Finite Group Databasebeta

← #14575415

Subgroups — #14575415

Order 2432.

454 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927359C211yesmaximal, characteristic, complemented
2#11927351C211yesmaximal, characteristic, complemented
3#11927347C211yesmaximal, characteristic, complemented
4#11926925C211yesmaximal, characteristic, complemented
5#11926817C211yesmaximal, characteristic, complemented
6#11926812C211yesmaximal, characteristic, complemented
7#11926807C211yesmaximal, characteristic, complemented
8#11926804C211yesmaximal, characteristic, complemented
9#11926722C211yesmaximal, characteristic, complemented
10#11926720C211yesmaximal, characteristic, complemented
11#11926717C211yesmaximal, characteristic, complemented
12#11926715C211yesmaximal, characteristic, complemented
13#11926661C211yesmaximal, characteristic, complemented
14#11926659C211yesmaximal, characteristic, complemented
15C19×#577C211yesmaximal, characteristic, complemented
16C19×2−1+4C2211yescharacteristic, complemented
17C19×H(5,𝔽2)C2211yescharacteristic
18#10597436C2211yescharacteristic, complemented
19#10597435C2211yescharacteristic
20C19×#137—21no—
21C19×#137C2211yescharacteristic
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#10597397—21no—
30#10597397C2211yescharacteristic
31#10597397C2211yescharacteristic, complemented
32#10597396—21no—
33#10597396—21no—
34#10597396C2211yescharacteristic
35#10597395—21no—
36#10597395C2211yescharacteristic
37#10597395C2211yescharacteristic, complemented
38#10597394C2211yescharacteristic
39#10597394C2211yescharacteristic, complemented
40#10597393C2211yescharacteristic, complemented
41C2×#64528—21no—
42C2×#64528C2211yescharacteristic, complemented
43#10597388—21no—
44#10597388C2211yescharacteristic, complemented
45#10597382C2211yescharacteristic, complemented
46#10597378—21no—
47#10597378C2211yescharacteristic
48C2×#64525—21no—
49C2×#64525C2211yescharacteristic
50#10597364—21no—
51#10597362—21no—
52SD16×D19—21no—
53#10597357—21no—
54C2×#64516C2211yescharacteristic, complemented
55#10597347C2211yescharacteristic, complemented
56#10597294C2211yescharacteristic
57#10597294C2211yescharacteristic, complemented
58#10597294C2211yescharacteristic, complemented
59#10597293C2211yescharacteristic, complemented
60#10597290C2211yescharacteristic, complemented
61#10597282C2211yescharacteristic, complemented
62#10597281C2211yescharacteristic, complemented
63#10597280C2211yescharacteristic, complemented
64#10597279C2211yescharacteristic, complemented
65#10597276C2211yescharacteristic, complemented
66C8×Dic19C2211yescharacteristic, 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
82#64545—21no—
83Q8×D19—21no—
84#64543—21no—
85#64543—41no—
86D4×D19—21no—
87D4×D19—41no—
88#64541—21no—
89#64541—21no—
90#64541C2311yescharacteristic
91C2×D76—21no—
92C2×D76C2311yescharacteristic
93C2×Dic38—21no—
94C2×Dic38C2311yescharacteristic
95Q16×C19—21no—
96Q16×C19D411yescharacteristic
97SD16×C19—21no—
98SD16×C19—21no—
99SD16×C19—21no—
100SD16×C19—21no—
101SD16×C19D411yescharacteristic
102SD16×C19D411yescharacteristic
103D8×C19—21no—
104D8×C19D411yescharacteristic
105M16×C19—21no—
106M16×C19C2311yescharacteristic
107C2×C8×C19—21no—
108C2×C8×C19C2311yescharacteristic
109C22⋊Dic19—41no—
110#64528—21no—
111#64528—21no—
112#64528—21no—
113#64528—21no—
114#64528—21no—
115#64528D411yescharacteristic
116#64527—21no—
117#64527—21no—
118#64527—21no—
119#64527D411yescharacteristic
120#64526—21no—
121#64526—21no—
122#64526—21no—
123#64526D411yescharacteristic
124#64525—21no—
125#64525—21no—
126#64525—21no—
127#64525—21no—
128#64525—21no—
129#64525D411yescharacteristic
