Finite Group Databasebeta

← #14575402

Subgroups — #14575402

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#11927356C211yesmaximal, characteristic, complemented
2#11927351C211yesmaximal, characteristic, complemented
3#11927349C211yesmaximal, characteristic, complemented
4#11927346C211yesmaximal, characteristic, complemented
5#11926933C211yesmaximal, characteristic, complemented
6#11926815C211yesmaximal, characteristic, complemented
7#11926814C211yesmaximal, characteristic, complemented
8#11926808C211yesmaximal, characteristic, complemented
9#11926807C211yesmaximal, characteristic, complemented
10#11926723C211yesmaximal, characteristic, complemented
11#11926718C211yesmaximal, characteristic, complemented
12#11926713C211yesmaximal, characteristic, complemented
13#11926713C211yesmaximal, characteristic, complemented
14#11926667C211yesmaximal, characteristic, complemented
15C19×#444C211yesmaximal, characteristic, complemented
16#10597436C2211yescharacteristic, complemented
17#10597435C2211yescharacteristic
18#10597435C2211yescharacteristic, complemented
19#10597435C2211yescharacteristic, complemented
20C19×#135C2211yescharacteristic
21C19×#131C2211yescharacteristic, complemented
22C19×#131C2211yescharacteristic, complemented
23#10597397C2211yescharacteristic, complemented
24#10597395C2211yescharacteristic
25#10597395C2211yescharacteristic, complemented
26#10597395C2211yescharacteristic, complemented
27#10597365—21no—
28#10597364—21no—
29#10597362—21no—
30#10597360—21no—
31#10597360—21no—
32SD16×D19—21no—
33#10597357—21no—
34D8×D19—21no—
35#10597355—21no—
36#10597355C2211yescharacteristic, complemented
37#10597354—21no—
38#10597354—21no—
39#10597354—21no—
40#10597354C2211yescharacteristic
41#10597354C2211yescharacteristic, complemented
42#10597354C2211yescharacteristic, complemented
43#10597350—21no—
44#10597350—21no—
45#10597350C2211yescharacteristic
46C2×D152—21no—
47C2×D152C2211yescharacteristic, complemented
48C2×D152C2211yescharacteristic, complemented
49C2×#64516—21no—
50C2×#64516C2211yescharacteristic, complemented
51C2×#64516C2211yescharacteristic, complemented
52#10597347C2211yescharacteristic, complemented
53#10597347C2211yescharacteristic, complemented
54#10597321C2211yescharacteristic, complemented
55#10597320C2211yescharacteristic, complemented
56C19×#108C2211yescharacteristic, complemented
57C19×#104C2211yescharacteristic, complemented
58C19×#104C2211yescharacteristic, complemented
59C19×#97C2211yescharacteristic, complemented
60#10597281C2211yescharacteristic, complemented
61#10597280C2211yescharacteristic, complemented
62#10597280C2211yescharacteristic, complemented
63#10597280C2211yescharacteristic, complemented
64#10597276C2211yescharacteristic, complemented
65#10597262C2211yescharacteristic, complemented
66#10597262C2211yescharacteristic, complemented
67#41×C19C2311yescharacteristic
68#41×C19C2311yescharacteristic
69#64545—21no—
70#64545—21no—
71#64545—21no—
72Q8×D19—21no—
73#64543—21no—
74#64543—41no—
75D4×D19—21no—
76D4×D19—21no—
77D4×D19—21no—
78D4×D19—41no—
79D4×D19—41no—
80D4×D19—41no—
81#64541—21no—
82#64541—21no—
83#64541—21no—
84#64541—21no—
85#64541C2311yescharacteristic
86#64541C2311yescharacteristic
87C2×D76—21no—
88C2×D76—21no—
89C2×D76—21no—
90C2×D76—41no—
91C2×D76C2311yescharacteristic
92C2×D76C2311yescharacteristic
93C2×D76C2311yescharacteristic
94C2×Dic38—21no—
95C2×Dic38C2311yescharacteristic
96Q16×C19D411yescharacteristic, complemented
97SD16×C19D411yescharacteristic, complemented
98SD16×C19D411yescharacteristic, complemented
99D8×C19D411yescharacteristic, complemented
100M16×C19—21no—
101M16×C19—21no—
102M16×C19C2311yescharacteristic
103M16×C19C2311yescharacteristic
104C2×C8×C19—21no—
105C2×C8×C19—21no—
106C2×C8×C19C2311yescharacteristic
107C2×C8×C19C2311yescharacteristic
108C42×C19C2311yescharacteristic
109#64528—21no—
110#64527—21no—
111#64527—21no—
112#64527—21no—
113#64526—21no—
114#64525—21no—
115#64525—21no—
116#64525—21no—
117(C2×D19)⋊C4—41no—
118#64520C2311yescharacteristic
119#64520C2311yescharacteristic
120Dic76—21no—
121Dic76D411yescharacteristic, complemented
122D152—21no—
123D152—21no—
124D152—21no—
125D152—21no—
126D152—21no—
127D152—21no—
128D152—21no—
129D152D411yescharacteristic, complemented
130#64516—21no—
131#64516—21no—
132#64516—21no—
133#64516—21no—
134#64516—21no—
135#64516—21no—
136#64516—21no—
137#64516—21no—
138#64516D411yescharacteristic, complemented
139#64516D411yescharacteristic, complemented
140#64515—21no—
141#64515—21no—
142C8×D19—21no—
143C8×D19—21no—
144C22×D19—21no—
145C22×D19—21no—
146C22×D19—21no—
147C22×D19—41no—
148C22×D19—41no—
149C22×D19—41no—
150Q8×C19C2×D411yescharacteristic
151Q8×C19C2×D411yescharacteristic
152D4×C19—21no—
153D4×C19—21no—
154D4×C19C2×D411yescharacteristic
155D4×C19C2×D411yescharacteristic
156C2×C4×C19—21no—
157C2×C4×C19—21no—
158C2×C4×C19—21no—
159C2×C4×C19C2411yescharacteristic
