Finite Group Databasebeta

← #11904943

Subgroups — #11904943

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
1C32×#518C211yesmaximal, characteristic, complemented
2#10596275C211yesmaximal, characteristic
3C2×#64144C211yesmaximal, characteristic, complemented
4#10596035C214yesmaximal, complemented
5#10596027C214yesmaximal, complemented
6#10596012C214yesmaximal, complemented
7#10596009C214yesmaximal, complemented
8#10596002C214yesmaximal, complemented
9#10595966C214yesmaximal, complemented
10C2×#64095C211yesmaximal, characteristic, complemented
11#10595957C211yesmaximal, characteristic, complemented
12#10595954C211yesmaximal, characteristic, complemented
13C2×#64086C211yesmaximal, characteristic, complemented
14#85859—34nomaximal
15C22×C32×D4C2211yescharacteristic
16C22×#638C2211yescharacteristic
17C23×C3⋊Dic3C2211yescharacteristic
18C32×C4×D4C2214yes—
19C32×C4×D4C2214yescomplemented
20C32×#117C2212yescomplemented
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×C32×C22⋊C4C2212yescomplemented
24#64162C2212yes—
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2212yescomplemented
28#64148C2214yes—
29#64146C2212yes—
30#64144C2214yes—
31#64144C2212yes—
32#64144C2212yescomplemented
33#64144C2212yescomplemented
34#64138C2212yes—
35#64138C2214yescomplemented
36C4×#638C2214yescomplemented
37C4×#638C2214yescomplemented
38C2×#3752C2212yescomplemented
39#64135C2214yescomplemented
40C2×C4⋊(C3⋊Dic3)C2212yescomplemented
41#64133C2214yescomplemented
42#64133C2214yescomplemented
43C2×#3750C2212yescomplemented
44C2×#3750C2212yescomplemented
45C2×C4×C3⋊Dic3C2212yescomplemented
46#64107C2214yescomplemented
47#64105C2214yescomplemented
48#64098C2214yescomplemented
49#64098C2214yescomplemented
50#64095C2214yes—
51#64095C2212yescomplemented
52#64095C2212yescomplemented
53#64094C2214yescomplemented
54#64092C2214yescomplemented
55#64090C2214yes—
56C22⋊C4×C3⋊D3C2212yescomplemented
57#64088C2214yescomplemented
58#64088C2214yescomplemented
59#64087C2214yescomplemented
60#64087C2214yescomplemented
61#64086C2214yescomplemented
62#64086C2214yescomplemented
63#64086C2212yescomplemented
64#64085C2214yescomplemented
65#64081C2214yescomplemented
66#64079C2214yescomplemented
67C4×#634C2214yescomplemented
68C3×#518D314yescomplemented
69#5804—34no—
70C2×#935—34no—
71#5564—316no—
72#5556—316no—
73#5541—316no—
74#5538—316no—
75#5531—316no—
76#5495—316no—
77C2×#886—34no—
78#5486—34no—
79#5483—34no—
80C2×#877—34no—
81C24×C32C2311yescharacteristic
82C24×C32C2311yescharacteristic
83C23×C3⋊D3C2311yescharacteristic
84C2×C32×D4—24no—
85C2×C32×D4C2312yes—
86C2×C32×D4C2312yes—
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2312yes—
89C22×C32×C4C2312yes—
90C22×C32×C4C2314yes—
91C2×#638—24no—
92C2×#638C2312yes—
93C2×#638C2312yes—
94C2×#638C2314yes—
95C22×C3⋊Dic3—24no—
96C22×C3⋊Dic3C2312yes—
97C22×C3⋊Dic3C2312yes—
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2312yes—
102C22×C3⋊Dic3C2312yes—
103C2×C4×C3⋊D3C2314yes—
104C2×#634C2314yes—
105C32×C4⋊C4C2314yes—
106C32×C22⋊C4C2312yes—
107C32×C22⋊C4C2312yes—
108C32×C22⋊C4C2312yes—
109C32×C22⋊C4C2312yes—
110C32×C22⋊C4C2314yes—
111C32×C42C2314yes—
112#3757C2312yes—
113#3757C2312yes—
114#3757C2312yes—
115#3757C2312yes—
116#3757C2314yes—
117#3757C2314yes—
118#3757C2314yes—
119#3752C2314yes—
120#3752C2314yes—
