Finite Group Databasebeta

← #11910508

Subgroups — #11910508

Order 1152.

4008 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×H(3,𝔽4)C211yesmaximal, characteristic, complemented
2#10596150C213yesmaximal, complemented
3#10596149C216yesmaximal, complemented
4#10596147C216yesmaximal, complemented
5#10596145C213yesmaximal, complemented
6#10596066C213yesmaximal, complemented
7#10596061C213yesmaximal, complemented
8#10596060C213yesmaximal, complemented
9C3⋊D3×#120C213yesmaximal, complemented
10#87090—34nomaximal
11C24×C3⋊D3C2211yescharacteristic, complemented
12C22×#638C2213yescomplemented
13C2×#3832C2213yescomplemented
14C2×D4×C3⋊D3C2213yescomplemented
15C2×D4×C3⋊D3C2216yescomplemented
16C32×#124C2213yescomplemented
17C32×#124C2216yescomplemented
18C32×#120C2213yescomplemented
19C32×#120C2213yescomplemented
20#64162C2213yescomplemented
21#64162C2211yescharacteristic, complemented
22#64156C2213yescomplemented
23#64155C2216yescomplemented
24#64149C2213yescomplemented
25#64148C2216yescomplemented
26#64147C2216yescomplemented
27#64146C2213yes—
28#64146C2216yescomplemented
29#64144C2213yescomplemented
30#64095C2213yescomplemented
31#64093C2216yescomplemented
32#64093C2216yescomplemented
33#64093C2216yescomplemented
34#64092C2216yescomplemented
35#64092C2216yescomplemented
36#64091C2216yescomplemented
37#64091C2213yescomplemented
38#64091C2216yescomplemented
39#64090C2216yescomplemented
40C22⋊C4×C3⋊D3C2216yescomplemented
41C22⋊C4×C3⋊D3C2213yescomplemented
42C22⋊C4×C3⋊D3C2213yescomplemented
43#64088C2216yescomplemented
44#64085C2212yescomplemented
45#64083C2211yescharacteristic, complemented
46C4×C4⋊(C3⋊D3)C2216yescomplemented
47#64081C2213yescomplemented
48C3×H(3,𝔽4)D314yescomplemented
49#5679—312no—
50#5678—324no—
51#5676—324no—
52#5674—312no—
53#5595—312no—
54#5590—312no—
55#5589—312no—
56D3×#120—312no—
57C24×C32C2311yescharacteristic
58C24×C32C2311yescharacteristic, complemented
59C23×C3⋊D3—46no—
60C23×C3⋊D3C2313yes—
61C23×C3⋊D3C2313yes—
62C23×C3⋊D3C2313yes—
63C2×C32×Q8C2313yescomplemented
64C2×C32×D4C2313yes—
65C2×C32×D4C2316yes—
66C2×#638—46no—
67C2×#638C2316yes—
68C2×#638C2316yes—
69C2×#638C2313yes—
70C2×#638C2313yes—
71C2×#638C2316yescomplemented
72C22×C3⋊Dic3C2313yescomplemented
73#3832—46no—
74D4×C3⋊D3—46no—
75D4×C3⋊D3—412no—
76C2×C4⋊(C3⋊D3)C2316yes—
77C2×C4⋊(C3⋊D3)C2313yes—
78C2×C4⋊(C3⋊D3)C2313yescomplemented
79C2×C4×C3⋊D3C2313yes—
80C2×C4×C3⋊D3C2316yes—
81C2×C4×C3⋊D3C2316yescomplemented
82C32×C22⋊C4C2316yes—
83C32×C22⋊C4C2313yes—
84C32×C22⋊C4C2313yescomplemented
85C32×C22⋊C4C2316yescomplemented
86C32×C42C2311yescharacteristic, complemented
87C32×C42C2312yescomplemented
88#3757C2313yes—
89#3757C2316yes—
90#3757C2313yescomplemented
91#3752C2316yes—
92#3752C2316yes—
93#3752C2316yes—
94#3752C2316yescomplemented
95C4⋊(C3⋊Dic3)C2316yescomplemented
96#3750C2316yescomplemented
97#3750C2316yescomplemented
98C4×C3⋊Dic3C2313yescomplemented
99#3532—91noSylow
100C24×D3—34no—
