Finite Group Databasebeta

← #11872707

Subgroups — #11872707

Order 1152.

627 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589821C211yesmaximal, characteristic, complemented
2#10589647C211yesmaximal, characteristic, complemented
3C9×#459C211yesmaximal, characteristic, complemented
4#10588836C211yesmaximal, characteristic, complemented
5#10588836C211yesmaximal, characteristic, complemented
6#10588832C211yesmaximal, characteristic, complemented
7D8×Dic9C211yesmaximal, characteristic, complemented
8#10588754C211yesmaximal, characteristic, complemented
9#10588692C211yesmaximal, characteristic, complemented
10#10588531C211yesmaximal, characteristic, complemented
11#10588524C211yesmaximal, characteristic, complemented
12#10588465C211yesmaximal, characteristic, complemented
13#10588464C211yesmaximal, characteristic, complemented
14#10588459C211yesmaximal, characteristic, complemented
15#10588436C211yesmaximal, characteristic, complemented
16#80317—31nomaximal
17C2×D4×D9C2211yescharacteristic
18C2×C9×D8C2211yescharacteristic
19C2×C9×D8C2211yescharacteristic
20C9×#127C2211yescharacteristic, complemented
21C4×D4×C9C2211yescharacteristic
22#63501—21no—
23#63501—21no—
24#63500C2211yescharacteristic
25#63500C2211yescharacteristic
26#63497—21no—
27#63497—21no—
28D4×Dic9C2211yescharacteristic
29D4×Dic9C2211yescharacteristic, complemented
30D4×Dic9C2211yescharacteristic, complemented
31C2×#3673C2211yescharacteristic
32C2×#3673C2211yescharacteristic
33C4×#611—21no—
34C2×(C2×D9)⋊C4—21no—
35#63455C2211yescharacteristic
36#63454C2211yescharacteristic
37#611⋊C4—21no—
38C22⋊C4×D9—21no—
39C4×D36C2211yescharacteristic
40#63434C2211yescharacteristic
41#63432C2211yescharacteristic, complemented
42C9×C4⋊C8C2211yescharacteristic, complemented
43C9×#102C2211yescharacteristic, complemented
44C9×#102C2211yescharacteristic, complemented
45#63392C2211yescharacteristic
46#63392C2211yescharacteristic
47#63392C2211yescharacteristic, complemented
48#63392C2211yescharacteristic, complemented
49#63380C2211yescharacteristic
50#63380C2211yescharacteristic
51(C2×D9)⋊C8C2211yescharacteristic
52(C2×D9)⋊C8C2211yescharacteristic
53#63378C2211yescharacteristic, complemented
54#63377C2211yescharacteristic, complemented
55#63375C2211yescharacteristic, complemented
56C8×Dic9C2211yescharacteristic, complemented
57#63367C2211yescharacteristic, complemented
58#63366C2211yescharacteristic, complemented
59C4⋊(C9⋊C8)C2211yescharacteristic, complemented
60#5719—31no—
61#5545—31no—
62C3×#459D311yescharacteristic
63#5156—31no—
64#5156—31no—
65#5152—31no—
66Dic3×D8—31no—
67#5072—31no—
68#5009—31no—
69#4847—31no—
70#4840—31no—
71#4785—31no—
72#4784—31no—
73#4779—31no—
74#4756—31no—
75C23×D9—21no—
76C2×D4×C9—21no—
77C2×D4×C9—21no—
78C2×D4×C9C2311yescharacteristic
79C2×D4×C9C2311yescharacteristic
80C2×D4×C9C2311yescharacteristic
81C22×C4×C9—21no—
82C2×#611—21no—
83C2×#611—21no—
84C2×#611—21no—
85C22×Dic9—21no—
86C22×Dic9—21no—
87C22×Dic9—21no—
88D4×D9—22no—
89D4×D9—22no—
90C2×D36C2311yescharacteristic
91C2×C4×D9—21no—
92C2×C4×D9—21no—
93C2×C4×D9C2311yescharacteristic
94C9×D8—22no—
95C9×D8—22no—
96C2×C8×C9C2311yescharacteristic
97C2×C8×C9C2311yescharacteristic
98C9×C4⋊C4C2311yescharacteristic
99C9×C22⋊C4—21no—
100C42×C9C2311yescharacteristic
