Finite Group Databasebeta

← #14575427

Subgroups — #14575427

Order 2432.

460 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927356C211yesmaximal, characteristic, complemented
2#11927354C211yesmaximal, characteristic, complemented
3#11927353C211yesmaximal, characteristic, complemented
4#11927350C211yesmaximal, characteristic, complemented
5#11926915C211yesmaximal, characteristic, complemented
6#11926810C211yesmaximal, characteristic, complemented
7#11926808C211yesmaximal, characteristic, complemented
8#11926806C211yesmaximal, characteristic, complemented
9#11926729C211yesmaximal, characteristic, complemented
10#11926725C211yesmaximal, characteristic, complemented
11#11926714C211yesmaximal, characteristic, complemented
12#11926710C211yesmaximal, characteristic, complemented
13#11926660C211yesmaximal, characteristic, complemented
14#11926659C211yesmaximal, characteristic, complemented
15C19×#471C211yesmaximal, characteristic, complemented
16#10597436C2211yescharacteristic
17#10597435C2211yescharacteristic, complemented
18#10597433C2211yescharacteristic
19#10597430C2211yescharacteristic, complemented
20C19×#137C2211yescharacteristic, complemented
21C19×AGL(1,ℤ/8)C2211yescharacteristic
22C2×SD16×C19C2211yescharacteristic, complemented
23C19×#131C2211yescharacteristic, complemented
24#10597396C2211yescharacteristic
25#10597390C2211yescharacteristic, complemented
26#10597388C2211yescharacteristic, complemented
27C2×#64527C2211yescharacteristic, complemented
28#10597386C2211yescharacteristic
29C2×#64526C2211yescharacteristic, complemented
30#10597378C2211yescharacteristic
31#10597365—21no—
32#10597364—21no—
33#10597362—21no—
34#10597361—21no—
35#10597361—21no—
36#10597360—21no—
37#10597360—21no—
38SD16×D19—21no—
39SD16×D19—21no—
40SD16×D19—21no—
41#10597358—21no—
42#10597357—21no—
43#10597355—21no—
44#10597355C2211yescharacteristic, complemented
45#10597355C2211yescharacteristic, complemented
46#10597354—21no—
47#10597354C2211yescharacteristic
48#10597354C2211yescharacteristic
49#10597353C2211yescharacteristic, complemented
50#10597353C2211yescharacteristic, complemented
51#10597350—21no—
52#10597350C2211yescharacteristic
53C2×#64516—21no—
54C2×#64516C2211yescharacteristic, complemented
55#10597347C2211yescharacteristic, complemented
56C19×#108C2211yescharacteristic, complemented
57C19×#101C2211yescharacteristic, complemented
58C19×#100C2211yescharacteristic, complemented
59#10597294C2211yescharacteristic, complemented
60#10597282C2211yescharacteristic, complemented
61#10597282C2211yescharacteristic, complemented
62#10597282C2211yescharacteristic, complemented
63#10597281C2211yescharacteristic, complemented
64#10597280C2211yescharacteristic, complemented
65#10597279C2211yescharacteristic, complemented
66C8×Dic19C2211yescharacteristic, complemented
67#41×C19C2311yescharacteristic
68C2×Q8×C19C2311yescharacteristic
69C2×D4×C19C2311yescharacteristic
70C2×C22⋊D19—41no—
71C2×C22⋊D19—41no—
