Finite Group Databasebeta

← #11901176

Subgroups — #11901176

Order 1152.

2334 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D9C212yesmaximal, complemented
2C9×#537C211yesmaximal, characteristic, complemented
3#10589935C212yesmaximal, complemented
4#10589730C214yesmaximal, complemented
5#10589729C214yesmaximal, complemented
6#10589709C214yesmaximal, complemented
7#10589708C214yesmaximal, complemented
8#10589707C214yesmaximal, complemented
9#10589698C214yesmaximal, complemented
10#10589612C211yesmaximal, characteristic, complemented
11C2×#63454C211yesmaximal, characteristic, complemented
12#86363—31nomaximal
13C2×C9×#41C2212yescomplemented
14#41×D9—216no—
15C2×#3701C2212yes—
16C2×Q8×D9C2212yescomplemented
17C2×#3699C2212yes—
18C2×#3699C2214yescomplemented
19C2×D4×D9C2214yes—
20C2×D4×D9C2212yescomplemented
21C2×#3697C2214yes—
22C2×#3697C2212yescomplemented
23C22×C4×D9C2211yescharacteristic
24C22×C4×D9C2214yescomplemented
25C9×C22⋊Q8C2214yescomplemented
26C9×#121C2214yescomplemented
27C9×#121C2214yescomplemented
28C2×C9×C4⋊C4C2211yescharacteristic, complemented
29#63508C2214yescomplemented
30#63502C2214yescomplemented
31#63501C2218yescomplemented
32#63500C2214yescomplemented
33#63499C2218yescomplemented
34D4×Dic9C2214yescomplemented
35#63492C2214yescomplemented
36#63492C2214yescomplemented
37C2×(C2×D9)⋊C4C2212yes—
38C2×C4⋊Dic9C2211yescharacteristic, complemented
39#63486C2214yescomplemented
40C2×C4×Dic9C2212yescomplemented
41#63459C2214yescomplemented
42#63457C2214yescomplemented
43#63456C2218yescomplemented
44#63455C2214yescomplemented
45#63454C2214yescomplemented
46#63454C2214yescomplemented
47#63450C2214yescomplemented
48#63447C2218yescomplemented
49#63445C2218yescomplemented
50#63444C2218yescomplemented
51#611⋊C4C2218yescomplemented
52C2×D3×#41—32no—
53C3×#537D311yescharacteristic
54#5833—32no—
55#5628—34no—
56#5627—34no—
57#5607—34no—
58#5606—34no—
59#5605—34no—
60#5596—34no—
61#5510—31no—
62C2×#892—31no—
63C23×D9C2314yes—
64C23×D9C2311yescharacteristic
65C9×#41—28no—
66C2×Q8×C9C2312yes—
67C2×D4×C9C2312yes—
68C2×D4×C9C2314yes—
69C2×D4×C9C2314yes—
70C22×C4×C9C2314yes—
71C22×C4×C9C2312yes—
72C22×C4×C9C2311yescharacteristic
73C2×#611C2314yes—
74C2×#611C2314yes—
75C2×#611C2314yes—
76C2×#611C2318yes—
77C22×Dic9C2314yes—
78C22×Dic9C2312yes—
79C22×Dic9C2311yescharacteristic
80#3701—28no—
81Q8×D9—28no—
82#3699—216no—
83#3699—28no—
84D4×D9—216no—
85D4×D9—28no—
86#3697—28no—
87#3697—216no—
88C2×D36C2312yes—
89C2×D36C2314yes—
90C2×D36C2314yes—
91C2×C4×D9—216no—
92C2×C4×D9D418yescomplemented
93C2×C4×D9C2314yes—
94C2×C4×D9C2314yes—
95C2×C4×D9C2314yes—
96C2×C4×D9C2312yes—
97C2×C4×D9C2312yes—
98C2×Dic18C2314yes—
99C2×Dic18C2312yes—
100C9×C4⋊C4C2314yes—
101C9×C4⋊C4C2314yes—
102C9×C22⋊C4C2318yes—
103#3676C2318yes—
104(C2×D9)⋊C4C2318yes—
105(C2×D9)⋊C4C2318yes—
106(C2×D9)⋊C4C2318yes—
107C4⋊Dic9C2314yes—
108C4⋊Dic9C2314yes—
