Finite Group Databasebeta

← #463×D283 #49130681

Subgroups — #463×D283 #49130681

Order 36224.

564 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D283C211yesmaximal, characteristic, complemented
2C2×D8×D283C211yesmaximal, characteristic
3#124×D283C211yesmaximal, characteristic, complemented
4C4×D4×D283C211yesmaximal, characteristic, complemented
5#31826683C211yesmaximal, characteristic, complemented
6#31826682C211yesmaximal, characteristic, complemented
7#31826681C211yesmaximal, characteristic, complemented
8#31826680C211yesmaximal, characteristic, complemented
9#31826679C211yesmaximal, characteristic, complemented
10#31826678C211yesmaximal, characteristic, complemented
11#31826677C211yesmaximal, characteristic, complemented
12C4⋊C8×D283C211yesmaximal, characteristic, complemented
13#103×D283C211yesmaximal, characteristic, complemented
14#102×D283C211yesmaximal, characteristic, complemented
15#463×C283C211yesmaximal, characteristic, complemented
16C2×Q8×D283C2211yescharacteristic
17C2×D4×D283C2211yescharacteristic
18C2×D4×D283C2211yescharacteristic
19C22×C4×D283—21no—
20C2×#17985381C2211yescharacteristic, complemented
21C2×#17985380C2211yescharacteristic, complemented
22C2×#17985379C2211yescharacteristic, complemented
23SD16×D283—24no—
24C2×D2264C2211yescharacteristic
25C2×#17985377C2211yescharacteristic
26C2×#17985377C2211yescharacteristic
27D8×D283—24no—
28C2×C8×D283C2211yescharacteristic
29C2×C8×D283C2211yescharacteristic
30#22583599C2211yescharacteristic, complemented
31#22583598C2211yescharacteristic, complemented
32#22583597C2211yescharacteristic, complemented
33#22583596—21no—
34#22583596—21no—
35C4×D1132C2211yescharacteristic, complemented
36D4×Dic283C2211yescharacteristic, complemented
37#22583572C2211yescharacteristic, complemented
38C4×C22⋊D283—21no—
39(C22⋊D283)⋊C4—21no—
40C4⋊C4×D283C2211yescharacteristic
41C22⋊C4×D283—21no—
42C22⋊C4×D283—21no—
43C22⋊C4×D283—21no—
44C42×D283C2211yescharacteristic
45C4⋊(C283⋊C8)C2211yescharacteristic, complemented
46Dic283⋊C8C2211yescharacteristic, complemented
47Dic283⋊C8C2211yescharacteristic, complemented
48#22583535C2211yescharacteristic, complemented
49#22583534C2211yescharacteristic, complemented
50#22583533C2211yescharacteristic, complemented
51#22583532C2211yescharacteristic, complemented
52#22583531C2211yescharacteristic, complemented
53#22583530C2211yescharacteristic, complemented
54C2×SD16×C283C2211yescharacteristic, complemented
55C2×D8×C283C2211yescharacteristic
56#124×C283C2211yescharacteristic, complemented
57C4×D4×C283C2211yescharacteristic, complemented
58C4⋊C8×C283C2211yescharacteristic, complemented
59#103×C283C2211yescharacteristic, complemented
60#102×C283C2211yescharacteristic, complemented
61C23×D283—21no—
62C23×D283—21no—
63C2×Dic566—21no—
64C2×Dic566C2311yescharacteristic
65Q8×D283—22no—
66Q8×D283—22no—
67C2×D1132C2311yescharacteristic
68C2×D1132C2311yescharacteristic
