Finite Group Databasebeta

← #11887361

Subgroups — #11887361

Order 1152.

1260 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596083C211yesmaximal, characteristic, complemented
2#10596001C211yesmaximal, characteristic, complemented
3C32×#482C211yesmaximal, characteristic, complemented
4#10592737C211yesmaximal, characteristic, complemented
5#10592701C211yesmaximal, characteristic, complemented
6#10592583C211yesmaximal, characteristic, complemented
7#10592571C211yesmaximal, characteristic, complemented
8#10592570C211yesmaximal, characteristic, complemented
9#10592563C211yesmaximal, characteristic, complemented
10#10592486C211yesmaximal, characteristic, complemented
11#10592472C211yesmaximal, characteristic, complemented
12C3⋊D3×#102C211yesmaximal, characteristic, complemented
13#10592467C211yesmaximal, characteristic, complemented
14#10592433C211yesmaximal, characteristic, complemented
15#10592424C211yesmaximal, characteristic, complemented
16#81382—34nomaximal
17C2×D4×C3⋊D3C2211yescharacteristic
18C2×#3828C2211yescharacteristic
19C32×#121C2211yescharacteristic
20C32×#117C2211yescharacteristic, complemented
21#64147—21no—
22#64146—21no—
23#64145C2211yescharacteristic
24C2×#3753C2211yescharacteristic
25#64139C2211yescharacteristic, complemented
26C4×#638C2211yescharacteristic
27C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
28C2×#3745C2211yescharacteristic
29C2×#3744C2211yescharacteristic, complemented
30C2×C8×C3⋊D3C2211yescharacteristic
31#64106C2211yescharacteristic
32#64104C2211yescharacteristic
33#64102C2211yescharacteristic
34#64102C2211yescharacteristic, complemented
35C4⋊C4×C3⋊D3C2211yescharacteristic
36#64099C2211yescharacteristic, complemented
37#64093—21no—
38#64092—21no—
39#64092—21no—
40C22⋊C4×C3⋊D3—21no—
41#64085—21no—
42C4×C4⋊(C3⋊D3)—21no—
43C32×#107C2211yescharacteristic, complemented
44C32×#106C2211yescharacteristic, complemented
45C32×#102C2211yescharacteristic
46C32×#102C2211yescharacteristic
47C32×C22⋊C8C2211yescharacteristic, complemented
48#63659C2211yescharacteristic
49#63648C2211yescharacteristic
50#63647C2211yescharacteristic
51#63643C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53C8×C3⋊Dic3C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55#63637C2211yescharacteristic, complemented
56#63636C2211yescharacteristic
57#63636C2211yescharacteristic
58#63636C2211yescharacteristic, complemented
59#63634C2211yescharacteristic, complemented
60#5612—34no—
61#5530—34no—
62C3×#482D314yescomplemented
63#5038—34no—
64#5002—34no—
65#4884—34no—
66#4872—34no—
67#4871—34no—
68#4864—34no—
69#4787—34no—
70#4773—34no—
71D3×#102—34no—
72#4768—34no—
73#4734—34no—
