Finite Group Databasebeta

← #11888574

Subgroups — #11888574

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×#547C211yesmaximal, characteristic, complemented
2#10589667C211yesmaximal, characteristic, complemented
3#10588919C211yesmaximal, characteristic, complemented
4#10588919C211yesmaximal, characteristic, complemented
5#10588917C211yesmaximal, characteristic, complemented
6#10588916C211yesmaximal, characteristic, complemented
7#10588768C211yesmaximal, characteristic, complemented
8#10588762C211yesmaximal, characteristic, complemented
9#10588732C211yesmaximal, characteristic, complemented
10#10588731C211yesmaximal, characteristic, complemented
11#10588725C211yesmaximal, characteristic, complemented
12#10588723C211yesmaximal, characteristic, complemented
13#10588697C211yesmaximal, characteristic, complemented
14#10588692C211yesmaximal, characteristic, complemented
15#10588688C211yesmaximal, characteristic, complemented
16#83512—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C2×C9×#41C2211yescharacteristic
19C9×C4⋊Q8C2211yescharacteristic
20C9×#123—21no—
21C9×#123—21no—
22C9×C22⋊Q8C2211yescharacteristic
23C9×C22⋊Q8C2211yescharacteristic
24C9×#121—21no—
25C4×D4×C9C2211yescharacteristic
26C4×D4×C9C2211yescharacteristic
27C2×C9×C4⋊C4—21no—
28C2×#3675C2211yescharacteristic
29C2×#3675C2211yescharacteristic
30#63501—21no—
31C2×#3673C2211yescharacteristic
32#63492C2211yescharacteristic
33#63492C2211yescharacteristic
34#63488C2211yescharacteristic
35C2×C4⋊Dic9C2211yescharacteristic
36C2×#3667C2211yescharacteristic
37C22×C9⋊C8C2211yescharacteristic
38#63460—21no—
39#63445—21no—
40#611⋊C4—21no—
41C4×D36C2211yescharacteristic
42#63432C2211yescharacteristic
43#63395C2211yescharacteristic
44#63395C2211yescharacteristic
45#63395C2211yescharacteristic
46#63395C2211yescharacteristic
47#63395C2211yescharacteristic
48#63395C2211yescharacteristic
49#63392C2211yescharacteristic
50#63392C2211yescharacteristic
51#63392C2211yescharacteristic
52#63389C2211yescharacteristic
53#63389C2211yescharacteristic
54#63369C2211yescharacteristic
55#63367C2211yescharacteristic
56#63367C2211yescharacteristic
57#63366C2211yescharacteristic
58C4⋊(C9⋊C8)C2211yescharacteristic
59#63362C2211yescharacteristic
60C3×#547D311yescharacteristic
61#5565—31no—
62#5238—31no—
63#5238—31no—
64#5233—31no—
65#5232—31no—
66#5083—31no—
67#5082—31no—
68#5049—31no—
69#5048—31no—
70#5045—31no—
71#5043—31no—
72#5014—31no—
73#5011—31no—
74#5009—31no—
75C9×#41—22no—
76C9×#41—22no—
77C9×#41—41no—
78C9×#41—41no—
79C2×Q8×C9C2311yescharacteristic
80C2×Q8×C9C2311yescharacteristic
81C2×D4×C9—21no—
82C2×D4×C9—21no—
83C2×D4×C9D411yescharacteristic
84C2×D4×C9C2311yescharacteristic
85C22×C4×C9—21no—
86C22×C4×C9—21no—
87C22×C4×C9—21no—
88C22×C4×C9C2311yescharacteristic
89C22×C4×C9C2311yescharacteristic
90C2×#611—21no—
91C2×#611—21no—
92C22×Dic9—21no—
93C2×D36C2311yescharacteristic
94C2×C4×D9—21no—
95C9×C4⋊C4—21no—
96C9×C4⋊C4—21no—
97C9×C4⋊C4—21no—
98C9×C4⋊C4—21no—
99C9×C4⋊C4D411yescharacteristic
100C9×C4⋊C4C2311yescharacteristic
101C9×C22⋊C4—21no—
102C9×C22⋊C4—21no—
103C9×C22⋊C4—21no—
104C9×C22⋊C4D411yescharacteristic
105C9×C22⋊C4D411yescharacteristic
106C42×C9C2311yescharacteristic
107#3676—21no—
108#3675—41no—
109#3675—41no—
110#3673—22no—
111(C2×D9)⋊C4—21no—
112(C2×D9)⋊C4—21no—
113(C2×D9)⋊C4—21no—
114C4⋊Dic9—21no—
115C4⋊Dic9C2311yescharacteristic
116C4⋊Dic9C2311yescharacteristic
117C4⋊Dic9C2311yescharacteristic
118Dic9⋊C4—21no—
119Dic9⋊C4—21no—
120C4×Dic9—21no—
121#3667—41no—
122C2×C9⋊C8—41no—