160C22⋊D19—21no—
161C22⋊D19—21no—
162C22⋊D19—41no—
163C22⋊D19—41no—
164C22⋊D19—41no—
165C22⋊D19—41no—
166C2×Dic19—21no—
167C2×Dic19—41no—
168D76—21no—
169D76—21no—
170D76—21no—
171D76—21no—
172D76—21no—
173D76—21no—
174D76—41no—
175D76—41no—
176D76—41no—
177D76—82no—
178D76C2×D411yescharacteristic
179D76C2×D411yescharacteristic
180C4×D19—21no—
181C4×D19—21no—
182C4×D19—41no—
183C4×D19—41no—
184C4×D19—41no—
185C4×D19—41no—
186Dic38—21no—
187Dic38—21no—
188Dic38—41no—
189Dic38C2×D411yescharacteristic
190Dic38C2×D411yescharacteristic
191C8×C19—21no—
192C8×C19—21no—
193C8×C19C2×D411yescharacteristic
194C8×C19C2×D411yescharacteristic
195C8×C19C2×D411yescharacteristic
196C8×C19C2×D411yescharacteristic
197C19⋊C8—21no—
198C19⋊C8—21no—
199#3288—191nomaximal, Sylow
200C22×C19—21no—
201C22×C19—21no—
202C22×C19H(5,𝔽2)11yescharacteristic
203C2×D19—21no—
204C2×D19—21no—
205C2×D19—41no—
206C2×D19—41no—
207C2×D19—41no—
208C2×D19—81no—
209C2×D19—81no—
210C2×D19—81no—
211C2×D19—161no—
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#453—191no—
235#444—191no—
236#444D1911yescharacteristic, complemented
237C2×C19—21no—
238C2×C19—41no—
239C2×C19—41no—
240C2×C19D4211yescharacteristic
241D19—41no—
242D19—41no—
243D19—81no—
244D19—81no—
245D19—81no—
2462−1+4—191no—
247H(5,𝔽2)—191no—
248H(5,𝔽2)—191no—
249H(5,𝔽2)—191no—
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)—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)—381no—
266#135—191no—
267#135—381no—
268#135—381no—
269#135—381no—
270#135—381no—
271#135C2×D1911yescharacteristic
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#131C2×D1911yescharacteristic, complemented
283#131C2×D1911yescharacteristic, complemented
284#127—191no—
285#124—191no—
286#108—191no—
287#108C2×D1911yescharacteristic, complemented
288#104—191no—
289#104—191no—
290#104C2×D1911yescharacteristic, complemented
291#104C2×D1911yescharacteristic, complemented
292#101—191no—
293#100—191no—
294#100—191no—
295#100—191no—
296#97C2×D1911yescharacteristic, complemented
297C19#328811yescharacteristic, complemented, Sylow
298#41—191no—
299#41—191no—
300#41—381no—
301#41—381no—
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—191no—
315C2×D4—191no—
316C2×D4—191no—
317C2×D4—381no—
318C2×D4—381no—
319C2×D4—381no—
320C2×D4—381no—
321C2×D4—381no—
322C2×D4—381no—
323C2×D4—761no—
324C2×D4—761no—
325C2×D4—761no—
326C2×D4—761no—
327Q16—191no—
328Q16—381no—
329Q16—381no—
330Q16D7611yescharacteristic, complemented
331SD16—191no—
332SD16—191no—
333SD16—381no—
334SD16—381no—
335SD16—381no—
336SD16—381no—
337SD16—381no—
338SD16—381no—
339SD16—381no—
340SD16—381no—
341SD16—381no—
342SD16—381no—
343SD16—381no—
344SD16—381no—
345SD16D7611yescharacteristic, complemented
346SD16D7611yescharacteristic, complemented
347D8—191no—
348D8—381no—
349D8—381no—
350D8—381no—
351D8—381no—
352D8—381no—
353D8—381no—
354D8—381no—
355D8—381no—
356D8—381no—
357D8—381no—
358D8D7611yescharacteristic, complemented
359M16—21no—
360M16—21no—
361M16—191no—
362M16—191no—
363M16—381no—
364M16—381no—
365M16C22×D1911yescharacteristic
366M16C22×D1911yescharacteristic
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—381no—
370C2×C8—381no—
371C2×C8C22×D1911yescharacteristic
372C2×C8C22×D1911yescharacteristic
373C22⋊C4—761no—
374C42C22×D1911yescharacteristic
375C23—381no—
376C23—381no—
377C23—381no—
378C23—761no—
379C23—761no—
380C23—761no—
381Q8—191no—
382Q8—191no—
383Q8—381no—
384Q8—381no—
385Q8—761no—
386Q8C2×D7611yescharacteristic
387Q8C2×D7611yescharacteristic
388D4—21no—
389D4—21no—
390D4—191no—
391D4—191no—
392D4—381no—
393D4—381no—
394D4—381no—
395D4—381no—
396D4—381no—
397D4—381no—
398D4—381no—
399D4—381no—
400D4—761no—
401D4—761no—
402D4—761no—
403D4—761no—
404D4—761no—
405D4—761no—
406D4—761no—
407D4—1522no—
408D4C2×D7611yescharacteristic
409D4C2×D7611yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—381no—
414C2×C4—381no—
415C2×C4—381no—
416C2×C4—761no—
417C2×C4—761no—
418C2×C4—761no—
419C2×C4—761no—
420C2×C4—761no—
421C2×C4C23×D1911yescharacteristic
422C8—21no—
423C8—21no—
424C8—381no—
425C8—381no—
426C8C2×D7611yescharacteristic
427C8C2×D7611yescharacteristic
428C8D4×D1911yescharacteristic
429C8D4×D1911yescharacteristic
430C22—21no—
431C22—21no—
432C22—381no—
433C22—381no—
434C22—3041no—
435C22—3041no—
436C22—3041no—
437C22—761no—
438C22—761no—
439C22—761no—
440C22—1521no—
441C22—1521no—
442C22—1521no—
443C22#1059743511yescharacteristic
444C4—21no—
445C4—21no—
446C4—41no—
447C4—381no—
448C4—381no—
449C4—761no—
450C4C22×D7611yescharacteristic
451C4C2×D4×D1911yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—761no—
456C2—761no—
457C2—1521no—
458C2—1521no—
459C2—1521no—
460C2D4×D7611yescharacteristic
subgroupG/H
centerC2D4×D76
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#444C2
socleC2×C19D42
hypercenter#444D19
hypocenterC19#3288
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ #444

