Finite Group Databasebeta

← #421×D283 #49129800

Subgroups — #421×D283 #49129800

Order 36224.

772 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D283C211yesmaximal, characteristic
2C2×M16×D283C211yesmaximal, characteristic, complemented
3#117×D283C211yesmaximal, characteristic, complemented
4#31826483C211yesmaximal, characteristic, complemented
5#31826482C211yesmaximal, characteristic, complemented
6#31826481C211yesmaximal, characteristic, complemented
7#31826480C214yesmaximal, complemented
8#104×D283C214yesmaximal, complemented
9#421×C283C211yesmaximal, characteristic, complemented
10C2×#17985393C411yescharacteristic, complemented
11C2×#17985392—21no—
12C2×#17985392C2211yescharacteristic
13C2×#17985391—21no—
14C2×#17985391C411yescharacteristic, complemented
15#41×D283—21no—
16#41×D283—21no—
17#41×D283—21no—
18#41×D283—21no—
19#41×D283C412yescomplemented
20#41×D283C412yescomplemented
21#41×D283C2212yes—
22#41×D283C2212yes—
23C2×Q8×D283C411yescharacteristic, complemented
24C2×D4×D283—21no—
25C2×D4×D283C411yescharacteristic, complemented
26C22×C4×D283—21no—
27C22×C4×D283C2211yescharacteristic
28C2×#17985376C2211yescharacteristic, complemented
29C2×#17985375—21no—
30M16×D283—21no—
31M16×D283—21no—
32M16×D283C2212yescomplemented
33M16×D283C2212yescomplemented
34C2×C8×D283—21no—
35#22583569C2211yescharacteristic, complemented
36#22583568—21no—
37#22583567C2212yescomplemented
38#22583566—21no—
39C4⋊C4×D283—21no—
40C22⋊C4×D283—21no—
41C42×D283C2212yescomplemented
42#22583538C2214yescomplemented
43#22583537C2214yescomplemented
44#22583536C2214yescomplemented
45C2×#41×C283C2211yescharacteristic
46C2×M16×C283C2211yescharacteristic, complemented
47#117×C283C2211yescharacteristic, complemented
48#104×C283C2214yescomplemented
49C23×D283—21no—
50C23×D283D411yescharacteristic
51#17985393—21no—
52#17985393—21no—
53#17985393C2×C412yes—
54#17985393C2×C412yescomplemented
55#17985392—22no—
56#17985392—22no—
57#17985392—22no—
58#17985392—22no—
59#17985392—21no—
60#17985392—21no—
61#17985392C2×C412yescomplemented
62#17985392C2312yes—
63#17985391—22no—
64#17985391—22no—
65#17985391—22no—
66#17985391—22no—
67#17985391—21no—
68#17985391—21no—
69#17985391C2×C412yes—
70#17985391C2×C412yescomplemented
71C2×Dic566—21no—
72C2×Dic566C2×C411yescharacteristic, complemented
73Q8×D283—21no—
74Q8×D283—21no—
75Q8×D283C2×C412yes—
76Q8×D283C2×C412yescomplemented
77C2×D1132—21no—
78C2×D1132C2×C411yescharacteristic, complemented
79C2×C22⋊D283—21no—
80C2×C22⋊D283—21no—
81C2×C22⋊D283—21no—
82D4×D283—22no—
83D4×D283—22no—
84D4×D283—22no—
85D4×D283—22no—
86D4×D283—21no—
87D4×D283—21no—
88D4×D283C2×C412yes—
89D4×D283C2×C412yescomplemented
90C22×Dic283—21no—
91C22×Dic283D411yescharacteristic
92C2×C4×D283—21no—
93C2×C4×D283—21no—
