Finite Group Databasebeta

← #11872100

Subgroups — #11872100

Order 1152.

609 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#518C211yesmaximal, characteristic, complemented
2#10589636C211yesmaximal, characteristic, complemented
3#10588898C211yesmaximal, characteristic
4#10588897C211yesmaximal, characteristic, complemented
5#10588699C211yesmaximal, characteristic, complemented
6#10588699C211yesmaximal, characteristic, complemented
7#10588697C211yesmaximal, characteristic, complemented
8C4×#3673C211yesmaximal, characteristic, complemented
9#10588694C211yesmaximal, characteristic, complemented
10C4×#3672C211yesmaximal, characteristic, complemented
11#10588691C211yesmaximal, characteristic, complemented
12#10588690C211yesmaximal, characteristic, complemented
13#10588684C211yesmaximal, characteristic, complemented
14#10588680C211yesmaximal, characteristic, complemented
15#10588678C211yesmaximal, characteristic, complemented
16#82541—31nomaximal
17C22×D4×C9C2211yescharacteristic
18C4×D4×C9—21no—
19C4×D4×C9—21no—
20C4×D4×C9C2211yescharacteristic
21C4×D4×C9C2211yescharacteristic
22C4×D4×C9C2211yescharacteristic
23C4×D4×C9C2211yescharacteristic
24C9×#117C2211yescharacteristic
25C9×#117C2211yescharacteristic
26C2×C9×C22⋊C4—21no—
27C2×C9×C22⋊C4—21no—
28C2×#3673C2211yescharacteristic
29C2×#3673C2211yescharacteristic
30C2×#3672C2211yescharacteristic
31C2×#3672C2211yescharacteristic
32#63492C2211yescharacteristic
33#63486C2211yescharacteristic
34#63460—21no—
35#63458—21no—
36#63447—21no—
37#63445—21no—
38#63437C2211yescharacteristic, complemented
39C4×D36C2211yescharacteristic, complemented
40#63431C2211yescharacteristic, complemented
41C4×Dic18C2211yescharacteristic, complemented
42#63392C2211yescharacteristic
43#63392C2211yescharacteristic
44#63392C2211yescharacteristic
45#63392C2211yescharacteristic
46#63389C2211yescharacteristic
47#63389C2211yescharacteristic
48#63369C2211yescharacteristic, complemented
49#63369C2211yescharacteristic, complemented
50#63368C2211yescharacteristic, complemented
51#63368C2211yescharacteristic, complemented
52#63367C2211yescharacteristic, complemented
53#63367C2211yescharacteristic, complemented
54#63366C2211yescharacteristic, complemented
55#63366C2211yescharacteristic, complemented
56C4⋊(C9⋊C8)C2211yescharacteristic, complemented
57C4⋊(C9⋊C8)C2211yescharacteristic, complemented
58#63362C2211yescharacteristic, complemented
59C4×C9⋊C8C2211yescharacteristic, complemented
60C3×#518D311yescharacteristic
61#5534—31no—
62#5218—31no—
63#5217—31no—
64#5018—31no—
65C4×#214—31no—
66#5016—31no—
67#5016—31no—
68#5014—31no—
69C4×#213—31no—
70#5008—31no—
71#5007—31no—
72#5003—31no—
73#5000—31no—
74#4996—31no—
75C24×C9—21no—
76C2×D4×C9—22no—
77C2×D4×C9—22no—
78C2×D4×C9—21no—
79C2×D4×C9C2311yescharacteristic
80C2×D4×C9C2311yescharacteristic
81C22×C4×C9—21no—
82C22×C4×C9—21no—
83C22×C4×C9—21no—
84C22×C4×C9—21no—
85C22×C4×C9C2311yescharacteristic
86C2×#611—21no—
87C2×D36C2311yescharacteristic
88C2×C4×D9—21no—
89C2×Dic18—21no—
90C2×Dic18C2311yescharacteristic
91C9×C4⋊C4D411yescharacteristic
92C9×C4⋊C4D411yescharacteristic
93C9×C4⋊C4C2311yescharacteristic
94C9×C4⋊C4C2311yescharacteristic
