Finite Group Databasebeta

← #11872103

Subgroups — #11872103

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
1#10589900C211yesmaximal, characteristic, complemented
2#10589745C211yesmaximal, characteristic, complemented
3C9×#450C211yesmaximal, characteristic, complemented
4#10588898C211yesmaximal, characteristic
5#10588845C211yesmaximal, characteristic, complemented
6#10588845C211yesmaximal, characteristic, complemented
7#10588844C211yesmaximal, characteristic, complemented
8SD16×Dic9C211yesmaximal, characteristic, complemented
9#10588725C211yesmaximal, characteristic, complemented
10#10588465C211yesmaximal, characteristic, complemented
11#10588441C211yesmaximal, characteristic, complemented
12#10588439C211yesmaximal, characteristic, complemented
13#10588436C211yesmaximal, characteristic, complemented
14#10588419C211yesmaximal, characteristic, complemented
15#10588400C211yesmaximal, characteristic, complemented
16#80136—31nomaximal
17C22×D4×C9C2211yescharacteristic
18C2×C9×SD16C2211yescharacteristic
19C2×C9×SD16C2211yescharacteristic
20C9×C22⋊Q8C2211yescharacteristic
21C2×#3676—21no—
22C2×#3676—21no—
23#63509C2211yescharacteristic, complemented
24Q8×Dic9C2211yescharacteristic, complemented
25D4×Dic9—21no—
26D4×Dic9—21no—
27D4×Dic9C2211yescharacteristic
28D4×Dic9C2211yescharacteristic
29D4×Dic9C2211yescharacteristic
30D4×Dic9C2211yescharacteristic
31C2×#3673C2211yescharacteristic
32C2×#3673C2211yescharacteristic
33#63492C2211yescharacteristic
34#63488C2211yescharacteristic
35#63488C2211yescharacteristic
36#63460—21no—
37#63459—21no—
38#63455C2211yescharacteristic, complemented
39#63450C2211yescharacteristic, complemented
40#63447—21no—
41#63445—21no—
42C9×#102C2211yescharacteristic
43C9×#102C2211yescharacteristic
44C9×C22⋊C8C2211yescharacteristic
45#63395C2211yescharacteristic, complemented
46#63395C2211yescharacteristic, complemented
47#63392C2211yescharacteristic
48#63392C2211yescharacteristic
49#63389C2211yescharacteristic
50#63380C2211yescharacteristic, complemented
51#63380C2211yescharacteristic, complemented
52#63378C2211yescharacteristic, complemented
53#63377C2211yescharacteristic, complemented
54#63375C2211yescharacteristic, complemented
55Dic9⋊C8C2211yescharacteristic, complemented
56Dic9⋊C8C2211yescharacteristic, complemented
57C8×Dic9C2211yescharacteristic, complemented
58#63367C2211yescharacteristic, complemented
59#63366C2211yescharacteristic, complemented
60#5798—31no—
61#5643—31no—
62C3×#450D311yescharacteristic
63#5217—31no—
64#5165—31no—
65#5165—31no—
66#5164—31no—
67Dic3×SD16—31no—
68#5045—31no—
69#4785—31no—
70#4761—31no—
71#4759—31no—
72#4756—31no—
73#4737—31no—
74#4720—31no—
75C24×C9—21no—
76C2×Q8×C9C2311yescharacteristic
77C2×D4×C9—22no—
78C2×D4×C9—22no—
79C2×D4×C9—21no—
80C2×D4×C9C2311yescharacteristic
81C2×D4×C9C2311yescharacteristic
82C22×C4×C9C2311yescharacteristic
83C2×#611—21no—
84C22×Dic9—21no—
85C22×Dic9—21no—
86C22×Dic9—21no—
87C22×Dic9—21no—
88C2×D36C2311yescharacteristic
89C2×C4×D9—21no—
