Finite Group Databasebeta

← #463×D101 #27180552

Subgroups — #463×D101 #27180552

Order 12928.

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×D101C211yesmaximal, characteristic, complemented
2C2×D8×D101C211yesmaximal, characteristic
3#124×D101C211yesmaximal, characteristic, complemented
4C4×D4×D101C211yesmaximal, characteristic, complemented
5#20265395C211yesmaximal, characteristic, complemented
6#20265394C211yesmaximal, characteristic, complemented
7#20265393C211yesmaximal, characteristic, complemented
8#20265392C211yesmaximal, characteristic, complemented
9#20265391C211yesmaximal, characteristic, complemented
10#20265390C211yesmaximal, characteristic, complemented
11#20265389C211yesmaximal, characteristic, complemented
12C4⋊C8×D101C211yesmaximal, characteristic, complemented
13#103×D101C211yesmaximal, characteristic, complemented
14#102×D101C211yesmaximal, characteristic, complemented
15#463×C101C211yesmaximal, characteristic, complemented
16C2×Q8×D101C2211yescharacteristic
17C2×D4×D101C2211yescharacteristic
18C2×D4×D101C2211yescharacteristic
19C22×C4×D101—21no—
20C2×#13108063C2211yescharacteristic, complemented
21C2×#13108062C2211yescharacteristic, complemented
22C2×#13108061C2211yescharacteristic, complemented
23SD16×D101—24no—
24C2×D808C2211yescharacteristic
25C2×#13108059C2211yescharacteristic
26C2×#13108059C2211yescharacteristic
27D8×D101—24no—
28C2×C8×D101C2211yescharacteristic
29C2×C8×D101C2211yescharacteristic
30#15692244C2211yescharacteristic, complemented
31#15692243C2211yescharacteristic, complemented
32#15692242C2211yescharacteristic, complemented
33#15692241—21no—
34#15692241—21no—
35C4×D404C2211yescharacteristic, complemented
36D4×Dic101C2211yescharacteristic, complemented
37#15692217C2211yescharacteristic, complemented
38C4×C22⋊D101—21no—
39#15692215—21no—
40C4⋊C4×D101C2211yescharacteristic
41C22⋊C4×D101—21no—
42C22⋊C4×D101—21no—
43C22⋊C4×D101—21no—
44C42×D101C2211yescharacteristic
45C4⋊#11717579C2211yescharacteristic, complemented
46#15692184C2211yescharacteristic, complemented
47#15692184C2211yescharacteristic, complemented
48#15692180C2211yescharacteristic, complemented
49#15692179C2211yescharacteristic, complemented
50#15692178C2211yescharacteristic, complemented
51#15692177C2211yescharacteristic, complemented
52#15692176C2211yescharacteristic, complemented
53#15692175C2211yescharacteristic, complemented
54C2×SD16×C101C2211yescharacteristic, complemented
55C2×D8×C101C2211yescharacteristic
56#124×C101C2211yescharacteristic, complemented
57C4×D4×C101C2211yescharacteristic, complemented
58C4⋊C8×C101C2211yescharacteristic, complemented
59#103×C101C2211yescharacteristic, complemented
60#102×C101C2211yescharacteristic, complemented
61C23×D101—21no—
62C23×D101—21no—
63C2×Dic202—21no—
64C2×Dic202C2311yescharacteristic
65Q8×D101—22no—
66Q8×D101—22no—
67C2×D404C2311yescharacteristic
68C2×D404C2311yescharacteristic
