Finite Group Databasebeta

← #11872109

Subgroups — #11872109

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#10589745C211yesmaximal, characteristic, complemented
2#10589623C211yesmaximal, characteristic, complemented
3C9×#485C211yesmaximal, characteristic, complemented
4#10588729C211yesmaximal, characteristic, complemented
5#10588684C211yesmaximal, characteristic, complemented
6#10588570C211yesmaximal, characteristic, complemented
7#10588552C211yesmaximal, characteristic, complemented
8#10588550C211yesmaximal, characteristic, complemented
9#10588549C211yesmaximal, characteristic, complemented
10#10588499C211yesmaximal, characteristic, complemented
11#10588499C211yesmaximal, characteristic, complemented
12#10588497C211yesmaximal, characteristic, complemented
13#10588468C211yesmaximal, characteristic, complemented
14#10588414C211yesmaximal, characteristic
15#10588400C211yesmaximal, characteristic, complemented
16#81496—31nomaximal
17C22×D36C2211yescharacteristic
18C9×C22⋊Q8C2211yescharacteristic
19C9×#117C2211yescharacteristic
20#63509C2211yescharacteristic, complemented
21Q8×Dic9C2211yescharacteristic, complemented
22C2×#3675C2211yescharacteristic
23C2×#3675C2211yescharacteristic
24#63492C2211yescharacteristic
25#63488C2211yescharacteristic
26C2×D72C2211yescharacteristic
27C2×D72C2211yescharacteristic
28#63460—21no—
29#63459—21no—
30#63455C2211yescharacteristic
31#63455C2211yescharacteristic
32#63455C2211yescharacteristic
33#63455C2211yescharacteristic
34#63455C2211yescharacteristic, complemented
35#63450C2211yescharacteristic, complemented
36#63447—21no—
37#63445—21no—
38C22⋊C4×D9—21no—
39C22⋊C4×D9—21no—
40C4×D36—21no—
41C4×D36—21no—
42C9×#107C2211yescharacteristic, complemented
43C9×#106C2211yescharacteristic, complemented
44C9×#103C2211yescharacteristic, complemented
45C9×#103C2211yescharacteristic, complemented
46C9×C22⋊C8C2211yescharacteristic
47#63389C2211yescharacteristic
48#63380C2211yescharacteristic
49#63380C2211yescharacteristic
50#63375C2211yescharacteristic, complemented
51Dic9⋊C8C2211yescharacteristic, complemented
52Dic9⋊C8C2211yescharacteristic, complemented
53C8×Dic9C2211yescharacteristic, complemented
54#63369C2211yescharacteristic
55#63369C2211yescharacteristic
56#63369C2211yescharacteristic, complemented
57#63369C2211yescharacteristic, complemented
58#63367C2211yescharacteristic, complemented
59#63366C2211yescharacteristic, complemented
60#5643—31no—
61#5521—31no—
62C3×#485D311yescharacteristic
63#5046—31no—
64#5003—31no—
65#4890—31no—
66#4872—31no—
67#4870—31no—
68#4869—31no—
69#4819—31no—
70#4819—31no—
71#4817—31no—
72#4788—31no—
73#4732—31no—
74#4720—31no—
75C23×D9—21no—
76C2×Q8×C9C2311yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C2×#611—21no—
79C2×D36—21no—
80C2×D36—22no—
81C2×D36—22no—
82C2×D36C2311yescharacteristic
83C2×D36C2311yescharacteristic
84C2×D36C2311yescharacteristic
85C2×C4×D9—21no—
86C2×C4×D9—21no—
87C2×C4×D9—21no—
88C2×C4×D9—21no—