90C2×Dic18—21no—
91C9×SD16—22no—
92C9×SD16—22no—
93C2×C8×C9C2311yescharacteristic
94C2×C8×C9C2311yescharacteristic
95C9×C4⋊C4—21no—
96C9×C4⋊C4C2311yescharacteristic
97C9×C22⋊C4—21no—
98#3676—21no—
99#3676—21no—
100#3676—21no—
101#3676—21no—
102#3676—21no—
103#3676D411yescharacteristic
104#3676D411yescharacteristic
105#3673—22no—
106#3673—22no—
107(C2×D9)⋊C4—21no—
108(C2×D9)⋊C4—21no—
109(C2×D9)⋊C4—21no—
110(C2×D9)⋊C4—21no—
111C4⋊Dic9—21no—
112C4⋊Dic9D411yescharacteristic
113C4⋊Dic9D411yescharacteristic
114C4⋊Dic9C2311yescharacteristic
115C4⋊Dic9C2311yescharacteristic
116C4⋊Dic9C2311yescharacteristic
117Dic9⋊C4—21no—
118C4×Dic9—21no—
119C4×Dic9—21no—
120C4×Dic9C2311yescharacteristic
121C4×Dic9C2311yescharacteristic
122C2×C9⋊C8C2311yescharacteristic
123C2×C9⋊C8C2311yescharacteristic
124#3118—91noSylow
125C22×C3×D4C2×D311yescharacteristic
126C2×C3×SD16C2×D311yescharacteristic
127C2×C3×SD16C2×D311yescharacteristic
128C3×C22⋊Q8C2×D311yescharacteristic
129C2×#217—61no—
130C2×#217—61no—
131#947—31no—
132Q8×Dic3—31no—
133D4×Dic3—31no—
134D4×Dic3—31no—
135D4×Dic3—31no—
136D4×Dic3—31no—
137D4×Dic3—61no—
138D4×Dic3—61no—
139C2×#213—31no—
140C2×#213—31no—
141#930—31no—
142#926—31no—
143#926—31no—
144#898—61no—
145#897—61no—
146#893—31no—
147#888—31no—
148#885—61no—
149#883—61no—
150C3×#102C2×D311yescharacteristic
151C3×#102C2×D311yescharacteristic
152C3×C22⋊C8C2×D311yescharacteristic
153#835—31no—
154#835—31no—
155#832—31no—
156#832—31no—
157#830—31no—
158#821—31no—
159#821—31no—
160#818—31no—
161#817—31no—
162#815—31no—
163Dic3⋊C8—31no—
164Dic3⋊C8—31no—
165C8×Dic3—31no—
166#808—31no—
167#807—31no—
168C23×C9—24no—
169C23×C9—21no—
170C23×C9—21no—
171C23×C9—81no—
172C23×C9—81no—
173C23×C9C2×D411yescharacteristic
174C22×D9—21no—
175Q8×C9—21no—
176Q8×C9—21no—
177D4×C9—24no—
178D4×C9—21no—
179D4×C9—21no—
180D4×C9#4112yes—
181D4×C9#4112yes—
182C2×C4×C9—21no—
183C2×C4×C9—21no—
184C2×C4×C9—21no—
185C2×C4×C9—21no—
186C2×C4×C9C2×D411yescharacteristic
187C2×C4×C9C2411yescharacteristic
188#611—81no—
189C2×Dic9—21no—
190C2×Dic9—21no—
191C2×Dic9—21no—
192C2×Dic9—81no—
193C2×Dic9—81no—
194C2×Dic9—81no—
195C2×Dic9—81no—
196C2×Dic9C2×D411yescharacteristic
197C2×Dic9C2×D411yescharacteristic
198C2×Dic9C2×D411yescharacteristic
199C2×Dic9C2×D411yescharacteristic
200D36—21no—
201D36—21no—
202C4×D9—81no—
203Dic18—81no—
204C8×C9—21no—
205C8×C9—21no—
206C9⋊C8—21no—
207C9⋊C8—21no—
208#542—91no—
209#518—91no—
210#485—91no—
211#482—91no—
212#476—91no—
213#474—91no—
214#463—91no—
215#463—91no—
216#450D911yescharacteristic, complemented
217#447—91no—
218#442—91no—
219#440—91no—
220C4×SD16—91no—
221C4×D8—91no—
222#433—91no—
223C24×C3—21no—
224C2×C3×Q8C22×D311yescharacteristic
225C2×C3×D4—22no—
226C2×C3×D4—22no—
227C2×C3×D4—21no—
228C2×C3×D4C22×D311yescharacteristic
229C2×C3×D4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C2×#67—61no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234C22×Dic3—61no—
235C22×Dic3—61no—
236C2×D12—31no—
237C2×C4×D3—61no—
238C2×Dic6—61no—