69C2×C22⋊D101—21no—
70C2×C22⋊D101—21no—
71D4×D101—22no—
72D4×D101—22no—
73D4×D101—22no—
74D4×D101D414yes—
75C22×Dic101—21no—
76C2×C4×D101—21no—
77C2×C4×D101—21no—
78C2×C4×D101—21no—
79C2×C4×D101—21no—
80C2×C4×D101—44no—
81C2×C4×D101D411yescharacteristic
82C2×C4×D101D411yescharacteristic
83C2×C4×D101C2311yescharacteristic
84#13108063—22no—
85#13108062—22no—
86#13108061—22no—
87D808—22no—
88#13108059—22no—
89#13108059—22no—
90C2×#11717579C2311yescharacteristic
91C2×#11717579C2311yescharacteristic
92C8×D101—22no—
93C8×D101—22no—
94C4⋊Dic101C2311yescharacteristic
95#13108053—21no—
96C22⋊Dic101—21no—
97C22⋊Dic101—21no—
98C22⋊Dic101—21no—
99#13108051—21no—
100#13108051—21no—
101#13108051—21no—
102#13108051—21no—
103#13108051—21no—
104#13108051—21no—
105C4×Dic101D411yescharacteristic
106C4×Dic101D411yescharacteristic
107C4×Dic101C2311yescharacteristic
108C2×Q8×C101C2311yescharacteristic
109C2×D4×C101C2311yescharacteristic
110C2×D4×C101C2311yescharacteristic
111C22×C4×C101—21no—
112SD16×C101—22no—
113D8×C101—22no—
114C2×C8×C101C2311yescharacteristic
115C2×C8×C101C2311yescharacteristic
116C4⋊C4×C101C2311yescharacteristic
117C22⋊C4×C101—21no—
118C22⋊C4×C101—21no—
119C22⋊C4×C101—21no—
120C42×C101C2311yescharacteristic
121C23×C101—21no—
122C23×C101—21no—
123C22×D101—21no—
124C22×D101—24no—
125C22×D101—21no—
126C22×D101—42no—
127C22×D101—42no—
128C22×D101—42no—
129C22×D101—42no—
130C22×D101—42no—
131C22×D101C2×D411yescharacteristic
132Q8×C101—21no—
133Q8×C101—21no—
134D4×C101—21no—
135D4×C101—21no—
136D4×C101—21no—
137D4×C101C2×D412yes—
138C2×C4×C101—21no—
139C2×C4×C101—21no—
140C2×C4×C101—42no—
141C2×C4×C101C2×D411yescharacteristic
142C2×C4×C101C2×D411yescharacteristic
143C2×C4×C101C2411yescharacteristic
144C22⋊D101—24no—
145C22⋊D101—42no—
146C2×Dic101—21no—
147C2×Dic101—21no—
148C2×Dic101—42no—
149C2×Dic101C2×D411yescharacteristic
150C2×Dic101C2×D411yescharacteristic
151C2×Dic101C2×D411yescharacteristic
152D404—21no—
153D404—21no—
154D404—21no—
155D404C2×D412yes—
156C4×D101—22no—
157C4×D101—22no—
158C4×D101—42no—
159C4×D101—42no—
160C4×D101—42no—
161C4×D101—42no—
162C4×D101C2×D412yes—
163C4×D101#4112yes—
164Dic202—21no—
165Dic202—21no—
166Dic202—42no—
167C8×C101—21no—
168C8×C101—21no—
169#11717579—21no—
170#11717579—21no—
171C22×C101—22no—
172C22×C101—41no—
173C22×C101—41no—
174C22×C101—41no—
175C22×C101—41no—
176C22×C101—41no—
177C22×C101C22×D411yescharacteristic
178C2×D101—22no—
179C2×D101—41no—
180C2×D101—41no—
181C2×D101—48no—
182C2×D101—41no—
183C2×D101—41no—
184C2×D101—41no—
185C2×D101—84no—
186C2×D101#12112yes—
187C2×D101#13512yes—
188C2×D101AGL(1,ℤ/8)12yes—
189C4×C101—21no—
190C4×C101—21no—
191C4×C101—41no—
192C4×C101—41no—
193C4×C101C22×D411yescharacteristic
194C4×C101C2×#4111yescharacteristic
195Dic101—21no—
196Dic101—21no—
197Dic101—41no—
198Dic101—41no—
199Dic101#12112yes—
200C2×C101—42no—
201C2×C101—81no—
