Finite Group Databasebeta

← D8×#626 #11885759

Subgroups — D8×#626 #11885759

Order 1152.

1409 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×D3×D8C211yesmaximal, characteristic, complemented
3D4×#626C212yesmaximal, complemented
4C3×Dic3×D8C211yesmaximal, characteristic, complemented
5#10591481C212yesmaximal, complemented
6#10591456C212yesmaximal, complemented
7#10591448C212yesmaximal, complemented
8#10590880C211yesmaximal, characteristic, complemented
9#10590844C211yesmaximal, characteristic, complemented
10#10590832C211yesmaximal, characteristic, complemented
11C8×#626C211yesmaximal, characteristic, complemented
12D8×#67—31nomaximal
13D8×D12—31nomaximal
14C2×D4×C3⋊D3C2212yescomplemented
15C2×C3×D3×D4C2212yescomplemented
16C22×#626—22no—
17C2×C32×D8C2211yescharacteristic
18C2×#3753C2212yescomplemented
19D8×C3⋊D3—24no—
20C2×#3745C2211yescharacteristic, complemented
21C2×C8×C3⋊D3C2211yescharacteristic, complemented
22C3×D4×Dic3C2212yescomplemented
23C2×C3×#213C2212yescomplemented
24C3×D3×D8—24no—
25C2×C3×D24C2211yescharacteristic, complemented
26C2×C3×D3×C8C2211yescharacteristic, complemented
27#63981—22no—
28#63978—22no—
29#63977—22no—
30#63916C2212yescomplemented
31#63911C2212yescomplemented
32#63909C2212yescomplemented
33C4×#626C2211yescharacteristic
34C2×#3714C2212yescomplemented
35C3×#832C2212yescomplemented
36C3×#818C2211yescharacteristic, complemented
37C3×C8×Dic3C2211yescharacteristic, complemented
38Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
39#63564C2212yescomplemented
40#63562C2212yescomplemented
41#63557C2211yescharacteristic, complemented
42(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
43C22×C3×D8—31no—
44D4×#67—32no—
45C2×D3×D8—31no—
46C2×D3×D8—31no—
47C2×D3×D8—61no—
48C2×D3×D8D311yescharacteristic, complemented
49D4×D12—32no—
50C3×C4×D8—31no—
51#5217—32no—
52#5157—31no—
53#5156—32no—
54#5151—31no—
55#5150—32no—
56Dic3×D8D311yescharacteristic, complemented
57#5115—31no—
58C8×#67—31no—
59#5015—32no—
60#4883—31no—
61#4883—31no—
62#4773—32no—
63#4773—32no—
64#4695—31no—
65C8×D12—31no—
66C23×C3⋊D3—22no—
67C23×C3×D3—22no—
68C2×C32×D4C2312yes—
69C2×#638—22no—
70D4×C3⋊D3—24no—
71D4×C3⋊D3—42no—
72C2×C4⋊(C3⋊D3)C2312yes—
73C2×C4×C3⋊D3C2311yescharacteristic
74C2×C3×#67—22no—
75C22×C3×Dic3—22no—
76C3×D3×D4—24no—
77C3×D3×D4—42no—
78C2×C3×D12C2312yes—
79C2×C3×C4×D3C2311yescharacteristic
80C2×#626—22no—
81C2×#626—22no—
82C2×#626—22no—
83C2×#626—22no—
84C2×#626—48no—
85C2×#626D411yescharacteristic
86C32×D8D414yescomplemented
87C2×C32×C8C2311yescharacteristic
