Finite Group Databasebeta

← #11865873

Subgroups — #11865873

Order 1152.

1251 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic, complemented
3C2×#63830C212yesmaximal, complemented
4C3×#4924C211yesmaximal, characteristic, complemented
5#10591106C212yesmaximal, complemented
6#10590366C214yesmaximal, complemented
7#10590365C212yesmaximal, complemented
8#10590349C212yesmaximal, complemented
9#82307—31nomaximal
10#79055—31nomaximal
11C2×#3828C2212yes—
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3—21no—
14C2×C32×C42C2211yescharacteristic
15#64139—21no—
16#64139—21no—
17#64084C2212yescomplemented
18#64083C2211yescharacteristic, complemented
19C4×C4⋊(C3⋊D3)—21no—
20C4×C4⋊(C3⋊D3)—21no—
21#64078C2211yescharacteristic, complemented
22C2×C3×(C2×D3)⋊C4—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×#208C2212yes—
25C3×C4×D12—21no—
26C3×C4×D12—21no—
27C3×C4×D12C2212yes—
28C3×C4×D12C2212yes—
29#63830—28no—
30C2×#3716C2214yes—
31C2×#3714C2214yes—
32C3×C4⋊(C3⋊C8)C2212yescomplemented
33C3×C4⋊(C3⋊C8)C2212yescomplemented
34#63567C2214yescomplemented
35#63564C2214yescomplemented
36C2×C3×C4×D4—31no—
37C2×#932—32no—
38C2×#908—32no—
39#5477—31no—
40#5477—31no—
41#5477—61no—
42C2×C4×D12D311yescharacteristic, complemented
43C3×#423—31no—
44#5133—32no—
45#5019—32no—
46#5016—34no—
47#5015—32no—
48#4966—32no—
49#4924D311yescharacteristic, complemented
50#4844—34no—
51#4843—32no—
52#4841—32no—
53C23×C3×D3—21no—
54C22×C32×C4D411yescharacteristic
55C22×C32×C4D411yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C2×#638—22no—
58#3828—24no—
59#3828—24no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)C2312yes—
63C2×C4×C3⋊D3—22no—
64C2×#634C2312yes—
65C22×C3×Dic3—21no—
66C2×C3×D12—21no—
67C2×C3×D12—22no—
68C2×C3×D12D414yescomplemented
69C2×C3×D12C2312yes—
70C2×C3×C4×D3—22no—
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3—44no—
73C32×C42D411yescharacteristic
74C32×C42D411yescharacteristic
75C32×C42C2311yescharacteristic
76C32×C42C2311yescharacteristic
77#3752—22no—
78#3752—22no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)—21no—
81C3×(C2×D3)⋊C4—22no—
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3C2312yes—
85C3×#208—24no—
86C2×C3×C3⋊C8C2314yes—
87#3716—28no—
88#3714—28no—
89#3036—91noSylow
90C22×C3×D4—31no—
91C23×C3×C4—61no—
92C2×#235—32no—
93C2×#235—32no—
94C2×#235—62no—
95C22×D12C2×D311yescharacteristic
96C22×C4×D3—21no—
97C2×C3×M16—32no—
98C3×C4×D4—32no—
99C3×C4×D4—32no—
100C3×C4×D4—61no—
101C3×C4×D4—61no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C22⋊C4—61no—
104C2×C3×C42—21no—
105C2×C3×C42C2×D311yescharacteristic
106C2×C3×C42C2×D311yescharacteristic
107C2×#214—34no—
108#932—68no—
109C2×#213—34no—
110#930—62no—
111#930—62no—
112#930—61no—
113#930—61no—
114#930—61no—
115#930—61no—
116C2×(C2×D3)⋊C4—21no—
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×#208C2×D312yes—
119#908—68no—
120C2×D24—34no—
121C2×#204—34no—
122#875—32no—
123#875—32no—
124#875—62no—
125#874—31no—
126#874—31no—
127#874—61no—
128C4×D12—21no—
129C4×D12—21no—
130C4×D12—62no—
131C4×D12—62no—
132C4×D12—61no—
133C4×D12—61no—
134C4×D12—61no—
135C4×D12—61no—
136C4×D12C2×D312yes—
137C4×D12C2×D312yes—
138#869—31no—