109Dic9⋊C4C2318yes—
110C4×Dic9C2314yes—
111C4×Dic9C2314yes—
112#3449—91noSylow
113C2×C3×#41C2×D312yes—
114D3×#41—616no—
115C2×#239—32no—
116C2×D3×Q8—32no—
117C2×#237—34no—
118C2×#237—32no—
119C2×D3×D4—34no—
120C2×D3×D4—32no—
121C2×#235—32no—
122C2×#235—34no—
123C22×C4×D3—31no—
124C22×C4×D3—34no—
125C3×C22⋊Q8C2×D314yes—
126C3×#121C2×D314yes—
127C3×#121C2×D314yes—
128C2×C3×C4⋊C4C2×D311yescharacteristic
129#946—34no—
130#940—34no—
131#939—38no—
132#938—34no—
133#937—38no—
134D4×Dic3—34no—
135#930—34no—
136#930—34no—
137C2×(C2×D3)⋊C4—32no—
138C2×C4⋊Dic3—31no—
139#924—34no—
140C2×C4×Dic3—32no—
141#897—34no—
142#895—34no—
143#894—38no—
144#893—34no—
145#892—34no—
146#892—34no—
147#888—34no—
148#885—38no—
149#883—38no—
150#882—38no—
151#67⋊C4—38no—
152C23×C9C2414yes—
153C23×C9C2411yescharacteristic
154C22×D9—28no—
155C22×D9—41no—
156C22×D9—41no—
157C22×D9—44no—
158C22×D9—44no—
159C22×D9C2×D414yes—
160C22×D9C2414yes—
161C22×D9C2412yes—
162Q8×C9—24no—
163D4×C9—28no—
164D4×C9—24no—
165D4×C9—44no—
166C2×C4×C9—28no—
167C2×C4×C9—42no—
168C2×C4×C9C2×D414yes—
169C2×C4×C9C2414yes—
170C2×C4×C9C2414yes—
171C2×C4×C9C2412yes—
172#611—28no—
173#611—28no—
174#611—28no—
175#611—48no—
176C2×Dic9—28no—
177C2×Dic9—42no—
178C2×Dic9C2×D414yes—
179C2×Dic9C2414yes—
180C2×Dic9C2414yes—
181C2×Dic9C2411yescharacteristic
182C2×Dic9C2411yescharacteristic
183D36—28no—
184D36—24no—
185D36—44no—
186C4×D9—28no—
187C4×D9—28no—
188C4×D9—28no—
189C4×D9C2×D418yes—
190C4×D9C2×D418yes—
191Dic18—24no—
192Dic18—28no—
193C22×#41—92no—
194#537—92no—
195#537—91no—
196#537D911yescharacteristic, complemented
197#536—94no—
198#535—94no—
199#534—94no—
200#532—94no—
201#525—94no—
202#525—94no—
203C2×#117—91no—
204C23×D3—31no—
205C23×D3—34no—
206C3×#41—28no—
207C2×C3×Q8C22×D312yes—
208C2×C3×D4C22×D312yes—
209C2×C3×D4C22×D314yes—
210C2×C3×D4C22×D314yes—
211C22×C3×C4C22×D314yes—
212C22×C3×C4C22×D312yes—
213C22×C3×C4C22×D311yescharacteristic
214C2×#67—34no—
215C2×#67—34no—
216C2×#67—34no—
217C2×#67—38no—
218C22×Dic3—31no—
219C22×Dic3—34no—
220C22×Dic3—32no—
221#239—68no—
222D3×Q8—68no—
223#237—68no—
224#237—616no—
225D3×D4—68no—
226D3×D4—616no—
227#235—616no—
228#235—68no—
229C2×D12—34no—
230C2×D12—32no—
231C2×D12—34no—
232C2×C4×D3—38no—
233C2×C4×D3—32no—
234C2×C4×D3—32no—
235C2×C4×D3—34no—
236C2×C4×D3—34no—
237C2×C4×D3—34no—
238C2×C4×D3—616no—
239C2×Dic6—34no—
240C2×Dic6—32no—
241C3×C4⋊C4C22×D314yes—
242C3×C4⋊C4C22×D314yes—
243C3×C22⋊C4C22×D318yes—
244#217—38no—
245(C2×D3)⋊C4—38no—
246(C2×D3)⋊C4—38no—
247(C2×D3)⋊C4—38no—
248C4⋊Dic3—34no—
249C4⋊Dic3—34no—
250Dic3⋊C4—38no—
251C4×Dic3—34no—
252C4×Dic3—34no—
253C22×C9—21no—
254C22×C9—21no—
255C22×C9—24no—
256C22×C9—24no—
257C22×C9—24no—
258C22×C9C22×D412yes—
259C22×C9C2511yescharacteristic
260C2×D9—22no—
261C2×D9—22no—
262C2×D9—24no—
263C2×D9—24no—
264C2×D9—24no—
265C2×D9—44no—
266C2×D9—416no—
267C2×D9C22×D414yes—
268C4×C9—24no—
269C4×C9—24no—
