Finite Group Databasebeta

← #11872101

Subgroups — #11872101

Order 1152.

1218 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#518C211yesmaximal, characteristic, complemented
2#10596005C211yesmaximal, characteristic, complemented
3#10592917C211yesmaximal, characteristic, complemented
4#10592916C211yesmaximal, characteristic
5#10592717C211yesmaximal, characteristic, complemented
6C4×#3754C211yesmaximal, characteristic, complemented
7#10592715C211yesmaximal, characteristic, complemented
8#10592715C211yesmaximal, characteristic, complemented
9#10592713C211yesmaximal, characteristic, complemented
10C4×#3753C211yesmaximal, characteristic, complemented
11#10592707C211yesmaximal, characteristic, complemented
12#10592706C211yesmaximal, characteristic, complemented
13#10592702C211yesmaximal, characteristic, complemented
14#10592699C211yesmaximal, characteristic, complemented
15#10592695C211yesmaximal, characteristic, complemented
16#82541—34nomaximal
17C22×C32×D4C2211yescharacteristic
18C32×C4×D4—21no—
19C32×C4×D4—21no—
20C32×C4×D4C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23C32×C4×D4C2211yescharacteristic
24C32×#117C2211yescharacteristic
25C32×#117C2211yescharacteristic
26C2×C32×C22⋊C4—21no—
27C2×C32×C22⋊C4—21no—
28C2×#3754C2211yescharacteristic
29C2×#3754C2211yescharacteristic
30C2×#3753C2211yescharacteristic
31C2×#3753C2211yescharacteristic
32#64139C2211yescharacteristic
33#64133C2211yescharacteristic
34#64107—21no—
35#64105—21no—
36#64094—21no—
37#64092—21no—
38#64084C2211yescharacteristic, complemented
39C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
40#64078C2211yescharacteristic, complemented
41C4×#634C2211yescharacteristic, complemented
42#63659C2211yescharacteristic
43#63659C2211yescharacteristic
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63657C2211yescharacteristic
47#63657C2211yescharacteristic
48#63637C2211yescharacteristic, complemented
49#63637C2211yescharacteristic, complemented
50#63636C2211yescharacteristic, complemented
51#63636C2211yescharacteristic, complemented
52#63635C2211yescharacteristic, complemented
53#63635C2211yescharacteristic, complemented
54#63634C2211yescharacteristic, complemented
55#63634C2211yescharacteristic, complemented
56C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
57C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
58#63630C2211yescharacteristic, complemented
59C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
60C3×#518D314yescomplemented
61#5534—34no—
62#5218—34no—
63#5217—34no—
64#5018—34no—
65C4×#214—34no—
66#5016—34no—
67#5016—34no—
68#5014—34no—
69C4×#213—34no—
70#5008—34no—
71#5007—34no—
72#5003—34no—
73#5000—34no—
74#4996—34no—
75C24×C32—21no—
76C2×C32×D4—22no—
77C2×C32×D4—22no—
78C2×C32×D4—21no—
79C2×C32×D4C2311yescharacteristic
80C2×C32×D4C2311yescharacteristic
81C22×C32×C4—21no—
82C22×C32×C4—21no—
83C22×C32×C4—21no—
84C22×C32×C4—21no—
85C22×C32×C4C2311yescharacteristic
86C2×#638—21no—
87C2×C4⋊(C3⋊D3)C2311yescharacteristic
88C2×C4×C3⋊D3—21no—
89C2×#634—21no—
90C2×#634C2311yescharacteristic
91C32×C4⋊C4D411yescharacteristic
92C32×C4⋊C4D411yescharacteristic
