Finite Group Databasebeta

← #11904614

Subgroups — #11904614

Order 1152.

4974 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×#64366C211yesmaximal, characteristic, complemented
2C2×#41×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×#520C211yesmaximal, characteristic, complemented
4#10596048C212yesmaximal, complemented
5#10596047C212yesmaximal, complemented
6#10596025C216yesmaximal, complemented
7D4×C4⋊(C3⋊D3)C216yesmaximal, complemented
8#10595996C213yesmaximal, complemented
9#10595995C213yesmaximal, complemented
10#10595981C213yesmaximal, complemented
11C2×#64104C213yesmaximal, complemented
12#85900—34nomaximal
13C2×C32×#41C2211yescharacteristic
14#64366—28no—
15#41×C3⋊D3—28no—
16C2×#3832C2211yescharacteristic, complemented
17C2×#3832C2212yescomplemented
18C2×Q8×C3⋊D3C2211yescharacteristic, complemented
19C2×#3830C2213yescomplemented
20C2×D4×C3⋊D3C2213yescomplemented
21C2×D4×C3⋊D3C2216yescomplemented
22C2×#3828C2213yescomplemented
23C2×#3828C2213yescomplemented
24C22×C4⋊(C3⋊D3)C2213yescomplemented
25C22×C4⋊(C3⋊D3)C2216yescomplemented
26C22×C4×C3⋊D3C2213yescomplemented
27C32×C4×Q8C2212yescomplemented
28C32×C4×D4C2216yescomplemented
29C32×#117C2213yescomplemented
30C2×C32×C4⋊C4C2213yescomplemented
31#64139C22112yescomplemented
32C2×#3752C2216yescomplemented
33#64106C2213yescomplemented
34#64106C2216yescomplemented
35#64106C2211yescharacteristic, complemented
36#64104C2213yescomplemented
37#64104C2216yescomplemented
38#64104C2216yescomplemented
39#64104C2216yescomplemented
40#64104C2216yescomplemented
41#64104C2213yescomplemented
42#64095C2216yescomplemented
43#64091C2216yescomplemented
44#64091C22112yescomplemented
45#64084C2216yescomplemented
46#64083C2216yescomplemented
47C4×C4⋊(C3⋊D3)C2216yescomplemented
48C4×C4⋊(C3⋊D3)C2216yescomplemented
49C2×#1009—34no—
50C2×D3×#41—34no—
51C3×#520D314yescomplemented
52#5577—38no—
53#5576—38no—
54#5554—324no—
55D4×D12—324no—
56#5525—312no—
57#5524—312no—
58#5510—312no—
59C2×#895—312no—
60C23×C3⋊D3C2313yes—
61C23×C3⋊D3C2316yes—
62C32×#41D418yescomplemented
63C2×C32×Q8C2311yescharacteristic
64C2×C32×D4C2313yes—
65C22×C32×C4C2316yes—
66C22×C32×C4C2313yes—
67C2×#638C2316yes—
68C2×#638C2316yes—
69C22×C3⋊Dic3C2313yes—
70#3832—24no—
71#3832—28no—
72Q8×C3⋊D3—24no—
73#3830—212no—
74D4×C3⋊D3—212no—
75D4×C3⋊D3—224no—
76#3828—212no—
77#3828—212no—
78C2×C4⋊(C3⋊D3)—212no—
79C2×C4⋊(C3⋊D3)—412no—
80C2×C4⋊(C3⋊D3)C2316yes—
81C2×C4⋊(C3⋊D3)C2313yes—
82C2×C4⋊(C3⋊D3)C2316yes—
83C2×C4⋊(C3⋊D3)C2313yes—
84C2×C4⋊(C3⋊D3)C2316yes—
85C2×C4⋊(C3⋊D3)C23112yes—
86C2×C4×C3⋊D3—212no—
87C2×C4×C3⋊D3C2313yes—
88C2×C4×C3⋊D3C2313yes—
89C2×C4×C3⋊D3C2316yes—
90C2×C4×C3⋊D3C2311yescharacteristic
91C2×C4×C3⋊D3C2313yes—
92C2×#634C2313yes—
93C2×#634C2311yescharacteristic
94C32×C4⋊C4C2313yes—
95C32×C4⋊C4C2316yes—
96C32×C4⋊C4C2311yescharacteristic
97C32×C22⋊C4C2316yes—
98C32×C42C2316yes—
99#3752C2312yes—
100#3752C2316yes—
101#3752C2316yes—
102#3752C2316yes—
103#3752C23112yes—
104C4⋊(C3⋊Dic3)C2312yes—
105C4⋊(C3⋊Dic3)C2316yes—
106#3488—91noSylow
107C2×C3×#41C2×D314yes—
108#1009—632no—
109D3×#41—632no—
110C2×#239—34no—
111C2×#239—38no—
112C2×D3×Q8—34no—
113C2×#237—312no—
