Finite Group Databasebeta

← #11871274

Subgroups — #11871274

Order 1152.

1075 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
2#10594910C211yesmaximal, characteristic, complemented
3#10592916C211yesmaximal, characteristic, complemented
4C3×#5217C211yesmaximal, characteristic, complemented
5#10591481C212yesmaximal, complemented
6#10591430C212yesmaximal, complemented
7#10591408C212yesmaximal, complemented
8#10591404C212yesmaximal, complemented
9#10591125C211yesmaximal, characteristic, complemented
10#10591091C211yesmaximal, characteristic, complemented
11#10591063C211yesmaximal, characteristic, complemented
12#82310—31nomaximal
13#79990—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C23×C3×Dic3—21no—
16C2×#3804—21no—
17C2×#3753C2212yes—
18#64139C2211yescharacteristic
19C2×C3×#217—21no—
20C3×D4×Dic3—21no—
21C3×D4×Dic3—21no—
22C3×D4×Dic3C2212yes—
23C3×D4×Dic3C2212yes—
24C2×C3×#213C2212yes—
25C3×#930C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28#63978—21no—
29#63918C2211yescharacteristic, complemented
30#63911C2211yescharacteristic, complemented
31#63894C2211yescharacteristic, complemented
32Dic3×D12C2211yescharacteristic, complemented
33#63880—21no—
34#63852—21no—
35#63659C2212yes—
36#63657C2211yescharacteristic
37C3×#832C2212yes—
38C3×#830C2211yescharacteristic
39#63574C2212yescomplemented
40#63573C2212yescomplemented
41Dic3⋊(C3⋊C8)C2212yescomplemented
42#63564C2212yescomplemented
43#63562C2212yescomplemented
44#63554C2212yescomplemented
45C2×C3×C4×D4—31no—
46C2×D4×Dic3D311yescharacteristic, complemented
47#5596—31no—
48#5477—31no—
49C3×#447—31no—
50#5217—31no—
51#5217—31no—
52#5217—61no—
53#5217D311yescharacteristic, complemented
54#5152—32no—
55#5150—32no—
56#5034—31no—
57#5015—32no—
58#5014—32no—
59#5014—32no—
60#5008—32no—
61#4968—31no—
62#4968—31no—
63#4926—31no—
64#4785—32no—
65#4761—32no—
66#4735—31no—
67#4719—31no—
68C24×C32—21no—
69C2×C32×D4—24no—
70C2×C32×D4—21no—
71C2×C32×D4C2312yes—
72C22×C32×C4C2311yescharacteristic
73C2×#638—21no—
74C2×C4⋊(C3⋊D3)C2311yescharacteristic
75C2×C3×#67—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3—22no—
78C22×C3×Dic3—22no—
79C22×C3×Dic3—44no—
80C22×C3×Dic3D411yescharacteristic
81C22×C3×Dic3D411yescharacteristic
82C2×C3×D12C2311yescharacteristic
83C2×#627—21no—
84C2×#626—21no—
85C2×#626—21no—
86C2×#624—21no—
87#3804—44no—
88C2×D3×Dic3—21no—
89#3753—24no—
90#3752—21no—
91C4⋊(C3⋊Dic3)C2311yescharacteristic
92C2×C3⋊(C3⋊C8)C2312yes—
93C3×#217—22no—
94C3×#217—22no—
95C3×#213—24no—
96C3×(C2×D3)⋊C4—21no—
97C3×C4⋊Dic3—21no—
98C3×C4⋊Dic3C2312yes—
99C3×C4⋊Dic3C2311yescharacteristic
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C2×C3×C3⋊C8C2312yes—
105Dic3⋊Dic3—21no—
106#3722—21no—
