Finite Group Databasebeta

← #11904952

Subgroups — #11904952

Order 1152.

3156 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#123C211yesmaximal, characteristic, complemented
2#10596275C211yesmaximal, characteristic
3#10596269C211yesmaximal, characteristic, complemented
4C2×#64138C211yesmaximal, characteristic, complemented
5C2×#64135C211yesmaximal, characteristic, complemented
6#10596136C214yesmaximal, complemented
7#10596129C214yesmaximal, complemented
8#10596121C214yesmaximal, complemented
9#10596120C214yesmaximal, complemented
10#10595984C214yesmaximal, complemented
11#10595966C214yesmaximal, complemented
12#10595957C211yesmaximal, characteristic, complemented
13#10595954C211yesmaximal, characteristic, complemented
14#86001—34nomaximal
15C22×C32×D4C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C22×#638C2211yescharacteristic
18C32×#123C2214yes—
19C32×#123C2212yescomplemented
20C32×#123C2212yescomplemented
21C2×C32×C4⋊C4C2212yescomplemented
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×C32×C22⋊C4C2212yescomplemented
24#64162C2212yes—
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C2×#3757C2212yescomplemented
29#64148C2214yes—
30#64146C2212yes—
31#64144C2212yes—
32D4×C3⋊Dic3C2214yes—
33D4×C3⋊Dic3C2214yescomplemented
34#64138C2214yes—
35#64138C2212yes—
36#64138C2212yescomplemented
37#64138C2212yescomplemented
38C4×#638C2214yes—
39C2×#3752C2212yescomplemented
40#64135C2214yescomplemented
41#64135C2214yescomplemented
42#64135C2212yescomplemented
43C2×C4⋊(C3⋊Dic3)C2212yescomplemented
44#64133C2214yescomplemented
45C2×#3750C2212yescomplemented
46C2×C4×C3⋊Dic3C2212yescomplemented
47#64107C2214yescomplemented
48#64107C2214yescomplemented
49#64106C2214yescomplemented
50#64101C2214yescomplemented
51#64099C2214yescomplemented
52#64098C2214yescomplemented
53#64098C2214yescomplemented
54#64096C2214yescomplemented
55#64095C2214yescomplemented
56#64094C2214yescomplemented
57#64092C2214yescomplemented
58#64090C2214yescomplemented
59#64090C2214yescomplemented
60C22⋊C4×C3⋊D3C2212yescomplemented
61#64088C2214yescomplemented
62#64088C2214yescomplemented
63#64087C2214yescomplemented
64#64087C2214yescomplemented
65#64087C2214yescomplemented
66#64086C2214yescomplemented
67#64086C2212yescomplemented
68C2×C3×#123D314yescomplemented
69#5804—34no—
70#5798—34no—
71C2×#929—34no—
72C2×#926—34no—
73#5665—316no—
74#5658—316no—
75#5650—316no—
76#5649—316no—
77#5513—316no—
78#5495—316no—
79#5486—34no—
80#5483—34no—
81C24×C32C2311yescharacteristic
82C24×C32C2311yescharacteristic
83C23×C3⋊D3C2311yescharacteristic
84C2×C32×D4—24no—
85C2×C32×D4C2312yes—
86C2×C32×D4C2312yes—
87C22×C32×C4—24no—
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2312yes—
