Finite Group Databasebeta

← #468×D283 #49130845

Subgroups — #468×D283 #49130845

Order 36224.

544 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D283C211yesmaximal, characteristic, complemented
2C2×M16×D283C211yesmaximal, characteristic, complemented
3C22⋊Q8×D283C211yesmaximal, characteristic, complemented
4#121×D283C211yesmaximal, characteristic
5#31826714C211yesmaximal, characteristic, complemented
6#31826713C211yesmaximal, characteristic, complemented
7#31826712C211yesmaximal, characteristic, complemented
8#31826711C211yesmaximal, characteristic, complemented
9#31826710C211yesmaximal, characteristic, complemented
10#31826709C211yesmaximal, characteristic, complemented
11#31826708C211yesmaximal, characteristic, complemented
12#107×D283C211yesmaximal, characteristic, complemented
13#103×D283C211yesmaximal, characteristic, complemented
14#102×D283C211yesmaximal, characteristic, complemented
15#468×C283C211yesmaximal, characteristic, complemented
16C2×Q8×D283C2211yescharacteristic
17C2×D4×D283—21no—
18C2×D4×D283C2211yescharacteristic
19C22×C4×D283C2211yescharacteristic
20C2×#17985381C2211yescharacteristic, complemented
21C2×#17985380C2211yescharacteristic, complemented
22C2×#17985379C2211yescharacteristic, complemented
23SD16×D283—24no—
24C2×#17985376C2211yescharacteristic, complemented
25C2×#17985375C2211yescharacteristic, complemented
26C2×#17985375C2211yescharacteristic, complemented
27M16×D283—24no—
28C2×C8×D283C2211yescharacteristic
29C2×C8×D283C2211yescharacteristic
30#22583590C2211yescharacteristic, complemented
31#22583589C2211yescharacteristic, complemented
32#22583588—21no—
33#22583587—21no—
34#22583586C2211yescharacteristic, complemented
35#22583585C2211yescharacteristic
36#22583584C2211yescharacteristic
37#22583583—21no—
38#22583582—21no—
39#22583581C2211yescharacteristic
40C4⋊C4×D283—21no—
41C4⋊C4×D283C2211yescharacteristic
42C4⋊C4×D283C2211yescharacteristic
43C22⋊C4×D283—21no—
44C22⋊C4×D283—21no—
45#22583544C2211yescharacteristic, complemented
46#22583543C2211yescharacteristic, complemented
47#22583543C2211yescharacteristic, complemented
48#22583535C2211yescharacteristic, complemented
49#22583534C2211yescharacteristic, complemented
50#22583533C2211yescharacteristic, complemented
51#22583532C2211yescharacteristic, complemented
52#22583531C2211yescharacteristic, complemented
53#22583530C2211yescharacteristic, complemented
54C2×SD16×C283C2211yescharacteristic, complemented
55C2×M16×C283C2211yescharacteristic, complemented
56C22⋊Q8×C283C2211yescharacteristic, complemented
57#121×C283C2211yescharacteristic
58#107×C283C2211yescharacteristic, complemented
59#103×C283C2211yescharacteristic, complemented
60#102×C283C2211yescharacteristic, complemented
61C23×D283—21no—
62C23×D283D411yescharacteristic
63C2×Dic566—21no—
64C2×Dic566C2311yescharacteristic
65Q8×D283—22no—
66Q8×D283—22no—
67C2×D1132—21no—
68C2×D1132C2311yescharacteristic
69C2×C22⋊D283—21no—
70C2×C22⋊D283—21no—
71C2×C22⋊D283—21no—
