Finite Group Databasebeta

← #41×D36 #11902764

Subgroups — #41×D36 #11902764

Order 1152.

2472 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D9C212yesmaximal, complemented
2C4×C9×#41C211yesmaximal, characteristic, complemented
3#10589679C211yesmaximal, characteristic, complemented
4#10589678C212yesmaximal, complemented
5Q8×D36C211yesmaximal, characteristic, complemented
6#10589657C213yesmaximal, complemented
7#10589656C216yesmaximal, complemented
8D4×D36C213yesmaximal, complemented
9#10589626C216yesmaximal, complemented
10#10589579C213yesmaximal, complemented
11C2×C4×D36C213yesmaximal, complemented
12#41×D12—31nomaximal
13C2×C9×#41C2211yescharacteristic
14#41×D9—216no—
15C2×#3701C2212yescomplemented
16C2×Q8×D9C2212yescomplemented
17C2×#3699C2216yescomplemented
18C2×D4×D9C2216yescomplemented
19C2×#3697C2216yescomplemented
20C22×D36C2213yes—
21C22×C4×D9C2216yescomplemented
22C4×Q8×C9C2211yescharacteristic, complemented
23C4×Q8×C9C2211yescharacteristic, complemented
24C4×D4×C9C2213yescomplemented
25C4×D4×C9C2213yescomplemented
26C9×#117C2213yescomplemented
27C2×C42×C9C2213yescomplemented
28#63492C2216yescomplemented
29#63492C2216yescomplemented
30C2×(C2×D9)⋊C4C2216yescomplemented
31C2×C4⋊Dic9C2213yescomplemented
32#63459C2216yescomplemented
33#63459C2216yescomplemented
34#63457C2216yescomplemented
35#63457C2216yescomplemented
36#63448C22112yescomplemented
37#63444C22112yescomplemented
38#63437C2216yescomplemented
39#63436C2213yescomplemented
40C4×D36C2211yescharacteristic
41C4×D36C2213yes—
42C4×D36C2213yescomplemented
43C4×D36C2216yescomplemented
44C4×D36C2216yescomplemented
45C4×D36C2213yescomplemented
46C4×D36C2216yescomplemented
47#63431C2213yescomplemented
48C2×D3×#41—32no—
49C3×C4×#41D311yescharacteristic
50#5577—31no—
51#5576—32no—
52Q8×D12—31no—
53#5555—33no—
54#5554—36no—
55D4×D12—33no—
56#5524—36no—
57#5477—33no—
58C2×C4×D12—33no—
59C23×D9C2316yes—
60C9×#41D418yescomplemented
61C2×Q8×C9C2311yescharacteristic
62C2×D4×C9C2313yes—
63C22×C4×C9C2313yes—
64C22×C4×C9C2313yes—
65C22×C4×C9C2313yes—
66C2×#611C23112yes—
67C22×Dic9C2316yes—
68#3701—28no—
69Q8×D9—28no—
70#3699—224no—
71D4×D9—224no—
72#3697—224no—
73C2×D36—212no—
74C2×D36C2313yes—
75C2×D36C2316yes—
76C2×D36C2316yes—
77C2×D36C2316yes—
78C2×D36C2311yescharacteristic
79C2×C4×D9—224no—
80C2×C4×D9C2312yes—
81C2×C4×D9C2316yes—
82C2×C4×D9C2316yes—
83C2×C4×D9C2316yes—
84C2×Dic18C2316yes—
85C9×C4⋊C4C2313yes—
86C9×C4⋊C4C2313yes—
87C9×C22⋊C4C2316yes—
88C42×C9C2311yescharacteristic
89C42×C9C2313yes—
90C42×C9C2313yes—
91C42×C9C2313yes—
92(C2×D9)⋊C4C2312yes—
93(C2×D9)⋊C4C2316yes—
94(C2×D9)⋊C4C2316yes—
95(C2×D9)⋊C4C2316yes—
96(C2×D9)⋊C4C23112yes—
97C4⋊Dic9C2313yes—
98C4⋊Dic9C2316yes—
99C4⋊Dic9C2311yescharacteristic
100C4⋊Dic9C2316yes—
101D4×#41—91noSylow