93C32×C4⋊C4C2311yescharacteristic
94C32×C4⋊C4C2311yescharacteristic
95C32×C22⋊C4—21no—
96C32×C22⋊C4—21no—
97C32×C22⋊C4—21no—
98C32×C22⋊C4—21no—
99C32×C22⋊C4—21no—
100C32×C22⋊C4D411yescharacteristic
101C32×C22⋊C4D411yescharacteristic
102C32×C42—21no—
103C32×C42C2311yescharacteristic
104C32×C42C2311yescharacteristic
105#3757—21no—
106#3754—22no—
107#3754—22no—
108#3753—22no—
109#3753—22no—
110#3752—21no—
111#3752—21no—
112#3752—21no—
113#3752—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3750—21no—
119C4×C3⋊Dic3—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3118—91noSylow
125C22×C3×D4C2×D314yes—
126C3×C4×D4—24no—
127C3×C4×D4—24no—
128C3×C4×D4C2×D314yes—
129C3×C4×D4C2×D314yes—
130C3×C4×D4C2×D314yes—
131C3×C4×D4C2×D314yes—
132C3×#117C2×D314yes—
133C3×#117C2×D314yes—
134C2×C3×C22⋊C4—24no—
135C2×C3×C22⋊C4—24no—
136C2×#214—34no—
137C2×#214—34no—
138C2×#213—34no—
139C2×#213—34no—
140#930—34no—
141#924—34no—
142#898—64no—
143#896—64no—
144#885—64no—
145#883—64no—
146#875—34no—
147C4×D12—34no—
148#869—34no—
149C4×Dic6—34no—
150#832—34no—
151#832—34no—
152#832—34no—
153#832—34no—
154#830—34no—
155#830—34no—
156#810—34no—
157#810—34no—
158#809—34no—
159#809—34no—
160#808—34no—
161#808—34no—
162#807—34no—
163#807—34no—
164C4⋊(C3⋊C8)—34no—
165C4⋊(C3⋊C8)—34no—
166#803—34no—
167C4×C3⋊C8—34no—
168C23×C32—24no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—81no—
172C23×C32—81no—
173C23×C32C2×D411yescharacteristic
174C22×C3⋊D3—21no—
175C32×D4—24no—
176C32×D4—21no—
177C32×D4—21no—
178C32×D4#4112yes—
179C32×D4#4112yes—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—81no—
185C2×C32×C4—81no—
186C2×C32×C4—81no—
187C2×C32×C4—81no—
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2411yescharacteristic
194#638—81no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C4⋊(C3⋊D3)—21no—
199C4⋊(C3⋊D3)—21no—
200C4×C3⋊D3—81no—
201#634—21no—
202#634—21no—
203#634—81no—
204C3⋊(C3⋊C8)—21no—
205C3⋊(C3⋊C8)—21no—
206C3⋊(C3⋊C8)—21no—
207C3⋊(C3⋊C8)—21no—
208#542—91no—
209#518C3⋊D311yescharacteristic, complemented
210#485—91no—
211#482—91no—
212#476—91no—
213#474—91no—
214#463—91no—
215#463—91no—
216#450—91no—
217#447—91no—
218#442—91no—
219#440—91no—
220C4×SD16—91no—
221C4×D8—91no—
222#433—91no—
223C24×C3—24no—
224C2×C3×D4—28no—
225C2×C3×D4—28no—
226C2×C3×D4—24no—
227C2×C3×D4C22×D314yes—
228C2×C3×D4C22×D314yes—
229C22×C3×C4—24no—
230C22×C3×C4—24no—
231C22×C3×C4—24no—
232C22×C3×C4—24no—
233C22×C3×C4C22×D314yes—
234C2×#67—64no—
235C2×D12—34no—
236C2×C4×D3—64no—
237C2×Dic6—34no—
238C2×Dic6—64no—
239C3×C4⋊C4#6714yes—
240C3×C4⋊C4#6714yes—
241C3×C4⋊C4C22×D314yes—
242C3×C4⋊C4C22×D314yes—
243C3×C22⋊C4—24no—
244C3×C22⋊C4—24no—
245C3×C22⋊C4—24no—
246C3×C22⋊C4—24no—
247C3×C22⋊C4—24no—
248C3×C22⋊C4#6714yes—
249C3×C22⋊C4#6714yes—
250C3×C42—24no—
251C3×C42C22×D314yes—
252C3×C42C22×D314yes—
253#217—64no—
254#214—68no—
255#214—68no—
256#213—68no—
257#213—68no—
258(C2×D3)⋊C4—64no—
259(C2×D3)⋊C4—64no—
260(C2×D3)⋊C4—64no—
261(C2×D3)⋊C4—64no—
262C4⋊Dic3—34no—
263C4⋊Dic3—34no—
264C4⋊Dic3—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267C4×Dic3—64no—
268C2×C3⋊C8—34no—
269C2×C3⋊C8—34no—
