Finite Group Databasebeta

← #11887331

Subgroups — #11887331

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#10596300C211yesmaximal, characteristic, complemented
2#10596085C211yesmaximal, characteristic, complemented
3C32×#449C211yesmaximal, characteristic, complemented
4#10592932C211yesmaximal, characteristic, complemented
5#10592870C211yesmaximal, characteristic, complemented
6#10592864C211yesmaximal, characteristic, complemented
7#10592855C211yesmaximal, characteristic, complemented
8D8×C3⋊Dic3C211yesmaximal, characteristic, complemented
9#10592737C211yesmaximal, characteristic, complemented
10#10592510C211yesmaximal, characteristic, complemented
11#10592499C211yesmaximal, characteristic, complemented
12C3⋊D3×#102C211yesmaximal, characteristic, complemented
13#10592462C211yesmaximal, characteristic, complemented
14#10592436C211yesmaximal, characteristic, complemented
15#10592424C211yesmaximal, characteristic, complemented
16#80102—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic, complemented
20C2×C32×D8C2211yescharacteristic
21C32×#121C2211yescharacteristic, complemented
22#64156C2211yescharacteristic
23#64155C2211yescharacteristic
24#64148—21no—
25#64147—21no—
26#64147C2211yescharacteristic
27#64146—21no—
28#64144—21no—
29D4×C3⋊Dic3C2211yescharacteristic
30D4×C3⋊Dic3C2211yescharacteristic, complemented
31C2×#3753C2211yescharacteristic
32#64139C2211yescharacteristic
33#64138—21no—
34C4×#638C2211yescharacteristic
35C2×#3752—21no—
36#64135C2211yescharacteristic, complemented
37C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
38C2×C8×C3⋊D3C2211yescharacteristic
39C4⋊C4×C3⋊D3C2211yescharacteristic
40#64099C2211yescharacteristic, complemented
41#64090—21no—
42#64088—21no—
43C32×#103C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic, complemented
46#63662C2211yescharacteristic, complemented
47#63662C2211yescharacteristic, complemented
48#63659C2211yescharacteristic
49#63659C2211yescharacteristic
50#63659C2211yescharacteristic, complemented
51#63648C2211yescharacteristic
52#63648C2211yescharacteristic
53#63647C2211yescharacteristic
54#63645C2211yescharacteristic, complemented
55#63644C2211yescharacteristic, complemented
56#63641C2211yescharacteristic, complemented
57C8×C3⋊Dic3C2211yescharacteristic, complemented
58#63636C2211yescharacteristic
59#63634C2211yescharacteristic, complemented
60#5829—34no—
61#5614—34no—
62C3×#449D314yescomplemented
63#5233—34no—
64#5171—34no—
65#5165—34no—
66#5156—34no—
67Dic3×D8—34no—
68#5038—34no—
69#4811—34no—
70#4800—34no—
71D3×#102—34no—
72#4763—34no—
73#4737—34no—
74#67⋊C8—34no—
75C23×C3⋊D3—21no—
76C32×#41—22no—
77C32×#41—41no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×D4—21no—
80C2×C32×D4—21no—
81C2×C32×D4C2311yescharacteristic
82C2×C32×D4C2311yescharacteristic
83C22×C32×C4—21no—
84C22×C32×C4C2311yescharacteristic
85C2×#638—21no—
86C2×#638—21no—
87C2×#638—21no—
88C2×#638D411yescharacteristic
89C22×C3⋊Dic3—21no—
90C22×C3⋊Dic3—21no—
91D4×C3⋊D3—22no—
92D4×C3⋊D3—41no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C32×SD16—41no—
97C32×D8—22no—
98C2×C32×C8C2311yescharacteristic
