Finite Group Databasebeta

← #463×D103 #27204564

Subgroups — #463×D103 #27204564

Order 13184.

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×D103C211yesmaximal, characteristic, complemented
2C2×D8×D103C211yesmaximal, characteristic
3#124×D103C211yesmaximal, characteristic, complemented
4C4×D4×D103C211yesmaximal, characteristic, complemented
5#20268009C211yesmaximal, characteristic, complemented
6#20268008C211yesmaximal, characteristic, complemented
7#20268007C211yesmaximal, characteristic, complemented
8#20268006C211yesmaximal, characteristic, complemented
9#20268005C211yesmaximal, characteristic, complemented
10#20268004C211yesmaximal, characteristic, complemented
11#20268003C211yesmaximal, characteristic, complemented
12C4⋊C8×D103C211yesmaximal, characteristic, complemented
13#103×D103C211yesmaximal, characteristic, complemented
14#102×D103C211yesmaximal, characteristic, complemented
15#463×C103C211yesmaximal, characteristic, complemented
16C2×Q8×D103C2211yescharacteristic
17C2×D4×D103C2211yescharacteristic
18C2×D4×D103C2211yescharacteristic
19C22×C4×D103—21no—
20C2×#13110094C2211yescharacteristic, complemented
21C2×#13110093C2211yescharacteristic, complemented
22C2×#13110092C2211yescharacteristic, complemented
23SD16×D103—24no—
24C2×D824C2211yescharacteristic
25C2×#13110090C2211yescharacteristic
26C2×#13110090C2211yescharacteristic
27D8×D103—24no—
28C2×C8×D103C2211yescharacteristic
29C2×C8×D103C2211yescharacteristic
30#15693010C2211yescharacteristic, complemented
31#15693009C2211yescharacteristic, complemented
32#15693008C2211yescharacteristic, complemented
33#15693007—21no—
34#15693007—21no—
35C4×D412C2211yescharacteristic, complemented
36D4×Dic103C2211yescharacteristic, complemented
37#15692983C2211yescharacteristic, complemented
38C4×C22⋊D103—21no—
39(C22⋊D103)⋊C4—21no—
40C4⋊C4×D103C2211yescharacteristic
41C22⋊C4×D103—21no—
42C22⋊C4×D103—21no—
43C22⋊C4×D103—21no—
44C42×D103C2211yescharacteristic
45C4⋊(C103⋊C8)C2211yescharacteristic, complemented
46Dic103⋊C8C2211yescharacteristic, complemented
47Dic103⋊C8C2211yescharacteristic, complemented
48#15692946C2211yescharacteristic, complemented
49#15692945C2211yescharacteristic, complemented
50#15692944C2211yescharacteristic, complemented
51#15692943C2211yescharacteristic, complemented
52#15692942C2211yescharacteristic, complemented
53#15692941C2211yescharacteristic, complemented
54C2×SD16×C103C2211yescharacteristic, complemented
55C2×D8×C103C2211yescharacteristic
56#124×C103C2211yescharacteristic, complemented
57C4×D4×C103C2211yescharacteristic, complemented
58C4⋊C8×C103C2211yescharacteristic, complemented
59#103×C103C2211yescharacteristic, complemented
60#102×C103C2211yescharacteristic, complemented
61C23×D103—21no—
62C23×D103—21no—
63C2×Dic206—21no—
64C2×Dic206C2311yescharacteristic
65Q8×D103—22no—
66Q8×D103—22no—
67C2×D412C2311yescharacteristic
68C2×D412C2311yescharacteristic
