Finite Group Databasebeta

← #463×D113 #28399994

Subgroups — #463×D113 #28399994

Order 14464.

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×D113C211yesmaximal, characteristic, complemented
2C2×D8×D113C211yesmaximal, characteristic
3#124×D113C211yesmaximal, characteristic, complemented
4C4×D4×D113C211yesmaximal, characteristic, complemented
5#20298816C211yesmaximal, characteristic, complemented
6#20298815C211yesmaximal, characteristic, complemented
7#20298814C211yesmaximal, characteristic, complemented
8#20298813C211yesmaximal, characteristic, complemented
9#20298812C211yesmaximal, characteristic, complemented
10#20298811C211yesmaximal, characteristic, complemented
11#20298810C211yesmaximal, characteristic, complemented
12C4⋊C8×D113C211yesmaximal, characteristic, complemented
13#103×D113C211yesmaximal, characteristic, complemented
14#102×D113C211yesmaximal, characteristic, complemented
15#463×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18C2×D4×D113C2211yescharacteristic
19C22×C4×D113—21no—
20C2×#14268636C2211yescharacteristic, complemented
21C2×#14268635C2211yescharacteristic, complemented
22C2×#14268634C2211yescharacteristic, complemented
23SD16×D113—24no—
24C2×D904C2211yescharacteristic
25C2×#14268632C2211yescharacteristic
26C2×#14268632C2211yescharacteristic
27D8×D113—24no—
28C2×C8×D113C2211yescharacteristic
29C2×C8×D113C2211yescharacteristic
30#16813611C2211yescharacteristic, complemented
31#16813610C2211yescharacteristic, complemented
32#16813609C2211yescharacteristic, complemented
33#16813608—21no—
34#16813608—21no—
35C4×D452C2211yescharacteristic, complemented
36D4×Dic113C2211yescharacteristic, complemented
37#16813584C2211yescharacteristic, complemented
38C4×C22⋊D113—21no—
39#16813582—21no—
40C4⋊C4×D113C2211yescharacteristic
41C22⋊C4×D113—21no—
42C22⋊C4×D113—21no—
43C22⋊C4×D113—21no—
44C42×D113C2211yescharacteristic
45C4⋊#11744751C2211yescharacteristic, complemented
46#16813551C2211yescharacteristic, complemented
47#16813551C2211yescharacteristic, complemented
48#16813547C2211yescharacteristic, complemented
49#16813546C2211yescharacteristic, complemented
50#16813545C2211yescharacteristic, complemented
51#16813544C2211yescharacteristic, complemented
52#16813543C2211yescharacteristic, complemented
53#16813542C2211yescharacteristic, complemented
54C2×SD16×C113C2211yescharacteristic, complemented
55C2×D8×C113C2211yescharacteristic
56#124×C113C2211yescharacteristic, complemented
57C4×D4×C113C2211yescharacteristic, complemented
58C4⋊C8×C113C2211yescharacteristic, complemented
59#103×C113C2211yescharacteristic, complemented
60#102×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62C23×D113—21no—
63C2×Dic226—21no—
64C2×Dic226C2311yescharacteristic
65Q8×D113—22no—
66Q8×D113—22no—
67C2×D452C2311yescharacteristic
68C2×D452C2311yescharacteristic
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71D4×D113—22no—