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
140#64516—21no—
141#64516—21no—
142#64515—21no—
143C8×D19—21no—
144C23×C19—21no—
145C23×C19—41no—
146C22×D19—21no—
147C22×D19—41no—
148Q8×C19—21no—
149Q8×C19—21no—
150Q8×C19—41no—
151Q8×C19C2×D411yescharacteristic
152Q8×C19C2×D411yescharacteristic
153Q8×C19C2×D411yescharacteristic
154D4×C19—21no—
155D4×C19—21no—
156D4×C19—21no—
157D4×C19—21no—
158D4×C19—21no—
159D4×C19—41no—
160D4×C19—41no—
161D4×C19—41no—
162D4×C19C2×D411yescharacteristic
163D4×C19C2×D411yescharacteristic
164D4×C19C2×D411yescharacteristic
165C2×C4×C19—21no—
166C2×C4×C19—21no—
167C2×C4×C19—21no—
168C2×C4×C19—21no—
169C2×C4×C19—41no—
170C2×C4×C19—41no—
171C2×C4×C19—41no—
172C2×C4×C19C2411yescharacteristic
173C22⋊D19—21no—
174C22⋊D19—41no—
175C22⋊D19—41no—
176C2×Dic19—21no—
177C2×Dic19—21no—
178C2×Dic19—41no—
179D76—21no—
180D76—21no—
181D76—41no—
182D76C2×D411yescharacteristic
183C4×D19—21no—
184C4×D19—41no—
185C4×D19—41no—
186Dic38—21no—
187Dic38—21no—
188Dic38—41no—
189Dic38C2×D411yescharacteristic
190C8×C19—21no—
191C8×C19C2×D411yescharacteristic
192C8×C19C2×D411yescharacteristic
193C19⋊C8—21no—
194C19⋊C8—21no—
195C19⋊C8—21no—
196C19⋊C8C2×D411yescharacteristic
197C19⋊C8C2×D411yescharacteristic
198#3290—191nomaximal, Sylow
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—41no—
203C22×C19—81no—
204C22×C19—161no—
205C22×C19H(5,𝔽2)11yescharacteristic
206C2×D19—21no—
207C2×D19—41no—
208C2×D19—81no—
209C2×D19—161no—
210C4×C19—21no—
211C4×C19—21no—
212C4×C19—21no—
213C4×C19—41no—
214C4×C19C22×D411yescharacteristic
215C4×C19C22×D411yescharacteristic
216Dic19—21no—
217Dic19—41no—
218Dic19—41no—
219#578—191no—
220#577—191no—
221#577D1911yescharacteristic, complemented
222#576—191no—
223#495—191no—
224#473—191no—
225#472—191no—
226#471—191no—
227#471—191no—
228#455—191no—
229#455—191no—
230#454—191no—
231#454—191no—
232#443—191no—
233#443—191no—
234C2×C19—21no—
235C2×C19—41no—
236C2×C19—41no—
237C2×C19—41no—
238C2×C19—81no—
239C2×C19D4211yescharacteristic
240D19—41no—
241D19—81no—
2422−1+4—191no—
2432−1+4C2×D1911yescharacteristic, complemented
244H(5,𝔽2)—191no—
245H(5,𝔽2)C2×D1911yescharacteristic
246#137—21no—
247#137—191no—
248#137—191no—
249#137—191no—
250#137—381no—
251#137—381no—
252#137—381no—
253#137C2×D1911yescharacteristic
254AGL(1,ℤ/8)—21no—
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)C2×D1911yescharacteristic, complemented
262#135—21no—
263#135—191no—
264#135—381no—
265#135—381no—
266#135—381no—
267#135C2×D1911yescharacteristic
268C2×Q16—191no—
269C2×Q16—381no—
270C2×SD16—21no—
271C2×SD16—191no—
272C2×SD16—381no—
273C2×SD16C2×D1911yescharacteristic, complemented
274C2×D8—191no—
275C2×D8—381no—
276#131—191no—
277#131—191no—
278#131—191no—
279#131C2×D1911yescharacteristic, complemented
280#124—191no—
281#124—191no—
282#108—191no—
283#108—191no—
284#104—191no—
285#104—191no—
286#104—191no—
287#104—191no—
288#101—191no—
289#101—191no—
290#100—191no—
291#100—191no—
292C4×C8—191no—
293C19#329011yescharacteristic, complemented, Sylow
294#41—21no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—41no—
299#41—191no—
300#41—381no—
301#41—381no—
302#41—381no—
303#41—381no—
304#41—761no—
305#41C22×D1911yescharacteristic
306#41C22×D1911yescharacteristic
307#41C22×D1911yescharacteristic
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—191no—
311C2×Q8—381no—
312C2×Q8—381no—
313C2×Q8C22×D1911yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—191no—
318C2×D4—381no—
319C2×D4—381no—
320C2×D4—761no—
321C2×D4C22×D1911yescharacteristic
322Q16—21no—
323Q16—191no—
324Q16—381no—
325Q16—381no—
326Q16—381no—
327Q16—381no—