Complements

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

NH ≅ G/Ntype
1. #11927356C2semidirect
2. #11927351C2semidirect
3. #11927349C2semidirect
4. #11927346C2semidirect
5. #11926933C2semidirect
6. #11926815C2semidirect
7. #11926814C2semidirect
8. #11926808C2semidirect
9. #11926807C2semidirect
10. #11926723C2semidirect
11. #11926718C2semidirect
12. #11926713C2semidirect
13. #11926713C2semidirect
14. #11926667C2semidirect
15. C19×#444C2semidirect
16. #10597436C22semidirect
18. #10597435C22semidirect
19. #10597435C22semidirect
21. C19×#131C22semidirect
22. C19×#131C22semidirect
23. #10597397C22semidirect
25. #10597395C22semidirect
26. #10597395C22semidirect
36. #10597355C22semidirect
41. #10597354C22semidirect
42. #10597354C22semidirect
47. C2×D152C22semidirect
48. C2×D152C22semidirect
50. C2×#64516C22semidirect
51. C2×#64516C22semidirect
52. #10597347C22semidirect
53. #10597347C22semidirect
54. #10597321C22semidirect
55. #10597320C22semidirect
56. C19×#108C22semidirect
57. C19×#104C22semidirect
58. C19×#104C22semidirect
59. C19×#97C22semidirect
60. #10597281C22semidirect
61. #10597280C22semidirect
62. #10597280C22semidirect
63. #10597280C22semidirect
64. #10597276C22semidirect
65. #10597262C22semidirect
66. #10597262C22semidirect
96. Q16×C19D4semidirect
97. SD16×C19D4semidirect
98. SD16×C19D4semidirect
99. D8×C19D4semidirect
121. Dic76D4semidirect
129. D152D4semidirect
138. #64516D4semidirect
139. #64516D4semidirect
236. #444D19semidirect
282. #131C2×D19semidirect
283. #131C2×D19semidirect
287. #108C2×D19semidirect
290. #104C2×D19semidirect
291. #104C2×D19semidirect
296. #97C2×D19semidirect
297. C19#3288semidirect
330. Q16D76semidirect
345. SD16D76semidirect
346. SD16D76semidirect
358. D8D76semidirect

Maximal subgroups

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

subgroupindex
#119273562
#119273512
#119273492
#119273462
#119269332
#119268152
#119268142
#119268082
#119268072
#119267232
#119267182
#119267132
#119266672
C19×#4442
#328819