69C2×C22⋊D103—21no—
70C2×C22⋊D103—21no—
71D4×D103—22no—
72D4×D103—22no—
73D4×D103—22no—
74D4×D103D414yes—
75C22×Dic103—21no—
76C2×C4×D103—21no—
77C2×C4×D103—21no—
78C2×C4×D103—21no—
79C2×C4×D103—21no—
80C2×C4×D103—44no—
81C2×C4×D103D411yescharacteristic
82C2×C4×D103D411yescharacteristic
83C2×C4×D103C2311yescharacteristic
84#13110094—22no—
85#13110093—22no—
86#13110092—22no—
87D824—22no—
88#13110090—22no—
89#13110090—22no—
90C2×C103⋊C8C2311yescharacteristic
91C2×C103⋊C8C2311yescharacteristic
92C8×D103—22no—
93C8×D103—22no—
94C4⋊Dic103C2311yescharacteristic
95Dic103⋊C4—21no—
96C22⋊Dic103—21no—
97C22⋊Dic103—21no—
98C22⋊Dic103—21no—
99(C2×D103)⋊C4—21no—
100(C2×D103)⋊C4—21no—
101(C2×D103)⋊C4—21no—
102(C2×D103)⋊C4—21no—
103(C2×D103)⋊C4—21no—
104(C2×D103)⋊C4—21no—
105C4×Dic103D411yescharacteristic
106C4×Dic103D411yescharacteristic
107C4×Dic103C2311yescharacteristic
108C2×Q8×C103C2311yescharacteristic
109C2×D4×C103C2311yescharacteristic
110C2×D4×C103C2311yescharacteristic
111C22×C4×C103—21no—
112SD16×C103—22no—
113D8×C103—22no—
114C2×C8×C103C2311yescharacteristic
115C2×C8×C103C2311yescharacteristic
116C4⋊C4×C103C2311yescharacteristic
117C22⋊C4×C103—21no—
118C22⋊C4×C103—21no—
119C22⋊C4×C103—21no—
120C42×C103C2311yescharacteristic
121C23×C103—21no—
122C23×C103—21no—
123C22×D103—21no—
124C22×D103—24no—
125C22×D103—21no—
126C22×D103—42no—
127C22×D103—42no—
128C22×D103—42no—
129C22×D103—42no—
130C22×D103—42no—
131C22×D103C2×D411yescharacteristic
132Q8×C103—21no—
133Q8×C103—21no—
134D4×C103—21no—
135D4×C103—21no—
136D4×C103—21no—
137D4×C103C2×D412yes—
138C2×C4×C103—21no—
139C2×C4×C103—21no—
140C2×C4×C103—42no—
141C2×C4×C103C2×D411yescharacteristic
142C2×C4×C103C2×D411yescharacteristic
143C2×C4×C103C2411yescharacteristic
144C22⋊D103—24no—
145C22⋊D103—42no—
146C2×Dic103—21no—
147C2×Dic103—21no—
148C2×Dic103—42no—
149C2×Dic103C2×D411yescharacteristic
150C2×Dic103C2×D411yescharacteristic
151C2×Dic103C2×D411yescharacteristic
152D412—21no—
153D412—21no—
154D412—21no—
155D412C2×D412yes—
156C4×D103—22no—
157C4×D103—22no—
158C4×D103—42no—
159C4×D103—42no—
160C4×D103—42no—
161C4×D103—42no—
162C4×D103C2×D412yes—
163C4×D103#4112yes—
164Dic206—21no—
165Dic206—21no—
166Dic206—42no—
167C8×C103—21no—
168C8×C103—21no—
169C103⋊C8—21no—
170C103⋊C8—21no—
171C22×C103—22no—
172C22×C103—41no—
173C22×C103—41no—
174C22×C103—41no—
175C22×C103—41no—
176C22×C103—41no—
177C22×C103C22×D411yescharacteristic
178C2×D103—22no—
179C2×D103—41no—
180C2×D103—41no—
181C2×D103—48no—
182C2×D103—41no—
183C2×D103—41no—
184C2×D103—41no—
185C2×D103—84no—
186C2×D103#12112yes—
187C2×D103#13512yes—
188C2×D103AGL(1,ℤ/8)12yes—
189C4×C103—21no—
190C4×C103—21no—
191C4×C103—41no—
192C4×C103—41no—
193C4×C103C22×D411yescharacteristic
194C4×C103C2×#4111yescharacteristic
195Dic103—21no—
196Dic103—21no—
197Dic103—41no—
198Dic103—41no—
199Dic103#12112yes—
200C2×C103—42no—
201C2×C103—81no—