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2312yes—
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2312yes—
94C2×#638—24no—
95C2×#638C2312yes—
96C2×#638C2312yes—
97C2×#638C2314yes—
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2314yes—
100C22×C3⋊Dic3C2312yes—
101C22×C3⋊Dic3C2312yes—
102C22×C3⋊Dic3C2312yes—
103C2×C4×C3⋊D3C2314yes—
104C2×#634C2314yes—
105C32×C4⋊C4C2314yes—
106C32×C4⋊C4C2314yes—
107C32×C22⋊C4C2312yes—
108C32×C22⋊C4C2314yes—
109C32×C22⋊C4C2312yes—
110C32×C22⋊C4C2314yes—
111#3757C2314yes—
112#3757C2312yes—
113#3757C2312yes—
114#3757C2312yes—
115#3757C2314yes—
116#3757C2312yes—
117#3757C2312yes—
118#3757C2312yes—
119#3752C2314yes—
120#3752C2314yes—
121#3752C2314yes—
122#3752C2314yes—
123C4⋊(C3⋊Dic3)C2314yes—
124C4⋊(C3⋊Dic3)C2314yes—
125C4⋊(C3⋊Dic3)C2314yes—
126C4⋊(C3⋊Dic3)C2314yes—
127#3750C2314yes—
128#3750C2314yes—
129#3750C2314yes—
130#3750C2314yes—
131#3750C2314yes—
132#3750C2314yes—
133C4×C3⋊Dic3C2314yes—
134C4×C3⋊Dic3C2314yes—
135C4×C3⋊Dic3C2314yes—
136C4×C3⋊Dic3C2314yes—
137#3491—91noSylow
138C22×C3×D4C2×D314yes—
139C23×C3×C4C2×D314yes—
140C22×#67—34no—
141C3×#123C2×D3116yes—
142C3×#123C2×D318yescomplemented
143C3×#123C2×D318yescomplemented
144C2×C3×C4⋊C4C2×D318yescomplemented
145C2×C3×C22⋊C4C2×D314yes—
146C2×C3×C22⋊C4C2×D318yescomplemented
147#953—38no—
148C2×#217—34no—
149C2×#217—34no—
150C2×#217—34no—
151C2×#217—38no—
152#939—316no—
153#937—38no—
154#935—38no—
155D4×Dic3—316no—
156D4×Dic3—316no—
157#929—38no—
158#929—38no—
159#929—316no—
160#929—38no—
161C4×#67—316no—
162C2×(C2×D3)⋊C4—38no—
163#926—316no—
164#926—316no—
165#926—38no—
166C2×C4⋊Dic3—38no—
167#924—316no—
168C2×Dic3⋊C4—38no—
169C2×C4×Dic3—38no—
170#898—316no—
171#898—316no—
172#897—316no—
173#892—316no—
174#890—316no—
175#889—316no—
176#889—316no—
177#887—316no—
178#886—316no—
179#885—316no—
180#883—316no—
181#67⋊C4—316no—
182#67⋊C4—316no—
183D3×C22⋊C4—38no—
184#879—316no—
185#879—316no—
186#878—316no—
187#878—316no—
188#878—316no—
189#877—316no—
190#877—38no—
191C23×C32—22no—
192C23×C32—42no—
193C23×C32—42no—
194C23×C32#4114yes—
195C23×C32C2412yes—
196C23×C32C2411yescharacteristic
197C23×C32C2411yescharacteristic
198C23×C32C2411yescharacteristic
199C22×C3⋊D3—22no—
200C22×C3⋊D3—42no—
201C22×C3⋊D3C2412yes—
202C32×D4—24no—
203C32×D4—24no—
204C2×C32×C4—24no—
205C2×C32×C4—24no—
206C2×C32×C4—22no—
207C2×C32×C4—22no—
208C2×C32×C4—22no—
209C2×C32×C4—42no—
210C2×C32×C4C2412yes—
211C2×C32×C4C2412yes—
212C2×C32×C4C2414yes—
213C2×C32×C4C2412yes—
214#638—24no—
215#638—24no—
216#638—44no—
217C2×C3⋊Dic3—22no—
218C2×C3⋊Dic3—42no—
219C2×C3⋊Dic3—44no—
220C2×C3⋊Dic3—42no—
221C2×C3⋊Dic3—42no—
222C2×C3⋊Dic3C2414yes—
223C2×C3⋊Dic3C2412yes—
224C2×C3⋊Dic3C2414yes—
225C2×C3⋊Dic3C2414yes—
226C4×C3⋊D3—44no—
227#634—44no—