88#3753—24no—
89C2×C3⋊(C3⋊C8)C2311yescharacteristic
90#3745—22no—
91C8×C3⋊D3—22no—
92C3×#217—22no—
93C3×#213—24no—
94C3×C4⋊Dic3C2312yes—
95C3×C4×Dic3C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98C3×D24—22no—
99C3×D3×C8—22no—
100Dic3⋊Dic3D411yescharacteristic
101#3722—22no—
102#3722D411yescharacteristic
103(C2×D3)⋊Dic3—22no—
104(C2×D3)⋊Dic3D411yescharacteristic
105#3714—42no—
106D4×D8—91noSylow
107C22×C3×D4—32no—
108C22×#67—62no—
109C2×D3×D4—32no—
110C2×D3×D4—32no—
111C2×D3×D4—62no—
112C2×D3×D4C2×D312yescomplemented
113C22×D12—62no—
114C2×C3×D8—21no—
115C2×C3×D8—32no—
116C2×C3×D8—31no—
117C2×C3×D8—64no—
118C2×C3×D8C2×D311yescharacteristic
119C2×C3×D8C2×D311yescharacteristic
120C22×C3×C8—31no—
121C3×C4×D4—32no—
122#953—62no—
123#940—32no—
124#939—62no—
125#938—32no—
126#937—62no—
127D4×Dic3C2×D312yescomplemented
128C2×#213—32no—
129C2×#213—32no—
130C2×#213—32no—
131C2×#213—62no—
132C2×#213C2×D312yescomplemented
133#930—32no—
134#930—62no—
135C4×#67—31no—
136D3×D8—24no—
137D3×D8—68no—
138D3×D8—64no—
139D3×D8—64no—
140C2×D24—31no—
141C2×D24—31no—
142C2×D24—32no—
143C2×D24—61no—
144C2×D24C2×D311yescharacteristic, complemented
145C2×D3×C8—31no—
146C2×D3×C8—31no—
147C2×D3×C8—61no—
148C2×D3×C8C2×D311yescharacteristic, complemented
149#895—32no—
150#895—32no—
151#882—62no—
152#882—62no—
153#874—32no—
154C4×D12—31no—
155C3×#107—31no—
156C3×#102—32no—
157C3×C4×C8—31no—
158#832—32no—
159#832C2×D312yescomplemented
160#830—31no—
161#821—32no—
162(C2×D3)⋊C8—31no—
163(C2×D3)⋊C8—31no—
164(C2×D3)⋊C8—31no—
165#818C2×D311yescharacteristic, complemented
166Dic3⋊C8—31no—
167C8×Dic3C2×D311yescharacteristic, complemented
168#809—32no—
169#809—32no—
170C4⋊(C3⋊C8)—31no—
171C23×C32—22no—
172C22×C3⋊D3—22no—
173C22×C3⋊D3—44no—
174C22×C3⋊D3—44no—
175C22×C3⋊D3—82no—
176C22×C3⋊D3C2×D411yescharacteristic
177C22×C3×D3—22no—
178C22×C3×D3—44no—
179C22×C3×D3—44no—
180C22×C3×D3—82no—
181C22×C3×D3C2×D411yescharacteristic
182C32×D4—22no—
183C32×D4C2×D414yescomplemented
184C2×C32×C4C2411yescharacteristic
185#638—44no—
186C2×C3⋊Dic3C2×D411yescharacteristic
187C4⋊(C3⋊D3)—22no—
188C4⋊(C3⋊D3)—22no—
189C4×C3⋊D3—21no—
190C4×C3⋊D3—21no—
191C3×#67—44no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—44no—
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C3×D12—22no—
198C3×D12—22no—
199C3×C4×D3—21no—
200C3×C4×D3—21no—
201#626—44no—
202#626—44no—
203#626—44no—
204#626—82no—
205#626D814yesdirect product factor
206C32×C8C2×D412yescomplemented
207C3⋊(C3⋊C8)—21no—
208C3×C3⋊C8—21no—
209C3×C3⋊C8—21no—
210C22×D8—31no—
