Finite Group Databasebeta

← Dic6×AGL(1,ℤ/8) #11675762

Subgroups — Dic6×AGL(1,ℤ/8) #11675762

Order 768.

2010 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic6C211yesmaximal, characteristic, complemented
2C2×D4×Dic6C211yesmaximal, characteristic, complemented
3C3×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic
4Dic3×AGL(1,ℤ/8)C212yesmaximal
5#82508C211yesmaximal, characteristic, complemented
6#82296C211yesmaximal, characteristic, complemented
7#79855C214yesmaximal, complemented
8#79760C214yesmaximal, complemented
9#79635C212yesmaximal, complemented
10SD16×Dic6C212yesmaximal, complemented
11#79576C212yesmaximal, complemented
12D8×Dic6C212yesmaximal, complemented
13#79203C212yesmaximal, complemented
14#78917C212yesmaximal, complemented
15#78870C212yesmaximal, complemented
16M16×Dic6C211yesmaximal, characteristic, complemented
17#78506C211yesmaximal, characteristic, complemented
18Q8×AGL(1,ℤ/8)—31nomaximal, Sylow
19C23×Dic6—21no—
20C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
21C3×C4×#41C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic
23Dic3×#41C2212yes—
24C2×D4×Dic3C2212yes—
25C2×#924—21no—
26#5570C2211yescharacteristic, complemented
27#5569C2212yescomplemented
28Q8×Dic6C2211yescharacteristic, complemented
29#5543—21no—
30#5543C2211yescharacteristic, complemented
31#5539—22no—
32#5539C2212yescomplemented
33D4×Dic6—21no—
34D4×Dic6—21no—
35D4×Dic6—21no—
36D4×Dic6—22no—
37D4×Dic6C2212yes—
38D4×Dic6C2212yes—
39D4×Dic6C2214yes—
40D4×Dic6C2211yescharacteristic, complemented
41#5517—22no—
42#5517C2212yes—
43C2×#888C2212yes—
44C2×#878—22no—
45#5470—21no—
46#5470C2211yescharacteristic
47C2×#869C2211yescharacteristic
48C2×C4×Dic6—21no—
49C2×C4×Dic6C2211yescharacteristic
50C3×#442C2212yes—
51C3×#440C2212yes—
52C3×C4×SD16C2212yes—
53C3×C4×D8C2212yes—
54C3×#428C2211yescharacteristic
55C3×#418C2211yescharacteristic
56C3×#417C2211yescharacteristic
57C3×C4×M16C2211yescharacteristic
58#5232C2212yes—
59#5215C2212yes—
60#5164C2214yes—
61Dic3×SD16C2214yes—
62#5152C2214yes—
63Dic3×D8C2214yes—
64#5121C2212yes—
65#5121C2212yes—
66#5118C2212yes—
67Dic3×M16C2212yes—
68#5021C2212yescomplemented
69#5020C2212yescomplemented
70#5009C2214yes—
71#5008C2212yes—
72#5008C2212yescomplemented
73#5007C2212yes—
74#5007C2212yescomplemented
75#4995C2212yes—
76#4964C2212yes—
77#4924C2211yescharacteristic
78#4876C2214yescomplemented
79#4874C2214yescomplemented
80#4856C2214yescomplemented
81#4855C2214yescomplemented
82#4793C2214yescomplemented
83#4791C2214yescomplemented
84#4766C2214yes—
85#4763C2214yes—
86#4761C2214yes—
87#4761C2214yescomplemented
88#4759C2214yes—
89#4759C2214yescomplemented
90#4702C2214yescomplemented
91#4701C2214yescomplemented
92#4682C2212yescomplemented
93#4680C2212yescomplemented
94#4679C2212yescomplemented