72#64545—21no—
73#64545—21no—
74#64545—21no—
75Q8×D19—21no—
76Q8×D19—21no—
77Q8×D19—21no—
78#64543—21no—
79#64543—21no—
80#64543—21no—
81#64543—41no—
82D4×D19—21no—
83D4×D19—21no—
84D4×D19—21no—
85D4×D19—41no—
86#64541—21no—
87#64541—21no—
88#64541—41no—
89#64541C2311yescharacteristic
90#64541C2311yescharacteristic
91#64541C2311yescharacteristic
92C2×D76—21no—
93C2×D76C2311yescharacteristic
94C2×Dic38—21no—
95C2×Dic38C2311yescharacteristic
96Q16×C19—21no—
97SD16×C19—21no—
98SD16×C19—21no—
99SD16×C19—21no—
100SD16×C19—21no—
101D8×C19—21no—
102M16×C19—21no—
103M16×C19C2311yescharacteristic
104M16×C19C2311yescharacteristic
105M16×C19C2311yescharacteristic
106C2×C8×C19—21no—
107C2×C8×C19C2311yescharacteristic
108#64528—21no—
109#64528D411yescharacteristic, complemented
110#64527—21no—
111#64527—21no—
112#64527—21no—
113#64527D411yescharacteristic, complemented
114#64526—21no—
115#64526—21no—
116#64526—21no—
117#64526D411yescharacteristic, complemented
118#64525—21no—
119#64525D411yescharacteristic, complemented
120Dic19⋊C4—41no—
121C4×Dic19C2311yescharacteristic
122#64520C2311yescharacteristic
123C2×C19⋊C8C2311yescharacteristic
124Dic76—21no—
125Dic76—21no—
126Dic76D411yescharacteristic, complemented
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#64516D411yescharacteristic, complemented
137#64516D411yescharacteristic, complemented
138#64515—21no—
139#64515—21no—
140#64515—21no—
141C8×D19—21no—
142C8×D19—21no—
143C8×D19—21no—
144C23×C19—21no—
145C22×D19—21no—
146C22×D19—41no—
147C22×D19—41no—
148Q8×C19—21no—
149Q8×C19—21no—
150Q8×C19C2×D411yescharacteristic
151D4×C19—21no—
152D4×C19—21no—
153D4×C19—21no—
154D4×C19C2×D411yescharacteristic
155C2×C4×C19—21no—
156C2×C4×C19—21no—
157C2×C4×C19C2411yescharacteristic
158C22⋊D19—21no—
159C22⋊D19—21no—
160C22⋊D19—21no—
161C22⋊D19—41no—
162C22⋊D19—41no—
163C22⋊D19—41no—
164C22⋊D19—41no—
165C22⋊D19—82no—
166C2×Dic19—21no—
167C2×Dic19—21no—
168C2×Dic19—41no—
169C2×Dic19—41no—
170D76—21no—
171D76—21no—
172D76—41no—
173D76—41no—
174D76C2×D411yescharacteristic
175D76C2×D411yescharacteristic
176D76C2×D411yescharacteristic
177C4×D19—21no—
178C4×D19—21no—
179C4×D19—21no—
180C4×D19—41no—
181C4×D19—41no—
182C4×D19—41no—
183C4×D19—41no—
184Dic38—21no—
185Dic38—21no—
186Dic38—41no—
187Dic38—41no—
188Dic38C2×D411yescharacteristic
189Dic38C2×D411yescharacteristic
190Dic38C2×D411yescharacteristic
191C8×C19—21no—
192C8×C19—21no—
193C8×C19—21no—
194C8×C19C2×D411yescharacteristic
195C8×C19C2×D411yescharacteristic
196C19⋊C8—21no—
197C19⋊C8C2×D411yescharacteristic
198C19⋊C8C2×D411yescharacteristic
199#3291—191nomaximal, Sylow
200C22×C19—21no—
201C22×C19—41no—
202C22×C19—81no—
203C22×C19H(5,𝔽2)11yescharacteristic
204C2×D19—21no—
205C2×D19—21no—
206C2×D19—21no—
207C2×D19—41no—
208C2×D19—81no—
209C2×D19—161no—
210C2×D19—161no—
211C4×C19—21no—
212C4×C19—41no—
213C4×C19C22×D411yescharacteristic
214C4×C19C22×D411yescharacteristic
215Dic19—22no—
216Dic19—21no—
217Dic19—21no—