74#67⋊C8—34no—
75C23×C3⋊D3—21no—
76C2×C32×D4—21no—
77C2×C32×D4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C2×#638—21no—
80C2×#638—21no—
81C2×#638—21no—
82C2×#638D411yescharacteristic
83D4×C3⋊D3—22no—
84D4×C3⋊D3—41no—
85#3828—22no—
86#3828—41no—
87C2×C4⋊(C3⋊D3)—21no—
88C2×C4⋊(C3⋊D3)C2311yescharacteristic
89C2×C4⋊(C3⋊D3)C2311yescharacteristic
90C2×C4×C3⋊D3—21no—
91C2×C4×C3⋊D3—21no—
92C2×C4×C3⋊D3—21no—
93C2×C4×C3⋊D3—21no—
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C32×C8C2311yescharacteristic
97C2×C32×C8C2311yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C4⋊C4C2311yescharacteristic
100C32×C4⋊C4C2311yescharacteristic
101C32×C22⋊C4—21no—
102C32×C22⋊C4—21no—
103C32×C42—21no—
104#3757—21no—
105#3757—21no—
106#3757D411yescharacteristic
107#3753—41no—
108#3752—21no—
109#3752—21no—
110#3752—21no—
111#3752—21no—
112#3752—21no—
113#3752D411yescharacteristic
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3750—21no—
119#3750D411yescharacteristic
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)—41no—
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3745—22no—
125#3744—41no—
126C8×C3⋊D3—41no—
127#3297—91noSylow
128C2×D3×D4—34no—
129C2×#235—34no—
130C3×#121C2×D314yes—
131C3×#117C2×D314yescomplemented
132#938—64no—
133#937—64no—
134#936—34no—
135C2×#213—34no—
136#930—34no—
137C4×#67—34no—
138C22×C3⋊C8—34no—
139C2×D24—34no—
140C2×#204—34no—
141C2×D3×C8—34no—
142#897—34no—
143#895—34no—
144#893—34no—
145#893—34no—
146D3×C4⋊C4—34no—
147#890—34no—
148#884—64no—
149#883—64no—
150#883—64no—
151D3×C22⋊C4—64no—
152#876—64no—
153C4×D12—64no—
154C3×#107C2×D314yescomplemented
155C3×#106C2×D314yescomplemented
156C3×#102C2×D314yes—
157C3×#102C2×D314yes—
158C3×C22⋊C8C2×D314yescomplemented
159#832—34no—
160#821—34no—
161(C2×D3)⋊C8—34no—
162#816—34no—
163Dic3⋊C8—34no—
164C8×Dic3—34no—
165#810—34no—
166#810—34no—
167#809—34no—
168#809—34no—
169#809—34no—
170#807—34no—
171C23×C32—21no—
172C23×C32C2×D411yescharacteristic
173C22×C3⋊D3—21no—
174C22×C3⋊D3—21no—
175C22×C3⋊D3—42no—
176C22×C3⋊D3—42no—
177C22×C3⋊D3—81no—
178C22×C3⋊D3C2×D411yescharacteristic
179C32×D4—21no—
180C32×D4—21no—
181C32×D4—81no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189#638—22no—
190#638—42no—
191#638—42no—
192#638—81no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3C2×D411yescharacteristic
196C2×C3⋊Dic3C2×D411yescharacteristic
197C2×C3⋊Dic3C2×D411yescharacteristic
198C4⋊(C3⋊D3)—21no—
199C4⋊(C3⋊D3)—21no—
200C4⋊(C3⋊D3)—21no—
201C4⋊(C3⋊D3)—42no—
202C4⋊(C3⋊D3)#4112yes—
203C4×C3⋊D3—21no—
204C4×C3⋊D3—21no—
205C4×C3⋊D3—42no—
206C4×C3⋊D3—81no—
207C4×C3⋊D3—81no—
208C4×C3⋊D3—81no—
209#634—21no—
