Finite Group Databasebeta

← #11887179

Subgroups — #11887179

Order 1152.

612 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#552C211yesmaximal, characteristic, complemented
2#10589652C211yesmaximal, characteristic
3#10588749C211yesmaximal, characteristic, complemented
4#10588747C211yesmaximal, characteristic, complemented
5#10588731C211yesmaximal, characteristic, complemented
6#10588730C211yesmaximal, characteristic, complemented
7#10588729C211yesmaximal, characteristic, complemented
8#10588727C211yesmaximal, characteristic, complemented
9#10588711C211yesmaximal, characteristic, complemented
10C4×#3675C211yesmaximal, characteristic, complemented
11D4×C9⋊C8C211yesmaximal, characteristic, complemented
12#10588684C211yesmaximal, characteristic, complemented
13#10588683C211yesmaximal, characteristic, complemented
14C2×#63369C211yesmaximal, characteristic, complemented
15#10588647C211yesmaximal, characteristic, complemented
16#83598—31nomaximal
17C2×#3697C2211yescharacteristic
18C22×D36C2211yescharacteristic
19C9×#126—21no—
20C9×#125—21no—
21C9×#125C2211yescharacteristic, complemented
22C9×#123—21no—
23C9×C22⋊Q8C2211yescharacteristic
24C9×C22⋊Q8C2211yescharacteristic, complemented
25C4×Q8×C9C2211yescharacteristic, complemented
26C4×D4×C9C2211yescharacteristic
27C9×#117—21no—
28C9×#117C2211yescharacteristic, complemented
29C2×C9×C4⋊C4C2211yescharacteristic
30C2×#3675C2211yescharacteristic
31C2×#3675C2211yescharacteristic
32C2×#3674C2211yescharacteristic, complemented
33#63499—21no—
34#63492C2211yescharacteristic
35#63486C2211yescharacteristic
36C22×C9⋊C8C2211yescharacteristic
37C22×C9⋊C8C2211yescharacteristic, complemented
38#63456—21no—
39#63446—21no—
40C22⋊C4×D9—21no—
41#63437C2211yescharacteristic
42C4×D36C2211yescharacteristic
43#63395C2211yescharacteristic, complemented
44#63389C2211yescharacteristic
45#63389C2211yescharacteristic, complemented
46#63369C2211yescharacteristic
47#63369C2211yescharacteristic
48#63369C2211yescharacteristic
49#63369C2211yescharacteristic
50#63369C2211yescharacteristic
51#63369C2211yescharacteristic
52#63368C2211yescharacteristic, complemented
53#63368C2211yescharacteristic, complemented
54#63368C2211yescharacteristic, complemented
55#63367C2211yescharacteristic, complemented
56#63367C2211yescharacteristic, complemented
57#63366C2211yescharacteristic, complemented
58C4⋊(C9⋊C8)C2211yescharacteristic, complemented
59C4×C9⋊C8C2211yescharacteristic, complemented
60C3×#552D311yescharacteristic
61#5550—31no—
62#5068—31no—
63#5066—31no—
64#5051—31no—
65#5048—31no—
66#5047—31no—
67#5046—31no—
68#5028—31no—
69C4×#215—31no—
70D4×C3⋊C8—31no—
71#5003—31no—
72#5002—31no—
73#4971—31no—
74C2×#809—31no—
75C23×D9—21no—
76C2×Q8×C9C2311yescharacteristic
77C2×D4×C9D411yescharacteristic
78C22×C4×C9—21no—
79C22×C4×C9C2311yescharacteristic
80C22×C4×C9C2311yescharacteristic
81C2×#611—21no—
82C2×#611—21no—
83#3697—22no—
84#3697—41no—
85C2×D36—22no—
86C2×D36—21no—
87C2×D36—41no—
88C2×D36C2311yescharacteristic
89C2×D36C2311yescharacteristic
90C2×C4×D9—21no—
91C2×C4×D9—21no—
92C2×Dic18C2311yescharacteristic
93C9×C4⋊C4—21no—
94C9×C4⋊C4—21no—
95C9×C4⋊C4—21no—
96C9×C4⋊C4—21no—
97C9×C4⋊C4—21no—
98C9×C4⋊C4—21no—
99C9×C4⋊C4D411yescharacteristic
100C9×C4⋊C4C2311yescharacteristic
