Finite Group Databasebeta

← #11870461

Subgroups — #11870461

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 643 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic, complemented
2#10594910C211yesmaximal, characteristic, complemented
3#10592666C211yesmaximal, characteristic, complemented
4C3×#4967C211yesmaximal, characteristic, complemented
5#10591162C211yesmaximal, characteristic, complemented
6#10591160C211yesmaximal, characteristic, complemented
7#10591053C211yesmaximal, characteristic, complemented
8#10590555C212yesmaximal, complemented
9#10590547C212yesmaximal, complemented
10#10590456C212yesmaximal, complemented
11#10590452C212yesmaximal, complemented
12#82308—31nomaximal
13#81268—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3—21no—
16C2×#3804—21no—
17C2×C32×C4⋊C4C2211yescharacteristic
18#64139C2211yescharacteristic
19C3×#930C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4—21no—
21C2×C3×C4×Dic3C2211yescharacteristic
22C3×#893—21no—
23C3×#893—21no—
24C3×#893C2212yes—
25C3×#893C2212yes—
26#63978—21no—
27#63918C2211yescharacteristic, complemented
28#63911C2211yescharacteristic, complemented
29#63894C2211yescharacteristic, complemented
30Dic3×D12C2211yescharacteristic, complemented
31#63880—21no—
32#63852—21no—
33C2×#3714C2212yes—
34C2×#3713C2212yes—
35#63657C2211yescharacteristic
36#63636C2212yescomplemented
37#63634C2212yescomplemented
38C3×#830C2211yescharacteristic
39C3×#809C2212yescomplemented
40C3×#807C2212yescomplemented
41Dic3⋊(C3⋊C8)C2212yescomplemented
42#63563C2212yes—
43#63562C2212yes—
44Dic3×C3⋊C8C2212yescomplemented
45C2×C3×C4×D4—31no—
46#5596—31no—
47C2×#893D311yescharacteristic, complemented
48#5477—31no—
49C3×#480—31no—
50#5217—31no—
51#5217—31no—
52#5036—31no—
53#5015—32no—
54C4×#213—32no—
55C4×#213—32no—
56#5007—32no—
57#4967—31no—
58#4967—31no—
59#4967—61no—
60#4967D311yescharacteristic, complemented
61#4925—31no—
62#4890—32no—
63#4872—32no—
64#4786—32no—
65#4756—32no—
66#4732—31no—
67#4718—31no—
68C23×C3×D3—21no—
69C22×C32×C4—21no—
70C22×C32×C4C2311yescharacteristic
71C2×#638—21no—
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C3×#67—21no—
74C22×C3×Dic3D411yescharacteristic
75C22×C3×Dic3D411yescharacteristic
76C2×C3×D12—21no—
77C2×C3×D12—24no—
78C2×C3×D12C2311yescharacteristic
79C2×C3×D12C2312yes—
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3—22no—
82C2×C3×C4×D3—44no—
83C2×#627—21no—
84C2×#626—21no—
85C2×#626—21no—
86C2×#624—21no—
87#3804—44no—
88C2×D3×Dic3—21no—
89C32×C4⋊C4—21no—
90C32×C4⋊C4C2312yes—
91#3752—21no—
92C4⋊(C3⋊Dic3)C2311yescharacteristic
93C2×C3⋊(C3⋊C8)C2312yes—
94C3×(C2×D3)⋊C4—21no—
95C3×(C2×D3)⋊C4—22no—