202C2×C103C2×#12111yescharacteristic
203C2×C103C2×#13511yescharacteristic
204C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
205D103—42no—
206D103—81no—
207D103#46314yesdirect product factor
208C2×#463—1031nomaximal, Sylow
209C103C2×#46311yescharacteristic, complemented, Sylow
210C22×SD16—1031no—
211C22×D8—1031no—
212C2×#124—1031no—
213C2×C4×D4—1031no—
214#463—1031no—
215#463—1031no—
216#463—1031no—
217#463—1031no—
218#463—1031no—
219#463—1031no—
220#463—1031no—
221#463D10311yescharacteristic, direct product factor
222C2×C4⋊C8—1031no—
223C2×#103—1031no—
224C2×#102—1031no—
225C22×Q8—1031no—
226C22×D4—1031no—
227C22×D4—1031no—
228C23×C4—2061no—
229C2×SD16—1031no—
230C2×SD16—1031no—
231C2×SD16—1031no—
232C2×SD16—2064no—
233C2×SD16C2×D10311yescharacteristic, complemented
234C2×D8—1031no—
235C2×D8—1031no—
236C2×D8—1031no—
237C2×D8—2064no—
238C2×D8C2×D10311yescharacteristic
239C22×C8—1031no—
240C22×C8—1031no—
241#124—1031no—
242#124—1031no—
243#124—1031no—
244#124—2061no—
245#124—2061no—
246#124C2×D10311yescharacteristic, complemented
247C4×D4—1031no—
248C4×D4—1031no—
249C4×D4—1031no—
250C4×D4—2061no—
251C4×D4—2061no—
252C4×D4C2×D10311yescharacteristic, complemented
253C2×C4⋊C4—1031no—
254C2×C22⋊C4—2061no—
255C2×C22⋊C4—2061no—
256C2×C22⋊C4—2061no—
257C2×C42—1031no—
258C4⋊C8—1031no—
259C4⋊C8—1031no—
260C4⋊C8—1031no—
261C4⋊C8C2×D10311yescharacteristic, complemented
262#103—1031no—
263#103—1031no—
264#103—1031no—
265#103C2×D10311yescharacteristic, complemented
266#102—1031no—
267#102—1031no—
268#102—1031no—
269#102C2×D10311yescharacteristic, complemented
270C24—2061no—
271C24—2061no—
272C2×Q8—1031no—
273C2×Q8—2061no—
274C2×Q8—2062no—
275C2×Q8—2062no—
276C2×Q8C22×D10311yescharacteristic
277C2×D4—1034no—
278C2×D4—1031no—
279C2×D4—1031no—
280C2×D4—2062no—
281C2×D4—2062no—
282C2×D4—2062no—
283C2×D4—2061no—
284C2×D4—2061no—
285C2×D4C22×D10311yescharacteristic
286C2×D4C22×D10311yescharacteristic
287C22×C4—21no—
288C22×C4—1031no—
289C22×C4—1031no—
290C22×C4—1031no—
291C22×C4—4124no—
292C22×C4—2061no—
293C22×C4—2061no—
294C22×C4—2061no—
295C22×C4—2061no—
296C22×C4—2061no—
297SD16—22no—
298SD16—2062no—
299SD16—2062no—
300SD16—2062no—
301D8—22no—
302D8—2062no—
303D8—2062no—
304D8—2062no—
305C2×C8—1031no—
306C2×C8—1031no—
307C2×C8—2062no—
308C2×C8—2062no—
309C2×C8C22×D10311yescharacteristic
310C2×C8C22×D10311yescharacteristic
311C4⋊C4—1031no—
312C4⋊C4—2061no—
313C4⋊C4C22×D10311yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—2061no—
318C22⋊C4—2061no—
319C22⋊C4—2061no—
320C22⋊C4—2061no—
321C22⋊C4—2061no—
322C22⋊C4—2061no—
323C22⋊C4—2061no—
324C22⋊C4—2061no—
325C22⋊C4—2061no—
326C42—1031no—
327C42—1031no—
328C42—1031no—
329C42C22×D10311yescharacteristic
330C23—21no—
331C23—21no—
332C23—1031no—
333C23—4122no—
334C23—4122no—
335C23—4122no—
336C23—4122no—
337C23—4122no—
338C23—2064no—
339C23—2061no—
340C23—2061no—
341Q8—21no—
342Q8—21no—