95C8×Dic6C2212yescomplemented
96Q8×#41—31no—
97C2×D4×Q8—31no—
98#3386—34no—
99#3386—32no—
100#3384—34no—
101#3384—32no—
102Q8×SD16—32no—
103Q8×D8—32no—
104#3165—32no—
105#3165—31no—
106#3079—32no—
107#3079—31no—
108#3077—32no—
109#3077—31no—
110Q8×M16—31no—
111C4×AGL(1,ℤ/8)—32no—
112C4×AGL(1,ℤ/8)D311yescharacteristic
113C2×C3×#41C2311yescharacteristic
114C22×C3×D4C2311yescharacteristic
115C23×C3×C4—21no—
116C23×Dic3—22no—
117C22×Dic6—21no—
118C22×Dic6—22no—
119C22×Dic6—22no—
120C22×Dic6—24no—
121C22×Dic6—22no—
122C22×Dic6—21no—
123C22×Dic6—48no—
124C22×Dic6D411yescharacteristic
125C3×AGL(1,ℤ/8)Q818yescomplemented
126C2×C3×SD16C2312yes—
127C2×C3×D8C2312yes—
128C2×C3×M16C2311yescharacteristic
129C2×C3×M16C2311yescharacteristic
130C3×C4×Q8C2311yescharacteristic
131C3×C4×Q8C2311yescharacteristic
132C3×C4×D4—21no—
133C3×C4×D4—21no—
134C3×C4×D4—21no—
135C3×C4×D4—21no—
136C3×C4×D4C2312yes—
137C3×C4×D4C2311yescharacteristic
138C3×C4×D4C2311yescharacteristic
139C3×C4×D4C2312yes—
140C3×#117—21no—
141C3×#117C2311yescharacteristic
142C2×C3×C4⋊C4C2311yescharacteristic
143C2×C3×C22⋊C4—21no—
144C2×C3×C42—21no—
145C2×C3×C42C2311yescharacteristic
146C2×#217—22no—
147Q8×Dic3C2312yes—
148Q8×Dic3C2312yes—
149D4×Dic3—22no—
150D4×Dic3—22no—
151D4×Dic3—22no—
152D4×Dic3—22no—
153D4×Dic3C2312yes—
154D4×Dic3C2314yes—
155D4×Dic3C2312yes—
156D4×Dic3C2314yes—
157#926—22no—
158#926C2312yes—
159C2×C4⋊Dic3—21no—
160C2×C4⋊Dic3—21no—
161C2×C4⋊Dic3D411yescharacteristic
162C2×C4⋊Dic3C2312yes—
163#924—21no—
164#924—21no—
165#924—21no—
166#924—21no—
167#924—22no—
168#924—22no—
169#924—24no—
170#924—22no—
171C2×Dic3⋊C4—22no—
172C2×Dic3⋊C4—22no—
173C2×Dic3⋊C4D412yes—
174C2×C4×Dic3—22no—
175C2×C4×Dic3C2312yes—
176C2×#208C2312yes—
177#890—22no—
178#890—22no—
179#890C2312yes—
180#890C2312yes—
181#888—22no—
182#888—22no—
183#888—22no—
184#888—22no—
185#888C2312yes—
186#888C2314yes—
187#888C2314yes—
188#888C2312yes—
189#878—22no—
190#878—22no—
191#878—22no—
192#878—22no—
193#878—24no—
194#878—24no—
195#878—24no—
196#878—24no—
197#878—22no—
198#878—22no—
199#870—22no—
200#870C2312yes—
201#869—21no—
202#869—21no—
203#869—21no—
204#869—21no—
205#869C2311yescharacteristic
206#869C2312yes—
207#869C2311yescharacteristic
208#869C2312yes—
209C4×Dic6—21no—
210C4×Dic6—21no—
211C4×Dic6—21no—
212C4×Dic6—21no—
213C4×Dic6—22no—
214C4×Dic6—22no—
215C4×Dic6—22no—
216C4×Dic6D411yescharacteristic
217C4×Dic6D411yescharacteristic
218C4×Dic6D412yes—
219C4×Dic6C2311yescharacteristic
220C4×Dic6C2311yescharacteristic
221C4×Dic6C2312yes—
222C3×#107C2312yes—
223C3×#106C2312yes—
224C3×#103C2312yes—
225C3×#102C2312yes—
226C3×#102C2312yes—
227C3×#102C2312yes—
228C3×#97C2312yes—
229C3×C4×C8C2312yes—
230#835C2314yes—
231#832C2314yes—
232#832C2314yes—
233#832C2314yes—