202C2×C101C2×#12111yescharacteristic
203C2×C101C2×#13511yescharacteristic
204C2×C101C2×AGL(1,ℤ/8)11yescharacteristic
205D101—42no—
206D101—81no—
207D101#46314yesdirect product factor
208C2×#463—1011nomaximal, Sylow
209C101C2×#46311yescharacteristic, complemented, Sylow
210C22×SD16—1011no—
211C22×D8—1011no—
212C2×#124—1011no—
213C2×C4×D4—1011no—
214#463—1011no—
215#463—1011no—
216#463—1011no—
217#463—1011no—
218#463—1011no—
219#463—1011no—
220#463—1011no—
221#463D10111yescharacteristic, direct product factor
222C2×C4⋊C8—1011no—
223C2×#103—1011no—
224C2×#102—1011no—
225C22×Q8—1011no—
226C22×D4—1011no—
227C22×D4—1011no—
228C23×C4—2021no—
229C2×SD16—1011no—
230C2×SD16—1011no—
231C2×SD16—1011no—
232C2×SD16—2024no—
233C2×SD16C2×D10111yescharacteristic, complemented
234C2×D8—1011no—
235C2×D8—1011no—
236C2×D8—1011no—
237C2×D8—2024no—
238C2×D8C2×D10111yescharacteristic
239C22×C8—1011no—
240C22×C8—1011no—
241#124—1011no—
242#124—1011no—
243#124—1011no—
244#124—2021no—
245#124—2021no—
246#124C2×D10111yescharacteristic, complemented
247C4×D4—1011no—
248C4×D4—1011no—
249C4×D4—1011no—
250C4×D4—2021no—
251C4×D4—2021no—
252C4×D4C2×D10111yescharacteristic, complemented
253C2×C4⋊C4—1011no—
254C2×C22⋊C4—2021no—
255C2×C22⋊C4—2021no—
256C2×C22⋊C4—2021no—
257C2×C42—1011no—
258C4⋊C8—1011no—
259C4⋊C8—1011no—
260C4⋊C8—1011no—
261C4⋊C8C2×D10111yescharacteristic, complemented
262#103—1011no—
263#103—1011no—
264#103—1011no—
265#103C2×D10111yescharacteristic, complemented
266#102—1011no—
267#102—1011no—
268#102—1011no—
269#102C2×D10111yescharacteristic, complemented
270C24—2021no—
271C24—2021no—
272C2×Q8—1011no—
273C2×Q8—2021no—
274C2×Q8—2022no—
275C2×Q8—2022no—
276C2×Q8C22×D10111yescharacteristic
277C2×D4—1014no—
278C2×D4—1011no—
279C2×D4—1011no—
280C2×D4—2022no—
281C2×D4—2022no—
282C2×D4—2022no—
283C2×D4—2021no—
284C2×D4—2021no—
285C2×D4C22×D10111yescharacteristic
286C2×D4C22×D10111yescharacteristic
287C22×C4—21no—
288C22×C4—1011no—
289C22×C4—1011no—
290C22×C4—1011no—
291C22×C4—4044no—
292C22×C4—2021no—
293C22×C4—2021no—
294C22×C4—2021no—
295C22×C4—2021no—
296C22×C4—2021no—
297SD16—22no—
298SD16—2022no—
299SD16—2022no—
300SD16—2022no—
301D8—22no—
302D8—2022no—
303D8—2022no—
304D8—2022no—
305C2×C8—1011no—
306C2×C8—1011no—
307C2×C8—2022no—
308C2×C8—2022no—
309C2×C8C22×D10111yescharacteristic
310C2×C8C22×D10111yescharacteristic
311C4⋊C4—1011no—
312C4⋊C4—2021no—
313C4⋊C4C22×D10111yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—2021no—
318C22⋊C4—2021no—
319C22⋊C4—2021no—
320C22⋊C4—2021no—
321C22⋊C4—2021no—
322C22⋊C4—2021no—
323C22⋊C4—2021no—
324C22⋊C4—2021no—
325C22⋊C4—2021no—
326C42—1011no—
327C42—1011no—
328C42—1011no—
329C42C22×D10111yescharacteristic
330C23—21no—
331C23—21no—
332C23—1011no—
333C23—4042no—
334C23—4042no—
335C23—4042no—
336C23—4042no—
337C23—4042no—
338C23—2024no—
339C23—2021no—
340C23—2021no—
341Q8—21no—
342Q8—21no—
343Q8—4042no—