96C3×(C2×D3)⋊C4—22no—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C3×C4×Dic3C2311yescharacteristic
102C2×C3×C3⋊C8C2312yes—
103Dic3⋊Dic3—21no—
104#3722—21no—
105(C2×D3)⋊Dic3—21no—
106#3714—24no—
107#3713—24no—
108#3100—91noSylow
109C22×C3×D4—31no—
110C23×C3×C4—61no—
111C2×#237—61no—
112C2×#235—61no—
113C22×D12C2×D311yescharacteristic
114C22×C4×D3—21no—
115C3×#121—31no—
116C3×C4×D4—32no—
117C3×C4×D4—32no—
118C3×C4×D4—61no—
119C3×C4×D4—61no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4C2×D311yescharacteristic
122C2×C3×C4⋊C4C2×D311yescharacteristic
123C2×C3×C22⋊C4—61no—
124C2×C3×C42—31no—
125#940—31no—
126#939—61no—
127D4×Dic3—31no—
128C2×#213—32no—
129C2×#213—32no—
130C2×#213—32no—
131#930—31no—
132#930—31no—
133#930—61no—
134#930—61no—
135#930C2×D311yescharacteristic
136C2×(C2×D3)⋊C4—21no—
137C2×C4×Dic3C2×D311yescharacteristic
138C2×D24—32no—
139#893—21no—
140#893—21no—
141#893—31no—
142#893C2×D312yes—
143#893C2×D312yes—
144#888—31no—
145#885—61no—
146#67⋊C4—61no—
147#875—61no—
148#874—31no—
149C4×D12—31no—
150C4×D12—31no—
151C4×D12—61no—
152#869—31no—
153C3×#107—32no—
154C3×#102—32no—
155C3×C22⋊C8—31no—
156#832—32no—
157#832—32no—
158#830—31no—
159#830—31no—
160#830—61no—
161#830C2×D311yescharacteristic
162#821—32no—
163Dic3⋊C8—32no—
164C8×Dic3—32no—
165#809—32no—
166#809—32no—
167#809—32no—
168#809—62no—
169#809C2×D312yescomplemented
170#807—32no—
171#807—32no—
172#807—62no—
173#807C2×D312yescomplemented
174C4⋊(C3⋊C8)—32no—
175C4×C3⋊C8—32no—
176C23×C32C2×D411yescharacteristic
177C22×C3⋊D3—21no—
178C22×C3×D3—24no—
179C22×C3×D3—22no—
180C22×C3×D3—21no—
181C22×C3×D3—42no—
182C22×C3×D3—42no—
183C2×C32×C4—22no—
184C2×C32×C4—22no—
185C2×C32×C4—42no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2411yescharacteristic
188#638—42no—
189C2×C3⋊Dic3—21no—
190C4⋊(C3⋊D3)—22no—
191C3×#67—42no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—41no—
194C2×C3×Dic3D814yescomplemented
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C3×D12—24no—
200C3×D12—22no—
201C3×D12—22no—
202C3×D12#4114yescomplemented
203C3×C4×D3—44no—
204C3×C4×D3—44no—
205#627—42no—
206#626—42no—
207#626—42no—
208#624—42no—
209D3×Dic3—42no—
210C3⋊(C3⋊C8)—22no—
211C3×C3⋊C8—22no—
212#532—91no—
213C2×C4×D4—31no—
214#480—31no—
215#480—91no—
216#474—92no—
217#459—92no—
218#447—91no—
219#447—91no—
220C4×D8—92no—
221C4×D8—92no—
222#431—91no—
223C24×C3—61no—
224C23×D3—21no—
225C2×C3×D4—32no—
226C2×C3×D4—31no—
227C2×C3×D4—64no—
228C2×C3×D4—61no—
229C2×C3×D4—61no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—31no—
234C22×C3×C4—31no—
235C22×C3×C4—41no—
236C22×C3×C4—62no—
237C22×C3×C4—62no—
238C22×C3×C4—124no—
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C2×#67—21no—
242C2×#67—61no—
243C2×#67—61no—