72D4×D283—22no—
73D4×D283—22no—
74D4×D283—44no—
75C22×Dic283D411yescharacteristic
76C2×C4×D283—22no—
77C2×C4×D283—22no—
78C2×C4×D283—21no—
79C2×C4×D283—21no—
80C2×C4×D283—21no—
81C2×C4×D283D411yescharacteristic
82C2×C4×D283D411yescharacteristic
83C2×C4×D283C2311yescharacteristic
84C2×C4×D283C2311yescharacteristic
85#17985381—22no—
86#17985380—22no—
87#17985379—22no—
88#17985376—22no—
89#17985375—22no—
90#17985375—22no—
91C2×C283⋊C8C2311yescharacteristic
92C2×C283⋊C8C2311yescharacteristic
93C8×D283—22no—
94C8×D283D414yescomplemented
95C4⋊Dic283—21no—
96C4⋊Dic283C2311yescharacteristic
97C4⋊Dic283C2311yescharacteristic
98Dic283⋊C4—21no—
99Dic283⋊C4—21no—
100Dic283⋊C4—21no—
101Dic283⋊C4—21no—
102C22⋊Dic283—21no—
103C22⋊Dic283—21no—
104(C2×D283)⋊C4—21no—
105(C2×D283)⋊C4—21no—
106(C2×D283)⋊C4—21no—
107(C2×D283)⋊C4—21no—
108C2×Q8×C283C2311yescharacteristic
109C2×D4×C283—21no—
110C2×D4×C283C2311yescharacteristic
111C22×C4×C283C2311yescharacteristic
112SD16×C283—22no—
113M16×C283—22no—
114C2×C8×C283C2311yescharacteristic
115C2×C8×C283C2311yescharacteristic
116C4⋊C4×C283—21no—
117C4⋊C4×C283C2311yescharacteristic
118C4⋊C4×C283C2311yescharacteristic
119C22⋊C4×C283—21no—
120C22⋊C4×C283—21no—
121C22×D283—22no—
122C22×D283—22no—
123C22×D283—22no—
124C22×D283—21no—
125C22×D283—42no—
126C22×D283—42no—
127C22×D283—42no—
128C22×D283C2×D411yescharacteristic
129C22×D283C2×D411yescharacteristic
130Dic566—21no—
131Dic566—21no—
132Dic566—42no—
133D1132—21no—
134D1132—21no—
135D1132—42no—
136C22⋊D283—42no—
137C22⋊D283—42no—
138C22⋊D283—42no—
139C2×Dic283—22no—
140C2×Dic283—21no—
141C2×Dic283—21no—
142C2×Dic283—21no—
143C2×Dic283C2×D411yescharacteristic
144C2×Dic283C2×D411yescharacteristic
145C4×D283—22no—
146C4×D283—21no—
147C4×D283—21no—
148C4×D283—22no—
149C4×D283—42no—
150C4×D283—42no—
151C4×D283—42no—
152C4×D283C2×D412yes—
153C4×D283#4112yes—
154C283⋊C8—21no—
155C283⋊C8C2×D412yescomplemented
156C23×C283—21no—
157C23×C283C2×D411yescharacteristic
158Q8×C283—21no—
159Q8×C283—21no—
160D4×C283—21no—
161D4×C283—21no—
162D4×C283—42no—
163C2×C4×C283—21no—
164C2×C4×C283—21no—
165C2×C4×C283—21no—
166C2×C4×C283—21no—
167C2×C4×C283—21no—
168C2×C4×C283C2×D411yescharacteristic
169C2×C4×C283C2411yescharacteristic
170C8×C283—21no—
171C8×C283C2×D412yescomplemented
172C22×C283—21no—
173C22×C283—21no—
174C22×C283—21no—
175C22×C283—41no—
176C22×C283—41no—
177C22×C283—41no—
178C22×C283C22×D411yescharacteristic
179C2×D283—21no—
180C2×D283—21no—
181C2×D283—21no—
182C2×D283—44no—
183C2×D283—41no—
184C2×D283—41no—
185C2×D283—41no—
186C2×D283—84no—
187C2×D283#12112yes—
188C2×D283AGL(1,ℤ/8)12yes—
189C2×D283#13712yes—
190C4×C283—21no—
191C4×C283—41no—
192C4×C283—41no—
193C4×C283—41no—
194C4×C283C22×D411yescharacteristic
195C4×C283C2×#4111yescharacteristic
196Dic283—21no—
197Dic283—41no—
198Dic283—41no—
199Dic283—41no—
200Dic283#12112yes—
201C2×C283—41no—
202C2×C283—81no—
203C2×C283C2×#12111yescharacteristic
204C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