101#3676—21no—
102#3676—21no—
103#3676—21no—
104#3676—21no—
105#3676—21no—
106#3673—22no—
107#3673—22no—
108(C2×D9)⋊C4—21no—
109(C2×D9)⋊C4—21no—
110(C2×D9)⋊C4—21no—
111(C2×D9)⋊C4D411yescharacteristic
112(C2×D9)⋊C4D411yescharacteristic
113C4⋊Dic9C2311yescharacteristic
114C4⋊Dic9C2311yescharacteristic
115C4⋊Dic9C2311yescharacteristic
116Dic9⋊C4—21no—
117Dic9⋊C4—21no—
118Dic9⋊C4D411yescharacteristic
119Dic9⋊C4D411yescharacteristic
120C4×Dic9—21no—
121C4×Dic9C2311yescharacteristic
122C2×C9⋊C8C2311yescharacteristic
123C2×C9⋊C8C2311yescharacteristic
124#3122—91noSylow
125C2×D3×D4—31no—
126C2×C3×D8C2×D311yescharacteristic
127C2×C3×D8C2×D311yescharacteristic
128C3×#127C2×D311yescharacteristic
129C3×C4×D4C2×D311yescharacteristic
130#939—61no—
131#939—61no—
132#938—31no—
133#938—31no—
134#935—61no—
135#935—61no—
136D4×Dic3—31no—
137D4×Dic3—31no—
138D4×Dic3—31no—
139C2×#213—31no—
140C2×#213—31no—
141C4×#67—61no—
142C2×(C2×D3)⋊C4—61no—
143#893—31no—
144#892—31no—
145#67⋊C4—61no—
146D3×C22⋊C4—61no—
147C4×D12—31no—
148#872—31no—
149#870—31no—
150C3×C4⋊C8C2×D311yescharacteristic
151C3×#102C2×D311yescharacteristic
152C3×#102C2×D311yescharacteristic
153#832—31no—
154#832—31no—
155#832—31no—
156#832—31no—
157#821—31no—
158#821—31no—
159(C2×D3)⋊C8—31no—
160(C2×D3)⋊C8—31no—
161#818—31no—
162#817—31no—
163#815—31no—
164C8×Dic3—31no—
165#808—31no—
166#807—31no—
167C4⋊(C3⋊C8)—31no—
168C23×C9—21no—
169C23×C9—21no—
170C23×C9—21no—
171C22×D9—21no—
172C22×D9—24no—
173C22×D9—81no—
174C22×D9—81no—
175C22×D9C2×D411yescharacteristic
176D4×C9—21no—
177D4×C9—21no—
178D4×C9—21no—
179D4×C9—21no—
180D4×C9—21no—
181D4×C9—81no—
182D4×C9—81no—
183D4×C9#4112yes—
184C2×C4×C9—21no—
185C2×C4×C9—81no—
186C2×C4×C9C2×D411yescharacteristic
187C2×C4×C9C2×D411yescharacteristic
188C2×C4×C9C2411yescharacteristic
189#611—24no—
190#611—81no—
191#611—81no—
192C2×Dic9—21no—
193C2×Dic9—21no—
194C2×Dic9—21no—
195C2×Dic9—81no—
196C2×Dic9—81no—
197C2×Dic9—81no—
198C2×Dic9C2×D411yescharacteristic
199C2×Dic9C2×D411yescharacteristic
200C2×Dic9C2×D411yescharacteristic
201D36—21no—
202D36#4112yes—
203C4×D9—21no—
204C4×D9—21no—
205C4×D9—81no—
206C4×D9—81no—
207C8×C9—21no—
208C8×C9—21no—
209C9⋊C8—21no—
210C9⋊C8—21no—
211#540—91no—
212#518—91no—
213#482—91no—
214#482—91no—
215#478—91no—
216#478—91no—
217#459—91no—
218#459D911yescharacteristic, complemented
219#447—91no—
220#447—91no—
221#442—91no—
222#442—91no—
223C4×D8—91no—
224C4×D8—91no—
225#433—91no—
226C23×D3—61no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4C22×D311yescharacteristic
230C2×C3×D4C22×D311yescharacteristic
231C2×C3×D4C22×D311yescharacteristic
232C22×C3×C4—21no—
233C2×#67—61no—
234C2×#67—61no—
235C2×#67—61no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238C22×Dic3—61no—
239D3×D4—62no—
240D3×D4—62no—
241C2×D12—31no—
242C2×C4×D3—31no—
243C2×C4×D3—61no—
244C2×C4×D3—61no—
245C3×D8—22no—
246C3×D8—22no—
247C2×C3×C8C22×D311yescharacteristic
248C2×C3×C8C22×D311yescharacteristic
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C22⋊C4—21no—
251C3×C42C22×D311yescharacteristic
252#217—61no—
253#217—61no—
254#217—61no—
255#217—61no—
256#217—61no—
257#213—62no—
258#213—62no—
259(C2×D3)⋊C4—31no—
260(C2×D3)⋊C4—31no—
261(C2×D3)⋊C4—61no—
262(C2×D3)⋊C4—61no—
263(C2×D3)⋊C4—61no—
264C4⋊Dic3—31no—