89C2×C4×D9—21no—
90C2×Dic18—21no—
91C2×C8×C9C2311yescharacteristic
92C2×C8×C9C2311yescharacteristic
93C9×C4⋊C4—21no—
94C9×C4⋊C4C2311yescharacteristic
95C9×C4⋊C4C2311yescharacteristic
96C9×C4⋊C4C2311yescharacteristic
97C9×C22⋊C4—21no—
98C9×C22⋊C4—21no—
99C42×C9—21no—
100#3676D411yescharacteristic
101#3676D411yescharacteristic
102#3675—22no—
103#3675—22no—
104(C2×D9)⋊C4—21no—
105(C2×D9)⋊C4—21no—
106(C2×D9)⋊C4—21no—
107(C2×D9)⋊C4—21no—
108(C2×D9)⋊C4—21no—
109(C2×D9)⋊C4—21no—
110(C2×D9)⋊C4—21no—
111(C2×D9)⋊C4—21no—
112C4⋊Dic9—21no—
113C4⋊Dic9D411yescharacteristic
114C4⋊Dic9D411yescharacteristic
115C4⋊Dic9C2311yescharacteristic
116Dic9⋊C4—21no—
117C4×Dic9—21no—
118C4×Dic9C2311yescharacteristic
119C4×Dic9C2311yescharacteristic
120C2×C9⋊C8C2311yescharacteristic
121C2×C9⋊C8C2311yescharacteristic
122D72—22no—
123D72—22no—
124#3118—91noSylow
125C22×D12—31no—
126C3×C22⋊Q8C2×D311yescharacteristic
127C3×#117C2×D311yescharacteristic
128#947—31no—
129Q8×Dic3—31no—
130C2×#215—31no—
131C2×#215—31no—
132#930—31no—
133#926—31no—
134C2×D24—31no—
135C2×D24—31no—
136#898—61no—
137#897—61no—
138#893—31no—
139#893—31no—
140#893—31no—
141#893—31no—
142#893—31no—
143#888—31no—
144#885—61no—
145#883—61no—
146D3×C22⋊C4—61no—
147D3×C22⋊C4—61no—
148C4×D12—61no—
149C4×D12—61no—
150C3×#107C2×D311yescharacteristic
151C3×#106C2×D311yescharacteristic
152C3×#103C2×D311yescharacteristic
153C3×#103C2×D311yescharacteristic
154C3×C22⋊C8C2×D311yescharacteristic
155#830—31no—
156#821—31no—
157#821—31no—
158#815—31no—
159Dic3⋊C8—31no—
160Dic3⋊C8—31no—
161C8×Dic3—31no—
162#809—31no—
163#809—31no—
164#809—31no—
165#809—31no—
166#808—31no—
167#807—31no—
168C23×C9C2×D411yescharacteristic
169C22×D9—21no—
170C22×D9—21no—
171C22×D9—24no—
172C22×D9—21no—
173C22×D9—81no—
174C22×D9—81no—
175Q8×C9—21no—
176Q8×C9—21no—
177C2×C4×C9—21no—
178C2×C4×C9—21no—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9C2×D411yescharacteristic
184C2×C4×C9C2411yescharacteristic
185#611—81no—
186C2×Dic9—21no—
187C2×Dic9C2×D411yescharacteristic
188C2×Dic9C2×D411yescharacteristic
189C2×Dic9C2×D411yescharacteristic
190C2×Dic9C2×D411yescharacteristic
191D36—24no—
192D36—21no—
193D36—21no—
194D36—21no—
195D36—21no—
196D36#4112yes—
197D36#4112yes—
198C4×D9—81no—
199C4×D9—81no—
200C4×D9—81no—
201C4×D9—81no—
202C4×D9—81no—
203Dic18—81no—
204C8×C9—21no—
205C8×C9—21no—
206C9⋊C8—21no—
207C9⋊C8—21no—
208#542—91no—
209#518—91no—
210#485D911yescharacteristic, complemented
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—
223C23×D3—61no—
224C2×C3×Q8C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C2×#67—61no—
227C2×D12—31no—
228C2×D12—31no—
229C2×D12—31no—
230C2×D12—62no—
231C2×D12—62no—
232C2×D12—61no—
233C2×C4×D3—61no—
234C2×C4×D3—61no—
235C2×C4×D3—61no—
236C2×C4×D3—61no—
237C2×C4×D3—61no—
238C2×Dic6—61no—
239C2×C3×C8C22×D311yescharacteristic
240C2×C3×C8C22×D311yescharacteristic
241C3×C4⋊C4—21no—
242C3×C4⋊C4C22×D311yescharacteristic
243C3×C4⋊C4C22×D311yescharacteristic
