Finite Group Databasebeta

← #463×D157 #34109556

Subgroups — #463×D157 #34109556

Order 20096.

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×D157C211yesmaximal, characteristic, complemented
2C2×D8×D157C211yesmaximal, characteristic
3#124×D157C211yesmaximal, characteristic, complemented
4C4×D4×D157C211yesmaximal, characteristic, complemented
5#23757491C211yesmaximal, characteristic, complemented
6#23757490C211yesmaximal, characteristic, complemented
7#23757489C211yesmaximal, characteristic, complemented
8#23757488C211yesmaximal, characteristic, complemented
9#23757487C211yesmaximal, characteristic, complemented
10#23757486C211yesmaximal, characteristic, complemented
11#23757485C211yesmaximal, characteristic, complemented
12C4⋊C8×D157C211yesmaximal, characteristic, complemented
13#103×D157C211yesmaximal, characteristic, complemented
14#102×D157C211yesmaximal, characteristic, complemented
15#463×C157C211yesmaximal, characteristic, complemented
16C2×Q8×D157C2211yescharacteristic
17C2×D4×D157C2211yescharacteristic
18C2×D4×D157C2211yescharacteristic
19C22×C4×D157—21no—
20C2×#14578943C2211yescharacteristic, complemented
21C2×#14578942C2211yescharacteristic, complemented
22C2×#14578941C2211yescharacteristic, complemented
23SD16×D157—24no—
24C2×D1256C2211yescharacteristic
25C2×#14578939C2211yescharacteristic
26C2×#14578939C2211yescharacteristic
27D8×D157—24no—
28C2×C8×D157C2211yescharacteristic
29C2×C8×D157C2211yescharacteristic
30#19097760C2211yescharacteristic, complemented
31#19097759C2211yescharacteristic, complemented
32#19097758C2211yescharacteristic, complemented
33#19097757—21no—
34#19097757—21no—
35C4×D628C2211yescharacteristic, complemented
36D4×Dic157C2211yescharacteristic, complemented
37#19097733C2211yescharacteristic, complemented
38C4×C22⋊D157—21no—
39#19097731—21no—
40C4⋊C4×D157C2211yescharacteristic
41C22⋊C4×D157—21no—
42C22⋊C4×D157—21no—
43C22⋊C4×D157—21no—
44C42×D157C2211yescharacteristic
45C4⋊#11929434C2211yescharacteristic, complemented
46#19097700C2211yescharacteristic, complemented
47#19097700C2211yescharacteristic, complemented
48#19097696C2211yescharacteristic, complemented
49#19097695C2211yescharacteristic, complemented
50#19097694C2211yescharacteristic, complemented
51#19097693C2211yescharacteristic, complemented
52#19097692C2211yescharacteristic, complemented
53#19097691C2211yescharacteristic, complemented
54C2×SD16×C157C2211yescharacteristic, complemented
55C2×D8×C157C2211yescharacteristic
56#124×C157C2211yescharacteristic, complemented
57C4×D4×C157C2211yescharacteristic, complemented
58C4⋊C8×C157C2211yescharacteristic, complemented
59#103×C157C2211yescharacteristic, complemented
60#102×C157C2211yescharacteristic, complemented
61C23×D157—21no—
62C23×D157—21no—
63C2×Dic314—21no—
64C2×Dic314C2311yescharacteristic
65Q8×D157—22no—
66Q8×D157—22no—
67C2×D628C2311yescharacteristic
68C2×D628C2311yescharacteristic
