Finite Group Databasebeta

← #34080585

Subgroups — #34080585

Order 19328.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012763C211yesmaximal, characteristic, complemented
2C2×D8×D151C211yesmaximal, characteristic, complemented
3#23752857C211yesmaximal, characteristic, complemented
4#23752847C211yesmaximal, characteristic, complemented
5#23752599C211yesmaximal, characteristic, complemented
6#23752464C211yesmaximal, characteristic, complemented
7#23752440C211yesmaximal, characteristic, complemented
8#23752428C211yesmaximal, characteristic, complemented
9#23752364C211yesmaximal, characteristic, complemented
10#23752354C211yesmaximal, characteristic, complemented
11#23752347C211yesmaximal, characteristic, complemented
12#23752344C211yesmaximal, characteristic, complemented
13#23752322C211yesmaximal, characteristic, complemented
14#23752282C211yesmaximal, characteristic, complemented
15#459×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic, complemented
17C2×D4×D151—21no—
18C2×D4×D151C2211yescharacteristic
19C2×D4×D151C2211yescharacteristic, complemented
20C2×D4×D151C2211yescharacteristic, complemented
21#18012763—24no—
22C2×#14558993C2211yescharacteristic, complemented
23C2×#14558992C2211yescharacteristic, complemented
24C2×#14558992C2211yescharacteristic, complemented
25C2×D1208C2211yescharacteristic
26C2×#14558989C2211yescharacteristic
27C2×#14558989C2211yescharacteristic, complemented
28C2×#14558989C2211yescharacteristic, complemented
29D8×D151—24no—
30C2×#14558987C2211yescharacteristic, complemented
31C2×C8×D151C2211yescharacteristic, complemented
32#18012727C2211yescharacteristic, complemented
33#18012723—21no—
34#18012719C2211yescharacteristic, complemented
35#18012714C2211yescharacteristic, complemented
36#18012713—21no—
37#18012710—21no—
38#18012710C2211yescharacteristic
39#18012710C2211yescharacteristic, complemented
40#18012709—21no—
41#18012707—21no—
42#18012707—21no—
43C4×D604C2211yescharacteristic
44C4×D604C2211yescharacteristic, complemented
45C2×(C2×D151)⋊C4—21no—
46#18012670C2211yescharacteristic, complemented
47#18012664C2211yescharacteristic, complemented
48#18012661C2211yescharacteristic, complemented
49#18012660C2211yescharacteristic, complemented
50#18012659C2211yescharacteristic, complemented
51(C2×D151)⋊C8C2211yescharacteristic, complemented
52(C2×D151)⋊C8C2211yescharacteristic, complemented
53#18012650C2211yescharacteristic, complemented
54C2×D8×C151C2211yescharacteristic, complemented
55C2×D8×C151C2211yescharacteristic, complemented
56#127×C151C2211yescharacteristic, complemented
57C4×D4×C151C2211yescharacteristic, complemented
58C4⋊C8×C151C2211yescharacteristic, complemented
59#102×C151C2211yescharacteristic, complemented
60#102×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62C23×D151—21no—
63C23×D151—21no—
64#14559003—22no—
65#14559003—41no—
66C2×Dic302C2311yescharacteristic
67C2×D604—21no—
68C2×D604D411yescharacteristic
69C2×D604C2311yescharacteristic
70C2×D604C2311yescharacteristic
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151—21no—
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76C2×C22⋊D151—21no—