121#3752C2314yes—
122#3752C2314yes—
123C4⋊(C3⋊Dic3)C2314yes—
124C4⋊(C3⋊Dic3)C2314yes—
125C4⋊(C3⋊Dic3)C2314yes—
126#3750C2314yes—
127#3750C2314yes—
128#3750C2314yes—
129#3750C2314yes—
130#3750C2314yes—
131#3750C2314yes—
132#3750C2314yes—
133#3750C2314yes—
134C4×C3⋊Dic3C2314yes—
135C4×C3⋊Dic3C2314yes—
136C4×C3⋊Dic3C2314yes—
137#3491—91noSylow
138C22×C3×D4C2×D314yes—
139C22×#67—34no—
140C23×Dic3—34no—
141C3×C4×D4C2×D3116yes—
142C3×C4×D4C2×D3116yescomplemented
143C3×#117C2×D318yescomplemented
144C2×C3×C22⋊C4C2×D314yes—
145C2×C3×C22⋊C4C2×D314yes—
146C2×C3×C22⋊C4C2×D318yescomplemented
147#953—38no—
148C2×#217—34no—
149C2×#217—34no—
150C2×#217—38no—
151#939—316no—
152#937—38no—
153#935—316no—
154#935—38no—
155#935—38no—
156#935—38no—
157#929—316no—
158#929—38no—
159C4×#67—316no—
160C4×#67—316no—
161C2×(C2×D3)⋊C4—38no—
162#926—316no—
163C2×C4⋊Dic3—38no—
164#924—316no—
165#924—316no—
166C2×Dic3⋊C4—38no—
167C2×Dic3⋊C4—38no—
168C2×C4×Dic3—38no—
169#898—316no—
170#896—316no—
171#889—316no—
172#889—316no—
173#886—316no—
174#886—38no—
175#886—38no—
176#885—316no—
177#883—316no—
178#67⋊C4—316no—
179D3×C22⋊C4—38no—
180#879—316no—
181#879—316no—
182#878—316no—
183#878—316no—
184#877—316no—
185#877—316no—
186#877—38no—
187#876—316no—
188#872—316no—
189#870—316no—
190C4×Dic6—316no—
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—22no—
205C2×C32×C4—42no—
206C2×C32×C4—44no—
207C2×C32×C4—42no—
208C2×C32×C4C2414yes—
209C2×C32×C4C2412yes—
210C2×C32×C4C2414yes—
211#638—24no—
212#638—24no—
213#638—44no—
214C2×C3⋊Dic3—24no—
215C2×C3⋊Dic3—24no—
216C2×C3⋊Dic3—22no—
217C2×C3⋊Dic3—22no—
218C2×C3⋊Dic3—22no—
219C2×C3⋊Dic3—42no—
220C2×C3⋊Dic3—42no—
221C2×C3⋊Dic3C2412yes—
222C2×C3⋊Dic3C2414yes—
223C2×C3⋊Dic3C2412yes—
224C2×C3⋊Dic3C2414yes—
225C2×C3⋊Dic3C2412yes—
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×#123—91no—
238#518—91no—
239#518C3⋊D311yescharacteristic, complemented
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×C4C22×D314yes—
248C22×C3×C4C22×D318yes—
249C22×C3×C4C22×D318yes—
250C22×C3×C4C22×D3116yes—
251C2×#67—38no—
252C2×#67—38no—
253C2×#67—316no—
254C2×#67—616no—
255C22×Dic3—38no—
256C22×Dic3—34no—
257C22×Dic3—38no—
258C22×Dic3—34no—
259C22×Dic3—34no—
260C22×Dic3—38no—
261C22×Dic3—38no—
262C22×Dic3—616no—
263C2×C4×D3—316no—
264C2×Dic6—316no—
265C3×C4⋊C4C22×D3116yes—
266C3×C22⋊C4C22×D318yes—
267C3×C22⋊C4C22×D318yes—
268C3×C22⋊C4C22×D318yes—
269C3×C22⋊C4C22×D318yes—
270C3×C22⋊C4C22×D3116yes—
271C3×C42C22×D3116yes—
272#217—38no—
273#217—38no—
274#217—38no—
275#217—38no—
276#217—316no—
277#217—316no—
278#217—316no—
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—
286Dic3⋊C4—316no—
287Dic3⋊C4—316no—
288Dic3⋊C4—316no—
289Dic3⋊C4—316no—
290Dic3⋊C4—316no—
291Dic3⋊C4—316no—
292Dic3⋊C4—316no—
293Dic3⋊C4—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—24no—
313C32×C4—24no—
314C3⋊Dic3—22no—
315C3⋊Dic3—22no—
316C3⋊Dic3—22no—
317C3⋊Dic3—24no—
318C3⋊Dic3—24no—
319C22×D4—91no—
320C22×D4C2×C3⋊D311yescharacteristic
321C23×C4—91no—
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—94no—
333#123—92no—
334#123—92no—
335#123—94no—
336#123—92no—
337#123—92no—
338#123—94no—
339#123—94no—
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×D4C2×C3⋊D314yes—
353C4×D4C2×C3⋊D314yescomplemented
354#117—94no—
355#117—94no—