94C2×C4×D283—22no—
95C2×C4×D283—22no—
96C2×C4×D283—22no—
97C2×C4×D283—22no—
98C2×C4×D283—22no—
99C2×C4×D283—21no—
100C2×C4×D283C2×C411yescharacteristic
101C2×C4×D283C2×C411yescharacteristic
102C2×C4×D283C2×C411yescharacteristic
103C2×C4×D283C2×C411yescharacteristic
104C2×C4×D283D411yescharacteristic
105C2×C4×D283D411yescharacteristic
106C2×C4×D283D411yescharacteristic
107C2×C4×D283D411yescharacteristic
108C2×C4×D283D411yescharacteristic
109C2×C4×D283D411yescharacteristic
110C2×C4×D283C2311yescharacteristic
111C2×C4×D283C2311yescharacteristic
112#17985376—21no—
113#17985376C2312yescomplemented
114#17985375—22no—
115#17985375—22no—
116C2×C283⋊C8—21no—
117C8×D283—22no—
118C8×D283—22no—
119C4⋊Dic283—21no—
120Dic283⋊C4—22no—
121C22⋊Dic283—21no—
122(C2×D283)⋊C4—22no—
123C4×Dic283—22no—
124C4×Dic283C2312yescomplemented
125#41×C283—21no—
126#41×C283—21no—
127#41×C283C2×C412yescomplemented
128#41×C283C2312yes—
129C2×Q8×C283C2×C411yescharacteristic, complemented
130C2×D4×C283—21no—
131C2×D4×C283C2×C411yescharacteristic, complemented
132C22×C4×C283—21no—
133C22×C4×C283C2311yescharacteristic
134M16×C283—21no—
135M16×C283C2312yescomplemented
136C2×C8×C283—21no—
137C4⋊C4×C283—21no—
138C22⋊C4×C283—21no—
139C42×C283C2312yescomplemented
140C22×D283—21no—
141C22×D283—22no—
142C22×D283—22no—
143C22×D283—42no—
144C22×D283—44no—
145C22×D283C22⋊C411yescharacteristic
146C22×D283C22⋊C411yescharacteristic
147C22×D283C22⋊C411yescharacteristic
148C22×D283C22⋊C411yescharacteristic
149C22×D283C2×D411yescharacteristic
150C22×D283C2×D411yescharacteristic
151Dic566—21no—
152Dic566—22no—
153Dic566—22no—
154Dic566C22×C412yes—
155D1132—22no—
156D1132—22no—
157D1132—21no—
158D1132C22×C412yes—
159C22⋊D283—22no—
160C22⋊D283—22no—
161C22⋊D283—22no—
162C22⋊D283—22no—
163C22⋊D283—22no—
164C22⋊D283—22no—
165C2×Dic283—21no—
166C2×Dic283—22no—
167C2×Dic283—22no—
168C2×Dic283—22no—
169C2×Dic283C22⋊C411yescharacteristic
170C2×Dic283C22⋊C411yescharacteristic
171C2×Dic283C22⋊C411yescharacteristic
172C2×Dic283C22⋊C411yescharacteristic
173C2×Dic283C2×D411yescharacteristic
174C2×Dic283C2×D411yescharacteristic
175C4×D283—22no—
176C4×D283—22no—
177C4×D283—22no—
178C4×D283—22no—
179C4×D283—22no—
180C4×D283—22no—
181C4×D283—44no—
182C4×D283C22⋊C411yescharacteristic
183C4×D283C22⋊C411yescharacteristic
184C4×D283C22⋊C411yescharacteristic
185C4×D283C22⋊C411yescharacteristic
186C4×D283C22⋊C411yescharacteristic
187C4×D283C22⋊C411yescharacteristic
188C4×D283C22⋊C411yescharacteristic
189C4×D283C22⋊C411yescharacteristic
190C4×D283C22×C411yescharacteristic
191C4×D283C22×C411yescharacteristic
192C4×D283C22×C411yescharacteristic
193C4×D283C22×C411yescharacteristic
194C4×D283C2×D411yescharacteristic
195C4×D283C2×D411yescharacteristic
196C4×D283C2×D411yescharacteristic