77D4×D151—22no—
78D4×D151—22no—
79D4×D151—22no—
80D4×D151—41no—
81D4×D151—41no—
82D4×D151—41no—
83D4×D151—44no—
84C22×Dic151—21no—
85C2×C4×D151—21no—
86C2×C4×D151C2311yescharacteristic
87C2×C4×D151C2311yescharacteristic
88#14558993—22no—
89#14558992—22no—
90#14558992—41no—
91D1208—22no—
92#14558989—22no—
93#14558989—41no—
94#14558989D414yescomplemented
95#14558987—22no—
96C2×C151⋊C8C2311yescharacteristic
97C2×C151⋊C8C2311yescharacteristic
98C8×D151—22no—
99C4⋊Dic151—21no—
100C4⋊Dic151D411yescharacteristic
101C4⋊Dic151C2311yescharacteristic
102C22⋊Dic151—21no—
103C22⋊Dic151—21no—
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4—21no—
106(C2×D151)⋊C4—21no—
107(C2×D151)⋊C4—21no—
108(C2×D151)⋊C4—21no—
109(C2×D151)⋊C4D411yescharacteristic
110(C2×D151)⋊C4D411yescharacteristic
111C2×D4×C151—21no—
112C2×D4×C151—21no—
113C2×D4×C151C2311yescharacteristic
114C2×D4×C151C2311yescharacteristic
115C2×D4×C151C2311yescharacteristic
116C22×C4×C151—21no—
117D8×C151—22no—
118D8×C151—22no—
119C2×C8×C151C2311yescharacteristic
120C2×C8×C151C2311yescharacteristic
121C4⋊C4×C151C2311yescharacteristic
122C22⋊C4×C151—21no—
123C42×C151C2311yescharacteristic
124C22×D151—21no—
125C22×D151—21no—
126C22×D151—42no—
127C22×D151—42no—
128C22×D151—42no—
129C22×D151—42no—
130C22×D151—42no—
131C22×D151—42no—
132C22×D151—81no—
133C22×D151—81no—
134C22×D151—81no—
135C22×D151C2×D411yescharacteristic
136C22×D151C2×D411yescharacteristic
137Dic302—21no—
138Dic302—21no—
139D604—22no—
140D604—21no—
141D604—21no—
142D604—21no—
143D604—81no—
144D604C2×D412yes—
145C22⋊D151—42no—
146C22⋊D151—42no—
147C22⋊D151—42no—
148C22⋊D151—42no—
149C22⋊D151—42no—
150C22⋊D151—42no—
151C2×Dic151—21no—
152C2×Dic151—21no—
153C2×Dic151—42no—
154C2×Dic151C2×D411yescharacteristic
155C2×Dic151C2×D411yescharacteristic
156C4×D151—21no—
157C4×D151—21no—
158C4×D151—21no—
159C4×D151—21no—
160C4×D151—42no—
161C151⋊C8—21no—
162C151⋊C8C2×D412yescomplemented
163C23×C151—21no—
164C23×C151—21no—
165C23×C151—21no—
166D4×C151—21no—
167D4×C151—21no—
168D4×C151—21no—
169D4×C151—21no—
170D4×C151—21no—
171D4×C151—42no—
172D4×C151—81no—
173D4×C151C2×D412yescomplemented
174C2×C4×C151—21no—
175C2×C4×C151—81no—
176C2×C4×C151C2×D411yescharacteristic
177C2×C4×C151C2×D411yescharacteristic
178C2×C4×C151C2411yescharacteristic
179C8×C151—21no—
180C8×C151—21no—
181C22×C151—22no—
182C22×C151—41no—
183C22×C151—41no—
184C22×C151—41no—
185C22×C151—41no—
186C22×C151—41no—
187C22×C151—41no—
188C22×C151—41no—
189C22×C151—41no—
190C22×C151C22×D411yescharacteristic
191C2×D151—21no—
192C2×D151—21no—
193C2×D151—21no—
194C2×D151—22no—
195C2×D151—21no—
196C2×D151—21no—
197C2×D151—41no—
198C2×D151—41no—
199C2×D151—41no—
200C2×D151—41no—
201C2×D151—41no—
202C2×D151—84no—
203C2×D151—84no—
204C2×D151—84no—
205C2×D151AGL(1,ℤ/8)12yescomplemented
206C4×C151—21no—
207C4×C151—21no—
208C4×C151—41no—
209C4×C151C22×D411yescharacteristic
210C4×C151H(5,𝔽2)11yescharacteristic
211Dic151—21no—
212Dic151—21no—
213Dic151—41no—
214Dic151—41no—
215C2×C151—42no—
216C2×C151—81no—
217C2×C151—81no—
218C2×C151D4211yescharacteristic
219C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