343Q8—4122no—
344Q8—2061no—
345Q8—2061no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—1032no—
350D4—4122no—
351D4—2064no—
352D4—2061no—
353D4—2061no—
354D4—2061no—
355D4D4×D10312yes—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—1031no—
360C2×C4—1032no—
361C2×C4—1032no—
362C2×C4—1031no—
363C2×C4—1031no—
364C2×C4—4122no—
365C2×C4—4122no—
366C2×C4—4122no—
367C2×C4—4122no—
368C2×C4—4122no—
369C2×C4—2062no—
370C2×C4—2062no—
371C2×C4—2061no—
372C2×C4—2061no—
373C2×C4D4×D10311yescharacteristic
374C2×C4D4×D10311yescharacteristic
375C2×C4C23×D10311yescharacteristic
376C8—21no—
377C8—21no—
378C8—2061no—
379C8—2061no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—8244no—
387C22—1032no—
388C22—1032no—
389C22—1032no—
390C22—4128no—
391C22—4121no—
392C22—4121no—
393C22—4121no—
394C22—4121no—
395C22—4121no—
396C22—2062no—
397C22C2×D4×D10311yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—1032no—
403C4—4121no—
404C4—4121no—
405C4—2061no—
406C4—2061no—
407C4C2×D4×D10311yescharacteristic
408C4#41×D10311yescharacteristic
409C2—42no—
410C2—81no—
411C2—8241no—
412C2—1034no—
413C2—4122no—
414C2#121×D10311yescharacteristic
415C2#135×D10311yescharacteristic
416C2AGL(1,ℤ/8)×D10311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#463×C103C2
socleC22×C103C22×D4
prime radicalC2×D8×D103C2
hypercenter#463D103
hypocenterC103C2×#463
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D103C2semidirect
3. #124×D103C2semidirect
4. C4×D4×D103C2semidirect
5. #20268009C2semidirect
6. #20268008C2semidirect
7. #20268007C2semidirect
8. #20268006C2semidirect
9. #20268005C2semidirect
10. #20268004C2semidirect
11. #20268003C2semidirect
12. C4⋊C8×D103C2semidirect
13. #103×D103C2semidirect
14. #102×D103C2semidirect
15. #463×C103C2semidirect
20. C2×#13110094C22semidirect
21. C2×#13110093C22semidirect
22. C2×#13110092C22semidirect
30. #15693010C22semidirect
31. #15693009C22semidirect
32. #15693008C22semidirect
35. C4×D412C22semidirect
36. D4×Dic103C22semidirect
37. #15692983C22semidirect
45. C4⋊(C103⋊C8)C22semidirect
46. Dic103⋊C8C22semidirect
47. Dic103⋊C8C22semidirect
48. #15692946C22semidirect
49. #15692945C22semidirect
50. #15692944C22semidirect
51. #15692943C22semidirect
52. #15692942C22semidirect
53. #15692941C22semidirect
54. C2×SD16×C103C22semidirect
56. #124×C103C22semidirect
57. C4×D4×C103C22semidirect
58. C4⋊C8×C103C22semidirect
59. #103×C103C22semidirect
60. #102×C103C22semidirect
207. D103#463direct (N × H)
209. C103C2×#463semidirect
221. #463D103direct (N × H)
233. C2×SD16C2×D103semidirect
246. #124C2×D103semidirect
252. C4×D4C2×D103semidirect
261. C4⋊C8C2×D103semidirect
265. #103C2×D103semidirect
269. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1032
C2×D8×D1032
#124×D1032
C4×D4×D1032
#202680092
#202680082
#202680072
#202680062
#202680052
#202680042
#202680032
C4⋊C8×D1032
#103×D1032
#102×D1032
#463×C1032
C2×#463103