Finite Group Databasebeta

← #34078375

Subgroups — #34078375

Order 19328.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012785C211yesmaximal, characteristic, complemented
2C2×#18012766C211yesmaximal, characteristic, complemented
3C2×D8×D151C211yesmaximal, characteristic, complemented
4#23752778C211yesmaximal, characteristic, complemented
5#23752360C211yesmaximal, characteristic, complemented
6#23752357C211yesmaximal, characteristic, complemented
7#23752356C211yesmaximal, characteristic, complemented
8#23752348C211yesmaximal, characteristic, complemented
9#23752347C211yesmaximal, characteristic, complemented
10#23752345C211yesmaximal, characteristic, complemented
11#23752344C211yesmaximal, characteristic, complemented
12#23752215C211yesmaximal, characteristic, complemented
13#23752207C211yesmaximal, characteristic, complemented
14#23752177C211yesmaximal, characteristic, complemented
15#449×C151C211yesmaximal, characteristic, complemented
16#18012785—24no—
17#18012785—24no—
18C2×#14559005C2211yescharacteristic
19C2×#14559005C2211yescharacteristic, complemented
20C2×#14559004—21no—
21C2×#14559004C2211yescharacteristic
22C22×D604—21no—
23C22×D604C2211yescharacteristic, complemented
24C2×D4×D151—21no—
25C2×D4×D151—21no—
26C2×D4×D151C2211yescharacteristic
27C2×D4×D151C2211yescharacteristic, complemented
28C2×D4×D151C2211yescharacteristic, complemented
29#18012766—24no—
30C2×#14558991C2211yescharacteristic, complemented
31C2×D1208C2211yescharacteristic, complemented
32C2×D1208C2211yescharacteristic, complemented
33C2×#14558989C2211yescharacteristic, complemented
34C2×#14558989C2211yescharacteristic, complemented
35C2×#14558989C2211yescharacteristic, complemented
36D8×D151—24no—
37C2×#14558987C2211yescharacteristic, complemented
38C2×C8×D151C2211yescharacteristic, complemented
39#18012735—21no—
40#18012725—21no—
41#18012714C2211yescharacteristic, complemented
42#18012713C2211yescharacteristic, complemented
43#18012710C2211yescharacteristic, complemented
44#18012709—21no—
45#18012707—21no—
46#18012697C2211yescharacteristic, complemented
47#18012663C2211yescharacteristic, complemented
48#18012661C2211yescharacteristic, complemented
49#18012661C2211yescharacteristic, complemented
50#18012660C2211yescharacteristic, complemented
51#18012659C2211yescharacteristic, complemented
52#18012659C2211yescharacteristic, complemented
53C22⋊(C151⋊C8)C2211yescharacteristic, complemented
54(C2×D151)⋊C8C2211yescharacteristic, complemented
55(C2×D151)⋊C8C2211yescharacteristic, complemented
56C2×#41×C151C2211yescharacteristic, complemented
57C2×SD16×C151C2211yescharacteristic, complemented
58C2×D8×C151C2211yescharacteristic, complemented
59#121×C151C2211yescharacteristic, complemented
60#103×C151C2211yescharacteristic, complemented
61#102×C151C2211yescharacteristic, complemented
62C22⋊C8×C151C2211yescharacteristic, complemented
63C23×D151—21no—
64C23×D151—21no—
65C23×D151—21no—
66C23×D151—21no—
67#14559005—22no—
68#14559005—22no—
69#14559005—22no—
70#14559005D414yescomplemented
71#14559004—28no—
72#14559004—22no—
73#14559004—22no—
74C2×Dic302D411yescharacteristic
75C2×D604—28no—
76C2×D604—21no—
77C2×D604—21no—
78C2×D604—22no—
79C2×D604—22no—
80C2×D604—21no—
81C2×D604—21no—
82C2×D604D411yescharacteristic
83C2×D604C2311yescharacteristic
84C2×D604C2311yescharacteristic