234#818C2314yes—
235#818C2314yes—
236#817C2314yes—
237#817C2314yes—
238#815C2314yes—
239Dic3⋊C8C2314yes—
240Dic3⋊C8C2314yes—
241C8×Dic3C2314yes—
242#808C2314yes—
243#808C2314yes—
244#807C2314yes—
245#807C2314yes—
246C4⋊(C3⋊C8)C2312yes—
247C4⋊(C3⋊C8)C2312yes—
248C23×Q8—61no—
249C2×AGL(1,ℤ/8)C2×D311yescharacteristic
250Q82—31no—
251#557—32no—
252#557—31no—
253#554—32no—
254#554—31no—
255#554—62no—
256#554—61no—
257D4×Q8—31no—
258D4×Q8—32no—
259D4×Q8—34no—
260D4×Q8—32no—
261D4×Q8—61no—
262D4×Q8—61no—
263D4×Q8—62no—
264D4×Q8—61no—
265#533—32no—
266#533—31no—
267#533—61no—
268#533—62no—
269C2×C4⋊Q8—32no—
270C2×C4⋊Q8—31no—
271C2×C22⋊Q8—62no—
272C2×C22⋊Q8—61no—
273C4×#41—32no—
274C4×#41C2×D311yescharacteristic
275C2×C4×Q8—31no—
276C2×C4×Q8—61no—
277C2×C4×D4—32no—
278C2×C4×D4C2×D311yescharacteristic
279#501—34no—
280#501—34no—
281#501—34no—
282#500—34no—
283#500—32no—
284#498—34no—
285#498—32no—
286#478—34no—
287#478—34no—
288#478—34no—
289#477—32no—
290#477—34no—
291#476—32no—
292#476—32no—
293#476—34no—
294#476—34no—
295#475—32no—
296#475—34no—
297#474—32no—
298#474—32no—
299#474—34no—
300#474—34no—
301#446—34no—
302#446—32no—
303C8×Q8—32no—
304#442—34no—
305#442C2×D312yes—
306#440—34no—
307#440C2×D312yes—
308C4×SD16—34no—
309C4×SD16C2×D312yes—
310C4×D8—34no—
311C4×D8C2×D312yes—
312#428—32no—
313#428—32no—
314#428—32no—
315#428—32no—
316#428C2×D311yescharacteristic
317#423—32no—
318#423—31no—
319#418—32no—
320#418C2×D311yescharacteristic
321#417—32no—
322#417C2×D311yescharacteristic
323C4×M16—32no—
324C4×M16C2×D311yescharacteristic
325C24×C3—21no—
326C3×#41—22no—
327C3×#41C2×Q814yescomplemented
328C2×C3×Q8C2411yescharacteristic
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—22no—
332C2×C3×D4C2×Q814yescomplemented
333C2×C3×D4C2412yes—
334C2×C3×D4C2411yescharacteristic
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—22no—
339C22×C3×C4—22no—
340C22×C3×C4—21no—
341C22×C3×C4—44no—
342C22×C3×C4C2×D411yescharacteristic
343C22×C3×C4C2×D411yescharacteristic
344C22×C3×C4C2411yescharacteristic
345C22×Dic3—22no—
346C22×Dic3—22no—
347C22×Dic3—24no—
348C22×Dic3—24no—
349C22×Dic3—22no—
350C22×Dic3—48no—
351C22×Dic3C2×D412yes—
352C22×Dic3C2×D412yes—
353C2×Dic6—24no—
354C2×Dic6—21no—
355C2×Dic6—22no—
356C2×Dic6—22no—
357C2×Dic6—22no—
358C2×Dic6—24no—
359C2×Dic6—24no—
360C2×Dic6—21no—
361C2×Dic6—22no—
362C2×Dic6—48no—
363C2×Dic6—416no—
364C2×Dic6—48no—
365C2×Dic6—44no—
366C2×Dic6—44no—
367C2×Dic6—48no—
368C2×Dic6C2×D411yescharacteristic
369C2×Dic6C2×D412yes—
370C2×Dic6C2×D411yescharacteristic
371C3×SD16C2×Q818yescomplemented
372C3×D8C2×Q818yescomplemented
373C3×M16—22no—
374C3×M16C2×Q814yescomplemented
375C2×C3×C8C2412yes—
376C2×C3×C8C2412yes—
377C3×C4⋊C4—21no—
378C3×C4⋊C4—21no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4C2411yescharacteristic
