Finite Group Databasebeta

← #11902761

Subgroups — #11902761

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
2C9×#550C211yesmaximal, characteristic, complemented
3#10589933C212yesmaximal, complemented
4#10589819C213yesmaximal, complemented
5#10589818C213yesmaximal, complemented
6#10589714C216yesmaximal, complemented
7#10589708C216yesmaximal, complemented
8Q8×D36C211yesmaximal, characteristic, complemented
9C4×#3701C211yesmaximal, characteristic, complemented
10#10589653C213yesmaximal, complemented
11C4×D4×D9C213yesmaximal, complemented
12#86766—31nomaximal
13C2×C9×#41C2212yescomplemented
14#41×D9—216no—
15C2×#3701C2211yescharacteristic
16C2×Q8×D9C2212yescomplemented
17C2×#3699C2216yescomplemented
18C2×D4×D9C2213yes—
19C2×D4×D9C2216yescomplemented
20C2×#3697C2216yescomplemented
21C22×C4×D9C2216yescomplemented
22C9×#127C2213yescomplemented
23C9×#121C2216yescomplemented
24C4×Q8×C9C2211yescharacteristic, complemented
25C4×D4×C9C2213yescomplemented
26Q8×Dic9C2211yescharacteristic, complemented
27#63500C2216yescomplemented
28#63500C2216yescomplemented
29#63500C2216yescomplemented
30#63499C22112yescomplemented
31#63498C2216yescomplemented
32D4×Dic9C2216yescomplemented
33D4×Dic9C2213yescomplemented
34C4×#611C2216yescomplemented
35#63486C2216yescomplemented
36#63459C2216yescomplemented
37#63455C2211yescharacteristic
38#63455C2213yescomplemented
39#63454C2213yescomplemented
40C4⋊C4×D9C2213yescomplemented
41#63445C22112yescomplemented
42#611⋊C4C2216yescomplemented
43C22⋊C4×D9C2216yescomplemented
44C4×D36C2213yes—
45C4×D36C2213yescomplemented
46C42×D9C2213yescomplemented
47#63431C2213yescomplemented
48C2×D3×#41—32no—
49C3×#550D311yescharacteristic
50#5831—32no—
51#5717—33no—
52#5716—33no—
53#5612—36no—
54#5606—36no—
55Q8×D12—31no—
56C4×#239—31no—
57#5551—33no—
58C4×D3×D4—33no—
59C23×D9C2316yes—
60C9×#41—28no—
61C2×Q8×C9C2311yescharacteristic
62C2×D4×C9C2313yes—
63C2×D4×C9C2316yes—
64C2×D4×C9C2316yes—
65C22×C4×C9C2316yes—
66C2×#611C2316yes—
67C2×#611C23112yes—
68C22×Dic9C2316yes—
69#3701D418yescomplemented
70Q8×D9—28no—
71#3699—224no—
72D4×D9—224no—
73D4×D9—212no—
74#3697—224no—
75C2×D36C2313yes—
76C2×D36C2311yescharacteristic
77C2×C4×D9—224no—
78C2×C4×D9C2316yes—
79C2×C4×D9C2313yes—
80C2×C4×D9C2316yes—
81C2×C4×D9C2312yes—
82C2×C4×D9C2313yes—
83C2×C4×D9C2313yes—
84C2×Dic18C2316yes—
85C9×C4⋊C4C2311yescharacteristic
86C9×C4⋊C4C2313yes—
87C9×C22⋊C4C2316yes—
88C42×C9C2313yes—
89#3676C2316yes—
90#3676C23112yes—
91(C2×D9)⋊C4C2312yes—
92(C2×D9)⋊C4C2316yes—
93(C2×D9)⋊C4C2316yes—
94C4⋊Dic9C2313yes—
95C4⋊Dic9C2316yes—
96C4⋊Dic9C2313yes—
97Dic9⋊C4C2316yes—
98C4×Dic9C2313yes—
