Finite Group Databasebeta

← #11904590

Subgroups — #11904590

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×C32×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2C2×#41×C3⋊D3C211yesmaximal, characteristic, complemented
3#10596305C212yesmaximal, complemented
4#10596304C213yesmaximal, complemented
5#10596302C212yesmaximal, complemented
6#10596299C213yesmaximal, complemented
7#10596298C211yesmaximal, characteristic, complemented
8#10596277C216yesmaximal, complemented
9#10596276C213yesmaximal, complemented
10D4×#638C216yesmaximal, complemented
11C2×#64147C213yesmaximal, complemented
12#87285—34nomaximal
13C32×H(5,𝔽2)—28no—
14C2×C32×#41C2211yescharacteristic
15C2×C32×#41C2213yescomplemented
16C2×C32×#41C2212yescomplemented
17C22×C32×D4C2213yescomplemented
18C22×C32×D4C2216yescomplemented
19C22×#638C2216yescomplemented
20#41×C3⋊D3—28no—
21C2×#3832C2211yescharacteristic, complemented
22C2×Q8×C3⋊D3C2211yescharacteristic, complemented
23C2×#3830C2213yescomplemented
24C2×D4×C3⋊D3C2213yescomplemented
25C2×#3828C2213yescomplemented
26C22×C4×C3⋊D3C2213yescomplemented
27#64162C22112yescomplemented
28C2×#3757C2216yescomplemented
29#64155C2211yescharacteristic, complemented
30#64155C2213yescomplemented
31Q8×C3⋊Dic3C2212yescomplemented
32#64149C2216yescomplemented
33#64148C22112yescomplemented
34#64147C2213yescomplemented
35#64147C2216yescomplemented
36#64147C2216yescomplemented
37#64147C2216yescomplemented
38#64147C2213yescomplemented
39#64146C2216yescomplemented
40#64145C2216yescomplemented
41#64144C2216yescomplemented
42D4×C3⋊Dic3C2216yescomplemented
43#64139C2216yescomplemented
44C4×#638C2216yescomplemented
45C4×#638C2216yescomplemented
46#64135C2213yescomplemented
47C2×C4⋊(C3⋊Dic3)C2213yescomplemented
48#64133C2216yescomplemented
49C2×C3×H(5,𝔽2)D314yescomplemented
50C2×D3×#41—34no—
51#5834—38no—
52#5833—312no—
53#5831—38no—
54#5828—312no—
55#5827—34no—
56#5806—324no—
57#5805—312no—
58D4×#67—324no—
59C2×#938—312no—
60C24×C32C2316yes—
61C23×C3⋊D3C2313yes—
62C32×#41—28no—
63C32×#41—212no—
64C32×#41D418yescomplemented
65C2×C32×Q8C2311yescharacteristic
66C2×C32×Q8C2311yescharacteristic
67C2×C32×D4—224no—
68C2×C32×D4—212no—
69C2×C32×D4C2316yes—
70C2×C32×D4C2316yes—
71C2×C32×D4C2313yes—
72C2×C32×D4C2313yes—
73C22×C32×C4C2316yes—
74C22×C32×C4C2313yes—
75C2×#638—412no—
76C2×#638C2316yes—
77C2×#638C2316yes—
78C2×#638C23112yes—
79C2×#638C2316yes—
80C22×C3⋊Dic3C2313yes—
81C22×C3⋊Dic3C2316yes—
