Finite Group Databasebeta

← #11872086

Subgroups — #11872086

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
1#10596074C211yesmaximal, characteristic, complemented
2#10595992C211yesmaximal, characteristic, complemented
3C32×#482C211yesmaximal, characteristic, complemented
4#10592735C211yesmaximal, characteristic
5#10592695C211yesmaximal, characteristic, complemented
6#10592589C211yesmaximal, characteristic, complemented
7#10592588C211yesmaximal, characteristic, complemented
8#10592569C211yesmaximal, characteristic, complemented
9#10592551C211yesmaximal, characteristic, complemented
10#10592486C211yesmaximal, characteristic, complemented
11#10592486C211yesmaximal, characteristic, complemented
12#10592484C211yesmaximal, characteristic, complemented
13#10592455C211yesmaximal, characteristic, complemented
14#10592430C211yesmaximal, characteristic, complemented
15#10592419C211yesmaximal, characteristic, complemented
16#81352—34nomaximal
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C32×#121C2211yescharacteristic
19C32×#117C2211yescharacteristic
20#64145—21no—
21#64145C2211yescharacteristic, complemented
22#64144—21no—
23D4×C3⋊Dic3C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic
25C2×#3753C2211yescharacteristic
26#64135C2211yescharacteristic
27#64133C2211yescharacteristic
28C2×#3744C2211yescharacteristic
29C2×#3744C2211yescharacteristic
30#64102C2211yescharacteristic
31#64102C2211yescharacteristic
32#64102C2211yescharacteristic
33#64102C2211yescharacteristic
34#64097C2211yescharacteristic, complemented
35#64096C2211yescharacteristic, complemented
36C22⋊C4×C3⋊D3—21no—
37C22⋊C4×C3⋊D3—21no—
38#64088—21no—
39#64087—21no—
40C4×C4⋊(C3⋊D3)—21no—
41C4×C4⋊(C3⋊D3)—21no—
42C32×#107C2211yescharacteristic, complemented
43C32×#106C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45C32×#102C2211yescharacteristic, complemented
46C32×C22⋊C8C2211yescharacteristic
47#63657C2211yescharacteristic
48#63648C2211yescharacteristic
49#63648C2211yescharacteristic
50#63642C2211yescharacteristic, complemented
51#63641C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53C8×C3⋊Dic3C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55#63637C2211yescharacteristic, complemented
56#63636C2211yescharacteristic
57#63636C2211yescharacteristic
58#63635C2211yescharacteristic, complemented
59#63634C2211yescharacteristic, complemented
60#5603—34no—
61#5521—34no—
62C3×#482D314yescomplemented
63#5036—34no—
64#4996—34no—
65#4890—34no—
66#4889—34no—
67#4870—34no—
68#4852—34no—
69#4787—34no—
70#4787—34no—
71#4785—34no—
72#4756—34no—
73#4731—34no—
74#4720—34no—
75C23×C3⋊D3—21no—
76C2×C32×D4—21no—
77C2×C32×D4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C22×C3⋊Dic3—21no—
80C2×C4⋊(C3⋊D3)—21no—
81C2×C4⋊(C3⋊D3)—22no—
82C2×C4⋊(C3⋊D3)—22no—
83C2×C4⋊(C3⋊D3)C2311yescharacteristic
84C2×C4⋊(C3⋊D3)C2311yescharacteristic
85C2×C4×C3⋊D3—21no—
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×#634—21no—
90C2×#634C2311yescharacteristic
91C2×C32×C8C2311yescharacteristic
92C2×C32×C8C2311yescharacteristic