220C2×C151#57611yescharacteristic
221D151—22no—
222D151—41no—
223D151—42no—
224D151—81no—
225C151#326411yescharacteristic, complemented, Sylow
226#3264—1511nomaximal, Sylow
227C2×AGL(1,ℤ/8)—1511no—
228C22×D8—1511no—
229#546—1511no—
230D42—1511no—
231#496—1511no—
232#469—1511no—
233#465—1511no—
234#463—1511no—
235#459D15111yescharacteristic, complemented
236#450—1511no—
237#449—1511no—
238#447—1511no—
239#447—1511no—
240#442—1511no—
241#435—1511no—
242C2×#41—1511no—
243C22×D4—3021no—
244C22×D4—1511no—
245C22×D4—1511no—
246C22×D4—1511no—
247AGL(1,ℤ/8)—3024no—
248C2×SD16—1511no—
249C2×SD16—1511no—
250C2×SD16—1511no—
251C2×D8—3024no—
252C2×D8—1511no—
253C2×D8—1511no—
254C2×D8—1511no—
255C2×D8—1511no—
256C2×D8C2×D15111yescharacteristic, complemented
257C2×D8C2×D15111yescharacteristic, complemented
258C2×M16—1511no—
259C22×C8—1511no—
260#127C2×D15111yescharacteristic, complemented
261#124—1511no—
262#123—3021no—
263C22⋊Q8—1511no—
264#121—3021no—
265#121—3021no—
266#121—1511no—
267#121—1511no—
268#121—1511no—
269#120—3021no—
270#120—3021no—
271#120—3021no—
272C4×D4—1511no—
273C4×D4—1511no—
274C4×D4C2×D15111yescharacteristic, complemented
275C2×C22⋊C4—3021no—
276#106—1511no—
277C4⋊C8C2×D15111yescharacteristic, complemented
278#103—1511no—
279#102—1511no—
280#102—1511no—
281#102—1511no—
282#102C2×D15111yescharacteristic, complemented
283#102C2×D15111yescharacteristic, complemented
284C22⋊C8—1511no—
285C22⋊C8—1511no—
286#97—1511no—
287C24—3021no—
288C24—3021no—
289C24—3021no—
290#41—3022no—
291#41—6041no—
292C2×Q8—1511no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—3021no—
296C2×D4—3022no—
297C2×D4—3022no—
298C2×D4—3022no—
299C2×D4—3021no—
300C2×D4—3021no—
301C2×D4—3021no—
302C2×D4—3021no—
303C2×D4—3021no—
304C2×D4—3021no—
305C2×D4—6041no—
306C2×D4—6041no—
307C2×D4—6041no—
308C2×D4—6044no—
309C2×D4—1511no—
310C2×D4—1511no—
311C2×D4—1511no—
312C2×D4C22×D15111yescharacteristic
313C2×D4C22×D15111yescharacteristic
314C2×D4C22×D15111yescharacteristic
315C22×C4—21no—
316C22×C4—3021no—
317C22×C4—3021no—
318C22×C4—1511no—
319C22×C4—1511no—
320SD16—3022no—
321SD16—3022no—
322SD16—6041no—
323D8—22no—
324D8—22no—
325D8—3022no—
326D8—3022no—
327D8—6041no—
328D8—1514no—
329M16—3022no—
330C2×C8—3022no—
331C2×C8—1511no—
332C2×C8—1511no—
333C2×C8C22×D15111yescharacteristic
334C2×C8C22×D15111yescharacteristic
335C4⋊C4—3021no—
336C4⋊C4—1511no—
337C4⋊C4—1511no—
338C4⋊C4C22×D15111yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—3021no—
341C22⋊C4—3021no—
342C22⋊C4—3021no—
343C22⋊C4—3021no—
344C22⋊C4—3021no—
345C22⋊C4—3021no—
346C22⋊C4—3021no—
347C22⋊C4—1511no—
348C22⋊C4—1511no—
349C42C22×D15111yescharacteristic
350C23—21no—
351C23—21no—
352C23—21no—
353C23—3021no—
354C23—3021no—
355C23—6042no—
356C23—6042no—
357C23—6042no—
358C23—6042no—
359C23—6042no—
360C23—6042no—
361C23—1511no—
362C23—1511no—
363C23—12081no—
364C23—12081no—
365C23—12081no—
366Q8—3021no—
367Q8—3021no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—21no—
373D4—42no—
374D4—81no—
375D4—3022no—
376D4—3021no—
377D4—3021no—
378D4—3021no—
379D4—6042no—
380D4—6042no—
381D4—6042no—