101C9×C4⋊C4C2311yescharacteristic
102C9×C4⋊C4C2311yescharacteristic
103C9×C22⋊C4—21no—
104C9×C22⋊C4—21no—
105C9×C22⋊C4—21no—
106C9×C22⋊C4D411yescharacteristic
107C9×C22⋊C4D411yescharacteristic
108C42×C9—21no—
109C42×C9—21no—
110C42×C9C2311yescharacteristic
111#3676—21no—
112#3675—22no—
113#3675—41no—
114#3674—41no—
115(C2×D9)⋊C4—21no—
116(C2×D9)⋊C4—21no—
117(C2×D9)⋊C4—21no—
118(C2×D9)⋊C4—21no—
119C4⋊Dic9C2311yescharacteristic
120Dic9⋊C4—21no—
121C2×C9⋊C8—41no—
122C2×C9⋊C8—41no—
123C2×C9⋊C8C2311yescharacteristic
124C2×C9⋊C8C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126C2×C9⋊C8C2311yescharacteristic
127#3296—91noSylow
128C2×#235—31no—
129C22×D12—31no—
130C3×#126—21no—
131C3×#125—21no—
132C3×#125C2×D311yescharacteristic
133C3×#123—21no—
134C3×C22⋊Q8C2×D311yescharacteristic
135C3×C22⋊Q8C2×D311yescharacteristic
136C3×C4×Q8C2×D311yescharacteristic
137C3×C4×D4C2×D311yescharacteristic
138C3×#117—21no—
139C3×#117C2×D311yescharacteristic
140C2×C3×C4⋊C4C2×D311yescharacteristic
141C2×#216—31no—
142C2×#215—31no—
143C2×#215—31no—
144#937—61no—
145#930—31no—
146#924—31no—
147C22×C3⋊C8—31no—
148C22×C3⋊C8—31no—
149#894—61no—
150#884—61no—
151D3×C22⋊C4—61no—
152#875—31no—
153C4×D12—31no—
154#835—31no—
155#830—31no—
156#830—31no—
157#810—31no—
158#810—31no—
159#810—31no—
160#809—31no—
161#809—31no—
162#809—31no—
163#809—31no—
164#809—31no—
165#809—31no—
166#808—31no—
167#808—31no—
168#807—31no—
169C4⋊(C3⋊C8)—31no—
170C4×C3⋊C8—31no—
171C23×C9C2×D411yescharacteristic
172C23×C9C2×D411yescharacteristic
173C22×D9—21no—
174C22×D9—21no—
175C22×D9—42no—
176C22×D9—42no—
177C22×D9—81no—
178Q8×C9—21no—
179Q8×C9—21no—
180D4×C9—22no—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9—21no—
184C2×C4×C9—21no—
185C2×C4×C9—21no—
186C2×C4×C9—21no—
187C2×C4×C9—21no—
188C2×C4×C9—21no—
189C2×C4×C9—42no—
190C2×C4×C9C2×D411yescharacteristic
191C2×C4×C9C2×D411yescharacteristic
192C2×C4×C9C2×D411yescharacteristic
193C2×C4×C9C2×D411yescharacteristic
194C2×C4×C9C2411yescharacteristic
195#611—42no—
196#611—81no—
197C2×Dic9—21no—
198C2×Dic9—21no—
199D36—21no—
200D36—21no—
201D36—21no—
202D36—42no—
203D36#4112yes—
204C4×D9—42no—
205C4×D9—81no—
206Dic18—21no—
207Dic18—21no—
208C9⋊C8—21no—
209C9⋊C8—21no—
210C9⋊C8—21no—
211C9⋊C8—21no—
212#552D911yescharacteristic, complemented
213#546—91no—
214#488—91no—
215#483—91no—
216#482—91no—
217#478—91no—
218#467—91no—
219#465—91no—
220#464—91no—
221#452—91no—
222#450—91no—
223C4×SD16—91no—
224C8×D4—91no—
225#416—91no—
226C2×#102—91no—
227C23×D3—61no—
228C2×C3×Q8C22×D311yescharacteristic
229C2×C3×D4#6711yescharacteristic
230C22×C3×C4—21no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C2×#67—61no—
234C2×#67—61no—
235#235—62no—
236#235—121no—
237C2×D12—31no—
238C2×D12—31no—
239C2×D12—62no—
240C2×D12—61no—
241C2×D12—121no—
242C2×C4×D3—61no—
243C2×C4×D3—61no—
244C2×Dic6—31no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4#6711yescharacteristic
252C3×C4⋊C4C22×D311yescharacteristic
253C3×C4⋊C4C22×D311yescharacteristic
254C3×C4⋊C4C22×D311yescharacteristic
255C3×C22⋊C4—21no—
256C3×C22⋊C4—21no—
257C3×C22⋊C4—21no—
258C3×C22⋊C4#6711yescharacteristic
259C3×C22⋊C4#6711yescharacteristic
260C3×C42—21no—
261C3×C42—21no—
262C3×C42C22×D311yescharacteristic
263#217—61no—
264#216—121no—
265#215—62no—