381C3×C4⋊C4C2412yes—
382C3×C4⋊C4C2411yescharacteristic
383C3×C22⋊C4—21no—
384C3×C22⋊C4—22no—
385C3×C22⋊C4—22no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—21no—
388C3×C42—21no—
389C3×C42—21no—
390C3×C42—21no—
391C3×C42C2×D411yescharacteristic
392C3×C42C2×D411yescharacteristic
393C3×C42C2411yescharacteristic
394C3×C42C2411yescharacteristic
395#217—22no—
396#217—22no—
397#217—22no—
398#217—24no—
399#217—24no—
400C4⋊Dic3—21no—
401C4⋊Dic3—21no—
402C4⋊Dic3—22no—
403C4⋊Dic3—22no—
404C4⋊Dic3—22no—
405C4⋊Dic3—22no—
406C4⋊Dic3—22no—
407C4⋊Dic3—22no—
408C4⋊Dic3—22no—
409C4⋊Dic3C2×D411yescharacteristic
410C4⋊Dic3C2×D411yescharacteristic
411C4⋊Dic3C2×D412yes—
412C4⋊Dic3C2412yes—
413C4⋊Dic3C2414yes—
414C4⋊Dic3C2412yes—
415Dic3⋊C4—22no—
416Dic3⋊C4—22no—
417Dic3⋊C4—22no—
418Dic3⋊C4—22no—
419Dic3⋊C4—22no—
420Dic3⋊C4—22no—
421Dic3⋊C4—24no—
422Dic3⋊C4—24no—
423Dic3⋊C4C2×D412yes—
424Dic3⋊C4C2×D412yes—
425Dic3⋊C4C2×D412yes—
426Dic3⋊C4C2×D412yes—
427C4×Dic3—22no—
428C4×Dic3—22no—
429C4×Dic3—22no—
430C4×Dic3C2×D412yes—
431C4×Dic3C2×D412yes—
432C4×Dic3C2412yes—
433C4×Dic3C2412yes—
434#208—24no—
435C2×C3⋊C8C2414yes—
436C2×#41C22×D311yescharacteristic
437C22×Q8—31no—
438C22×Q8—62no—
439C22×Q8—61no—
440C22×Q8—62no—
441C22×Q8—64no—
442C22×Q8—62no—
443C22×Q8—61no—
444C22×Q8—128no—
445C22×D4C22×D311yescharacteristic
446C23×C4—21no—
447C23×C4—62no—
448AGL(1,ℤ/8)Dic618yesdirect product factor
449C2×SD16C22×D312yes—
450C2×D8C22×D312yes—
451C2×M16—32no—
452C2×M16C22×D311yescharacteristic
453C2×M16C22×D311yescharacteristic
454C4⋊Q8—34no—
455C4⋊Q8—34no—
456C4⋊Q8—32no—
457C4⋊Q8—32no—
458C4⋊Q8—32no—
459C4⋊Q8—32no—
460C4⋊Q8—31no—
461C4⋊Q8—31no—
462C4⋊Q8—61no—
463C4⋊Q8—61no—
464C4⋊Q8—62no—
465C4⋊Q8—62no—
466C4⋊Q8—62no—
467C4⋊Q8—62no—
468C4⋊Q8—61no—
469C4⋊Q8—61no—
470#125—32no—
471#125—32no—
472#125—32no—
473#125—62no—
474#125—62no—
475#125—62no—
476C22⋊Q8—64no—
477C22⋊Q8—64no—
478C22⋊Q8—64no—
479C22⋊Q8—64no—
480C22⋊Q8—62no—
481C22⋊Q8—62no—
482C22⋊Q8—62no—
483C22⋊Q8—62no—
484C22⋊Q8—62no—
485C22⋊Q8—62no—
486C22⋊Q8—62no—
487C22⋊Q8—64no—
488C22⋊Q8—62no—
489C22⋊Q8—61no—
490C22⋊Q8—62no—
491C22⋊Q8—61no—
492C22⋊Q8—61no—
493C22⋊Q8—61no—
494C4×Q8—31no—
495C4×Q8—32no—
496C4×Q8—31no—
497C4×Q8—31no—
498C4×Q8—32no—
499C4×Q8—31no—
500C4×Q8—32no—
501C4×Q8—32no—
502C4×Q8—62no—
503C4×Q8—62no—
504C4×Q8—62no—
505C4×Q8—61no—
506C4×Q8—61no—
507C4×Q8—61no—
508C4×Q8—61no—
509C4×Q8C22×D311yescharacteristic
510C4×Q8C22×D311yescharacteristic
511C4×D4—21no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—34no—
516C4×D4—34no—
517C4×D4—32no—
518C4×D4—32no—
519C4×D4—62no—
520C4×D4—62no—
521C4×D4—62no—
522C4×D4—62no—
523C4×D4C22×D312yes—
524C4×D4C22×D312yes—
525C4×D4C22×D311yescharacteristic
526C4×D4C22×D311yescharacteristic
527#117—21no—