265C4⋊Dic3—31no—
266C4⋊Dic3—31no—
267Dic3⋊C4—31no—
268Dic3⋊C4—31no—
269Dic3⋊C4—61no—
270Dic3⋊C4—61no—
271C4×Dic3—31no—
272C4×Dic3—61no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C22×C9—22no—
276C22×C9—41no—
277C22×C9—41no—
278C22×C9—41no—
279C22×C9—41no—
280C22×C9—41no—
281C22×C9—41no—
282C22×C9—41no—
283C22×C9—41no—
284C22×C9C22×D411yescharacteristic
285C2×D9—21no—
286C2×D9—22no—
287C2×D9—21no—
288C2×D9—21no—
289C2×D9—41no—
290C2×D9—41no—
291C2×D9—84no—
292C4×C9—21no—
293C4×C9—21no—
294C4×C9—41no—
295C4×C9C2×#4111yescharacteristic
296C4×C9C2×#4111yescharacteristic
297Dic9—21no—
298Dic9—21no—
299Dic9—21no—
300Dic9—41no—
301Dic9—41no—
302Dic9—41no—
303C22×D4—91no—
304C2×D8—91no—
305C2×D8—91no—
306C2×D8C2×D911yescharacteristic
307C2×D8C2×D911yescharacteristic
308#127C2×D911yescharacteristic, complemented
309#125—91no—
310#123—181no—
311#123—181no—
312#121—91no—
313#121—91no—
314#121—181no—
315#121—181no—
316C4×D4—91no—
317C4×D4—91no—
318C4×D4—91no—
319C4×D4—91no—
320C4×D4—91no—
321C4×D4—181no—
322C4×D4—181no—
323C4×D4C2×D911yescharacteristic
324#117—91no—
325#117—91no—
326C2×C22⋊C4—181no—
327C2×C22⋊C4—181no—
328#107—91no—
329#107—91no—
330#106—91no—
331#106—91no—
332C4⋊C8—91no—
333C4⋊C8C2×D911yescharacteristic, complemented
334#102—91no—
335#102—91no—
336#102—91no—
337#102—91no—
338#102—91no—
339#102—91no—
340#102C2×D911yescharacteristic, complemented
341#102C2×D911yescharacteristic, complemented
342C22⋊C8—91no—
343C22⋊C8—91no—
344#97—91no—
345C4×C8—91no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3—21no—
349C22×D3—31no—
350C22×D3—61no—
351C22×D3—64no—
352C22×D3—241no—
353C22×D3—241no—
354C3×D4—21no—
355C3×D4—21no—
356C3×D4—21no—
357C3×D4—21no—
358C3×D4—21no—
359C3×D4—81no—
360C3×D4—81no—
361C3×D4#23712yes—
362C2×C3×C4—21no—
363C2×C3×C4—81no—
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367#67—64no—
368#67—241no—
369#67—241no—
370C2×Dic3—31no—
371C2×Dic3—31no—
372C2×Dic3—31no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—241no—
377C2×Dic3—241no—
378C2×Dic3—241no—
379D12—32no—
380D12—61no—
381C4×D3—61no—
382C4×D3—61no—
383C4×D3—241no—
384C4×D3—241no—
385C3×C8—21no—
386C3×C8—21no—
387C3⋊C8—61no—
388C3⋊C8—61no—
389C2×C9—42no—
390C2×C9—81no—
391C2×C9—81no—
392C2×C9#52511yescharacteristic
393C2×C9#57611yescharacteristic
394C2×C9#57611yescharacteristic
395D9—41no—
396D9—42no—
397C24—181no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—91no—
401C2×D4—181no—
402C2×D4—182no—
403C2×D4—182no—
404C2×D4—181no—
405C2×D4—181no—
406C2×D4C22×D911yescharacteristic
407C2×D4C22×D911yescharacteristic
408C2×D4C22×D911yescharacteristic
409C22×C4—21no—
410C22×C4—91no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4—181no—
414C22×C4—181no—
415C22×C4—181no—
416D8—22no—
417D8—22no—
418D8—182no—
419D8—182no—
420C2×C8—91no—
421C2×C8—91no—
422C2×C8C22×D911yescharacteristic
423C2×C8C22×D911yescharacteristic
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—91no—
427C4⋊C4—91no—
428C4⋊C4—91no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C4⋊C4C22×D911yescharacteristic
432C22⋊C4—21no—
433C22⋊C4—91no—
434C22⋊C4—91no—
435C22⋊C4—181no—
436C22⋊C4—181no—
437C22⋊C4—181no—
438C22⋊C4—181no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C42—91no—
444C42—181no—