69C2×C22⋊D283—21no—
70C2×C22⋊D283—21no—
71D4×D283—22no—
72D4×D283—22no—
73D4×D283—22no—
74D4×D283D414yes—
75C22×Dic283—21no—
76C2×C4×D283—21no—
77C2×C4×D283—21no—
78C2×C4×D283—21no—
79C2×C4×D283—21no—
80C2×C4×D283—44no—
81C2×C4×D283D411yescharacteristic
82C2×C4×D283D411yescharacteristic
83C2×C4×D283C2311yescharacteristic
84#17985381—22no—
85#17985380—22no—
86#17985379—22no—
87D2264—22no—
88#17985377—22no—
89#17985377—22no—
90C2×C283⋊C8C2311yescharacteristic
91C2×C283⋊C8C2311yescharacteristic
92C8×D283—22no—
93C8×D283—22no—
94C4⋊Dic283C2311yescharacteristic
95Dic283⋊C4—21no—
96C22⋊Dic283—21no—
97C22⋊Dic283—21no—
98C22⋊Dic283—21no—
99(C2×D283)⋊C4—21no—
100(C2×D283)⋊C4—21no—
101(C2×D283)⋊C4—21no—
102(C2×D283)⋊C4—21no—
103(C2×D283)⋊C4—21no—
104(C2×D283)⋊C4—21no—
105C4×Dic283D411yescharacteristic
106C4×Dic283D411yescharacteristic
107C4×Dic283C2311yescharacteristic
108C2×Q8×C283C2311yescharacteristic
109C2×D4×C283C2311yescharacteristic
110C2×D4×C283C2311yescharacteristic
111C22×C4×C283—21no—
112SD16×C283—22no—
113D8×C283—22no—
114C2×C8×C283C2311yescharacteristic
115C2×C8×C283C2311yescharacteristic
116C4⋊C4×C283C2311yescharacteristic
117C22⋊C4×C283—21no—
118C22⋊C4×C283—21no—
119C22⋊C4×C283—21no—
120C42×C283C2311yescharacteristic
121C22×D283—21no—
122C22×D283—24no—
123C22×D283—21no—
124C22×D283—42no—
125C22×D283—42no—
126C22×D283—42no—
127C22×D283—42no—
128C22×D283—42no—
129C22×D283C2×D411yescharacteristic
130Dic566—21no—
131Dic566—21no—
132Dic566—42no—
133D1132—21no—
134D1132—21no—
135D1132—21no—
136D1132C2×D412yes—
137C22⋊D283—24no—
138C22⋊D283—42no—
139C2×Dic283—21no—
140C2×Dic283—21no—
141C2×Dic283—42no—
142C2×Dic283C2×D411yescharacteristic
143C2×Dic283C2×D411yescharacteristic
144C2×Dic283C2×D411yescharacteristic
145C4×D283—22no—
146C4×D283—22no—
147C4×D283—42no—
148C4×D283—42no—
149C4×D283—42no—
150C4×D283—42no—
151C4×D283C2×D412yes—
152C4×D283#4112yes—
153C283⋊C8—21no—
154C283⋊C8—21no—
155C23×C283—21no—
156C23×C283—21no—
157Q8×C283—21no—
158Q8×C283—21no—
159D4×C283—21no—
160D4×C283—21no—
161D4×C283—21no—
162D4×C283C2×D412yes—
163C2×C4×C283—21no—
164C2×C4×C283—21no—
165C2×C4×C283—42no—
166C2×C4×C283C2×D411yescharacteristic
167C2×C4×C283C2×D411yescharacteristic
168C2×C4×C283C2411yescharacteristic
169C8×C283—21no—
170C8×C283—21no—
171C22×C283—22no—
172C22×C283—41no—
173C22×C283—41no—
174C22×C283—41no—
175C22×C283—41no—
176C22×C283—41no—
177C22×C283C22×D411yescharacteristic
178C2×D283—22no—
179C2×D283—41no—
180C2×D283—41no—
181C2×D283—48no—
182C2×D283—41no—
183C2×D283—41no—
184C2×D283—41no—
185C2×D283—84no—
186C2×D283#12112yes—
187C2×D283#13512yes—
188C2×D283AGL(1,ℤ/8)12yes—
189C4×C283—21no—
190C4×C283—21no—
191C4×C283—41no—
192C4×C283—41no—
193C4×C283C22×D411yescharacteristic
194C4×C283C2×#4111yescharacteristic
195Dic283—21no—
196Dic283—21no—
197Dic283—41no—
198Dic283—41no—
199Dic283#12112yes—
200C2×C283—42no—
201C2×C283—81no—