99C2×C32×C8C2311yescharacteristic
100C32×C4⋊C4C2311yescharacteristic
101C32×C22⋊C4—21no—
102#3757—21no—
103#3757—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#3752D411yescharacteristic
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3750—21no—
119#3750—21no—
120#3750D411yescharacteristic
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3C2311yescharacteristic
123C2×C3⋊(C3⋊C8)—41no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C8×C3⋊D3—41no—
127#3297—91noSylow
128C2×C3×#41C2×D314yes—
129C2×D3×D4—34no—
130C2×C3×SD16C2×D314yescomplemented
131C2×C3×D8C2×D314yes—
132C3×#121C2×D314yescomplemented
133#947—34no—
134#946—34no—
135#939—64no—
136#938—34no—
137#938—64no—
138#937—64no—
139#935—64no—
140D4×Dic3—34no—
141D4×Dic3—34no—
142C2×#213—34no—
143#930—34no—
144#929—64no—
145C4×#67—34no—
146C2×(C2×D3)⋊C4—64no—
147#926—34no—
148C22×C3⋊C8—34no—
149C2×D3×C8—34no—
150D3×C4⋊C4—34no—
151#890—34no—
152#67⋊C4—64no—
153#879—64no—
154C3×#103C2×D314yescomplemented
155C3×#102C2×D314yes—
156C3×C22⋊C8C2×D314yescomplemented
157#835—34no—
158#835—34no—
159#832—34no—
160#832—34no—
161#832—34no—
162#821—34no—
163#821—34no—
164(C2×D3)⋊C8—34no—
165#818—34no—
166#817—34no—
167Dic3⋊C8—34no—
168C8×Dic3—34no—
169#809—34no—
170#807—34no—
171C23×C32—21no—
172C23×C32—21no—
173C23×C32C2×D411yescharacteristic
174C22×C3⋊D3—21no—
175C22×C3⋊D3—42no—
176C22×C3⋊D3—42no—
177C22×C3⋊D3—81no—
178C22×C3⋊D3C2×D411yescharacteristic
179C32×Q8—21no—
180C32×Q8—21no—
181C32×D4—21no—
182C32×D4—21no—
183C32×D4—21no—
184C32×D4—42no—
185C32×D4—81no—
186C32×D4#4112yes—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4—42no—
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2411yescharacteristic
194#638—22no—
195#638—42no—
196#638—42no—
197#638—81no—
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3—21no—
201C2×C3⋊Dic3—81no—
202C2×C3⋊Dic3—81no—
203C2×C3⋊Dic3C2×D411yescharacteristic
204C2×C3⋊Dic3C2×D411yescharacteristic
205C2×C3⋊Dic3C2×D411yescharacteristic
206C4⋊(C3⋊D3)—21no—
207C4⋊(C3⋊D3)—21no—
208C4×C3⋊D3—21no—
209C4×C3⋊D3—21no—
210C4×C3⋊D3—81no—
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#482—91no—
220#478—91no—
221#466—91no—
222#465—91no—
223#463—91no—
224#449C3⋊D311yescharacteristic, complemented
225#447—91no—
226C4×D8—91no—
227C8×D4—91no—
228#416—91no—
229C2×#102—91no—
230C23×D3—64no—
231C3×#41—28no—
232C3×#41—44no—
233C2×C3×Q8C22×D314yes—
234C2×C3×D4—24no—
235C2×C3×D4—24no—
236C2×C3×D4C22×D314yes—
237C2×C3×D4C22×D314yes—
238C22×C3×C4—24no—
239C22×C3×C4C22×D314yes—
240C2×#67—34no—
241C2×#67—64no—
242C2×#67—64no—
243C2×#67—64no—
244C22×Dic3—64no—
245C22×Dic3—64no—
246D3×D4—68no—
247D3×D4—124no—
248C2×D12—34no—
249C2×C4×D3—34no—
250C2×C4×D3—64no—
251C3×SD16—44no—
252C3×D8—28no—
253C2×C3×C8C22×D314yes—
254C2×C3×C8C22×D314yes—
255C3×C4⋊C4C22×D314yes—
256C3×C22⋊C4—24no—
257#217—34no—
258#217—64no—
259#217—64no—
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—
268C4⋊Dic3—34no—
269C4⋊Dic3—34no—
270C4⋊Dic3—34no—
271C4⋊Dic3—64no—
272Dic3⋊C4—34no—
273Dic3⋊C4—64no—
274Dic3⋊C4—64no—
275Dic3⋊C4—64no—
276C4×Dic3—34no—
277C4×Dic3—64no—
278C2×C3⋊C8—34no—
279C2×C3⋊C8—34no—