445C42C22×D911yescharacteristic
446C22×C3—22no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3—41no—
450C22×C3—41no—
451C22×C3—41no—
452C22×C3—41no—
453C22×C3—41no—
454C22×C3—41no—
455C22×C3C2×D3×D411yescharacteristic
456C2×D3—61no—
457C2×D3—61no—
458C2×D3—61no—
459C2×D3—62no—
460C2×D3—121no—
461C2×D3—121no—
462C2×D3—244no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—41no—
466C3×C4C2×#23711yescharacteristic
467C3×C4D3×#4111yescharacteristic
468Dic3—61no—
469Dic3—61no—
470Dic3—61no—
471Dic3—121no—
472Dic3—121no—
473Dic3—121no—
474C9#312211yescharacteristic, complemented, Sylow
475C23—21no—
476C23—21no—
477C23—21no—
478C23—91no—
479C23—184no—
480C23—181no—
481C23—721no—
482C23—721no—
483D4—21no—
484D4—21no—
485D4—21no—
486D4—21no—
487D4—21no—
488D4—81no—
489D4—81no—
490D4—92no—
491D4—184no—
492D4—181no—
493D4—721no—
494D4—721no—
495D4#369912yes—
496C2×C4—21no—
497C2×C4—81no—
498C2×C4—91no—
499C2×C4—91no—
500C2×C4—91no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—721no—
507C2×C4—721no—
508C2×C4—721no—
509C2×C4—721no—
510C2×C4—721no—
511C2×C4D4×D911yescharacteristic
512C2×C4D4×D911yescharacteristic
513C2×C4C23×D911yescharacteristic
514C8—21no—
515C8—21no—
516C8—181no—
517C8—181no—
518C2×C3—42no—
519C2×C3—81no—
520C2×C3—81no—
521C2×C3#560611yescharacteristic
522C2×C3#575711yescharacteristic
523C2×C3#577411yescharacteristic
524D3—121no—
525D3—122no—
526C22—22no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—181no—
536C22—182no—
537C22—181no—
538C22—181no—
539C22—361no—
540C22—361no—
541C22—724no—
542C22C2×D4×D911yescharacteristic
543C4—21no—
544C4—21no—
545C4—41no—
546C4—181no—
547C4—181no—
548C4—181no—
549C4—361no—
550C4—361no—
551C4—361no—
552C4C2×#369911yescharacteristic
553C4#41×D911yescharacteristic
554C3#8031711yescharacteristic
555C2—42no—
556C2—81no—
557C2—81no—
558C2—361no—
559C2—362no—
560C2#1058970811yescharacteristic
561C2#1058985911yescharacteristic
562C2#1058987611yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#459C2
socleC22×C3C2×D3×D4
hypercenter#459D9
hypocenterC9#3122
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #10589821C2semidirect
2. #10589647C2semidirect
3. C9×#459C2semidirect
4. #10588836C2semidirect
5. #10588836C2semidirect
6. #10588832C2semidirect
7. D8×Dic9C2semidirect
8. #10588754C2semidirect
9. #10588692C2semidirect
10. #10588531C2semidirect
11. #10588524C2semidirect
12. #10588465C2semidirect
13. #10588464C2semidirect
14. #10588459C2semidirect
15. #10588436C2semidirect
20. C9×#127C22semidirect
29. D4×Dic9C22semidirect
30. D4×Dic9C22semidirect
41. #63432C22semidirect
42. C9×C4⋊C8C22semidirect
43. C9×#102C22semidirect
44. C9×#102C22semidirect
47. #63392C22semidirect
48. #63392C22semidirect
53. #63378C22semidirect
54. #63377C22semidirect
55. #63375C22semidirect
56. C8×Dic9C22semidirect
57. #63367C22semidirect
58. #63366C22semidirect
59. C4⋊(C9⋊C8)C22semidirect
218. #459D9semidirect
308. #127C2×D9semidirect
333. C4⋊C8C2×D9semidirect
340. #102C2×D9semidirect
341. #102C2×D9semidirect
474. C9#3122semidirect

Maximal subgroups

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

subgroupindex
#105898212
#105896472
C9×#4592
#105888362
#105888322
D8×Dic92
#105887542
#105886922
#105885312
#105885242
#105884652
#105884642
#105884592
#105884362
#803173