114C2×D3×D4—312no—
115C2×D3×D4—324no—
116C2×#235—312no—
117C2×#235—312no—
118C22×D12—312no—
119C22×D12—324no—
120C22×C4×D3—312no—
121C3×C4×Q8C2×D318yescomplemented
122C3×C4×D4C2×D3124yescomplemented
123C3×#117C2×D3112yescomplemented
124C2×C3×C4⋊C4C2×D3112yescomplemented
125#930—348no—
126C2×(C2×D3)⋊C4—324no—
127#897—312no—
128#897—324no—
129#897—34no—
130#895—312no—
131#895—324no—
132#895—324no—
133#895—324no—
134#895—324no—
135#895—312no—
136#886—324no—
137#882—324no—
138#882—348no—
139#875—324no—
140#874—324no—
141C4×D12—324no—
142C4×D12—324no—
143C23×C32C2413yes—
144C22×C3⋊D3—26no—
145C22×C3⋊D3—212no—
146C22×C3⋊D3—26no—
147C22×C3⋊D3—43no—
148C22×C3⋊D3—46no—
149C22×C3⋊D3—46no—
150C22×C3⋊D3C2416yes—
151C22×C3⋊D3C2413yes—
152C22×C3⋊D3C2411yescharacteristic
153C32×Q8C2×D414yescomplemented
154C32×D4C2×D4112yescomplemented
155C2×C32×C4—46no—
156C2×C32×C4C2×D4112yescomplemented
157C2×C32×C4C2412yes—
158C2×C32×C4C2416yes—
159C2×C32×C4C2413yes—
160C2×C32×C4C2411yescharacteristic
161#638—212no—
162#638—212no—
163C2×C3⋊Dic3—26no—
164C2×C3⋊Dic3C2412yes—
165C2×C3⋊Dic3C2413yes—
166C2×C3⋊Dic3C2411yescharacteristic
167C4⋊(C3⋊D3)—212no—
168C4⋊(C3⋊D3)—26no—
169C4⋊(C3⋊D3)—212no—
170C4⋊(C3⋊D3)—26no—
171C4⋊(C3⋊D3)—412no—
172C4⋊(C3⋊D3)—46no—
173C4×C3⋊D3—22no—
174C4×C3⋊D3—26no—
175C4×C3⋊D3—26no—
176C4×C3⋊D3—26no—
177C4×C3⋊D3—212no—
178#634—22no—
179#634—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#520C3⋊D311yescharacteristic, complemented
191C23×D3—312no—
192C23×D3—324no—
193C3×#41D12132yescomplemented
194C2×C3×Q8C22×D314yes—
195C2×C3×D4C22×D3112yes—
196C22×C3×C4C22×D3124yes—
197C22×C3×C4C22×D3112yes—
198C2×#67—324no—
199C2×#67—324no—
200C22×Dic3—312no—
201#239—616no—
202#239—632no—
203D3×Q8—616no—
204#237—648no—
205D3×D4—648no—
206D3×D4—696no—
207#235—648no—
208#235—648no—
209C2×D12—324no—
210C2×D12—312no—
211C2×D12—324no—
212C2×D12—312no—
213C2×D12—324no—
214C2×D12—348no—
215C2×D12—648no—
216C2×D12—1248no—
217C2×C4×D3—312no—
218C2×C4×D3—312no—
219C2×C4×D3—324no—
220C2×C4×D3—34no—
221C2×C4×D3—312no—
222C2×C4×D3—648no—
223C2×Dic6—312no—
224C2×Dic6—34no—
225C3×C4⋊C4C22×D3112yes—
226C3×C4⋊C4C22×D3124yes—
227C3×C4⋊C4C22×D314yes—
228C3×C22⋊C4C22×D3124yes—
229C3×C42C22×D3124yes—
230(C2×D3)⋊C4—38no—
231(C2×D3)⋊C4—324no—
232(C2×D3)⋊C4—324no—
233(C2×D3)⋊C4—324no—
234(C2×D3)⋊C4—348no—
235C4⋊Dic3—38no—
236C4⋊Dic3—324no—
237C22×C32—23no—
238C22×C32—23no—
239C22×C32C22×D416yes—
240C22×C32C2511yescharacteristic
241C2×C3⋊D3—21no—
242C2×C3⋊D3—21no—
243C2×C3⋊D3—23no—
244C2×C3⋊D3—26no—
245C2×C3⋊D3—26no—
246C2×C3⋊D3—23no—
247C2×C3⋊D3—23no—
248C2×C3⋊D3—26no—
249C2×C3⋊D3—412no—
250C2×C3⋊D3—812no—
251C2×C3⋊D3H(5,𝔽2)12yescomplemented
252C32×C4—26no—
253C32×C4—22no—
254C32×C4C22×D412yes—
255C32×C4C22×D416yes—
256C3⋊Dic3—23no—
257C3⋊Dic3—22no—
258C3⋊Dic3—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×C3⋊D311yescharacteristic
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×C3⋊D312yescomplemented
289C4×D4—96no—
290C4×D4—96no—
291C4×D4C2×C3⋊D316yescomplemented
292#117C2×C3⋊D313yescomplemented
293C2×C4⋊C4C2×C3⋊D313yescomplemented
294C2×C22⋊C4—96no—
295C23×C3C23×D3112yes—
296C22×D3—34no—
297C22×D3—324no—
