Finite Group Databasebeta

← #11888556

Subgroups — #11888556

Order 1152.

591 conjugacy classes of subgroups.

The subgroup lattice has 555 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#553C211yesmaximal, characteristic, complemented
2#10589653C211yesmaximal, characteristic, complemented
3#10588747C211yesmaximal, characteristic, complemented
4#10588746C211yesmaximal, characteristic, complemented
5#10588720C211yesmaximal, characteristic, complemented
6#10588720C211yesmaximal, characteristic, complemented
7#10588718C211yesmaximal, characteristic, complemented
8#10588717C211yesmaximal, characteristic, complemented
9#10588697C211yesmaximal, characteristic, complemented
10#10588695C211yesmaximal, characteristic, complemented
11#10588688C211yesmaximal, characteristic, complemented
12#10588683C211yesmaximal, characteristic, complemented
13#10588680C211yesmaximal, characteristic, complemented
14#10588649C211yesmaximal, characteristic, complemented
15#10588647C211yesmaximal, characteristic, complemented
16#83615—31nomaximal
17C2×#3697C2211yescharacteristic
18C2×#3697C2211yescharacteristic
19C9×#126—21no—
20C9×#125C2211yescharacteristic
21C9×#123—21no—
22C9×#121—21no—
23C9×#121C2211yescharacteristic
24C9×#121C2211yescharacteristic
25C4×D4×C9—21no—
26C4×D4×C9C2211yescharacteristic
27C4×D4×C9C2211yescharacteristic
28C9×#117C2211yescharacteristic
29C2×C9×C4⋊C4C2211yescharacteristic
30#63500—21no—
31C2×#3673C2211yescharacteristic
32C2×#3672C2211yescharacteristic
33C2×#3672C2211yescharacteristic
34#63486C2211yescharacteristic
35#63486C2211yescharacteristic
36C2×#3667C2211yescharacteristic
37C22×C9⋊C8C2211yescharacteristic
38C4⋊C4×D9—21no—
39#63445—21no—
40#63445—21no—
41C4×D36C2211yescharacteristic
42#63431C2211yescharacteristic
43#63392C2211yescharacteristic
44#63389C2211yescharacteristic
45#63389C2211yescharacteristic
46#63369C2211yescharacteristic
47#63369C2211yescharacteristic
48#63369C2211yescharacteristic
49#63368C2211yescharacteristic
50#63368C2211yescharacteristic
51#63368C2211yescharacteristic
52#63368C2211yescharacteristic
53#63368C2211yescharacteristic
54#63368C2211yescharacteristic
55#63367C2211yescharacteristic
56#63367C2211yescharacteristic
57#63366C2211yescharacteristic
58C4⋊(C9⋊C8)C2211yescharacteristic
59#63362C2211yescharacteristic
60C3×#553D311yescharacteristic
61#5551—31no—
62#5069—31no—
63#5066—31no—
64#5042—31no—
65#5041—31no—
66#5037—31no—
67#5037—31no—
68#5019—31no—
69#5014—31no—
70#5011—31no—
71#5002—31no—
72#4996—31no—
73#4971—31no—
74#4966—31no—
75C2×D4×C9—21no—
76C2×D4×C9—21no—
77C2×D4×C9D411yescharacteristic
78C2×D4×C9C2311yescharacteristic
79C22×C4×C9—21no—
80C22×C4×C9—21no—
81C22×C4×C9C2311yescharacteristic
82C22×C4×C9C2311yescharacteristic
83C2×#611—21no—
84C2×#611—21no—
85#3697—22no—
86#3697—22no—
87#3697—41no—
88#3697—41no—
89C2×D36C2311yescharacteristic
90C2×C4×D9—21no—
91C2×C4×D9—21no—
92C2×C4×D9—21no—
93C2×Dic18C2311yescharacteristic
94C2×Dic18C2311yescharacteristic
95C9×C4⋊C4—21no—
96C9×C4⋊C4—21no—
97C9×C4⋊C4—21no—