205C2×C283C2×#13711yescharacteristic
206D283—41no—
207D283—81no—
208D283#46814yesdirect product factor
209C283C2×#46811yescharacteristic, complemented, Sylow
210C2×#468—2831nomaximal, Sylow
211C22×SD16—2831no—
212C22×M16—2831no—
213C2×C22⋊Q8—2831no—
214C2×#121—2831no—
215#468—2831no—
216#468—2831no—
217#468—2831no—
218#468—2831no—
219#468—2831no—
220#468—2831no—
221#468—2831no—
222#468D28311yescharacteristic, direct product factor
223C2×#107—2831no—
224C2×#103—2831no—
225C2×#102—2831no—
226C22×Q8—2831no—
227C22×D4—2831no—
228C22×D4—5661no—
229C23×C4—2831no—
230C2×SD16—2831no—
231C2×SD16—2831no—
232C2×SD16—2831no—
233C2×SD16—5664no—
234C2×SD16C2×D28311yescharacteristic, complemented
235C2×M16—2831no—
236C2×M16—2831no—
237C2×M16—2831no—
238C2×M16—5664no—
239C2×M16C2×D28311yescharacteristic, complemented
240C22×C8—2831no—
241C22×C8—2831no—
242C22⋊Q8—2831no—
243C22⋊Q8—2831no—
244C22⋊Q8—2831no—
245C22⋊Q8—5661no—
246C22⋊Q8—5661no—
247C22⋊Q8C2×D28311yescharacteristic, complemented
248#121—2831no—
249#121—2831no—
250#121—2831no—
251#121—5661no—
252#121—5661no—
253#121C2×D28311yescharacteristic
254C2×C4⋊C4—2831no—
255C2×C4⋊C4—2831no—
256C2×C4⋊C4—5661no—
257C2×C22⋊C4—5661no—
258C2×C22⋊C4—5661no—
259#107—2831no—
260#107—2831no—
261#107—2831no—
262#107C2×D28311yescharacteristic, complemented
263#103—2831no—
264#103—2831no—
265#103—2831no—
266#103C2×D28311yescharacteristic, complemented
267#102—2831no—
268#102—2831no—
269#102—2831no—
270#102C2×D28311yescharacteristic, complemented
271C24—2831no—
272C24—5661no—
273C2×Q8—2831no—
274C2×Q8—5661no—
275C2×Q8—5662no—
276C2×Q8—5662no—
277C2×Q8C22×D28311yescharacteristic
278C2×D4—21no—
279C2×D4—2831no—
280C2×D4—5661no—
281C2×D4—5662no—
282C2×D4—5662no—
283C2×D4—5661no—
284C2×D4—5661no—
285C2×D4—5661no—
286C2×D4—11324no—
287C2×D4C22×D28311yescharacteristic
288C22×C4—2831no—
289C22×C4—2831no—
290C22×C4—2831no—
291C22×C4—2831no—
292C22×C4—2831no—
293C22×C4—5662no—
294C22×C4—5662no—
295C22×C4—5661no—
296C22×C4—5661no—
297C22×C4—5661no—
298C22×C4C22×D28311yescharacteristic
299SD16—22no—
300SD16—5662no—
301SD16—5662no—
302SD16—5662no—
303M16—22no—
304M16—5662no—
305M16—5662no—
306M16—5662no—
307C2×C8—2831no—
308C2×C8—2834no—
309C2×C8—2831no—
310C2×C8—5662no—
311C2×C8C22×D28311yescharacteristic
312C2×C8C22×D28311yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—2831no—
315C4⋊C4—2831no—
316C4⋊C4—5661no—
317C4⋊C4—5661no—
318C4⋊C4—5661no—
319C4⋊C4—5661no—
320C4⋊C4—5661no—
321C4⋊C4C22×D28311yescharacteristic
322C4⋊C4C22×D28311yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—5661no—
326C22⋊C4—5661no—
327C22⋊C4—5661no—
328C22⋊C4—5661no—
329C22⋊C4—5661no—
330C22⋊C4—5661no—
331C23—21no—
332C23—2831no—
333C23—2831no—
334C23—5662no—
335C23—5662no—
336C23—5662no—
337C23—5661no—
338C23—11322no—
339C23—11322no—
340C23—11322no—
341C23D4×D28311yescharacteristic
342Q8—21no—
343Q8—21no—
344Q8—5661no—
345Q8—5661no—
346Q8—11322no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—5661no—
