Finite Group Databasebeta

← #11872088

Subgroups — #11872088

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#10589663C211yesmaximal, characteristic, complemented
2#10589647C211yesmaximal, characteristic, complemented
3C4×C9×D8C211yesmaximal, characteristic, complemented
4#10588836C211yesmaximal, characteristic
5#10588833C211yesmaximal, characteristic, complemented
6#10588697C211yesmaximal, characteristic, complemented
7#10588694C211yesmaximal, characteristic, complemented
8#10588570C211yesmaximal, characteristic, complemented
9#10588568C211yesmaximal, characteristic, complemented
10#10588467C211yesmaximal, characteristic, complemented
11#10588459C211yesmaximal, characteristic, complemented
12#10588456C211yesmaximal, characteristic, complemented
13#10588441C211yesmaximal, characteristic, complemented
14C4×#3664C211yesmaximal, characteristic, complemented
15#10588372C211yesmaximal, characteristic, complemented
16#79594—31nomaximal
17C2×D4×D9C2211yescharacteristic
18C2×C9×D8C2211yescharacteristic
19C4×D4×C9C2211yescharacteristic
20C4×D4×C9C2211yescharacteristic, complemented
21#63500C2211yescharacteristic
22#63498C2211yescharacteristic, complemented
23D4×Dic9C2211yescharacteristic
24C2×#3673C2211yescharacteristic
25C2×#3672C2211yescharacteristic
26#63491—21no—
27C4×#611—21no—
28C2×(C2×D9)⋊C4—21no—
29#63486—21no—
30C2×#3664C2211yescharacteristic
31#63459C2211yescharacteristic
32#63455C2211yescharacteristic
33#63454C2211yescharacteristic
34#63450C2211yescharacteristic, complemented
35#63447—21no—
36#611⋊C4—21no—
37C22⋊C4×D9—21no—
38#63441—21no—
39C4×D36C2211yescharacteristic
40#63434C2211yescharacteristic
41C4×Dic18C2211yescharacteristic, complemented
42C9×#107C2211yescharacteristic, complemented
43C9×#102C2211yescharacteristic
44C9×#102C2211yescharacteristic, complemented
45C4×C8×C9C2211yescharacteristic, complemented
46#63392C2211yescharacteristic
47#63392C2211yescharacteristic, complemented
48#63380C2211yescharacteristic
49(C2×D9)⋊C8C2211yescharacteristic
50(C2×D9)⋊C8C2211yescharacteristic
51#63377C2211yescharacteristic, complemented
52#63376C2211yescharacteristic, complemented
53Dic9⋊C8C2211yescharacteristic, complemented
54Dic9⋊C8C2211yescharacteristic, complemented
55#63369C2211yescharacteristic
56#63368C2211yescharacteristic, complemented
57#63367C2211yescharacteristic, complemented
58#63366C2211yescharacteristic, complemented
59#63362C2211yescharacteristic, complemented
60#5561—31no—
61#5545—31no—
62C3×C4×D8D311yescharacteristic
63#5156—31no—
64#5153—31no—
65#5018—31no—
66#5014—31no—
67#4890—31no—
68#4888—31no—
69#4787—31no—
70#4779—31no—
71#4776—31no—
72#4761—31no—
73C4×#204—31no—
74#4690—31no—
75C23×D9—21no—
76C2×D4×C9C2311yescharacteristic
77C2×D4×C9C2311yescharacteristic
78C22×C4×C9—21no—
79C22×C4×C9—21no—
80C2×#611—21no—
81C2×#611—21no—
82C22×Dic9—21no—
83D4×D9—22no—
84D4×D9—22no—
85C2×D36C2311yescharacteristic
86C2×C4×D9—21no—
87C2×C4×D9—21no—
88C2×C4×D9C2311yescharacteristic
89C2×Dic18—21no—
90C2×Dic18C2311yescharacteristic
91C9×D8—22no—