139#869—31no—
140#869—61no—
141C3×C4⋊C8—32no—
142C3×C4⋊C8—32no—
143#821—34no—
144#816—34no—
145#810—34no—
146#809—34no—
147C4⋊(C3⋊C8)C2×D312yescomplemented
148C4⋊(C3⋊C8)C2×D312yescomplemented
149C23×C32C2×D411yescharacteristic
150C22×C3⋊D3—22no—
151C22×C3×D3—24no—
152C22×C3×D3—22no—
153C22×C3×D3—42no—
154C22×C3×D3—42no—
155C2×C32×C4—22no—
156C2×C32×C4—41no—
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4#4112yes—
164C2×C32×C4C2411yescharacteristic
165#638—44no—
166C2×C3⋊Dic3—22no—
167C4⋊(C3⋊D3)—22no—
168C4⋊(C3⋊D3)—22no—
169C4⋊(C3⋊D3)—42no—
170C4⋊(C3⋊D3)—42no—
171C4×C3⋊D3—44no—
172#634—22no—
173#634—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—42no—
176C3×D12—24no—
177C3×D12—22no—
178C3×D12C2×D414yes—
179C3×C4×D3—44no—
180C3×C4×D3—44no—
181C3×C3⋊C8—24no—
182C2×AGL(1,ℤ/8)—92no—
183#532—91no—
184C2×C4×D4—31no—
185#463—94no—
186#461—92no—
187#459—92no—
188#423—31no—
189#417—92no—
190C24×C3—61no—
191C23×D3—21no—
192C2×C3×D4—34no—
193C2×C3×D4—32no—
194C2×C3×D4—61no—
195C2×C3×D4—62no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—61no—
200C22×C3×C4—62no—
201C22×C3×C4—62no—
202C22×C3×C4—124no—
203C22×C3×C4D1211yescharacteristic
204C22×C3×C4D1211yescharacteristic
205C22×C3×C4#6711yescharacteristic
206C22×C3×C4#6711yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C2×#67—64no—
210C2×#67—62no—
211C2×#67—62no—
212C22×Dic3—21no—
213#235—64no—
214#235—64no—
215#235—64no—
216#235—64no—
217#235—124no—
218#235—124no—
219C2×D12—22no—
220C2×D12—21no—
221C2×D12—32no—
222C2×D12—32no—
223C2×D12—62no—
224C2×D12—62no—
225C2×D12—62no—
226C2×D12—61no—
227C2×D12—61no—
228C2×D12—61no—
229C2×D12—61no—
230C2×D12D1214yescomplemented
231C2×D12C22×D312yes—
232C2×C4×D3—22no—
233C2×C4×D3—22no—
234C2×C4×D3—44no—
235C2×C4×D3—64no—
236C2×C4×D3—62no—
237C2×C4×D3—62no—
238C2×Dic6—32no—
239C2×Dic6—32no—
240C2×Dic6—62no—
241C3×M16—64no—
242C2×C3×C8—34no—
243C3×C4⋊C4—32no—
244C3×C4⋊C4—61no—
245C3×C22⋊C4—62no—
246C3×C22⋊C4—62no—
247C3×C42—21no—
248C3×C42—21no—
249C3×C42—21no—
250C3×C42—21no—
251C3×C42D1211yescharacteristic
252C3×C42D1211yescharacteristic
253C3×C42#6711yescharacteristic
254C3×C42#6711yescharacteristic
255C3×C42C22×D311yescharacteristic
256C3×C42C22×D311yescharacteristic
257C3×C42C22×D311yescharacteristic
258C3×C42C22×D311yescharacteristic
259#214—68no—
260#213—68no—
261(C2×D3)⋊C4—22no—
262(C2×D3)⋊C4—22no—
263(C2×D3)⋊C4—64no—
264(C2×D3)⋊C4—64no—
265(C2×D3)⋊C4—62no—
266(C2×D3)⋊C4—62no—
267(C2×D3)⋊C4—62no—
268(C2×D3)⋊C4—62no—
269C4⋊Dic3—21no—
270C4⋊Dic3—62no—
271C4⋊Dic3—62no—
272C4⋊Dic3—61no—
273C4⋊Dic3—61no—
274C4⋊Dic3—61no—
275C4⋊Dic3—61no—
276C4⋊Dic3C22×D312yes—
277#208—24no—
278C2×C3⋊C8C22×D314yes—
279D24—68no—
280#204—68no—
281C22×C32—21no—
282C22×C32—21no—
283C22×C32#12112yes—
284C22×C32C22×D411yescharacteristic
285C2×C3⋊D3—42no—
286C2×C3⋊D3—42no—
287C2×C3⋊D3—42no—
288C2×C3×D3—24no—
289C2×C3×D3—48no—
290C2×C3×D3—42no—
291C2×C3×D3—42no—
292C32×C4—21no—
293C32×C4—21no—
294C32×C4—21no—
295C32×C4#12112yes—
296C32×C4AGL(1,ℤ/8)12yescomplemented
297C32×C4C22×D411yescharacteristic
298C32×C4C2×#4111yescharacteristic
299C3⋊Dic3—42no—
300C3×Dic3—42no—
301C2×#41—92no—
302C22×D4—31no—
303C23×C4—61no—
304AGL(1,ℤ/8)—188no—
