Finite Group Databasebeta

← #46820148

Subgroups — #46820148

Order 34432.

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×#22575498C211yesmaximal, characteristic, complemented
2C2×#22575477C211yesmaximal, characteristic, complemented
3C2×D8×D269C211yesmaximal, characteristic, complemented
4#31771171C211yesmaximal, characteristic, complemented
5#31770752C211yesmaximal, characteristic, complemented
6#31770751C211yesmaximal, characteristic, complemented
7#31770748C211yesmaximal, characteristic, complemented
8#31770747C211yesmaximal, characteristic, complemented
9#31770740C211yesmaximal, characteristic, complemented
10#31770739C211yesmaximal, characteristic, complemented
11#31770737C211yesmaximal, characteristic, complemented
12#31770608C211yesmaximal, characteristic, complemented
13#31770598C211yesmaximal, characteristic, complemented
14#31770570C211yesmaximal, characteristic, complemented
15#447×C269C211yesmaximal, characteristic, complemented
16#22575498—24no—
17#22575498—24no—
18C2×#16864402C2211yescharacteristic
19C2×#16864402C2211yescharacteristic, complemented
20C2×#16864401—21no—
21C2×#16864401C2211yescharacteristic
22C2×#16864401C2211yescharacteristic, complemented
23C22×C22⋊D269—21no—
24C22×C22⋊D269—21no—
25C2×D4×D269—21no—
26C2×D4×D269C2211yescharacteristic
27C2×D4×D269C2211yescharacteristic, complemented
28C2×D4×D269C2211yescharacteristic, complemented
29#22575477—24no—
30C2×#16864391C2211yescharacteristic, complemented
31C2×#16864390C2211yescharacteristic, complemented
32C2×D2152C2211yescharacteristic, complemented
33C2×#16864387C2211yescharacteristic, complemented
34C2×#16864387C2211yescharacteristic, complemented
35C2×#16864387C2211yescharacteristic, complemented
36D8×D269—24no—
37C2×#16864385C2211yescharacteristic, complemented
38C2×C8×D269C2211yescharacteristic, complemented
39#22575449—21no—
40#22575439—21no—
41#22575428C2211yescharacteristic, complemented
42#22575427C2211yescharacteristic, complemented
43#22575424C2211yescharacteristic, complemented
44#22575423—21no—
45#22575421—21no—
46#22575411C2211yescharacteristic, complemented
47#22575378C2211yescharacteristic, complemented
48#22575376C2211yescharacteristic, complemented
49#22575375C2211yescharacteristic, complemented
50#22575374C2211yescharacteristic, complemented
51#22575374C2211yescharacteristic, complemented
52#22575373C2211yescharacteristic, complemented
53C22⋊#14524130C2211yescharacteristic, complemented
54#22575365C2211yescharacteristic, complemented
55#22575365C2211yescharacteristic, complemented
56C22×D4×C269C2211yescharacteristic, complemented
57C2×D8×C269C2211yescharacteristic, complemented
58C2×D8×C269C2211yescharacteristic, complemented
59#121×C269C2211yescharacteristic, complemented
60#102×C269C2211yescharacteristic, complemented
61#102×C269C2211yescharacteristic, complemented
62C22⋊C8×C269C2211yescharacteristic, complemented
63C23×D269—21no—
64C23×D269—21no—
65C23×D269—21no—
66#16864402—22no—
67#16864402—22no—
68#16864402—22no—
69#16864402—22no—
70#16864401—28no—
71#16864401—22no—
72#16864401—22no—
73#16864401—22no—
74#16864401D414yescomplemented
75C2×Dic538D411yescharacteristic
76C2×Dic538C2311yescharacteristic
77C2×D1076—21no—
78C2×D1076D411yescharacteristic
79C2×D1076C2311yescharacteristic
80C2×D1076C2311yescharacteristic
81C2×C22⋊D269—28no—
82C2×C22⋊D269—28no—