244C2×#67—61no—
245C2×#67—61no—
246C2×#67—121no—
247C22×Dic3—61no—
248C22×Dic3#6711yescharacteristic
249C22×Dic3#6711yescharacteristic
250#237—124no—
251#235—124no—
252C2×D12—21no—
253C2×D12—24no—
254C2×D12—31no—
255C2×D12—31no—
256C2×D12—61no—
257C2×D12—61no—
258C2×D12—61no—
259C2×D12C22×D311yescharacteristic
260C2×D12C22×D312yes—
261C2×C4×D3—22no—
262C2×C4×D3—22no—
263C2×C4×D3—44no—
264C2×C4×D3—61no—
265C2×C4×D3—61no—
266C2×C4×D3—61no—
267C2×Dic6—61no—
268C2×Dic6—61no—
269C2×C3×C8—32no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—22no—
273C3×C4⋊C4—31no—
274C3×C4⋊C4—41no—
275C3×C4⋊C4C22×D312yes—
276C3×C4⋊C4C22×D312yes—
277C3×C22⋊C4—62no—
278C3×C22⋊C4—62no—
279C3×C22⋊C4—61no—
280C3×C42—31no—
281C3×C42—31no—
282C3×C42—31no—
283C3×C42—31no—
284#217—61no—
285#213—64no—
286#213—64no—
287#213—64no—
288(C2×D3)⋊C4—21no—
289(C2×D3)⋊C4—22no—
290(C2×D3)⋊C4—22no—
291(C2×D3)⋊C4—61no—
292(C2×D3)⋊C4—61no—
293(C2×D3)⋊C4—61no—
294(C2×D3)⋊C4—61no—
295(C2×D3)⋊C4—61no—
296(C2×D3)⋊C4—121no—
297C4⋊Dic3—31no—
298C4⋊Dic3—31no—
299C4⋊Dic3—61no—
300C4⋊Dic3—61no—
301C4⋊Dic3C22×D311yescharacteristic
302Dic3⋊C4—61no—
303C4×Dic3#6711yescharacteristic
304C4×Dic3#6711yescharacteristic
305C4×Dic3C22×D311yescharacteristic
306C4×Dic3C22×D311yescharacteristic
307C2×C3⋊C8—32no—
308C2×C3⋊C8—32no—
309C2×C3⋊C8—62no—
310C2×C3⋊C8C22×D312yes—
311D24—64no—
312C22×C32—21no—
313C22×C32—21no—
314C22×C32C2×D812yes—
315C22×C32C22×D411yescharacteristic
316C2×C3⋊D3—41no—
317C2×C3⋊D3—41no—
318C2×C3⋊D3—41no—
319C2×C3×D3—24no—
320C2×C3×D3—48no—
321C2×C3×D3—42no—
322C2×C3×D3—42no—
323C2×C3×D3—41no—
324C2×C3×D3—41no—
325C2×C3×D3—41no—
326C32×C4—21no—
327C32×C4—42no—
328C32×C4C2×#4112yes—
329C3⋊Dic3—41no—
330C3×Dic3—21no—
331C3×Dic3—21no—
332C3×Dic3—41no—
333C3×Dic3C2×D812yes—
334C3×Dic3C2×D812yes—
335C2×#41—181no—
336C22×D4—31no—
337C23×C4—61no—
338C2×D8—92no—
339C2×D8—92no—
340C4⋊Q8—91no—
341#127—91no—
342#124—181no—
343#121—31no—
344#121—91no—
345#121—181no—
346C4×D4—32no—
347C4×D4—32no—
348C4×D4—61no—
349C4×D4—61no—
350C4×D4—91no—
351C4×D4—91no—
352C4×D4—181no—
353C2×C4⋊C4D3211yescharacteristic
354C2×C22⋊C4—61no—
355C2×C42—31no—
356#107—32no—
357#107—92no—
358C4⋊C8—92no—
359#102—32no—
360#102—92no—
361#102—92no—
362#102—92no—
363C22⋊C8—31no—
364C22⋊C8—91no—
365C4×C8—92no—
366C23×C3—21no—
367C23×C3—64no—
368C23×C3—62no—
369C23×C3—61no—
370C23×C3—122no—
371C23×C3—122no—
372C23×C3D3×D411yescharacteristic
373C23×C3C2×#6711yescharacteristic
374C22×D3—24no—
375C22×D3—22no—
376C22×D3—21no—
377C22×D3—42no—
378C22×D3—42no—
379C22×D3—61no—
380C22×D3—61no—
381C22×D3—121no—
382C3×D4—34no—
383C3×D4—64no—
384C3×D4—62no—
385C3×D4—62no—
386C3×D4—122no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—34no—