82#3832—24no—
83Q8×C3⋊D3—24no—
84#3830—212no—
85D4×C3⋊D3—212no—
86#3828—212no—
87C2×C4⋊(C3⋊D3)C2313yes—
88C2×C4×C3⋊D3—212no—
89C2×C4×C3⋊D3C2311yescharacteristic
90C2×C4×C3⋊D3C2313yes—
91C2×C4×C3⋊D3C2313yes—
92C2×C4×C3⋊D3C2313yes—
93C2×#634C2313yes—
94#3757C23112yes—
95#3757C2316yes—
96#3757C2316yes—
97#3757C2316yes—
98#3752C2312yes—
99#3752C2316yes—
100C4⋊(C3⋊Dic3)C2316yes—
101C4⋊(C3⋊Dic3)C2313yes—
102C4⋊(C3⋊Dic3)C2311yescharacteristic
103#3750C2316yes—
104#3750C2312yes—
105C4×C3⋊Dic3C2316yes—
106#3488—91noSylow
107C3×H(5,𝔽2)—232no—
108C2×C3×#41C2×D314yes—
109C2×C3×#41C2×D3112yescomplemented
110C2×C3×#41C2×D318yescomplemented
111C22×C3×D4C2×D3112yescomplemented
112C22×C3×D4C2×D3124yescomplemented
113C22×#67—324no—
114D3×#41—632no—
115C2×#239—34no—
116C2×D3×Q8—34no—
117C2×#237—312no—
118C2×D3×D4—312no—
119C2×#235—312no—
120C22×C4×D3—312no—
121#953—348no—
122C2×#217—324no—
123#946—34no—
124#946—312no—
125Q8×Dic3—38no—
126#940—324no—
127#939—348no—
128#938—312no—
129#938—324no—
130#938—324no—
131#938—324no—
132#938—312no—
133#937—324no—
134#936—324no—
135#935—324no—
136D4×Dic3—324no—
137#930—324no—
138C4×#67—324no—
139C4×#67—324no—
140#926—312no—
141C2×C4⋊Dic3—312no—
142#924—324no—
143C23×C32—212no—
144C23×C32—46no—
145C23×C32—46no—
146C23×C32C2416yes—
147C23×C32C2413yes—
148C22×C3⋊D3—26no—
149C22×C3⋊D3—26no—
150C22×C3⋊D3—43no—
151C22×C3⋊D3C2413yes—
152C22×C3⋊D3C2411yescharacteristic
153C32×Q8—22no—
154C32×Q8C2×D414yescomplemented
155C32×D4—212no—
156C32×D4—212no—
157C32×D4—26no—
158C32×D4C2×D4112yescomplemented
159C2×C32×C4—212no—
160C2×C32×C4C2×D4112yescomplemented
161C2×C32×C4C2412yes—
162C2×C32×C4C2413yes—
163C2×C32×C4C2411yescharacteristic
164#638—212no—
165#638—212no—
166#638—412no—
167#638—46no—
168C2×C3⋊Dic3—26no—
169C2×C3⋊Dic3—46no—
170C2×C3⋊Dic3C2412yes—
171C2×C3⋊Dic3C2416yes—
172C2×C3⋊Dic3C2413yes—
173C2×C3⋊Dic3C2411yescharacteristic
174C4⋊(C3⋊D3)—26no—
175C4×C3⋊D3—22no—
176C4×C3⋊D3—26no—
177C4×C3⋊D3—26no—
178C4×C3⋊D3—26no—
179#634—26no—
180C2×H(5,𝔽2)C3⋊D311yescharacteristic, complemented
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#520—91no—
191C24×C3C22×D3124yes—
192C23×D3—312no—
193C3×#41—232no—
194C3×#41—248no—
195C3×#41#67132yescomplemented
196C2×C3×Q8C22×D314yes—
197C2×C3×Q8C22×D314yes—
198C2×C3×D4—296no—
199C2×C3×D4—248no—
200C2×C3×D4C22×D3124yes—
201C2×C3×D4C22×D3124yes—
202C2×C3×D4C22×D3112yes—
203C2×C3×D4C22×D3112yes—
204C22×C3×C4C22×D3124yes—