85C2×D604C2311yescharacteristic
86C2×C22⋊D151—21no—
87C2×C22⋊D151—21no—
88C2×C22⋊D151—21no—
89C2×C22⋊D151—21no—
90C2×C22⋊D151—21no—
91C2×C22⋊D151D411yescharacteristic
92C2×C22⋊D151D411yescharacteristic
93D4×D151—28no—
94D4×D151—28no—
95D4×D151—22no—
96D4×D151—22no—
97D4×D151—22no—
98D4×D151—22no—
99D4×D151—22no—
100D4×D151D414yescomplemented
101C2×C4×D151—21no—
102C2×C4×D151—21no—
103C2×C4×D151C2311yescharacteristic
104C2×C4×D151C2311yescharacteristic
105#14558991—22no—
106D1208—22no—
107D1208—22no—
108#14558989—22no—
109#14558989—22no—
110#14558989—22no—
111#14558987—22no—
112C2×C151⋊C8C2311yescharacteristic
113C2×C151⋊C8C2311yescharacteristic
114C8×D151—22no—
115C4⋊Dic151C2311yescharacteristic
116C22⋊Dic151—21no—
117(C2×D151)⋊C4—21no—
118(C2×D151)⋊C4—21no—
119(C2×D151)⋊C4—21no—
120C4×Dic151—21no—
121#41×C151—22no—
122#41×C151—22no—
123C2×Q8×C151C2311yescharacteristic
124C2×D4×C151—21no—
125C2×D4×C151—21no—
126C2×D4×C151C2311yescharacteristic
127C2×D4×C151C2311yescharacteristic
128C22×C4×C151—21no—
129C22×C4×C151C2311yescharacteristic
130SD16×C151—22no—
131D8×C151—22no—
132C2×C8×C151C2311yescharacteristic
133C2×C8×C151C2311yescharacteristic
134C4⋊C4×C151C2311yescharacteristic
135C22⋊C4×C151—21no—
136C22×D151—21no—
137C22×D151—21no—
138C22×D151—24no—
139C22×D151—24no—
140C22×D151—24no—
141C22×D151—21no—
142C22×D151—42no—
143C22×D151—81no—
144C22×D151—81no—
145C22×D151—81no—
146C22×D151—81no—
147C22×D151—81no—
148C22×D151—81no—
149C22×D151—81no—
150C22×D151—81no—
151C22×D151C2×D411yescharacteristic
152C22×D151C2×D411yescharacteristic
153Dic302—22no—
154D604—24no—
155D604—24no—
156D604—24no—
157D604—22no—
158D604—21no—
159D604—21no—
160D604—21no—
161D604—21no—
162D604—81no—
163D604C2×D412yes—
164D604C2×D412yes—
165C22⋊D151—24no—
166C22⋊D151—22no—
167C22⋊D151—22no—
168C22⋊D151—24no—
169C22⋊D151—42no—
170C22⋊D151—81no—
171C22⋊D151—81no—
172C2×Dic151—21no—
173C2×Dic151C2×D411yescharacteristic
174C2×Dic151C2×D411yescharacteristic
175C4×D151—24no—
176C4×D151—21no—
177C4×D151—21no—
178C4×D151—24no—
179C4×D151C2×D412yes—
180C4×D151C2×D412yes—
181C151⋊C8—21no—
182C151⋊C8—21no—
183C23×C151—21no—
184C23×C151—21no—
185C23×C151C2×D411yescharacteristic
186Q8×C151—21no—
187Q8×C151C2×D412yes—
188D4×C151—24no—
189D4×C151—21no—
190D4×C151—21no—
191D4×C151—21no—
192D4×C151—81no—
193D4×C151C2×D412yes—
194C2×C4×C151—24no—
195C2×C4×C151—21no—
196C2×C4×C151—21no—
197C2×C4×C151—21no—
198C2×C4×C151—21no—
199C2×C4×C151C2×D411yescharacteristic
200C2×C4×C151C2411yescharacteristic
201C8×C151—21no—
202C8×C151—21no—
203C22×C151—21no—
204C22×C151—22no—
205C22×C151—21no—
206C22×C151—21no—
207C22×C151—41no—
208C22×C151—41no—
209C22×C151—41no—
210C22×C151—41no—
211C22×C151—41no—
212C22×C151C22×D411yescharacteristic
213C2×D151—21no—
214C2×D151—21no—
215C2×D151—21no—
216C2×D151—22no—
217C2×D151—22no—
218C2×D151—21no—
219C2×D151—21no—
220C2×D151—41no—
221C2×D151—41no—
222C2×D151—41no—
223C2×D151—41no—
224C2×D151—41no—
225C2×D151—41no—
226C2×D151—41no—
227C2×D151—84no—
228C2×D151—84no—
229C2×D151—84no—
230C2×D151—84no—
231C2×D151#12012yes—
232C4×C151—21no—
233C4×C151—22no—
234C4×C151—41no—
235C4×C151C22×D411yescharacteristic
236C4×C151C22×D411yescharacteristic
237Dic151—21no—
238Dic151—41no—
239Dic151#12012yes—
240C2×C151—41no—
241C2×C151—42no—
242C2×C151—81no—
243C2×C151C2×#12011yescharacteristic