351D4—5661no—
352D4—11322no—
353D4—11322no—
354D4—11322no—
355D4—11322no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—2831no—
362C2×C4—2832no—
363C2×C4—2832no—
364C2×C4—2831no—
365C2×C4—5662no—
366C2×C4—5662no—
367C2×C4—5662no—
368C2×C4—5661no—
369C2×C4—5661no—
370C2×C4—5661no—
371C2×C4—5661no—
372C2×C4—5661no—
373C2×C4—11322no—
374C2×C4—11322no—
375C2×C4—11322no—
376C2×C4D4×D28311yescharacteristic
377C2×C4C23×D28311yescharacteristic
378C8—21no—
379C8—2832no—
380C8—5661no—
381C8D4×D28312yescomplemented
382C22—21no—
383C22—21no—
384C22—21no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—2832no—
389C22—2832no—
390C22—2832no—
391C22—5661no—
392C22—5661no—
393C22—5661no—
394C22—11324no—
395C22—11321no—
396C22—11321no—
397C22—11321no—
398C22—22644no—
399C22C2×D4×D28311yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—2832no—
405C4—5661no—
406C4—11321no—
407C4—11321no—
408C4—11321no—
409C4C2×D4×D28311yescharacteristic
410C4#41×D28311yescharacteristic
411C2—41no—
412C2—81no—
413C2—2834no—
414C2—11321no—
415C2—22641no—
416C2#121×D28311yescharacteristic
417C2AGL(1,ℤ/8)×D28311yescharacteristic
418C2#137×D28311yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#468×C283C2
socleC22×C283C22×D4
prime radical#121×D283C2
hypercenter#468D283
hypocenterC283C2×#468
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D283C2semidirect
2. C2×M16×D283C2semidirect
3. C22⋊Q8×D283C2semidirect
5. #31826714C2semidirect
6. #31826713C2semidirect
7. #31826712C2semidirect
8. #31826711C2semidirect
9. #31826710C2semidirect
10. #31826709C2semidirect
11. #31826708C2semidirect
12. #107×D283C2semidirect
13. #103×D283C2semidirect
14. #102×D283C2semidirect
15. #468×C283C2semidirect
20. C2×#17985381C22semidirect
21. C2×#17985380C22semidirect
22. C2×#17985379C22semidirect
24. C2×#17985376C22semidirect
25. C2×#17985375C22semidirect
26. C2×#17985375C22semidirect
30. #22583590C22semidirect
31. #22583589C22semidirect
34. #22583586C22semidirect
45. #22583544C22semidirect
46. #22583543C22semidirect
47. #22583543C22semidirect
48. #22583535C22semidirect
49. #22583534C22semidirect
50. #22583533C22semidirect
51. #22583532C22semidirect
52. #22583531C22semidirect
53. #22583530C22semidirect
54. C2×SD16×C283C22semidirect
55. C2×M16×C283C22semidirect
56. C22⋊Q8×C283C22semidirect
58. #107×C283C22semidirect
59. #103×C283C22semidirect
60. #102×C283C22semidirect
94. C8×D283D4semidirect
155. C283⋊C8C2×D4semidirect
171. C8×C283C2×D4semidirect
208. D283#468direct (N × H)
209. C283C2×#468semidirect
222. #468D283direct (N × H)
234. C2×SD16C2×D283semidirect
239. C2×M16C2×D283semidirect
247. C22⋊Q8C2×D283semidirect
262. #107C2×D283semidirect
266. #103C2×D283semidirect
270. #102C2×D283semidirect
381. C8D4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D2832
C2×M16×D2832
C22⋊Q8×D2832
#121×D2832
#318267142
#318267132
#318267122
#318267112
#318267102
#318267092
#318267082
#107×D2832
#103×D2832
#102×D2832
#468×C2832
C2×#468283