72D4×D113—22no—
73D4×D113—22no—
74D4×D113D414yes—
75C22×Dic113—21no—
76C2×C4×D113—21no—
77C2×C4×D113—21no—
78C2×C4×D113—21no—
79C2×C4×D113—21no—
80C2×C4×D113—44no—
81C2×C4×D113D411yescharacteristic
82C2×C4×D113D411yescharacteristic
83C2×C4×D113C2311yescharacteristic
84#14268636—22no—
85#14268635—22no—
86#14268634—22no—
87D904—22no—
88#14268632—22no—
89#14268632—22no—
90C2×#11744751C2311yescharacteristic
91C2×#11744751C2311yescharacteristic
92C8×D113—22no—
93C8×D113—22no—
94C4⋊Dic113C2311yescharacteristic
95#14268626—21no—
96C22⋊Dic113—21no—
97C22⋊Dic113—21no—
98C22⋊Dic113—21no—
99#14268624—21no—
100#14268624—21no—
101#14268624—21no—
102#14268624—21no—
103#14268624—21no—
104#14268624—21no—
105C4×Dic113D411yescharacteristic
106C4×Dic113D411yescharacteristic
107C4×Dic113C2311yescharacteristic
108C2×Q8×C113C2311yescharacteristic
109C2×D4×C113C2311yescharacteristic
110C2×D4×C113C2311yescharacteristic
111C22×C4×C113—21no—
112SD16×C113—22no—
113D8×C113—22no—
114C2×C8×C113C2311yescharacteristic
115C2×C8×C113C2311yescharacteristic
116C4⋊C4×C113C2311yescharacteristic
117C22⋊C4×C113—21no—
118C22⋊C4×C113—21no—
119C22⋊C4×C113—21no—
120C42×C113C2311yescharacteristic
121C23×C113—21no—
122C23×C113—21no—
123C22×D113—21no—
124C22×D113—24no—
125C22×D113—21no—
126C22×D113—42no—
127C22×D113—42no—
128C22×D113—42no—
129C22×D113—42no—
130C22×D113—42no—
131C22×D113C2×D411yescharacteristic
132Q8×C113—21no—
133Q8×C113—21no—
134D4×C113—21no—
135D4×C113—21no—
136D4×C113—21no—
137D4×C113C2×D412yes—
138C2×C4×C113—21no—
139C2×C4×C113—21no—
140C2×C4×C113—42no—
141C2×C4×C113C2×D411yescharacteristic
142C2×C4×C113C2×D411yescharacteristic
143C2×C4×C113C2411yescharacteristic
144C22⋊D113—24no—
145C22⋊D113—42no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—42no—
149C2×Dic113C2×D411yescharacteristic
150C2×Dic113C2×D411yescharacteristic
151C2×Dic113C2×D411yescharacteristic
152D452—21no—
153D452—21no—
154D452—21no—
155D452C2×D412yes—
156C4×D113—22no—
157C4×D113—22no—
158C4×D113—42no—
159C4×D113—42no—
160C4×D113—42no—
161C4×D113—42no—
162C4×D113C2×D412yes—
163C4×D113#4112yes—
164Dic226—21no—
165Dic226—21no—
166Dic226—42no—
167C8×C113—21no—
168C8×C113—21no—
169#11744751—21no—
170#11744751—21no—
171C22×C113—22no—
172C22×C113—41no—
173C22×C113—41no—
174C22×C113—41no—
175C22×C113—41no—
176C22×C113—41no—
177C22×C113C22×D411yescharacteristic
178C2×D113—22no—
179C2×D113—41no—
180C2×D113—41no—
181C2×D113—48no—
182C2×D113—41no—
183C2×D113—41no—
184C2×D113—41no—
185C2×D113—84no—
186C2×D113#12112yes—
187C2×D113#13512yes—
188C2×D113AGL(1,ℤ/8)12yes—
189C4×C113—21no—
190C4×C113—21no—
191C4×C113—41no—
192C4×C113—41no—
193C4×C113C22×D411yescharacteristic
194C4×C113C2×#4111yescharacteristic
195Dic113—21no—
196Dic113—21no—
197Dic113—41no—
198Dic113—41no—
199Dic113#12112yes—
200C2×C113—42no—
201C2×C113—81no—
202C2×C113C2×#12111yescharacteristic