211C22×D8—91no—
212D42—92no—
213#493—91no—
214#466—91no—
215#466—91no—
216#459—92no—
217#447—92no—
218#447—92no—
219C4×D8—31no—
220C8×D4—91no—
221C24×C3—62no—
222C23×D3—22no—
223C23×D3—62no—
224C23×D3—62no—
225C23×D3—122no—
226C2×C3×D4—22no—
227C2×C3×D4—32no—
228C2×C3×D4—62no—
229C2×C3×D4—64no—
230C2×C3×D4—122no—
231C2×C3×D4C22×D312yes—
232C2×C3×D4C22×D312yes—
233C22×C3×C4—31no—
234C22×C3×C4—62no—
235C2×#67—22no—
236C2×#67—31no—
237C2×#67—62no—
238C2×#67—62no—
239C2×#67—62no—
240C2×#67—62no—
241C2×#67—62no—
242C2×#67—62no—
243C2×#67—122no—
244C2×#67—128no—
245C22×Dic3—22no—
246D3×D4—24no—
247D3×D4—42no—
248D3×D4—68no—
249D3×D4—64no—
250D3×D4—64no—
251D3×D4—122no—
252D3×D4—122no—
253D3×D4—124no—
254C2×D12—31no—
255C2×D12—32no—
256C2×D12—32no—
257C2×D12—62no—
258C2×D12—62no—
259C2×D12—62no—
260C2×D12—62no—
261C2×D12—62no—
262C2×D12—128no—
263C2×D12C22×D312yes—
264C2×C4×D3—31no—
265C2×C4×D3—31no—
266C2×C4×D3—61no—
267C2×C4×D3C22×D311yescharacteristic
268C3×D8—24no—
269C3×D8—64no—
270C3×D8—62no—
271C3×D8D1214yescomplemented
272C3×D8#6714yescomplemented
273C2×C3×C8—21no—
274C2×C3×C8—31no—
275C2×C3×C8—31no—
276C2×C3×C8—62no—
277C2×C3×C8C22×D311yescharacteristic
278C2×C3×C8C22×D311yescharacteristic
279C3×C4⋊C4—32no—
280C3×C22⋊C4—62no—
281C3×C42—31no—
282#217—22no—
283#217—31no—
284#217—62no—
285#213—24no—
286#213—68no—
287#213—64no—
288#213—64no—
289#213—122no—
290(C2×D3)⋊C4—31no—
291(C2×D3)⋊C4—31no—
292(C2×D3)⋊C4—31no—
293(C2×D3)⋊C4—62no—
294(C2×D3)⋊C4—62no—
295(C2×D3)⋊C4—62no—
296C4⋊Dic3—31no—
297C4⋊Dic3C22×D312yes—
298Dic3⋊C4—31no—
299C4×Dic3C22×D311yescharacteristic
300C2×C3⋊C8—31no—
301C2×C3⋊C8—31no—
302C2×C3⋊C8—61no—
303C2×C3⋊C8C22×D311yescharacteristic
304C2×C3⋊C8C22×D311yescharacteristic
305D24—22no—
306D24—64no—
307D24—62no—
308D24—62no—
309D24—122no—
310D3×C8—22no—
311D3×C8—64no—
312D3×C8—62no—
313D3×C8—62no—
314C22×C32—24no—
315C22×C32—42no—
316C22×C32—42no—
317C22×C32C22×D411yescharacteristic
318C2×C3⋊D3—21no—
319C2×C3⋊D3—21no—
320C2×C3⋊D3—42no—
321C2×C3⋊D3—42no—
322C2×C3⋊D3—42no—
323C2×C3⋊D3—88no—
324C2×C3⋊D3C2×D812yescomplemented
325C2×C3×D3—21no—
326C2×C3×D3—21no—
327C2×C3×D3—42no—
328C2×C3×D3—42no—
329C2×C3×D3—42no—
330C2×C3×D3—88no—
331C2×C3×D3C2×D812yescomplemented
332C32×C4C22×D411yescharacteristic
333C32×C4H(5,𝔽2)11yescharacteristic
334C3⋊Dic3—21no—
335C3×Dic3—21no—
336C3×Dic3—21no—
337C3×Dic3—42no—
338C3×Dic3C2×D812yescomplemented
339C22×D4—32no—
340C22×D4—92no—
341C22×D4—182no—
342C2×D8—32no—
343C2×D8—31no—
344C2×D8—64no—
345C2×D8—92no—
346C2×D8—92no—
347C2×D8—91no—