218Dic19—21no—
219Dic19—41no—
220#577—191no—
221#577—191no—
222#577—191no—
223#577—191no—
224#492—191no—
225#471—191no—
226#471—191no—
227#471—191no—
228#471D1911yescharacteristic, complemented
229#456—191no—
230#456—191no—
231#453—191no—
232#453—191no—
233#443—191no—
234#443—191no—
235C2×C19—21no—
236C2×C19—41no—
237C2×C19—81no—
238C2×C19D4211yescharacteristic
239D19—41no—
240D19—41no—
241D19—41no—
242D19—81no—
2432−1+4—191no—
2442−1+4—191no—
245H(5,𝔽2)—191no—
246H(5,𝔽2)—191no—
247#137—191no—
248#137—191no—
249#137—191no—
250#137—381no—
251#137—381no—
252#137—381no—
253#137—381no—
254#137C2×D1911yescharacteristic, complemented
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)C2×D1911yescharacteristic
263#135—191no—
264#135—191no—
265#135—381no—
266#135—381no—
267#135—381no—
268#135—381no—
269C2×SD16—191no—
270C2×SD16—191no—
271C2×SD16—191no—
272C2×SD16—381no—
273C2×SD16—381no—
274C2×SD16—381no—
275C2×SD16—381no—
276C2×SD16C2×D1911yescharacteristic, complemented
277#131—191no—
278#131—191no—
279#131—191no—
280#131C2×D1911yescharacteristic, complemented
281C4⋊Q8—191no—
282#127—191no—
283#108—191no—
284#108C2×D1911yescharacteristic, complemented
285#104—191no—
286#104—191no—
287#104—191no—
288#104—191no—
289#101—191no—
290#101C2×D1911yescharacteristic, complemented
291#100—191no—
292#100C2×D1911yescharacteristic, complemented
293C4×C8—191no—
294C19#329111yescharacteristic, complemented, Sylow
295#41—191no—
296#41—191no—
297#41—191no—
298#41—381no—
299#41—381no—
300#41—381no—
301#41—381no—
302#41—381no—
303#41—381no—
304#41—381no—
305#41—381no—
306#41—761no—
307#41—761no—
308#41C22×D1911yescharacteristic
309C2×Q8—191no—
310C2×Q8—381no—
311C2×Q8—381no—
312C2×Q8—381no—
313C2×Q8—381no—
314C2×Q8C22×D1911yescharacteristic
315C2×D4—191no—
316C2×D4—381no—
317C2×D4—381no—
318C2×D4—381no—
319C2×D4—381no—
320C2×D4—761no—
321C2×D4—761no—
322C2×D4—761no—
323C2×D4C22×D1911yescharacteristic
324Q16—21no—
325Q16—191no—
326Q16—191no—
327Q16—381no—
328Q16—381no—
329Q16—381no—
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—191no—
335SD16—191no—
336SD16—191no—
337SD16—191no—
338SD16—381no—
339SD16—381no—
340SD16—381no—
341SD16—381no—
342SD16—381no—
343SD16—381no—
344SD16—381no—
345SD16—381no—
346SD16—381no—
347SD16—381no—
348SD16—381no—
349SD16—381no—
350D8—21no—
351D8—191no—
352D8—191no—
353D8—381no—
354D8—381no—
355D8—381no—
356M16—21no—
357M16—191no—
358M16—381no—
359M16—381no—
360M16—381no—
361M16C22×D1911yescharacteristic
362M16C22×D1911yescharacteristic
363M16C22×D1911yescharacteristic
364C2×C8—21no—
365C2×C8—191no—
366C2×C8—381no—
367C2×C8—381no—
368C2×C8—381no—
369C2×C8C22×D1911yescharacteristic
370C4⋊C4—761no—
371C42—191no—
372C23—21no—
373C23—381no—
374C23—761no—
375C23—761no—
376Q8—21no—
377Q8—21no—
378Q8—191no—
379Q8—191no—
380Q8—191no—
381Q8—381no—
382Q8—381no—
383Q8—761no—
384Q8—761no—
385Q8D4×D1911yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—191no—
390D4—191no—
391D4—191no—