270C2×C3⋊C8—34no—
271C2×C3⋊C8—34no—
272C22×C32—21no—
273C22×C32—22no—
274C22×C32—22no—
275C22×C32—21no—
276C22×C32—21no—
277C22×C32—41no—
278C22×C32—41no—
279C22×C32—41no—
280C22×C32—41no—
281C22×C32—84no—
282C22×C32C22×D411yescharacteristic
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C32×C4—21no—
287C32×C4—21no—
288C32×C4—21no—
289C32×C4—21no—
290C32×C4—21no—
291C32×C4—41no—
292C32×C4—41no—
293C32×C4C2×#4111yescharacteristic
294C32×C4C2×#4111yescharacteristic
295C3⋊Dic3—41no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C22×D4C2×C3⋊D311yescharacteristic
299C2×SD16—91no—
300C2×SD16—91no—
301C2×D8—91no—
302C2×D8—91no—
303C4⋊Q8—91no—
304#126—181no—
305#124—91no—
306#124—181no—
307#123—181no—
308C22⋊Q8—91no—
309C22⋊Q8—181no—
310#121—91no—
311C4×Q8—91no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—91no—
315C4×D4C2×C3⋊D311yescharacteristic
316C4×D4C2×C3⋊D311yescharacteristic
317C4×D4C2×C3⋊D311yescharacteristic
318C4×D4C2×C3⋊D311yescharacteristic
319#117C2×C3⋊D311yescharacteristic
320#117C2×C3⋊D311yescharacteristic
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323#107—91no—
324#107—91no—
325#106—91no—
326#106—91no—
327C4⋊C8—91no—
328C4⋊C8—91no—
329#103—91no—
330#103—91no—
331#102—91no—
332#102—91no—
333#102—91no—
334#102—91no—
335#102—91no—
336#102—91no—
337C22⋊C8—91no—
338C22⋊C8—91no—
339#97—91no—
340C4×C8—91no—
341C23×C3—216no—
342C23×C3—24no—
343C23×C3—24no—
344C23×C3—84no—
345C23×C3—84no—
346C23×C3C2×#6714yes—
347C22×D3—64no—
348C3×D4—216no—
349C3×D4—24no—
350C3×D4—24no—
351C3×D4#23518yes—
352C3×D4#23518yes—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4—24no—
356C2×C3×C4—24no—
357C2×C3×C4—84no—
358C2×C3×C4—84no—
359C2×C3×C4—84no—
360C2×C3×C4—84no—
361C2×C3×C4C2×#6714yes—
362C2×C3×C4C2×#6714yes—
363C2×C3×C4C2×#6714yes—
364C2×C3×C4C2×#6714yes—
365C2×C3×C4C2×#6714yes—
366C2×C3×C4C23×D314yes—
367#67—244no—
368C2×Dic3—64no—
369C2×Dic3—64no—
370C2×Dic3—64no—
371D12—64no—
372D12—64no—
373C4×D3—244no—
374Dic6—64no—
375Dic6—64no—
376Dic6—244no—
377C3⋊C8—64no—
378C3⋊C8—64no—
379C3⋊C8—64no—
380C3⋊C8—64no—
381C2×C32—41no—
382C2×C32—42no—
383C2×C32—42no—
384C2×C32#52511yescharacteristic
385C2×C32#57611yescharacteristic
386C2×C32#57711yescharacteristic
387C3⋊D3—81no—
388C24—21no—
389C2×Q8—91no—
390C2×Q8—181no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—21no—
394C2×D4—91no—
395C2×D4—181no—
396C2×D4C22×C3⋊D311yescharacteristic
397C2×D4C22×C3⋊D311yescharacteristic
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—181no—
403C22×C4C22×C3⋊D311yescharacteristic
404SD16—182no—
405SD16—182no—
406D8—182no—
407D8—182no—
408C2×C8—91no—
409C2×C8—91no—
410C2×C8—91no—
411C2×C8—91no—
412C4⋊C4—91no—
413C4⋊C4—91no—
414C4⋊C4—181no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C4⋊C4#63811yescharacteristic
418C4⋊C4#63811yescharacteristic
419C4⋊C4C22×C3⋊D311yescharacteristic
420C4⋊C4C22×C3⋊D311yescharacteristic
421C22⋊C4—21no—
422C22⋊C4—21no—
423C22⋊C4—21no—
424C22⋊C4—21no—
425C22⋊C4—21no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4#63811yescharacteristic
432C22⋊C4#63811yescharacteristic
433C42—21no—
434C42—181no—