344Q8—2021no—
345Q8—2021no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—1012no—
350D4—4042no—
351D4—2024no—
352D4—2021no—
353D4—2021no—
354D4—2021no—
355D4D4×D10112yes—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—1011no—
360C2×C4—1012no—
361C2×C4—1012no—
362C2×C4—1011no—
363C2×C4—1011no—
364C2×C4—4042no—
365C2×C4—4042no—
366C2×C4—4042no—
367C2×C4—4042no—
368C2×C4—4042no—
369C2×C4—2022no—
370C2×C4—2022no—
371C2×C4—2021no—
372C2×C4—2021no—
373C2×C4D4×D10111yescharacteristic
374C2×C4D4×D10111yescharacteristic
375C2×C4C23×D10111yescharacteristic
376C8—21no—
377C8—21no—
378C8—2021no—
379C8—2021no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—8084no—
387C22—1012no—
388C22—1012no—
389C22—1012no—
390C22—4048no—
391C22—4041no—
392C22—4041no—
393C22—4041no—
394C22—4041no—
395C22—4041no—
396C22—2022no—
397C22C2×D4×D10111yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—1012no—
403C4—4041no—
404C4—4041no—
405C4—2021no—
406C4—2021no—
407C4C2×D4×D10111yescharacteristic
408C4#41×D10111yescharacteristic
409C2—42no—
410C2—81no—
411C2—8081no—
412C2—1014no—
413C2—4042no—
414C2#121×D10111yescharacteristic
415C2#135×D10111yescharacteristic
416C2AGL(1,ℤ/8)×D10111yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#463×C101C2
socleC22×C101C22×D4
prime radicalC2×D8×D101C2
hypercenter#463D101
hypocenterC101C2×#463
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D101C2semidirect
3. #124×D101C2semidirect
4. C4×D4×D101C2semidirect
5. #20265395C2semidirect
6. #20265394C2semidirect
7. #20265393C2semidirect
8. #20265392C2semidirect
9. #20265391C2semidirect
10. #20265390C2semidirect
11. #20265389C2semidirect
12. C4⋊C8×D101C2semidirect
13. #103×D101C2semidirect
14. #102×D101C2semidirect
15. #463×C101C2semidirect
20. C2×#13108063C22semidirect
21. C2×#13108062C22semidirect
22. C2×#13108061C22semidirect
30. #15692244C22semidirect
31. #15692243C22semidirect
32. #15692242C22semidirect
35. C4×D404C22semidirect
36. D4×Dic101C22semidirect
37. #15692217C22semidirect
45. C4⋊#11717579C22semidirect
46. #15692184C22semidirect
47. #15692184C22semidirect
48. #15692180C22semidirect
49. #15692179C22semidirect
50. #15692178C22semidirect
51. #15692177C22semidirect
52. #15692176C22semidirect
53. #15692175C22semidirect
54. C2×SD16×C101C22semidirect
56. #124×C101C22semidirect
57. C4×D4×C101C22semidirect
58. C4⋊C8×C101C22semidirect
59. #103×C101C22semidirect
60. #102×C101C22semidirect
207. D101#463direct (N × H)
209. C101C2×#463semidirect
221. #463D101direct (N × H)
233. C2×SD16C2×D101semidirect
246. #124C2×D101semidirect
252. C4×D4C2×D101semidirect
261. C4⋊C8C2×D101semidirect
265. #103C2×D101semidirect
269. #102C2×D101semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1012
C2×D8×D1012
#124×D1012
C4×D4×D1012
#202653952
#202653942
#202653932
#202653922
#202653912
#202653902
#202653892
C4⋊C8×D1012
#103×D1012
#102×D1012
#463×C1012
C2×#463101