Finite Group Databasebeta

← #11900879

Subgroups — #11900879

Order 1152.

1818 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#533C211yesmaximal, characteristic, complemented
2#10589830C212yesmaximal, complemented
3#10589827C212yesmaximal, complemented
4#10589793C214yesmaximal, complemented
5#10589729C214yesmaximal, complemented
6#10589726C214yesmaximal, complemented
7#10589682C214yesmaximal, complemented
8C4×#3701C214yesmaximal, complemented
9#10589626C212yesmaximal, complemented
10#10589624C212yesmaximal, complemented
11#10589579C211yesmaximal, characteristic, complemented
12C2×C42×D9C211yesmaximal, characteristic, complemented
13#86257—31nomaximal
14C2×#3701C2214yes—
15C2×#3697C2212yes—
16C22×C4×D9C2212yes—
17C22×C4×D9C2211yescharacteristic
18C9×C4⋊Q8C2212yescomplemented
19C9×#125C2212yescomplemented
20C9×C22⋊Q8C2214yes—
21C4×Q8×C9C2214yescomplemented
22C9×#117C2212yes—
23C2×C42×C9C2211yescharacteristic
24#63509C2214yescomplemented
25#63508C2214yes—
26Q8×Dic9C2214yescomplemented
27#63492C2214yes—
28C2×C4×Dic9C2212yes—
29C2×C4×Dic9C2211yescharacteristic
30#63460C2218yescomplemented
31#63459C2214yes—
32#63457C2214yes—
33#63457C2214yes—
34#63456C2218yes—
35#63455C2218yes—
36#63455C2214yescomplemented
37#63455C2214yescomplemented
38#63454C2214yes—
39#63454C2218yescomplemented
40#63452C2214yescomplemented
41#63449C2214yescomplemented
42#63448C2214yes—
43#63444C2214yes—
44#611⋊C4C2218yes—
45#63437C2212yescomplemented
46#63436C2211yescharacteristic, complemented
47C4×D36C2218yes—
48C4×D36C2214yescomplemented
49#63434C2214yescomplemented
50C42×D9C2212yes—
51C42×D9C2212yes—
52C42×D9C2212yes—
53C42×D9C2212yes—
54C42×D9C2214yescomplemented
55#63431C2211yescharacteristic, complemented
56C3×#533D311yescharacteristic
57#5728—32no—
58#5725—32no—
59#5691—34no—
60#5627—34no—
61#5624—34no—
62#5580—34no—
63C4×#239—34no—
64#5524—32no—
65#5522—32no—
66#5477—31no—
67C2×C42×D3—31no—
68C23×D9C2311yescharacteristic
69C2×Q8×C9C2314yes—
70C22×C4×C9C2312yes—
71C22×C4×C9C2311yescharacteristic
72C2×#611C2314yes—
73C22×Dic9C2312yes—
74C22×Dic9C2311yescharacteristic
75#3701—216no—
76#3697—28no—
77C2×D36C2314yes—
78C2×D36C2318yes—
79C2×D36C2312yes—
80C2×C4×D9—24no—
81C2×C4×D9—28no—
82C2×C4×D9C2312yes—
83C2×C4×D9C2312yes—
84C2×C4×D9C2312yes—
85C2×C4×D9C2312yes—
86C2×C4×D9C2312yes—
87C2×C4×D9C2314yes—
88C2×C4×D9C2318yes—
89C2×C4×D9C2312yes—
90C2×Dic18C2312yes—
91C9×C4⋊C4C2314yes—
92C9×C4⋊C4C2318yes—
93C9×C4⋊C4C2314yes—
94C9×C22⋊C4C2314yes—
95C42×C9C2312yes—
96C42×C9C2311yescharacteristic
97C42×C9C2311yescharacteristic
98C42×C9C2314yes—
99(C2×D9)⋊C4C2318yes—
100(C2×D9)⋊C4C2318yes—
101(C2×D9)⋊C4C2318yes—
102(C2×D9)⋊C4C2318yes—