101C22×#67—312no—
102C2×#239—312no—
103C2×D3×D4—312no—
104C2×D3×D4—324no—
105C3×#124C2×D3112yescomplemented
106C3×#124C2×D3124yescomplemented
107C3×#120C2×D3112yescomplemented
108C3×#120C2×D3112yescomplemented
109#953—312no—
110#953—34no—
111#947—312no—
112#946—324no—
113#940—312no—
114#939—324no—
115#938—324no—
116#937—324no—
117#937—312no—
118#935—312no—
119#886—312no—
120#884—324no—
121#884—324no—
122#884—324no—
123#883—324no—
124#883—324no—
125#882—324no—
126#882—312no—
127#882—324no—
128#67⋊C4—324no—
129D3×C22⋊C4—324no—
130D3×C22⋊C4—312no—
131D3×C22⋊C4—312no—
132#879—324no—
133#876—38no—
134#874—34no—
135C4×D12—324no—
136#872—312no—
137C23×C32—43no—
138C23×C32—43no—
139C23×C32C2413yes—
140C23×C32C2413yes—
141C22×C3⋊D3—212no—
142C22×C3⋊D3—26no—
143C22×C3⋊D3—26no—
144C22×C3⋊D3—43no—
145C22×C3⋊D3—46no—
146C22×C3⋊D3—46no—
147C22×C3⋊D3—416no—
148C22×C3⋊D3C2411yescharacteristic
149C22×C3⋊D3C2413yes—
150C22×C3⋊D3C2413yes—
151C32×Q8—43no—
152C32×D4—43no—
153C32×D4—46no—
154C2×C32×C4C2413yes—
155C2×C32×C4C2416yes—
156#638—212no—
157#638—43no—
158#638—43no—
159#638—46no—
160#638—46no—
161C2×C3⋊Dic3—43no—
162C2×C3⋊Dic3C2416yes—
163C2×C3⋊Dic3C2413yes—
164C4⋊(C3⋊D3)—212no—
165C4⋊(C3⋊D3)—43no—
166C4⋊(C3⋊D3)—43no—
167C4×C3⋊D3—26no—
168C4×C3⋊D3—46no—
169C4×C3⋊D3—46no—
170H(3,𝔽4)C3⋊D311yescharacteristic, complemented
171#560—93no—
172#551—93no—
173#546—96no—
174D42—93no—
175#538—96no—
176#535—93no—
177#534—93no—
178C2×#120—93no—
179C24×C3C22×D314yes—
180C24×C3C22×D314yescomplemented
181C23×D3—312no—
182C23×D3—312no—
183C23×D3—312no—
184C23×D3—1224no—
185C2×C3×Q8C22×D3112yescomplemented
186C2×C3×D4C22×D3112yes—
187C2×C3×D4C22×D3124yes—
188C2×#67—324no—
189C2×#67—324no—
190C2×#67—312no—
191C2×#67—324no—
192C2×#67—312no—
193C2×#67—1224no—
194C22×Dic3—312no—
195#239—1224no—
196D3×D4—1224no—
197D3×D4—1248no—
198C2×D12—324no—
199C2×D12—312no—
200C2×D12—312no—
201C2×C4×D3—312no—
202C2×C4×D3—324no—
203C2×C4×D3—324no—
204C3×C22⋊C4C22×D3124yes—
205C3×C22⋊C4C22×D3112yes—
206C3×C22⋊C4C22×D3112yescomplemented
207C3×C22⋊C4C22×D3124yescomplemented
208C3×C42C22×D314yescomplemented
209C3×C42C22×D318yescomplemented
210#217—312no—
211#217—324no—
212#217—312no—
213(C2×D3)⋊C4—324no—
214(C2×D3)⋊C4—324no—
215(C2×D3)⋊C4—324no—
216(C2×D3)⋊C4—324no—
217C4⋊Dic3—324no—
218Dic3⋊C4—324no—
219Dic3⋊C4—324no—
220C4×Dic3—312no—
221C22×C32—23no—
222C22×C32—26no—
223C22×C32—23no—
224C22×C32—26no—
225C22×C32—44no—
226C22×C32—82no—
227C22×C32C2511yescharacteristic
228C2×C3⋊D3—26no—
229C2×C3⋊D3—26no—
230C2×C3⋊D3—23no—
231C2×C3⋊D3—23no—
232C2×C3⋊D3—412no—
233C2×C3⋊D3—412no—
234C2×C3⋊D3—86no—
235C2×C3⋊D3H(5,𝔽2)16yes—
236C32×C4—23no—
237C32×C4—26no—
238C3⋊Dic3—23no—
239C3⋊Dic3—26no—
240C25—91no—
241C2×#41—93no—
242C22×D4—93no—
243C22×D4—93no—
244C22×D4—96no—
245#127—93no—
246#127—91no—
247#126—96no—
248#126—92no—
249#124—93no—
250#124C2×C3⋊D313yescomplemented
251#124C2×C3⋊D316yescomplemented
252#123—93no—
253#123—96no—