205C22×C3×C4C22×D3112yes—
206C2×#67—324no—
207C2×#67—324no—
208C2×#67—324no—
209C2×#67—348no—
210C2×#67—1248no—
211C22×Dic3—312no—
212C22×Dic3—324no—
213#239—616no—
214D3×Q8—616no—
215#237—648no—
216D3×D4—648no—
217#235—648no—
218C2×D12—312no—
219C2×C4×D3—312no—
220C2×C4×D3—312no—
221C2×C4×D3—34no—
222C2×C4×D3—312no—
223C2×C4×D3—648no—
224C2×Dic6—312no—
225#217—348no—
226#217—324no—
227#217—324no—
228#217—324no—
229(C2×D3)⋊C4—38no—
230(C2×D3)⋊C4—324no—
231C4⋊Dic3—324no—
232C4⋊Dic3—312no—
233C4⋊Dic3—34no—
234Dic3⋊C4—324no—
235Dic3⋊C4—38no—
236C4×Dic3—324no—
237C22×C32—23no—
238C22×C32—23no—
239C22×C32—26no—
240C22×C32—26no—
241C22×C32—26no—
242C22×C32—812no—
243C22×C32C22×D416yes—
244C22×C32C2511yescharacteristic
245C2×C3⋊D3—21no—
246C2×C3⋊D3—21no—
247C2×C3⋊D3—23no—
248C2×C3⋊D3—23no—
249C2×C3⋊D3—23no—
250C2×C3⋊D3—412no—
251C2×C3⋊D3H(5,𝔽2)12yescomplemented
252C32×C4—22no—
253C32×C4C22×D416yes—
254C32×C4C22×D412yes—
255C3⋊Dic3—23no—
256C3⋊Dic3—21no—
257C3⋊Dic3—26no—
258C3⋊Dic3—22no—
259H(5,𝔽2)—28no—
260C2×#41—91no—
261C2×#41—93no—
262C2×#41—93no—
263C2×#41—188no—
264C2×#41C2×C3⋊D311yescharacteristic
265C2×#41C2×C3⋊D313yescomplemented
266C2×#41C2×C3⋊D312yescomplemented
267C22×Q8—91no—
268C22×D4—96no—
269C22×D4—93no—
270C22×D4C2×C3⋊D313yescomplemented
271C22×D4C2×C3⋊D316yescomplemented
272C23×C4—93no—
273#127—96no—
274#124—96no—
275#123—96no—
276C22⋊Q8—91no—
277C22⋊Q8—93no—
278C22⋊Q8—96no—
279#121—93no—
280#121—96no—
281#121—96no—
282#121—96no—
283#121—93no—
284#121—912no—
285#121—96no—
286#120—912no—
287#120—96no—
288C4×Q8—92no—
289C4×D4—96no—
290C4×D4—96no—
291C4×D4—96no—
292#117—93no—
293C2×C4⋊C4—93no—
294C2×C22⋊C4—96no—
295C23×C3—248no—
296C23×C3—424no—
297C23×C3—424no—
298C23×C3C23×D3124yes—
299C23×C3C23×D3112yes—
300C22×D3—34no—
301C22×D3—312no—
302C22×D3—624no—
303C22×D3—624no—
304C22×D3—1212no—
305C3×Q8—28no—
306C3×Q8C2×#67116yescomplemented
307C3×D4—248no—
308C3×D4—248no—
309C3×D4—224no—
310C3×D4C2×#67148yescomplemented
311C2×C3×C4—248no—
312C2×C3×C4C2×#67148yescomplemented
313C2×C3×C4C23×D318yes—
314C2×C3×C4C23×D3112yes—
315C2×C3×C4C23×D314yes—
316#67—648no—
317#67—648no—
318#67—1224no—
319#67—1248no—
320C2×Dic3—38no—
321C2×Dic3—324no—
322C2×Dic3—312no—
323C2×Dic3—34no—
324C2×Dic3—624no—
325C2×Dic3—1224no—
326D12—624no—
327C4×D3—68no—
328C4×D3—624no—
329C4×D3—624no—
330C4×D3—624no—
331Dic6—624no—
332C2×C32—26no—
333C2×C32—46no—
334C2×C32C23×D411yescharacteristic
