Finite Group Databasebeta

← #11869652

Subgroups — #11869652

Order 1152.

630 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589729C211yesmaximal, characteristic
2D9×#117C211yesmaximal, characteristic, complemented
3C9×#485C211yesmaximal, characteristic, complemented
4#10588725C211yesmaximal, characteristic, complemented
5#10588684C211yesmaximal, characteristic, complemented
6#10588562C211yesmaximal, characteristic, complemented
7#10588560C211yesmaximal, characteristic, complemented
8#10588543C211yesmaximal, characteristic, complemented
9#10588540C211yesmaximal, characteristic, complemented
10#10588491C211yesmaximal, characteristic, complemented
11#10588485C211yesmaximal, characteristic, complemented
12#10588484C211yesmaximal, characteristic, complemented
13#10588484C211yesmaximal, characteristic, complemented
14#10588419C211yesmaximal, characteristic, complemented
15D9×C22⋊C8C211yesmaximal, characteristic, complemented
16#81515—31nomaximal
17C2×#3701C2211yescharacteristic
18C22×C4×D9C2211yescharacteristic
19C9×C22⋊Q8C2211yescharacteristic
20C9×#117C2211yescharacteristic
21#63508C2211yescharacteristic
22#63492C2211yescharacteristic
23#63488C2211yescharacteristic
24C2×C8×D9C2211yescharacteristic
25C2×C8×D9C2211yescharacteristic
26#63457C2211yescharacteristic
27#63456—21no—
28#63455—21no—
29#63454C2211yescharacteristic
30#63454C2211yescharacteristic
31#63454C2211yescharacteristic
32C4⋊C4×D9C2211yescharacteristic
33C4⋊C4×D9C2211yescharacteristic
34#63444—21no—
35#611⋊C4—21no—
36C22⋊C4×D9—21no—
37#63439—21no—
38#63434—21no—
39C42×D9—21no—
40C9×#107C2211yescharacteristic, complemented
41C9×#106C2211yescharacteristic, complemented
42C9×#103C2211yescharacteristic, complemented
43C9×#103C2211yescharacteristic, complemented
44C9×C22⋊C8C2211yescharacteristic
45#63395C2211yescharacteristic, complemented
46#63395C2211yescharacteristic, complemented
47#63389C2211yescharacteristic
48#63380C2211yescharacteristic, complemented
49#63380C2211yescharacteristic, complemented
50(C2×D9)⋊C8C2211yescharacteristic
51(C2×D9)⋊C8C2211yescharacteristic
52#63378C2211yescharacteristic, complemented
53#63377C2211yescharacteristic, complemented
54#63369C2211yescharacteristic, complemented
55#63369C2211yescharacteristic, complemented
56#63367C2211yescharacteristic, complemented
57#63367C2211yescharacteristic, complemented
58#63366C2211yescharacteristic, complemented
59#63366C2211yescharacteristic, complemented
60#5627—31no—
61D3×#117—31no—
62C3×#485D311yescharacteristic
63#5045—31no—
64#5003—31no—
65#4882—31no—
66#4880—31no—
67#4863—31no—
68#4860—31no—
69#4811—31no—
70#4805—31no—
71#4804—31no—
72#4804—31no—
73#4737—31no—
74D3×C22⋊C8—31no—
75C23×D9D411yescharacteristic
76C2×Q8×C9C2311yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C2×#611—21no—
79C22×Dic9D411yescharacteristic
80#3701—22no—
81#3701—22no—
82C2×D36—21no—
83C2×D36—21no—
84C2×D36C2311yescharacteristic
85C2×C4×D9—22no—
86C2×C4×D9—22no—
87C2×C4×D9—21no—
88C2×C4×D9—21no—
89C2×C4×D9—21no—
90C2×C4×D9D411yescharacteristic
91C2×C4×D9D411yescharacteristic
92C2×C4×D9C2311yescharacteristic