102C2×C3×#41C2×D311yescharacteristic
103D3×#41—616no—
104C2×#239—32no—
105C2×D3×Q8—32no—
106C2×#237—36no—
107C2×D3×D4—36no—
108C2×#235—36no—
109C22×D12—33no—
110C22×C4×D3—36no—
111C3×C4×Q8C2×D311yescharacteristic
112C3×C4×Q8C2×D311yescharacteristic
113C3×C4×D4C2×D313yes—
114C3×C4×D4C2×D313yes—
115C3×#117C2×D313yes—
116C2×C3×C42C2×D313yes—
117#930—36no—
118#930—36no—
119C2×(C2×D3)⋊C4—36no—
120C2×C4⋊Dic3—33no—
121#897—36no—
122#897—36no—
123#895—36no—
124#895—36no—
125#886—312no—
126#882—312no—
127#875—36no—
128#874—33no—
129C4×D12—31no—
130C4×D12—33no—
131C4×D12—36no—
132C4×D12—33no—
133C4×D12—36no—
134C4×D12—33no—
135C4×D12—36no—
136#869—33no—
137C23×C9C2413yes—
138C22×D9—212no—
139C22×D9—212no—
140C22×D9—46no—
141C22×D9C2416yes—
142C22×D9C2412yes—
143Q8×C9C2×D414yescomplemented
144D4×C9C2×D4112yescomplemented
145C2×C4×C9—26no—
146C2×C4×C9—43no—
147C2×C4×C9C2×D4112yescomplemented
148C2×C4×C9C2413yes—
149C2×C4×C9C2413yes—
150C2×C4×C9C2411yescharacteristic
151C2×C4×C9C2411yescharacteristic
152C2×C4×C9C2413yes—
153C2×C4×C9C2411yescharacteristic
154#611—224no—
155C2×Dic9—212no—
156C2×Dic9C2416yes—
157C2×Dic9C2412yes—
158D36—212no—
159D36—212no—
160D36—26no—
161D36—46no—
162D36#4114yesdirect product factor
163C4×D9—24no—
164C4×D9—212no—
165C4×D9—212no—
166C4×D9—212no—
167Dic18—212no—
168C22×#41—92no—
169#550—91no—
170D4×Q8—91no—
171#548—92no—
172#547—93no—
173#546—96no—
174D42—93no—
175#532—93no—
176#525—96no—
177C4×#41D911yescharacteristic, complemented
178C2×C4×D4—93no—
179C23×D3—36no—
180C3×#41D1218yes—
181C2×C3×Q8C22×D311yescharacteristic
182C2×C3×D4C22×D313yes—
183C22×C3×C4C22×D313yes—
184C22×C3×C4C22×D313yes—
185C22×C3×C4C22×D313yes—
186C2×#67—312no—
187C22×Dic3—36no—
188#239—68no—
189D3×Q8—68no—
190#237—624no—
191D3×D4—624no—
192#235—624no—
193C2×D12—31no—
194C2×D12—33no—
195C2×D12—36no—
196C2×D12—36no—
197C2×D12—36no—
198C2×D12—612no—
199C2×C4×D3—32no—
200C2×C4×D3—36no—
201C2×C4×D3—36no—
202C2×C4×D3—36no—
203C2×C4×D3—624no—
204C2×Dic6—36no—
205C3×C4⋊C4C22×D313yes—
206C3×C4⋊C4C22×D313yes—
207C3×C22⋊C4C22×D316yes—
208C3×C42C22×D313yes—
209C3×C42C22×D311yescharacteristic
210C3×C42C22×D313yes—
211C3×C42C22×D313yes—
212(C2×D3)⋊C4—32no—
213(C2×D3)⋊C4—36no—
214(C2×D3)⋊C4—36no—
215(C2×D3)⋊C4—36no—
216(C2×D3)⋊C4—312no—
217C4⋊Dic3—33no—
218C4⋊Dic3—36no—
219C4⋊Dic3—31no—
220C4⋊Dic3—36no—
221C22×C9—23no—
222C22×C9—23no—
223C22×C9C22×D416yes—
224C22×C9C2511yescharacteristic
225C2×D9—22no—
226C2×D9—22no—
227C2×D9—26no—
228C2×D9—26no—
229C2×D9—26no—
230C2×D9—424no—
231C2×D9C2×#4114yescomplemented
232C4×C9—23no—
233C4×C9—23no—
234C4×C9—21no—
235C4×C9C22×D416yes—
236C4×C9C22×D412yes—
237C4×C9C2×#4112yescomplemented
238Dic9—26no—
239Dic9—22no—
240C2×#41—92no—
241C2×#41—96no—
242C2×#41—96no—
243C2×#41—1816no—
244C2×#41C2×D911yescharacteristic
245C22×Q8—92no—