69C2×C22⋊D157—21no—
70C2×C22⋊D157—21no—
71D4×D157—22no—
72D4×D157—22no—
73D4×D157—22no—
74D4×D157D414yes—
75C22×Dic157—21no—
76C2×C4×D157—21no—
77C2×C4×D157—21no—
78C2×C4×D157—21no—
79C2×C4×D157—21no—
80C2×C4×D157—44no—
81C2×C4×D157D411yescharacteristic
82C2×C4×D157D411yescharacteristic
83C2×C4×D157C2311yescharacteristic
84#14578943—22no—
85#14578942—22no—
86#14578941—22no—
87D1256—22no—
88#14578939—22no—
89#14578939—22no—
90C2×#11929434C2311yescharacteristic
91C2×#11929434C2311yescharacteristic
92C8×D157—22no—
93C8×D157—22no—
94C4⋊Dic157C2311yescharacteristic
95#14578933—21no—
96C22⋊Dic157—21no—
97C22⋊Dic157—21no—
98C22⋊Dic157—21no—
99#14578931—21no—
100#14578931—21no—
101#14578931—21no—
102#14578931—21no—
103#14578931—21no—
104#14578931—21no—
105C4×Dic157D411yescharacteristic
106C4×Dic157D411yescharacteristic
107C4×Dic157C2311yescharacteristic
108C2×Q8×C157C2311yescharacteristic
109C2×D4×C157C2311yescharacteristic
110C2×D4×C157C2311yescharacteristic
111C22×C4×C157—21no—
112SD16×C157—22no—
113D8×C157—22no—
114C2×C8×C157C2311yescharacteristic
115C2×C8×C157C2311yescharacteristic
116C4⋊C4×C157C2311yescharacteristic
117C22⋊C4×C157—21no—
118C22⋊C4×C157—21no—
119C22⋊C4×C157—21no—
120C42×C157C2311yescharacteristic
121C22×D157—21no—
122C22×D157—24no—
123C22×D157—21no—
124C22×D157—42no—
125C22×D157—42no—
126C22×D157—42no—
127C22×D157—42no—
128C22×D157—42no—
129C22×D157C2×D411yescharacteristic
130Dic314—21no—
131Dic314—21no—
132Dic314—42no—
133D628—21no—
134D628—21no—
135D628—21no—
136D628C2×D412yes—
137C22⋊D157—24no—
138C22⋊D157—42no—
139C2×Dic157—21no—
140C2×Dic157—21no—
141C2×Dic157—42no—
142C2×Dic157C2×D411yescharacteristic
143C2×Dic157C2×D411yescharacteristic
144C2×Dic157C2×D411yescharacteristic
145C4×D157—22no—
146C4×D157—22no—
147C4×D157—42no—
148C4×D157—42no—
149C4×D157—42no—
150C4×D157—42no—
151C4×D157C2×D412yes—
152C4×D157#4112yes—
153#11929434—21no—
154#11929434—21no—
155C23×C157—21no—
156C23×C157—21no—
157Q8×C157—21no—
158Q8×C157—21no—
159D4×C157—21no—
160D4×C157—21no—
161D4×C157—21no—
162D4×C157C2×D412yes—
163C2×C4×C157—21no—
164C2×C4×C157—21no—
165C2×C4×C157—42no—
166C2×C4×C157C2×D411yescharacteristic
167C2×C4×C157C2×D411yescharacteristic
168C2×C4×C157C2411yescharacteristic
169C8×C157—21no—
170C8×C157—21no—
171C22×C157—22no—
172C22×C157—41no—
173C22×C157—41no—
174C22×C157—41no—
175C22×C157—41no—
176C22×C157—41no—
177C22×C157C22×D411yescharacteristic
178C2×D157—22no—
179C2×D157—41no—
180C2×D157—41no—
181C2×D157—48no—
182C2×D157—41no—
183C2×D157—41no—
184C2×D157—41no—
185C2×D157—84no—
186C2×D157#12112yes—
187C2×D157#13512yes—
188C2×D157AGL(1,ℤ/8)12yes—
189C4×C157—21no—
190C4×C157—21no—
191C4×C157—41no—
192C4×C157—41no—
193C4×C157C22×D411yescharacteristic
194C4×C157C2×#4111yescharacteristic
195Dic157—21no—
196Dic157—21no—
197Dic157—41no—
198Dic157—41no—
199Dic157#12112yes—
200C2×C157—42no—
201C2×C157—81no—