280C2×C3⋊C8—124no—
281D3×C8—124no—
282C22×C32—22no—
283C22×C32—21no—
284C22×C32—21no—
285C22×C32—21no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32—41no—
289C22×C32—41no—
290C22×C32—41no—
291C22×C32C22×D411yescharacteristic
292C2×C3⋊D3—21no—
293C2×C3⋊D3—21no—
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×C4C2×#4111yescharacteristic
303C32×C4H(5,𝔽2)11yescharacteristic
304C3⋊Dic3—21no—
305C3⋊Dic3—21no—
306C3⋊Dic3—21no—
307C3⋊Dic3—41no—
308C3⋊Dic3—41no—
309C3⋊Dic3—41no—
310C2×#41C2×C3⋊D311yescharacteristic
311C22×D4—91no—
312C2×SD16C2×C3⋊D311yescharacteristic, complemented
313C2×D8—91no—
314C2×D8C2×C3⋊D311yescharacteristic
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, complemented
328#120—181no—
329C4×D4—91no—
330C4×D4—91no—
331C4×D4—91no—
332C4×D4—181no—
333#117—91no—
334C2×C4⋊C4—91no—
335C2×C22⋊C4—181no—
336#107—91no—
337#107—91no—
338#106—91no—
339C4⋊C8—91no—
340#103—91no—
341#103—91no—
342#103C2×C3⋊D311yescharacteristic, complemented
343#102—91no—
344#102—91no—
345#102—91no—
346#102—91no—
347#102—91no—
348#102—91no—
349#102C2×C3⋊D311yescharacteristic
350C22⋊C8—91no—
351C22⋊C8C2×C3⋊D311yescharacteristic, complemented
352C4×C8—91no—
353C23×C3—24no—
354C23×C3—24no—
355C23×C3D3×D414yes—
356C22×D3—34no—
357C22×D3—64no—
358C22×D3—128no—
359C22×D3—128no—
360C22×D3—244no—
361C3×Q8—24no—
362C3×Q8—24no—
363C3×D4—24no—
364C3×D4—24no—
365C3×D4—24no—
366C3×D4—48no—
367C3×D4—84no—
368C3×D4#23718yes—
369C2×C3×C4—24no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—24no—
373C2×C3×C4—48no—
374C2×C3×C4D3×D414yes—
375C2×C3×C4C23×D314yes—
376#67—68no—
377#67—128no—
378#67—128no—
379#67—244no—
380C2×Dic3—34no—
381C2×Dic3—34no—
382C2×Dic3—34no—
383C2×Dic3—64no—
384C2×Dic3—64no—
385C2×Dic3—64no—
386C2×Dic3—244no—
387C2×Dic3—244no—
388D12—64no—
389D12—64no—
390C4×D3—64no—
391C4×D3—64no—
392C4×D3—244no—
393C3×C8—24no—
394C3×C8—24no—
395C3⋊C8—64no—
396C3⋊C8—64no—
397C2×C32—42no—
398C2×C32—41no—
399C2×C32—81no—
400C2×C32#54611yescharacteristic
401C2×C32C2×#13511yescharacteristic
402C2×C32#57611yescharacteristic
403C3⋊D3—22no—
404C3⋊D3—81no—
405C24—181no—
406#41—22no—
407#41—41no—
408C2×Q8C22×C3⋊D311yescharacteristic
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—91no—
412C2×D4—91no—
413C2×D4—181no—
414C2×D4—182no—
415C2×D4—181no—
416C2×D4—181no—
417C2×D4—361no—
418C2×D4C22×C3⋊D311yescharacteristic
419C2×D4C22×C3⋊D311yescharacteristic
420C22×C4—21no—
421C22×C4—91no—
422C22×C4—181no—
423C22×C4—181no—
424C22×C4—181no—
425C22×C4C22×C3⋊D311yescharacteristic
426SD16—41no—
427D8—22no—
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—91no—
438C4⋊C4—91no—
439C4⋊C4—181no—
440C4⋊C4—181no—
441C4⋊C4—181no—
442C4⋊C4—181no—
443C4⋊C4C22×C3⋊D311yescharacteristic
444C22⋊C4—21no—
445C22⋊C4—91no—
446C22⋊C4—91no—
447C22⋊C4—181no—
448C22⋊C4—181no—
449C22⋊C4—181no—
450C22⋊C4—181no—
451C22⋊C4—181no—
452C22⋊C4—181no—
453C22⋊C4—181no—
454C22⋊C4—181no—
455C42—91no—
456C42—181no—
457C22×C3—24no—
458C22×C3—24no—
459C22×C3—28no—
460C22×C3—24no—
461C22×C3—44no—
462C22×C3—44no—
463C22×C3—44no—
464C22×C3—44no—
465C22×C3—44no—
466C22×C3C2×D3×D414yes—
467C2×D3—38no—