107(C2×D3)⋊Dic3—21no—
108#3109—91noSylow
109C22×C3×D4—21no—
110C22×C3×D4C2×D311yescharacteristic
111C22×C3×D4C2×D311yescharacteristic
112C23×C3×C4—61no—
113C23×Dic3—21no—
114C2×#237—61no—
115C2×#235—61no—
116C2×C3×D8—32no—
117C3×#121—31no—
118C3×C4×D4—32no—
119C3×C4×D4—32no—
120C3×C4×D4—61no—
121C3×C4×D4—61no—
122C2×C3×C4⋊C4—31no—
123C2×C3×C22⋊C4—61no—
124C2×C3×C42—31no—
125C2×#217—21no—
126#940—31no—
127#939—61no—
128D4×Dic3—21no—
129D4×Dic3—21no—
130D4×Dic3—31no—
131D4×Dic3C2×D312yes—
132D4×Dic3C2×D312yes—
133C2×#213—32no—
134C2×#213—32no—
135C2×#213—62no—
136C2×#213C2×D312yes—
137#930—31no—
138#930—31no—
139#930—61no—
140#930—61no—
141#930C2×D311yescharacteristic
142C2×C4⋊Dic3C2×D311yescharacteristic
143C2×C4×Dic3C2×D311yescharacteristic
144#893—31no—
145#888—31no—
146#885—61no—
147#67⋊C4—61no—
148#875—61no—
149#874—31no—
150C4×D12—31no—
151C4×D12—31no—
152C4×D12—61no—
153#869—31no—
154C3×#102—32no—
155C3×C22⋊C8—31no—
156#832—32no—
157#832—32no—
158#832—32no—
159#832—62no—
160#832C2×D312yes—
161#830—31no—
162#830—31no—
163#830—61no—
164#830C2×D311yescharacteristic
165#821—32no—
166#817—32no—
167#815—32no—
168Dic3⋊C8—32no—
169#809—32no—
170#809—32no—
171#808—32no—
172#808—32no—
173#808—32no—
174C4⋊(C3⋊C8)—32no—
175#803—32no—
176C23×C32—24no—
177C23×C32—22no—
178C23×C32—42no—
179C23×C32—42no—
180C23×C32C2×D411yescharacteristic
181C22×C3⋊D3—21no—
182C22×C3×D3—21no—
183C32×D4—24no—
184C32×D4—22no—
185C32×D4#4114yescomplemented
186C2×C32×C4—22no—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189#638—42no—
190C2×C3⋊Dic3—21no—
191C4⋊(C3⋊D3)—22no—
192C3×#67—42no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—44no—
198C2×C3×Dic3—42no—
199C2×C3×Dic3—44no—
200C2×C3×Dic3C2×D411yescharacteristic
201C2×C3×Dic3C2×D411yescharacteristic
202C2×C3×Dic3C2×D411yescharacteristic
203C2×C3×Dic3C2×D411yescharacteristic
204C3×D12—22no—
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#481—91no—
215#481—91no—
216#476—92no—
217#459—92no—
218#447—31no—
219#447—91no—
220#442—92no—
221#442—92no—
222#432—91no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—41no—
226C2×C3×D4—24no—
227C2×C3×D4—24no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—22no—
231C2×C3×D4—31no—
232C2×C3×D4—41no—
233C2×C3×D4—44no—
234C2×C3×D4—61no—
235C2×C3×D4C22×D312yes—
236C2×C3×D4C22×D312yes—
237C22×C3×C4—21no—
238C22×C3×C4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—62no—
241C22×C3×C4—62no—
242C22×C3×C4—61no—
243C22×C3×C4—124no—
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C2×#67—21no—
247C2×#67—61no—
248C2×#67—61no—
249C2×#67—61no—
250C2×#67—61no—
251C2×#67—121no—
252C22×Dic3—21no—
253C22×Dic3—22no—
254C22×Dic3—22no—
255C22×Dic3—44no—
256C22×Dic3—61no—