210#634—21no—
211C32×C8—21no—
212C32×C8—21no—
213C3⋊(C3⋊C8)—21no—
214C3⋊(C3⋊C8)—21no—
215#553—91no—
216#546—91no—
217#488—91no—
218#484—91no—
219#482C3⋊D311yescharacteristic, complemented
220#478—91no—
221#466—91no—
222#465—91no—
223#463—91no—
224#449—91no—
225#447—91no—
226C4×D8—91no—
227C8×D4—91no—
228#416—91no—
229C2×#102—91no—
230C23×D3—64no—
231C2×C3×D4—24no—
232C2×C3×D4C22×D314yes—
233C22×C3×C4C22×D314yes—
234C2×#67—34no—
235C2×#67—64no—
236C2×#67—64no—
237C2×#67—64no—
238D3×D4—68no—
239D3×D4—124no—
240#235—68no—
241#235—124no—
242C2×D12—34no—
243C2×D12—34no—
244C2×D12—64no—
245C2×C4×D3—34no—
246C2×C4×D3—64no—
247C2×C4×D3—64no—
248C2×C4×D3—64no—
249C2×C4×D3—64no—
250C2×Dic6—34no—
251C2×C3×C8C22×D314yes—
252C2×C3×C8C22×D314yes—
253C3×C4⋊C4C22×D314yes—
254C3×C4⋊C4C22×D314yes—
255C3×C4⋊C4C22×D314yes—
256C3×C22⋊C4—24no—
257C3×C22⋊C4—24no—
258C3×C42—24no—
259#217—34no—
260#217—64no—
261#217—64no—
262#213—124no—
263(C2×D3)⋊C4—34no—
264(C2×D3)⋊C4—64no—
265(C2×D3)⋊C4—64no—
266(C2×D3)⋊C4—64no—
267(C2×D3)⋊C4—64no—
268(C2×D3)⋊C4—64no—
269C4⋊Dic3—34no—
270C4⋊Dic3—64no—
271C4⋊Dic3—64no—
272Dic3⋊C4—34no—
273Dic3⋊C4—64no—
274Dic3⋊C4—64no—
275C4×Dic3—34no—
276C2×C3⋊C8—34no—
277C2×C3⋊C8—34no—
278C2×C3⋊C8—124no—
279D24—68no—
280#204—124no—
281D3×C8—124no—
282C22×C32—21no—
283C22×C32—21no—
284C22×C32—21no—
285C22×C32—41no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32C22×D411yescharacteristic
289C2×C3⋊D3—21no—
290C2×C3⋊D3—21no—
291C2×C3⋊D3—22no—
292C2×C3⋊D3—41no—
293C2×C3⋊D3—41no—
294C2×C3⋊D3—41no—
295C2×C3⋊D3—41no—
296C2×C3⋊D3—41no—
297C2×C3⋊D3—84no—
298C2×C3⋊D3#13512yes—
299C32×C4—21no—
300C32×C4—41no—
301C32×C4—41no—
302C32×C4—41no—
303C32×C4C2×#4111yescharacteristic
304C32×C4H(5,𝔽2)11yescharacteristic
305C3⋊Dic3—21no—
306C3⋊Dic3—21no—
307C3⋊Dic3—21no—
308C3⋊Dic3—41no—
309C3⋊Dic3—41no—
310C2×#41—91no—
311C22×D4—91no—
312C2×SD16—91no—
313C2×D8—91no—
314C2×D8—91no—
315C22×C8—91no—
316C22×C8—91no—
317#126—181no—
318#125—91no—
319#124—91no—
320#123—181no—
321#123—181no—
322C22⋊Q8—91no—
323#121—91no—
324#121—91no—
325#121—181no—
326#121—181no—
327#121C2×C3⋊D311yescharacteristic
328#120—181no—
329C4×D4—91no—
330C4×D4—91no—
331C4×D4—91no—
332C4×D4—181no—
333#117C2×C3⋊D311yescharacteristic, complemented
334C2×C4⋊C4—91no—
335C2×C22⋊C4—181no—
336#107—91no—
337#107C2×C3⋊D311yescharacteristic, complemented
338#106C2×C3⋊D311yescharacteristic, complemented
339C4⋊C8—91no—
340#103—91no—
341#103—91no—
342#103—91no—
343#102—91no—
344#102—91no—
345#102—91no—
346#102—91no—
347#102—91no—
348#102C2×C3⋊D311yescharacteristic
349#102C2×C3⋊D311yescharacteristic
350C22⋊C8—91no—
351C22⋊C8C2×C3⋊D311yescharacteristic, complemented