348C2×D8—184no—
349C2×D8D3211yescharacteristic
350C22×C8—31no—
351C22×C8—91no—
352#127—92no—
353#121—92no—
354#121—92no—
355#121—182no—
356#120—182no—
357#120—182no—
358C4×D4—32no—
359C4×D4—91no—
360#107—31no—
361C4⋊C8—91no—
362#102—32no—
363#102—92no—
364#102—92no—
365C22⋊C8—91no—
366C22⋊C8—91no—
367C4×C8—31no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—31no—
371C23×C3—42no—
372C23×C3—62no—
373C23×C3—124no—
374C23×C3—124no—
375C23×C3—242no—
376C22×D3—22no—
377C22×D3—31no—
378C22×D3—31no—
379C22×D3—44no—
380C22×D3—44no—
381C22×D3—61no—
382C22×D3—62no—
383C22×D3—62no—
384C22×D3—82no—
385C22×D3—122no—
386C22×D3—124no—
387C22×D3—124no—
388C22×D3—124no—
389C22×D3—124no—
390C22×D3—128no—
391C22×D3—244no—
392C22×D3—242no—
393C22×D3—242no—
394C22×D3—244no—
395C22×D3D3×D411yescharacteristic
396C3×D4—22no—
397C3×D4—22no—
398C3×D4—24no—
399C3×D4—42no—
400C3×D4—62no—
401C3×D4—62no—
402C3×D4—124no—
403C3×D4C2×D1214yescomplemented
404C3×D4C2×#6714yescomplemented
405C2×C3×C4—21no—
406C2×C3×C4—31no—
407C2×C3×C4—31no—
408C2×C3×C4—31no—
409C2×C3×C4—61no—
410C2×C3×C4—61no—
411C2×C3×C4—62no—
412C2×C3×C4—124no—
413C2×C3×C4C23×D311yescharacteristic
414C2×C3×C4C23×D311yescharacteristic
415#67—34no—
416#67—44no—
417#67—124no—
418#67—124no—
419#67—124no—
420#67—124no—
421#67—128no—
422#67—124no—
423#67—242no—
424C2×Dic3—22no—
425C2×Dic3—31no—
426C2×Dic3—31no—
427C2×Dic3—44no—
428C2×Dic3—61no—
429C2×Dic3D3×D411yescharacteristic
430C2×Dic3D3×D411yescharacteristic
431C2×Dic3D3×D411yescharacteristic
432D12—22no—
433D12—22no—
434D12—34no—
435D12—64no—
436D12—62no—
437D12—62no—
438D12—62no—
439D12—62no—
440D12—122no—
441D12—124no—
442D12—124no—
443D12—124no—
444D12—242no—
445C4×D3—21no—
446C4×D3—21no—
447C4×D3—62no—
448C4×D3—62no—
449C4×D3—61no—
450C4×D3—61no—
451C4×D3—61no—
452C4×D3—61no—
453C3×C8—22no—
454C3×C8—61no—
455C3×C8—61no—
456C3×C8C2×D1212yescomplemented
457C3×C8C2×#6712yescomplemented
458C3⋊C8—21no—
459C3⋊C8—21no—
460C3⋊C8—62no—
461C3⋊C8—61no—
462C3⋊C8—61no—
463C2×C32—44no—
464C2×C32D4211yescharacteristic
465C2×C32C22×D811yescharacteristic
466C2×C32#57611yescharacteristic
467C3⋊D3—22no—
468C3⋊D3—82no—
469C3×D3—22no—
470C3×D3—82no—
471C24—62no—
472C24—182no—
473C2×D4—32no—
474C2×D4—62no—
475C2×D4—64no—
476C2×D4—91no—
477C2×D4—92no—
478C2×D4—122no—
479C2×D4—182no—
480C2×D4—182no—
481C2×D4—182no—
482C2×D4—182no—
483C2×D4—182no—
484C2×D4—184no—
485C2×D4—368no—
486C2×D4—362no—
487C2×D4C2×D3212yes—
488C22×C4—31no—
489C22×C4—62no—
490C22×C4—91no—
491D8—64no—
492D8—62no—
493D8—184no—
494D8—182no—