298C22×D3—312no—
299C22×D3—624no—
300C22×D3—624no—
301C22×D3—648no—
302C22×D3—1212no—
303C22×D3—1224no—
304C22×D3—1224no—
305C3×Q8C2×D12116yescomplemented
306C3×D4C2×D12148yescomplemented
307C2×C3×C4—424no—
308C2×C3×C4C2×D12148yescomplemented
309C2×C3×C4C23×D318yes—
310C2×C3×C4C23×D3124yes—
311C2×C3×C4C23×D3112yes—
312C2×C3×C4C23×D314yes—
313#67—648no—
314#67—648no—
315C2×Dic3—38no—
316C2×Dic3—312no—
317C2×Dic3—34no—
318C2×Dic3—624no—
319D12—648no—
320D12—624no—
321D12—648no—
322D12—624no—
323D12—1224no—
324D12—1248no—
325C4×D3—68no—
326C4×D3—624no—
327C4×D3—624no—
328C4×D3—624no—
329C4×D3—648no—
330Dic6—68no—
331Dic6—624no—
332C2×C32—26no—
333C2×C32C23×D411yescharacteristic
334C2×C32C2×H(5,𝔽2)11yescharacteristic
335C2×C32#58511yescharacteristic
336C3⋊D3—22no—
337C3⋊D3—43no—
338C3⋊D3—46no—
339C24—93no—
340C24—96no—
341#41—184no—
342#41—188no—
343#41—1812no—
344#41—1812no—
345#41—1812no—
346#41C4⋊(C3⋊D3)18yescomplemented
347C2×Q8—91no—
348C2×Q8—93no—
349C2×Q8—184no—
350C2×Q8C22×C3⋊D311yescharacteristic
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×C3⋊D313yes—
364C22×C4—93no—
365C22×C4—93no—
366C22×C4—93no—
367C22×C4—96no—
368C22×C4—91no—
369C22×C4—93no—
370C22×C4—1812no—
371C22×C4C22×C3⋊D316yes—
372C22×C4C22×C3⋊D313yes—
373C4⋊C4—92no—
374C4⋊C4—96no—
375C4⋊C4C22×C3⋊D313yes—
376C4⋊C4C22×C3⋊D316yes—
377C4⋊C4C22×C3⋊D311yescharacteristic
378C22⋊C4—96no—
379C22⋊C4—912no—
380C22⋊C4—92no—
381C22⋊C4—96no—
382C22⋊C4—96no—
383C22⋊C4C22×C3⋊D316yes—
384C42C22×C3⋊D316yes—
385C22×C3—212no—
386C22×C3—212no—
387C22×C3C22×D12124yes—
388C22×C3C24×D314yes—
389C2×D3—38no—
390C2×D3—64no—
391C2×D3—64no—
392C2×D3—612no—
393C2×D3—624no—
394C2×D3—624no—
395C2×D3—612no—
396C2×D3—612no—
397C2×D3—624no—
398C2×D3—1248no—
399C2×D3—2448no—
400C3×C4—224no—
401C3×C4—28no—
402C3×C4C22×D1218yes—
403C3×C4C22×D12124yes—
404Dic3—612no—
405Dic3—68no—
406Dic3—64no—
407C32#348811yescharacteristic, complemented, Sylow
408C23—91no—
409C23—96no—
410C23—93no—
411C23—186no—
412C23—186no—
413C23—1812no—
414C23—363no—
415C23—366no—
416C23—366no—
417C23C23×C3⋊D313yes—
418Q8—186no—
419Q8—182no—
420Q8C2×C4⋊(C3⋊D3)14yescomplemented
421D4—1812no—
422D4—1812no—
423D4—1812no—
424D4—186no—
425D4—1812no—
426D4—186no—
427D4—3612no—
428D4—366no—
429D4C2×C4⋊(C3⋊D3)112yescomplemented
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×C4⋊(C3⋊D3)112yescomplemented
441C2×C4C23×C3⋊D312yes—
442C2×C4C23×C3⋊D316yes—
443C2×C4C23×C3⋊D313yes—
444C2×C4C23×C3⋊D311yescharacteristic
445C2×C3—224no—
446C2×C3C23×D1214yes—
447C2×C3D3×H(5,𝔽2)14yes—
448C2×C3#596814yes—
449D3—68no—
450D3—1212no—
451D3—1224no—
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×C4⋊(C3⋊D3)16yes—
466C22C24×C3⋊D311yescharacteristic
467C4—26no—
468C4—22no—
469C4—181no—
470C4—182no—
471C4—183no—
472C4C22×C4⋊(C3⋊D3)12yes—
473C4C22×C4⋊(C3⋊D3)16yes—
474C3#8590014yescomplemented
475C2—26no—
476C2—182no—
477C2—363no—
478C2—366no—
479C2C23×C4⋊(C3⋊D3)11yescharacteristic
480C2C3⋊D3×H(5,𝔽2)11yescharacteristic
481C2#1059676011yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#520C2
hypercenter#520C3⋊D3
hypocenterC32#3488
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #520