244C3×C4⋊C4C22×D311yescharacteristic
245C3×C22⋊C4—21no—
246C3×C22⋊C4—21no—
247C3×C42—21no—
248#217—31no—
249#217—31no—
250#215—62no—
251#215—62no—
252(C2×D3)⋊C4—61no—
253(C2×D3)⋊C4—61no—
254(C2×D3)⋊C4—61no—
255(C2×D3)⋊C4—61no—
256(C2×D3)⋊C4—61no—
257(C2×D3)⋊C4—61no—
258(C2×D3)⋊C4—61no—
259(C2×D3)⋊C4—61no—
260C4⋊Dic3—31no—
261C4⋊Dic3—31no—
262C4⋊Dic3—31no—
263C4⋊Dic3—61no—
264Dic3⋊C4—61no—
265C4×Dic3—31no—
266C4×Dic3—31no—
267C4×Dic3—61no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—31no—
270D24—62no—
271D24—62no—
272C22×C9—21no—
273C22×C9—21no—
274C22×C9—21no—
275C22×C9C22×D411yescharacteristic
276C2×D9—22no—
277C2×D9—22no—
278C2×D9—41no—
279C2×D9—41no—
280C2×D9—41no—
281C2×D9—41no—
282C2×D9—41no—
283C2×D9—41no—
284C2×D9—41no—
285C2×D9—84no—
286C4×C9—21no—
287C4×C9—41no—
288C4×C9—41no—
289C4×C9—41no—
290C4×C9—41no—
291C4×C9C2×#4111yescharacteristic
292C4×C9C2×#4111yescharacteristic
293Dic9—21no—
294Dic9—21no—
295Dic9—21no—
296Dic9—21no—
297Dic9—41no—
298C22×D4—91no—
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—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#117C2×D911yescharacteristic
321C2×C22⋊C4—181no—
322C2×C22⋊C4—181no—
323#107—91no—
324#107C2×D911yescharacteristic, complemented
325#106—91no—
326#106C2×D911yescharacteristic, complemented
327C4⋊C8—91no—
328C4⋊C8—91no—
329#103C2×D911yescharacteristic, complemented
330#103C2×D911yescharacteristic, complemented
331#102—91no—
332#102—91no—
333#102—91no—
334#102—91no—
335#102—91no—
336#102—91no—
337C22⋊C8—91no—
338C22⋊C8C2×D911yescharacteristic
339#97—91no—
340C4×C8—91no—
341C23×C3D3×D411yescharacteristic
342C22×D3—61no—
343C22×D3—61no—
344C22×D3—64no—
345C22×D3—61no—
346C22×D3—241no—
347C22×D3—241no—
348C3×Q8—21no—
349C3×Q8—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358#67—241no—
359C2×Dic3—31no—
360C2×Dic3—31no—
361C2×Dic3—31no—
362C2×Dic3—31no—
363C2×Dic3—61no—
364D12—32no—
365D12—32no—
366D12—64no—
367D12—61no—
368D12—61no—
369D12—61no—
370D12—61no—
371C4×D3—241no—
372C4×D3—241no—
373C4×D3—241no—
374C4×D3—241no—
375C4×D3—241no—
376Dic6—241no—
377C3×C8—21no—
378C3×C8—21no—
379C3⋊C8—61no—
380C3⋊C8—61no—
381C2×C9—41no—
382C2×C9#52511yescharacteristic
383C2×C9#57611yescharacteristic
384C2×C9#57711yescharacteristic
385D9—42no—
386D9—42no—
387D9—81no—
388C24—181no—
389C2×Q8—181no—
390C2×Q8C22×D911yescharacteristic
391C2×D4—91no—
392C2×D4—91no—
393C2×D4—91no—
394C2×D4—182no—
395C2×D4—182no—
396C2×D4—181no—
397C2×D4—181no—
398C22×C4—181no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4—181no—
403C22×C4C22×D911yescharacteristic
404SD16—182no—
405SD16—182no—
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—181no—
417C4⋊C4—181no—
418C4⋊C4C22×D911yescharacteristic
419C4⋊C4C22×D911yescharacteristic
420C4⋊C4C22×D911yescharacteristic
421C22⋊C4—21no—
422C22⋊C4—21no—
423C22⋊C4—91no—
424C22⋊C4—91no—
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—21no—
434C42—91no—
435C42—91no—
