Finite Group Databasebeta

← #11904613

Subgroups — #11904613

Order 1152.

2487 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63715C211yesmaximal, characteristic, complemented
2C2×#41×D9C211yesmaximal, characteristic, complemented
3C9×#520C211yesmaximal, characteristic, complemented
4#10589679C212yesmaximal, complemented
5#10589678C212yesmaximal, complemented
6#10589656C216yesmaximal, complemented
7D4×D36C216yesmaximal, complemented
8#10589627C213yesmaximal, complemented
9#10589626C213yesmaximal, complemented
10#10589612C213yesmaximal, complemented
11C2×#63457C213yesmaximal, complemented
12#85900—31nomaximal
13C2×C9×#41C2211yescharacteristic
14#63715—28no—
15#41×D9—28no—
16C2×#3701C2211yescharacteristic, complemented
17C2×#3701C2212yescomplemented
18C2×Q8×D9C2211yescharacteristic, complemented
19C2×#3699C2213yescomplemented
20C2×D4×D9C2213yescomplemented
21C2×D4×D9C2216yescomplemented
22C2×#3697C2213yescomplemented
23C2×#3697C2213yescomplemented
24C22×D36C2213yescomplemented
25C22×D36C2216yescomplemented
26C22×C4×D9C2213yescomplemented
27C4×Q8×C9C2212yescomplemented
28C4×D4×C9C2216yescomplemented
29C9×#117C2213yescomplemented
30C2×C9×C4⋊C4C2213yescomplemented
31#63492C22112yescomplemented
32C2×(C2×D9)⋊C4C2216yescomplemented
33#63459C2213yescomplemented
34#63459C2216yescomplemented
35#63459C2211yescharacteristic, complemented
36#63457C2213yescomplemented
37#63457C2216yescomplemented
38#63457C2216yescomplemented
39#63457C2216yescomplemented
40#63457C2216yescomplemented
41#63457C2213yescomplemented
42#63448C2216yescomplemented
43#63444C2216yescomplemented
44#63444C22112yescomplemented
45#63437C2216yescomplemented
46#63436C2216yescomplemented
47C4×D36C2216yescomplemented
48C4×D36C2216yescomplemented
49C2×#1009—31no—
50C2×D3×#41—31no—
51C3×#520D311yescharacteristic
52#5577—32no—
53#5576—32no—
54#5554—36no—
55D4×D12—36no—
56#5525—33no—
57#5524—33no—
58#5510—33no—
59C2×#895—33no—
60C23×D9C2313yes—
61C23×D9C2316yes—
62C9×#41D418yescomplemented
63C2×Q8×C9C2311yescharacteristic
64C2×D4×C9C2313yes—
65C22×C4×C9C2316yes—
66C22×C4×C9C2313yes—
67C2×#611C2316yes—
68C2×#611C2316yes—
69C22×Dic9C2313yes—
70#3701—24no—
71#3701—28no—
72Q8×D9—24no—
73#3699—212no—
74D4×D9—212no—
75D4×D9—224no—
76#3697—212no—
77#3697—212no—
78C2×D36—212no—
79C2×D36—412no—
80C2×D36C2316yes—
81C2×D36C2313yes—
82C2×D36C2316yes—
83C2×D36C2313yes—
84C2×D36C23112yes—
85C2×D36C2316yes—
86C2×C4×D9—212no—
87C2×C4×D9C2313yes—
88C2×C4×D9C2313yes—
89C2×C4×D9C2316yes—
90C2×C4×D9C2311yescharacteristic
91C2×C4×D9C2313yes—
92C2×Dic18C2313yes—
93C2×Dic18C2311yescharacteristic
94C9×C4⋊C4C2313yes—
95C9×C4⋊C4C2316yes—
96C9×C4⋊C4C2311yescharacteristic
97C9×C22⋊C4C2316yes—
98C42×C9C2316yes—
99(C2×D9)⋊C4C2316yes—
100(C2×D9)⋊C4C23112yes—
101(C2×D9)⋊C4C2316yes—
102(C2×D9)⋊C4C2312yes—
103(C2×D9)⋊C4C2316yes—
104C4⋊Dic9C2316yes—
105C4⋊Dic9C2312yes—
106#3488—91noSylow
107C2×C3×#41C2×D311yescharacteristic
108#1009—68no—
109D3×#41—68no—
110C2×#239—31no—
111C2×#239—32no—
112C2×D3×Q8—31no—
113C2×#237—33no—
114C2×D3×D4—33no—
115C2×D3×D4—36no—
116C2×#235—33no—
117C2×#235—33no—
118C22×D12—33no—
119C22×D12—36no—
120C22×C4×D3—33no—
121C3×C4×Q8C2×D312yes—
122C3×C4×D4C2×D316yes—
123C3×#117C2×D313yes—
124C2×C3×C4⋊C4C2×D313yes—
125#930—312no—
126C2×(C2×D3)⋊C4—36no—