228#552—94no—
229#552—94no—
230#551—94no—
231#551—94no—
232#543—91no—
233#539—94no—
234#534—91no—
235#529—94no—
236C2×#123—91no—
237C2×#123C3⋊D311yescharacteristic, complemented
238#518—91no—
239#518—91no—
240C2×#117—91no—
241C24×C3C22×D314yes—
242C24×C3C22×D314yes—
243C23×D3—34no—
244C2×C3×D4—216no—
245C2×C3×D4C22×D318yes—
246C2×C3×D4C22×D318yes—
247C22×C3×C4—216no—
248C22×C3×C4C22×D314yes—
249C22×C3×C4C22×D318yes—
250C22×C3×C4C22×D314yes—
251C22×C3×C4C22×D318yes—
252C22×C3×C4C22×D314yes—
253C22×C3×C4C22×D318yes—
254C2×#67—38no—
255C2×#67—38no—
256C2×#67—316no—
257C2×#67—616no—
258C22×Dic3—34no—
259C22×Dic3—316no—
260C22×Dic3—38no—
261C22×Dic3—38no—
262C22×Dic3—38no—
263C2×C4×D3—316no—
264C2×Dic6—316no—
265C3×C4⋊C4C22×D3116yes—
266C3×C4⋊C4C22×D3116yes—
267C3×C22⋊C4C22×D318yes—
268C3×C22⋊C4C22×D3116yes—
269C3×C22⋊C4C22×D318yes—
270C3×C22⋊C4C22×D3116yes—
271#217—316no—
272#217—38no—
273#217—38no—
274#217—38no—
275#217—316no—
276#217—38no—
277#217—38no—
278#217—38no—
279(C2×D3)⋊C4—316no—
280(C2×D3)⋊C4—316no—
281(C2×D3)⋊C4—316no—
282(C2×D3)⋊C4—316no—
283C4⋊Dic3—316no—
284C4⋊Dic3—316no—
285C4⋊Dic3—316no—
286C4⋊Dic3—316no—
287Dic3⋊C4—316no—
288Dic3⋊C4—316no—
289Dic3⋊C4—316no—
290Dic3⋊C4—316no—
291Dic3⋊C4—316no—
292Dic3⋊C4—316no—
293C4×Dic3—316no—
294C4×Dic3—316no—
295C4×Dic3—316no—
296C4×Dic3—316no—
297C22×C32—22no—
298C22×C32—22no—
299C22×C32—22no—
300C22×C32—22no—
301C22×C32—24no—
302C22×C32—44no—
303C22×C32—82no—
304C22×C32C2×#4112yes—
305C22×C32C2×#4112yes—
306C22×C32C2×#4112yes—
307C22×C32C2511yescharacteristic
308C2×C3⋊D3—22no—
309C2×C3⋊D3—24no—
310C2×C3⋊D3—82no—
311C32×C4—22no—
312C32×C4—22no—
313C32×C4—22no—
314C32×C4—24no—
315C3⋊Dic3—22no—
316C3⋊Dic3—24no—
317C3⋊Dic3—24no—
318C3⋊Dic3—24no—
319C22×D4—91no—
320C22×D4C2×C3⋊D311yescharacteristic
321C23×C4C2×C3⋊D311yescharacteristic
322#126—94no—
323#126—94no—
324#126—94no—
325#126—94no—
326#125—94no—
327#125—94no—
328#125—94no—
329#124—94no—
330#123—92no—
331#123—92no—
332#123—92no—
333#123—94no—
334#123—92no—
335#123—94no—
336#123—94no—
337#123C2×C3⋊D314yes—
338#123C2×C3⋊D312yescomplemented
339#123C2×C3⋊D312yescomplemented
340C22⋊Q8—94no—
341C22⋊Q8—94no—
342C22⋊Q8—94no—
343C22⋊Q8—94no—
344C22⋊Q8—94no—
345#121—94no—
346#120—92no—
347#120—92no—
348C4×Q8—94no—
349C4×D4—94no—
350C4×D4—94no—
351C4×D4—94no—
352C4×D4—94no—
353C4×D4—94no—
354#117—94no—
355#117—94no—
356#117—92no—
357#117—94no—
358#117—92no—
359#117—94no—
360C2×C4⋊C4—92no—
361C2×C4⋊C4—92no—
362C2×C4⋊C4C2×C3⋊D312yescomplemented
363C2×C22⋊C4—91no—
364C2×C22⋊C4—91no—
365C2×C22⋊C4—91no—
366C2×C22⋊C4—92no—
367C2×C22⋊C4—92no—
368C2×C22⋊C4—92no—
369C2×C22⋊C4C2×C3⋊D311yescharacteristic
370C2×C22⋊C4C2×C3⋊D312yescomplemented
371C2×C42—92no—
372C23×C3—28no—
373C23×C3—48no—