93C32×C4⋊C4C2311yescharacteristic
94C32×C4⋊C4C2311yescharacteristic
95C32×C4⋊C4C2311yescharacteristic
96C32×C22⋊C4—21no—
97C32×C22⋊C4—21no—
98C32×C42—21no—
99#3757—21no—
100#3757—21no—
101#3757—21no—
102#3757—21no—
103#3757D411yescharacteristic
104#3757D411yescharacteristic
105#3753—22no—
106#3753—22no—
107#3752—21no—
108#3752—21no—
109#3752—21no—
110#3752—21no—
111C4⋊(C3⋊Dic3)D411yescharacteristic
112C4⋊(C3⋊Dic3)D411yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750—21no—
116#3750—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3C2311yescharacteristic
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122#3744—22no—
123#3744—22no—
124#3118—91noSylow
125C22×D12—34no—
126C3×#121C2×D314yes—
127C3×#117C2×D314yes—
128#936—34no—
129#936—64no—
130#935—64no—
131D4×Dic3—34no—
132C2×#213—34no—
133C2×#213—34no—
134#926—34no—
135#924—34no—
136C2×#204—34no—
137C2×#204—34no—
138#893—34no—
139#893—34no—
140#893—34no—
141#893—34no—
142#888—34no—
143#887—34no—
144D3×C22⋊C4—64no—
145D3×C22⋊C4—64no—
146#879—64no—
147#878—64no—
148C4×D12—64no—
149C4×D12—64no—
150C3×#107C2×D314yescomplemented
151C3×#106C2×D314yescomplemented
152C3×#102C2×D314yescomplemented
153C3×#102C2×D314yescomplemented
154C3×C22⋊C8C2×D314yes—
155#830—34no—
156#821—34no—
157#821—34no—
158#815—34no—
159Dic3⋊C8—34no—
160Dic3⋊C8—34no—
161C8×Dic3—34no—
162#810—34no—
163#810—34no—
164#809—34no—
165#809—34no—
166#808—34no—
167#807—34no—
168C23×C32—21no—
169C23×C32C2×D411yescharacteristic
170C22×C3⋊D3—21no—
171C22×C3⋊D3—21no—
172C22×C3⋊D3—24no—
173C22×C3⋊D3—81no—
174C22×C3⋊D3—81no—
175C32×D4—21no—
176C32×D4—21no—
177C32×D4—81no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—81no—
188C2×C3⋊Dic3C2×D411yescharacteristic
189C2×C3⋊Dic3C2×D411yescharacteristic
190C2×C3⋊Dic3C2×D411yescharacteristic
191C2×C3⋊Dic3C2×D411yescharacteristic
192C4⋊(C3⋊D3)—24no—
193C4⋊(C3⋊D3)—21no—
194C4⋊(C3⋊D3)—21no—
195C4⋊(C3⋊D3)#4112yes—
196C4⋊(C3⋊D3)#4112yes—
197C4×C3⋊D3—81no—
198C4×C3⋊D3—81no—
199C4×C3⋊D3—81no—
200C4×C3⋊D3—81no—
201#634—21no—
202#634—21no—
203#634—81no—
204C32×C8—21no—
205C32×C8—21no—
206C3⋊(C3⋊C8)—21no—
207C3⋊(C3⋊C8)—21no—
208#542—91no—
209#518—91no—
210#485—91no—
211#482C3⋊D311yescharacteristic, complemented
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—
223C23×D3—64no—
224C2×C3×D4—24no—
225C2×C3×D4C22×D314yes—
226C22×C3×C4C22×D314yes—
227C22×Dic3—64no—
228C2×D12—34no—
229C2×D12—34no—
230C2×D12—68no—
231C2×D12—68no—
232C2×D12—64no—
233C2×C4×D3—64no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×Dic6—34no—
238C2×Dic6—64no—
239C2×C3×C8C22×D314yes—
240C2×C3×C8C22×D314yes—
241C3×C4⋊C4C22×D314yes—
242C3×C4⋊C4C22×D314yes—
243C3×C4⋊C4C22×D314yes—
244C3×C22⋊C4—24no—
245C3×C22⋊C4—24no—
246C3×C42—24no—
247#217—34no—
248#217—34no—
249#217—64no—
250#217—64no—
251#217—64no—
252#217—64no—
253#213—68no—
254#213—68no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259C4⋊Dic3—34no—
260C4⋊Dic3—34no—
261C4⋊Dic3—34no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265C4×Dic3—34no—
266C4×Dic3—34no—
267C4×Dic3—64no—
268C2×C3⋊C8—34no—