127#897—33no—
128#897—36no—
129#897—31no—
130#895—33no—
131#895—36no—
132#895—36no—
133#895—36no—
134#895—36no—
135#895—33no—
136#886—36no—
137#882—36no—
138#882—312no—
139#875—36no—
140#874—36no—
141C4×D12—36no—
142C4×D12—36no—
143C23×C9C2413yes—
144C22×D9—26no—
145C22×D9—212no—
146C22×D9—26no—
147C22×D9—43no—
148C22×D9—46no—
149C22×D9—46no—
150C22×D9C2416yes—
151C22×D9C2413yes—
152C22×D9C2411yescharacteristic
153Q8×C9C2×D414yescomplemented
154D4×C9C2×D4112yescomplemented
155C2×C4×C9—46no—
156C2×C4×C9C2×D4112yescomplemented
157C2×C4×C9C2412yes—
158C2×C4×C9C2416yes—
159C2×C4×C9C2413yes—
160C2×C4×C9C2411yescharacteristic
161#611—212no—
162#611—212no—
163C2×Dic9—26no—
164C2×Dic9C2412yes—
165C2×Dic9C2413yes—
166C2×Dic9C2411yescharacteristic
167D36—212no—
168D36—26no—
169D36—212no—
170D36—26no—
171D36—412no—
172D36—46no—
173C4×D9—22no—
174C4×D9—26no—
175C4×D9—26no—
176C4×D9—26no—
177C4×D9—212no—
178Dic18—22no—
179Dic18—26no—
180C2×H(5,𝔽2)—91no—
181C22×#41—91no—
182#550—92no—
183#548—92no—
184#546—96no—
185D42—96no—
186#537—93no—
187#535—93no—
188#525—93no—
189C2×#121—93no—
190#520D911yescharacteristic, complemented
191C23×D3—33no—
192C23×D3—36no—
193C3×#41D1218yes—
194C2×C3×Q8C22×D311yescharacteristic
195C2×C3×D4C22×D313yes—
196C22×C3×C4C22×D316yes—
197C22×C3×C4C22×D313yes—
198C2×#67—36no—
199C2×#67—36no—
200C22×Dic3—33no—
201#239—64no—
202#239—68no—
203D3×Q8—64no—
204#237—612no—
205D3×D4—612no—
206D3×D4—624no—
207#235—612no—
208#235—612no—
209C2×D12—36no—
210C2×D12—33no—
211C2×D12—36no—
212C2×D12—33no—
213C2×D12—36no—
214C2×D12—312no—
215C2×D12—612no—
216C2×D12—1212no—
217C2×C4×D3—33no—
218C2×C4×D3—33no—
219C2×C4×D3—36no—
220C2×C4×D3—31no—
221C2×C4×D3—33no—
222C2×C4×D3—612no—
223C2×Dic6—33no—
224C2×Dic6—31no—
225C3×C4⋊C4C22×D313yes—
226C3×C4⋊C4C22×D316yes—
227C3×C4⋊C4C22×D311yescharacteristic
228C3×C22⋊C4C22×D316yes—
229C3×C42C22×D316yes—
230(C2×D3)⋊C4—32no—
231(C2×D3)⋊C4—36no—
232(C2×D3)⋊C4—36no—
233(C2×D3)⋊C4—36no—
234(C2×D3)⋊C4—312no—
235C4⋊Dic3—32no—
236C4⋊Dic3—36no—
237C22×C9—23no—
238C22×C9—23no—
239C22×C9C22×D416yes—
240C22×C9C2511yescharacteristic
241C2×D9—21no—
242C2×D9—21no—
243C2×D9—23no—
244C2×D9—26no—
245C2×D9—26no—
246C2×D9—23no—
247C2×D9—23no—
248C2×D9—26no—
249C2×D9—412no—
250C2×D9—812no—
251C2×D9H(5,𝔽2)12yescomplemented
252C4×C9—26no—
253C4×C9—22no—
254C4×C9C22×D412yes—
255C4×C9C22×D416yes—
256Dic9—23no—
257Dic9—22no—
258Dic9—21no—
259H(5,𝔽2)—188no—
260C2×#41—92no—
261C2×#41—91no—
262C2×#41—93no—
263C2×#41—93no—
264C2×#41—93no—
265C2×#41—188no—
266C2×#41C2×D911yescharacteristic
267C22×Q8—91no—
268C22×D4—93no—
269C22×D4—96no—
270C22×D4—93no—
271C22×D4—96no—
272C23×C4—93no—
273#127—96no—
274#124—96no—
275#123—96no—
276C22⋊Q8—91no—
277C22⋊Q8—93no—
278C22⋊Q8—96no—
279#121—912no—
280#121—93no—
281#121—96no—
282#121—96no—
283#121—96no—
284#121—93no—
285#121—96no—
286#120—96no—
287#120—912no—
288C4×Q8C2×D912yescomplemented
289C4×D4—96no—
290C4×D4—96no—
291C4×D4C2×D916yescomplemented
292#117C2×D913yescomplemented
293C2×C4⋊C4C2×D913yescomplemented
294C2×C22⋊C4—96no—
295C23×C3C23×D313yes—
296C22×D3—31no—
297C22×D3—36no—
298C22×D3—33no—
299C22×D3—66no—
300C22×D3—66no—
301C22×D3—612no—
302C22×D3—123no—
303C22×D3—126no—
304C22×D3—126no—
305C3×Q8C2×D1214yes—
306C3×D4C2×D12112yes—