356#117—94no—
357#117—92no—
358#117—94no—
359#117C2×C3⋊D312yescomplemented
360C2×C4⋊C4—92no—
361C2×C4⋊C4—92no—
362C2×C4⋊C4—92no—
363C2×C22⋊C4—91no—
364C2×C22⋊C4—91no—
365C2×C22⋊C4—92no—
366C2×C22⋊C4—92no—
367C2×C22⋊C4—92no—
368C2×C22⋊C4C2×C3⋊D311yescharacteristic
369C2×C22⋊C4C2×C3⋊D311yescharacteristic
370C2×C22⋊C4C2×C3⋊D312yescomplemented
371C2×C42—92no—
372C23×C3—28no—
373C23×C3—48no—
374C23×C3—48no—
375C23×C3#235116yes—
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—28no—
386C2×C3×C4—48no—
387C2×C3×C4—416no—
388C2×C3×C4—48no—
389C2×C3×C4C23×D3116yes—
390C2×C3×C4C23×D318yes—
391C2×C3×C4C23×D3116yes—
392#67—616no—
393#67—616no—
394#67—1216no—
395C2×Dic3—38no—
396C2×Dic3—316no—
397C2×Dic3—38no—
398C2×Dic3—316no—
399C2×Dic3—38no—
400C2×Dic3—616no—
401C2×Dic3—616no—
402C2×Dic3—68no—
403C2×Dic3—68no—
404C2×Dic3—68no—
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—91no—
428C22×C4—92no—
429C22×C4—92no—
430C22×C4—91no—
431C22×C4—91no—
432C22×C4—92no—
433C22×C4—92no—
434C22×C4—94no—
435C22×C4—184no—
436C22×C4C22×C3⋊D311yescharacteristic
437C22×C4C22×C3⋊D312yes—
438C22×C4C22×C3⋊D312yes—
439C22×C4C22×C3⋊D314yes—
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⋊C4—94no—
451C4⋊C4C22×C3⋊D314yes—
452C22⋊C4—92no—
453C22⋊C4—92no—
454C22⋊C4—92no—
455C22⋊C4—94no—
456C22⋊C4—92no—
457C22⋊C4—94no—
458C22⋊C4—94no—
459C22⋊C4—94no—
460C22⋊C4—94no—
461C22⋊C4—94no—
462C22⋊C4—94no—
463C22⋊C4C22×C3⋊D312yes—
464C22⋊C4C22×C3⋊D312yes—
465C22⋊C4C22×C3⋊D312yes—
466C22⋊C4C22×C3⋊D312yes—
467C22⋊C4C22×C3⋊D314yes—
468C42—94no—
469C42—94no—
470C42—94no—
471C42C22×C3⋊D314yes—
472C22×C3—28no—
473C22×C3—28no—
474C22×C3—28no—
475C22×C3—28no—
476C22×C3—216no—
477C22×C3—416no—
478C22×C3—88no—
479C22×C3C2×#23518yes—
480C22×C3C2×#23518yes—
481C22×C3C2×#23518yes—
482C22×C3C24×D314yes—
483C2×D3—68no—
484C2×D3—616no—
485C2×D3—248no—
486C3×C4—28no—
487C3×C4—216no—
488C3×C4—216no—
489Dic3—68no—
490Dic3—68no—
491Dic3—68no—
492Dic3—616no—
493Dic3—616no—
494C32#349111yescharacteristic, complemented, Sylow
495C23—22no—
496C23—42no—
497C23—42no—
498C23—92no—
499C23—182no—
500C23—362no—
501C23#382814yes—
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—22no—
513C2×C4—42no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—92no—
517C2×C4—94no—
518C2×C4—92no—
519C2×C4—94no—
520C2×C4—92no—
521C2×C4—184no—
522C2×C4—184no—
523C2×C4—182no—
524C2×C4—182no—
525C2×C4—182no—
526C2×C4—364no—
527C2×C4—362no—
528C2×C4—362no—
529C2×C4C23×C3⋊D314yes—
530C2×C4C23×C3⋊D312yes—
531C2×C4C23×C3⋊D314yes—
532C2×C3—28no—
533C2×C3—28no—
534C2×C3—28no—
535C2×C3—48no—
536C2×C3C22×#23514yes—
537C2×C3#596618yes—
538D3—128no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22—22no—
543C22—24no—
544C22—44no—
545C22—82no—
546C22—182no—
547C22—184no—
548C22—722no—
549C22C2×#382812yes—
550C22C2×#382812yes—
551C22C2×#382812yes—
552C22C24×C3⋊D311yescharacteristic
553C4—22no—
554C4—24no—
555C4—24no—
556C4—182no—
557C4—182no—
558C4—182no—
559C4—184no—
560C4—184no—
561C3#8585914yescomplemented
562C2—22no—
563C2—22no—
564C2—22no—
565C2—42no—
566C2—362no—
567C2C22×#382811yescharacteristic
568C2#1059675812yes—
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#518C2
prime radical#10596275C2
hypercenter#518C3⋊D3
hypocenterC32#3491
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #518