95C9×C22⋊C4—21no—
96C9×C22⋊C4—21no—
97C9×C22⋊C4—21no—
98C9×C22⋊C4—21no—
99C9×C22⋊C4—21no—
100C9×C22⋊C4D411yescharacteristic
101C9×C22⋊C4D411yescharacteristic
102C42×C9—21no—
103C42×C9C2311yescharacteristic
104C42×C9C2311yescharacteristic
105#3676—21no—
106#3673—22no—
107#3673—22no—
108#3672—22no—
109#3672—22no—
110(C2×D9)⋊C4—21no—
111(C2×D9)⋊C4—21no—
112(C2×D9)⋊C4—21no—
113(C2×D9)⋊C4—21no—
114C4⋊Dic9—21no—
115C4⋊Dic9C2311yescharacteristic
116C4⋊Dic9C2311yescharacteristic
117Dic9⋊C4—21no—
118Dic9⋊C4—21no—
119C4×Dic9—21no—
120C2×C9⋊C8C2311yescharacteristic
121C2×C9⋊C8C2311yescharacteristic
122C2×C9⋊C8C2311yescharacteristic
123C2×C9⋊C8C2311yescharacteristic
124#3118—91noSylow
125C22×C3×D4C2×D311yescharacteristic
126C3×C4×D4—21no—
127C3×C4×D4—21no—
128C3×C4×D4C2×D311yescharacteristic
129C3×C4×D4C2×D311yescharacteristic
130C3×C4×D4C2×D311yescharacteristic
131C3×C4×D4C2×D311yescharacteristic
132C3×#117C2×D311yescharacteristic
133C3×#117C2×D311yescharacteristic
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—21no—
136C2×#214—31no—
137C2×#214—31no—
138C2×#213—31no—
139C2×#213—31no—
140#930—31no—
141#924—31no—
142#898—61no—
143#896—61no—
144#885—61no—
145#883—61no—
146#875—31no—
147C4×D12—31no—
148#869—31no—
149C4×Dic6—31no—
150#832—31no—
151#832—31no—
152#832—31no—
153#832—31no—
154#830—31no—
155#830—31no—
156#810—31no—
157#810—31no—
158#809—31no—
159#809—31no—
160#808—31no—
161#808—31no—
162#807—31no—
163#807—31no—
164C4⋊(C3⋊C8)—31no—
165C4⋊(C3⋊C8)—31no—
166#803—31no—
167C4×C3⋊C8—31no—
168C23×C9—24no—
169C23×C9—21no—
170C23×C9—21no—
171C23×C9—81no—
172C23×C9—81no—
173C23×C9C2×D411yescharacteristic
174C22×D9—21no—
175D4×C9—24no—
176D4×C9—21no—
177D4×C9—21no—
178D4×C9#4112yes—
179D4×C9#4112yes—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9—21no—
184C2×C4×C9—81no—
185C2×C4×C9—81no—
186C2×C4×C9—81no—
187C2×C4×C9—81no—
188C2×C4×C9C2×D411yescharacteristic
189C2×C4×C9C2×D411yescharacteristic
190C2×C4×C9C2×D411yescharacteristic
191C2×C4×C9C2×D411yescharacteristic
192C2×C4×C9C2×D411yescharacteristic
193C2×C4×C9C2411yescharacteristic
194#611—81no—
195C2×Dic9—21no—
196C2×Dic9—21no—
197C2×Dic9—21no—
198D36—21no—
199D36—21no—
200C4×D9—81no—
201Dic18—21no—
202Dic18—21no—
203Dic18—81no—
204C9⋊C8—21no—
205C9⋊C8—21no—
206C9⋊C8—21no—
207C9⋊C8—21no—
208#542—91no—
209#518D911yescharacteristic, complemented
210#485—91no—
211#482—91no—
212#476—91no—
213#474—91no—
214#463—91no—
215#463—91no—
216#450—91no—
217#447—91no—
218#442—91no—
219#440—91no—
220C4×SD16—91no—
221C4×D8—91no—
222#433—91no—
223C24×C3—21no—
224C2×C3×D4—22no—
225C2×C3×D4—22no—
226C2×C3×D4—21no—
227C2×C3×D4C22×D311yescharacteristic
228C2×C3×D4C22×D311yescharacteristic
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4C22×D311yescharacteristic
234C2×#67—61no—
235C2×D12—31no—
236C2×C4×D3—61no—
237C2×Dic6—31no—
238C2×Dic6—61no—
239C3×C4⋊C4#6711yescharacteristic
240C3×C4⋊C4#6711yescharacteristic
241C3×C4⋊C4C22×D311yescharacteristic
242C3×C4⋊C4C22×D311yescharacteristic
243C3×C22⋊C4—21no—
244C3×C22⋊C4—21no—
245C3×C22⋊C4—21no—
246C3×C22⋊C4—21no—
247C3×C22⋊C4—21no—
248C3×C22⋊C4#6711yescharacteristic
249C3×C22⋊C4#6711yescharacteristic