83C2×C22⋊D269—21no—
84C2×C22⋊D269—21no—
85C2×C22⋊D269—21no—
86C2×C22⋊D269—21no—
87C2×C22⋊D269—21no—
88C2×C22⋊D269—21no—
89C2×C22⋊D269—21no—
90C2×C22⋊D269—21no—
91C2×C22⋊D269D411yescharacteristic
92C2×C22⋊D269D411yescharacteristic
93D4×D269—28no—
94D4×D269—22no—
95D4×D269—22no—
96D4×D269—22no—
97D4×D269—22no—
98D4×D269—22no—
99D4×D269D414yescomplemented
100C22×Dic269—21no—
101C22×Dic269—21no—
102C2×C4×D269—21no—
103C2×C4×D269C2311yescharacteristic
104C2×C4×D269C2311yescharacteristic
105#16864391—22no—
106#16864390—22no—
107D2152—22no—
108#16864387—22no—
109#16864387—22no—
110#16864387—22no—
111#16864385—22no—
112C2×#14524130C2311yescharacteristic
113C2×#14524130C2311yescharacteristic
114C8×D269—22no—
115C4⋊Dic269C2311yescharacteristic
116C22⋊Dic269—21no—
117#16864379—21no—
118#16864379—21no—
119#16864379—21no—
120C4×Dic269—21no—
121C24×C269—21no—
122C2×D4×C269—22no—
123C2×D4×C269—22no—
124C2×D4×C269—21no—
125C2×D4×C269—21no—
126C2×D4×C269C2311yescharacteristic
127C2×D4×C269C2311yescharacteristic
128C2×D4×C269C2311yescharacteristic
129C22×C4×C269C2311yescharacteristic
130D8×C269—22no—
131D8×C269—22no—
132C2×C8×C269C2311yescharacteristic
133C2×C8×C269C2311yescharacteristic
134C4⋊C4×C269C2311yescharacteristic
135C22⋊C4×C269—21no—
136C22×D269—21no—
137C22×D269—24no—
138C22×D269—24no—
139C22×D269—21no—
140C22×D269—42no—
141C22×D269—81no—
142C22×D269—81no—
143C22×D269—81no—
144C22×D269—81no—
145C22×D269—81no—
146C22×D269—81no—
147C22×D269C2×D411yescharacteristic
148C22×D269C2×D411yescharacteristic
149Dic538—21no—
150Dic538—22no—
151Dic538C2×D412yes—
152D1076—22no—
153D1076—21no—
154D1076—21no—
155D1076—21no—
156D1076—81no—
157D1076C2×D412yes—
158C22⋊D269—24no—
159C22⋊D269—24no—
160C22⋊D269—24no—
161C22⋊D269—24no—
162C22⋊D269—22no—
163C22⋊D269—24no—
164C22⋊D269—22no—
165C22⋊D269—42no—
166C22⋊D269—81no—
167C22⋊D269—81no—
168C2×Dic269—24no—
169C2×Dic269—21no—
170C2×Dic269—24no—
171C2×Dic269—21no—
172C2×Dic269C2×D411yescharacteristic
173C2×Dic269C2×D411yescharacteristic
174C4×D269—24no—
175C4×D269—21no—
176C4×D269—21no—
177C4×D269C2×D412yes—
178C4×D269C2×D412yes—
179#14524130—21no—
180#14524130—21no—
181C23×C269—24no—
182C23×C269—21no—
183C23×C269—21no—
184C23×C269—21no—
185C23×C269—81no—
186C23×C269—81no—
187C23×C269C2×D411yescharacteristic
188D4×C269—24no—
189D4×C269—21no—
190D4×C269—21no—
191D4×C269—21no—
192D4×C269—21no—
193D4×C269—81no—
194D4×C269C2×D412yes—
195D4×C269C2×D412yes—
196C2×C4×C269—21no—
197C2×C4×C269—21no—
198C2×C4×C269—21no—
199C2×C4×C269C2×D411yescharacteristic
200C2×C4×C269C2411yescharacteristic
201C8×C269—21no—
202C8×C269—21no—
203C22×C269—21no—
204C22×C269—22no—
205C22×C269—22no—
206C22×C269—21no—
207C22×C269—21no—
208C22×C269—41no—
209C22×C269—41no—
210C22×C269—41no—
211C22×C269—41no—
212C22×C269—41no—
213C22×C269—41no—
214C22×C269—41no—
215C22×C269—84no—
216C22×C269C22×D411yescharacteristic
217C2×D269—21no—
218C2×D269—21no—
219C2×D269—21no—
220C2×D269—22no—
221C2×D269—21no—
222C2×D269—21no—
223C2×D269—41no—
224C2×D269—41no—
225C2×D269—41no—
226C2×D269—41no—
227C2×D269—41no—
228C2×D269—84no—
229C2×D269—84no—
230C2×D269—84no—
231C2×D269#12012yes—
232C4×C269—21no—
233C4×C269—41no—
234C4×C269C22×D411yescharacteristic
235C4×C269C22×D411yescharacteristic
236Dic269—22no—
237Dic269—21no—
238Dic269—41no—
239Dic269#12012yes—
240C2×C269—42no—
241C2×C269—42no—
242C2×C269—41no—