266#215—121no—
267(C2×D3)⋊C4—61no—
268(C2×D3)⋊C4—61no—
269(C2×D3)⋊C4—61no—
270(C2×D3)⋊C4—61no—
271C4⋊Dic3—31no—
272Dic3⋊C4—61no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—31no—
276C2×C3⋊C8—31no—
277C2×C3⋊C8—121no—
278C2×C3⋊C8—121no—
279C22×C9—21no—
280C22×C9—21no—
281C22×C9—21no—
282C22×C9—21no—
283C22×C9—21no—
284C22×C9#13512yes—
285C22×C9C22×D411yescharacteristic
286C2×D9—22no—
287C2×D9—41no—
288C2×D9—41no—
289C2×D9—41no—
290C2×D9—41no—
291C2×D9—41no—
292C2×D9—84no—
293C4×C9—21no—
294C4×C9—21no—
295C4×C9—21no—
296C4×C9—21no—
297C4×C9—41no—
298C4×C9—41no—
299C4×C9—41no—
300C4×C9—41no—
301C4×C9C2×#4111yescharacteristic
302C4×C9H(5,𝔽2)11yescharacteristic
303Dic9—41no—
304Dic9—41no—
305C2×#41—91no—
306C22×D4—91no—
307C2×Q16—91no—
308C2×SD16—91no—
309C2×SD16—91no—
310C22×C8—91no—
311C22×C8—91no—
312#126—21no—
313#125—21no—
314#125C2×D911yescharacteristic, complemented
315#124—91no—
316#123—21no—
317#123—181no—
318C22⋊Q8—91no—
319C22⋊Q8C2×D911yescharacteristic
320C22⋊Q8C2×D911yescharacteristic, complemented
321#121—91no—
322#121—181no—
323#120—181no—
324C4×Q8C2×D911yescharacteristic, complemented
325C4×D4—91no—
326C4×D4C2×D911yescharacteristic
327#117—21no—
328#117C2×D911yescharacteristic, complemented
329C2×C4⋊C4C2×D911yescharacteristic
330C2×C22⋊C4—181no—
331#107—91no—
332#106—91no—
333#106—91no—
334C4⋊C8—91no—
335#103—91no—
336#103—91no—
337#103—91no—
338#103—91no—
339#102—91no—
340#102—91no—
341#102—91no—
342#102—91no—
343#102—91no—
344#102—91no—
345C22⋊C8—91no—
346C22⋊C8—91no—
347C4×C8—91no—
348C23×C3C2×#6711yescharacteristic
349C23×C3C2×#6711yescharacteristic
350C22×D3—61no—
351C22×D3—61no—
352C22×D3—122no—
353C22×D3—122no—
354C22×D3—241no—
355C3×Q8—21no—
356C3×Q8—21no—
357C3×D4—22no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—42no—
367C2×C3×C4C2×#6711yescharacteristic
368C2×C3×C4C2×#6711yescharacteristic
369C2×C3×C4C2×#6711yescharacteristic
370C2×C3×C4C2×#6711yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372#67—122no—
373#67—241no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376D12—32no—
377D12—61no—
378D12—61no—
379D12—61no—
380D12—122no—
381C4×D3—122no—
382C4×D3—241no—
383Dic6—61no—
384Dic6—61no—
385C3⋊C8—61no—
386C3⋊C8—61no—
387C3⋊C8—61no—
388C3⋊C8—61no—
389C2×C9—22no—
390C2×C9—41no—
391C2×C9#54611yescharacteristic
392C2×C9C2×#13511yescharacteristic
393C2×C9#57711yescharacteristic
394D9—42no—
395D9—81no—
396C24—181no—
397#41—182no—
398#41—361no—
399C2×Q8—91no—
400C2×Q8C22×D911yescharacteristic
401C2×D4—91no—
402C2×D4—91no—
403C2×D4—182no—
404C2×D4—181no—
405C2×D4—181no—
406C2×D4—181no—
407C2×D4—361no—
408C2×D4#61111yescharacteristic
409C22×C4—21no—
410C22×C4—181no—
411C22×C4—181no—
412C22×C4C22×D911yescharacteristic
413C22×C4C22×D911yescharacteristic
414Q16—361no—
415SD16—182no—
416SD16—361no—
417C2×C8—91no—
418C2×C8—91no—
419C2×C8—91no—
420C2×C8—91no—
421C2×C8—361no—
422C2×C8—361no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—91no—
430C4⋊C4—181no—
431C4⋊C4#61111yescharacteristic
432C4⋊C4C22×D911yescharacteristic
433C4⋊C4C22×D911yescharacteristic
434C4⋊C4C22×D911yescharacteristic
435C22⋊C4—21no—
436C22⋊C4—21no—
437C22⋊C4—21no—
438C22⋊C4—181no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C22⋊C4#61111yescharacteristic
