Finite Group Databasebeta

← #11675773

Subgroups — #11675773

Order 768.

1826 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic6C211yesmaximal, characteristic, complemented
2C2×#5543C211yesmaximal, 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#79856C214yesmaximal, complemented
8#79762C214yesmaximal, complemented
9#79634C212yesmaximal, complemented
10#79632C212yesmaximal, complemented
11#79576C212yesmaximal, complemented
12#79574C212yesmaximal, complemented
13#79204C212yesmaximal, complemented
14#78917C212yesmaximal, complemented
15#78871C212yesmaximal, complemented
16M16×Dic6C211yesmaximal, characteristic, complemented
17#78506C211yesmaximal, characteristic, complemented
18#61367—31nomaximal, Sylow
19C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
20C3×C4×#41C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22Dic3×#41C2212yes—
23C2×D4×Dic3C2212yes—
24C22×C4⋊Dic3—21no—
25C2×#924—21no—
26#5570C2211yescharacteristic, complemented
27#5569C2212yescomplemented
28Q8×Dic6C2211yescharacteristic, complemented
29#5543—21no—
30#5543—21no—
31#5543—21no—
32#5543—22no—
33#5543C2212yes—
34#5543C2212yes—
35#5543C2214yes—
36#5543C2211yescharacteristic, complemented
37#5539—22no—
38#5539C2212yescomplemented
39D4×Dic6—21no—
40D4×Dic6C2211yescharacteristic, complemented
41#5517—22no—
42#5517C2212yes—
43C2×#890C2212yes—
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#4878C2214yescomplemented
79#4876C2214yescomplemented
80#4858C2214yescomplemented
81#4856C2214yescomplemented
82#4799C2214yescomplemented
83#4796C2214yescomplemented
84#4766C2214yes—
85#4766C2214yescomplemented
86#4763C2214yes—
87#4763C2214yescomplemented
88#4761C2214yes—
89#4759C2214yes—
90#4702C2214yescomplemented
91#4701C2214yescomplemented
92#4682C2212yescomplemented
93#4680C2212yescomplemented
94#4679C2212yescomplemented
95C8×Dic6C2212yescomplemented
96Q8×#41—31no—
97C2×#554—31no—
98#3389—34no—
99#3388—34no—
100#3385—32no—
101#3384—32no—
102#3381—32no—
103#3380—32no—
104#3166—32no—
105#3165—31no—
106#3080—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—21no—
119C22×Dic6D411yescharacteristic
120C3×AGL(1,ℤ/8)Q818yescomplemented
121C2×C3×SD16C2312yes—
122C2×C3×D8C2312yes—
123C2×C3×M16C2311yescharacteristic
124C2×C3×M16C2311yescharacteristic
125C3×C4×Q8C2311yescharacteristic
126C3×C4×Q8C2311yescharacteristic
127C3×C4×D4—21no—
128C3×C4×D4—21no—
129C3×C4×D4—21no—
130C3×C4×D4—21no—
131C3×C4×D4C2312yes—
132C3×C4×D4C2311yescharacteristic
133C3×C4×D4C2311yescharacteristic
134C3×C4×D4C2312yes—
135C3×#117—21no—
136C3×#117C2311yescharacteristic
137C2×C3×C4⋊C4C2311yescharacteristic
138C2×C3×C22⋊C4—21no—
139C2×C3×C42—21no—
140C2×C3×C42C2311yescharacteristic