468C2×D3—64no—
469C2×D3—64no—
470C2×D3—124no—
471C2×D3—124no—
472C2×D3—124no—
473C2×D3—2416no—
474C3×C4—24no—
475C3×C4—44no—
476C3×C4—44no—
477C3×C4C2×#23714yes—
478C3×C4#100414yes—
479Dic3—64no—
480Dic3—64no—
481Dic3—64no—
482Dic3—124no—
483Dic3—124no—
484Dic3—124no—
485C32#329711yescharacteristic, complemented, Sylow
486C23—21no—
487C23—21no—
488C23—91no—
489C23—181no—
490C23—362no—
491C23—362no—
492C23—721no—
493C23D4×C3⋊D311yescharacteristic
494Q8—21no—
495Q8—21no—
496D4—21no—
497D4—21no—
498D4—21no—
499D4—42no—
500D4—81no—
501D4—182no—
502D4—181no—
503D4—181no—
504D4—362no—
505D4—362no—
506D4—721no—
507D4#383012yes—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—42no—
513C2×C4—91no—
514C2×C4—91no—
515C2×C4—91no—
516C2×C4—181no—
517C2×C4—181no—
518C2×C4—181no—
519C2×C4—181no—
520C2×C4—181no—
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—48no—
531C2×C3—44no—
532C2×C3—84no—
533C2×C3#559114yes—
534C2×C3D3×#13514yes—
535C2×C3#577414yes—
536D3—68no—
537D3—244no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—22no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—92no—
548C22—181no—
549C22—181no—
550C22—361no—
551C22—361no—
552C22—361no—
553C22—724no—
554C22C2×D4×C3⋊D311yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—181no—
559C4—181no—
560C4—181no—
561C4—361no—
562C4—361no—
563C4—361no—
564C4C2×#383011yescharacteristic
565C4#6436111yescharacteristic
566C3#8010214yescomplemented
567C2—41no—
568C2—42no—
569C2—81no—
570C2—182no—
571C2—721no—
572C2#1059606211yescharacteristic
573C2C3⋊D3×#13511yescharacteristic
574C2#1059624511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#449C2
socleC22×C32C22×D4
hypercenter#449C3⋊D3
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #10596300C2semidirect
2. #10596085C2semidirect
3. C32×#449C2semidirect
4. #10592932C2semidirect
5. #10592870C2semidirect
6. #10592864C2semidirect
7. #10592855C2semidirect
8. D8×C3⋊Dic3C2semidirect
9. #10592737C2semidirect
10. #10592510C2semidirect
11. #10592499C2semidirect
12. C3⋊D3×#102C2semidirect
13. #10592462C2semidirect
14. #10592436C2semidirect
15. #10592424C2semidirect
19. C2×C32×SD16C22semidirect
21. C32×#121C22semidirect
30. D4×C3⋊Dic3C22semidirect
36. #64135C22semidirect
37. C22×C3⋊(C3⋊C8)C22semidirect
40. #64099C22semidirect
43. C32×#103C22semidirect
45. C32×C22⋊C8C22semidirect
46. #63662C22semidirect
47. #63662C22semidirect
50. #63659C22semidirect
54. #63645C22semidirect
55. #63644C22semidirect
56. #63641C22semidirect
57. C8×C3⋊Dic3C22semidirect
59. #63634C22semidirect
62. C3×#449D3semidirect
130. C2×C3×SD16C2×D3semidirect
132. C3×#121C2×D3semidirect
154. C3×#103C2×D3semidirect
156. C3×C22⋊C8C2×D3semidirect
224. #449C3⋊D3semidirect
312. C2×SD16C2×C3⋊D3semidirect
327. #121C2×C3⋊D3semidirect
342. #103C2×C3⋊D3semidirect
351. C22⋊C8C2×C3⋊D3semidirect
485. C32#3297semidirect
566. C3#80102semidirect

Maximal subgroups

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

subgroupindex
#105963002
#105960852
C32×#4492
#105929322
#105928702
#105928642
#105928552
D8×C3⋊Dic32
#105927372
#105925102
#105924992
C3⋊D3×#1022
#105924622
#105924362
#105924242
#801023