250C3×C42—21no—
251C3×C42C22×D311yescharacteristic
252C3×C42C22×D311yescharacteristic
253#217—61no—
254#214—62no—
255#214—62no—
256#213—62no—
257#213—62no—
258(C2×D3)⋊C4—61no—
259(C2×D3)⋊C4—61no—
260(C2×D3)⋊C4—61no—
261(C2×D3)⋊C4—61no—
262C4⋊Dic3—31no—
263C4⋊Dic3—31no—
264C4⋊Dic3—61no—
265Dic3⋊C4—61no—
266Dic3⋊C4—61no—
267C4×Dic3—61no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C22×C9—21no—
273C22×C9—22no—
274C22×C9—22no—
275C22×C9—21no—
276C22×C9—21no—
277C22×C9—41no—
278C22×C9—41no—
279C22×C9—41no—
280C22×C9—41no—
281C22×C9—84no—
282C22×C9C22×D411yescharacteristic
283C2×D9—41no—
284C2×D9—41no—
285C2×D9—41no—
286C4×C9—21no—
287C4×C9—21no—
288C4×C9—21no—
289C4×C9—21no—
290C4×C9—21no—
291C4×C9—41no—
292C4×C9—41no—
293C4×C9C2×#4111yescharacteristic
294C4×C9C2×#4111yescharacteristic
295Dic9—41no—
296Dic9—41no—
297Dic9—41no—
298C22×D4C2×D911yescharacteristic
299C2×SD16—91no—
300C2×SD16—91no—
301C2×D8—91no—
302C2×D8—91no—
303C4⋊Q8—91no—
304#126—181no—
305#124—91no—
306#124—181no—
307#123—181no—
308C22⋊Q8—91no—
309C22⋊Q8—181no—
310#121—91no—
311C4×Q8—91no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—91no—
315C4×D4C2×D911yescharacteristic
316C4×D4C2×D911yescharacteristic
317C4×D4C2×D911yescharacteristic
318C4×D4C2×D911yescharacteristic
319#117C2×D911yescharacteristic
320#117C2×D911yescharacteristic
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323#107—91no—
324#107—91no—
325#106—91no—
326#106—91no—
327C4⋊C8—91no—
328C4⋊C8—91no—
329#103—91no—
330#103—91no—
331#102—91no—
332#102—91no—
333#102—91no—
334#102—91no—
335#102—91no—
336#102—91no—
337C22⋊C8—91no—
338C22⋊C8—91no—
339#97—91no—
340C4×C8—91no—
341C23×C3—24no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—81no—
345C23×C3—81no—
346C23×C3C2×#6711yescharacteristic
347C22×D3—61no—
348C3×D4—24no—
349C3×D4—21no—
350C3×D4—21no—
351C3×D4#23512yes—
352C3×D4#23512yes—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—81no—
358C2×C3×C4—81no—
359C2×C3×C4—81no—
360C2×C3×C4—81no—
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367#67—241no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371D12—61no—
372D12—61no—
373C4×D3—241no—
374Dic6—61no—
375Dic6—61no—
376Dic6—241no—
377C3⋊C8—61no—
378C3⋊C8—61no—
379C3⋊C8—61no—
380C3⋊C8—61no—
381C2×C9—41no—
382C2×C9—42no—
383C2×C9—42no—
384C2×C9#52511yescharacteristic
385C2×C9#57611yescharacteristic
386C2×C9#57711yescharacteristic
387D9—81no—
388C24—21no—
389C2×Q8—91no—
390C2×Q8—181no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—21no—
394C2×D4—91no—
395C2×D4—181no—
396C2×D4C22×D911yescharacteristic
397C2×D4C22×D911yescharacteristic
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—181no—
403C22×C4C22×D911yescharacteristic
404SD16—182no—
405SD16—182no—
406D8—182no—
407D8—182no—
408C2×C8—91no—
409C2×C8—91no—
410C2×C8—91no—
411C2×C8—91no—
412C4⋊C4—91no—
413C4⋊C4—91no—
414C4⋊C4—181no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C4⋊C4#61111yescharacteristic
418C4⋊C4#61111yescharacteristic
419C4⋊C4C22×D911yescharacteristic
420C4⋊C4C22×D911yescharacteristic
421C22⋊C4—21no—
422C22⋊C4—21no—
423C22⋊C4—21no—
424C22⋊C4—21no—