93C2×C4×D9C2311yescharacteristic
94C2×C8×C9C2311yescharacteristic
95C2×C8×C9C2311yescharacteristic
96C9×C4⋊C4—21no—
97C9×C4⋊C4C2311yescharacteristic
98C9×C4⋊C4C2311yescharacteristic
99C9×C4⋊C4C2311yescharacteristic
100C9×C22⋊C4—21no—
101C9×C22⋊C4—21no—
102C42×C9—21no—
103#3676—21no—
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—
110C4⋊Dic9C2311yescharacteristic
111C4⋊Dic9C2311yescharacteristic
112C4⋊Dic9C2311yescharacteristic
113Dic9⋊C4—21no—
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116C4×Dic9—21no—
117C4×Dic9—21no—
118C4×Dic9—21no—
119C4×Dic9—21no—
120C2×C9⋊C8C2311yescharacteristic
121C2×C9⋊C8C2311yescharacteristic
122C8×D9—22no—
123C8×D9—22no—
124#3091—91noSylow
125C2×#239—31no—
126C22×C4×D3—31no—
127C3×C22⋊Q8C2×D311yescharacteristic
128C3×#117C2×D311yescharacteristic
129#946—31no—
130#930—31no—
131#926—31no—
132C2×D3×C8—31no—
133C2×D3×C8—31no—
134#895—31no—
135#894—61no—
136#893—61no—
137#892—31no—
138#892—31no—
139#892—31no—
140D3×C4⋊C4—31no—
141D3×C4⋊C4—31no—
142#882—61no—
143#67⋊C4—61no—
144D3×C22⋊C4—61no—
145#877—61no—
146#872—61no—
147C42×D3—61no—
148C3×#107C2×D311yescharacteristic
149C3×#106C2×D311yescharacteristic
150C3×#103C2×D311yescharacteristic
151C3×#103C2×D311yescharacteristic
152C3×C22⋊C8C2×D311yescharacteristic
153#835—31no—
154#835—31no—
155#830—31no—
156#821—31no—
157#821—31no—
158(C2×D3)⋊C8—31no—
159(C2×D3)⋊C8—31no—
160#818—31no—
161#817—31no—
162#809—31no—
163#809—31no—
164#808—31no—
165#808—31no—
166#807—31no—
167#807—31no—
168C23×C9C2×D411yescharacteristic
169C22×D9—22no—
170C22×D9—22no—
171C22×D9—21no—
172C22×D9—41no—
173C22×D9C2×D411yescharacteristic
174C22×D9C2×D411yescharacteristic
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—42no—
186C2×Dic9—22no—
187C2×Dic9—21no—
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9C2×D411yescharacteristic
191C2×Dic9C2×D411yescharacteristic
192D36—21no—
193D36—21no—
194D36—42no—
195D36—42no—
196C4×D9—22no—
197C4×D9—21no—
198C4×D9—21no—
199C4×D9—22no—
200C4×D9—42no—
201C4×D9—42no—
202C4×D9—42no—
203C4×D9#4112yes—
204C4×D9#4112yes—
205C8×C9—21no—
206C8×C9—21no—
207C9⋊C8—21no—
208C9⋊C8—21no—
209#525—91no—
210C2×#117—91no—
211#485—91no—
212#485D911yescharacteristic, complemented
213#484—91no—
214#483—91no—
215#482—91no—
216#482—91no—
217#481—91no—
218#480—91no—
219#427—91no—
220#427—91no—
221#416—91no—
222#416—91no—
223C2×C22⋊C8—91no—
224C23×D3—31no—
225C2×C3×Q8C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C2×#67—61no—
228C22×Dic3—31no—
229#239—62no—
230#239—62no—
231C2×D12—31no—
232C2×D12—61no—
233C2×D12—61no—
234C2×C4×D3—31no—
235C2×C4×D3—31no—
236C2×C4×D3—31no—
237C2×C4×D3—31no—
238C2×C4×D3—62no—
239C2×C4×D3—62no—
240C2×C4×D3—61no—
241C2×C4×D3—61no—
242C2×C4×D3—61no—
243C2×C3×C8C22×D311yescharacteristic
244C2×C3×C8C22×D311yescharacteristic
245C3×C4⋊C4—21no—
246C3×C4⋊C4C22×D311yescharacteristic
247C3×C4⋊C4C22×D311yescharacteristic
248C3×C4⋊C4C22×D311yescharacteristic
249C3×C22⋊C4—21no—
250C3×C22⋊C4—21no—
251C3×C42—21no—
252#217—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—
259C4⋊Dic3—31no—
260C4⋊Dic3—31no—
261C4⋊Dic3—31no—
262Dic3⋊C4—61no—