254#123—93no—
255#123—96no—
256C22⋊Q8—96no—
257#121—96no—
258#121—96no—
259#121—96no—
260#121—96no—
261#121—96no—
262#120—93no—
263#120—91no—
264#120—96no—
265#120—93no—
266#120—96no—
267#120—93no—
268#120—96no—
269#120C2×C3⋊D313yescomplemented
270#120C2×C3⋊D313yescomplemented
271C4×D4—96no—
272C4×D4—96no—
273#117—93no—
274C2×C22⋊C4—93no—
275C2×C22⋊C4—96no—
276C2×C22⋊C4—93no—
277C23×C3—412no—
278C23×C3—412no—
279C23×C3C23×D3112yes—
280C23×C3C23×D3112yes—
281C22×D3—312no—
282C22×D3—34no—
283C22×D3—312no—
284C22×D3—648no—
285C22×D3—624no—
286C22×D3—624no—
287C22×D3—1212no—
288C22×D3—1224no—
289C22×D3—1224no—
290C22×D3—1264no—
291C3×Q8—412no—
292C3×D4—412no—
293C3×D4—424no—
294C2×C3×C4C23×D3112yes—
295C2×C3×C4C23×D3124yes—
296#67—648no—
297#67—1212no—
298#67—1212no—
299#67—1224no—
300#67—1224no—
301C2×Dic3—324no—
302C2×Dic3—312no—
303C2×Dic3—1212no—
304D12—648no—
305D12—1212no—
306D12—1212no—
307C4×D3—624no—
308C4×D3—1224no—
309C4×D3—1224no—
310C2×C32—43no—
311C2×C32—43no—
312C2×C32C2×H(5,𝔽2)13yes—
313C3⋊D3—26no—
314C3⋊D3—41no—
315C3⋊D3—43no—
316C24—93no—
317C24—93no—
318C24—93no—
319C24—366no—
320C24C22×C3⋊D311yescharacteristic
321C24C22×C3⋊D311yescharacteristic, complemented
322#41—366no—
323C2×Q8C22×C3⋊D313yescomplemented
324C2×D4—96no—
325C2×D4—93no—
326C2×D4—93no—
327C2×D4—96no—
328C2×D4—96no—
329C2×D4—96no—
330C2×D4—93no—
331C2×D4—93no—
332C2×D4—366no—
333C2×D4—3612no—
334C2×D4—366no—
335C2×D4C22×C3⋊D316yes—
336C2×D4C22×C3⋊D313yes—
337C22×C4—93no—
338C22×C4—93no—
339C22×C4—96no—
340C22×C4—96no—
341C4⋊C4—96no—
342C4⋊C4—96no—
343C4⋊C4—96no—
344C22⋊C4—93no—
345C22⋊C4—96no—
346C22⋊C4—93no—
347C22⋊C4—96no—
348C22⋊C4—96no—
349C22⋊C4—96no—
350C22⋊C4—96no—
351C22⋊C4C22×C3⋊D316yes—
352C22⋊C4C22×C3⋊D313yes—
353C22⋊C4C22×C3⋊D313yescomplemented
354C22⋊C4C22×C3⋊D316yescomplemented
355C42—93no—
356C42C22×C3⋊D311yescharacteristic, complemented
357C42C22×C3⋊D312yescomplemented
358C22×C3—212no—
359C22×C3—224no—
360C22×C3—212no—
361C22×C3—224no—
362C22×C3—416no—
363C22×C3—88no—
364C22×C3C24×D314yes—
365C2×D3—324no—
366C2×D3—624no—
367C2×D3—624no—
368C2×D3—612no—
369C2×D3—612no—
370C2×D3—1248no—
371C2×D3—1248no—
372C2×D3—2424no—
373C3×C4—212no—
374C3×C4—224no—
375Dic3—612no—
376Dic3—624no—
377C32#353211yescharacteristic, complemented, Sylow
378C23—43no—
379C23—43no—
380C23—93no—
381C23—91no—
382C23—93no—
383C23—1812no—
384C23—186no—
385C23—186no—
386C23—363no—
387C23—366no—
388C23—366no—
389C23—3616no—
390C23C23×C3⋊D313yes—
391C23C23×C3⋊D313yes—
392Q8—43no—
393D4—43no—
394D4—46no—
395D4—1812no—
396D4—1812no—
397D4—363no—
398D4—363no—
399D4—363no—
400D4—363no—
401D4—366no—
402D4—366no—
403C2×C4—96no—
404C2×C4—93no—
405C2×C4—186no—
406C2×C4—366no—
407C2×C4—366no—
408C2×C4—363no—
409C2×C4C23×C3⋊D313yes—
410C2×C4C23×C3⋊D316yes—
411C2×C3—412no—
412C2×C3—412no—
413C2×C3D3×H(5,𝔽2)112yes—
414D3—624no—
415D3—124no—
416D3—1212no—
417C22—23no—
418C22—26no—
419C22—23no—
420C22—26no—
421C22—44no—