103C4⋊Dic9C2314yes—
104C4⋊Dic9C2318yes—
105Dic9⋊C4C2318yes—
106C4×Dic9C2312yes—
107C4×Dic9C2318yes—
108C4×Dic9C2312yes—
109C4×Dic9C2311yescharacteristic
110C4×Dic9C2311yescharacteristic
111C4×Dic9C2312yes—
112C4×Dic9C2312yes—
113C4×Dic9C2312yes—
114#3444—91noSylow
115C2×#239—34no—
116C2×#235—32no—
117C22×C4×D3—31no—
118C22×C4×D3—32no—
119C3×C4⋊Q8C2×D312yes—
120C3×#125C2×D312yes—
121C3×C22⋊Q8C2×D314yes—
122C3×C4×Q8C2×D314yes—
123C3×#117C2×D312yes—
124C2×C3×C42C2×D311yescharacteristic
125#947—34no—
126#946—34no—
127Q8×Dic3—34no—
128#930—34no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—32no—
131#898—38no—
132#897—34no—
133#895—34no—
134#895—34no—
135#894—38no—
136#893—34no—
137#893—38no—
138#893—34no—
139#892—38no—
140#892—34no—
141#890—34no—
142#887—34no—
143#886—34no—
144#882—34no—
145#67⋊C4—38no—
146#875—32no—
147#874—31no—
148C4×D12—34no—
149C4×D12—38no—
150#872—34no—
151C42×D3—32no—
152C42×D3—32no—
153C42×D3—32no—
154C42×D3—32no—
155C42×D3—34no—
156#869—31no—
157C23×C9C2411yescharacteristic
158C22×D9—22no—
159C22×D9—24no—
160C22×D9C2414yes—
161C22×D9C2412yes—
162Q8×C9—28no—
163C2×C4×C9—24no—
164C2×C4×C9#4114yescomplemented
165C2×C4×C9C2412yes—
166C2×C4×C9C2418yes—
167C2×C4×C9C2412yes—
168C2×C4×C9C2411yescharacteristic
169C2×C4×C9C2411yescharacteristic
170#611—28no—
171C2×Dic9—22no—
172C2×Dic9—24no—
173C2×Dic9C2412yes—
174C2×Dic9C2412yes—
175C2×Dic9C2414yes—
176C2×Dic9C2412yes—
177D36—216no—
178D36—24no—
179D36—28no—
180C4×D9—24no—
181C4×D9—24no—
182C4×D9—24no—
183C4×D9—24no—
184C4×D9—28no—
185C4×D9—24no—
186C4×D9—216no—
187C4×D9#4118yescomplemented
188Dic18—24no—
189#533—92no—
190#533D911yescharacteristic, complemented
191#532—92no—
192#532—91no—
193#529—94no—
194#529—94no—
195#529—94no—
196#525—94no—
197#525—92no—
198C4×#41—94no—
199C4×#41—92no—
200C22×C42—91no—
201C23×D3—31no—
202C2×C3×Q8C22×D314yes—
203C22×C3×C4C22×D312yes—
204C22×C3×C4C22×D311yescharacteristic
205C2×#67—34no—
206C22×Dic3—32no—
207C22×Dic3—31no—
208#239—616no—
209#235—68no—
210C2×D12—34no—
211C2×D12—38no—
212C2×D12—32no—
213C2×C4×D3—32no—
214C2×C4×D3—32no—
215C2×C4×D3—32no—
216C2×C4×D3—32no—
217C2×C4×D3—32no—
218C2×C4×D3—32no—
219C2×C4×D3—34no—
220C2×C4×D3—38no—
221C2×C4×D3—68no—
222C2×C4×D3—64no—
223C2×Dic6—32no—
224C3×C4⋊C4C22×D314yes—
225C3×C4⋊C4C22×D314yes—
226C3×C4⋊C4C22×D318yes—
227C3×C22⋊C4C22×D314yes—
228C3×C42C22×D311yescharacteristic
229C3×C42C22×D312yes—
230C3×C42C22×D311yescharacteristic
231C3×C42C22×D314yes—
232(C2×D3)⋊C4—38no—
233(C2×D3)⋊C4—38no—
234(C2×D3)⋊C4—38no—
235(C2×D3)⋊C4—38no—
236C4⋊Dic3—34no—
237C4⋊Dic3—38no—
238Dic3⋊C4—38no—
239C4×Dic3—31no—
240C4×Dic3—31no—
241C4×Dic3—32no—
242C4×Dic3—32no—
243C4×Dic3—32no—