246C22×D4—96no—
247C22×D4—93no—
248C23×C4—96no—
249C4⋊Q8—93no—
250#127—93no—
251#124—96no—
252#123—912no—
253C22⋊Q8—96no—
254C22⋊Q8—96no—
255#121—96no—
256#121—96no—
257#121—96no—
258#121—96no—
259#120—912no—
260C4×Q8C2×D911yescharacteristic, complemented
261C4×Q8C2×D911yescharacteristic, complemented
262C4×D4—91no—
263C4×D4—96no—
264C4×D4—93no—
265C4×D4—93no—
266C4×D4—96no—
267C4×D4—93no—
268C4×D4—96no—
269C4×D4C2×D913yescomplemented
270C4×D4C2×D913yescomplemented
271#117C2×D913yescomplemented
272C2×C4⋊C4—93no—
273C2×C22⋊C4—96no—
274C2×C42C2×D913yescomplemented
275C23×C3C23×D313yes—
276C22×D3—32no—
277C22×D3—36no—
278C22×D3—612no—
279C22×D3—612no—
280C22×D3—126no—
281C3×Q8C2×D1214yes—
282C3×D4C2×D12112yes—
283C2×C3×C4—26no—
284C2×C3×C4—43no—
285C2×C3×C4C2×D12112yes—
286C2×C3×C4C23×D313yes—
287C2×C3×C4C23×D313yes—
288C2×C3×C4C23×D311yescharacteristic
289C2×C3×C4C23×D313yes—
290C2×C3×C4C23×D311yescharacteristic
291C2×C3×C4C23×D311yescharacteristic
292#67—624no—
293C2×Dic3—36no—
294C2×Dic3—32no—
295C2×Dic3—612no—
296D12—34no—
297D12—612no—
298D12—612no—
299D12—66no—
300D12—126no—
301C4×D3—64no—
302C4×D3—612no—
303C4×D3—612no—
304C4×D3—612no—
305Dic6—612no—
306C2×C9—26no—
307C2×C9C23×D411yescharacteristic
308C2×C9C22×#4111yescharacteristic
309C2×C9#58511yescharacteristic
310D9—24no—
311D9—46no—
312C24—96no—
313#41—188no—
314#41—1824no—
315#41—1824no—
316#41D3618yesdirect product factor
317C2×Q8—96no—
318C2×Q8—188no—
319C2×Q8C22×D911yescharacteristic
320C2×D4—912no—
321C2×D4—91no—
322C2×D4—96no—
323C2×D4—93no—
324C2×D4—96no—
325C2×D4—96no—
326C2×D4—1812no—
327C2×D4—1824no—
328C2×D4C22×D913yes—
329C22×C4—96no—
330C22×C4—96no—
331C22×C4—96no—
332C22×C4—92no—
333C22×C4—96no—
334C22×C4—1824no—
335C22×C4C22×D913yes—
336C22×C4C22×D913yes—
337C22×C4C22×D913yes—
338C4⋊C4—91no—
339C4⋊C4—93no—
340C4⋊C4—96no—
341C4⋊C4—96no—
342C4⋊C4C22×D913yes—
343C4⋊C4C22×D913yes—
344C22⋊C4—92no—
345C22⋊C4—96no—
346C22⋊C4—96no—
347C22⋊C4—96no—
348C22⋊C4—912no—
349C22⋊C4C22×D916yes—
350C42C22×D913yes—
351C42C22×D913yes—
352C42C22×D911yescharacteristic
353C42C22×D913yes—
354C22×C3—23no—
355C22×C3—23no—
356C22×C3C22×D1216yes—
357C22×C3C24×D311yescharacteristic
358C2×D3—34no—
359C2×D3—62no—
360C2×D3—62no—
361C2×D3—66no—
362C2×D3—66no—
363C2×D3—66no—
364C2×D3—1224no—
365C3×C4—23no—
366C3×C4—23no—
367C3×C4—21no—
368C3×C4C22×D1216yes—
369C3×C4C22×D1212yes—
370C3×C4D3×#4112yes—
371Dic3—66no—
372Dic3—62no—
373C9D4×#4111yescharacteristic, complemented, Sylow
374C23—92no—
375C23—96no—
376C23—1812no—
377C23—1812no—
378C23—366no—
379C23C23×D913yes—
380Q8—1812no—
381Q8C2×D3614yescomplemented
382D4—94no—
383D4—1812no—
384D4—1824no—
385D4—1812no—
386D4—186no—
387D4—366no—
388D4C2×D36112yescomplemented
389C2×C4—26no—
390C2×C4—43no—
391C2×C4—92no—
392C2×C4—96no—
