Finite Group Databasebeta

← #463×D151 #34078530

Subgroups — #463×D151 #34078530

Order 19328.

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×D151C211yesmaximal, characteristic, complemented
2C2×D8×D151C211yesmaximal, characteristic
3#124×D151C211yesmaximal, characteristic, complemented
4C4×D4×D151C211yesmaximal, characteristic, complemented
5#23752430C211yesmaximal, characteristic, complemented
6#23752429C211yesmaximal, characteristic, complemented
7#23752428C211yesmaximal, characteristic, complemented
8#23752427C211yesmaximal, characteristic, complemented
9#23752426C211yesmaximal, characteristic, complemented
10#23752425C211yesmaximal, characteristic, complemented
11#23752424C211yesmaximal, characteristic, complemented
12C4⋊C8×D151C211yesmaximal, characteristic, complemented
13#103×D151C211yesmaximal, characteristic, complemented
14#102×D151C211yesmaximal, characteristic, complemented
15#463×C151C211yesmaximal, characteristic, complemented
16C2×Q8×D151C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C2×D4×D151C2211yescharacteristic
19C22×C4×D151—21no—
20C2×#14558993C2211yescharacteristic, complemented
21C2×#14558992C2211yescharacteristic, complemented
22C2×#14558991C2211yescharacteristic, complemented
23SD16×D151—24no—
24C2×D1208C2211yescharacteristic
25C2×#14558989C2211yescharacteristic
26C2×#14558989C2211yescharacteristic
27D8×D151—24no—
28C2×C8×D151C2211yescharacteristic
29C2×C8×D151C2211yescharacteristic
30#18012728C2211yescharacteristic, complemented
31#18012727C2211yescharacteristic, complemented
32#18012726C2211yescharacteristic, complemented
33#18012725—21no—
34#18012725—21no—
35C4×D604C2211yescharacteristic, complemented
36D4×Dic151C2211yescharacteristic, complemented
37#18012701C2211yescharacteristic, complemented
38C4×C22⋊D151—21no—
39(C22⋊D151)⋊C4—21no—
40C4⋊C4×D151C2211yescharacteristic
41C22⋊C4×D151—21no—
42C22⋊C4×D151—21no—
43C22⋊C4×D151—21no—
44C42×D151C2211yescharacteristic
45C4⋊(C151⋊C8)C2211yescharacteristic, complemented
46Dic151⋊C8C2211yescharacteristic, complemented
47Dic151⋊C8C2211yescharacteristic, complemented
48#18012664C2211yescharacteristic, complemented
49#18012663C2211yescharacteristic, complemented
50#18012662C2211yescharacteristic, complemented
51#18012661C2211yescharacteristic, complemented
52#18012660C2211yescharacteristic, complemented
53#18012659C2211yescharacteristic, complemented
54C2×SD16×C151C2211yescharacteristic, complemented
55C2×D8×C151C2211yescharacteristic
56#124×C151C2211yescharacteristic, complemented
57C4×D4×C151C2211yescharacteristic, complemented
58C4⋊C8×C151C2211yescharacteristic, complemented
59#103×C151C2211yescharacteristic, complemented
60#102×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62C23×D151—21no—
63C2×Dic302—21no—
64C2×Dic302C2311yescharacteristic
65Q8×D151—22no—
66Q8×D151—22no—
67C2×D604C2311yescharacteristic
68C2×D604C2311yescharacteristic