123C2×C9⋊C8C2311yescharacteristic
124C2×C9⋊C8C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126C2×C9⋊C8C2311yescharacteristic
127#3307—91noSylow
128C2×C3×#41C2×D311yescharacteristic
129C2×C3×#41C2×D311yescharacteristic
130C3×C4⋊Q8C2×D311yescharacteristic
131C3×#123—21no—
132C3×#123—21no—
133C3×C22⋊Q8C2×D311yescharacteristic
134C3×C22⋊Q8C2×D311yescharacteristic
135C3×#121—21no—
136C3×C4×D4C2×D311yescharacteristic
137C3×C4×D4C2×D311yescharacteristic
138C2×C3×C4⋊C4—21no—
139C2×#215—31no—
140C2×#215—31no—
141#939—61no—
142C2×#213—31no—
143#930—31no—
144#930—31no—
145#926—31no—
146C2×C4⋊Dic3—31no—
147C2×#208—31no—
148C22×C3⋊C8—31no—
149#898—61no—
150#883—61no—
151#67⋊C4—61no—
152C4×D12—31no—
153#870—31no—
154#835—31no—
155#835—31no—
156#835—31no—
157#835—31no—
158#835—31no—
159#835—31no—
160#832—31no—
161#832—31no—
162#832—31no—
163#830—31no—
164#830—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—
175Q8×C9—21no—
176Q8×C9—21no—
177Q8×C9—21no—
178Q8×C9—21no—
179D4×C9—21no—
180D4×C9—41no—
181D4×C9—42no—
182D4×C9—42no—
183D4×C9#4112yes—
184C2×C4×C9—21no—
185C2×C4×C9—21no—
186C2×C4×C9—21no—
187C2×C4×C9—21no—
188C2×C4×C9—21no—
189C2×C4×C9—21no—
190C2×C4×C9—21no—
191C2×C4×C9—42no—
192C2×C4×C9—42no—
193C2×C4×C9—42no—
194C2×C4×C9C2×D411yescharacteristic
195C2×C4×C9C2×D411yescharacteristic
196C2×C4×C9C2×D411yescharacteristic
197C2×C4×C9C2×D411yescharacteristic
198C2×C4×C9C2411yescharacteristic
199#611—42no—
200#611—81no—
201C2×Dic9—21no—
202C2×Dic9—21no—
203C2×Dic9—21no—
204C2×Dic9—81no—
205D36—21no—
206D36—21no—
207C4×D9—81no—
208C9⋊C8—21no—
209C9⋊C8—21no—
210C9⋊C8—21no—
211C9⋊C8—21no—
212#553—91no—
213#547D911yescharacteristic, complemented
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—
227C3×#41—22no—
228C3×#41—22no—
229C3×#41—41no—
230C3×#41—41no—
231C2×C3×Q8C22×D311yescharacteristic
232C2×C3×Q8C22×D311yescharacteristic
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4#6711yescharacteristic
236C2×C3×D4C22×D311yescharacteristic
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4C22×D311yescharacteristic
241C22×C3×C4C22×D311yescharacteristic
242C2×#67—61no—
243C2×#67—61no—
244C22×Dic3—61no—
245C2×D12—31no—
246C2×C4×D3—61no—
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×C22⋊C4—21no—
254C3×C22⋊C4—21no—
255C3×C22⋊C4—21no—
256C3×C22⋊C4#6711yescharacteristic
257C3×C22⋊C4#6711yescharacteristic
258C3×C42C22×D311yescharacteristic
259#217—61no—
260#215—121no—
261#215—121no—
262#213—62no—
263(C2×D3)⋊C4—61no—
264(C2×D3)⋊C4—61no—
265(C2×D3)⋊C4—61no—
266C4⋊Dic3—31no—
267C4⋊Dic3—31no—
268C4⋊Dic3—31no—
269C4⋊Dic3—61no—
270Dic3⋊C4—61no—
271Dic3⋊C4—61no—
272C4×Dic3—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—22no—
282C22×C9—21no—
283C22×C9—21no—
284C22×C9—21no—
285C22×C9—21no—
286C22×C9—41no—
287C22×C9—41no—
288C22×C9C22×D411yescharacteristic
289C2×D9—41no—
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×#41C2×D911yescharacteristic
305C2×#41C2×D911yescharacteristic
306C2×SD16—91no—
307C2×SD16—91no—
308C2×D8—91no—
309C2×M16—91no—
310C22×C8—91no—
311C4⋊Q8C2×D911yescharacteristic
312#126—181no—
313#125—91no—
314#123—21no—
315#123—21no—
316#123—181no—
317C22⋊Q8C2×D911yescharacteristic
318C22⋊Q8C2×D911yescharacteristic
319#121—21no—
320#121—91no—
321#121—91no—
322#121—181no—
323C4×D4—91no—
324C4×D4—181no—
325C4×D4C2×D911yescharacteristic
326C4×D4C2×D911yescharacteristic
327#117—91no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—91no—
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×Q8—21no—
352C3×Q8—21no—
353C3×Q8—21no—