92C2×C8×C9C2311yescharacteristic
93C2×C8×C9C2311yescharacteristic
94C9×C4⋊C4C2311yescharacteristic
95C9×C4⋊C4C2311yescharacteristic
96C9×C22⋊C4—21no—
97C9×C22⋊C4—21no—
98C42×C9C2311yescharacteristic
99#3676—21no—
100#3676—21no—
101#3676—21no—
102#3676—21no—
103#3673—22no—
104#3672—22no—
105(C2×D9)⋊C4—21no—
106(C2×D9)⋊C4—21no—
107(C2×D9)⋊C4—21no—
108(C2×D9)⋊C4—21no—
109(C2×D9)⋊C4D411yescharacteristic
110(C2×D9)⋊C4D411yescharacteristic
111C4⋊Dic9—21no—
112C4⋊Dic9C2311yescharacteristic
113C4⋊Dic9C2311yescharacteristic
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116Dic9⋊C4D411yescharacteristic
117Dic9⋊C4D411yescharacteristic
118C4×Dic9—21no—
119C4×Dic9—21no—
120C4×Dic9C2311yescharacteristic
121C2×C9⋊C8C2311yescharacteristic
122C2×C9⋊C8C2311yescharacteristic
123#3664—22no—
124#3118—91noSylow
125C2×D3×D4—31no—
126C2×C3×D8C2×D311yescharacteristic
127C3×C4×D4C2×D311yescharacteristic
128C3×C4×D4C2×D311yescharacteristic
129#938—31no—
130#936—31no—
131D4×Dic3—31no—
132C2×#214—31no—
133C2×#213—31no—
134#929—61no—
135C4×#67—61no—
136C2×(C2×D3)⋊C4—61no—
137#924—61no—
138C2×#204—31no—
139#897—31no—
140#893—31no—
141#892—31no—
142#888—31no—
143#885—61no—
144#67⋊C4—61no—
145D3×C22⋊C4—61no—
146#879—61no—
147C4×D12—31no—
148#872—31no—
149C4×Dic6—31no—
150C3×#107C2×D311yescharacteristic
151C3×#102C2×D311yescharacteristic
152C3×#102C2×D311yescharacteristic
153C3×C4×C8C2×D311yescharacteristic
154#832—31no—
155#832—31no—
156#821—31no—
157(C2×D3)⋊C8—31no—
158(C2×D3)⋊C8—31no—
159#817—31no—
160#816—31no—
161Dic3⋊C8—31no—
162Dic3⋊C8—31no—
163#810—31no—
164#809—31no—
165#808—31no—
166#807—31no—
167#803—31no—
168C23×C9—21no—
169C23×C9—21no—
170C22×D9—21no—
171C22×D9—24no—
172C22×D9—81no—
173C22×D9—81no—
174C22×D9C2×D411yescharacteristic
175D4×C9—21no—
176D4×C9—21no—
177D4×C9—21no—
178D4×C9#4112yes—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
181C2×C4×C9—81no—
182C2×C4×C9—81no—
183C2×C4×C9C2×D411yescharacteristic
184C2×C4×C9C2×D411yescharacteristic
185C2×C4×C9C2411yescharacteristic
186#611—24no—
187#611—81no—
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9—21no—
191C2×Dic9—81no—
192C2×Dic9C2×D411yescharacteristic
193C2×Dic9C2×D411yescharacteristic
194C2×Dic9C2×D411yescharacteristic
195D36—21no—
196D36#4112yes—
197C4×D9—21no—
198C4×D9—21no—
199C4×D9—81no—
200C4×D9—81no—
201Dic18—21no—
202Dic18—21no—
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#450—91no—
217#447—91no—
218#442—91no—
219#440—91no—
220C4×SD16—91no—
221C4×D8D911yescharacteristic, complemented
222#433—91no—
223C23×D3—61no—
224C2×C3×D4C22×D311yescharacteristic
225C2×C3×D4C22×D311yescharacteristic
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C2×#67—61no—
229C2×#67—61no—
230C22×Dic3—61no—
231D3×D4—62no—
232D3×D4—62no—
233C2×D12—31no—
234C2×C4×D3—31no—
235C2×C4×D3—61no—
236C2×C4×D3—61no—
237C2×Dic6—31no—
238C2×Dic6—61no—
239C3×D8—22no—
240C2×C3×C8C22×D311yescharacteristic
241C2×C3×C8C22×D311yescharacteristic
242C3×C4⋊C4C22×D311yescharacteristic
243C3×C4⋊C4C22×D311yescharacteristic
244C3×C22⋊C4—21no—
245C3×C22⋊C4—21no—