352C4×C8—91no—
353C23×C3—24no—
354C23×C3D3×D414yes—
355C22×D3—34no—
356C22×D3—64no—
357C22×D3—64no—
358C22×D3—128no—
359C22×D3—128no—
360C22×D3—244no—
361C3×D4—24no—
362C3×D4—24no—
363C3×D4—84no—
364C2×C3×C4—24no—
365C2×C3×C4—24no—
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—24no—
369C2×C3×C4D3×D414yes—
370C2×C3×C4C23×D314yes—
371#67—68no—
372#67—128no—
373#67—128no—
374#67—244no—
375C2×Dic3—34no—
376C2×Dic3—34no—
377C2×Dic3—34no—
378C2×Dic3—64no—
379C2×Dic3—64no—
380D12—38no—
381D12—64no—
382D12—64no—
383D12—64no—
384D12—128no—
385C4×D3—64no—
386C4×D3—64no—
387C4×D3—128no—
388C4×D3—244no—
389C4×D3—244no—
390C4×D3—244no—
391Dic6—64no—
392Dic6—64no—
393C3×C8—24no—
394C3×C8—24no—
395C3⋊C8—64no—
396C3⋊C8—64no—
397C2×C32—41no—
398C2×C32—81no—
399C2×C32#54611yescharacteristic
400C2×C32C2×#13511yescharacteristic
401C2×C32#57611yescharacteristic
402C3⋊D3—22no—
403C3⋊D3—42no—
404C3⋊D3—81no—
405C24—181no—
406#41—182no—
407#41—361no—
408C2×Q8—91no—
409C2×D4—21no—
410C2×D4—91no—
411C2×D4—91no—
412C2×D4—91no—
413C2×D4—181no—
414C2×D4—181no—
415C2×D4—182no—
416C2×D4—181no—
417C2×D4—181no—
418C2×D4—361no—
419C2×D4C22×C3⋊D311yescharacteristic
420C22×C4—91no—
421C22×C4—181no—
422C22×C4—181no—
423C22×C4—181no—
424C22×C4—181no—
425C22×C4C22×C3⋊D311yescharacteristic
426SD16—361no—
427D8—182no—
428D8—361no—
429C2×C8—91no—
430C2×C8—91no—
431C2×C8—361no—
432C2×C8—361no—
433C2×C8C22×C3⋊D311yescharacteristic
434C2×C8C22×C3⋊D311yescharacteristic
435C4⋊C4—91no—
436C4⋊C4—91no—
437C4⋊C4—181no—
438C4⋊C4—181no—
439C4⋊C4—181no—
440C4⋊C4—181no—
441C4⋊C4C22×C3⋊D311yescharacteristic
442C4⋊C4C22×C3⋊D311yescharacteristic
443C4⋊C4C22×C3⋊D311yescharacteristic
444C22⋊C4—21no—
445C22⋊C4—21no—
446C22⋊C4—91no—
447C22⋊C4—91no—
448C22⋊C4—181no—
449C22⋊C4—181no—
450C22⋊C4—181no—
451C22⋊C4—181no—
452C22⋊C4—181no—
453C22⋊C4—181no—
454C22⋊C4—181no—
455C42—21no—
456C42—91no—
457C22×C3—24no—
458C22×C3—24no—
459C22×C3—24no—
460C22×C3—44no—
461C22×C3—44no—
462C22×C3—44no—
463C22×C3C2×D3×D414yes—
464C2×D3—38no—
465C2×D3—64no—
466C2×D3—64no—
467C2×D3—68no—
468C2×D3—124no—
469C2×D3—124no—
470C2×D3—124no—
471C2×D3—124no—
472C2×D3—124no—
473C2×D3—2416no—
474C3×C4—24no—
475C3×C4—44no—
476C3×C4—44no—
477C3×C4—44no—
478C3×C4D3×#4114yes—
479C3×C4#100914yes—
480Dic3—64no—
481Dic3—64no—
482Dic3—64no—
483Dic3—124no—
484Dic3—124no—
485C32#329711yescharacteristic, complemented, Sylow
486C23—21no—
487C23—91no—
488C23—181no—
489C23—181no—
490C23—362no—
491C23—362no—
492C23—721no—
493C23D4×C3⋊D311yescharacteristic
494Q8—181no—
495Q8—181no—
496D4—21no—
497D4—21no—
498D4—81no—
499D4—92no—
500D4—182no—
501D4—181no—
502D4—181no—
503D4—181no—