305C2×SD16—94no—
306C2×D8—94no—
307C2×M16—32no—
308C4⋊Q8—91no—
309#127—91no—
310#124—92no—
311#121—181no—
312#121—181no—
313C4×D4—32no—
314C4×D4—32no—
315C4×D4—61no—
316C4×D4—61no—
317C4×D4—181no—
318C4×D4—181no—
319C2×C4⋊C4—31no—
320C2×C22⋊C4—61no—
321C2×C42D3211yescharacteristic
322C4⋊C8—32no—
323C4⋊C8—32no—
324#103—94no—
325#102—94no—
326C23×C3—21no—
327C23×C3—64no—
328C23×C3—62no—
329C23×C3—122no—
330C23×C3—122no—
331C23×C3C2×D1211yescharacteristic
332C23×C3C2×#6711yescharacteristic
333C22×D3—24no—
334C22×D3—22no—
335C22×D3—42no—
336C22×D3—42no—
337C22×D3—64no—
338C22×D3—62no—
339C22×D3—62no—
340C3×D4—34no—
341C3×D4—64no—
342C3×D4—62no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—42no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4—42no—
357C2×C3×C4—62no—
358C2×C3×C4—124no—
359C2×C3×C4—122no—
360C2×C3×C4—124no—
361C2×C3×C4C2×D1212yes—
362C2×C3×C4C2×D1211yescharacteristic
363C2×C3×C4C2×D1211yescharacteristic
364C2×C3×C4C2×D1211yescharacteristic
365C2×C3×C4C2×D1211yescharacteristic
366C2×C3×C4C2×D1211yescharacteristic
367C2×C3×C4#23512yes—
368C2×C3×C4D3×D412yes—
369C2×C3×C4#23912yes—
370C2×C3×C4C2×#6711yescharacteristic
371C2×C3×C4C2×#6711yescharacteristic
372C2×C3×C4C2×#6711yescharacteristic
373C2×C3×C4C2×#6711yescharacteristic
374C2×C3×C4C2×#6711yescharacteristic
375C2×C3×C4C23×D311yescharacteristic
376C2×C3×C4C23×D311yescharacteristic
377#67—128no—
378#67—124no—
379#67—124no—
380C2×Dic3—22no—
381C2×Dic3—42no—
382C2×Dic3—64no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385D12—24no—
386D12—22no—
387D12—62no—
388D12—62no—
389D12—62no—
390D12—62no—
391D12—122no—
392D12—122no—
393D12—124no—
394D12—122no—
395D12—122no—
396D12—124no—
397D12—122no—
398D12—122no—
399D12C2×D1214yes—
400C4×D3—44no—
401C4×D3—44no—
402C4×D3—128no—
403C4×D3—124no—
404C4×D3—124no—
405Dic6—62no—
406Dic6—62no—
407Dic6—62no—
408Dic6—62no—
409Dic6—122no—
410Dic6—122no—
411C3×C8—64no—
412C3⋊C8—24no—
413C2×C32—22no—
414C2×C32C2×#12111yescharacteristic
415C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
416C2×C32#57511yescharacteristic
417C3⋊D3—82no—
418C3×D3—44no—
419C24—61no—
420#41—184no—
421#41—184no—
422C2×Q8—92no—
423C2×D4—32no—
424C2×D4—34no—
425C2×D4—62no—
426C2×D4—61no—
427C2×D4—92no—
428C2×D4—182no—
429C2×D4—181no—
430C2×D4—181no—
431C22×C4—61no—
432C22×C4—62no—
433C22×C4—62no—
434C22×C4—124no—
435C22×C4—182no—
436C22×C4#62611yescharacteristic
437C22×C4#62611yescharacteristic
438C22×C4C2×D3211yescharacteristic
439SD16—188no—
440D8—188no—
441M16—64no—
442C2×C8—34no—
443C4⋊C4—32no—
444C4⋊C4—61no—
445C4⋊C4—181no—
446C4⋊C4—181no—
447C22⋊C4—62no—
448C22⋊C4—62no—
449C22⋊C4—182no—
450C22⋊C4—182no—
451C42#62611yescharacteristic
452C42#62611yescharacteristic
453C42C2×D3211yescharacteristic
454C42C2×D3211yescharacteristic
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—22no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—64no—
464C22×C3—128no—
465C22×C3—122no—
466C22×C3—122no—
467C22×C3#89512yes—
468C22×C3#93012yes—
469C22×C3C22×D1211yescharacteristic
470C22×C3C22×#6711yescharacteristic
471C2×D3—24no—
472C2×D3—48no—
473C2×D3—42no—
474C2×D3—42no—
475C2×D3—124no—
476C2×D3—124no—
477C2×D3—124no—
478C2×D3—122no—