354C3×Q8—21no—
355C3×D4—21no—
356C3×D4—41no—
357C3×D4—42no—
358C3×D4—42no—
359C3×D4#23712yes—
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—21no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4—42no—
370C2×C3×C4C2×#6711yescharacteristic
371C2×C3×C4C2×#6711yescharacteristic
372C2×C3×C4C2×#6711yescharacteristic
373C2×C3×C4C2×#6711yescharacteristic
374C2×C3×C4C23×D311yescharacteristic
375#67—122no—
376#67—241no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—241no—
381D12—61no—
382D12—61no—
383C4×D3—241no—
384C3⋊C8—61no—
385C3⋊C8—61no—
386C3⋊C8—61no—
387C3⋊C8—61no—
388C2×C9—41no—
389C2×C9—41no—
390C2×C9—42no—
391C2×C9#54611yescharacteristic
392C2×C9#57511yescharacteristic
393C2×C9#57711yescharacteristic
394D9—81no—
395#41—22no—
396#41—22no—
397#41—41no—
398#41—41no—
399C2×Q8C22×D911yescharacteristic
400C2×Q8C22×D911yescharacteristic
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—21no—
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—21no—
428C4⋊C4—91no—
429C4⋊C4—91no—
430C4⋊C4—91no—
431C4⋊C4—181no—
432C4⋊C4—181no—
433C4⋊C4—181no—
434C4⋊C4#61111yescharacteristic
435C4⋊C4C22×D911yescharacteristic
436C22⋊C4—21no—
437C22⋊C4—21no—
438C22⋊C4—21no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C22⋊C4#61111yescharacteristic
444C22⋊C4#61111yescharacteristic
445C42—181no—
446C42C22×D911yescharacteristic
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—22no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—41no—
455C22×C3—41no—
456C22×C3C22×#6711yescharacteristic
457C2×D3—121no—
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×C4C2×#23711yescharacteristic
468C3×C4#100411yescharacteristic
469Dic3—121no—
470Dic3—121no—
471Dic3—121no—
472C9#330711yescharacteristic, complemented, Sylow
473C23—21no—
474C23—181no—
475C23C2×#61111yescharacteristic
476C23C2×#61111yescharacteristic
477Q8—21no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481D4—21no—
482D4—41no—
483D4—42no—
484D4—42no—
485D4—181no—
486D4—181no—
487D4—362no—
488D4—721no—
489D4#369912yes—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—721no—
504C2×C4—721no—
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—42no—
517C2×C3#580611yescharacteristic
518C2×C3#582211yescharacteristic
519C2×C3#583711yescharacteristic
520D3—241no—
521C22—21no—
522C22—21no—
523C22—22no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—41no—
529C22—41no—
530C22—361no—
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—
544C4C2×#369911yescharacteristic
545C4#6371011yescharacteristic
546C3#8351211yescharacteristic
547C2—41no—
548C2—41no—
549C2—42no—
550C2—721no—
551C2#1058990811yescharacteristic
552C2#1058992511yescharacteristic
553C2#1058993911yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#547C2
socleC22×C3C22×#67
hypercenter#547D9
hypocenterC9#3307
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C9×#547C2semidirect
2. #10589667C2semidirect
3. #10588919C2semidirect
4. #10588919C2semidirect
5. #10588917C2semidirect
6. #10588916C2semidirect
7. #10588768C2semidirect
8. #10588762C2semidirect
9. #10588732C2semidirect
10. #10588731C2semidirect
11. #10588725C2semidirect
12. #10588723C2semidirect
13. #10588697C2semidirect
14. #10588692C2semidirect
15. #10588688C2semidirect
213. #547D9semidirect
472. C9#3307semidirect

Maximal subgroups

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

subgroupindex
C9×#5472
#105896672
#105889192
#105889172
#105889162
#105887682
#105887622
#105887322
#105887312
#105887252
#105887232
#105886972
#105886922
#105886882
#835123