Complements

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

NH ≅ G/Ntype
1. C32×#518C2semidirect
3. C2×#64144C2semidirect
4. #10596035C2semidirect
5. #10596027C2semidirect
6. #10596012C2semidirect
7. #10596009C2semidirect
8. #10596002C2semidirect
9. #10595966C2semidirect
10. C2×#64095C2semidirect
11. #10595957C2semidirect
12. #10595954C2semidirect
13. C2×#64086C2semidirect
19. C32×C4×D4C22semidirect
20. C32×#117C22semidirect
23. C2×C32×C22⋊C4C22semidirect
27. C2×#3757C22semidirect
32. #64144C22semidirect
33. #64144C22semidirect
35. #64138C22semidirect
36. C4×#638C22semidirect
37. C4×#638C22semidirect
38. C2×#3752C22semidirect
39. #64135C22semidirect
40. C2×C4⋊(C3⋊Dic3)C22semidirect
41. #64133C22semidirect
42. #64133C22semidirect
43. C2×#3750C22semidirect
44. C2×#3750C22semidirect
45. C2×C4×C3⋊Dic3C22semidirect
46. #64107C22semidirect
47. #64105C22semidirect
48. #64098C22semidirect
49. #64098C22semidirect
51. #64095C22semidirect
52. #64095C22semidirect
53. #64094C22semidirect
54. #64092C22semidirect
56. C22⋊C4×C3⋊D3C22semidirect
57. #64088C22semidirect
58. #64088C22semidirect
59. #64087C22semidirect
60. #64087C22semidirect
61. #64086C22semidirect
62. #64086C22semidirect
63. #64086C22semidirect
64. #64085C22semidirect
65. #64081C22semidirect
66. #64079C22semidirect
67. C4×#634C22semidirect
68. C3×#518D3semidirect
142. C3×C4×D4C2×D3semidirect
143. C3×#117C2×D3semidirect
146. C2×C3×C22⋊C4C2×D3semidirect
239. #518C3⋊D3semidirect
353. C4×D4C2×C3⋊D3semidirect
359. #117C2×C3⋊D3semidirect
370. C2×C22⋊C4C2×C3⋊D3semidirect
494. C32#3491semidirect
561. C3#85859semidirect

Maximal subgroups

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

subgroupindex
C32×#5182
#105962752
C2×#641442
#105960352
#105960272
#105960122
#105960092
#105960022
#105959662
C2×#640952
#105959572
#105959542
C2×#640862
#858593