392D4—381no—
393D4—381no—
394D4—381no—
395D4—381no—
396D4—381no—
397D4—761no—
398D4—761no—
399D4—761no—
400D4—761no—
401D4—761no—
402D4—761no—
403D4—1522no—
404D4D4×D1911yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—381no—
408C2×C4—381no—
409C2×C4—381no—
410C2×C4—381no—
411C2×C4—381no—
412C2×C4—761no—
413C2×C4—761no—
414C2×C4—761no—
415C2×C4—761no—
416C2×C4—761no—
417C2×C4—761no—
418C2×C4C23×D1911yescharacteristic
419C8—21no—
420C8—21no—
421C8—21no—
422C8—191no—
423C8—191no—
424C8—381no—
425C8D4×D1911yescharacteristic
426C8D4×D1911yescharacteristic
427C22—21no—
428C22—41no—
429C22—81no—
430C22—381no—
431C22—381no—
432C22—381no—
433C22—3041no—
434C22—3041no—
435C22—761no—
436C22—1521no—
437C22#1059743511yescharacteristic
438C4—21no—
439C4—41no—
440C4—382no—
441C4—381no—
442C4—381no—
443C4—381no—
444C4—761no—
445C4C2×D4×D1911yescharacteristic
446C4C2×D4×D1911yescharacteristic
447C2—21no—
448C2—41no—
449C2—81no—
450C2—761no—
451C2—761no—
452C2—761no—
453C2—1521no—
454C2#1192717811yescharacteristic
subgroupG/H
centerC2#11927178
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#471C2
socleC2×C19D42
hypercenter#471D19
hypocenterC19#3291
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #11927356C2semidirect
2. #11927354C2semidirect
3. #11927353C2semidirect
4. #11927350C2semidirect
5. #11926915C2semidirect
6. #11926810C2semidirect
7. #11926808C2semidirect
8. #11926806C2semidirect
9. #11926729C2semidirect
10. #11926725C2semidirect
11. #11926714C2semidirect
12. #11926710C2semidirect
13. #11926660C2semidirect
14. #11926659C2semidirect
15. C19×#471C2semidirect
17. #10597435C22semidirect
19. #10597430C22semidirect
20. C19×#137C22semidirect
22. C2×SD16×C19C22semidirect
23. C19×#131C22semidirect
25. #10597390C22semidirect
26. #10597388C22semidirect
27. C2×#64527C22semidirect
29. C2×#64526C22semidirect
44. #10597355C22semidirect
45. #10597355C22semidirect
49. #10597353C22semidirect
50. #10597353C22semidirect
54. C2×#64516C22semidirect
55. #10597347C22semidirect
56. C19×#108C22semidirect
57. C19×#101C22semidirect
58. C19×#100C22semidirect
59. #10597294C22semidirect
60. #10597282C22semidirect
61. #10597282C22semidirect
62. #10597282C22semidirect
63. #10597281C22semidirect
64. #10597280C22semidirect
65. #10597279C22semidirect
66. C8×Dic19C22semidirect
109. #64528D4semidirect
113. #64527D4semidirect
117. #64526D4semidirect
119. #64525D4semidirect
126. Dic76D4semidirect
129. D152D4semidirect
136. #64516D4semidirect
137. #64516D4semidirect
228. #471D19semidirect
254. #137C2×D19semidirect
276. C2×SD16C2×D19semidirect
280. #131C2×D19semidirect
284. #108C2×D19semidirect
290. #101C2×D19semidirect
292. #100C2×D19semidirect
294. C19#3291semidirect

Maximal subgroups

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

subgroupindex
#119273562
#119273542
#119273532
#119273502
#119269152
#119268102
#119268082
#119268062
#119267292
#119267252
#119267142
#119267102
#119266602
#119266592
C19×#4712
#329119