98C9×C4⋊C4D411yescharacteristic
99C9×C4⋊C4C2311yescharacteristic
100C9×C4⋊C4C2311yescharacteristic
101C9×C4⋊C4C2311yescharacteristic
102C9×C22⋊C4—21no—
103C9×C22⋊C4—21no—
104C9×C22⋊C4—21no—
105C9×C22⋊C4—21no—
106C9×C22⋊C4D411yescharacteristic
107C9×C22⋊C4D411yescharacteristic
108C42×C9—21no—
109C42×C9C2311yescharacteristic
110#3676—21no—
111#3676—21no—
112#3673—22no—
113#3672—41no—
114#3672—41no—
115(C2×D9)⋊C4—21no—
116C4⋊Dic9—21no—
117C4⋊Dic9—21no—
118C4⋊Dic9C2311yescharacteristic
119Dic9⋊C4—21no—
120Dic9⋊C4—21no—
121#3667—41no—
122C2×C9⋊C8—41no—
123C2×C9⋊C8C2311yescharacteristic
124C2×C9⋊C8C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126C2×C9⋊C8C2311yescharacteristic
127#3307—91noSylow
128C2×#235—31no—
129C2×#235—31no—
130C3×#126—21no—
131C3×#125C2×D311yescharacteristic
132C3×#123—21no—
133C3×#121—21no—
134C3×#121C2×D311yescharacteristic
135C3×#121C2×D311yescharacteristic
136C3×C4×D4—21no—
137C3×C4×D4C2×D311yescharacteristic
138C3×C4×D4C2×D311yescharacteristic
139C3×#117C2×D311yescharacteristic
140C2×C3×C4⋊C4C2×D311yescharacteristic
141#938—61no—
142C2×#214—31no—
143C2×#214—31no—
144C2×#213—31no—
145#924—31no—
146#924—31no—
147C2×#208—31no—
148C22×C3⋊C8—31no—
149D3×C4⋊C4—61no—
150#883—61no—
151#883—61no—
152C4×D12—31no—
153#869—31no—
154#832—31no—
155#830—31no—
156#830—31no—
157#810—31no—
158#810—31no—
159#810—31no—
160#810—31no—
161#810—31no—
162#810—31no—
163#809—31no—
164#809—31no—
165#809—31no—
166#808—31no—
167#808—31no—
168#807—31no—
169C4⋊(C3⋊C8)—31no—
170#803—31no—
171C23×C9—21no—
172C23×C9C2×D411yescharacteristic
173C23×C9C2×D411yescharacteristic
174C22×D9—21no—
175D4×C9—21no—
176D4×C9—21no—
177D4×C9—41no—
178D4×C9—42no—
179D4×C9—81no—
180C2×C4×C9—21no—
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—81no—
188C2×C4×C9—81no—
189C2×C4×C9C2×D411yescharacteristic
190C2×C4×C9C2×D411yescharacteristic
191C2×C4×C9C2×D411yescharacteristic
192C2×C4×C9C2×D411yescharacteristic
193C2×C4×C9C2411yescharacteristic
194#611—42no—
195#611—42no—
196C2×Dic9—21no—
197C2×Dic9—21no—
198C2×Dic9—21no—
199D36—21no—
200D36#4112yes—
201C4×D9—42no—
202C4×D9—42no—
203C4×D9—42no—
204Dic18—21no—
205Dic18—21no—
206Dic18—21no—
207Dic18—21no—
208C9⋊C8—21no—
209C9⋊C8—21no—
210C9⋊C8—21no—
211C9⋊C8—21no—
212#553D911yescharacteristic, complemented
213#547—91no—
214#491—91no—
215#485—91no—
216#483—91no—
217#478—91no—
218#468—91no—
219#465—91no—
220#461—91no—
221#449—91no—
222#449—91no—
223#442—91no—
224#435—91no—
225#417—91no—
226#416—91no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4#6711yescharacteristic
230C2×C3×D4C22×D311yescharacteristic
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—61no—
236C2×#67—61no—
237#235—62no—
238#235—62no—
239#235—121no—
240#235—121no—
241C2×D12—31no—
242C2×C4×D3—61no—
243C2×C4×D3—61no—
244C2×C4×D3—61no—
245C2×Dic6—31no—
246C2×Dic6—31no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4#6711yescharacteristic
251C3×C4⋊C4C22×D311yescharacteristic
252C3×C4⋊C4C22×D311yescharacteristic
253C3×C4⋊C4C22×D311yescharacteristic
254C3×C22⋊C4—21no—