382D4—6042no—
383D4—6042no—
384D4—6042no—
385D4—1512no—
386D4—12081no—
387D4D4×D15112yescomplemented
388C2×C4—21no—
389C2×C4—81no—
390C2×C4—3021no—
391C2×C4—3021no—
392C2×C4—3021no—
393C2×C4—3021no—
394C2×C4—3021no—
395C2×C4—3021no—
396C2×C4—6042no—
397C2×C4—6042no—
398C2×C4—1511no—
399C2×C4—1511no—
400C2×C4D4×D15111yescharacteristic
401C2×C4D4×D15111yescharacteristic
402C2×C4C23×D15111yescharacteristic
403C8—21no—
404C8—21no—
405C8—3021no—
406C8—1512no—
407C22—22no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—3021no—
417C22—3021no—
418C22—3021no—
419C22—3021no—
420C22—3021no—
421C22—3022no—
422C22—6041no—
423C22—6041no—
424C22—6041no—
425C22—6041no—
426C22—6041no—
427C22—1512no—
428C22—12084no—
429C22—12084no—
430C22—12084no—
431C22C2×D4×D15111yescharacteristic
432C4—21no—
433C4—21no—
434C4—41no—
435C4—3021no—
436C4—3021no—
437C4—6041no—
438C4—6041no—
439C4C2×D4×D15111yescharacteristic
440C4#1801278511yescharacteristic
441C2—42no—
442C2—81no—
443C2—81no—
444C2—3022no—
445C2—6041no—
446C2—6042no—
447C2—12081no—
448C2#2375284611yescharacteristic
449C2AGL(1,ℤ/8)×D15111yescharacteristic
450C2#2375301311yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#459×C151C2
socleC22×C151C22×D4
hypercenter#459D151
hypocenterC151#3264
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#18012763C2semidirect
2. C2×D8×D151C2semidirect
3. #23752857C2semidirect
4. #23752847C2semidirect
5. #23752599C2semidirect
6. #23752464C2semidirect
7. #23752440C2semidirect
8. #23752428C2semidirect
9. #23752364C2semidirect
10. #23752354C2semidirect
11. #23752347C2semidirect
12. #23752344C2semidirect
13. #23752322C2semidirect
14. #23752282C2semidirect
15. #459×C151C2semidirect
16. C2×#14559003C22semidirect
19. C2×D4×D151C22semidirect
20. C2×D4×D151C22semidirect
22. C2×#14558993C22semidirect
23. C2×#14558992C22semidirect
24. C2×#14558992C22semidirect
27. C2×#14558989C22semidirect
28. C2×#14558989C22semidirect
30. C2×#14558987C22semidirect
31. C2×C8×D151C22semidirect
32. #18012727C22semidirect
34. #18012719C22semidirect
35. #18012714C22semidirect
39. #18012710C22semidirect
44. C4×D604C22semidirect
46. #18012670C22semidirect
47. #18012664C22semidirect
48. #18012661C22semidirect
49. #18012660C22semidirect
50. #18012659C22semidirect
51. (C2×D151)⋊C8C22semidirect
52. (C2×D151)⋊C8C22semidirect
53. #18012650C22semidirect
54. C2×D8×C151C22semidirect
55. C2×D8×C151C22semidirect
56. #127×C151C22semidirect
57. C4×D4×C151C22semidirect
58. C4⋊C8×C151C22semidirect
59. #102×C151C22semidirect
60. #102×C151C22semidirect
94. #14558989D4semidirect
162. C151⋊C8C2×D4semidirect
173. D4×C151C2×D4semidirect
205. C2×D151AGL(1,ℤ/8)semidirect
225. C151#3264semidirect
235. #459D151semidirect
256. C2×D8C2×D151semidirect
257. C2×D8C2×D151semidirect
260. #127C2×D151semidirect
274. C4×D4C2×D151semidirect
277. C4⋊C8C2×D151semidirect
282. #102C2×D151semidirect
283. #102C2×D151semidirect
387. D4D4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127632
C2×D8×D1512
#237528572
#237528472
#237525992
#237524642
#237524402
#237524282
#237523642
#237523542
#237523472
#237523442
#237523222
#237522822
#459×C1512
#3264151