic
82C2×C22⋊D19—41no—
83#64545—21no—
84#64545—21no—
85D4×D19—21no—
86D4×D19—21no—
87D4×D19—41no—
88D4×D19—41no—
89#64541—21no—
90#64541—21no—
91#64541C2311yescharacteristic
92C2×D76—21no—
93C2×D76—21no—
94C2×D76C2311yescharacteristic
95C2×D76C2311yescharacteristic
96Q16×C19—21no—
97Q16×C19D411yescharacteristic, complemented
98SD16×C19—21no—
99SD16×C19—21no—
100SD16×C19—21no—
101SD16×C19—21no—
102SD16×C19D411yescharacteristic, complemented
103SD16×C19D411yescharacteristic, complemented
104D8×C19—21no—
105D8×C19D411yescharacteristic, complemented
106M16×C19—21no—
107M16×C19C2311yescharacteristic
108C2×C8×C19—21no—
109C2×C8×C19C2311yescharacteristic
110#64528—21no—
111#64528D411yescharacteristic, complemented
112#64527—21no—
113#64527—21no—
114#64527—21no—
115#64527—21no—
116#64527—21no—
117#64527—21no—
118#64527—21no—
119#64527D411yescharacteristic, complemented
120#64526—21no—
121#64526D411yescharacteristic, complemented
122#64525—21no—
123#64525—21no—
124#64525—21no—
125#64525—21no—
126#64525—21no—
127#64525—21no—
128#64525—21no—
129#64525D411yescharacteristic, complemented
130(C2×D19)⋊C4—41no—
131C4×Dic19C2311yescharacteristic
132#64520—21no—
133#64520—21no—
134#64520C2311yescharacteristic
135#64520C2311yescharacteristic
136#64520C2311yescharacteristic
137C2×C19⋊C8—21no—
138C2×C19⋊C8—21no—
139C2×C19⋊C8C2311yescharacteristic
140D152—21no—
141D152—21no—
142#64515—21no—
143C8×D19—21no—
144C23×C19—21no—
145C23×C19—41no—
146C22×D19—21no—
147C22×D19—21no—
148C22×D19—41no—
149C22×D19—41no—
150Q8×C19—21no—
151Q8×C19—21no—
152Q8×C19—41no—
153Q8×C19C2×D411yescharacteristic
154Q8×C19C2×D411yescharacteristic
155Q8×C19C2×D411yescharacteristic
156D4×C19—21no—
157D4×C19—21no—
158D4×C19—21no—
159D4×C19—21no—
160D4×C19—21no—
161D4×C19—41no—
162D4×C19—41no—
163D4×C19—41no—
164D4×C19C2×D411yescharacteristic
165D4×C19C2×D411yescharacteristic
166D4×C19C2×D411yescharacteristic
167C2×C4×C19—21no—
168C2×C4×C19—21no—
169C2×C4×C19—21no—
170C2×C4×C19—21no—
171C2×C4×C19—41no—
172C2×C4×C19—41no—
173C2×C4×C19—41no—
174C2×C4×C19C2411yescharacteristic
175C22⋊D19—21no—
176C22⋊D19—41no—
177C22⋊D19—41no—
178C22⋊D19—82no—
179C2×Dic19—21no—
180D76—21no—
181D76—21no—
182D76—21no—
183D76—21no—
184D76—41no—
185D76—41no—
186D76C2×D411yescharacteristic
187C4×D19—21no—
188C4×D19—41no—
189C4×D19—41no—
190Dic38C2×D411yescharacteristic
191C8×C19—21no—
192C8×C19C2×D411yescharacteristic
193C8×C19C2×D411yescharacteristic
194C19⋊C8—21no—
195C19⋊C8—21no—
196C19⋊C8—21no—
197C19⋊C8C2×D411yescharacteristic
198C19⋊C8C2×D411yescharacteristic
199#3288—191nomaximal, Sylow
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—21no—
203C22×C19—41no—
204C22×C19—81no—
205C22×C19—161no—
206C22×C19H(5,𝔽2)11yescharacteristic
207C2×D19—21no—
208C2×D19—41no—
209C2×D19—41no—
210C2×D19—81no—
211C2×D19—81no—
212C2×D19—161no—
213C2×D19—161no—
214C4×C19—21no—
215C4×C19—21no—
216C4×C19—21no—
217C4×C19—41no—
218C4×C19C22×D411yescharacteristic
219C4×C19C22×D411yescharacteristic
220Dic19—21no—
221Dic19—41no—
222#577—191no—
223#577D1911yescharacteristic, complemented