244C4×Dic3—32no—
245C4×Dic3—32no—
246C4×Dic3—38no—
247C22×C9—22no—
248C22×C9C2×#4112yes—
249C22×C9C2511yescharacteristic
250C2×D9—28no—
251C2×D9—22no—
252C2×D9—22no—
253C2×D9—28no—
254C2×D9—24no—
255C2×D9C2×#4114yes—
256C4×C9—22no—
257C4×C9—28no—
258C4×C9C2×#4112yes—
259C4×C9C2×#4112yes—
260C4×C9C2×#4114yes—
261Dic9—24no—
262Dic9—22no—
263Dic9—22no—
264Dic9C2×#4114yes—
265C2×#41—94no—
266C2×#41—92no—
267C23×C4—92no—
268C23×C4—91no—
269C4⋊Q8—91no—
270C4⋊Q8C2×D912yescomplemented
271#127—91no—
272#126—98no—
273#125—94no—
274#125C2×D912yescomplemented
275#124—94no—
276#124—92no—
277#123—98no—
278#123—94no—
279C22⋊Q8—94no—
280C22⋊Q8—94no—
281C22⋊Q8C2×D914yes—
282#121—94no—
283#121—94no—
284#121—94no—
285#120—94no—
286C4×Q8—94no—
287C4×Q8—94no—
288C4×Q8C2×D914yescomplemented
289C4×D4—98no—
290C4×D4—94no—
291C4×D4—94no—
292C4×D4—98no—
293C4×D4—98no—
294C4×D4—94no—
295#117—94no—
296#117—98no—
297#117—94no—
298#117C2×D912yes—
299C2×C42—91no—
300C2×C42—92no—
301C2×C42—94no—
302C2×C42—92no—
303C2×C42—92no—
304C2×C42—92no—
305C2×C42—92no—
306C2×C42C2×D911yescharacteristic
307C23×C3C23×D311yescharacteristic
308C22×D3—32no—
309C22×D3—34no—
310C22×D3—64no—
311C22×D3—62no—
312C3×Q8—28no—
313C2×C3×C4—24no—
314C2×C3×C4#23914yes—
315C2×C3×C4C23×D312yes—
316C2×C3×C4C23×D318yes—
317C2×C3×C4C23×D311yescharacteristic
318C2×C3×C4C23×D312yes—
319C2×C3×C4C23×D311yescharacteristic
320#67—68no—
321C2×Dic3—32no—
322C2×Dic3—32no—
323C2×Dic3—32no—
324C2×Dic3—34no—
325C2×Dic3—64no—
326C2×Dic3—62no—
327D12—616no—
328D12—64no—
329D12—68no—
330C4×D3—38no—
331C4×D3—64no—
332C4×D3—616no—
333C4×D3—64no—
334C4×D3—64no—
335C4×D3—64no—
336C4×D3—68no—
337C4×D3—64no—
338Dic6—64no—
339C2×C9—22no—
340C2×C9C22×#4111yescharacteristic
341C2×C9C22×#4112yes—
342D9—24no—
343D9—44no—
344C24—91no—
345#41—1816no—
346#41—188no—
347C2×Q8—92no—
348C2×Q8C22×D914yes—
349C2×D4—94no—
350C2×D4—98no—
351C2×D4—92no—
352C2×D4—94no—
353C22×C4—92no—
354C22×C4—92no—
355C22×C4—91no—
356C22×C4—92no—
357C22×C4—92no—
358C22×C4—92no—
359C22×C4—92no—
360C22×C4—98no—
361C22×C4—92no—
362C22×C4—94no—
363C22×C4—188no—
364C22×C4—184no—
365C22×C4C22×D912yes—
366C22×C4C22×D911yescharacteristic
367C4⋊C4—94no—
368C4⋊C4—98no—
369C4⋊C4—98no—
370C4⋊C4C22×D914yes—
371C4⋊C4C22×D918yes—
372C4⋊C4C22×D914yes—
373C22⋊C4—98no—
374C22⋊C4—98no—
375C22⋊C4—98no—
376C22⋊C4—98no—
377C22⋊C4C22×D914yes—
378C42—92no—
379C42—92no—
380C42—92no—
381C42—92no—
382C42—92no—
383C42—98no—
384C42—91no—
385C42—91no—
386C42C22×D911yescharacteristic
387C42C22×D911yescharacteristic
388C42C22×D912yes—
389C42C22×D914yes—
390C22×C3—22no—
391C22×C3C2×#23912yes—
392C22×C3C24×D311yescharacteristic
393C2×D3—34no—