141C2×#217—22no—
142Q8×Dic3C2312yes—
143Q8×Dic3C2312yes—
144D4×Dic3—22no—
145D4×Dic3—22no—
146D4×Dic3—22no—
147D4×Dic3—22no—
148D4×Dic3C2312yes—
149D4×Dic3C2314yes—
150D4×Dic3C2312yes—
151D4×Dic3C2314yes—
152#926—22no—
153#926C2312yes—
154C2×C4⋊Dic3—21no—
155C2×C4⋊Dic3—22no—
156C2×C4⋊Dic3—21no—
157C2×C4⋊Dic3—22no—
158C2×C4⋊Dic3—22no—
159C2×C4⋊Dic3—24no—
160C2×C4⋊Dic3D411yescharacteristic
161C2×C4⋊Dic3C2312yes—
162#924—21no—
163#924—21no—
164#924—21no—
165#924—22no—
166#924—22no—
167#924—24no—
168#924—21no—
169#924—22no—
170C2×Dic3⋊C4—22no—
171C2×Dic3⋊C4—22no—
172C2×Dic3⋊C4D412yes—
173C2×C4×Dic3—22no—
174C2×C4×Dic3C2312yes—
175C2×#208C2312yes—
176#890—22no—
177#890—22no—
178#890—22no—
179#890—22no—
180#890C2314yes—
181#890C2312yes—
182#890C2314yes—
183#890C2312yes—
184#888—22no—
185#888—22no—
186#888C2312yes—
187#888C2312yes—
188#878—22no—
189#878—22no—
190#878—22no—
191#878—22no—
192#878—24no—
193#878—24no—
194#878—24no—
195#878—24no—
196#878—22no—
197#878—22no—
198#870—22no—
199#870C2312yes—
200#869—21no—
201#869—21no—
202#869—21no—
203#869—21no—
204#869C2311yescharacteristic
205#869C2312yes—
206#869C2311yescharacteristic
207#869C2312yes—
208C4×Dic6—21no—
209C4×Dic6—21no—
210C4×Dic6—21no—
211C4×Dic6—21no—
212C4×Dic6—22no—
213C4×Dic6—22no—
214C4×Dic6—22no—
215C4×Dic6D411yescharacteristic
216C4×Dic6D411yescharacteristic
217C4×Dic6D412yes—
218C4×Dic6C2311yescharacteristic
219C4×Dic6C2311yescharacteristic
220C4×Dic6C2312yes—
221C3×#107C2312yes—
222C3×#106C2312yes—
223C3×#103C2312yes—
224C3×#102C2312yes—
225C3×#102C2312yes—
226C3×#102C2312yes—
227C3×#97C2312yes—
228C3×C4×C8C2312yes—
229#835C2314yes—
230#832C2314yes—
231#832C2314yes—
232#832C2314yes—
233#818C2314yes—
234#818C2314yes—
235#817C2314yes—
236#817C2314yes—
237#815C2314yes—
238Dic3⋊C8C2314yes—
239Dic3⋊C8C2314yes—
240C8×Dic3C2314yes—
241#808C2314yes—
242#808C2314yes—
243#807C2314yes—
244#807C2314yes—
245C4⋊(C3⋊C8)C2312yes—
246C4⋊(C3⋊C8)C2312yes—
247C2×AGL(1,ℤ/8)C2×D311yescharacteristic
248Q82—31no—
249#557—31no—
250#557—32no—
251#554—31no—
252#554—32no—
253#554—32no—
254#554—34no—
255#554—32no—
256#554—62no—
257#554—61no—
258#554—61no—
259#554—62no—
260#554—61no—
261D4×Q8—31no—
262D4×Q8—61no—
263#533—32no—
264#533—31no—
265#533—61no—
266#533—62no—
267C2×C4⋊Q8—31no—
268C2×#125—32no—
269C2×C22⋊Q8—62no—
270C2×C22⋊Q8—61no—
271C4×#41—32no—
272C4×#41C2×D311yescharacteristic
273C2×C4×Q8—31no—
274C2×C4×Q8—61no—
275C2×C4×D4—32no—
276C2×C4×D4C2×D311yescharacteristic
277C22×C4⋊C4—61no—
278#501—34no—
279#501—34no—
280#501—34no—
281#500—32no—
282#499—34no—
283#499—34no—
284#498—32no—
285#479—34no—
286#479—34no—
287#478—34no—
288#478—34no—
289#478—34no—
290#478—34no—
