Finite Group Databasebeta

← #11887355

Subgroups — #11887355

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#10596001C211yesmaximal, characteristic, complemented
3C32×#416C211yesmaximal, characteristic, complemented
4#10592937C211yesmaximal, characteristic, complemented
5#10592814C211yesmaximal, characteristic, complemented
6C8×#638C211yesmaximal, characteristic, complemented
7#10592702C211yesmaximal, characteristic, complemented
8#10592518C211yesmaximal, characteristic, complemented
9#10592510C211yesmaximal, characteristic, complemented
10#10592506C211yesmaximal, characteristic, complemented
11#10592499C211yesmaximal, characteristic, complemented
12#10592472C211yesmaximal, characteristic, complemented
13C3⋊D3×#102C211yesmaximal, characteristic, complemented
14#10592465C211yesmaximal, characteristic, complemented
15#10592455C211yesmaximal, characteristic, complemented
16#78846—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×D4×C3⋊D3C2211yescharacteristic
19C22×C32×C8C2211yescharacteristic, complemented
20C32×#117C2211yescharacteristic, complemented
21#64156C2211yescharacteristic
22#64155C2211yescharacteristic
23C2×#3755C2211yescharacteristic, complemented
24#64148—21no—
25#64146—21no—
26D4×C3⋊Dic3C2211yescharacteristic
27C2×#3753C2211yescharacteristic
28#64139C2211yescharacteristic
29#64139C2211yescharacteristic, complemented
30#64138—21no—
31C4×#638C2211yescharacteristic
32C2×#3752—21no—
33C2×#3745C2211yescharacteristic
34C2×C8×C3⋊D3C2211yescharacteristic
35#64104C2211yescharacteristic
36#64102C2211yescharacteristic, complemented
37C4⋊C4×C3⋊D3C2211yescharacteristic
38#64099C2211yescharacteristic, complemented
39#64093—21no—
40#64092—21no—
41#64085—21no—
42C4×C4⋊(C3⋊D3)—21no—
43C32×#103C2211yescharacteristic, complemented
44C32×#103C2211yescharacteristic, complemented
45C32×#102C2211yescharacteristic
46C32×#102C2211yescharacteristic
47#63662C2211yescharacteristic, complemented
48#63659C2211yescharacteristic
49#63657C2211yescharacteristic, complemented
50#63648C2211yescharacteristic
51#63648C2211yescharacteristic, complemented
52#63647C2211yescharacteristic
53#63645C2211yescharacteristic, complemented
54#63641C2211yescharacteristic, complemented
55C8×C3⋊Dic3C2211yescharacteristic, complemented
56#63636C2211yescharacteristic
57#63636C2211yescharacteristic
58#63635C2211yescharacteristic, complemented
59#63634C2211yescharacteristic, complemented
60#5829—34no—
61#5530—34no—
62C3×#416D314yescomplemented
63#5238—34no—
64#5115—34no—
65C8×#67—34no—
66#5003—34no—
67#4819—34no—
68#4811—34no—
69#4807—34no—
70#4800—34no—
71#4773—34no—
72D3×#102—34no—
73#4766—34no—
74#4756—34no—
75C23×C3⋊D3—21no—
76C32×#41—22no—
77C32×#41—41no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×D4—21no—
80C2×C32×D4C2311yescharacteristic
81C22×C32×C4—21no—
82C22×C32×C4C2311yescharacteristic
83C2×#638—21no—
84C2×#638—21no—
85C2×#638—21no—
86C2×#638D411yescharacteristic
87C22×C3⋊Dic3—21no—
88D4×C3⋊D3—22no—
89D4×C3⋊D3—41no—
90C2×C4⋊(C3⋊D3)—21no—
91C2×C4⋊(C3⋊D3)C2311yescharacteristic
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×C4×C3⋊D3—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C32×C8—41no—
97C2×C32×C8C2311yescharacteristic
98C2×C32×C8C2311yescharacteristic
99C32×C4⋊C4C2311yescharacteristic
100C32×C4⋊C4C2311yescharacteristic
101C32×C22⋊C4—21no—
102C32×C42—21no—
103#3757—21no—
104#3757D411yescharacteristic
105#3755—41no—
106#3753—22no—
107#3752—21no—
108#3752—21no—
109#3752—21no—
110#3752—21no—
111#3752—21no—
112#3752—21no—
113#3752—21no—
114#3752D411yescharacteristic
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119#3750—21no—
120#3750—21no—
121#3750D411yescharacteristic
122C4×C3⋊Dic3C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125#3745—41no—