239C3×SD16—22no—
240C3×SD16—22no—
241C2×C3×C8C22×D311yescharacteristic
242C2×C3×C8C22×D311yescharacteristic
243C3×C4⋊C4—21no—
244C3×C4⋊C4C22×D311yescharacteristic
245C3×C22⋊C4—21no—
246#217—31no—
247#217—31no—
248#217—61no—
249#217—61no—
250#217—61no—
251#217—61no—
252#217—61no—
253#213—62no—
254#213—62no—
255(C2×D3)⋊C4—61no—
256(C2×D3)⋊C4—61no—
257(C2×D3)⋊C4—61no—
258(C2×D3)⋊C4—61no—
259C4⋊Dic3—31no—
260C4⋊Dic3—31no—
261C4⋊Dic3—31no—
262C4⋊Dic3—31no—
263C4⋊Dic3—31no—
264C4⋊Dic3—61no—
265Dic3⋊C4—61no—
266C4×Dic3—31no—
267C4×Dic3—31no—
268C4×Dic3—61no—
269C4×Dic3—61no—
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—41no—
288C4×C9—41no—
289C4×C9C2×#4111yescharacteristic
290C4×C9C2×#4111yescharacteristic
291Dic9—21no—
292Dic9—21no—
293Dic9—21no—
294Dic9—21no—
295Dic9—41no—
296Dic9—41no—
297Dic9—41no—
298C22×D4C2×D911yescharacteristic
299C2×SD16C2×D911yescharacteristic
300C2×SD16C2×D911yescharacteristic
301C2×D8—91no—
302C2×D8—91no—
303C4⋊Q8—91no—
304#126—181no—
305#124—91no—
306#124—181no—
307#123—181no—
308C22⋊Q8—181no—
309C22⋊Q8C2×D911yescharacteristic
310#121—91no—
311C4×Q8—91no—
312C4×D4—91no—
313C4×D4—91no—
314C4×D4—91no—
315C4×D4—91no—
316C4×D4—91no—
317C4×D4—181no—
318C4×D4—181no—
319#117—91no—
320#117—91no—
321C2×C22⋊C4—181no—
322C2×C22⋊C4—181no—
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#102C2×D911yescharacteristic
336#102C2×D911yescharacteristic
337C22⋊C8—91no—
338C22⋊C8C2×D911yescharacteristic
339#97—91no—
340C4×C8—91no—
341C23×C3—24no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—81no—
345C23×C3—81no—
346C23×C3D3×D411yescharacteristic
347C22×D3—61no—
348C3×Q8—21no—
349C3×Q8—21no—
350C3×D4—24no—
351C3×D4—21no—
352C3×D4—21no—
353C3×D4#23712yes—
354C3×D4#23712yes—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361#67—241no—
362C2×Dic3—31no—
363C2×Dic3—31no—
364C2×Dic3—31no—
365C2×Dic3—31no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—241no—
370C2×Dic3—241no—
371C2×Dic3—241no—
372C2×Dic3—241no—
373D12—61no—
374D12—61no—
375C4×D3—241no—
376Dic6—241no—
377C3×C8—21no—
378C3×C8—21no—
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—181no—
390C2×Q8C22×D911yescharacteristic
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—21no—
394C2×D4—91no—
395C2×D4—181no—
396C2×D4C22×D911yescharacteristic
397C2×D4C22×D911yescharacteristic
398C22×C4—181no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4—181no—
403C22×C4C22×D911yescharacteristic
404SD16—22no—
405SD16—22no—
406D8—182no—
407D8—182no—
408C2×C8—91no—
409C2×C8—91no—
410C2×C8C22×D911yescharacteristic
411C2×C8C22×D911yescharacteristic
412C4⋊C4—21no—
413C4⋊C4—91no—
414C4⋊C4—91no—
415C4⋊C4—91no—
416C4⋊C4—91no—
417C4⋊C4—91no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4C22×D911yescharacteristic
421C22⋊C4—21no—
422C22⋊C4—91no—
423C22⋊C4—91no—
424C22⋊C4—181no—
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C42—91no—
434C42—91no—
435C42—181no—
436C42—181no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—22no—