528#117—32no—
529#117—62no—
530#117C22×D311yescharacteristic
531C2×C4⋊C4—32no—
532C2×C4⋊C4—31no—
533C2×C4⋊C4—32no—
534C2×C4⋊C4—62no—
535C2×C4⋊C4—61no—
536C2×C4⋊C4—62no—
537C2×C4⋊C4—61no—
538C2×C4⋊C4C22×D311yescharacteristic
539C2×C22⋊C4—21no—
540C2×C22⋊C4—62no—
541C2×C42—21no—
542C2×C42—32no—
543C2×C42—62no—
544C2×C42C22×D311yescharacteristic
545#107—34no—
546#107—34no—
547#107—34no—
548#107—34no—
549#107C22×D312yes—
550#106—34no—
551#106—34no—
552#106—34no—
553#106—34no—
554#106C22×D312yes—
555C4⋊C8—34no—
556C4⋊C8—34no—
557C4⋊C8—32no—
558C4⋊C8—32no—
559#103—34no—
560#103C22×D312yes—
561#102—34no—
562#102—34no—
563#102—34no—
564#102C22×D312yes—
565#102C22×D312yes—
566#102C22×D312yes—
567#97—34no—
568#97C22×D312yes—
569C4×C8—34no—
570C4×C8C22×D312yes—
571C23×C3—24no—
572C23×C3—21no—
573C23×C3—22no—
574C23×C3—42no—
575C23×C3—42no—
576C23×C3C22×D411yescharacteristic
577C3×Q8—21no—
578C3×Q8C22×Q812yescomplemented
579C3×D4—24no—
580C3×D4—24no—
581C3×D4—22no—
582C3×D4—21no—
583C3×D4C22×Q814yes—
584C3×D4C22×Q812yescomplemented
585C2×C3×C4—21no—
586C2×C3×C4—24no—
587C2×C3×C4—22no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—22no—
591C2×C3×C4—41no—
592C2×C3×C4—44no—
593C2×C3×C4—42no—
594C2×C3×C4—44no—
595C2×C3×C4—42no—
596C2×C3×C4—81no—
597C2×C3×C4C22×D411yescharacteristic
598C2×C3×C4C22×D411yescharacteristic
599C2×C3×C4C22×D411yescharacteristic
600C2×C3×C4C22×D411yescharacteristic
601C2×C3×C4C22×D411yescharacteristic
602C2×C3×C4C22×Q812yes—
603C2×C3×C42−1+412yes—
604C2×C3×C4C2511yescharacteristic
605C2×Dic3—24no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—24no—
609C2×Dic3—42no—
610C2×Dic3—48no—
611C2×Dic3—44no—
612C2×Dic3—48no—
613C2×Dic3—44no—
614C2×Dic3—82no—
615C2×Dic3C22×D412yes—
616C2×Dic3C22×D412yes—
617C2×Dic3C22×D412yes—
618C2×Dic3C22×D412yes—
619Dic6—22no—
620Dic6—24no—
621Dic6—48no—
622Dic6—44no—
623Dic6—42no—
624Dic6—44no—
625Dic6—44no—
626Dic6—48no—
627Dic6—82no—
628Dic6—81no—
629Dic6AGL(1,ℤ/8)14yesdirect product factor
630C3×C8—22no—
631C3×C8C22×Q814yescomplemented
632C3⋊C8—24no—
633C24—21no—
634#41—22no—
635#41C2×Dic614yescomplemented
636C2×Q8—31no—
637C2×Q8—32no—
638C2×Q8—31no—
639C2×Q8—62no—
640C2×Q8—64no—
641C2×Q8—64no—
642C2×Q8—62no—
643C2×Q8—64no—
644C2×Q8—61no—
645C2×Q8—62no—
646C2×Q8—62no—
647C2×Q8—61no—
648C2×Q8—124no—
649C2×Q8—128no—
650C2×Q8—128no—
651C2×Q8—124no—
652C2×Q8—1216no—
653C2×Q8—128no—
654C2×Q8C23×D311yescharacteristic
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4C2×Dic614yescomplemented
659C2×D4C23×D312yes—
660C2×D4C23×D311yescharacteristic
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—21no—
667C22×C4—32no—
668C22×C4—32no—
669C22×C4—44no—
670C22×C4—62no—
671C22×C4—64no—
672C22×C4—64no—
673C22×C4—62no—
674C22×C4—62no—
675C22×C4—128no—