255C3×C22⋊C4—21no—
256C3×C22⋊C4—21no—
257C3×C22⋊C4—21no—
258C3×C22⋊C4#6711yescharacteristic
259C3×C22⋊C4#6711yescharacteristic
260C3×C42—21no—
261C3×C42C22×D311yescharacteristic
262#217—61no—
263#217—61no—
264#214—121no—
265#214—121no—
266#213—62no—
267(C2×D3)⋊C4—61no—
268C4⋊Dic3—31no—
269C4⋊Dic3—61no—
270C4⋊Dic3—61no—
271Dic3⋊C4—61no—
272Dic3⋊C4—61no—
273#208—121no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—31no—
276C2×C3⋊C8—31no—
277C2×C3⋊C8—31no—
278C2×C3⋊C8—121no—
279C22×C9—21no—
280C22×C9—21no—
281C22×C9—21no—
282C22×C9—21no—
283C22×C9—21no—
284C22×C9—21no—
285C22×C9—41no—
286C22×C9—41no—
287C22×C9—41no—
288C22×C9C22×D411yescharacteristic
289C2×D9—22no—
290C2×D9—41no—
291C2×D9—41no—
292C4×C9—21no—
293C4×C9—21no—
294C4×C9—21no—
295C4×C9—21no—
296C4×C9—41no—
297C4×C9—41no—
298C4×C9—41no—
299C4×C9C2×#4111yescharacteristic
300C4×C9H(5,𝔽2)11yescharacteristic
301Dic9—41no—
302Dic9—41no—
303Dic9—41no—
304C2×#41—91no—
305C2×#41—91no—
306C2×SD16—91no—
307C2×SD16—91no—
308C2×D8—91no—
309C2×M16—91no—
310C22×C8—91no—
311C4⋊Q8—91no—
312#126—21no—
313#125C2×D911yescharacteristic
314#123—21no—
315#123—181no—
316#123—181no—
317C22⋊Q8—91no—
318C22⋊Q8—91no—
319#121—21no—
320#121—181no—
321#121C2×D911yescharacteristic
322#121C2×D911yescharacteristic
323C4×D4—21no—
324C4×D4—91no—
325C4×D4C2×D911yescharacteristic
326C4×D4C2×D911yescharacteristic
327#117C2×D911yescharacteristic
328C2×C4⋊C4—181no—
329C2×C4⋊C4C2×D911yescharacteristic
330#107—91no—
331#106—91no—
332#106—91no—
333C4⋊C8—91no—
334#103—91no—
335#103—91no—
336#103—91no—
337#103—91no—
338#103—91no—
339#103—91no—
340#102—91no—
341#102—91no—
342#102—91no—
343#102—91no—
344C22⋊C8—91no—
345C22⋊C8—91no—
346#97—91no—
347C23×C3—21no—
348C23×C3C2×#6711yescharacteristic
349C23×C3C2×#6711yescharacteristic
350C22×D3—61no—
351C3×D4—21no—
352C3×D4—21no—
353C3×D4—41no—
354C3×D4—42no—
355C3×D4—81no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—81no—
364C2×C3×C4—81no—
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368C2×C3×C4C2×#6711yescharacteristic
369C2×C3×C4C23×D311yescharacteristic
370#67—122no—
371#67—122no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375D12—32no—
376D12—61no—
377C4×D3—122no—
378C4×D3—122no—
379C4×D3—122no—
380Dic6—61no—
381Dic6—61no—
382Dic6—61no—
383Dic6—61no—
384C3⋊C8—61no—
385C3⋊C8—61no—
386C3⋊C8—61no—
387C3⋊C8—61no—
388C2×C9—41no—
389C2×C9—41no—
390C2×C9—81no—
391C2×C9#54611yescharacteristic
392C2×C9#57511yescharacteristic
393C2×C9#57711yescharacteristic
394D9—42no—
395#41—182no—
396#41—182no—
397#41—361no—
398#41—361no—
399C2×Q8—91no—
400C2×Q8—91no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—91no—
404C2×D4—181no—
405C2×D4—181no—
406C2×D4#61111yescharacteristic
407C2×D4C22×D911yescharacteristic
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—181no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4C22×D911yescharacteristic
414C22×C4C22×D911yescharacteristic
415SD16—361no—
416SD16—361no—
417D8—182no—
418M16—361no—
419C2×C8—91no—
420C2×C8—91no—
421C2×C8—91no—