202C2×C157C2×#12111yescharacteristic
203C2×C157C2×#13511yescharacteristic
204C2×C157C2×AGL(1,ℤ/8)11yescharacteristic
205D157—42no—
206D157—81no—
207D157#46314yesdirect product factor
208C157C2×#46311yescharacteristic, complemented, Sylow
209C2×#463—1571nomaximal, Sylow
210C22×SD16—1571no—
211C22×D8—1571no—
212C2×#124—1571no—
213C2×C4×D4—1571no—
214#463—1571no—
215#463—1571no—
216#463—1571no—
217#463—1571no—
218#463—1571no—
219#463—1571no—
220#463—1571no—
221#463D15711yescharacteristic, direct product factor
222C2×C4⋊C8—1571no—
223C2×#103—1571no—
224C2×#102—1571no—
225C22×Q8—1571no—
226C22×D4—1571no—
227C22×D4—1571no—
228C23×C4—3141no—
229C2×SD16—3144no—
230C2×SD16—1571no—
231C2×SD16—1571no—
232C2×SD16—1571no—
233C2×SD16C2×D15711yescharacteristic, complemented
234C2×D8—3144no—
235C2×D8—1571no—
236C2×D8—1571no—
237C2×D8—1571no—
238C2×D8C2×D15711yescharacteristic
239C22×C8—1571no—
240C22×C8—1571no—
241#124—3141no—
242#124—3141no—
243#124—1571no—
244#124—1571no—
245#124—1571no—
246#124C2×D15711yescharacteristic, complemented
247C4×D4—3141no—
248C4×D4—3141no—
249C4×D4—1571no—
250C4×D4—1571no—
251C4×D4—1571no—
252C4×D4C2×D15711yescharacteristic, complemented
253C2×C4⋊C4—1571no—
254C2×C22⋊C4—3141no—
255C2×C22⋊C4—3141no—
256C2×C22⋊C4—3141no—
257C2×C42—1571no—
258C4⋊C8—1571no—
259C4⋊C8—1571no—
260C4⋊C8—1571no—
261C4⋊C8C2×D15711yescharacteristic, complemented
262#103—1571no—
263#103—1571no—
264#103—1571no—
265#103C2×D15711yescharacteristic, complemented
266#102—1571no—
267#102—1571no—
268#102—1571no—
269#102C2×D15711yescharacteristic, complemented
270C24—3141no—
271C24—3141no—
272C2×Q8—3141no—
273C2×Q8—3142no—
274C2×Q8—3142no—
275C2×Q8—1571no—
276C2×Q8C22×D15711yescharacteristic
277C2×D4—3142no—
278C2×D4—3142no—
279C2×D4—3142no—
280C2×D4—3141no—
281C2×D4—3141no—
282C2×D4—1574no—
283C2×D4—1571no—
284C2×D4—1571no—
285C2×D4C22×D15711yescharacteristic
286C2×D4C22×D15711yescharacteristic
287C22×C4—21no—
288C22×C4—3141no—
289C22×C4—3141no—
290C22×C4—3141no—
291C22×C4—3141no—
292C22×C4—3141no—
293C22×C4—6284no—
294C22×C4—1571no—
295C22×C4—1571no—
296C22×C4—1571no—
297SD16—22no—
298SD16—3142no—
299SD16—3142no—
300SD16—3142no—
301D8—22no—
302D8—3142no—
303D8—3142no—
304D8—3142no—
305C2×C8—3142no—
306C2×C8—3142no—
307C2×C8—1571no—
308C2×C8—1571no—
309C2×C8C22×D15711yescharacteristic
310C2×C8C22×D15711yescharacteristic
311C4⋊C4—3141no—
312C4⋊C4—1571no—
313C4⋊C4C22×D15711yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—3141no—
318C22⋊C4—3141no—
319C22⋊C4—3141no—
320C22⋊C4—3141no—
321C22⋊C4—3141no—
322C22⋊C4—3141no—
323C22⋊C4—3141no—
324C22⋊C4—3141no—
325C22⋊C4—3141no—
326C42—1571no—
327C42—1571no—
328C42—1571no—
329C42C22×D15711yescharacteristic
330C23—21no—
331C23—21no—
332C23—3144no—
333C23—3141no—
334C23—3141no—
335C23—6282no—
336C23—6282no—
337C23—6282no—
338C23—6282no—
339C23—6282no—
340C23—1571no—
341Q8—21no—
342Q8—21no—
343Q8—3141no—