328Q16—381no—
329Q16C22⋊D1911yescharacteristic
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—191no—
335SD16—191no—
336SD16—381no—
337SD16—381no—
338SD16—381no—
339SD16—381no—
340SD16—381no—
341SD16—381no—
342SD16—381no—
343SD16—381no—
344SD16C22⋊D1911yescharacteristic
345SD16C22⋊D1911yescharacteristic
346D8—21no—
347D8—191no—
348D8—381no—
349D8—381no—
350D8—381no—
351D8—381no—
352D8—381no—
353D8C22⋊D1911yescharacteristic
354M16—21no—
355M16—191no—
356M16—191no—
357M16—191no—
358M16—381no—
359M16—381no—
360M16—381no—
361M16C22×D1911yescharacteristic
362C2×C8—21no—
363C2×C8—191no—
364C2×C8—381no—
365C2×C8—381no—
366C2×C8—381no—
367C2×C8C22×D1911yescharacteristic
368C22⋊C4—761no—
369C22⋊C4—761no—
370C42—191no—
371C23—21no—
372C23—41no—
373C23—381no—
374C23—761no—
375Q8—21no—
376Q8—21no—
377Q8—41no—
378Q8—191no—
379Q8—381no—
380Q8—381no—
381Q8—761no—
382Q8D4×D1911yescharacteristic
383Q8C2×C22⋊D1911yescharacteristic
384Q8C2×C22⋊D1911yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—41no—
391D4—41no—
392D4—41no—
393D4—191no—
394D4—381no—
395D4—381no—
396D4—381no—
397D4—761no—
398D4—761no—
399D4—761no—
400D4D4×D1911yescharacteristic
401D4C2×C22⋊D1911yescharacteristic
402D4C2×C22⋊D1911yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—381no—
411C2×C4—381no—
412C2×C4—381no—
413C2×C4—761no—
414C2×C4—761no—
415C2×C4—761no—
416C2×C4C23×D1911yescharacteristic
417C8—21no—
418C8—191no—
419C8—191no—
420C8—381no—
421C8—381no—
422C8—381no—
423C8C2×C22⋊D1911yescharacteristic
424C8C2×C22⋊D1911yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—41no—
429C22—81no—
430C22—161no—
431C22—381no—
432C22—3041no—
433C22—761no—
434C22—1521no—
435C22#1059743011yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—381no—
441C4—761no—
442C4—761no—
443C4C2×D4×D1911yescharacteristic
444C4C22×C22⋊D1911yescharacteristic
445C2—21no—
446C2—41no—
447C2—41no—
448C2—41no—
449C2—81no—
450C2—761no—
451C2—1521no—
452C2D4×C22⋊D1911yescharacteristic
subgroupG/H
centerC2D4×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#577C2
socleC2×C19D42
hypercenter#577D19
hypocenterC19#3290
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. #11927359C2semidirect
2. #11927351C2semidirect
3. #11927347C2semidirect
4. #11926925C2semidirect
5. #11926817C2semidirect
6. #11926812C2semidirect
7. #11926807C2semidirect
8. #11926804C2semidirect
9. #11926722C2semidirect
10. #11926720C2semidirect
11. #11926717C2semidirect
12. #11926715C2semidirect
13. #11926661C2semidirect
14. #11926659C2semidirect
15. C19×#577C2semidirect
16. C19×2−1+4C22semidirect
18. #10597436C22semidirect
23. C19×AGL(1,ℤ/8)C22semidirect
27. C2×SD16×C19C22semidirect
28. C19×#131C22semidirect
31. #10597397C22semidirect
37. #10597395C22semidirect
39. #10597394C22semidirect
40. #10597393C22semidirect
42. C2×#64528C22semidirect
44. #10597388C22semidirect
45. #10597382C22semidirect
54. C2×#64516C22semidirect
55. #10597347C22semidirect
57. #10597294C22semidirect
58. #10597294C22semidirect
59. #10597293C22semidirect
60. #10597290C22semidirect
61. #10597282C22semidirect
62. #10597281C22semidirect
63. #10597280C22semidirect
64. #10597279C22semidirect
65. #10597276C22semidirect
66. C8×Dic19C22semidirect
221. #577D19semidirect
243. 2−1+4C2×D19semidirect
261. AGL(1,ℤ/8)C2×D19semidirect
273. C2×SD16C2×D19semidirect
279. #131C2×D19semidirect
293. C19#3290semidirect

Maximal subgroups

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

subgroupindex
#119273592
#119273512
#119273472
#119269252
#119268172
#119268122
#119268072
#119268042
#119267222
#119267202
#119267172
#119267152
#119266612
#119266592
C19×#5772
#329019