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#453—191no—
235#444—191no—
236#444—191no—
237C2×C19—21no—
238C2×C19—41no—
239C2×C19—41no—
240C2×C19—41no—
241C2×C19—81no—
242C2×C19D4211yescharacteristic
243D19—41no—
244D19—81no—
245D19—81no—
2462−1+4C2×D1911yescharacteristic, complemented
247H(5,𝔽2)—191no—
248H(5,𝔽2)—191no—
249H(5,𝔽2)C2×D1911yescharacteristic, complemented
250#137—21no—
251#137—191no—
252#137—381no—
253#137C2×D1911yescharacteristic, complemented
254AGL(1,ℤ/8)—21no—
255AGL(1,ℤ/8)—191no—
256AGL(1,ℤ/8)—191no—
257AGL(1,ℤ/8)—191no—
258AGL(1,ℤ/8)—191no—
259AGL(1,ℤ/8)—191no—
260AGL(1,ℤ/8)—381no—
261AGL(1,ℤ/8)—381no—
262AGL(1,ℤ/8)—381no—
263AGL(1,ℤ/8)—381no—
264AGL(1,ℤ/8)—381no—
265AGL(1,ℤ/8)C2×D1911yescharacteristic, complemented
266#135—21no—
267#135—191no—
268#135—381no—
269#135—381no—
270#135—381no—
271#135C2×D1911yescharacteristic
272C2×SD16—21no—
273C2×SD16—191no—
274C2×SD16—381no—
275C2×SD16C2×D1911yescharacteristic, complemented
276C2×D8—191no—
277C2×D8—191no—
278C2×D8—381no—
279C2×D8—381no—
280#131—191no—
281#131—191no—
282#131—191no—
283#131C2×D1911yescharacteristic, complemented
284#127—191no—
285#124—191no—
286#108—191no—
287#108—191no—
288#104—191no—
289#104—191no—
290#104—191no—
291#104—191no—
292#101—191no—
293#100—191no—
294#100—191no—
295#100—191no—
296#97—191no—
297C19#328811yescharacteristic, complemented, Sylow
298#41—21no—
299#41—21no—
300#41—21no—
301#41—21no—
302#41—41no—
303#41—191no—
304#41—381no—
305#41—381no—
306#41—381no—
307#41—381no—
308#41C22×D1911yescharacteristic
309#41C22×D1911yescharacteristic
310#41C22×D1911yescharacteristic
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8C22×D1911yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—191no—
318C2×D4—191no—
319C2×D4—381no—
320C2×D4—381no—
321C2×D4—381no—
322C2×D4—381no—
323C2×D4—761no—
324C2×D4—761no—
325C2×D4—761no—
326C2×D4C22×D1911yescharacteristic
327Q16—21no—
328Q16—191no—
329Q16—381no—
330Q16C22⋊D1911yescharacteristic, complemented
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—21no—
335SD16—191no—
336SD16—191no—
337SD16—381no—
338SD16—381no—
339SD16—381no—
340SD16—381no—
341SD16—381no—
342SD16—381no—
343SD16—381no—
344SD16—381no—
345SD16C22⋊D1911yescharacteristic, complemented
346SD16C22⋊D1911yescharacteristic, complemented
347D8—21no—
348D8—191no—
349D8—381no—
350D8—381no—
351D8—381no—
352D8—381no—
353D8—381no—
354D8—381no—
355D8—381no—
356D8—381no—
357D8—381no—
358D8C22⋊D1911yescharacteristic, complemented
359M16—21no—
360M16—191no—
361M16—191no—
362M16—191no—
363M16—381no—
364M16—381no—
365M16—381no—
366M16C22×D1911yescharacteristic
367C2×C8—21no—
368C2×C8—191no—
369C2×C8—381no—
370C2×C8—381no—
371C2×C8—381no—
372C2×C8C22×D1911yescharacteristic
373C22⋊C4—761no—
374C42—191no—
375C23—21no—
376C23—41no—
377C23—381no—
378C23—381no—
379C23—761no—
380C23—761no—
381Q8—21no—
382Q8—21no—
383Q8—41no—
384Q8—191no—
385Q8D4×D1911yescharacteristic
386Q8C2×C22⋊D1911yescharacteristic
387Q8C2×C22⋊D1911yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—191no—
397D4—381no—
398D4—381no—
399D4—381no—