99C4×Dic9C2311yescharacteristic
100C4×Dic9C2313yes—
101D4×#41—91noSylow
102C2×C3×#41C2×D312yes—
103D3×#41—616no—
104C2×#239—31no—
105C2×D3×Q8—32no—
106C2×#237—36no—
107C2×D3×D4—36no—
108C2×D3×D4—33no—
109C2×#235—36no—
110C22×C4×D3—36no—
111C3×#127C2×D313yes—
112C3×#121C2×D316yes—
113C3×C4×Q8C2×D311yescharacteristic
114C3×C4×D4C2×D313yes—
115Q8×Dic3—31no—
116#938—36no—
117#938—36no—
118#938—36no—
119#937—312no—
120#936—36no—
121D4×Dic3—33no—
122D4×Dic3—36no—
123C4×#67—36no—
124#924—36no—
125#897—36no—
126#893—31no—
127#893—33no—
128#892—33no—
129D3×C4⋊C4—33no—
130#883—312no—
131#67⋊C4—36no—
132D3×C22⋊C4—36no—
133C4×D12—33no—
134C4×D12—33no—
135C42×D3—33no—
136#869—33no—
137C23×C9C2416yes—
138C22×D9—212no—
139C22×D9—212no—
140C22×D9—46no—
141C22×D9C2413yes—
142C22×D9C2412yes—
143Q8×C9C2×D414yescomplemented
144D4×C9—212no—
145D4×C9—26no—
146D4×C9—46no—
147C2×C4×C9—212no—
148C2×C4×C9C2413yes—
149C2×C4×C9C2412yes—
150C2×C4×C9C2413yes—
151C2×C4×C9C2411yescharacteristic
152#611—224no—
153#611—212no—
154C2×Dic9—212no—
155C2×Dic9C2411yescharacteristic
156C2×Dic9C2413yes—
157C2×Dic9C2416yes—
158C2×Dic9C2411yescharacteristic
159D36C2×D4112yescomplemented
160D36#4114yescomplemented
161C4×D9—212no—
162C4×D9—212no—
163C4×D9—26no—
164C4×D9—24no—
165C4×D9—43no—
166C4×D9C2×D4112yescomplemented
167Dic18—212no—
168C22×#41—92no—
169#550D911yescharacteristic, complemented
170D4×Q8—91no—
171#548—92no—
172#547—93no—
173#546—96no—
174D42—93no—
175#532—93no—
176#525—96no—
177C4×#41—91no—
178C2×C4×D4—93no—
179C23×D3—36no—
180C3×#41—28no—
181C2×C3×Q8C22×D311yescharacteristic
182C2×C3×D4C22×D313yes—
183C2×C3×D4C22×D316yes—
184C2×C3×D4C22×D316yes—
185C22×C3×C4C22×D316yes—
186C2×#67—36no—
187C2×#67—312no—
188C22×Dic3—36no—
189#239—38no—
190D3×Q8—68no—
191#237—624no—
192D3×D4—612no—
193D3×D4—624no—
194#235—624no—
195C2×D12—31no—
196C2×D12—33no—
197C2×C4×D3—33no—
198C2×C4×D3—33no—
199C2×C4×D3—36no—
200C2×C4×D3—36no—
201C2×C4×D3—32no—
202C2×C4×D3—33no—
203C2×C4×D3—624no—
204C2×Dic6—36no—
205C3×C4⋊C4C22×D311yescharacteristic
206C3×C4⋊C4C22×D313yes—
207C3×C22⋊C4C22×D316yes—
208C3×C42C22×D313yes—
209#217—36no—
210#217—312no—
211(C2×D3)⋊C4—36no—
212(C2×D3)⋊C4—36no—
213(C2×D3)⋊C4—32no—
214C4⋊Dic3—33no—
215C4⋊Dic3—36no—
216C4⋊Dic3—33no—
217Dic3⋊C4—36no—
218C4×Dic3—31no—
219C4×Dic3—33no—
220C4×Dic3—33no—
221C22×C9—26no—
222C22×C9—26no—
223C22×C9—26no—
224C22×C9C2511yescharacteristic
225C2×D9—22no—
226C2×D9—23no—
227C2×D9—23no—
228C2×D9—22no—
229C2×D9—424no—
230C2×D9C22×D416yes—
231C2×D9C2×#4114yescomplemented
232C4×C9—22no—
233C4×C9—23no—
234C4×C9C22×D416yes—
235C4×C9C2×#4112yescomplemented
236Dic9—26no—
237Dic9—23no—
238Dic9—21no—