307C2×C3×C4—46no—
308C2×C3×C4C2×D12112yes—
309C2×C3×C4C23×D312yes—
310C2×C3×C4C23×D316yes—
311C2×C3×C4C23×D313yes—
312C2×C3×C4C23×D311yescharacteristic
313#67—612no—
314#67—612no—
315C2×Dic3—32no—
316C2×Dic3—33no—
317C2×Dic3—31no—
318C2×Dic3—66no—
319D12—612no—
320D12—66no—
321D12—612no—
322D12—66no—
323D12—126no—
324D12—1212no—
325C4×D3—62no—
326C4×D3—66no—
327C4×D3—66no—
328C4×D3—66no—
329C4×D3—612no—
330Dic6—62no—
331Dic6—66no—
332C2×C9—26no—
333C2×C9C23×D411yescharacteristic
334C2×C9C2×H(5,𝔽2)11yescharacteristic
335C2×C9#58511yescharacteristic
336D9—22no—
337D9—43no—
338D9—46no—
339C24—93no—
340C24—96no—
341#41—184no—
342#41—188no—
343#41—1812no—
344#41—1812no—
345#41—1812no—
346#41D3618yescomplemented
347C2×Q8—91no—
348C2×Q8—93no—
349C2×Q8—184no—
350C2×Q8C22×D911yescharacteristic
351C2×D4—96no—
352C2×D4—96no—
353C2×D4—96no—
354C2×D4—93no—
355C2×D4—96no—
356C2×D4—93no—
357C2×D4—96no—
358C2×D4—912no—
359C2×D4—1812no—
360C2×D4—1824no—
361C2×D4—1812no—
362C2×D4—3612no—
363C2×D4C22×D913yes—
364C22×C4—93no—
365C22×C4—93no—
366C22×C4—93no—
367C22×C4—96no—
368C22×C4—91no—
369C22×C4—93no—
370C22×C4—1812no—
371C22×C4C22×D916yes—
372C22×C4C22×D913yes—
373C4⋊C4—92no—
374C4⋊C4—96no—
375C4⋊C4C22×D913yes—
376C4⋊C4C22×D916yes—
377C4⋊C4C22×D911yescharacteristic
378C22⋊C4—96no—
379C22⋊C4—912no—
380C22⋊C4—92no—
381C22⋊C4—96no—
382C22⋊C4—96no—
383C22⋊C4C22×D916yes—
384C42C22×D916yes—
385C22×C3—23no—
386C22×C3—23no—
387C22×C3C22×D1216yes—
388C22×C3C24×D311yescharacteristic
389C2×D3—32no—
390C2×D3—61no—
391C2×D3—61no—
392C2×D3—63no—
393C2×D3—66no—
394C2×D3—66no—
395C2×D3—63no—
396C2×D3—63no—
397C2×D3—66no—
398C2×D3—1212no—
399C2×D3—2412no—
400C3×C4—26no—
401C3×C4—22no—
402C3×C4C22×D1212yes—
403C3×C4C22×D1216yes—
404Dic3—63no—
405Dic3—62no—
406Dic3—61no—
407C9#348811yescharacteristic, complemented, Sylow
408C23—91no—
409C23—96no—
410C23—93no—
411C23—186no—
412C23—186no—
413C23—1812no—
414C23—363no—
415C23—366no—
416C23—366no—
417C23C23×D913yes—
418Q8—186no—
419Q8—182no—
420Q8C2×D3614yescomplemented
421D4—1812no—
422D4—1812no—
423D4—1812no—
424D4—186no—
425D4—1812no—
426D4—186no—
427D4—3612no—
428D4—366no—
429D4C2×D36112yescomplemented
430C2×C4—46no—
431C2×C4—91no—
432C2×C4—93no—
433C2×C4—92no—
434C2×C4—186no—
435C2×C4—182no—
436C2×C4—186no—
437C2×C4—186no—
438C2×C4—186no—
439C2×C4—1812no—
440C2×C4C2×D36112yescomplemented
441C2×C4C23×D912yes—
442C2×C4C23×D916yes—
443C2×C4C23×D913yes—
444C2×C4C23×D911yescharacteristic
445C2×C3—26no—
446C2×C3C23×D1211yescharacteristic
447C2×C3D3×H(5,𝔽2)11yescharacteristic
448C2×C3#596811yescharacteristic
449D3—62no—
450D3—123no—
451D3—126no—
452C22—23no—
453C22—23no—
454C22—92no—
455C22—181no—
456C22—181no—
457C22—183no—
458C22—186no—
459C22—186no—
460C22—183no—
461C22—183no—
462C22—186no—
463C22—3612no—
464C22—7212no—
465C22C22×D3616yes—
466C22C24×D911yescharacteristic
467C4—26no—
468C4—22no—
469C4—181no—
470C4—182no—
471C4—183no—
472C4C22×D3612yes—
473C4C22×D3616yes—
474C3#8590011yescharacteristic
475C2—26no—
476C2—182no—
477C2—363no—
478C2—366no—
479C2C23×D3611yescharacteristic
480C2D9×H(5,𝔽2)11yescharacteristic
481C2#1059314311yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#520C2
hypercenter#520D9
hypocenterC9#3488
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #520