257C22×Dic3#6711yescharacteristic
258C22×Dic3#6711yescharacteristic
259#237—124no—
260#235—124no—
261C2×D12—31no—
262C2×D12—31no—
263C2×D12—61no—
264C2×D12—61no—
265C2×D12—61no—
266C2×D12C22×D311yescharacteristic
267C2×C4×D3—61no—
268C2×C4×D3—61no—
269C2×C4×D3—61no—
270C2×Dic6—61no—
271C2×Dic6—61no—
272C3×D8—64no—
273C2×C3×C8—32no—
274C3×C4⋊C4—32no—
275C3×C4⋊C4—31no—
276C3×C4⋊C4—61no—
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—22no—
285#217—22no—
286#217—61no—
287#213—24no—
288#213—64no—
289#213—64no—
290#213—124no—
291(C2×D3)⋊C4—21no—
292(C2×D3)⋊C4—61no—
293(C2×D3)⋊C4—61no—
294(C2×D3)⋊C4—61no—
295(C2×D3)⋊C4—61no—
296(C2×D3)⋊C4—61no—
297(C2×D3)⋊C4—121no—
298C4⋊Dic3—21no—
299C4⋊Dic3—31no—
300C4⋊Dic3—31no—
301C4⋊Dic3—61no—
302C4⋊Dic3—61no—
303C4⋊Dic3C22×D311yescharacteristic
304C4⋊Dic3C22×D312yes—
305Dic3⋊C4—61no—
306C4×Dic3#6711yescharacteristic
307C4×Dic3#6711yescharacteristic
308C4×Dic3C22×D311yescharacteristic
309C4×Dic3C22×D311yescharacteristic
310C2×C3⋊C8—32no—
311C2×C3⋊C8—32no—
312C2×C3⋊C8—62no—
313C2×C3⋊C8C22×D312yes—
314C22×C32—21no—
315C22×C32—21no—
316C22×C32—24no—
317C22×C32—48no—
318C22×C32—42no—
319C22×C32—42no—
320C22×C32AGL(1,ℤ/8)12yes—
321C22×C32C22×D411yescharacteristic
322C2×C3⋊D3—41no—
323C2×C3⋊D3—41no—
324C2×C3⋊D3—41no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C32×C4—21no—
329C32×C4C2×#4112yes—
330C3⋊Dic3—41no—
331C3×Dic3—21no—
332C3×Dic3—21no—
333C3×Dic3—21no—
334C3×Dic3—41no—
335C3×Dic3—42no—
336C3×Dic3AGL(1,ℤ/8)12yes—
337C2×#41—181no—
338C22×D4D3211yescharacteristic
339C23×C4—61no—
340C2×D8—32no—
341C2×D8—92no—
342C4⋊Q8—91no—
343#127—91no—
344#124—181no—
345#121—31no—
346#121—91no—
347#121—181no—
348C4×D4—32no—
349C4×D4—32no—
350C4×D4—61no—
351C4×D4—61no—
352C4×D4—91no—
353C4×D4—91no—
354C4×D4—181no—
355C2×C4⋊C4—31no—
356C2×C22⋊C4—61no—
357C2×C42—31no—
358#106—92no—
359#106—92no—
360C4⋊C8—92no—
361#102—32no—
362#102—92no—
363#102—92no—
364#102—92no—
365C22⋊C8—31no—
366C22⋊C8—91no—
367#97—92no—
368C23×C3—24no—
369C23×C3—24no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—21no—
373C23×C3—42no—
374C23×C3—44no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—61no—
380C23×C3—82no—
381C23×C3—82no—
382C23×C3D3×D411yescharacteristic
383C23×C3C2×#6711yescharacteristic
384C22×D3—21no—
385C22×D3—61no—
386C22×D3—61no—
387C22×D3—121no—
388C3×D4—24no—
389C3×D4—24no—
390C3×D4—22no—
391C3×D4—22no—
392C3×D4—24no—
393C3×D4—42no—
394C3×D4—44no—
395C3×D4—62no—
396C3×D4—122no—
397C3×D4#23514yescomplemented
398C3×D4#23714yescomplemented
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—31no—
404C2×C3×C4—31no—
405C2×C3×C4—31no—
406C2×C3×C4—31no—
407C2×C3×C4—42no—
408C2×C3×C4—62no—
409C2×C3×C4—62no—