126C8×C3⋊D3—41no—
127#3297—91noSylow
128C2×C3×#41C2×D314yes—
129C2×D3×D4—34no—
130C22×C3×C8C2×D314yescomplemented
131C3×#117C2×D314yescomplemented
132#947—34no—
133#946—34no—
134C2×#215—34no—
135#939—64no—
136#937—64no—
137D4×Dic3—34no—
138C2×#213—34no—
139#930—34no—
140#930—34no—
141#929—64no—
142C4×#67—34no—
143C2×(C2×D3)⋊C4—64no—
144C2×D24—34no—
145C2×D3×C8—34no—
146#895—34no—
147#893—34no—
148D3×C4⋊C4—34no—
149#890—34no—
150#884—64no—
151#883—64no—
152#876—64no—
153C4×D12—64no—
154C3×#103C2×D314yescomplemented
155C3×#103C2×D314yescomplemented
156C3×#102C2×D314yes—
157C3×#102C2×D314yes—
158#835—34no—
159#832—34no—
160#830—34no—
161#821—34no—
162#821—34no—
163(C2×D3)⋊C8—34no—
164#818—34no—
165Dic3⋊C8—34no—
166C8×Dic3—34no—
167#809—34no—
168#809—34no—
169#808—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×Q8—21no—
180C32×Q8—21no—
181C32×D4—21no—
182C32×D4—42no—
183C32×D4#4112yes—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4—42no—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2411yescharacteristic
192#638—22no—
193#638—42no—
194#638—81no—
195#638—81no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3—81no—
199C2×C3⋊Dic3C2×D411yescharacteristic
200C2×C3⋊Dic3C2×D411yescharacteristic
201C2×C3⋊Dic3C2×D411yescharacteristic
202C4⋊(C3⋊D3)—21no—
203C4⋊(C3⋊D3)—21no—
204C4⋊(C3⋊D3)—21no—
205C4⋊(C3⋊D3)—21no—
206C4⋊(C3⋊D3)—42no—
207C4×C3⋊D3—21no—
208C4×C3⋊D3—21no—
209C4×C3⋊D3—81no—
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#449—91no—
225#447—91no—
226C4×D8—91no—
227C8×D4—91no—
228#416C3⋊D311yescharacteristic, complemented
229C2×#102—91no—
230C23×D3—64no—
231C3×#41—28no—
232C3×#41—44no—
233C2×C3×Q8C22×D314yes—
234C2×C3×D4—24no—
235C2×C3×D4C22×D314yes—
236C22×C3×C4—24no—
237C22×C3×C4C22×D314yes—
238C2×#67—34no—
239C2×#67—64no—
240C2×#67—64no—
241C2×#67—64no—
242C22×Dic3—64no—
243D3×D4—68no—
244D3×D4—124no—
245C2×D12—34no—
246C2×D12—34no—
247C2×D12—64no—
248C2×C4×D3—34no—
249C2×C4×D3—64no—
250C2×C4×D3—64no—
251C2×C3×C8—44no—
252C2×C3×C8C22×D314yes—
253C2×C3×C8C22×D314yes—
254C3×C4⋊C4C22×D314yes—
255C3×C4⋊C4C22×D314yes—
256C3×C22⋊C4—24no—
257C3×C42—24no—
258#217—34no—
259#217—64no—
260#215—124no—
261#213—68no—
262(C2×D3)⋊C4—34no—
263(C2×D3)⋊C4—64no—
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—
269(C2×D3)⋊C4—64no—
270C4⋊Dic3—34no—
271C4⋊Dic3—34no—
272C4⋊Dic3—64no—
273Dic3⋊C4—34no—
274Dic3⋊C4—64no—
275Dic3⋊C4—64no—
276Dic3⋊C4—64no—
277C4×Dic3—34no—
278C2×C3⋊C8—34no—
279C2×C3⋊C8—34no—
280D24—124no—
281D3×C8—124no—
282C22×C32—22no—
283C22×C32—21no—
284C22×C32—21no—
285C22×C32—21no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32C22×D411yescharacteristic
289C2×C3⋊D3—21no—
290C2×C3⋊D3—21no—
291C2×C3⋊D3—41no—
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×#41C2×C3⋊D311yescharacteristic
311C22×D4—91no—
312C2×SD16—91no—
313C2×D8—91no—
314C2×D8—91no—
315C22×C8—91no—
316C22×C8C2×C3⋊D311yescharacteristic, complemented
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—91no—
326#121—181no—
327#121—181no—
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#107—91no—
338#106—91no—
339C4⋊C8—91no—
340#103—91no—
341#103C2×C3⋊D311yescharacteristic, complemented
342#103C2×C3⋊D311yescharacteristic, complemented
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⋊C8—91no—
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×Q8—24no—
362C3×Q8—24no—
363C3×D4—24no—
364C3×D4—48no—
365C3×D4#23518yes—
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—24no—
369C2×C3×C4—24no—
370C2×C3×C4—24no—
371C2×C3×C4—48no—
372C2×C3×C4D3×D414yes—
373C2×C3×C4C23×D314yes—
374#67—68no—
375#67—128no—
376#67—244no—
377#67—244no—
378C2×Dic3—34no—
379C2×Dic3—34no—
380C2×Dic3—34no—
381C2×Dic3—64no—
382C2×Dic3—64no—