243C2×C269—81no—
244C2×C269C2×#12011yescharacteristic
245C2×C269#57611yescharacteristic
246C2×C269#57611yescharacteristic
247D269—22no—
248D269—41no—
249D269—42no—
250D269—81no—
251C269#300811yescharacteristic, complemented, Sylow
252#3008—2691nomaximal, Sylow
253C2×H(5,𝔽2)—2691no—
254C2×AGL(1,ℤ/8)—2691no—
255C22×D8—2691no—
256#535—2691no—
257#449—2691no—
258#449—2691no—
259#449—2691no—
260#449—2691no—
261#447—2691no—
262#447—2691no—
263#447—2691no—
264#447D26911yescharacteristic, complemented
265#418—2691no—
266#416—2691no—
267#408—2691no—
268H(5,𝔽2)—5384no—
269H(5,𝔽2)—5384no—
270C2×#41—2691no—
271C2×#41—2691no—
272C2×#41—2691no—
273C2×#41—2691no—
274C2×#41—5381no—
275C22×D4—2691no—
276C22×D4—2691no—
277C22×D4—2691no—
278C22×D4—5381no—
279C22×D4—5381no—
280C22×D4—5381no—
281C22×D4C2×D26911yescharacteristic, complemented
282AGL(1,ℤ/8)—5384no—
283C2×SD16—2691no—
284C2×SD16—2691no—
285C2×D8—2691no—
286C2×D8—2691no—
287C2×D8—2691no—
288C2×D8—2691no—
289C2×D8—5384no—
290C2×D8C2×D26911yescharacteristic, complemented
291C2×D8C2×D26911yescharacteristic, complemented
292C2×M16—2691no—
293C22×C8—2691no—
294#127—5381no—
295#124—5381no—
296#121—2691no—
297#121—2691no—
298#121—2691no—
299#121C2×D26911yescharacteristic, complemented
300#120—5381no—
301#120—5381no—
302#117—2691no—
303#103—2691no—
304#103—2691no—
305#102—2691no—
306#102—2691no—
307#102—2691no—
308#102—2691no—
309#102C2×D26911yescharacteristic, complemented
310#102C2×D26911yescharacteristic, complemented
311C22⋊C8—2691no—
312C22⋊C8—2691no—
313C22⋊C8—2691no—
314C22⋊C8C2×D26911yescharacteristic, complemented
315C24—21no—
316C24—5381no—
317C24—5381no—
318C24—5381no—
319#41—2694no—
320#41—5382no—
321#41—5382no—
322#41—5382no—
323#41—5382no—
324#41—5382no—
325#41—5382no—
326#41—5388no—
327#41—5382no—
328C2×Q8—2691no—
329C2×Q8—2691no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—2694no—
335C2×D4—2691no—
336C2×D4—2691no—
337C2×D4—2691no—
338C2×D4—2691no—
339C2×D4—2691no—
340C2×D4—5381no—
341C2×D4—5382no—
342C2×D4—5382no—
343C2×D4—5382no—
344C2×D4—5381no—
345C2×D4—5381no—
346C2×D4—5381no—
347C2×D4—5382no—
348C2×D4—5388no—
349C2×D4—5381no—
350C2×D4—5381no—
351C2×D4—5388no—
352C2×D4—5388no—
353C2×D4—5381no—
354C2×D4—5382no—
355C2×D4—5381no—
356C2×D4—5381no—
357C2×D4C22×D26911yescharacteristic
358C2×D4C22×D26911yescharacteristic
359C2×D4C22×D26911yescharacteristic
360C22×C4—2691no—
361C22×C4—2691no—
362C22×C4—5381no—
363C22×C4—5381no—
364C22×C4—5381no—
365C22×C4C22×D26911yescharacteristic
366SD16—5382no—
367SD16—5382no—
368D8—22no—
369D8—22no—
370D8—5382no—
371D8—5382no—
372D8—5382no—
373D8—5382no—
374M16—5382no—
375C2×C8—2691no—
376C2×C8—2691no—
377C2×C8—5382no—
378C2×C8C22×D26911yescharacteristic
379C2×C8C22×D26911yescharacteristic
380C4⋊C4—2691no—
381C4⋊C4C22×D26911yescharacteristic
382C22⋊C4—21no—
383C22⋊C4—5381no—
384C22⋊C4—5381no—
385C22⋊C4—5381no—
386C22⋊C4—5381no—
387C42—5381no—
388C23—24no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—81no—
393C23—81no—
394C23—2691no—
395C23—2691no—
396C23—5384no—
397C23—5384no—
398C23—5381no—
399C23—5381no—
400C23—10762no—
401C23—21521no—
402C23—21521no—
403C23—21521no—
404C23—21521no—
405C23—21521no—
406C23—21521no—
407C23D4×D26911yescharacteristic
408Q8—2692no—
409Q8—5382no—
410Q8—5381no—
411D4—24no—
412D4—21no—
413D4—21no—
414D4—21no—
415D4—21no—
416D4—81no—