393C2×C4—1812no—
394C2×C4—184no—
395C2×C4—1812no—
396C2×C4—1812no—
397C2×C4—1812no—
398C2×C4C2×D36112yescomplemented
399C2×C4C23×D911yescharacteristic
400C2×C4C23×D913yes—
401C2×C4C23×D913yes—
402C2×C4C23×D913yes—
403C2×C4C23×D911yescharacteristic
404C2×C4C23×D911yescharacteristic
405C2×C3—26no—
406C2×C3C23×D1211yescharacteristic
407C2×C3C2×D3×#4111yescharacteristic
408C2×C3#596411yescharacteristic
409D3—64no—
410D3—126no—
411C22—23no—
412C22—23no—
413C22—94no—
414C22—182no—
415C22—182no—
416C22—186no—
417C22—186no—
418C22—186no—
419C22—3624no—
420C22C22×D3616yes—
421C22C24×D911yescharacteristic
422C4—23no—
423C4—21no—
424C4—23no—
425C4—182no—
426C4—186no—
427C4C22×D3612yes—
428C4C22×D3616yes—
429C4#41×D912yescomplemented
430C3#41×D1211yescharacteristic
431C2—26no—
432C2—184no—
433C2—366no—
434C2C23×D3611yescharacteristic
435C2C2×#41×D911yescharacteristic
436C2#1059313911yescharacteristic
subgroupG/H
centerC2×C4C23×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC4×C9×#41C2
hypercenterC4×#41D9
hypocenterC9D4×#41
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×D9C2semidirect
2. C4×C9×#41C2semidirect
3. #10589679C2semidirect
4. #10589678C2semidirect
5. Q8×D36C2semidirect
6. #10589657C2semidirect
7. #10589656C2semidirect
8. D4×D36C2semidirect
9. #10589626C2semidirect
10. #10589579C2semidirect
11. C2×C4×D36C2semidirect
15. C2×#3701C22semidirect
16. C2×Q8×D9C22semidirect
17. C2×#3699C22semidirect
18. C2×D4×D9C22semidirect
19. C2×#3697C22semidirect
21. C22×C4×D9C22semidirect
22. C4×Q8×C9C22semidirect
23. C4×Q8×C9C22semidirect
24. C4×D4×C9C22semidirect
25. C4×D4×C9C22semidirect
26. C9×#117C22semidirect
27. C2×C42×C9C22semidirect
28. #63492C22semidirect
29. #63492C22semidirect
30. C2×(C2×D9)⋊C4C22semidirect
31. C2×C4⋊Dic9C22semidirect
32. #63459C22semidirect
33. #63459C22semidirect
34. #63457C22semidirect
35. #63457C22semidirect
36. #63448C22semidirect
37. #63444C22semidirect
38. #63437C22semidirect
39. #63436C22semidirect
42. C4×D36C22semidirect
43. C4×D36C22semidirect
44. C4×D36C22semidirect
45. C4×D36C22semidirect
46. C4×D36C22semidirect
47. #63431C22semidirect
60. C9×#41D4semidirect
143. Q8×C9C2×D4semidirect
144. D4×C9C2×D4semidirect
147. C2×C4×C9C2×D4semidirect
162. D36#41direct (N × H)
177. C4×#41D9semidirect
231. C2×D9C2×#41semidirect
237. C4×C9C2×#41semidirect
260. C4×Q8C2×D9semidirect
261. C4×Q8C2×D9semidirect
269. C4×D4C2×D9semidirect
270. C4×D4C2×D9semidirect
271. #117C2×D9semidirect
274. C2×C42C2×D9semidirect
316. #41D36direct (N × H)
373. C9D4×#41semidirect
381. Q8C2×D36semidirect
388. D4C2×D36semidirect
398. C2×C4C2×D36semidirect
429. C4#41×D9semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D92
C4×C9×#412
#105896792
#105896782
Q8×D362
#105896572
#105896562
D4×D362
#105896262
#105895792
C2×C4×D362
#41×D123