270C4×C9C22×D414yes—
271Dic9—24no—
272Dic9—24no—
273Dic9C22×D412yes—
274Dic9C22×D412yes—
275C2×#41—92no—
276C2×#41—92no—
277C2×#41—94no—
278C2×#41—94no—
279C2×#41—92no—
280C2×#41—1816no—
281C2×#41C2×D912yescomplemented
282C22×Q8—92no—
283C22×D4—94no—
284C22×D4—92no—
285C23×C4—91no—
286C23×C4—94no—
287C4⋊Q8—94no—
288#127—94no—
289#124—98no—
290#123—98no—
291#123—98no—
292C22⋊Q8—94no—
293C22⋊Q8—94no—
294C22⋊Q8—94no—
295C22⋊Q8C2×D914yescomplemented
296#121—94no—
297#121—98no—
298#121—94no—
299#121—94no—
300#121—94no—
301#121C2×D914yescomplemented
302#121C2×D914yescomplemented
303#120—98no—
304#120—98no—
305C4×D4—94no—
306C4×D4—94no—
307C4×D4—98no—
308#117—94no—
309#117—94no—
310C2×C4⋊C4—91no—
311C2×C4⋊C4C2×D911yescharacteristic, complemented
312C2×C22⋊C4—92no—
313C2×C42—92no—
314C23×C3C23×D314yes—
315C23×C3C23×D311yescharacteristic
316C22×D3—32no—
317C22×D3—34no—
318C22×D3—34no—
319C22×D3—68no—
320C22×D3—121no—
321C22×D3—124no—
322C22×D3—121no—
323C22×D3—124no—
324C3×Q8—24no—
325C3×D4—28no—
326C3×D4—24no—
327C3×D4—44no—
328C2×C3×C4—28no—
329C2×C3×C4—42no—
330C2×C3×C4D3×D414yes—
331C2×C3×C4C23×D314yes—
332C2×C3×C4C23×D314yes—
333C2×C3×C4C23×D312yes—
334#67—68no—
335#67—68no—
336#67—68no—
337#67—128no—
338C2×Dic3—34no—
339C2×Dic3—31no—
340C2×Dic3—31no—
341C2×Dic3—34no—
342C2×Dic3—34no—
343C2×Dic3—68no—
344C2×Dic3—122no—
345D12—68no—
346D12—64no—
347D12—124no—
348C4×D3—38no—
349C4×D3—38no—
350C4×D3—68no—
351C4×D3—68no—
352C4×D3—68no—
353Dic6—68no—
354Dic6—64no—
355C2×C9—22no—
356C2×C9—44no—
357C2×C9C23×D411yescharacteristic
358C2×C9#58511yescharacteristic
359C2×C9#58511yescharacteristic
360D9—24no—
361D9—44no—
362C24—91no—
363C24—94no—
364#41—28no—
365#41—1816no—
366#41—1816no—
367#41—188no—
368#41—188no—
369#41—188no—
370C2×Q8—92no—
371C2×Q8—94no—
372C2×Q8—188no—
373C2×Q8C22×D912yes—
374C2×D4—94no—
375C2×D4—94no—
376C2×D4—94no—
377C2×D4—98no—
378C2×D4—94no—
379C2×D4—92no—
380C2×D4—94no—
381C2×D4—188no—
382C2×D4—1816no—
383C2×D4C22×D914yes—
384C2×D4C22×D912yes—
385C2×D4C22×D914yes—
386C22×C4—91no—
387C22×C4—98no—
388C22×C4—92no—
389C22×C4—92no—
390C22×C4—94no—
391C22×C4—92no—
392C22×C4—94no—
393C22×C4—94no—
394C22×C4—94no—
395C22×C4—1816no—
396C22×C4C22×D914yes—
397C22×C4C22×D912yes—
398C22×C4C22×D911yescharacteristic
399C4⋊C4—94no—
400C4⋊C4—98no—
401C4⋊C4—94no—
402C4⋊C4C22×D914yes—
403C4⋊C4C22×D914yes—
404C22⋊C4—98no—
405C22⋊C4—98no—
406C22⋊C4—98no—
407C22⋊C4—98no—
408C22⋊C4C22×D918yes—
409C42—94no—
410C42—94no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—24no—
414C22×C3—24no—
415C22×C3—24no—
416C22×C3C2×D3×D412yes—
417C22×C3C24×D311yescharacteristic
418C2×D3—34no—
419C2×D3—62no—
420C2×D3—62no—
421C2×D3—64no—
422C2×D3—64no—
423C2×D3—64no—
424C2×D3—124no—
425C2×D3—1216no—
426C3×C4—24no—
427C3×C4—24no—
428C3×C4C2×D3×D414yes—
429Dic3—32no—
430Dic3—32no—
431Dic3—64no—
432Dic3—64no—
433C9#344911yescharacteristic, complemented, Sylow