676C22×C4D3×D411yescharacteristic
677C22×C4D3×D411yescharacteristic
678C22×C4C23×D311yescharacteristic
679SD16C2×Dic618yescomplemented
680D8C2×Dic618yescomplemented
681M16—22no—
682M16—64no—
683M16C2×Dic614yescomplemented
684C2×C8—34no—
685C2×C8C23×D312yes—
686C2×C8C23×D312yes—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—32no—
691C4⋊C4—31no—
692C4⋊C4—32no—
693C4⋊C4—32no—
694C4⋊C4—32no—
695C4⋊C4—32no—
696C4⋊C4—31no—
697C4⋊C4—32no—
698C4⋊C4—32no—
699C4⋊C4—34no—
700C4⋊C4—62no—
701C4⋊C4—62no—
702C4⋊C4—62no—
703C4⋊C4—64no—
704C4⋊C4—64no—
705C4⋊C4—62no—
706C4⋊C4—62no—
707C4⋊C4—62no—
708C4⋊C4—62no—
709C4⋊C4—62no—
710C4⋊C4—62no—
711C4⋊C4—62no—
712C4⋊C4—61no—
713C4⋊C4—62no—
714C4⋊C4—62no—
715C4⋊C4—62no—
716C4⋊C4—61no—
717C4⋊C4C23×D311yescharacteristic
718C4⋊C4C23×D311yescharacteristic
719C4⋊C4C23×D312yes—
720C22⋊C4—21no—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—64no—
726C22⋊C4—64no—
727C22⋊C4—62no—
728C22⋊C4—62no—
729C22⋊C4—62no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—32no—
734C42—32no—
735C42—32no—
736C42—32no—
737C42—62no—
738C42—62no—
739C42—62no—
740C42D3×D411yescharacteristic
741C42D3×D411yescharacteristic
742C42C23×D311yescharacteristic
743C42C23×D311yescharacteristic
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—22no—
747C22×C3—24no—
748C22×C3—48no—
749C22×C3—41no—
750C22×C3—42no—
751C22×C3—42no—
752C22×C3—41no—
753C22×C3D4×Q812yes—
754C22×C3C23×D411yescharacteristic
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—22no—
758C3×C4—21no—
759C3×C4—41no—
760C3×C4—42no—
761C3×C4—41no—
762C3×C4D4×Q812yes—
763C3×C4C2×AGL(1,ℤ/8)12yes—
764C3×C4C23×Q811yescharacteristic
765C3×C4C2×2−1+411yescharacteristic
766Dic3—22no—
767Dic3—22no—
768Dic3—22no—
769Dic3—42no—
770Dic3—44no—
771Dic3—42no—
772Dic3C2×AGL(1,ℤ/8)14yes—
773C23—21no—
774C23—22no—
775C23—24no—
776C23—42no—
777C23—42no—
778C23C2×D3×D411yescharacteristic
779Q8—21no—
780Q8—34no—
781Q8—64no—
782Q8—62no—
783Q8—124no—
784Q8—128no—
785Q8—124no—
786Q8—128no—
787Q8—124no—
788Q8—122no—
789Q8—241no—
790Q8—242no—
791Q8C22×Dic612yescomplemented
792D4—24no—
793D4—22no—
794D4—21no—
795D4—24no—
796D4C22×Dic614yes—
797D4C22×Dic612yescomplemented
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—32no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—41no—
809C2×C4—44no—
810C2×C4—42no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—64no—
814C2×C4—62no—
815C2×C4—62no—
816C2×C4—64no—
817C2×C4—81no—
818C2×C4—128no—
819C2×C4—124no—
820C2×C4—122no—
821C2×C4—128no—
822C2×C4—124no—
823C2×C4—242no—
824C2×C4C22×Dic612yes—
825C2×C4C2×D3×D411yescharacteristic
826C2×C4C2×D3×D411yescharacteristic
827C2×C4C2×D3×D411yescharacteristic
828C2×C4C2×D3×D411yescharacteristic
829C2×C4C2×D3×D411yescharacteristic
830C2×C4#101012yes—
831C2×C4C24×D311yescharacteristic