504D4—362no—
505D4—362no—
506D4—362no—
507D4—721no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—91no—
514C2×C4—91no—
515C2×C4—91no—
516C2×C4—181no—
517C2×C4—181no—
518C2×C4—181no—
519C2×C4—181no—
520C2×C4—362no—
521C2×C4—721no—
522C2×C4—721no—
523C2×C4—721no—
524C2×C4D4×C3⋊D311yescharacteristic
525C2×C4C23×C3⋊D311yescharacteristic
526C8—21no—
527C8—21no—
528C8—181no—
529C8—181no—
530C2×C3—44no—
531C2×C3—84no—
532C2×C3#565414yes—
533C2×C3D3×#13514yes—
534C2×C3#577414yes—
535D3—68no—
536D3—128no—
537D3—244no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—92no—
545C22—181no—
546C22—181no—
547C22—182no—
548C22—361no—
549C22—361no—
550C22—361no—
551C22—361no—
552C22—361no—
553C22—724no—
554C22C2×D4×C3⋊D311yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—181no—
560C4—181no—
561C4—181no—
562C4—361no—
563C4—361no—
564C4#41×C3⋊D311yescharacteristic
565C4#6436611yescharacteristic
566C3#8138214yescomplemented
567C2—41no—
568C2—81no—
569C2—182no—
570C2—362no—
571C2—721no—
572C2#1059612511yescharacteristic
573C2C3⋊D3×#13511yescharacteristic
574C2#1059624511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#482C2
socleC22×C32C22×D4
hypercenter#482C3⋊D3
hypocenterC32#3297
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. #10596083C2semidirect
2. #10596001C2semidirect
3. C32×#482C2semidirect
4. #10592737C2semidirect
5. #10592701C2semidirect
6. #10592583C2semidirect
7. #10592571C2semidirect
8. #10592570C2semidirect
9. #10592563C2semidirect
10. #10592486C2semidirect
11. #10592472C2semidirect
12. C3⋊D3×#102C2semidirect
13. #10592467C2semidirect
14. #10592433C2semidirect
15. #10592424C2semidirect
20. C32×#117C22semidirect
25. #64139C22semidirect
27. C22×C3⋊(C3⋊C8)C22semidirect
29. C2×#3744C22semidirect
34. #64102C22semidirect
36. #64099C22semidirect
43. C32×#107C22semidirect
44. C32×#106C22semidirect
47. C32×C22⋊C8C22semidirect
51. #63643C22semidirect
52. #63641C22semidirect
53. C8×C3⋊Dic3C22semidirect
54. #63637C22semidirect
55. #63637C22semidirect
58. #63636C22semidirect
59. #63634C22semidirect
62. C3×#482D3semidirect
131. C3×#117C2×D3semidirect
154. C3×#107C2×D3semidirect
155. C3×#106C2×D3semidirect
158. C3×C22⋊C8C2×D3semidirect
219. #482C3⋊D3semidirect
333. #117C2×C3⋊D3semidirect
337. #107C2×C3⋊D3semidirect
338. #106C2×C3⋊D3semidirect
351. C22⋊C8C2×C3⋊D3semidirect
485. C32#3297semidirect
566. C3#81382semidirect

Maximal subgroups

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

subgroupindex
#105960832
#105960012
C32×#4822
#105927372
#105927012
#105925832
#105925712
#105925702
#105925632
#105924862
#105924722
C3⋊D3×#1022
#105924672
#105924332
#105924242
#813823