202C2×C283C2×#12111yescharacteristic
203C2×C283C2×#13511yescharacteristic
204C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
205D283—42no—
206D283—81no—
207D283#46314yesdirect product factor
208C283C2×#46311yescharacteristic, complemented, Sylow
209C2×#463—2831nomaximal, Sylow
210C22×SD16—2831no—
211C22×D8—2831no—
212C2×#124—2831no—
213C2×C4×D4—2831no—
214#463—2831no—
215#463—2831no—
216#463—2831no—
217#463—2831no—
218#463—2831no—
219#463—2831no—
220#463—2831no—
221#463D28311yescharacteristic, direct product factor
222C2×C4⋊C8—2831no—
223C2×#103—2831no—
224C2×#102—2831no—
225C22×Q8—2831no—
226C22×D4—2831no—
227C22×D4—2831no—
228C23×C4—5661no—
229C2×SD16—2831no—
230C2×SD16—2831no—
231C2×SD16—2831no—
232C2×SD16—5664no—
233C2×SD16C2×D28311yescharacteristic, complemented
234C2×D8—2831no—
235C2×D8—2831no—
236C2×D8—2831no—
237C2×D8—5664no—
238C2×D8C2×D28311yescharacteristic
239C22×C8—2831no—
240C22×C8—2831no—
241#124—2831no—
242#124—2831no—
243#124—2831no—
244#124—5661no—
245#124—5661no—
246#124C2×D28311yescharacteristic, complemented
247C4×D4—2831no—
248C4×D4—2831no—
249C4×D4—2831no—
250C4×D4—5661no—
251C4×D4—5661no—
252C4×D4C2×D28311yescharacteristic, complemented
253C2×C4⋊C4—2831no—
254C2×C22⋊C4—5661no—
255C2×C22⋊C4—5661no—
256C2×C22⋊C4—5661no—
257C2×C42—2831no—
258C4⋊C8—2831no—
259C4⋊C8—2831no—
260C4⋊C8—2831no—
261C4⋊C8C2×D28311yescharacteristic, complemented
262#103—2831no—
263#103—2831no—
264#103—2831no—
265#103C2×D28311yescharacteristic, complemented
266#102—2831no—
267#102—2831no—
268#102—2831no—
269#102C2×D28311yescharacteristic, complemented
270C24—5661no—
271C24—5661no—
272C2×Q8—2831no—
273C2×Q8—5661no—
274C2×Q8—5662no—
275C2×Q8—5662no—
276C2×Q8C22×D28311yescharacteristic
277C2×D4—2834no—
278C2×D4—2831no—
279C2×D4—2831no—
280C2×D4—5662no—
281C2×D4—5662no—
282C2×D4—5662no—
283C2×D4—5661no—
284C2×D4—5661no—
285C2×D4C22×D28311yescharacteristic
286C2×D4C22×D28311yescharacteristic
287C22×C4—21no—
288C22×C4—2831no—
289C22×C4—2831no—
290C22×C4—2831no—
291C22×C4—5661no—
292C22×C4—5661no—
293C22×C4—5661no—
294C22×C4—5661no—
295C22×C4—5661no—
296C22×C4—11324no—
297SD16—22no—
298SD16—5662no—
299SD16—5662no—
300SD16—5662no—
301D8—22no—
302D8—5662no—
303D8—5662no—
304D8—5662no—
305C2×C8—2831no—
306C2×C8—2831no—
307C2×C8—5662no—
308C2×C8—5662no—
309C2×C8C22×D28311yescharacteristic
310C2×C8C22×D28311yescharacteristic
311C4⋊C4—2831no—
312C4⋊C4—5661no—
313C4⋊C4C22×D28311yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—5661no—
318C22⋊C4—5661no—
319C22⋊C4—5661no—
320C22⋊C4—5661no—
321C22⋊C4—5661no—
322C22⋊C4—5661no—
323C22⋊C4—5661no—
324C22⋊C4—5661no—
325C22⋊C4—5661no—
326C42—2831no—
327C42—2831no—
328C42—2831no—
329C42C22×D28311yescharacteristic
330C23—21no—
331C23—21no—
332C23—2831no—
333C23—5664no—
334C23—5661no—
335C23—5661no—
336C23—11322no—
337C23—11322no—
338C23—11322no—
339C23—11322no—
340C23—11322no—
341Q8—21no—
342Q8—21no—