244C2×C151#57611yescharacteristic
245C2×C151#57611yescharacteristic
246D151—22no—
247D151—41no—
248D151—42no—
249D151—42no—
250D151—81no—
251C151#300811yescharacteristic, complemented, Sylow
252#3008—1511nomaximal, Sylow
253C2×H(5,𝔽2)—1511no—
254C2×AGL(1,ℤ/8)—1511no—
255C22×D8—1511no—
256#535—1511no—
257#449—1511no—
258#449—1511no—
259#449—1511no—
260#449D15111yescharacteristic, complemented
261#447—1511no—
262#447—1511no—
263#447—1511no—
264#447—1511no—
265#418—1511no—
266#416—1511no—
267#408—1511no—
268H(5,𝔽2)—3024no—
269H(5,𝔽2)—3024no—
270C2×#41—3021no—
271C2×#41—1511no—
272C2×#41—1511no—
273C2×#41—1511no—
274C2×#41C2×D15111yescharacteristic, complemented
275C22×D4—3021no—
276C22×D4—3021no—
277C22×D4—3021no—
278C22×D4—1511no—
279C22×D4—1511no—
280C22×D4—1511no—
281C22×D4—1511no—
282AGL(1,ℤ/8)—3024no—
283C2×SD16—1511no—
284C2×SD16C2×D15111yescharacteristic, complemented
285C2×D8—3024no—
286C2×D8—1511no—
287C2×D8—1511no—
288C2×D8—1511no—
289C2×D8—1511no—
290C2×D8—1511no—
291C2×D8C2×D15111yescharacteristic, complemented
292C2×M16—1511no—
293C22×C8—1511no—
294#127—3021no—
295#124—3021no—
296#121—1511no—
297#121—1511no—
298#121—1511no—
299#121C2×D15111yescharacteristic, complemented
300#120—3021no—
301#120—3021no—
302#117—1511no—
303#103—1511no—
304#103C2×D15111yescharacteristic, complemented
305#102—1511no—
306#102—1511no—
307#102—1511no—
308#102—1511no—
309#102—1511no—
310#102C2×D15111yescharacteristic, complemented
311C22⋊C8—1511no—
312C22⋊C8—1511no—
313C22⋊C8—1511no—
314C22⋊C8C2×D15111yescharacteristic, complemented
315C24—3021no—
316C24—3021no—
317C24—3021no—
318C24—3021no—
319#41—22no—
320#41—22no—
321#41—3028no—
322#41—3022no—
323#41—3022no—
324#41—3022no—
325#41—3022no—
326#41—3022no—
327#41—1514no—
328C2×Q8—1511no—
329C2×Q8C22×D15111yescharacteristic
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—3028no—
333C2×D4—3021no—
334C2×D4—3021no—
335C2×D4—3022no—
336C2×D4—3022no—
337C2×D4—3021no—
338C2×D4—3028no—
339C2×D4—3028no—
340C2×D4—3022no—
341C2×D4—3022no—
342C2×D4—3021no—
343C2×D4—3021no—
344C2×D4—3022no—
345C2×D4—3022no—
346C2×D4—3022no—
347C2×D4—3021no—
348C2×D4—3021no—
349C2×D4—3021no—
350C2×D4—3021no—
351C2×D4—1511no—
352C2×D4—1511no—
353C2×D4—1514no—
354C2×D4—1511no—
355C2×D4—1511no—
356C2×D4—1511no—
357C2×D4—1511no—
358C2×D4C22×D15111yescharacteristic
359C2×D4C22×D15111yescharacteristic
360C22×C4—21no—
361C22×C4—3021no—
362C22×C4—3021no—
363C22×C4—1511no—
364C22×C4—1511no—
365C22×C4C22×D15111yescharacteristic
366SD16—22no—
367SD16—3022no—
368D8—22no—
369D8—3022no—
370D8—3022no—
371D8—3022no—
372D8—3022no—
373D8—3022no—
374M16—3022no—
375C2×C8—3022no—
376C2×C8—1511no—
377C2×C8—1511no—
378C2×C8C22×D15111yescharacteristic
379C2×C8C22×D15111yescharacteristic
380C4⋊C4—1511no—
381C4⋊C4C22×D15111yescharacteristic
382C22⋊C4—21no—
383C22⋊C4—3021no—
384C22⋊C4—3021no—
385C22⋊C4—3021no—
386C22⋊C4—3021no—
387C42—3021no—
388C23—21no—
389C23—21no—
390C23—3024no—
391C23—3024no—
392C23—3024no—
393C23—3021no—
394C23—3021no—
395C23—3021no—
396C23—6042no—
397C23—1511no—
398C23—1511no—
399C23—12081no—
400C23—12081no—
401C23—12081no—
402C23—12081no—
403C23—12081no—
404C23—12081no—
405C23—12081no—
406C23—12081no—
407C23D4×D15111yescharacteristic
408Q8—21no—
409Q8—3022no—
410Q8D4×D15112yes—
411D4—24no—
412D4—21no—
413D4—21no—
414D4—21no—
415D4—81no—
416D4—3024no—