246C3×C42C22×D311yescharacteristic
247#217—61no—
248#217—61no—
249#217—61no—
250#217—61no—
251#214—62no—
252#213—62no—
253(C2×D3)⋊C4—31no—
254(C2×D3)⋊C4—31no—
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—61no—
262Dic3⋊C4—31no—
263Dic3⋊C4—31no—
264Dic3⋊C4—61no—
265Dic3⋊C4—61no—
266C4×Dic3—31no—
267C4×Dic3—61no—
268C4×Dic3—61no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271#204—62no—
272C22×C9—22no—
273C22×C9—41no—
274C22×C9—41no—
275C22×C9—41no—
276C22×C9—41no—
277C22×C9—41no—
278C22×C9C22×D411yescharacteristic
279C2×D9—21no—
280C2×D9—22no—
281C2×D9—21no—
282C2×D9—21no—
283C2×D9—41no—
284C2×D9—41no—
285C2×D9—84no—
286C4×C9—21no—
287C4×C9—21no—
288C4×C9—41no—
289C4×C9—41no—
290C4×C9C2×#4111yescharacteristic
291C4×C9C2×#4111yescharacteristic
292Dic9—21no—
293Dic9—21no—
294Dic9—21no—
295Dic9—41no—
296Dic9—41no—
297Dic9—41no—
298C22×D4—91no—
299C2×SD16—91no—
300C2×SD16—91no—
301C2×D8—91no—
302C2×D8C2×D911yescharacteristic
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—91no—
313C4×D4—91no—
314C4×D4—91no—
315C4×D4—181no—
316C4×D4—181no—
317C4×D4C2×D911yescharacteristic
318C4×D4C2×D911yescharacteristic, complemented
319#117—91no—
320#117—91no—
321C2×C22⋊C4—181no—
322C2×C22⋊C4—181no—
323#107—91no—
324#107C2×D911yescharacteristic, complemented
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, complemented
337C22⋊C8—91no—
338C22⋊C8—91no—
339#97—91no—
340C4×C8C2×D911yescharacteristic, complemented
341C23×C3—21no—
342C23×C3—21no—
343C22×D3—31no—
344C22×D3—61no—
345C22×D3—64no—
346C22×D3—241no—
347C22×D3—241no—
348C3×D4—21no—
349C3×D4—21no—
350C3×D4—21no—
351C3×D4#23512yes—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—81no—
355C2×C3×C4—81no—
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359#67—64no—
360#67—241no—
361C2×Dic3—31no—
362C2×Dic3—31no—
363C2×Dic3—31no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—241no—
368D12—32no—
369D12—61no—
370C4×D3—61no—
371C4×D3—61no—
372C4×D3—241no—
373C4×D3—241no—
374Dic6—61no—
375Dic6—61no—
376Dic6—241no—
377C3×C8—21no—
378C3×C8—21no—
379C3⋊C8—61no—
380C3⋊C8—61no—
381C2×C9—42no—
382C2×C9—81no—
383C2×C9#52511yescharacteristic
384C2×C9#57611yescharacteristic
385C2×C9#57711yescharacteristic
386D9—41no—
387D9—42no—
388C24—181no—
389C2×Q8—91no—
390C2×Q8—181no—
391C2×D4—91no—
392C2×D4—181no—
393C2×D4—182no—
394C2×D4—182no—
395C2×D4—181no—
396C2×D4C22×D911yescharacteristic
397C2×D4C22×D911yescharacteristic
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—91no—
401C22×C4—181no—
402C22×C4—181no—
403C22×C4—181no—
404SD16—182no—
405SD16—182no—
406D8—22no—
407D8—182no—
408C2×C8—91no—
409C2×C8—91no—
410C2×C8C22×D911yescharacteristic
411C2×C8C22×D911yescharacteristic
412C4⋊C4—91no—
413C4⋊C4—91no—
414C4⋊C4—91no—
415C4⋊C4—91no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
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—91no—
434C42—181no—
435C42—181no—
436C42C22×D911yescharacteristic
437C22×C3—22no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3C2×D3×D411yescharacteristic
444C2×D3—61no—