444C22⋊C4#61111yescharacteristic
445C42—21no—
446C42—21no—
447C42C22×D911yescharacteristic
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3#95012yes—
454C22×C3C22×#6711yescharacteristic
455C2×D3—62no—
456C2×D3—121no—
457C2×D3—121no—
458C2×D3—121no—
459C2×D3—121no—
460C2×D3—121no—
461C2×D3—244no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—41no—
467C3×C4—41no—
468C3×C4—41no—
469C3×C4—41no—
470C3×C4D3×#4111yescharacteristic
471C3×C4#100911yescharacteristic
472Dic3—121no—
473Dic3—121no—
474C9#329611yescharacteristic, complemented, Sylow
475C23—181no—
476C23—181no—
477C23—362no—
478C23—362no—
479C23—721no—
480C23C2×#61111yescharacteristic
481C23C2×#61111yescharacteristic
482Q8—21no—
483Q8—21no—
484Q8—181no—
485Q8—181no—
486D4—22no—
487D4—92no—
488D4—181no—
489D4—181no—
490D4—181no—
491D4—362no—
492D4—362no—
493D4—721no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—42no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—362no—
506C2×C4—721no—
507C2×C4C2×#61111yescharacteristic
508C2×C4C2×#61111yescharacteristic
509C2×C4C2×#61111yescharacteristic
510C2×C4C2×#61111yescharacteristic
511C2×C4C23×D911yescharacteristic
512C8—181no—
513C8—181no—
514C8—181no—
515C8—181no—
516C2×C3—22no—
517C2×C3—41no—
518C2×C3C2×#95011yescharacteristic
519C2×C3#582911yescharacteristic
520C2×C3#583711yescharacteristic
521D3—122no—
522D3—241no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—182no—
529C22—361no—
530C22—361no—
531C22—361no—
532C22—361no—
533C22—361no—
534C22—724no—
535C22#6351312yes—
536C22C22×#61111yescharacteristic
537C4—21no—
538C4—21no—
539C4—21no—
540C4—21no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—361no—
546C4—361no—
547C4#41×D911yescharacteristic
548C4#6371511yescharacteristic
549C3#8359811yescharacteristic
550C2—22no—
551C2—41no—
552C2—362no—
553C2—721no—
554C2C2×#6351311yescharacteristic
555C2#1058993111yescharacteristic
556C2#1058993911yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#552C2
socleC22×C3C22×#67
prime radical#10589652C2
hypercenter#552D9
hypocenterC9#3296
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
1. C9×#552C2semidirect
3. #10588749C2semidirect
4. #10588747C2semidirect
5. #10588731C2semidirect
6. #10588730C2semidirect
7. #10588729C2semidirect
8. #10588727C2semidirect
9. #10588711C2semidirect
10. C4×#3675C2semidirect
11. D4×C9⋊C8C2semidirect
12. #10588684C2semidirect
13. #10588683C2semidirect
14. C2×#63369C2semidirect
15. #10588647C2semidirect
21. C9×#125C22semidirect
24. C9×C22⋊Q8C22semidirect
25. C4×Q8×C9C22semidirect
28. C9×#117C22semidirect
32. C2×#3674C22semidirect
37. C22×C9⋊C8C22semidirect
43. #63395C22semidirect
45. #63389C22semidirect
52. #63368C22semidirect
53. #63368C22semidirect
54. #63368C22semidirect
55. #63367C22semidirect
56. #63367C22semidirect
57. #63366C22semidirect
58. C4⋊(C9⋊C8)C22semidirect
59. C4×C9⋊C8C22semidirect
212. #552D9semidirect
314. #125C2×D9semidirect
320. C22⋊Q8C2×D9semidirect
324. C4×Q8C2×D9semidirect
328. #117C2×D9semidirect
474. C9#3296semidirect

Maximal subgroups

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

subgroupindex
C9×#5522
#105896522
#105887492
#105887472
#105887312
#105887302
#105887292
#105887272
#105887112
C4×#36752
D4×C9⋊C82
#105886842
#105886832
C2×#633692
#105886472
#835983