Complements

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

NH ≅ G/Ntype
1. C2×#64366C2semidirect
2. C2×#41×C3⋊D3C2semidirect
3. C32×#520C2semidirect
4. #10596048C2semidirect
5. #10596047C2semidirect
6. #10596025C2semidirect
7. D4×C4⋊(C3⋊D3)C2semidirect
8. #10595996C2semidirect
9. #10595995C2semidirect
10. #10595981C2semidirect
11. C2×#64104C2semidirect
16. C2×#3832C22semidirect
17. C2×#3832C22semidirect
18. C2×Q8×C3⋊D3C22semidirect
19. C2×#3830C22semidirect
20. C2×D4×C3⋊D3C22semidirect
21. C2×D4×C3⋊D3C22semidirect
22. C2×#3828C22semidirect
23. C2×#3828C22semidirect
24. C22×C4⋊(C3⋊D3)C22semidirect
25. C22×C4⋊(C3⋊D3)C22semidirect
26. C22×C4×C3⋊D3C22semidirect
27. C32×C4×Q8C22semidirect
28. C32×C4×D4C22semidirect
29. C32×#117C22semidirect
30. C2×C32×C4⋊C4C22semidirect
31. #64139C22semidirect
32. C2×#3752C22semidirect
33. #64106C22semidirect
34. #64106C22semidirect
35. #64106C22semidirect
36. #64104C22semidirect
37. #64104C22semidirect
38. #64104C22semidirect
39. #64104C22semidirect
40. #64104C22semidirect
41. #64104C22semidirect
42. #64095C22semidirect
43. #64091C22semidirect
44. #64091C22semidirect
45. #64084C22semidirect
46. #64083C22semidirect
47. C4×C4⋊(C3⋊D3)C22semidirect
48. C4×C4⋊(C3⋊D3)C22semidirect
51. C3×#520D3semidirect
62. C32×#41D4semidirect
121. C3×C4×Q8C2×D3semidirect
122. C3×C4×D4C2×D3semidirect
123. C3×#117C2×D3semidirect
124. C2×C3×C4⋊C4C2×D3semidirect
153. C32×Q8C2×D4semidirect
154. C32×D4C2×D4semidirect
156. C2×C32×C4C2×D4semidirect
190. #520C3⋊D3semidirect
193. C3×#41D12semidirect
251. C2×C3⋊D3H(5,𝔽2)semidirect
288. C4×Q8C2×C3⋊D3semidirect
291. C4×D4C2×C3⋊D3semidirect
292. #117C2×C3⋊D3semidirect
293. C2×C4⋊C4C2×C3⋊D3semidirect
305. C3×Q8C2×D12semidirect
306. C3×D4C2×D12semidirect
308. C2×C3×C4C2×D12semidirect
346. #41C4⋊(C3⋊D3)semidirect
407. C32#3488semidirect
420. Q8C2×C4⋊(C3⋊D3)semidirect
429. D4C2×C4⋊(C3⋊D3)semidirect
440. C2×C4C2×C4⋊(C3⋊D3)semidirect
474. C3#85900semidirect

Maximal subgroups

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

subgroupindex
C2×#643662
C2×#41×C3⋊D32
C32×#5202
#105960482
#105960472
#105960252
D4×C4⋊(C3⋊D3)2
#105959962
#105959952
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