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71D4×D151—22no—
72D4×D151—22no—
73D4×D151—22no—
74D4×D151D414yes—
75C22×Dic151—21no—
76C2×C4×D151—21no—
77C2×C4×D151—21no—
78C2×C4×D151—21no—
79C2×C4×D151—21no—
80C2×C4×D151—44no—
81C2×C4×D151D411yescharacteristic
82C2×C4×D151D411yescharacteristic
83C2×C4×D151C2311yescharacteristic
84#14558993—22no—
85#14558992—22no—
86#14558991—22no—
87D1208—22no—
88#14558989—22no—
89#14558989—22no—
90C2×C151⋊C8C2311yescharacteristic
91C2×C151⋊C8C2311yescharacteristic
92C8×D151—22no—
93C8×D151—22no—
94C4⋊Dic151C2311yescharacteristic
95Dic151⋊C4—21no—
96C22⋊Dic151—21no—
97C22⋊Dic151—21no—
98C22⋊Dic151—21no—
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4—21no—
101(C2×D151)⋊C4—21no—
102(C2×D151)⋊C4—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4—21no—
105C4×Dic151D411yescharacteristic
106C4×Dic151D411yescharacteristic
107C4×Dic151C2311yescharacteristic
108C2×Q8×C151C2311yescharacteristic
109C2×D4×C151C2311yescharacteristic
110C2×D4×C151C2311yescharacteristic
111C22×C4×C151—21no—
112SD16×C151—22no—
113D8×C151—22no—
114C2×C8×C151C2311yescharacteristic
115C2×C8×C151C2311yescharacteristic
116C4⋊C4×C151C2311yescharacteristic
117C22⋊C4×C151—21no—
118C22⋊C4×C151—21no—
119C22⋊C4×C151—21no—
120C42×C151C2311yescharacteristic
121C22×D151—21no—
122C22×D151—24no—
123C22×D151—21no—
124C22×D151—42no—
125C22×D151—42no—
126C22×D151—42no—
127C22×D151—42no—
128C22×D151—42no—
129C22×D151C2×D411yescharacteristic
130Dic302—21no—
131Dic302—21no—
132Dic302—42no—
133D604—21no—
134D604—21no—
135D604—21no—
136D604C2×D412yes—
137C22⋊D151—24no—
138C22⋊D151—42no—
139C2×Dic151—21no—
140C2×Dic151—21no—
141C2×Dic151—42no—
142C2×Dic151C2×D411yescharacteristic
143C2×Dic151C2×D411yescharacteristic
144C2×Dic151C2×D411yescharacteristic
145C4×D151—22no—
146C4×D151—22no—
147C4×D151—42no—
148C4×D151—42no—
149C4×D151—42no—
150C4×D151—42no—
151C4×D151C2×D412yes—
152C4×D151#4112yes—
153C151⋊C8—21no—
154C151⋊C8—21no—
155C23×C151—21no—
156C23×C151—21no—
157Q8×C151—21no—
158Q8×C151—21no—
159D4×C151—21no—
160D4×C151—21no—
161D4×C151—21no—
162D4×C151C2×D412yes—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—42no—
166C2×C4×C151C2×D411yescharacteristic
167C2×C4×C151C2×D411yescharacteristic
168C2×C4×C151C2411yescharacteristic
169C8×C151—21no—
170C8×C151—21no—
171C22×C151—22no—
172C22×C151—41no—
173C22×C151—41no—
174C22×C151—41no—
175C22×C151—41no—
176C22×C151—41no—
177C22×C151C22×D411yescharacteristic
178C2×D151—22no—
179C2×D151—41no—
180C2×D151—41no—
181C2×D151—48no—
182C2×D151—41no—
183C2×D151—41no—
184C2×D151—41no—
185C2×D151—84no—
186C2×D151#12112yes—
187C2×D151#13512yes—
188C2×D151AGL(1,ℤ/8)12yes—
189C4×C151—21no—
190C4×C151—21no—
191C4×C151—41no—
192C4×C151—41no—
193C4×C151C22×D411yescharacteristic
194C4×C151C2×#4111yescharacteristic
195Dic151—21no—
196Dic151—21no—
197Dic151—41no—
198Dic151—41no—
199Dic151#12112yes—
200C2×C151—42no—