203C2×C113C2×#13511yescharacteristic
204C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
205D113—42no—
206D113—81no—
207D113#46314yesdirect product factor
208C2×#463—1131nomaximal, Sylow
209C113C2×#46311yescharacteristic, complemented, Sylow
210C22×SD16—1131no—
211C22×D8—1131no—
212C2×#124—1131no—
213C2×C4×D4—1131no—
214#463—1131no—
215#463—1131no—
216#463—1131no—
217#463—1131no—
218#463—1131no—
219#463—1131no—
220#463—1131no—
221#463D11311yescharacteristic, direct product factor
222C2×C4⋊C8—1131no—
223C2×#103—1131no—
224C2×#102—1131no—
225C22×Q8—1131no—
226C22×D4—1131no—
227C22×D4—1131no—
228C23×C4—2261no—
229C2×SD16—1131no—
230C2×SD16—1131no—
231C2×SD16—1131no—
232C2×SD16—2264no—
233C2×SD16C2×D11311yescharacteristic, complemented
234C2×D8—1131no—
235C2×D8—1131no—
236C2×D8—1131no—
237C2×D8—2264no—
238C2×D8C2×D11311yescharacteristic
239C22×C8—1131no—
240C22×C8—1131no—
241#124—1131no—
242#124—1131no—
243#124—1131no—
244#124—2261no—
245#124—2261no—
246#124C2×D11311yescharacteristic, complemented
247C4×D4—1131no—
248C4×D4—1131no—
249C4×D4—1131no—
250C4×D4—2261no—
251C4×D4—2261no—
252C4×D4C2×D11311yescharacteristic, complemented
253C2×C4⋊C4—1131no—
254C2×C22⋊C4—2261no—
255C2×C22⋊C4—2261no—
256C2×C22⋊C4—2261no—
257C2×C42—1131no—
258C4⋊C8—1131no—
259C4⋊C8—1131no—
260C4⋊C8—1131no—
261C4⋊C8C2×D11311yescharacteristic, complemented
262#103—1131no—
263#103—1131no—
264#103—1131no—
265#103C2×D11311yescharacteristic, complemented
266#102—1131no—
267#102—1131no—
268#102—1131no—
269#102C2×D11311yescharacteristic, complemented
270C24—2261no—
271C24—2261no—
272C2×Q8—1131no—
273C2×Q8—2261no—
274C2×Q8—2262no—
275C2×Q8—2262no—
276C2×Q8C22×D11311yescharacteristic
277C2×D4—1134no—
278C2×D4—1131no—
279C2×D4—1131no—
280C2×D4—2262no—
281C2×D4—2262no—
282C2×D4—2262no—
283C2×D4—2261no—
284C2×D4—2261no—
285C2×D4C22×D11311yescharacteristic
286C2×D4C22×D11311yescharacteristic
287C22×C4—21no—
288C22×C4—1131no—
289C22×C4—1131no—
290C22×C4—1131no—
291C22×C4—4524no—
292C22×C4—2261no—
293C22×C4—2261no—
294C22×C4—2261no—
295C22×C4—2261no—
296C22×C4—2261no—
297SD16—22no—
298SD16—2262no—
299SD16—2262no—
300SD16—2262no—
301D8—22no—
302D8—2262no—
303D8—2262no—
304D8—2262no—
305C2×C8—1131no—
306C2×C8—1131no—
307C2×C8—2262no—
308C2×C8—2262no—
309C2×C8C22×D11311yescharacteristic
310C2×C8C22×D11311yescharacteristic
311C4⋊C4—1131no—
312C4⋊C4—2261no—
313C4⋊C4C22×D11311yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—2261no—
318C22⋊C4—2261no—
319C22⋊C4—2261no—
320C22⋊C4—2261no—
321C22⋊C4—2261no—
322C22⋊C4—2261no—
323C22⋊C4—2261no—
324C22⋊C4—2261no—
325C22⋊C4—2261no—
326C42—1131no—
327C42—1131no—
328C42—1131no—
329C42C22×D11311yescharacteristic
330C23—21no—
331C23—21no—
332C23—1131no—
333C23—4522no—
334C23—4522no—
335C23—4522no—
336C23—4522no—
337C23—4522no—
338C23—2264no—
339C23—2261no—
340C23—2261no—
341Q8—21no—
342Q8—21no—
343Q8—4522no—