410C2×C3×C4—62no—
411C2×C3×C4—61no—
412C2×C3×C4—124no—
413C2×C3×C4—124no—
414C2×C3×C4—122no—
415C2×C3×C4D3×D411yescharacteristic
416C2×C3×C4C2×#6711yescharacteristic
417C2×C3×C4C23×D311yescharacteristic
418C2×C3×C4C23×D311yescharacteristic
419#67—42no—
420#67—122no—
421#67—122no—
422#67—122no—
423#67—122no—
424#67—242no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—21no—
428C2×Dic3—22no—
429C2×Dic3—44no—
430C2×Dic3—42no—
431C2×Dic3—44no—
432C2×Dic3—61no—
433C2×Dic3—61no—
434C2×Dic3—121no—
435C2×Dic3—122no—
436C2×Dic3C2×#6711yescharacteristic
437C2×Dic3C2×#6711yescharacteristic
438C2×Dic3C2×#6711yescharacteristic
439C2×Dic3C2×#6711yescharacteristic
440D12—22no—
441D12—62no—
442D12—62no—
443D12—122no—
444D12—122no—
445D12—122no—
446C4×D3—122no—
447C4×D3—122no—
448C4×D3—122no—
449Dic6—122no—
450Dic6—122no—
451C3×C8—62no—
452C3⋊C8—22no—
453C3⋊C8—62no—
454C3⋊C8—62no—
455C3⋊C8—122no—
456C2×C32—22no—
457C2×C32—44no—
458C2×C32#52511yescharacteristic
459C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
460C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
461C3⋊D3—81no—
462C3×D3—81no—
463C24—21no—
464#41—364no—
465C2×Q8—181no—
466C2×D4—24no—
467C2×D4—21no—
468C2×D4—31no—
469C2×D4—61no—
470C2×D4—91no—
471C2×D4—181no—
472C2×D4—181no—
473C2×D4—181no—
474C2×D4C2×D3212yes—
475C22×C4—31no—
476C22×C4—31no—
477C22×C4—62no—
478C22×C4—62no—
479C22×C4—61no—
480C22×C4—124no—
481C22×C4—181no—
482C22×C4—181no—
483C22×C4C2×D3211yescharacteristic
484D8—64no—
485D8—184no—
486C2×C8—32no—
487C2×C8—92no—
488C4⋊C4—31no—
489C4⋊C4—32no—
490C4⋊C4—61no—
491C4⋊C4—91no—
492C4⋊C4—181no—
493C22⋊C4—62no—
494C22⋊C4—62no—
495C22⋊C4—61no—
496C22⋊C4—181no—
497C22⋊C4—181no—
498C22⋊C4—181no—
499C42—31no—
500C42—31no—
501C42—31no—
502C42—31no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—24no—
508C22×C3—24no—
509C22×C3—21no—
510C22×C3—22no—
511C22×C3—41no—
512C22×C3—41no—
513C22×C3—44no—
514C22×C3—48no—
515C22×C3—48no—
516C22×C3—42no—
517C22×C3—42no—
518C22×C3—42no—
519C22×C3—42no—
520C22×C3—82no—
521C22×C3—82no—
522C22×C3—88no—
523C22×C3—121no—
524C22×C3—121no—
525C22×C3—121no—
526C22×C3#91112yes—
527C22×C3#94912yes—
528C22×C3C2×D3×D411yescharacteristic
529C22×C3C22×#6711yescharacteristic
530C2×D3—41no—
531C2×D3—41no—
532C2×D3—41no—
533C2×D3—121no—
534C2×D3—121no—
535C2×D3—121no—
536C2×D3—121no—
537C2×D3—121no—
538C2×D3—121no—
539C2×D3—241no—
540C2×D3—241no—
541C2×D3—241no—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—22no—
545C3×C4—32no—
546C3×C4—41no—
547C3×C4—61no—
548C3×C4—61no—
549C3×C4—61no—
550C3×C4—122no—
551C3×C4—121no—
552C3×C4C2×#23512yes—
553C3×C4C2×#23712yes—
554Dic3—21no—
555Dic3—21no—
556Dic3—21no—
557Dic3—41no—
558Dic3—42no—
559Dic3—121no—