269C2×C3⋊C8—34no—
270#204—68no—
271#204—68no—
272C22×C32—21no—
273C22×C32—21no—
274C22×C32—21no—
275C22×C32—41no—
276C22×C32—41no—
277C22×C32—41no—
278C22×C32C22×D411yescharacteristic
279C2×C3⋊D3—22no—
280C2×C3⋊D3—22no—
281C2×C3⋊D3—41no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3—84no—
286C32×C4—21no—
287C32×C4—41no—
288C32×C4—41no—
289C32×C4—41no—
290C32×C4C2×#4111yescharacteristic
291C32×C4C2×#4111yescharacteristic
292C3⋊Dic3—21no—
293C3⋊Dic3—21no—
294C3⋊Dic3—21no—
295C3⋊Dic3—21no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C22×D4—91no—
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#121C2×C3⋊D311yescharacteristic
311C4×Q8—91no—
312C4×D4—91no—
313C4×D4—91no—
314C4×D4—91no—
315C4×D4—91no—
316C4×D4—91no—
317C4×D4—181no—
318C4×D4—181no—
319#117—91no—
320#117C2×C3⋊D311yescharacteristic
321C2×C22⋊C4—181no—
322C2×C22⋊C4—181no—
323#107—91no—
324#107C2×C3⋊D311yescharacteristic, complemented
325#106—91no—
326#106C2×C3⋊D311yescharacteristic, complemented
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#102C2×C3⋊D311yescharacteristic, complemented
336#102C2×C3⋊D311yescharacteristic, complemented
337C22⋊C8—91no—
338C22⋊C8C2×C3⋊D311yescharacteristic
339#97—91no—
340C4×C8—91no—
341C23×C3—24no—
342C23×C3D3×D414yes—
343C22×D3—64no—
344C22×D3—64no—
345C22×D3—616no—
346C22×D3—244no—
347C22×D3—244no—
348C3×D4—24no—
349C3×D4—24no—
350C3×D4—84no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4—24no—
356C2×C3×C4D3×D414yes—
357C2×C3×C4C23×D314yes—
358C2×Dic3—34no—
359C2×Dic3—34no—
360C2×Dic3—34no—
361C2×Dic3—34no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364C2×Dic3—244no—
365D12—38no—
366D12—38no—
367D12—616no—
368D12—64no—
369D12—64no—
370C4×D3—244no—
371C4×D3—244no—
372C4×D3—244no—
373C4×D3—244no—
374Dic6—64no—
375Dic6—64no—
376Dic6—244no—
377C3×C8—24no—
378C3×C8—24no—
379C3⋊C8—64no—
380C3⋊C8—64no—
381C2×C32—41no—
382C2×C32—81no—
383C2×C32#52511yescharacteristic
384C2×C32#57611yescharacteristic
385C2×C32#57711yescharacteristic
386C3⋊D3—42no—
387C3⋊D3—42no—
388C24—181no—
389C2×Q8—91no—
390C2×Q8—181no—
391C2×D4—21no—
392C2×D4—91no—
393C2×D4—91no—
394C2×D4—182no—
395C2×D4—182no—
396C2×D4—181no—
397C2×D4C22×C3⋊D311yescharacteristic
398C22×C4—181no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4—181no—
403C22×C4C22×C3⋊D311yescharacteristic
404SD16—182no—
405SD16—182no—
406D8—182no—
407D8—182no—
408C2×C8—91no—
409C2×C8—91no—
410C2×C8C22×C3⋊D311yescharacteristic
411C2×C8C22×C3⋊D311yescharacteristic
412C4⋊C4—91no—
413C4⋊C4—91no—
414C4⋊C4—91no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4C22×C3⋊D311yescharacteristic
419C4⋊C4C22×C3⋊D311yescharacteristic
420C4⋊C4C22×C3⋊D311yescharacteristic
421C22⋊C4—21no—
422C22⋊C4—21no—
423C22⋊C4—91no—
424C22⋊C4—91no—
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C42—21no—
434C42—91no—
435C42—91no—
436C42—181no—
437C22×C3—24no—
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—44no—
441C22×C3—44no—
442C22×C3—44no—
443C22×C3C2×D3×D414yes—
444C2×D3—68no—
445C2×D3—68no—
446C2×D3—124no—
447C2×D3—124no—
448C2×D3—124no—