374C23×C3—48no—
375C23×C3#237116yes—
376C23×C3C23×D318yes—
377C23×C3C23×D314yes—
378C23×C3C23×D314yes—
379C23×C3C23×D314yes—
380C22×D3—38no—
381C22×D3—68no—
382C22×D3—128no—
383C3×D4—216no—
384C3×D4—216no—
385C2×C3×C4—216no—
386C2×C3×C4—216no—
387C2×C3×C4—28no—
388C2×C3×C4—28no—
389C2×C3×C4—28no—
390C2×C3×C4—48no—
391C2×C3×C4C23×D318yes—
392C2×C3×C4C23×D318yes—
393C2×C3×C4C23×D3116yes—
394C2×C3×C4C23×D318yes—
395#67—616no—
396#67—616no—
397#67—1216no—
398C2×Dic3—316no—
399C2×Dic3—38no—
400C2×Dic3—316no—
401C2×Dic3—316no—
402C2×Dic3—68no—
403C2×Dic3—128no—
404C2×Dic3—1216no—
405C2×Dic3—128no—
406C2×Dic3—128no—
407C4×D3—1216no—
408Dic6—1216no—
409C2×C32—22no—
410C2×C32—22no—
411C2×C32—22no—
412C2×C32—42no—
413C2×C32C22×#4111yescharacteristic
414C2×C32#58512yes—
415C3⋊D3—42no—
416C24—91no—
417C24C22×C3⋊D311yescharacteristic
418C24C22×C3⋊D311yescharacteristic
419C2×Q8—94no—
420C2×D4—24no—
421C2×D4—92no—
422C2×D4—92no—
423C2×D4—94no—
424C2×D4—184no—
425C2×D4C22×C3⋊D312yes—
426C2×D4C22×C3⋊D312yes—
427C22×C4—24no—
428C22×C4—91no—
429C22×C4—92no—
430C22×C4—92no—
431C22×C4—92no—
432C22×C4—94no—
433C22×C4—94no—
434C22×C4C22×C3⋊D311yescharacteristic
435C22×C4C22×C3⋊D312yes—
436C22×C4C22×C3⋊D312yes—
437C22×C4C22×C3⋊D311yescharacteristic
438C22×C4C22×C3⋊D311yescharacteristic
439C22×C4C22×C3⋊D312yes—
440C4⋊C4—94no—
441C4⋊C4—94no—
442C4⋊C4—94no—
443C4⋊C4—94no—
444C4⋊C4—94no—
445C4⋊C4—94no—
446C4⋊C4—94no—
447C4⋊C4—94no—
448C4⋊C4—94no—
449C4⋊C4—94no—
450C4⋊C4C22×C3⋊D314yes—
451C4⋊C4C22×C3⋊D314yes—
452C22⋊C4—92no—
453C22⋊C4—92no—
454C22⋊C4—92no—
455C22⋊C4—92no—
456C22⋊C4—92no—
457C22⋊C4—92no—
458C22⋊C4—94no—
459C22⋊C4—94no—
460C22⋊C4—94no—
461C22⋊C4—94no—
462C22⋊C4—94no—
463C22⋊C4—94no—
464C22⋊C4C22×C3⋊D312yes—
465C22⋊C4C22×C3⋊D312yes—
466C22⋊C4C22×C3⋊D314yes—
467C22⋊C4C22×C3⋊D314yes—
468C42—94no—
469C42—94no—
470C42—94no—
471C42—94no—
472C22×C3—28no—
473C22×C3—28no—
474C22×C3—28no—
475C22×C3—28no—
476C22×C3—216no—
477C22×C3—416no—
478C22×C3—88no—
479C22×C3C2×#23718yes—
480C22×C3C2×#23718yes—
481C22×C3C2×#23718yes—
482C22×C3C24×D314yes—
483C2×D3—68no—
484C2×D3—616no—
485C2×D3—248no—
486C3×C4—28no—
487C3×C4—28no—
488C3×C4—28no—
489C3×C4—216no—
490Dic3—68no—
491Dic3—616no—
492Dic3—616no—
493Dic3—616no—
494C32#349111yescharacteristic, complemented, Sylow
495C23—22no—
496C23—42no—
497C23—42no—
498C23—92no—
499C23—182no—
500C23—362no—
501C23#383014yes—
502C23C23×C3⋊D312yes—
503C23C23×C3⋊D311yescharacteristic
504C23C23×C3⋊D311yescharacteristic
505C23C23×C3⋊D311yescharacteristic
506Q8—364no—
507D4—24no—
508D4—24no—
509D4—184no—
510D4—184no—
511D4—364no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—42no—
518C2×C4—94no—
519C2×C4—94no—
520C2×C4—92no—
521C2×C4—94no—
522C2×C4—182no—
523C2×C4—364no—