441C22×C3—22no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—84no—
447C22×C3C2×D3×D411yescharacteristic
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—121no—
451C3×C4—21no—
452C3×C4—41no—
453C3×C4—41no—
454C3×C4C2×#23711yescharacteristic
455C3×C4C2×#23711yescharacteristic
456Dic3—61no—
457Dic3—61no—
458Dic3—61no—
459Dic3—61no—
460Dic3—121no—
461Dic3—121no—
462Dic3—121no—
463C9#311811yescharacteristic, complemented, Sylow
464C23—24no—
465C23—21no—
466C23—21no—
467C23—81no—
468C23—81no—
469C23—181no—
470C23D4×D911yescharacteristic
471Q8—21no—
472Q8—21no—
473Q8—721no—
474D4—24no—
475D4—21no—
476D4—21no—
477D4—181no—
478D4—181no—
479D4—721no—
480D4#369912yes—
481D4#369912yes—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—91no—
487C2×C4—91no—
488C2×C4—91no—
489C2×C4—91no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—721no—
494C2×C4—721no—
495C2×C4—721no—
496C2×C4—721no—
497C2×C4—721no—
498C2×C4D4×D911yescharacteristic
499C2×C4C23×D911yescharacteristic
500C8—21no—
501C8—21no—
502C8—181no—
503C8—181no—
504C2×C3—41no—
505C2×C3—42no—
506C2×C3—42no—
507C2×C3#558611yescharacteristic
508C2×C3#576211yescharacteristic
509C2×C3#577411yescharacteristic
510D3—241no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—22no—
515C22—22no—
516C22—41no—
517C22—41no—
518C22—41no—
519C22—41no—
520C22—84no—
521C22—361no—
522C22—361no—
523C22—361no—
524C22C2×D4×D911yescharacteristic
525C4—21no—
526C4—41no—
527C4—41no—
528C4—181no—
529C4—181no—
530C4—181no—
531C4—181no—
532C4—361no—
533C4—361no—
534C4—361no—
535C4C2×#369911yescharacteristic
536C4C2×#369911yescharacteristic
537C3#8013611yescharacteristic
538C2—41no—
539C2—42no—
540C2—42no—
541C2—721no—
542C2#1058968811yescharacteristic
543C2#1058986411yescharacteristic
544C2#1058987611yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#450C2
socleC22×C3C2×D3×D4
prime radical#10588898C2
hypercenter#450D9
hypocenterC9#3118
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #10589900C2semidirect
2. #10589745C2semidirect
3. C9×#450C2semidirect
5. #10588845C2semidirect
6. #10588845C2semidirect
7. #10588844C2semidirect
8. SD16×Dic9C2semidirect
9. #10588725C2semidirect
10. #10588465C2semidirect
11. #10588441C2semidirect
12. #10588439C2semidirect
13. #10588436C2semidirect
14. #10588419C2semidirect
15. #10588400C2semidirect
23. #63509C22semidirect
24. Q8×Dic9C22semidirect
38. #63455C22semidirect
39. #63450C22semidirect
45. #63395C22semidirect
46. #63395C22semidirect
50. #63380C22semidirect
51. #63380C22semidirect
52. #63378C22semidirect
53. #63377C22semidirect
54. #63375C22semidirect
55. Dic9⋊C8C22semidirect
56. Dic9⋊C8C22semidirect
57. C8×Dic9C22semidirect
58. #63367C22semidirect
59. #63366C22semidirect
216. #450D9semidirect
463. C9#3118semidirect

Maximal subgroups

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

subgroupindex
#105899002
#105897452
C9×#4502
#105888982
#105888452
#105888442
SD16×Dic92
#105887252
#105884652
#105884412
#105884392
#105884362
#105884192
#105884002
#801363