560Dic3—121no—
561Dic3—241no—
562Dic3#93212yes—
563C32#310911yescharacteristic, complemented, Sylow
564C23—24no—
565C23—22no—
566C23—42no—
567C23—42no—
568C23—61no—
569C23—181no—
570C23D3×#6711yescharacteristic
571Q8—362no—
572D4—24no—
573D4—22no—
574D4—62no—
575D4—122no—
576D4—182no—
577D4—362no—
578D4—362no—
579D4—362no—
580D4#380414yescomplemented
581C2×C4—22no—
582C2×C4—31no—
583C2×C4—31no—
584C2×C4—31no—
585C2×C4—31no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—61no—
590C2×C4—124no—
591C2×C4—124no—
592C2×C4—122no—
593C2×C4—181no—
594C2×C4—362no—
595C2×C4—362no—
596C2×C4D3×#6711yescharacteristic
597C2×C4C22×D3211yescharacteristic
598C8—62no—
599C8—182no—
600C2×C3—22no—
601C2×C3—22no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—42no—
606C2×C3—44no—
607C2×C3—44no—
608C2×C3—84no—
609C2×C3—241no—
610C2×C3#558611yescharacteristic
611C2×C3C2×#91111yescharacteristic
612C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
613C2×C3#579111yescharacteristic
614C2×C3C2×#93211yescharacteristic
615C2×C3C2×#94911yescharacteristic
616D3—81no—
617D3—241no—
618D3—241no—
619D3—481no—
620C22—21no—
621C22—21no—
622C22—24no—
623C22—48no—
624C22—42no—
625C22—42no—
626C22—121no—
627C22—121no—
628C22—121no—
629C22—361no—
630C22—361no—
631C22—361no—
632C22#6392512yes—
633C22C2×D3×#6711yescharacteristic
634C4—21no—
635C4—32no—
636C4—61no—
637C4—61no—
638C4—61no—
639C4—121no—
640C4—122no—
641C4—361no—
642C4C2×#380412yes—
643C3—21no—
644C3#7999011yescharacteristic, complemented
645C3#8231011yescharacteristic, complemented
646C2—22no—
647C2—44no—
648C2—241no—
649C2—721no—
650C2C2×#6392511yescharacteristic
651C2D3×#93211yescharacteristic
652C2#1059549811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3109
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×Dic3C2semidirect
2. #10594910C2semidirect
3. #10592916C2semidirect
4. C3×#5217C2semidirect
5. #10591481C2semidirect
6. #10591430C2semidirect
7. #10591408C2semidirect
8. #10591404C2semidirect
9. #10591125C2semidirect
10. #10591091C2semidirect
11. #10591063C2semidirect
29. #63918C22semidirect
30. #63911C22semidirect
31. #63894C22semidirect
32. Dic3×D12C22semidirect
39. #63574C22semidirect
40. #63573C22semidirect
41. Dic3⋊(C3⋊C8)C22semidirect
42. #63564C22semidirect
43. #63562C22semidirect
44. #63554C22semidirect
46. C2×D4×Dic3D3semidirect
53. #5217D3semidirect
185. C32×D4#41semidirect
397. C3×D4#235semidirect
398. C3×D4#237semidirect
563. C32#3109semidirect
580. D4#3804semidirect
644. C3#79990semidirect
645. C3#82310semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
#105949102
#105929162
C3×#52172
#105914812
#105914302
#105914082
#105914042
#105911252
#105910912
#105910632
#823103
#799903