524C2×C4—362no—
525C2×C4—364no—
526C2×C4—362no—
527C2×C4—362no—
528C2×C4C23×C3⋊D312yes—
529C2×C4C23×C3⋊D312yes—
530C2×C4C23×C3⋊D314yes—
531C2×C4C23×C3⋊D312yes—
532C2×C3—28no—
533C2×C3—28no—
534C2×C3—28no—
535C2×C3—48no—
536C2×C3C22×#23714yes—
537C2×C3#596418yes—
538D3—128no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22—22no—
543C22—24no—
544C22—44no—
545C22—82no—
546C22—182no—
547C22—184no—
548C22—722no—
549C22C2×#383012yes—
550C22C2×#383012yes—
551C22C2×#383012yes—
552C22C24×C3⋊D311yescharacteristic
553C4—22no—
554C4—22no—
555C4—22no—
556C4—24no—
557C4—182no—
558C4—184no—
559C4—184no—
560C4—184no—
561C3#8600114yescomplemented
562C2—22no—
563C2—22no—
564C2—22no—
565C2—42no—
566C2—362no—
567C2C22×#383011yescharacteristic
568C2#1059675612yes—
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#123C2
prime radical#10596275C2
hypercenterC2×#123C3⋊D3
hypocenterC32#3491
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×C32×#123C2semidirect
3. #10596269C2semidirect
4. C2×#64138C2semidirect
5. C2×#64135C2semidirect
6. #10596136C2semidirect
7. #10596129C2semidirect
8. #10596121C2semidirect
9. #10596120C2semidirect
10. #10595984C2semidirect
11. #10595966C2semidirect
12. #10595957C2semidirect
13. #10595954C2semidirect
19. C32×#123C22semidirect
20. C32×#123C22semidirect
21. C2×C32×C4⋊C4C22semidirect
23. C2×C32×C22⋊C4C22semidirect
28. C2×#3757C22semidirect
33. D4×C3⋊Dic3C22semidirect
36. #64138C22semidirect
37. #64138C22semidirect
39. C2×#3752C22semidirect
40. #64135C22semidirect
41. #64135C22semidirect
42. #64135C22semidirect
43. C2×C4⋊(C3⋊Dic3)C22semidirect
44. #64133C22semidirect
45. C2×#3750C22semidirect
46. C2×C4×C3⋊Dic3C22semidirect
47. #64107C22semidirect
48. #64107C22semidirect
49. #64106C22semidirect
50. #64101C22semidirect
51. #64099C22semidirect
52. #64098C22semidirect
53. #64098C22semidirect
54. #64096C22semidirect
55. #64095C22semidirect
56. #64094C22semidirect
57. #64092C22semidirect
58. #64090C22semidirect
59. #64090C22semidirect
60. C22⋊C4×C3⋊D3C22semidirect
61. #64088C22semidirect
62. #64088C22semidirect
63. #64087C22semidirect
64. #64087C22semidirect
65. #64087C22semidirect
66. #64086C22semidirect
67. #64086C22semidirect
68. C2×C3×#123D3semidirect
142. C3×#123C2×D3semidirect
143. C3×#123C2×D3semidirect
144. C2×C3×C4⋊C4C2×D3semidirect
146. C2×C3×C22⋊C4C2×D3semidirect
237. C2×#123C3⋊D3semidirect
338. #123C2×C3⋊D3semidirect
339. #123C2×C3⋊D3semidirect
362. C2×C4⋊C4C2×C3⋊D3semidirect
370. C2×C22⋊C4C2×C3⋊D3semidirect
494. C32#3491semidirect
561. C3#86001semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1232
#105962752
#105962692
C2×#641382
C2×#641352
#105961362
#105961292
#105961212
#105961202
#105959842
#105959662
#105959572
#105959542
#860013