832C8—22no—
833C8—64no—
834C8C22×Dic614yescomplemented
835C2×C3—22no—
836C2×C3—42no—
837C2×C3—44no—
838C2×C3C2×D4×Q811yescharacteristic
839C2×C3C22×AGL(1,ℤ/8)11yescharacteristic
840C2×C3#358611yescharacteristic
841C22—21no—
842C22—21no—
843C22—22no—
844C22—24no—
845C22—48no—
846C22—42no—
847C22—41no—
848C22—41no—
849C22—42no—
850C22D4×Dic612yes—
851C22C22×D3×D411yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—22no—
856C4—34no—
857C4—42no—
858C4—41no—
859C4—41no—
860C4—62no—
861C4—62no—
862C4—62no—
863C4—124no—
864C4—122no—
865C4—122no—
866C4D4×Dic612yes—
867C4D3×AGL(1,ℤ/8)12yes—
868C4C23×Dic611yescharacteristic
869C4C2×#101011yescharacteristic
870C3Q8×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
871C2—22no—
872C2—44no—
873C2—42no—
874C2C2×D4×Dic611yescharacteristic
875C2C2×D3×AGL(1,ℤ/8)11yescharacteristic
876C2#8720111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×C4×AGL(1,ℤ/8)C2
socleC22×C3C23×D4
prime radicalC2×C3×AGL(1,ℤ/8)C22
hypercenterC4×AGL(1,ℤ/8)D3
hypocenterC3Q8×AGL(1,ℤ/8)
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×Dic6C2semidirect
2. C2×D4×Dic6C2semidirect
5. #82508C2semidirect
6. #82296C2semidirect
7. #79855C2semidirect
8. #79760C2semidirect
9. #79635C2semidirect
10. SD16×Dic6C2semidirect
11. #79576C2semidirect
12. D8×Dic6C2semidirect
13. #79203C2semidirect
14. #78917C2semidirect
15. #78870C2semidirect
16. M16×Dic6C2semidirect
17. #78506C2semidirect
26. #5570C22semidirect
27. #5569C22semidirect
28. Q8×Dic6C22semidirect
30. #5543C22semidirect
32. #5539C22semidirect
40. D4×Dic6C22semidirect
68. #5021C22semidirect
69. #5020C22semidirect
72. #5008C22semidirect
74. #5007C22semidirect
78. #4876C22semidirect
79. #4874C22semidirect
80. #4856C22semidirect
81. #4855C22semidirect
82. #4793C22semidirect
83. #4791C22semidirect
87. #4761C22semidirect
89. #4759C22semidirect
90. #4702C22semidirect
91. #4701C22semidirect
92. #4682C22semidirect
93. #4680C22semidirect
94. #4679C22semidirect
95. C8×Dic6C22semidirect
125. C3×AGL(1,ℤ/8)Q8semidirect
327. C3×#41C2×Q8semidirect
332. C2×C3×D4C2×Q8semidirect
371. C3×SD16C2×Q8semidirect
372. C3×D8C2×Q8semidirect
374. C3×M16C2×Q8semidirect
448. AGL(1,ℤ/8)Dic6direct (N × H)
578. C3×Q8C22×Q8semidirect
584. C3×D4C22×Q8semidirect
629. Dic6AGL(1,ℤ/8)direct (N × H)
631. C3×C8C22×Q8semidirect
635. #41C2×Dic6semidirect
658. C2×D4C2×Dic6semidirect
679. SD16C2×Dic6semidirect
680. D8C2×Dic6semidirect
683. M16C2×Dic6semidirect
791. Q8C22×Dic6semidirect
797. D4C22×Dic6semidirect
834. C8C22×Dic6semidirect
870. C3Q8×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
#41×Dic62
C2×D4×Dic62
C3×C4×AGL(1,ℤ/8)2
Dic3×AGL(1,ℤ/8)2
#825082
#822962
#798552
#797602
#796352
SD16×Dic62
#795762
D8×Dic62
#792032
#789172
#788702
M16×Dic62
#785062
Q8×AGL(1,ℤ/8)3