197C4×D283C2×D411yescharacteristic
198C283⋊C8—22no—
199C23×C283—21no—
200C23×C283C2×D411yescharacteristic
201Q8×C283—21no—
202Q8×C283C22×C412yes—
203D4×C283—22no—
204D4×C283—22no—
205D4×C283—21no—
206D4×C283C22×C412yes—
207C2×C4×C283—21no—
208C2×C4×C283—22no—
209C2×C4×C283—22no—
210C2×C4×C283—22no—
211C2×C4×C283C22×C411yescharacteristic
212C2×C4×C283C22×C411yescharacteristic
213C2×C4×C283C2×D411yescharacteristic
214C2×C4×C283C2×D411yescharacteristic
215C2×C4×C283C2×D411yescharacteristic
216C2×C4×C283C2411yescharacteristic
217C8×C283—22no—
218C22×C283—22no—
219C22×C283—41no—
220C22×C283—42no—
221C22×C283C2×C22⋊C411yescharacteristic
222C22×C283C2×C22⋊C411yescharacteristic
223C22×C283C22×D411yescharacteristic
224C2×D283—22no—
225C2×D283—22no—
226C2×D283—22no—
227C2×D283—22no—
228C2×D283—41no—
229C2×D283—41no—
230C2×D283—41no—
231C2×D283—44no—
232C2×D283—42no—
233C2×D283—44no—
234C2×D283C2×C22⋊C411yescharacteristic
235C2×D283C2×C22⋊C411yescharacteristic
236C2×D283C2×C22⋊C411yescharacteristic
237C2×D283C2×C22⋊C411yescharacteristic
238C4×C283—22no—
239C4×C283—42no—
240C4×C283C2×C22⋊C411yescharacteristic
241C4×C283C2×C22⋊C411yescharacteristic
242C4×C283C23×C411yescharacteristic
243C4×C283C22×D411yescharacteristic
244Dic283—22no—
245Dic283—42no—
246Dic283C2×C22⋊C411yescharacteristic
247Dic283C2×C22⋊C411yescharacteristic
248Dic283C2×C22⋊C411yescharacteristic
249Dic283C2×C22⋊C411yescharacteristic
250C2×C283—21no—
251C2×C283—21no—
252C2×C283—21no—
253C2×C283—42no—
254C2×C283C22×C22⋊C411yescharacteristic
255D283—21no—
256D283—21no—
257D283—21no—
258D283—42no—
259D283#42112yesdirect product factor
260C283C2×#42111yescharacteristic, complemented, Sylow
261C2×#421—2831nomaximal, Sylow
262C22×#41—2831no—
263C22×M16—2831no—
264C2×#117—2831no—
265#421—2831no—
266#421—2831no—
267#421—2831no—
268#421—2834no—
269#421D28311yescharacteristic, direct product factor
270C2×#104—2834no—
271C2×#41—2832no—
272C2×#41—2832no—
273C2×#41—2832no—
274C2×#41—2832no—
275C2×#41—2831no—
276C2×#41—2831no—
277C2×#41—2831no—
278C2×#41—5661no—
279C2×#41—5661no—
280C2×#41—5661no—
281C2×#41—5661no—
282C2×#41—5661no—
283C2×#41—5661no—
284C2×#41C2×D28311yescharacteristic
285C22×Q8—2831no—
286C22×D4—2831no—
287C22×D4—5661no—
288C23×C4—2831no—
289C23×C4—5661no—
290C2×M16—2831no—
291C2×M16—2832no—
292C2×M16—2832no—
293C2×M16—5661no—
294C2×M16—5661no—
295C2×M16—5661no—
296C2×M16C2×D28311yescharacteristic, complemented
297C22×C8—5661no—
298#117—2831no—
299#117—2832no—
300#117—5661no—
301#117—5661no—
302#117C2×D28311yescharacteristic, complemented
303C2×C4⋊C4—5661no—
304C2×C22⋊C4—5661no—
305C2×C42—2832no—
306#104—2834no—
307#104—2834no—
308#104—2834no—
309#104C2×D28314yescomplemented
310C24—2831no—
311C24—5661no—
312#41—21no—
313#41—21no—