436C42—181no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3C2×D3×D411yescharacteristic
441C2×D3—62no—
442C2×D3—62no—
443C2×D3—121no—
444C2×D3—121no—
445C2×D3—121no—
446C2×D3—121no—
447C2×D3—121no—
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—244no—
451C3×C4—21no—
452C3×C4—41no—
453C3×C4—41no—
454C3×C4—41no—
455C3×C4—41no—
456C3×C4D3×#4111yescharacteristic
457C3×C4D3×#4111yescharacteristic
458Dic3—61no—
459Dic3—61no—
460Dic3—61no—
461Dic3—61no—
462Dic3—121no—
463C9#311811yescharacteristic, complemented, Sylow
464C23—184no—
465C23—181no—
466C23—181no—
467C23—181no—
468C23—721no—
469C23—721no—
470C23D4×D911yescharacteristic
471Q8—21no—
472Q8—21no—
473Q8—721no—
474D4—92no—
475D4—92no—
476D4—184no—
477D4—181no—
478D4—181no—
479D4—181no—
480D4—181no—
481D4—721no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—91no—
489C2×C4—91no—
490C2×C4—91no—
491C2×C4—91no—
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#565611yescharacteristic
506C2×C3#576911yescharacteristic
507C2×C3#577811yescharacteristic
508D3—122no—
509D3—122no—
510D3—241no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—182no—
515C22—182no—
516C22—361no—
517C22—361no—
518C22—361no—
519C22—361no—
520C22—361no—
521C22—361no—
522C22—361no—
523C22—724no—
524C22C2×D4×D911yescharacteristic
525C4—21no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—181no—
531C4—181no—
532C4—181no—
533C4—181no—
534C4—361no—
535C4#41×D911yescharacteristic
536C4#41×D911yescharacteristic
537C3#8149611yescharacteristic
538C2—41no—
539C2—362no—
540C2—362no—
541C2—721no—
542C2#1058975811yescharacteristic
543C2#1058987111yescharacteristic
544C2#1058988011yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#485C2
socleC22×C3C2×D3×D4
prime radical#10588414C2
hypercenter#485D9
hypocenterC9#3118
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #10589745C2semidirect
2. #10589623C2semidirect
3. C9×#485C2semidirect
4. #10588729C2semidirect
5. #10588684C2semidirect
6. #10588570C2semidirect
7. #10588552C2semidirect
8. #10588550C2semidirect
9. #10588549C2semidirect
10. #10588499C2semidirect
11. #10588499C2semidirect
12. #10588497C2semidirect
13. #10588468C2semidirect
15. #10588400C2semidirect
20. #63509C22semidirect
21. Q8×Dic9C22semidirect
34. #63455C22semidirect
35. #63450C22semidirect
42. C9×#107C22semidirect
43. C9×#106C22semidirect
44. C9×#103C22semidirect
45. C9×#103C22semidirect
50. #63375C22semidirect
51. Dic9⋊C8C22semidirect
52. Dic9⋊C8C22semidirect
53. C8×Dic9C22semidirect
56. #63369C22semidirect
57. #63369C22semidirect
58. #63367C22semidirect
59. #63366C22semidirect
210. #485D9semidirect
324. #107C2×D9semidirect
326. #106C2×D9semidirect
329. #103C2×D9semidirect
330. #103C2×D9semidirect
463. C9#3118semidirect

Maximal subgroups

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

subgroupindex
#105897452
#105896232
C9×#4852
#105887292
#105886842
#105885702
#105885522
#105885502
#105885492
#105884992
#105884972
#105884682
#105884142
#105884002
#814963