422C2×C8—91no—
423C2×C8—361no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—91no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C4⋊C4—181no—
432C4⋊C4#61111yescharacteristic
433C4⋊C4C22×D911yescharacteristic
434C4⋊C4C22×D911yescharacteristic
435C4⋊C4C22×D911yescharacteristic
436C22⋊C4—21no—
437C22⋊C4—21no—
438C22⋊C4—21no—
439C22⋊C4—21no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C22⋊C4#61111yescharacteristic
444C22⋊C4#61111yescharacteristic
445C42—21no—
446C42C22×D911yescharacteristic
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—41no—
454C22×C3—41no—
455C22×C3—41no—
456C22×C3C22×#6711yescharacteristic
457C2×D3—62no—
458C2×D3—121no—
459C2×D3—121no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—41no—
467C3×C4D3×#4111yescharacteristic
468C3×C4#100911yescharacteristic
469Dic3—121no—
470Dic3—121no—
471Dic3—121no—
472C9#330711yescharacteristic, complemented, Sylow
473C23—21no—
474C23—181no—
475C23C2×#61111yescharacteristic
476C23C2×#61111yescharacteristic
477Q8—181no—
478Q8—181no—
479Q8—181no—
480Q8—181no—
481D4—21no—
482D4—21no—
483D4—41no—
484D4—42no—
485D4—81no—
486D4—92no—
487D4—181no—
488D4—362no—
489D4—362no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—81no—
498C2×C4—81no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—362no—
503C2×C4—362no—
504C2×C4—362no—
505C2×C4C2×#61111yescharacteristic
506C2×C4C2×#61111yescharacteristic
507C2×C4C2×#61111yescharacteristic
508C2×C4C2×#61111yescharacteristic
509C2×C4C23×D911yescharacteristic
510C8—181no—
511C8—181no—
512C8—181no—
513C8—181no—
514C2×C3—41no—
515C2×C3—41no—
516C2×C3—81no—
517C2×C3#582211yescharacteristic
518C2×C3#582911yescharacteristic
519C2×C3#583611yescharacteristic
520D3—122no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—182no—
531C22—361no—
532C22—361no—
533C22C22×#61111yescharacteristic
534C4—21no—
535C4—21no—
536C4—21no—
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—361no—
542C4—361no—
543C4—361no—
544C4#41×D911yescharacteristic
545C4#6371511yescharacteristic
546C3#8361511yescharacteristic
547C2—41no—
548C2—41no—
549C2—81no—
550C2—362no—
551C2#1058992511yescharacteristic
552C2#1058993111yescharacteristic
553C2#1058993811yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#553C2
socleC22×C3C22×#67
hypercenter#553D9
hypocenterC9#3307
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. C9×#553C2semidirect
2. #10589653C2semidirect
3. #10588747C2semidirect
4. #10588746C2semidirect
5. #10588720C2semidirect
6. #10588720C2semidirect
7. #10588718C2semidirect
8. #10588717C2semidirect
9. #10588697C2semidirect
10. #10588695C2semidirect
11. #10588688C2semidirect
12. #10588683C2semidirect
13. #10588680C2semidirect
14. #10588649C2semidirect
15. #10588647C2semidirect
212. #553D9semidirect
472. C9#3307semidirect

Maximal subgroups

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

subgroupindex
C9×#5532
#105896532
#105887472
#105887462
#105887202
#105887182
#105887172
#105886972
#105886952
#105886882
#105886832
#105886802
#105886492
#105886472
#836153