314#41—2832no—
315#41—2832no—
316#41—2832no—
317#41—2832no—
318#41—2832no—
319#41—2832no—
320#41—5662no—
321#41—5662no—
322#41—5662no—
323#41—5662no—
324#41—5662no—
325#41—5662no—
326#41—5662no—
327#41—5662no—
328#41—5661no—
329#41—5661no—
330#41—5661no—
331#41—5661no—
332#41—5661no—
333#41—5661no—
334#41C4×D28312yescomplemented
335#41C22×D28312yes—
336C2×Q8—2832no—
337C2×Q8—2832no—
338C2×Q8—2831no—
339C2×Q8—5661no—
340C2×Q8—5661no—
341C2×Q8—5661no—
342C2×Q8C4×D28311yescharacteristic, complemented
343C2×D4—21no—
344C2×D4—2832no—
345C2×D4—2832no—
346C2×D4—2831no—
347C2×D4—5661no—
348C2×D4—5661no—
349C2×D4—5661no—
350C2×D4—5661no—
351C2×D4—5662no—
352C2×D4—5662no—
353C2×D4—5662no—
354C2×D4—5662no—
355C2×D4—5661no—
356C2×D4—5661no—
357C2×D4C4×D28311yescharacteristic, complemented
358C22×C4—21no—
359C22×C4—2831no—
360C22×C4—2831no—
361C22×C4—2831no—
362C22×C4—2831no—
363C22×C4—2831no—
364C22×C4—2831no—
365C22×C4—2831no—
366C22×C4—2831no—
367C22×C4—2831no—
368C22×C4—2831no—
369C22×C4—2831no—
370C22×C4—2831no—
371C22×C4—2831no—
372C22×C4—5661no—
373C22×C4—5662no—
374C22×C4—5662no—
375C22×C4—5662no—
376C22×C4—5662no—
377C22×C4—5661no—
378C22×C4—5662no—
379C22×C4—5661no—
380C22×C4—5661no—
381C22×C4C22×D28311yescharacteristic
382M16—21no—
383M16—2832no—
384M16—5662no—
385M16—5662no—
386M16—5661no—
387M16C22×D28312yescomplemented
388C2×C8—21no—
389C2×C8—5662no—
390C2×C8—5662no—
391C2×C8—5661no—
392C4⋊C4—21no—
393C4⋊C4—5662no—
394C4⋊C4—5661no—
395C22⋊C4—21no—
396C22⋊C4—5662no—
397C22⋊C4—5661no—
398C42—2832no—
399C42—5662no—
400C42C22×D28312yescomplemented
401C23—21no—
402C23—2831no—
403C23—2831no—
404C23—2831no—
405C23—2831no—
406C23—2831no—
407C23—2831no—
408C23—5662no—
409C23—5662no—
410C23—5661no—
411C23—11322no—
412C23—11324no—
413C23D4×D28311yescharacteristic
414Q8—21no—
415Q8—2832no—
416Q8—5662no—
417Q8—5662no—
418Q8—5661no—
419Q8C2×C4×D28312yes—
420D4—22no—
421D4—22no—
422D4—21no—
423D4—2832no—
424D4—5662no—
425D4—5662no—
426D4—5662no—
427D4—5662no—
428D4—5662no—
429D4—5662no—
430D4—5662no—
431D4—5662no—
432D4—5661no—
433D4C2×C4×D28312yes—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—2831no—
439C2×C4—2831no—
440C2×C4—2831no—
441C2×C4—2831no—
442C2×C4—2831no—
443C2×C4—2831no—
444C2×C4—2831no—
445C2×C4—2831no—
446C2×C4—2831no—
447C2×C4—2831no—
448C2×C4—2831no—
449C2×C4—2831no—
450C2×C4—2831no—
451C2×C4—2831no—
452C2×C4—2831no—
453C2×C4—2831no—
454C2×C4—2831no—
455C2×C4—2831no—
456C2×C4—2831no—
457C2×C4—2831no—
458C2×C4—2831no—
459C2×C4—2831no—
460C2×C4—5662no—
461C2×C4—5662no—
462C2×C4—5662no—
463C2×C4—5662no—
464C2×C4—5662no—
465C2×C4—5662no—
466C2×C4—5661no—
467C2×C4—5662no—
468C2×C4—5662no—
469C2×C4—5662no—
470C2×C4—11324no—
471C2×C4C2×C4×D28311yescharacteristic
472C2×C4C2×C4×D28311yescharacteristic