344Q8—2261no—
345Q8—2261no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—1132no—
350D4—4522no—
351D4—2264no—
352D4—2261no—
353D4—2261no—
354D4—2261no—
355D4D4×D11312yes—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—1131no—
360C2×C4—1132no—
361C2×C4—1132no—
362C2×C4—1131no—
363C2×C4—1131no—
364C2×C4—4522no—
365C2×C4—4522no—
366C2×C4—4522no—
367C2×C4—4522no—
368C2×C4—4522no—
369C2×C4—2262no—
370C2×C4—2262no—
371C2×C4—2261no—
372C2×C4—2261no—
373C2×C4D4×D11311yescharacteristic
374C2×C4D4×D11311yescharacteristic
375C2×C4C23×D11311yescharacteristic
376C8—21no—
377C8—21no—
378C8—2261no—
379C8—2261no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—1132no—
387C22—1132no—
388C22—1132no—
389C22—9044no—
390C22—4528no—
391C22—4521no—
392C22—4521no—
393C22—4521no—
394C22—4521no—
395C22—4521no—
396C22—2262no—
397C22C2×D4×D11311yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—1132no—
403C4—4521no—
404C4—4521no—
405C4—2261no—
406C4—2261no—
407C4C2×D4×D11311yescharacteristic
408C4#41×D11311yescharacteristic
409C2—42no—
410C2—81no—
411C2—1134no—
412C2—9041no—
413C2—4522no—
414C2#121×D11311yescharacteristic
415C2#135×D11311yescharacteristic
416C2AGL(1,ℤ/8)×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#463×C113C2
socleC22×C113C22×D4
prime radicalC2×D8×D113C2
hypercenter#463D113
hypocenterC113C2×#463
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D113C2semidirect
3. #124×D113C2semidirect
4. C4×D4×D113C2semidirect
5. #20298816C2semidirect
6. #20298815C2semidirect
7. #20298814C2semidirect
8. #20298813C2semidirect
9. #20298812C2semidirect
10. #20298811C2semidirect
11. #20298810C2semidirect
12. C4⋊C8×D113C2semidirect
13. #103×D113C2semidirect
14. #102×D113C2semidirect
15. #463×C113C2semidirect
20. C2×#14268636C22semidirect
21. C2×#14268635C22semidirect
22. C2×#14268634C22semidirect
30. #16813611C22semidirect
31. #16813610C22semidirect
32. #16813609C22semidirect
35. C4×D452C22semidirect
36. D4×Dic113C22semidirect
37. #16813584C22semidirect
45. C4⋊#11744751C22semidirect
46. #16813551C22semidirect
47. #16813551C22semidirect
48. #16813547C22semidirect
49. #16813546C22semidirect
50. #16813545C22semidirect
51. #16813544C22semidirect
52. #16813543C22semidirect
53. #16813542C22semidirect
54. C2×SD16×C113C22semidirect
56. #124×C113C22semidirect
57. C4×D4×C113C22semidirect
58. C4⋊C8×C113C22semidirect
59. #103×C113C22semidirect
60. #102×C113C22semidirect
207. D113#463direct (N × H)
209. C113C2×#463semidirect
221. #463D113direct (N × H)
233. C2×SD16C2×D113semidirect
246. #124C2×D113semidirect
252. C4×D4C2×D113semidirect
261. C4⋊C8C2×D113semidirect
265. #103C2×D113semidirect
269. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1132
C2×D8×D1132
#124×D1132
C4×D4×D1132
#202988162
#202988152
#202988142
#202988132
#202988122
#202988112
#202988102
C4⋊C8×D1132
#103×D1132
#102×D1132
#463×C1132
C2×#463113