417D4—3024no—
418D4—3024no—
419D4—3022no—
420D4—3024no—
421D4—3022no—
422D4—3022no—
423D4—3024no—
424D4—3021no—
425D4—3021no—
426D4—3021no—
427D4—3021no—
428D4—6042no—
429D4—1512no—
430D4—1512no—
431D4—12081no—
432D4—12081no—
433D4—12081no—
434D4D4×D15112yes—
435C2×C4—24no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—3024no—
441C2×C4—3024no—
442C2×C4—3021no—
443C2×C4—3021no—
444C2×C4—3021no—
445C2×C4—1511no—
446C2×C4—1511no—
447C2×C4—1512no—
448C2×C4—1512no—
449C2×C4D4×D15111yescharacteristic
450C2×C4C23×D15111yescharacteristic
451C8—21no—
452C8—21no—
453C8—3021no—
454C8—3021no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—22no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—3021no—
465C22—3021no—
466C22—3021no—
467C22—3021no—
468C22—3021no—
469C22—3022no—
470C22—3022no—
471C22—6041no—
472C22—6041no—
473C22—6041no—
474C22—6041no—
475C22—6041no—
476C22—6041no—
477C22—6041no—
478C22—1512no—
479C22—12084no—
480C22—12084no—
481C22—12084no—
482C22—12084no—
483C22C2×D4×D15111yescharacteristic
484C4—21no—
485C4—22no—
486C4—41no—
487C4—3021no—
488C4—6041no—
489C4—1512no—
490C4C2×D4×D15111yescharacteristic
491C4C2×D4×D15111yescharacteristic
492C2—41no—
493C2—42no—
494C2—81no—
495C2—3022no—
496C2—6041no—
497C2—6042no—
498C2—6042no—
499C2—12081no—
500C2#120×D15111yescharacteristic
501C2#2375301411yescharacteristic
502C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#449×C151C2
socleC22×C151C22×D4
hypercenter#449D151
hypocenterC151#3008
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#18012785C2semidirect
2. C2×#18012766C2semidirect
3. C2×D8×D151C2semidirect
4. #23752778C2semidirect
5. #23752360C2semidirect
6. #23752357C2semidirect
7. #23752356C2semidirect
8. #23752348C2semidirect
9. #23752347C2semidirect
10. #23752345C2semidirect
11. #23752344C2semidirect
12. #23752215C2semidirect
13. #23752207C2semidirect
14. #23752177C2semidirect
15. #449×C151C2semidirect
19. C2×#14559005C22semidirect
23. C22×D604C22semidirect
27. C2×D4×D151C22semidirect
28. C2×D4×D151C22semidirect
30. C2×#14558991C22semidirect
31. C2×D1208C22semidirect
32. C2×D1208C22semidirect
33. C2×#14558989C22semidirect
34. C2×#14558989C22semidirect
35. C2×#14558989C22semidirect
37. C2×#14558987C22semidirect
38. C2×C8×D151C22semidirect
41. #18012714C22semidirect
42. #18012713C22semidirect
43. #18012710C22semidirect
46. #18012697C22semidirect
47. #18012663C22semidirect
48. #18012661C22semidirect
49. #18012661C22semidirect
50. #18012660C22semidirect
51. #18012659C22semidirect
52. #18012659C22semidirect
53. C22⋊(C151⋊C8)C22semidirect
54. (C2×D151)⋊C8C22semidirect
55. (C2×D151)⋊C8C22semidirect
56. C2×#41×C151C22semidirect
57. C2×SD16×C151C22semidirect
58. C2×D8×C151C22semidirect
59. #121×C151C22semidirect
60. #103×C151C22semidirect
61. #102×C151C22semidirect
62. C22⋊C8×C151C22semidirect
70. #14559005D4semidirect
100. D4×D151D4semidirect
251. C151#3008semidirect
260. #449D151semidirect
274. C2×#41C2×D151semidirect
284. C2×SD16C2×D151semidirect
291. C2×D8C2×D151semidirect
299. #121C2×D151semidirect
304. #103C2×D151semidirect
310. #102C2×D151semidirect
314. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127852
C2×#180127662
C2×D8×D1512
#237527782
#237523602
#237523572
#237523562
#237523482
#237523472
#237523452
#237523442
#237522152
#237522072
#237521772
#449×C1512
#3008151