Complements

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

NH ≅ G/Ntype
1. C2×#63715C2semidirect
2. C2×#41×D9C2semidirect
3. C9×#520C2semidirect
4. #10589679C2semidirect
5. #10589678C2semidirect
6. #10589656C2semidirect
7. D4×D36C2semidirect
8. #10589627C2semidirect
9. #10589626C2semidirect
10. #10589612C2semidirect
11. C2×#63457C2semidirect
16. C2×#3701C22semidirect
17. C2×#3701C22semidirect
18. C2×Q8×D9C22semidirect
19. C2×#3699C22semidirect
20. C2×D4×D9C22semidirect
21. C2×D4×D9C22semidirect
22. C2×#3697C22semidirect
23. C2×#3697C22semidirect
24. C22×D36C22semidirect
25. C22×D36C22semidirect
26. C22×C4×D9C22semidirect
27. C4×Q8×C9C22semidirect
28. C4×D4×C9C22semidirect
29. C9×#117C22semidirect
30. C2×C9×C4⋊C4C22semidirect
31. #63492C22semidirect
32. C2×(C2×D9)⋊C4C22semidirect
33. #63459C22semidirect
34. #63459C22semidirect
35. #63459C22semidirect
36. #63457C22semidirect
37. #63457C22semidirect
38. #63457C22semidirect
39. #63457C22semidirect
40. #63457C22semidirect
41. #63457C22semidirect
42. #63448C22semidirect
43. #63444C22semidirect
44. #63444C22semidirect
45. #63437C22semidirect
46. #63436C22semidirect
47. C4×D36C22semidirect
48. C4×D36C22semidirect
62. C9×#41D4semidirect
153. Q8×C9C2×D4semidirect
154. D4×C9C2×D4semidirect
156. C2×C4×C9C2×D4semidirect
190. #520D9semidirect
251. C2×D9H(5,𝔽2)semidirect
288. C4×Q8C2×D9semidirect
291. C4×D4C2×D9semidirect
292. #117C2×D9semidirect
293. C2×C4⋊C4C2×D9semidirect
346. #41D36semidirect
407. C9#3488semidirect
420. Q8C2×D36semidirect
429. D4C2×D36semidirect
440. C2×C4C2×D36semidirect

Maximal subgroups

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

subgroupindex
C2×#637152
C2×#41×D92
C9×#5202
#105896792
#105896782
#105896562
D4×D362
#105896272
#105896262
#105896122
C2×#634572
#859003