239Dic9C22×D412yes—
240C2×#41—91no—
241C2×#41—96no—
242C2×#41—96no—
243C2×#41—1816no—
244C2×#41C2×D912yescomplemented
245C22×Q8—92no—
246C22×D4—93no—
247C22×D4—96no—
248C23×C4—96no—
249C4⋊Q8—93no—
250#127C2×D913yescomplemented
251#124—96no—
252#123—912no—
253C22⋊Q8—96no—
254C22⋊Q8—96no—
255#121—96no—
256#121—96no—
257#121—96no—
258#121C2×D916yescomplemented
259#120—912no—
260C4×Q8—91no—
261C4×Q8C2×D911yescharacteristic, complemented
262C4×D4—93no—
263C4×D4—96no—
264C4×D4—96no—
265C4×D4—91no—
266C4×D4—93no—
267C4×D4—96no—
268C4×D4—93no—
269C4×D4—93no—
270C4×D4C2×D913yescomplemented
271#117—93no—
272C2×C4⋊C4—93no—
273C2×C22⋊C4—96no—
274C2×C42—93no—
275C23×C3C23×D316yes—
276C22×D3—32no—
277C22×D3—33no—
278C22×D3—612no—
279C22×D3—612no—
280C22×D3—126no—
281C3×Q8D3×D414yes—
282C3×D4—212no—
283C3×D4—26no—
284C3×D4—46no—
285C2×C3×C4—212no—
286C2×C3×C4C23×D313yes—
287C2×C3×C4C23×D312yes—
288C2×C3×C4C23×D313yes—
289C2×C3×C4C23×D311yescharacteristic
290#67—624no—
291#67—612no—
292C2×Dic3—31no—
293C2×Dic3—31no—
294C2×Dic3—33no—
295C2×Dic3—36no—
296C2×Dic3—612no—
297D12—312no—
298D12—34no—
299C4×D3—312no—
300C4×D3—64no—
301C4×D3—612no—
302C4×D3—612no—
303C4×D3—66no—
304C4×D3—123no—
305Dic6—612no—
306C2×C9—46no—
307C2×C9C23×D411yescharacteristic
308C2×C9C22×#4111yescharacteristic
309C2×C9#58511yescharacteristic
310D9—24no—
311D9—26no—
312C24—96no—
313#41—28no—
314#41—98no—
315#41—1824no—
316#41—1824no—
317C2×Q8—96no—
318C2×Q8—188no—
319C2×Q8C22×D911yescharacteristic
320C2×D4—96no—
321C2×D4—912no—
322C2×D4—91no—
323C2×D4—93no—
324C2×D4—1824no—
325C2×D4—1812no—
326C2×D4C22×D913yes—
327C2×D4C22×D916yes—
328C2×D4C22×D916yes—
329C22×C4—93no—
330C22×C4—96no—
331C22×C4—93no—
332C22×C4—96no—
333C22×C4—92no—
334C22×C4—96no—
335C22×C4—93no—
336C22×C4—1824no—
337C22×C4C22×D916yes—
338C4⋊C4—93no—
339C4⋊C4—96no—
340C4⋊C4—93no—
341C4⋊C4—96no—
342C4⋊C4C22×D911yescharacteristic
343C4⋊C4C22×D913yes—
344C22⋊C4—96no—
345C22⋊C4—912no—
346C22⋊C4—92no—
347C22⋊C4—96no—
348C22⋊C4—96no—
349C22⋊C4C22×D916yes—
350C42—91no—
351C42—93no—
352C42—93no—
353C42C22×D913yes—
354C22×C3—26no—
355C22×C3—26no—
356C22×C3—26no—
357C22×C3C24×D311yescharacteristic
358C2×D3—36no—
359C2×D3—34no—
360C2×D3—62no—
361C2×D3—63no—
362C2×D3—63no—
363C2×D3—62no—
364C2×D3—1224no—
365C3×C4—22no—
366C3×C4—23no—
367C3×C4C2×D3×D416yes—
368C3×C4D3×#4112yes—
369Dic3—32no—
370Dic3—66no—
371Dic3—63no—
372Dic3—61no—
373C9D4×#4111yescharacteristic, complemented, Sylow
374C23—92no—
375C23—93no—
376C23—1812no—
377C23—1812no—
378C23—366no—
379C23C23×D916yes—
380Q8—1812no—
381Q8D4×D914yescomplemented
382D4—212no—
383D4—26no—
384D4—46no—
385D4—912no—