479C2×D3—122no—
480C2×D3—122no—
481C2×D3—122no—
482C2×D3—122no—
483C2×D3—122no—
484C3×C4—22no—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—22no—
494C3×C4—22no—
495C3×C4—41no—
496C3×C4—41no—
497C3×C4—122no—
498C3×C4#89512yes—
499C3×C4#90812yescomplemented
500C3×C4#93012yes—
501C3×C4#93212yescomplemented
502C3×C4C22×D1211yescharacteristic
503C3×C4C2×#23511yescharacteristic
504C3×C4C2×D3×D411yescharacteristic
505C3×C4C2×#23911yescharacteristic
506Dic3—42no—
507Dic3—124no—
508Dic3—122no—
509Dic3—122no—
510C32#303611yescharacteristic, complemented, Sylow
511C23—62no—
512C23—64no—
513C23—122no—
514C23—122no—
515C23—182no—
516C23C2×#62611yescharacteristic
517Q8—182no—
518Q8—182no—
519D4—34no—
520D4—62no—
521D4—64no—
522D4—182no—
523D4—182no—
524D4—362no—
525D4—364no—
526D4—362no—
527C2×C4—22no—
528C2×C4—41no—
529C2×C4—62no—
530C2×C4—124no—
531C2×C4—122no—
532C2×C4—124no—
533C2×C4—182no—
534C2×C4—364no—
535C2×C4#379912yes—
536C2×C4D3×D1212yes—
537C2×C4C2×#62611yescharacteristic
538C2×C4C2×#62611yescharacteristic
539C2×C4C2×#62611yescharacteristic
540C2×C4C2×#62611yescharacteristic
541C2×C4C2×#62611yescharacteristic
542C2×C4C22×D3211yescharacteristic
543C8—64no—
544C2×C3—22no—
545C2×C3—22no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—42no—
550C2×C3—124no—
551C2×C3C2×#89511yescharacteristic
552C2×C3C2×#90811yescharacteristic
553C2×C3#574811yescharacteristic
554C2×C3C2×#93011yescharacteristic
555C2×C3C2×#93211yescharacteristic
556C2×C3#582211yescharacteristic
557D3—44no—
558D3—244no—
559D3—242no—
560D3—242no—
561C22—21no—
562C22—21no—
563C22—64no—
564C22—128no—
565C22—122no—
566C22—122no—
567C22—362no—
568C22—362no—
569C22—362no—
570C22#6390912yes—
571C22C22×#62611yescharacteristic
572C4—21no—
573C4—21no—
574C4—21no—
575C4—122no—
576C4—362no—
577C4#6383012yescomplemented
578C4#6390912yes—
579C4C2×#379911yescharacteristic
580C4C2×D3×D1211yescharacteristic
581C3—21no—
582C3#7905511yescharacteristic, complemented
583C3#8230711yescharacteristic, complemented
584C2—22no—
585C2—124no—
586C2—722no—
587C2C2×#6383011yescharacteristic
588C2#1059479511yescharacteristic
589C2C2×#6390911yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
hypercenterC2×C42D32
hypocenterC32#3036
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595948C2semidirect
2. C2×C3×C4×D12C2semidirect
3. C2×#63830C2semidirect
4. C3×#4924C2semidirect
5. #10591106C2semidirect
6. #10590366C2semidirect
7. #10590365C2semidirect
8. #10590349C2semidirect
17. #64084C22semidirect
18. #64083C22semidirect
21. #64078C22semidirect
32. C3×C4⋊(C3⋊C8)C22semidirect
33. C3×C4⋊(C3⋊C8)C22semidirect
34. #63567C22semidirect
35. #63564C22semidirect
42. C2×C4×D12D3semidirect
49. #4924D3semidirect
68. C2×C3×D12D4semidirect
147. C4⋊(C3⋊C8)C2×D3semidirect
148. C4⋊(C3⋊C8)C2×D3semidirect
230. C2×D12D12semidirect
296. C32×C4AGL(1,ℤ/8)semidirect
499. C3×C4#908semidirect
501. C3×C4#932semidirect
510. C32#3036semidirect
577. C4#63830semidirect
582. C3#79055semidirect
583. C3#82307semidirect

Maximal subgroups

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

subgroupindex
#105959482
C2×C3×C4×D122
C2×#638302
C3×#49242
#105911062
#105903662
#105903652
#105903492
#823073
#790553