344Q8—3141no—
345Q8—6282no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—3144no—
350D4—3141no—
351D4—3141no—
352D4—3141no—
353D4—6282no—
354D4—1572no—
355D4D4×D15712yes—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—3142no—
360C2×C4—3142no—
361C2×C4—3141no—
362C2×C4—3141no—
363C2×C4—6282no—
364C2×C4—6282no—
365C2×C4—6282no—
366C2×C4—6282no—
367C2×C4—6282no—
368C2×C4—1571no—
369C2×C4—1571no—
370C2×C4—1571no—
371C2×C4—1572no—
372C2×C4—1572no—
373C2×C4D4×D15711yescharacteristic
374C2×C4D4×D15711yescharacteristic
375C2×C4C23×D15711yescharacteristic
376C8—21no—
377C8—21no—
378C8—3141no—
379C8—3141no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—3142no—
387C22—6288no—
388C22—6281no—
389C22—6281no—
390C22—6281no—
391C22—6281no—
392C22—6281no—
393C22—1572no—
394C22—1572no—
395C22—1572no—
396C22—12564no—
397C22C2×D4×D15711yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—3141no—
403C4—3141no—
404C4—6281no—
405C4—6281no—
406C4—1572no—
407C4C2×D4×D15711yescharacteristic
408C4#41×D15711yescharacteristic
409C2—42no—
410C2—81no—
411C2—6282no—
412C2—1574no—
413C2—12561no—
414C2#121×D15711yescharacteristic
415C2#135×D15711yescharacteristic
416C2AGL(1,ℤ/8)×D15711yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#463×C157C2
socleC22×C157C22×D4
prime radicalC2×D8×D157C2
hypercenter#463D157
hypocenterC157C2×#463
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D157C2semidirect
3. #124×D157C2semidirect
4. C4×D4×D157C2semidirect
5. #23757491C2semidirect
6. #23757490C2semidirect
7. #23757489C2semidirect
8. #23757488C2semidirect
9. #23757487C2semidirect
10. #23757486C2semidirect
11. #23757485C2semidirect
12. C4⋊C8×D157C2semidirect
13. #103×D157C2semidirect
14. #102×D157C2semidirect
15. #463×C157C2semidirect
20. C2×#14578943C22semidirect
21. C2×#14578942C22semidirect
22. C2×#14578941C22semidirect
30. #19097760C22semidirect
31. #19097759C22semidirect
32. #19097758C22semidirect
35. C4×D628C22semidirect
36. D4×Dic157C22semidirect
37. #19097733C22semidirect
45. C4⋊#11929434C22semidirect
46. #19097700C22semidirect
47. #19097700C22semidirect
48. #19097696C22semidirect
49. #19097695C22semidirect
50. #19097694C22semidirect
51. #19097693C22semidirect
52. #19097692C22semidirect
53. #19097691C22semidirect
54. C2×SD16×C157C22semidirect
56. #124×C157C22semidirect
57. C4×D4×C157C22semidirect
58. C4⋊C8×C157C22semidirect
59. #103×C157C22semidirect
60. #102×C157C22semidirect
207. D157#463direct (N × H)
208. C157C2×#463semidirect
221. #463D157direct (N × H)
233. C2×SD16C2×D157semidirect
246. #124C2×D157semidirect
252. C4×D4C2×D157semidirect
261. C4⋊C8C2×D157semidirect
265. #103C2×D157semidirect
269. #102C2×D157semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1572
C2×D8×D1572
#124×D1572
C4×D4×D1572
#237574912
#237574902
#237574892
#237574882
#237574872
#237574862
#237574852
C4⋊C8×D1572
#103×D1572
#102×D1572
#463×C1572
C2×#463157