383C2×Dic3—244no—
384D12—64no—
385D12—64no—
386D12—64no—
387D12—64no—
388D12—128no—
389C4×D3—64no—
390C4×D3—64no—
391C4×D3—244no—
392C4×D3—244no—
393C3×C8—24no—
394C3×C8—24no—
395C3⋊C8—64no—
396C3⋊C8—64no—
397C2×C32—42no—
398C2×C32—41no—
399C2×C32#54611yescharacteristic
400C2×C32C2×#13511yescharacteristic
401C2×C32#57611yescharacteristic
402C3⋊D3—22no—
403C3⋊D3—81no—
404C3⋊D3—81no—
405C24—181no—
406#41—22no—
407#41—41no—
408C2×Q8C22×C3⋊D311yescharacteristic
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—21no—
421C22×C4—91no—
422C22×C4—181no—
423C22×C4—181no—
424C22×C4—181no—
425C22×C4C22×C3⋊D311yescharacteristic
426SD16—361no—
427D8—182no—
428D8—361no—
429C2×C8—41no—
430C2×C8—91no—
431C2×C8—91no—
432C2×C8—361no—
433C2×C8C22×C3⋊D311yescharacteristic
434C2×C8C22×C3⋊D311yescharacteristic
435C4⋊C4—91no—
436C4⋊C4—91no—
437C4⋊C4—91no—
438C4⋊C4—181no—
439C4⋊C4—181no—
440C4⋊C4—181no—
441C4⋊C4—181no—
442C4⋊C4C22×C3⋊D311yescharacteristic
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—21no—
456C42—91no—
457C22×C3—28no—
458C22×C3—24no—
459C22×C3—24no—
460C22×C3—24no—
461C22×C3—44no—
462C22×C3—44no—
463C22×C3C2×D3×D414yes—
464C2×D3—38no—
465C2×D3—64no—
466C2×D3—64no—
467C2×D3—124no—
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×C4C2×#23514yes—
479C3×C4#100414yes—
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—21no—
495Q8—21no—
496D4—21no—
497D4—42no—
498D4—182no—
499D4—181no—
500D4—181no—
501D4—181no—
502D4—181no—
503D4—362no—
504D4—362no—
505D4—721no—
506D4—721no—
507D4#382812yes—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—42no—
514C2×C4—91no—
515C2×C4—91no—
516C2×C4—91no—
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#549014yes—
533C2×C3D3×#13514yes—
534C2×C3#576914yes—
535D3—68no—
536D3—244no—
537D3—244no—
538C22—21no—
539C22—22no—
540C22—21no—
541C22—21no—
542C22—41no—
543C22—41no—
544C22—92no—
545C22—181no—
546C22—181no—
547C22—361no—
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—
564C4C2×#382811yescharacteristic
565C4#6436111yescharacteristic
566C3#7884614yescomplemented
567C2—41no—
568C2—42no—
569C2—182no—
570C2—721no—
571C2—721no—
572C2#1059596111yescharacteristic
573C2C3⋊D3×#13511yescharacteristic
574C2#1059624011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#416C2
socleC22×C32C22×D4
hypercenter#416C3⋊D3
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #10596300C2semidirect
2. #10596001C2semidirect
3. C32×#416C2semidirect
4. #10592937C2semidirect
5. #10592814C2semidirect
6. C8×#638C2semidirect
7. #10592702C2semidirect
8. #10592518C2semidirect
9. #10592510C2semidirect
10. #10592506C2semidirect
11. #10592499C2semidirect
12. #10592472C2semidirect
13. C3⋊D3×#102C2semidirect
14. #10592465C2semidirect
15. #10592455C2semidirect
19. C22×C32×C8C22semidirect
20. C32×#117C22semidirect
23. C2×#3755C22semidirect
29. #64139C22semidirect
36. #64102C22semidirect
38. #64099C22semidirect
43. C32×#103C22semidirect
44. C32×#103C22semidirect
47. #63662C22semidirect
49. #63657C22semidirect
51. #63648C22semidirect
53. #63645C22semidirect
54. #63641C22semidirect
55. C8×C3⋊Dic3C22semidirect
58. #63635C22semidirect
59. #63634C22semidirect
62. C3×#416D3semidirect
130. C22×C3×C8C2×D3semidirect
131. C3×#117C2×D3semidirect
154. C3×#103C2×D3semidirect
155. C3×#103C2×D3semidirect
228. #416C3⋊D3semidirect
316. C22×C8C2×C3⋊D3semidirect
333. #117C2×C3⋊D3semidirect
341. #103C2×C3⋊D3semidirect
342. #103C2×C3⋊D3semidirect
485. C32#3297semidirect
566. C3#78846semidirect

Maximal subgroups

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

subgroupindex
#105963002
#105960012
C32×#4162
#105929372
#105928142
C8×#6382
#105927022
#105925182
#105925102
#105925062
#105924992
#105924722
C3⋊D3×#1022
#105924652
#105924552
#788463