201C2×C151—81no—
202C2×C151C2×#12111yescharacteristic
203C2×C151C2×#13511yescharacteristic
204C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
205D151—42no—
206D151—81no—
207D151#46314yesdirect product factor
208C151C2×#46311yescharacteristic, complemented, Sylow
209C2×#463—1511nomaximal, Sylow
210C22×SD16—1511no—
211C22×D8—1511no—
212C2×#124—1511no—
213C2×C4×D4—1511no—
214#463—1511no—
215#463—1511no—
216#463—1511no—
217#463—1511no—
218#463—1511no—
219#463—1511no—
220#463—1511no—
221#463D15111yescharacteristic, direct product factor
222C2×C4⋊C8—1511no—
223C2×#103—1511no—
224C2×#102—1511no—
225C22×Q8—1511no—
226C22×D4—1511no—
227C22×D4—1511no—
228C23×C4—3021no—
229C2×SD16—3024no—
230C2×SD16—1511no—
231C2×SD16—1511no—
232C2×SD16—1511no—
233C2×SD16C2×D15111yescharacteristic, complemented
234C2×D8—3024no—
235C2×D8—1511no—
236C2×D8—1511no—
237C2×D8—1511no—
238C2×D8C2×D15111yescharacteristic
239C22×C8—1511no—
240C22×C8—1511no—
241#124—3021no—
242#124—3021no—
243#124—1511no—
244#124—1511no—
245#124—1511no—
246#124C2×D15111yescharacteristic, complemented
247C4×D4—3021no—
248C4×D4—3021no—
249C4×D4—1511no—
250C4×D4—1511no—
251C4×D4—1511no—
252C4×D4C2×D15111yescharacteristic, complemented
253C2×C4⋊C4—1511no—
254C2×C22⋊C4—3021no—
255C2×C22⋊C4—3021no—
256C2×C22⋊C4—3021no—
257C2×C42—1511no—
258C4⋊C8—1511no—
259C4⋊C8—1511no—
260C4⋊C8—1511no—
261C4⋊C8C2×D15111yescharacteristic, complemented
262#103—1511no—
263#103—1511no—
264#103—1511no—
265#103C2×D15111yescharacteristic, complemented
266#102—1511no—
267#102—1511no—
268#102—1511no—
269#102C2×D15111yescharacteristic, complemented
270C24—3021no—
271C24—3021no—
272C2×Q8—3021no—
273C2×Q8—3022no—
274C2×Q8—3022no—
275C2×Q8—1511no—
276C2×Q8C22×D15111yescharacteristic
277C2×D4—3022no—
278C2×D4—3022no—
279C2×D4—3022no—
280C2×D4—3021no—
281C2×D4—3021no—
282C2×D4—1514no—
283C2×D4—1511no—
284C2×D4—1511no—
285C2×D4C22×D15111yescharacteristic
286C2×D4C22×D15111yescharacteristic
287C22×C4—21no—
288C22×C4—3021no—
289C22×C4—3021no—
290C22×C4—3021no—
291C22×C4—3021no—
292C22×C4—3021no—
293C22×C4—6044no—
294C22×C4—1511no—
295C22×C4—1511no—
296C22×C4—1511no—
297SD16—22no—
298SD16—3022no—
299SD16—3022no—
300SD16—3022no—
301D8—22no—
302D8—3022no—
303D8—3022no—
304D8—3022no—
305C2×C8—3022no—
306C2×C8—3022no—
307C2×C8—1511no—
308C2×C8—1511no—
309C2×C8C22×D15111yescharacteristic
310C2×C8C22×D15111yescharacteristic
311C4⋊C4—3021no—
312C4⋊C4—1511no—
313C4⋊C4C22×D15111yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—3021no—
318C22⋊C4—3021no—
319C22⋊C4—3021no—
320C22⋊C4—3021no—
321C22⋊C4—3021no—
322C22⋊C4—3021no—
323C22⋊C4—3021no—
324C22⋊C4—3021no—
325C22⋊C4—3021no—
326C42—1511no—
327C42—1511no—
328C42—1511no—
329C42C22×D15111yescharacteristic
330C23—21no—
331C23—21no—
332C23—3024no—
333C23—3021no—
334C23—3021no—
335C23—6042no—
336C23—6042no—
337C23—6042no—
338C23—6042no—
339C23—6042no—
340C23—1511no—
341Q8—21no—