400D4—381no—
401D4—381no—
402D4—761no—
403D4—761no—
404D4—761no—
405D4—761no—
406D4—1522no—
407D4D4×D1911yescharacteristic
408D4C2×C22⋊D1911yescharacteristic
409D4C2×C22⋊D1911yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—381no—
418C2×C4—381no—
419C2×C4—761no—
420C2×C4—761no—
421C2×C4C23×D1911yescharacteristic
422C8—21no—
423C8—191no—
424C8—191no—
425C8—381no—
426C8—381no—
427C8—381no—
428C8C2×C22⋊D1911yescharacteristic
429C8C2×C22⋊D1911yescharacteristic
430C22—21no—
431C22—21no—
432C22—21no—
433C22—41no—
434C22—81no—
435C22—161no—
436C22—381no—
437C22—3041no—
438C22—3041no—
439C22—761no—
440C22—761no—
441C22—1521no—
442C22—1521no—
443C22#1059743011yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—41no—
448C4—381no—
449C4—761no—
450C4C2×D4×D1911yescharacteristic
451C4C22×C22⋊D1911yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—41no—
456C2—81no—
457C2—761no—
458C2—1521no—
459C2—1521no—
460C2D4×C22⋊D1911yescharacteristic
subgroupG/H
centerC2D4×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#577C2
socleC2×C19D42
hypercenter#577D19
hypocenterC19#3288
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #11927352C2semidirect
2. #11927347C2semidirect
3. #11927346C2semidirect
4. #11926930C2semidirect
5. #11926814C2semidirect
6. #11926812C2semidirect
7. #11926809C2semidirect
8. #11926804C2semidirect
9. #11926720C2semidirect
10. #11926717C2semidirect
11. #11926712C2semidirect
12. #11926710C2semidirect
13. #11926666C2semidirect
14. #11926664C2semidirect
15. C19×#577C2semidirect
16. C19×2−1+4C22semidirect
17. C19×H(5,𝔽2)C22semidirect
19. #10597435C22semidirect
21. C19×#137C22semidirect
23. C19×AGL(1,ℤ/8)C22semidirect
27. C2×SD16×C19C22semidirect
28. C19×#131C22semidirect
35. #10597395C22semidirect
36. #10597395C22semidirect
37. #10597395C22semidirect
38. #10597394C22semidirect
39. #10597394C22semidirect
40. #10597393C22semidirect
42. #10597388C22semidirect
44. C2×#64527C22semidirect
45. #10597386C22semidirect
49. C2×#64525C22semidirect
54. C2×D152C22semidirect
55. #10597347C22semidirect
56. #10597294C22semidirect
57. #10597294C22semidirect
58. #10597294C22semidirect
59. #10597293C22semidirect
60. #10597290C22semidirect
61. #10597282C22semidirect
62. #10597280C22semidirect
63. #10597280C22semidirect
64. #10597279C22semidirect
65. #10597276C22semidirect
66. #10597272C22semidirect
97. Q16×C19D4semidirect
102. SD16×C19D4semidirect
103. SD16×C19D4semidirect
105. D8×C19D4semidirect
111. #64528D4semidirect
119. #64527D4semidirect
121. #64526D4semidirect
129. #64525D4semidirect
223. #577D19semidirect
246. 2−1+4C2×D19semidirect
249. H(5,𝔽2)C2×D19semidirect
253. #137C2×D19semidirect
265. AGL(1,ℤ/8)C2×D19semidirect
275. C2×SD16C2×D19semidirect
283. #131C2×D19semidirect
297. C19#3288semidirect
330. Q16C22⋊D19semidirect
345. SD16C22⋊D19semidirect
346. SD16C22⋊D19semidirect
358. D8C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
#119273522
#119273472
#119273462
#119269302
#119268142
#119268122
#119268092
#119268042
#119267202
#119267172
#119267122
#119267102
#119266662
#119266642
C19×#5772
#328819