263Dic3⋊C4—61no—
264Dic3⋊C4—61no—
265C4×Dic3—61no—
266C4×Dic3—61no—
267C4×Dic3—61no—
268C4×Dic3—61no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271D3×C8—62no—
272D3×C8—62no—
273C22×C9—21no—
274C22×C9—21no—
275C22×C9—21no—
276C22×C9C22×D411yescharacteristic
277C2×D9—21no—
278C2×D9—21no—
279C2×D9—21no—
280C2×D9—21no—
281C2×D9—44no—
282C2×D9—41no—
283C2×D9—41no—
284C2×D9—41no—
285C2×D9#12312yes—
286C2×D9#13512yes—
287C4×C9—21no—
288C4×C9—41no—
289C4×C9—41no—
290C4×C9—41no—
291C4×C9—41no—
292C4×C9C2×#4111yescharacteristic
293C4×C9C2×#4111yescharacteristic
294Dic9—21no—
295Dic9—41no—
296Dic9—41no—
297Dic9—41no—
298Dic9#12312yes—
299C2×#41—91no—
300C23×C4—91no—
301C22×C8—91no—
302C22×C8—91no—
303#123—181no—
304C22⋊Q8—91no—
305C22⋊Q8C2×D911yescharacteristic
306#121—91no—
307#121—91no—
308#120—181no—
309C4×D4—181no—
310C4×D4—181no—
311#117—91no—
312#117—91no—
313#117—91no—
314#117—91no—
315#117—181no—
316#117—181no—
317#117C2×D911yescharacteristic
318C2×C4⋊C4—91no—
319C2×C4⋊C4—91no—
320C2×C22⋊C4—181no—
321C2×C42—181no—
322#107—91no—
323#107—91no—
324#107—91no—
325#107C2×D911yescharacteristic, complemented
326#106—91no—
327#106—91no—
328#106—91no—
329#106C2×D911yescharacteristic, complemented
330#103—91no—
331#103—91no—
332#103C2×D911yescharacteristic, complemented
333#103C2×D911yescharacteristic, complemented
334#102—91no—
335#102—91no—
336#102—91no—
337#102—91no—
338C22⋊C8—91no—
339C22⋊C8—91no—
340C22⋊C8—91no—
341C22⋊C8C2×D911yescharacteristic
342C23×C3D3×D411yescharacteristic
343C22×D3—31no—
344C22×D3—31no—
345C22×D3—62no—
346C22×D3—62no—
347C22×D3—61no—
348C22×D3—121no—
349C3×Q8—21no—
350C3×Q8—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359#67—122no—
360C2×Dic3—31no—
361C2×Dic3—31no—
362C2×Dic3—62no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366D12—61no—
367D12—61no—
368D12—122no—
369D12—122no—
370C4×D3—32no—
371C4×D3—32no—
372C4×D3—62no—
373C4×D3—62no—
374C4×D3—61no—
375C4×D3—61no—
376C4×D3—122no—
377C4×D3—122no—
378C4×D3—122no—
379C3×C8—21no—
380C3×C8—21no—
381C3⋊C8—61no—
382C3⋊C8—61no—
383C2×C9—41no—
384C2×C9C2×#12311yescharacteristic
385C2×C9C2×#13511yescharacteristic
386C2×C9#57511yescharacteristic
387D9—22no—
388D9—22no—
389D9—81no—
390C24—91no—
391#41—182no—
392#41—182no—
393C2×Q8C22×D911yescharacteristic
394C2×D4—91no—
395C2×D4—181no—
396C2×D4—181no—
397C2×D4—181no—
398C22×C4—91no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—91no—
402C22×C4—91no—
403C22×C4—182no—
404C22×C4—182no—
405C22×C4—181no—
406C22×C4—181no—
407C22×C4—181no—
408C22×C4C22×D911yescharacteristic
409C2×C8—91no—
410C2×C8—91no—
411C2×C8—182no—
412C2×C8—182no—
413C2×C8C22×D911yescharacteristic
414C2×C8C22×D911yescharacteristic
415C4⋊C4—21no—
416C4⋊C4—91no—
417C4⋊C4—91no—
418C4⋊C4—91no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4C22×D911yescharacteristic
423C4⋊C4C22×D911yescharacteristic
424C4⋊C4C22×D911yescharacteristic
425C22⋊C4—21no—
426C22⋊C4—21no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C22⋊C4—181no—
434C42—21no—
435C42—181no—
436C42—181no—
437C42—181no—
438C42—181no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3C2×D3×D411yescharacteristic