342Q8—21no—
343Q8—3021no—
344Q8—3021no—
345Q8—6042no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—3024no—
350D4—3021no—
351D4—3021no—
352D4—3021no—
353D4—6042no—
354D4—1512no—
355D4D4×D15112yes—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—3022no—
360C2×C4—3022no—
361C2×C4—3021no—
362C2×C4—3021no—
363C2×C4—6042no—
364C2×C4—6042no—
365C2×C4—6042no—
366C2×C4—6042no—
367C2×C4—6042no—
368C2×C4—1511no—
369C2×C4—1511no—
370C2×C4—1511no—
371C2×C4—1512no—
372C2×C4—1512no—
373C2×C4D4×D15111yescharacteristic
374C2×C4D4×D15111yescharacteristic
375C2×C4C23×D15111yescharacteristic
376C8—21no—
377C8—21no—
378C8—3021no—
379C8—3021no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—3022no—
387C22—6048no—
388C22—6041no—
389C22—6041no—
390C22—6041no—
391C22—6041no—
392C22—6041no—
393C22—1512no—
394C22—1512no—
395C22—1512no—
396C22—12084no—
397C22C2×D4×D15111yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—3021no—
403C4—3021no—
404C4—6041no—
405C4—6041no—
406C4—1512no—
407C4C2×D4×D15111yescharacteristic
408C4#41×D15111yescharacteristic
409C2—42no—
410C2—81no—
411C2—6042no—
412C2—1514no—
413C2—12081no—
414C2#121×D15111yescharacteristic
415C2#135×D15111yescharacteristic
416C2AGL(1,ℤ/8)×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#463×C151C2
socleC22×C151C22×D4
prime radicalC2×D8×D151C2
hypercenter#463D151
hypocenterC151C2×#463
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D151C2semidirect
3. #124×D151C2semidirect
4. C4×D4×D151C2semidirect
5. #23752430C2semidirect
6. #23752429C2semidirect
7. #23752428C2semidirect
8. #23752427C2semidirect
9. #23752426C2semidirect
10. #23752425C2semidirect
11. #23752424C2semidirect
12. C4⋊C8×D151C2semidirect
13. #103×D151C2semidirect
14. #102×D151C2semidirect
15. #463×C151C2semidirect
20. C2×#14558993C22semidirect
21. C2×#14558992C22semidirect
22. C2×#14558991C22semidirect
30. #18012728C22semidirect
31. #18012727C22semidirect
32. #18012726C22semidirect
35. C4×D604C22semidirect
36. D4×Dic151C22semidirect
37. #18012701C22semidirect
45. C4⋊(C151⋊C8)C22semidirect
46. Dic151⋊C8C22semidirect
47. Dic151⋊C8C22semidirect
48. #18012664C22semidirect
49. #18012663C22semidirect
50. #18012662C22semidirect
51. #18012661C22semidirect
52. #18012660C22semidirect
53. #18012659C22semidirect
54. C2×SD16×C151C22semidirect
56. #124×C151C22semidirect
57. C4×D4×C151C22semidirect
58. C4⋊C8×C151C22semidirect
59. #103×C151C22semidirect
60. #102×C151C22semidirect
207. D151#463direct (N × H)
208. C151C2×#463semidirect
221. #463D151direct (N × H)
233. C2×SD16C2×D151semidirect
246. #124C2×D151semidirect
252. C4×D4C2×D151semidirect
261. C4⋊C8C2×D151semidirect
265. #103C2×D151semidirect
269. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1512
C2×D8×D1512
#124×D1512
C4×D4×D1512
#237524302
#237524292
#237524282
#237524272
#237524262
#237524252
#237524242
C4⋊C8×D1512
#103×D1512
#102×D1512
#463×C1512
C2×#463151