425C22⋊C4—21no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4#61111yescharacteristic
432C22⋊C4#61111yescharacteristic
433C42—21no—
434C42—181no—
435C42C22×D911yescharacteristic
436C42C22×D911yescharacteristic
437C22×C3—21no—
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—84no—
447C22×C3C22×#6711yescharacteristic
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—121no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—41no—
457C3×C4—41no—
458C3×C4C2×#23511yescharacteristic
459C3×C4C2×#23511yescharacteristic
460Dic3—121no—
461Dic3—121no—
462Dic3—121no—
463C9#311811yescharacteristic, complemented, Sylow
464C23—24no—
465C23—21no—
466C23—21no—
467C23—81no—
468C23—81no—
469C23—181no—
470C23C2×#61111yescharacteristic
471Q8—181no—
472Q8—181no—
473Q8—721no—
474D4—24no—
475D4—21no—
476D4—21no—
477D4—181no—
478D4—181no—
479D4—721no—
480D4#369712yes—
481D4#369712yes—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—81no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—721no—
494C2×C4C2×#61111yescharacteristic
495C2×C4C2×#61111yescharacteristic
496C2×C4C2×#61111yescharacteristic
497C2×C4C2×#61111yescharacteristic
498C2×C4C2×#61111yescharacteristic
499C2×C4C23×D911yescharacteristic
500C8—181no—
501C8—181no—
502C8—181no—
503C8—181no—
504C2×C3—41no—
505C2×C3—42no—
506C2×C3—42no—
507C2×C3#579111yescharacteristic
508C2×C3#583511yescharacteristic
509C2×C3#583611yescharacteristic
510D3—241no—
511C22—21no—
512C22—22no—
513C22—22no—
514C22—21no—
515C22—21no—
516C22—41no—
517C22—41no—
518C22—41no—
519C22—41no—
520C22—84no—
521C22—361no—
522C22—361no—
523C22—361no—
524C22C22×#61111yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—41no—
531C4—41no—
532C4—361no—
533C4—361no—
534C4—361no—
535C4C2×#369711yescharacteristic
536C4C2×#369711yescharacteristic
537C3#8254111yescharacteristic
538C2—41no—
539C2—42no—
540C2—42no—
541C2—721no—
542C2#1058989311yescharacteristic
543C2#1058993711yescharacteristic
544C2#1058993811yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#518C2
socleC22×C3C22×#67
prime radical#10588898C2
hypercenter#518D9
hypocenterC9#3118
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. C9×#518C2semidirect
2. #10589636C2semidirect
4. #10588897C2semidirect
5. #10588699C2semidirect
6. #10588699C2semidirect
7. #10588697C2semidirect
8. C4×#3673C2semidirect
9. #10588694C2semidirect
10. C4×#3672C2semidirect
11. #10588691C2semidirect
12. #10588690C2semidirect
13. #10588684C2semidirect
14. #10588680C2semidirect
15. #10588678C2semidirect
38. #63437C22semidirect
39. C4×D36C22semidirect
40. #63431C22semidirect
41. C4×Dic18C22semidirect
48. #63369C22semidirect
49. #63369C22semidirect
50. #63368C22semidirect
51. #63368C22semidirect
52. #63367C22semidirect
53. #63367C22semidirect
54. #63366C22semidirect
55. #63366C22semidirect
56. C4⋊(C9⋊C8)C22semidirect
57. C4⋊(C9⋊C8)C22semidirect
58. #63362C22semidirect
59. C4×C9⋊C8C22semidirect
209. #518D9semidirect
463. C9#3118semidirect

Maximal subgroups

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

subgroupindex
C9×#5182
#105896362
#105888982
#105888972
#105886992
#105886972
C4×#36732
#105886942
C4×#36722
#105886912
#105886902
#105886842
#105886802
#105886782
#825413