445C2×D3—61no—
446C2×D3—61no—
447C2×D3—62no—
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—244no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—41no—
454C3×C4—41no—
455C3×C4C2×#23511yescharacteristic
456C3×C4D3×#4111yescharacteristic
457Dic3—61no—
458Dic3—61no—
459Dic3—61no—
460Dic3—121no—
461Dic3—121no—
462Dic3—121no—
463C9#311811yescharacteristic, complemented, Sylow
464C23—21no—
465C23—21no—
466C23—91no—
467C23—184no—
468C23—181no—
469C23—721no—
470C23—721no—
471Q8—181no—
472Q8—181no—
473Q8—721no—
474D4—21no—
475D4—21no—
476D4—21no—
477D4—92no—
478D4—184no—
479D4—181no—
480D4—721no—
481D4#369712yes—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4—91no—
487C2×C4—91no—
488C2×C4—91no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—181no—
494C2×C4—721no—
495C2×C4—721no—
496C2×C4—721no—
497C2×C4D4×D911yescharacteristic
498C2×C4D4×D911yescharacteristic
499C2×C4C23×D911yescharacteristic
500C8—21no—
501C8—21no—
502C8—181no—
503C8—181no—
504C2×C3—42no—
505C2×C3—81no—
506C2×C3#554711yescharacteristic
507C2×C3#575711yescharacteristic
508C2×C3#577011yescharacteristic
509D3—121no—
510D3—122no—
511C22—22no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—181no—
518C22—181no—
519C22—181no—
520C22—182no—
521C22—361no—
522C22—361no—
523C22—724no—
524C22C2×D4×D911yescharacteristic
525C4—21no—
526C4—21no—
527C4—41no—
528C4—41no—
529C4—181no—
530C4—181no—
531C4—181no—
532C4—361no—
533C4—361no—
534C4—361no—
535C4C2×#369711yescharacteristic
536C4#41×D911yescharacteristic
537C3#7959411yescharacteristic
538C2—42no—
539C2—81no—
540C2—361no—
541C2—362no—
542C2#1058964911yescharacteristic
543C2#1058985911yescharacteristic
544C2#1058987211yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC4×C9×D8C2
socleC22×C3C2×D3×D4
prime radical#10588836C2
hypercenterC4×D8D9
hypocenterC9#3118
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #10589663C2semidirect
2. #10589647C2semidirect
3. C4×C9×D8C2semidirect
5. #10588833C2semidirect
6. #10588697C2semidirect
7. #10588694C2semidirect
8. #10588570C2semidirect
9. #10588568C2semidirect
10. #10588467C2semidirect
11. #10588459C2semidirect
12. #10588456C2semidirect
13. #10588441C2semidirect
14. C4×#3664C2semidirect
15. #10588372C2semidirect
20. C4×D4×C9C22semidirect
22. #63498C22semidirect
34. #63450C22semidirect
41. C4×Dic18C22semidirect
42. C9×#107C22semidirect
44. C9×#102C22semidirect
45. C4×C8×C9C22semidirect
47. #63392C22semidirect
51. #63377C22semidirect
52. #63376C22semidirect
53. Dic9⋊C8C22semidirect
54. Dic9⋊C8C22semidirect
56. #63368C22semidirect
57. #63367C22semidirect
58. #63366C22semidirect
59. #63362C22semidirect
221. C4×D8D9semidirect
318. C4×D4C2×D9semidirect
324. #107C2×D9semidirect
336. #102C2×D9semidirect
340. C4×C8C2×D9semidirect
463. C9#3118semidirect

Maximal subgroups

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

subgroupindex
#105896632
#105896472
C4×C9×D82
#105888362
#105888332
#105886972
#105886942
#105885702
#105885682
#105884672
#105884592
#105884562
#105884412
C4×#36642
#105883722
#795943