443C2×D3—32no—
444C2×D3—32no—
445C2×D3—61no—
446C2×D3—61no—
447C2×D3—61no—
448C2×D3—61no—
449C2×D3—124no—
450C2×D3—121no—
451C2×D3—121no—
452C2×D3—121no—
453C3×C4—21no—
454C3×C4—41no—
455C3×C4—41no—
456C3×C4—41no—
457C3×C4—41no—
458C3×C4D3×#4111yescharacteristic
459C3×C4D3×#4111yescharacteristic
460Dic3—32no—
461Dic3—61no—
462Dic3—121no—
463Dic3—121no—
464Dic3—121no—
465C9#309111yescharacteristic, complemented, Sylow
466C23—91no—
467C23—91no—
468C23—182no—
469C23—182no—
470C23—181no—
471C23—361no—
472C23D4×D911yescharacteristic
473Q8—21no—
474Q8—21no—
475D4—181no—
476D4—181no—
477D4—362no—
478D4—362no—
479D4—362no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—91no—
487C2×C4—92no—
488C2×C4—92no—
489C2×C4—91no—
490C2×C4—182no—
491C2×C4—182no—
492C2×C4—182no—
493C2×C4—181no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—181no—
498C2×C4—362no—
499C2×C4—362no—
500C2×C4—362no—
501C2×C4D4×D911yescharacteristic
502C2×C4C23×D911yescharacteristic
503C8—21no—
504C8—21no—
505C8—181no—
506C8—181no—
507C2×C3—41no—
508C2×C3D3×#12311yescharacteristic
509C2×C3D3×#13511yescharacteristic
510C2×C3#577711yescharacteristic
511D3—62no—
512D3—62no—
513D3—241no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—92no—
518C22—92no—
519C22—181no—
520C22—181no—
521C22—181no—
522C22—181no—
523C22—364no—
524C22—361no—
525C22—361no—
526C22—361no—
527C22C2×D4×D911yescharacteristic
528C4—21no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—92no—
534C4—181no—
535C4—361no—
536C4—361no—
537C4—361no—
538C4#41×D911yescharacteristic
539C4#41×D911yescharacteristic
540C3#8151511yescharacteristic
541C2—41no—
542C2—182no—
543C2—182no—
544C2—721no—
545C2D9×#12311yescharacteristic
546C2D9×#13511yescharacteristic
547C2#1058987911yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#485C2
socleC22×C3C2×D3×D4
prime radical#10589729C2
hypercenter#485D9
hypocenterC9#3091
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
2. D9×#117C2semidirect
3. C9×#485C2semidirect
4. #10588725C2semidirect
5. #10588684C2semidirect
6. #10588562C2semidirect
7. #10588560C2semidirect
8. #10588543C2semidirect
9. #10588540C2semidirect
10. #10588491C2semidirect
11. #10588485C2semidirect
12. #10588484C2semidirect
13. #10588484C2semidirect
14. #10588419C2semidirect
15. D9×C22⋊C8C2semidirect
40. C9×#107C22semidirect
41. C9×#106C22semidirect
42. C9×#103C22semidirect
43. C9×#103C22semidirect
45. #63395C22semidirect
46. #63395C22semidirect
48. #63380C22semidirect
49. #63380C22semidirect
52. #63378C22semidirect
53. #63377C22semidirect
54. #63369C22semidirect
55. #63369C22semidirect
56. #63367C22semidirect
57. #63367C22semidirect
58. #63366C22semidirect
59. #63366C22semidirect
212. #485D9semidirect
325. #107C2×D9semidirect
329. #106C2×D9semidirect
332. #103C2×D9semidirect
333. #103C2×D9semidirect
465. C9#3091semidirect

Maximal subgroups

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

subgroupindex
#105897292
D9×#1172
C9×#4852
#105887252
#105886842
#105885622
#105885602
#105885432
#105885402
#105884912
#105884852
#105884842
#105884192
D9×C22⋊C82
#815153