449C2×D3—124no—
450C2×D3—2416no—
451C3×C4—24no—
452C3×C4—44no—
453C3×C4—44no—
454C3×C4—44no—
455C3×C4D3×#4114yes—
456C3×C4D3×#4114yes—
457Dic3—64no—
458Dic3—64no—
459Dic3—64no—
460Dic3—64no—
461Dic3—124no—
462Dic3—124no—
463C32#311811yescharacteristic, complemented, Sylow
464C23—21no—
465C23—184no—
466C23—181no—
467C23—181no—
468C23—721no—
469C23—721no—
470C23D4×C3⋊D311yescharacteristic
471Q8—181no—
472Q8—181no—
473Q8—721no—
474D4—21no—
475D4—21no—
476D4—81no—
477D4—92no—
478D4—92no—
479D4—184no—
480D4—181no—
481D4—181no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—91no—
488C2×C4—91no—
489C2×C4—91no—
490C2×C4—91no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—721no—
494C2×C4—721no—
495C2×C4—721no—
496C2×C4—721no—
497C2×C4—721no—
498C2×C4D4×C3⋊D311yescharacteristic
499C2×C4C23×C3⋊D311yescharacteristic
500C8—21no—
501C8—21no—
502C8—181no—
503C8—181no—
504C2×C3—44no—
505C2×C3—84no—
506C2×C3#565614yes—
507C2×C3#577014yes—
508C2×C3#577414yes—
509D3—128no—
510D3—128no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—182no—
518C22—182no—
519C22—361no—
520C22—361no—
521C22—361no—
522C22—361no—
523C22—724no—
524C22C2×D4×C3⋊D311yescharacteristic
525C4—21no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—181no—
530C4—181no—
531C4—181no—
532C4—181no—
533C4—361no—
534C4—361no—
535C4#41×C3⋊D311yescharacteristic
536C4#41×C3⋊D311yescharacteristic
537C3#8135214yescomplemented
538C2—41no—
539C2—81no—
540C2—362no—
541C2—362no—
542C2#1059612711yescharacteristic
543C2#1059624111yescharacteristic
544C2#1059624511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#482C2
socleC22×C32C22×D4
prime radical#10592735C2
hypercenter#482C3⋊D3
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #10596074C2semidirect
2. #10595992C2semidirect
3. C32×#482C2semidirect
5. #10592695C2semidirect
6. #10592589C2semidirect
7. #10592588C2semidirect
8. #10592569C2semidirect
9. #10592551C2semidirect
10. #10592486C2semidirect
11. #10592486C2semidirect
12. #10592484C2semidirect
13. #10592455C2semidirect
14. #10592430C2semidirect
15. #10592419C2semidirect
21. #64145C22semidirect
23. D4×C3⋊Dic3C22semidirect
34. #64097C22semidirect
35. #64096C22semidirect
42. C32×#107C22semidirect
43. C32×#106C22semidirect
44. C32×#102C22semidirect
45. C32×#102C22semidirect
50. #63642C22semidirect
51. #63641C22semidirect
52. #63641C22semidirect
53. C8×C3⋊Dic3C22semidirect
54. #63637C22semidirect
55. #63637C22semidirect
58. #63635C22semidirect
59. #63634C22semidirect
62. C3×#482D3semidirect
150. C3×#107C2×D3semidirect
151. C3×#106C2×D3semidirect
152. C3×#102C2×D3semidirect
153. C3×#102C2×D3semidirect
211. #482C3⋊D3semidirect
324. #107C2×C3⋊D3semidirect
326. #106C2×C3⋊D3semidirect
335. #102C2×C3⋊D3semidirect
336. #102C2×C3⋊D3semidirect
463. C32#3118semidirect
537. C3#81352semidirect

Maximal subgroups

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

subgroupindex
#105960742
#105959922
C32×#4822
#105927352
#105926952
#105925892
#105925882
#105925692
#105925512
#105924862
#105924842
#105924552
#105924302
#105924192
#813523