394C2×C3×C4—31no—
395C2×C3×C4—31no—
396C2×C3×C4—31no—
397C2×C3×C4—31no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—61no—
403C2×C3×C4—82no—
404C2×C3×C4—124no—
405C2×C3×C4—124no—
406C2×C3×C4—121no—
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4C2×#6711yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411#67—42no—
412#67—122no—
413#67—122no—
414#67—122no—
415#67—122no—
416#67—242no—
417C2×Dic3—21no—
418C2×Dic3—41no—
419C2×Dic3—61no—
420C2×Dic3—61no—
421C2×Dic3—121no—
422C2×Dic3—122no—
423C2×Dic3#21314yescomplemented
424C2×Dic3C2×#6711yescharacteristic
425C2×Dic3C2×#6711yescharacteristic
426C2×Dic3C2×#6711yescharacteristic
427C2×Dic3C2×#6711yescharacteristic
428D12—24no—
429D12—22no—
430D12—22no—
431D12—62no—
432D12—62no—
433D12—122no—
434D12—122no—
435D12—122no—
436D12#23514yescomplemented
437C4×D3—44no—
438C4×D3—44no—
439C4×D3—122no—
440C4×D3—122no—
441C4×D3—122no—
442Dic6—122no—
443Dic6—122no—
444C3×C8—62no—
445C3⋊C8—22no—
446C3⋊C8—62no—
447C3⋊C8—62no—
448C3⋊C8—122no—
449C2×C32—22no—
450C2×C32#52511yescharacteristic
451C2×C32C22×D811yescharacteristic
452C2×C32#57511yescharacteristic
453C3⋊D3—81no—
454C3×D3—44no—
455C3×D3—81no—
456C24—61no—
457#41—364no—
458C2×Q8—181no—
459C2×D4—32no—
460C2×D4—31no—
461C2×D4—64no—
462C2×D4—61no—
463C2×D4—61no—
464C2×D4—91no—
465C2×D4—181no—
466C2×D4—181no—
467C2×D4—181no—
468C22×C4—21no—
469C22×C4—31no—
470C22×C4—31no—
471C22×C4—62no—
472C22×C4—62no—
473C22×C4—124no—
474C22×C4—181no—
475C22×C4—181no—
476C22×C4C2×D3211yescharacteristic
477D8—184no—
478D8—184no—
479C2×C8—32no—
480C2×C8—92no—
481C4⋊C4—21no—
482C4⋊C4—31no—
483C4⋊C4—91no—
484C4⋊C4—181no—
485C4⋊C4C2×D3212yes—
486C22⋊C4—62no—
487C22⋊C4—62no—
488C22⋊C4—61no—
489C22⋊C4—181no—
490C22⋊C4—181no—
491C22⋊C4—181no—
492C42—31no—
493C42—31no—
494C42—31no—
495C42—31no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—22no—
502C22×C3—41no—
503C22×C3—41no—
504C22×C3—64no—
505C22×C3—128no—
506C22×C3—122no—
507C22×C3—122no—
508C22×C3—121no—
509C22×C3—121no—
510C22×C3—121no—
511C22×C3D3×D812yes—
512C22×C3C2×#21312yes—
513C22×C3C2×D3×D411yescharacteristic
514C22×C3C22×#6711yescharacteristic
515C2×D3—24no—
516C2×D3—48no—
517C2×D3—42no—
518C2×D3—42no—
519C2×D3—41no—
520C2×D3—41no—
521C2×D3—41no—
522C2×D3—121no—
523C2×D3—121no—
524C2×D3—121no—
525C2×D3—121no—
526C2×D3—121no—
527C2×D3—121no—
528C2×D3—241no—
529C2×D3—241no—
530C2×D3—241no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—22no—
534C3×C4—32no—
535C3×C4—32no—
536C3×C4—41no—
537C3×C4—42no—
538C3×C4—42no—
539C3×C4—61no—
540C3×C4—61no—
541C3×C4—82no—
542C3×C4—121no—
543C3×C4C2×#23512yes—
544C3×C4D3×#4112yes—
545Dic3—21no—
546Dic3—21no—
547Dic3—41no—
548Dic3—121no—