435C42C22×C3⋊D311yescharacteristic
436C42C22×C3⋊D311yescharacteristic
437C22×C3—24no—
438C22×C3—28no—
439C22×C3—28no—
440C22×C3—24no—
441C22×C3—24no—
442C22×C3—44no—
443C22×C3—44no—
444C22×C3—44no—
445C22×C3—44no—
446C22×C3—816no—
447C22×C3C22×#6714yes—
448C2×D3—124no—
449C2×D3—124no—
450C2×D3—124no—
451C3×C4—24no—
452C3×C4—24no—
453C3×C4—24no—
454C3×C4—24no—
455C3×C4—24no—
456C3×C4—44no—
457C3×C4—44no—
458C3×C4C2×#23514yes—
459C3×C4C2×#23514yes—
460Dic3—124no—
461Dic3—124no—
462Dic3—124no—
463C32#311811yescharacteristic, complemented, Sylow
464C23—24no—
465C23—21no—
466C23—21no—
467C23—81no—
468C23—81no—
469C23—181no—
470C23C2×#63811yescharacteristic
471Q8—181no—
472Q8—181no—
473Q8—721no—
474D4—24no—
475D4—21no—
476D4—21no—
477D4—181no—
478D4—181no—
479D4—721no—
480D4#382812yes—
481D4#382812yes—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—81no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—721no—
494C2×C4C2×#63811yescharacteristic
495C2×C4C2×#63811yescharacteristic
496C2×C4C2×#63811yescharacteristic
497C2×C4C2×#63811yescharacteristic
498C2×C4C2×#63811yescharacteristic
499C2×C4C23×C3⋊D311yescharacteristic
500C8—181no—
501C8—181no—
502C8—181no—
503C8—181no—
504C2×C3—44no—
505C2×C3—48no—
506C2×C3—48no—
507C2×C3#579114yes—
508C2×C3#583514yes—
509C2×C3#583614yes—
510D3—244no—
511C22—21no—
512C22—22no—
513C22—22no—
514C22—21no—
515C22—21no—
516C22—41no—
517C22—41no—
518C22—41no—
519C22—41no—
520C22—84no—
521C22—361no—
522C22—361no—
523C22—361no—
524C22C22×#63811yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—41no—
531C4—41no—
532C4—361no—
533C4—361no—
534C4—361no—
535C4C2×#382811yescharacteristic
536C4C2×#382811yescharacteristic
537C3#8254114yescomplemented
538C2—41no—
539C2—42no—
540C2—42no—
541C2—721no—
542C2#1059626211yescharacteristic
543C2#1059630611yescharacteristic
544C2#1059630711yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#518C2
socleC22×C32C22×D4
prime radical#10592916C2
hypercenter#518C3⋊D3
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. C32×#518C2semidirect
2. #10596005C2semidirect
3. #10592917C2semidirect
5. #10592717C2semidirect
6. C4×#3754C2semidirect
7. #10592715C2semidirect
8. #10592715C2semidirect
9. #10592713C2semidirect
10. C4×#3753C2semidirect
11. #10592707C2semidirect
12. #10592706C2semidirect
13. #10592702C2semidirect
14. #10592699C2semidirect
15. #10592695C2semidirect
38. #64084C22semidirect
39. C4×C4⋊(C3⋊D3)C22semidirect
40. #64078C22semidirect
41. C4×#634C22semidirect
48. #63637C22semidirect
49. #63637C22semidirect
50. #63636C22semidirect
51. #63636C22semidirect
52. #63635C22semidirect
53. #63635C22semidirect
54. #63634C22semidirect
55. #63634C22semidirect
56. C4⋊(C3⋊(C3⋊C8))C22semidirect
57. C4⋊(C3⋊(C3⋊C8))C22semidirect
58. #63630C22semidirect
59. C4×C3⋊(C3⋊C8)C22semidirect
60. C3×#518D3semidirect
209. #518C3⋊D3semidirect
463. C32#3118semidirect
537. C3#82541semidirect

Maximal subgroups

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

subgroupindex
C32×#5182
#105960052
#105929172
#105929162
#105927172
C4×#37542
#105927152
#105927132
C4×#37532
#105927072
#105927062
#105927022
#105926992
#105926952
#825413