434C23—92no—
435C23—94no—
436C23—94no—
437C23—188no—
438C23—361no—
439C23—361no—
440C23—364no—
441C23—364no—
442C23C23×D914yes—
443C23C23×D911yescharacteristic
444Q8—24no—
445Q8—188no—
446Q8—184no—
447D4—28no—
448D4—24no—
449D4—44no—
450D4—188no—
451D4—188no—
452D4—188no—
453D4—188no—
454D4—184no—
455D4—364no—
456D4—368no—
457C2×C4—28no—
458C2×C4—42no—
459C2×C4—91no—
460C2×C4—91no—
461C2×C4—94no—
462C2×C4—98no—
463C2×C4—98no—
464C2×C4—94no—
465C2×C4—94no—
466C2×C4—188no—
467C2×C4—188no—
468C2×C4—188no—
469C2×C4—188no—
470C2×C4—362no—
471C2×C4D4×D914yes—
472C2×C4C23×D914yes—
473C2×C4C23×D914yes—
474C2×C4C23×D912yes—
475C2×C3—22no—
476C2×C3—44no—
477C2×C3C22×D3×D411yescharacteristic
478C2×C3#596611yescharacteristic
479C2×C3#596811yescharacteristic
480D3—64no—
481D3—124no—
482C22—21no—
483C22—21no—
484C22—24no—
485C22—24no—
486C22—24no—
487C22—94no—
488C22—182no—
489C22—182no—
490C22—184no—
491C22—184no—
492C22—184no—
493C22—364no—
494C22—3616no—
495C22C2×D4×D912yes—
496C22C24×D911yescharacteristic
497C4—24no—
498C4—24no—
499C4—92no—
500C4—92no—
501C4—184no—
502C4—184no—
503C4C2×D4×D914yes—
504C3#8636311yescharacteristic
505C2—22no—
506C2—44no—
507C2—184no—
508C2—364no—
509C2C22×D4×D911yescharacteristic
510C2#1059314111yescharacteristic
511C2#1059314311yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#537C2
hypercenter#537D9
hypocenterC9#3449
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#41×D9C2semidirect
2. C9×#537C2semidirect
3. #10589935C2semidirect
4. #10589730C2semidirect
5. #10589729C2semidirect
6. #10589709C2semidirect
7. #10589708C2semidirect
8. #10589707C2semidirect
9. #10589698C2semidirect
10. #10589612C2semidirect
11. C2×#63454C2semidirect
13. C2×C9×#41C22semidirect
16. C2×Q8×D9C22semidirect
18. C2×#3699C22semidirect
20. C2×D4×D9C22semidirect
22. C2×#3697C22semidirect
24. C22×C4×D9C22semidirect
25. C9×C22⋊Q8C22semidirect
26. C9×#121C22semidirect
27. C9×#121C22semidirect
28. C2×C9×C4⋊C4C22semidirect
29. #63508C22semidirect
30. #63502C22semidirect
31. #63501C22semidirect
32. #63500C22semidirect
33. #63499C22semidirect
34. D4×Dic9C22semidirect
35. #63492C22semidirect
36. #63492C22semidirect
38. C2×C4⋊Dic9C22semidirect
39. #63486C22semidirect
40. C2×C4×Dic9C22semidirect
41. #63459C22semidirect
42. #63457C22semidirect
43. #63456C22semidirect
44. #63455C22semidirect
45. #63454C22semidirect
46. #63454C22semidirect
47. #63450C22semidirect
48. #63447C22semidirect
49. #63445C22semidirect
50. #63444C22semidirect
51. #611⋊C4C22semidirect
92. C2×C4×D9D4semidirect
196. #537D9semidirect
281. C2×#41C2×D9semidirect
295. C22⋊Q8C2×D9semidirect
301. #121C2×D9semidirect
302. #121C2×D9semidirect
311. C2×C4⋊C4C2×D9semidirect
433. C9#3449semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D92
C9×#5372
#105899352
#105897302
#105897292
#105897092
#105897082
#105897072
#105896982
#105896122
C2×#634542
#863633