473C2×C4D4×D28311yescharacteristic
474C2×C4D4×D28311yescharacteristic
475C2×C4D4×D28311yescharacteristic
476C2×C4C23×D28311yescharacteristic
477C8—22no—
478C8—5662no—
479C22—22no—
480C22—41no—
481C22—42no—
482C22—2831no—
483C22—2831no—
484C22—2831no—
485C22—2831no—
486C22—5662no—
487C22—5662no—
488C22—5662no—
489C22—5662no—
490C22—11321no—
491C22—11321no—
492C22—11321no—
493C22—11322no—
494C22—11324no—
495C22—11324no—
496C22C22⋊C4×D28311yescharacteristic
497C22C22⋊C4×D28311yescharacteristic
498C22C2×D4×D28311yescharacteristic
499C4—22no—
500C4—42no—
501C4—2831no—
502C4—2831no—
503C4—2831no—
504C4—2831no—
505C4—5662no—
506C4—11322no—
507C4C22⋊C4×D28311yescharacteristic
508C4C22⋊C4×D28311yescharacteristic
509C4C22×C4×D28311yescharacteristic
510C4C2×D4×D28311yescharacteristic
511C2—21no—
512C2—21no—
513C2—21no—
514C2—42no—
515C2—2832no—
516C2—5661no—
517C2—5661no—
518C2—5661no—
519C2—11322no—
520C2C2×C22⋊C4×D28311yescharacteristic
subgroupG/H
centerC4C2×D4×D283
commutatorC4×C283C23×C4
FrattiniC2×C4C23×D283
Fitting#421×C283C2
socleC2×C283C22×C22⋊C4
prime radicalC2×#41×D283C2
cosocleC2×C4×C283C24
hypercenter#421D283
hypocenterC283C2×#421
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. C2×M16×D283C2semidirect
3. #117×D283C2semidirect
4. #31826483C2semidirect
5. #31826482C2semidirect
6. #31826481C2semidirect
7. #31826480C2semidirect
8. #104×D283C2semidirect
9. #421×C283C2semidirect
10. C2×#17985393C4semidirect
14. C2×#17985391C4semidirect
19. #41×D283C4semidirect
20. #41×D283C4semidirect
23. C2×Q8×D283C4semidirect
25. C2×D4×D283C4semidirect
28. C2×#17985376C22semidirect
32. M16×D283C22semidirect
33. M16×D283C22semidirect
35. #22583569C22semidirect
37. #22583567C22semidirect
41. C42×D283C22semidirect
42. #22583538C22semidirect
43. #22583537C22semidirect
44. #22583536C22semidirect
46. C2×M16×C283C22semidirect
47. #117×C283C22semidirect
48. #104×C283C22semidirect
54. #17985393C2×C4semidirect
61. #17985392C2×C4semidirect
70. #17985391C2×C4semidirect
72. C2×Dic566C2×C4semidirect
76. Q8×D283C2×C4semidirect
78. C2×D1132C2×C4semidirect
89. D4×D283C2×C4semidirect
113. #17985376C23semidirect
124. C4×Dic283C23semidirect
127. #41×C283C2×C4semidirect
129. C2×Q8×C283C2×C4semidirect
131. C2×D4×C283C2×C4semidirect
135. M16×C283C23semidirect
139. C42×C283C23semidirect
259. D283#421direct (N × H)
260. C283C2×#421semidirect
269. #421D283direct (N × H)
296. C2×M16C2×D283semidirect
302. #117C2×D283semidirect
309. #104C2×D283semidirect
334. #41C4×D283semidirect
342. C2×Q8C4×D283semidirect
357. C2×D4C4×D283semidirect
387. M16C22×D283semidirect
400. C42C22×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D2832
C2×M16×D2832
#117×D2832
#318264832
#318264822
#318264812
#318264802
#104×D2832
#421×C2832
C2×#421283