495D8—362no—
496D8#62614yesdirect product factor
497C2×C8—31no—
498C2×C8—31no—
499C2×C8—62no—
500C2×C8—91no—
501C2×C8—182no—
502C2×C8C2×D3211yescharacteristic
503C4⋊C4—32no—
504C4⋊C4—91no—
505C22⋊C4—62no—
506C22⋊C4—91no—
507C22⋊C4—91no—
508C22⋊C4—182no—
509C22⋊C4—182no—
510C42—31no—
511C22×C3—24no—
512C22×C3—24no—
513C22×C3—21no—
514C22×C3—32no—
515C22×C3—44no—
516C22×C3—42no—
517C22×C3—42no—
518C22×C3—42no—
519C22×C3—42no—
520C22×C3—61no—
521C22×C3—61no—
522C22×C3—82no—
523C22×C3—82no—
524C22×C3—122no—
525C22×C3—122no—
526C22×C3—122no—
527C22×C3—248no—
528C22×C3C2×D3×D411yescharacteristic
529C22×C3C2×D3×D411yescharacteristic
530C2×D3—21no—
531C2×D3—21no—
532C2×D3—32no—
533C2×D3—32no—
534C2×D3—42no—
535C2×D3—42no—
536C2×D3—42no—
537C2×D3—62no—
538C2×D3—62no—
539C2×D3—62no—
540C2×D3—61no—
541C2×D3—61no—
542C2×D3—61no—
543C2×D3—61no—
544C2×D3—88no—
545C2×D3—124no—
546C2×D3—122no—
547C2×D3—122no—
548C2×D3—122no—
549C2×D3—122no—
550C2×D3—122no—
551C2×D3—122no—
552C2×D3—242no—
553C2×D3—242no—
554C2×D3—248no—
555C2×D3—248no—
556C2×D3—2416no—
557C2×D3D3×D812yescomplemented
558C3×C4—21no—
559C3×C4—21no—
560C3×C4—32no—
561C3×C4—61no—
562C3×C4—61no—
563C3×C4—122no—
564C3×C4C22×D1211yescharacteristic
565C3×C4#100411yescharacteristic
566C3×C4#100911yescharacteristic
567C3×C4C22×#6711yescharacteristic
568Dic3—21no—
569Dic3—21no—
570Dic3—42no—
571Dic3—62no—
572Dic3—61no—
573Dic3—61no—
574Dic3D3×D812yescomplemented
575C32D4×D811yescharacteristic, complemented, Sylow
576C23—22no—
577C23—31no—
578C23—62no—
579C23—91no—
580C23—124no—
581C23—124no—
582C23—182no—
583C23—242no—
584C23—364no—
585C23—364no—
586C23—722no—
587D4—22no—
588D4—62no—
589D4—62no—
590D4—94no—
591D4—124no—
592D4—182no—
593D4—182no—
594D4—364no—
595D4—364no—
596D4—364no—
597D4—364no—
598D4—722no—
599D4C2×#62614yescomplemented
600C2×C4—31no—
601C2×C4—31no—
602C2×C4—31no—
603C2×C4—61no—
604C2×C4—61no—
605C2×C4—62no—
606C2×C4—91no—
607C2×C4—124no—
608C2×C4—181no—
609C2×C4—181no—
610C2×C4C22×D3211yescharacteristic
611C8—61no—
612C8—61no—
613C8—181no—
614C8C2×#62612yescomplemented
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—21no—
618C2×C3—44no—
619C2×C3—44no—
620C2×C3—62no—
621C2×C3—84no—
622C2×C3—242no—
623C2×C3D4×D1211yescharacteristic
624C2×C3C2×D3×D811yescharacteristic
625C2×C3C2×D3×D811yescharacteristic
626C2×C3#575711yescharacteristic
627C2×C3#576911yescharacteristic
628C2×C3D4×#6711yescharacteristic
629D3—22no—
630D3—64no—
631D3—62no—
632D3—62no—
633D3—82no—
634D3—244no—
635D3—242no—
636D3—242no—
637C22—24no—
638C22—32no—