386D4—94no—
387D4—1824no—
388D4—1812no—
389C2×C4—212no—
390C2×C4—91no—
391C2×C4—912no—
392C2×C4—91no—
393C2×C4—93no—
394C2×C4—96no—
395C2×C4—184no—
396C2×C4—1812no—
397C2×C4—1812no—
398C2×C4—1812no—
399C2×C4—186no—
400C2×C4—363no—
401C2×C4C23×D913yes—
402C2×C4C23×D912yes—
403C2×C4C23×D913yes—
404C2×C4C23×D911yescharacteristic
405C2×C3—46no—
406C2×C3C22×D3×D411yescharacteristic
407C2×C3C2×D3×#4111yescharacteristic
408C2×C3#596611yescharacteristic
409D3—64no—
410D3—66no—
411C22—26no—
412C22—26no—
413C22—26no—
414C22—96no—
415C22—94no—
416C22—182no—
417C22—183no—
418C22—183no—
419C22—182no—
420C22—3624no—
421C22C24×D911yescharacteristic
422C4—22no—
423C4—23no—
424C4—92no—
425C4—186no—
426C4—183no—
427C4—181no—
428C4C2×D4×D916yes—
429C4#41×D912yescomplemented
430C3#8676611yescharacteristic
431C2—46no—
432C2—184no—
433C2—186no—
434C2C22×D4×D911yescharacteristic
435C2C2×#41×D911yescharacteristic
436C2#1059314111yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#550C2
hypercenter#550D9
hypocenterC9D4×#41
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#41×D9C2semidirect
2. C9×#550C2semidirect
3. #10589933C2semidirect
4. #10589819C2semidirect
5. #10589818C2semidirect
6. #10589714C2semidirect
7. #10589708C2semidirect
8. Q8×D36C2semidirect
9. C4×#3701C2semidirect
10. #10589653C2semidirect
11. C4×D4×D9C2semidirect
13. C2×C9×#41C22semidirect
16. C2×Q8×D9C22semidirect
17. C2×#3699C22semidirect
19. C2×D4×D9C22semidirect
20. C2×#3697C22semidirect
21. C22×C4×D9C22semidirect
22. C9×#127C22semidirect
23. C9×#121C22semidirect
24. C4×Q8×C9C22semidirect
25. C4×D4×C9C22semidirect
26. Q8×Dic9C22semidirect
27. #63500C22semidirect
28. #63500C22semidirect
29. #63500C22semidirect
30. #63499C22semidirect
31. #63498C22semidirect
32. D4×Dic9C22semidirect
33. D4×Dic9C22semidirect
34. C4×#611C22semidirect
35. #63486C22semidirect
36. #63459C22semidirect
38. #63455C22semidirect
39. #63454C22semidirect
40. C4⋊C4×D9C22semidirect
41. #63445C22semidirect
42. #611⋊C4C22semidirect
43. C22⋊C4×D9C22semidirect
45. C4×D36C22semidirect
46. C42×D9C22semidirect
47. #63431C22semidirect
69. #3701D4semidirect
143. Q8×C9C2×D4semidirect
159. D36C2×D4semidirect
160. D36#41semidirect
166. C4×D9C2×D4semidirect
169. #550D9semidirect
231. C2×D9C2×#41semidirect
235. C4×C9C2×#41semidirect
244. C2×#41C2×D9semidirect
250. #127C2×D9semidirect
258. #121C2×D9semidirect
261. C4×Q8C2×D9semidirect
270. C4×D4C2×D9semidirect
373. C9D4×#41semidirect
381. Q8D4×D9semidirect
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
C9×#5502
#105899332
#105898192
#105898182
#105897142
#105897082
Q8×D362
C4×#37012
#105896532
C4×D4×D92
#867663