417D4—2692no—
418D4—5382no—
419D4—5382no—
420D4—5384no—
421D4—5382no—
422D4—5384no—
423D4—5384no—
424D4—5384no—
425D4—5384no—
426D4—5381no—
427D4—5381no—
428D4—5381no—
429D4—10762no—
430D4—21521no—
431D4—21521no—
432D4—21521no—
433D4D4×D26912yes—
434D4D4×D26912yes—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—2691no—
439C2×C4—2692no—
440C2×C4—2692no—
441C2×C4—2691no—
442C2×C4—5384no—
443C2×C4—5384no—
444C2×C4—5384no—
445C2×C4—5381no—
446C2×C4—5381no—
447C2×C4—5381no—
448C2×C4—5381no—
449C2×C4D4×D26911yescharacteristic
450C2×C4C23×D26911yescharacteristic
451C8—21no—
452C8—21no—
453C8—5381no—
454C8—5381no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—22no—
459C22—22no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—84no—
468C22—2692no—
469C22—5381no—
470C22—5381no—
471C22—5381no—
472C22—5381no—
473C22—5382no—
474C22—5381no—
475C22—10761no—
476C22—10761no—
477C22—10761no—
478C22—10761no—
479C22—10761no—
480C22—21524no—
481C22—21524no—
482C22—21524no—
483C22C2×D4×D26911yescharacteristic
484C4—21no—
485C4—41no—
486C4—2692no—
487C4—5381no—
488C4—5382no—
489C4—10761no—
490C4C2×D4×D26911yescharacteristic
491C4C2×D4×D26911yescharacteristic
492C2—41no—
493C2—42no—
494C2—42no—
495C2—81no—
496C2—5382no—
497C2—10761no—
498C2—10762no—
499C2—21521no—
500C2#120×D26911yescharacteristic
501C2#3177140611yescharacteristic
502C2#3177140911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#447×C269C2
socleC22×C269C22×D4
hypercenter#447D269
hypocenterC269#3008
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#22575498C2semidirect
2. C2×#22575477C2semidirect
3. C2×D8×D269C2semidirect
4. #31771171C2semidirect
5. #31770752C2semidirect
6. #31770751C2semidirect
7. #31770748C2semidirect
8. #31770747C2semidirect
9. #31770740C2semidirect
10. #31770739C2semidirect
11. #31770737C2semidirect
12. #31770608C2semidirect
13. #31770598C2semidirect
14. #31770570C2semidirect
15. #447×C269C2semidirect
19. C2×#16864402C22semidirect
22. C2×#16864401C22semidirect
27. C2×D4×D269C22semidirect
28. C2×D4×D269C22semidirect
30. C2×#16864391C22semidirect
31. C2×#16864390C22semidirect
32. C2×D2152C22semidirect
33. C2×#16864387C22semidirect
34. C2×#16864387C22semidirect
35. C2×#16864387C22semidirect
37. C2×#16864385C22semidirect
38. C2×C8×D269C22semidirect
41. #22575428C22semidirect
42. #22575427C22semidirect
43. #22575424C22semidirect
46. #22575411C22semidirect
47. #22575378C22semidirect
48. #22575376C22semidirect
49. #22575375C22semidirect
50. #22575374C22semidirect
51. #22575374C22semidirect
52. #22575373C22semidirect
53. C22⋊#14524130C22semidirect
54. #22575365C22semidirect
55. #22575365C22semidirect
56. C22×D4×C269C22semidirect
57. C2×D8×C269C22semidirect
58. C2×D8×C269C22semidirect
59. #121×C269C22semidirect
60. #102×C269C22semidirect
61. #102×C269C22semidirect
62. C22⋊C8×C269C22semidirect
74. #16864401D4semidirect
99. D4×D269D4semidirect
251. C269#3008semidirect
264. #447D269semidirect
281. C22×D4C2×D269semidirect
290. C2×D8C2×D269semidirect
291. C2×D8C2×D269semidirect
299. #121C2×D269semidirect
309. #102C2×D269semidirect
310. #102C2×D269semidirect
314. C22⋊C8C2×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754982
C2×#225754772
C2×D8×D2692
#317711712
#317707522
#317707512
#317707482
#317707472
#317707402
#317707392
#317707372
#317706082
#317705982
#317705702
#447×C2692
#3008269