335C2×C32C2×H(5,𝔽2)11yescharacteristic
336C2×C32#58511yescharacteristic
337C3⋊D3—22no—
338C3⋊D3—43no—
339C24—93no—
340C24C22×C3⋊D316yes—
341#41—28no—
342#41—212no—
343#41—184no—
344#41—1812no—
345#41—1812no—
346#41#63818yescomplemented
347C2×Q8—93no—
348C2×Q8—184no—
349C2×Q8C22×C3⋊D311yescharacteristic
350C2×Q8C22×C3⋊D311yescharacteristic
351C2×D4—224no—
352C2×D4—212no—
353C2×D4—96no—
354C2×D4—96no—
355C2×D4—96no—
356C2×D4—912no—
357C2×D4—93no—
358C2×D4—1812no—
359C2×D4—3612no—
360C2×D4C22×C3⋊D316yes—
361C2×D4C22×C3⋊D313yes—
362C2×D4C22×C3⋊D316yes—
363C2×D4C22×C3⋊D313yes—
364C22×C4—93no—
365C22×C4—96no—
366C22×C4—93no—
367C22×C4—93no—
368C22×C4—91no—
369C22×C4—93no—
370C22×C4—1812no—
371C22×C4C22×C3⋊D316yes—
372C22×C4C22×C3⋊D313yes—
373C4⋊C4—93no—
374C4⋊C4—96no—
375C4⋊C4—91no—
376C4⋊C4—92no—
377C4⋊C4—96no—
378C22⋊C4—96no—
379C22⋊C4—912no—
380C22⋊C4—96no—
381C22⋊C4—96no—
382C22⋊C4—92no—
383C22⋊C4—96no—
384C42—96no—
385C22×C3—212no—
386C22×C3—212no—
387C22×C3—224no—
388C22×C3—224no—
389C22×C3—224no—
390C22×C3—848no—
391C22×C3C22×#67124yes—
392C22×C3C24×D314yes—
393C2×D3—38no—
394C2×D3—64no—
395C2×D3—64no—
396C2×D3—612no—
397C2×D3—612no—
398C2×D3—612no—
399C2×D3—1248no—
400C3×C4—28no—
401C3×C4C22×#67124yes—
402C3×C4C22×#6718yes—
403Dic3—624no—
404Dic3—68no—
405Dic3—612no—
406Dic3—64no—
407C32#348811yescharacteristic, complemented, Sylow
408C23—212no—
409C23—46no—
410C23—46no—
411C23—91no—
412C23—93no—
413C23—186no—
414C23—186no—
415C23—363no—
416C23C23×C3⋊D316yes—
417C23C23×C3⋊D313yes—
418Q8—22no—
419Q8—186no—
420Q8C2×#63814yescomplemented
421D4—212no—
422D4—212no—
423D4—26no—
424D4—1812no—
425D4—1812no—
426D4—186no—
427D4—3612no—
428D4—366no—
429D4C2×#638112yescomplemented
430C2×C4—212no—
431C2×C4—92no—
432C2×C4—96no—
433C2×C4—91no—
434C2×C4—93no—
435C2×C4—186no—
436C2×C4—182no—
437C2×C4—186no—
438C2×C4—186no—
439C2×C4—186no—
440C2×C4—366no—
441C2×C4C2×#638112yescomplemented
442C2×C4C23×C3⋊D312yes—
443C2×C4C23×C3⋊D313yes—
444C2×C4C23×C3⋊D311yescharacteristic
445C2×C3—224no—
446C2×C3—424no—
447C2×C3D3×H(5,𝔽2)14yes—
448C2×C3#596614yes—
449C2×C3C23×#6714yes—
450D3—68no—
451D3—1212no—
452C22—23no—
453C22—23no—
454C22—26no—
455C22—26no—
456C22—26no—
457C22—812no—
458C22—92no—
459C22—181no—
460C22—181no—
461C22—183no—
462C22—183no—
463C22—183no—
464C22—3612no—
465C22C22×#63816yes—
466C22C24×C3⋊D311yescharacteristic
467C4—22no—
468C4—186no—
469C4—182no—
470C4—181no—
471C4—183no—
472C4C22×#63816yes—