394C2×D3—68no—
395C2×D3—62no—
396C2×D3—62no—
397C2×D3—64no—
398C2×D3—68no—
399C3×C4—22no—
400C3×C4—28no—
401C3×C4C2×#23912yes—
402C3×C4C2×#23912yes—
403C3×C4D3×#4114yes—
404Dic3—34no—
405Dic3—64no—
406Dic3—62no—
407Dic3—62no—
408C9#344411yescharacteristic, complemented, Sylow
409C23—92no—
410C23—94no—
411C23—184no—
412C23—182no—
413C23C23×D911yescharacteristic
414Q8—28no—
415Q8—184no—
416D4—1816no—
417D4—188no—
418D4—184no—
419D4—188no—
420C2×C4—24no—
421C2×C4—92no—
422C2×C4—98no—
423C2×C4—92no—
424C2×C4—92no—
425C2×C4—94no—
426C2×C4—184no—
427C2×C4—1816no—
428C2×C4—184no—
429C2×C4—184no—
430C2×C4—182no—
431C2×C4—184no—
432C2×C4—184no—
433C2×C4—188no—
434C2×C4—184no—
435C2×C4#370114yescomplemented
436C2×C4C23×D912yes—
437C2×C4C23×D918yes—
438C2×C4C23×D911yescharacteristic
439C2×C4C23×D912yes—
440C2×C4C23×D911yescharacteristic
441C2×C3—22no—
442C2×C3C22×#23911yescharacteristic
443C2×C3C2×D3×#4112yes—
444D3—64no—
445D3—124no—
446C22—22no—
447C22—94no—
448C22—188no—
449C22—182no—
450C22—182no—
451C22—184no—
452C22—188no—
453C22C2×#370112yes—
454C22C24×D911yescharacteristic
455C4—22no—
456C4—28no—
457C4—94no—
458C4—182no—
459C4—184no—
460C4—182no—
461C4C2×#370112yes—
462C4C2×#370112yes—
463C4#41×D914yes—
464C3#8625711yescharacteristic
465C2—22no—
466C2—184no—
467C2—364no—
468C2C22×#370111yescharacteristic
469C2C2×#41×D912yes—
subgroupG/H
centerC2×C4C23×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#533C2
hypercenter#533D9
hypocenterC9#3444
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C9×#533C2semidirect
2. #10589830C2semidirect
3. #10589827C2semidirect
4. #10589793C2semidirect
5. #10589729C2semidirect
6. #10589726C2semidirect
7. #10589682C2semidirect
8. C4×#3701C2semidirect
9. #10589626C2semidirect
10. #10589624C2semidirect
11. #10589579C2semidirect
12. C2×C42×D9C2semidirect
18. C9×C4⋊Q8C22semidirect
19. C9×#125C22semidirect
21. C4×Q8×C9C22semidirect
24. #63509C22semidirect
26. Q8×Dic9C22semidirect
30. #63460C22semidirect
36. #63455C22semidirect
37. #63455C22semidirect
39. #63454C22semidirect
40. #63452C22semidirect
41. #63449C22semidirect
45. #63437C22semidirect
46. #63436C22semidirect
48. C4×D36C22semidirect
49. #63434C22semidirect
54. C42×D9C22semidirect
55. #63431C22semidirect
164. C2×C4×C9#41semidirect
187. C4×D9#41semidirect
190. #533D9semidirect
270. C4⋊Q8C2×D9semidirect
274. #125C2×D9semidirect
288. C4×Q8C2×D9semidirect
408. C9#3444semidirect
435. C2×C4#3701semidirect

Maximal subgroups

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

subgroupindex
C9×#5332
#105898302
#105898272
#105897932
#105897292
#105897262
#105896822
C4×#37012
#105896262
#105896242
#105895792
C2×C42×D92
#862573