422C22—82no—
423C22—96no—
424C22—186no—
425C22—186no—
426C22—183no—
427C22—183no—
428C22—3612no—
429C22—3612no—
430C22—726no—
431C22C24×C3⋊D311yescharacteristic
432C4—23no—
433C4—26no—
434C4—183no—
435C4—186no—
436C3#8709014yescomplemented
437C2—43no—
438C2—43no—
439C2—186no—
440C2—361no—
441C2—363no—
442C2C3⋊D3×H(5,𝔽2)13yes—
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×H(3,𝔽4)C2
hypercenterH(3,𝔽4)C3⋊D3
hypocenterC32#3532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. C32×H(3,𝔽4)C2semidirect
2. #10596150C2semidirect
3. #10596149C2semidirect
4. #10596147C2semidirect
5. #10596145C2semidirect
6. #10596066C2semidirect
7. #10596061C2semidirect
8. #10596060C2semidirect
9. C3⋊D3×#120C2semidirect
11. C24×C3⋊D3C22semidirect
12. C22×#638C22semidirect
13. C2×#3832C22semidirect
14. C2×D4×C3⋊D3C22semidirect
15. C2×D4×C3⋊D3C22semidirect
16. C32×#124C22semidirect
17. C32×#124C22semidirect
18. C32×#120C22semidirect
19. C32×#120C22semidirect
20. #64162C22semidirect
21. #64162C22semidirect
22. #64156C22semidirect
23. #64155C22semidirect
24. #64149C22semidirect
25. #64148C22semidirect
26. #64147C22semidirect
28. #64146C22semidirect
29. #64144C22semidirect
30. #64095C22semidirect
31. #64093C22semidirect
32. #64093C22semidirect
33. #64093C22semidirect
34. #64092C22semidirect
35. #64092C22semidirect
36. #64091C22semidirect
37. #64091C22semidirect
38. #64091C22semidirect
39. #64090C22semidirect
40. C22⋊C4×C3⋊D3C22semidirect
41. C22⋊C4×C3⋊D3C22semidirect
42. C22⋊C4×C3⋊D3C22semidirect
43. #64088C22semidirect
44. #64085C22semidirect
45. #64083C22semidirect
46. C4×C4⋊(C3⋊D3)C22semidirect
47. #64081C22semidirect
48. C3×H(3,𝔽4)D3semidirect
58. C24×C32C23semidirect
63. C2×C32×Q8C23semidirect
71. C2×#638C23semidirect
72. C22×C3⋊Dic3C23semidirect
78. C2×C4⋊(C3⋊D3)C23semidirect
81. C2×C4×C3⋊D3C23semidirect
84. C32×C22⋊C4C23semidirect
85. C32×C22⋊C4C23semidirect
86. C32×C42C23semidirect
87. C32×C42C23semidirect
90. #3757C23semidirect
94. #3752C23semidirect
95. C4⋊(C3⋊Dic3)C23semidirect
96. #3750C23semidirect
97. #3750C23semidirect
98. C4×C3⋊Dic3C23semidirect
105. C3×#124C2×D3semidirect
106. C3×#124C2×D3semidirect
107. C3×#120C2×D3semidirect
108. C3×#120C2×D3semidirect
170. H(3,𝔽4)C3⋊D3semidirect
180. C24×C3C22×D3semidirect
185. C2×C3×Q8C22×D3semidirect
206. C3×C22⋊C4C22×D3semidirect
207. C3×C22⋊C4C22×D3semidirect
208. C3×C42C22×D3semidirect
209. C3×C42C22×D3semidirect
250. #124C2×C3⋊D3semidirect
251. #124C2×C3⋊D3semidirect
269. #120C2×C3⋊D3semidirect
270. #120C2×C3⋊D3semidirect
321. C24C22×C3⋊D3semidirect
323. C2×Q8C22×C3⋊D3semidirect
353. C22⋊C4C22×C3⋊D3semidirect
354. C22⋊C4C22×C3⋊D3semidirect
356. C42C22×C3⋊D3semidirect
357. C42C22×C3⋊D3semidirect
377. C32#3532semidirect
436. C3#87090semidirect

Maximal subgroups

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

subgroupindex
C32×H(3,𝔽4)2
#105961502
#105961492
#105961472
#105961452
#105960662
#105960612
#105960602
C3⋊D3×#1202
#870903