473C4C22×#63812yes—
474C3#8728514yescomplemented
475C2—26no—
476C2—46no—
477C2—182no—
478C2—363no—
479C2C3⋊D3×H(5,𝔽2)11yescharacteristic
480C2#1059675811yescharacteristic
481C2C23×#63811yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC2×C32×H(5,𝔽2)C2
hypercenterC2×H(5,𝔽2)C3⋊D3
hypocenterC32#3488
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×C32×H(5,𝔽2)C2semidirect
2. C2×#41×C3⋊D3C2semidirect
3. #10596305C2semidirect
4. #10596304C2semidirect
5. #10596302C2semidirect
6. #10596299C2semidirect
7. #10596298C2semidirect
8. #10596277C2semidirect
9. #10596276C2semidirect
10. D4×#638C2semidirect
11. C2×#64147C2semidirect
15. C2×C32×#41C22semidirect
16. C2×C32×#41C22semidirect
17. C22×C32×D4C22semidirect
18. C22×C32×D4C22semidirect
19. C22×#638C22semidirect
21. C2×#3832C22semidirect
22. C2×Q8×C3⋊D3C22semidirect
23. C2×#3830C22semidirect
24. C2×D4×C3⋊D3C22semidirect
25. C2×#3828C22semidirect
26. C22×C4×C3⋊D3C22semidirect
27. #64162C22semidirect
28. C2×#3757C22semidirect
29. #64155C22semidirect
30. #64155C22semidirect
31. Q8×C3⋊Dic3C22semidirect
32. #64149C22semidirect
33. #64148C22semidirect
34. #64147C22semidirect
35. #64147C22semidirect
36. #64147C22semidirect
37. #64147C22semidirect
38. #64147C22semidirect
39. #64146C22semidirect
40. #64145C22semidirect
41. #64144C22semidirect
42. D4×C3⋊Dic3C22semidirect
43. #64139C22semidirect
44. C4×#638C22semidirect
45. C4×#638C22semidirect
46. #64135C22semidirect
47. C2×C4⋊(C3⋊Dic3)C22semidirect
48. #64133C22semidirect
49. C2×C3×H(5,𝔽2)D3semidirect
64. C32×#41D4semidirect
109. C2×C3×#41C2×D3semidirect
110. C2×C3×#41C2×D3semidirect
111. C22×C3×D4C2×D3semidirect
112. C22×C3×D4C2×D3semidirect
154. C32×Q8C2×D4semidirect
158. C32×D4C2×D4semidirect
160. C2×C32×C4C2×D4semidirect
180. C2×H(5,𝔽2)C3⋊D3semidirect
195. C3×#41#67semidirect
251. C2×C3⋊D3H(5,𝔽2)semidirect
265. C2×#41C2×C3⋊D3semidirect
266. C2×#41C2×C3⋊D3semidirect
270. C22×D4C2×C3⋊D3semidirect
271. C22×D4C2×C3⋊D3semidirect
306. C3×Q8C2×#67semidirect
310. C3×D4C2×#67semidirect
312. C2×C3×C4C2×#67semidirect
346. #41#638semidirect
407. C32#3488semidirect
420. Q8C2×#638semidirect
429. D4C2×#638semidirect
441. C2×C4C2×#638semidirect
474. C3#87285semidirect

Maximal subgroups

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

subgroupindex
C2×C32×H(5,𝔽2)2
C2×#41×C3⋊D32
#105963052
#105963042
#105963022
#105962992
#105962982
#105962772
#105962762
D4×#6382
C2×#641472
#872853