549Dic3—121no—
550Dic3—241no—
551Dic3C2×#21312yes—
552Dic3C2×#21312yes—
553C32#310011yescharacteristic, complemented, Sylow
554C23—64no—
555C23—62no—
556C23—61no—
557C23—122no—
558C23—122no—
559C23—181no—
560C23D3×#6711yescharacteristic
561Q8—362no—
562D4—34no—
563D4—64no—
564D4—62no—
565D4—62no—
566D4—122no—
567D4—182no—
568D4—362no—
569D4—362no—
570D4—362no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—31no—
574C2×C4—31no—
575C2×C4—34no—
576C2×C4—31no—
577C2×C4—31no—
578C2×C4—42no—
579C2×C4—61no—
580C2×C4—124no—
581C2×C4—124no—
582C2×C4—121no—
583C2×C4—181no—
584C2×C4—362no—
585C2×C4—362no—
586C2×C4D3×#6711yescharacteristic
587C2×C4C22×D3211yescharacteristic
588C8—62no—
589C8—182no—
590C2×C3—22no—
591C2×C3—22no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—42no—
596C2×C3—124no—
597C2×C3—241no—
598C2×C3#565611yescharacteristic
599C2×C3C2×D3×D811yescharacteristic
600C2×C3#577711yescharacteristic
601C2×C3#579111yescharacteristic
602C2×C3C22×#21311yescharacteristic
603C2×C3#582211yescharacteristic
604D3—44no—
605D3—81no—
606D3—241no—
607D3—241no—
608D3—481no—
609C22—21no—
610C22—21no—
611C22—64no—
612C22—128no—
613C22—122no—
614C22—122no—
615C22—121no—
616C22—121no—
617C22—121no—
618C22—361no—
619C22—361no—
620C22—361no—
621C22D3×#21312yes—
622C22C2×D3×#6711yescharacteristic
623C4—21no—
624C4—32no—
625C4—32no—
626C4—42no—
627C4—61no—
628C4—61no—
629C4—121no—
630C4—361no—
631C4D3×#23512yes—
632C3—21no—
633C3#8126811yescharacteristic, complemented
634C3#8230811yescharacteristic, complemented
635C2—22no—
636C2—124no—
637C2—241no—
638C2—721no—
639C2#1059489611yescharacteristic
640C2C2×D3×#21311yescharacteristic
641C2#1059531711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#893C2semidirect
2. #10594910C2semidirect
3. #10592666C2semidirect
4. C3×#4967C2semidirect
5. #10591162C2semidirect
6. #10591160C2semidirect
7. #10591053C2semidirect
8. #10590555C2semidirect
9. #10590547C2semidirect
10. #10590456C2semidirect
11. #10590452C2semidirect
27. #63918C22semidirect
28. #63911C22semidirect
29. #63894C22semidirect
30. Dic3×D12C22semidirect
36. #63636C22semidirect
37. #63634C22semidirect
39. C3×#809C22semidirect
40. C3×#807C22semidirect
41. Dic3⋊(C3⋊C8)C22semidirect
44. Dic3×C3⋊C8C22semidirect
47. C2×#893D3semidirect
60. #4967D3semidirect
169. #809C2×D3semidirect
173. #807C2×D3semidirect
194. C2×C3×Dic3D8semidirect
202. C3×D12#41semidirect
423. C2×Dic3#213semidirect
436. D12#235semidirect
553. C32#3100semidirect
633. C3#81268semidirect
634. C3#82308semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
#105949102
#105926662
C3×#49672
#105911622
#105911602
#105910532
#105905552
#105905472
#105904562
#105904522
#823083
#812683