343Q8—5661no—
344Q8—5661no—
345Q8—11322no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—2832no—
350D4—5664no—
351D4—5661no—
352D4—5661no—
353D4—5661no—
354D4—11322no—
355D4D4×D28312yes—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—2831no—
360C2×C4—2832no—
361C2×C4—2832no—
362C2×C4—2831no—
363C2×C4—2831no—
364C2×C4—5662no—
365C2×C4—5662no—
366C2×C4—5661no—
367C2×C4—5661no—
368C2×C4—11322no—
369C2×C4—11322no—
370C2×C4—11322no—
371C2×C4—11322no—
372C2×C4—11322no—
373C2×C4D4×D28311yescharacteristic
374C2×C4D4×D28311yescharacteristic
375C2×C4C23×D28311yescharacteristic
376C8—21no—
377C8—21no—
378C8—5661no—
379C8—5661no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—2832no—
387C22—2832no—
388C22—2832no—
389C22—5662no—
390C22—11328no—
391C22—11321no—
392C22—11321no—
393C22—11321no—
394C22—11321no—
395C22—11321no—
396C22—22644no—
397C22C2×D4×D28311yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—2832no—
403C4—5661no—
404C4—5661no—
405C4—11321no—
406C4—11321no—
407C4C2×D4×D28311yescharacteristic
408C4#41×D28311yescharacteristic
409C2—42no—
410C2—81no—
411C2—2834no—
412C2—11322no—
413C2—22641no—
414C2#121×D28311yescharacteristic
415C2#135×D28311yescharacteristic
416C2AGL(1,ℤ/8)×D28311yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#463×C283C2
socleC22×C283C22×D4
prime radicalC2×D8×D283C2
hypercenter#463D283
hypocenterC283C2×#463
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D283C2semidirect
3. #124×D283C2semidirect
4. C4×D4×D283C2semidirect
5. #31826683C2semidirect
6. #31826682C2semidirect
7. #31826681C2semidirect
8. #31826680C2semidirect
9. #31826679C2semidirect
10. #31826678C2semidirect
11. #31826677C2semidirect
12. C4⋊C8×D283C2semidirect
13. #103×D283C2semidirect
14. #102×D283C2semidirect
15. #463×C283C2semidirect
20. C2×#17985381C22semidirect
21. C2×#17985380C22semidirect
22. C2×#17985379C22semidirect
30. #22583599C22semidirect
31. #22583598C22semidirect
32. #22583597C22semidirect
35. C4×D1132C22semidirect
36. D4×Dic283C22semidirect
37. #22583572C22semidirect
45. C4⋊(C283⋊C8)C22semidirect
46. Dic283⋊C8C22semidirect
47. Dic283⋊C8C22semidirect
48. #22583535C22semidirect
49. #22583534C22semidirect
50. #22583533C22semidirect
51. #22583532C22semidirect
52. #22583531C22semidirect
53. #22583530C22semidirect
54. C2×SD16×C283C22semidirect
56. #124×C283C22semidirect
57. C4×D4×C283C22semidirect
58. C4⋊C8×C283C22semidirect
59. #103×C283C22semidirect
60. #102×C283C22semidirect
207. D283#463direct (N × H)
208. C283C2×#463semidirect
221. #463D283direct (N × H)
233. C2×SD16C2×D283semidirect
246. #124C2×D283semidirect
252. C4×D4C2×D283semidirect
261. C4⋊C8C2×D283semidirect
265. #103C2×D283semidirect
269. #102C2×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×D8×D2832
#124×D2832
C4×D4×D2832
#318266832
#318266822
#318266812
#318266802
#318266792
#318266782
#318266772
C4⋊C8×D2832
#103×D2832
#102×D2832
#463×C2832
C2×#463283