639C22—42no—
640C22—42no—
641C22—61no—
642C22—61no—
643C22—92no—
644C22—122no—
645C22—122no—
646C22—122no—
647C22—181no—
648C22—181no—
649C22—248no—
650C22—362no—
651C22—362no—
652C22—362no—
653C22—728no—
654C22D32×D411yescharacteristic
655C4—32no—
656C4—61no—
657C4—61no—
658C4—122no—
659C4—181no—
660C4#6431411yescharacteristic
661C4C22×#62611yescharacteristic
662C3—21no—
663C3D8×D1211yescharacteristic, complemented
664C3D8×#6711yescharacteristic, complemented
665C2—44no—
666C2—62no—
667C2—182no—
668C2—242no—
669C2—722no—
670C2D32×D811yescharacteristic
671C2#1059473411yescharacteristic
672C2D4×#62611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D8×C3⋊D3C2semidirect
2. C2×C3×D3×D8C2semidirect
3. D4×#626C2semidirect
4. C3×Dic3×D8C2semidirect
5. #10591481C2semidirect
6. #10591456C2semidirect
7. #10591448C2semidirect
8. #10590880C2semidirect
9. #10590844C2semidirect
10. #10590832C2semidirect
11. C8×#626C2semidirect
14. C2×D4×C3⋊D3C22semidirect
15. C2×C3×D3×D4C22semidirect
18. C2×#3753C22semidirect
20. C2×#3745C22semidirect
21. C2×C8×C3⋊D3C22semidirect
22. C3×D4×Dic3C22semidirect
23. C2×C3×#213C22semidirect
25. C2×C3×D24C22semidirect
26. C2×C3×D3×C8C22semidirect
30. #63916C22semidirect
31. #63911C22semidirect
32. #63909C22semidirect
34. C2×#3714C22semidirect
35. C3×#832C22semidirect
36. C3×#818C22semidirect
37. C3×C8×Dic3C22semidirect
38. Dic3⋊(C3⋊C8)C22semidirect
39. #63564C22semidirect
40. #63562C22semidirect
41. #63557C22semidirect
42. (C2×D3)⋊(C3⋊C8)C22semidirect
48. C2×D3×D8D3semidirect
56. Dic3×D8D3semidirect
86. C32×D8D4semidirect
112. C2×D3×D4C2×D3semidirect
127. D4×Dic3C2×D3semidirect
132. C2×#213C2×D3semidirect
144. C2×D24C2×D3semidirect
148. C2×D3×C8C2×D3semidirect
159. #832C2×D3semidirect
165. #818C2×D3semidirect
167. C8×Dic3C2×D3semidirect
183. C32×D4C2×D4semidirect
205. #626D8direct (N × H)
206. C32×C8C2×D4semidirect
271. C3×D8D12semidirect
272. C3×D8#67semidirect
324. C2×C3⋊D3C2×D8semidirect
331. C2×C3×D3C2×D8semidirect
338. C3×Dic3C2×D8semidirect
403. C3×D4C2×D12semidirect
404. C3×D4C2×#67semidirect
456. C3×C8C2×D12semidirect
457. C3×C8C2×#67semidirect
496. D8#626direct (N × H)
557. C2×D3D3×D8semidirect
574. Dic3D3×D8semidirect
575. C32D4×D8semidirect
599. D4C2×#626semidirect
614. C8C2×#626semidirect
663. C3D8×D12semidirect
664. C3D8×#67semidirect

Maximal subgroups

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

subgroupindex
C2×D8×C3⋊D32
C2×C3×D3×D82
D4×#6262
C3×Dic3×D82
#105914812
#105914562
#105914482
#105908802
#105908442
#105908322
C8×#6262
D8×#673
D8×D123