291#478—34no—
292#477—32no—
293#476—32no—
294#476—32no—
295#476—34no—
296#475—32no—
297#474—32no—
298#474—32no—
299#474—34no—
300#446—34no—
301#446—32no—
302C8×Q8—32no—
303#442—34no—
304#442C2×D312yes—
305#440—34no—
306#440C2×D312yes—
307C4×SD16—34no—
308C4×SD16C2×D312yes—
309C4×D8—34no—
310C4×D8C2×D312yes—
311#428—32no—
312#428—32no—
313#428—32no—
314#428—32no—
315#428C2×D311yescharacteristic
316#423—32no—
317#423—31no—
318#418—32no—
319#418C2×D311yescharacteristic
320#417—32no—
321#417C2×D311yescharacteristic
322C4×M16—32no—
323C4×M16C2×D311yescharacteristic
324C24×C3—21no—
325C3×#41—22no—
326C3×#41C2×Q814yes—
327C2×C3×Q8C2411yescharacteristic
328C2×C3×D4—21no—
329C2×C3×D4—21no—
330C2×C3×D4—22no—
331C2×C3×D4C2×Q814yescomplemented
332C2×C3×D4C2411yescharacteristic
333C2×C3×D4C2412yes—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—22no—
337C22×C3×C4—22no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—44no—
341C22×C3×C4C2×D411yescharacteristic
342C22×C3×C4C2×D411yescharacteristic
343C22×C3×C4C2411yescharacteristic
344C22×Dic3—22no—
345C22×Dic3—22no—
346C22×Dic3—22no—
347C22×Dic3—24no—
348C22×Dic3—24no—
349C22×Dic3—84no—
350C22×Dic3C2×D412yes—
351C22×Dic3C2×D412yes—
352C2×Dic6—21no—
353C2×Dic6—22no—
354C2×Dic6—21no—
355C2×Dic6—22no—
356C2×Dic6—22no—
357C2×Dic6—22no—
358C2×Dic6—42no—
359C2×Dic6—44no—
360C2×Dic6—82no—
361C2×Dic6C2×D411yescharacteristic
362C2×Dic6C2×D411yescharacteristic
363C2×Dic6C2×D412yes—
364C3×SD16C2×Q818yescomplemented
365C3×D8C2×Q818yescomplemented
366C3×M16—22no—
367C3×M16C2×Q814yescomplemented
368C2×C3×C8C2412yes—
369C2×C3×C8C2412yes—
370C3×C4⋊C4—21no—
371C3×C4⋊C4—21no—
372C3×C4⋊C4—21no—
373C3×C4⋊C4C2411yescharacteristic
374C3×C4⋊C4C2412yes—
375C3×C4⋊C4C2411yescharacteristic
376C3×C22⋊C4—21no—
377C3×C22⋊C4—22no—
378C3×C22⋊C4—22no—
379C3×C22⋊C4—21no—
380C3×C22⋊C4—21no—
381C3×C42—21no—
382C3×C42—21no—
383C3×C42—21no—
384C3×C42C2×D411yescharacteristic
385C3×C42C2×D411yescharacteristic
386C3×C42C2411yescharacteristic
387C3×C42C2411yescharacteristic
388#217—22no—
389#217—22no—
390#217—22no—
391#217—24no—
392#217—24no—
393C4⋊Dic3—21no—
394C4⋊Dic3—21no—
395C4⋊Dic3—22no—
396C4⋊Dic3—22no—
397C4⋊Dic3—22no—
398C4⋊Dic3—22no—
399C4⋊Dic3—22no—
400C4⋊Dic3—22no—
401C4⋊Dic3—22no—
402C4⋊Dic3—24no—
403C4⋊Dic3—24no—
404C4⋊Dic3C2×D411yescharacteristic
405C4⋊Dic3C2×D411yescharacteristic
406C4⋊Dic3C2×D412yes—
407C4⋊Dic3C2412yes—
408C4⋊Dic3C2414yes—
409C4⋊Dic3C2412yes—
410Dic3⋊C4—22no—
411Dic3⋊C4—22no—
412Dic3⋊C4—22no—
413Dic3⋊C4—22no—
414Dic3⋊C4—22no—
415Dic3⋊C4—22no—
416Dic3⋊C4—24no—
417Dic3⋊C4—24no—
418Dic3⋊C4C2×D412yes—
419Dic3⋊C4C2×D412yes—
420Dic3⋊C4C2×D412yes—
421Dic3⋊C4C2×D412yes—
422C4×Dic3—22no—
423C4×Dic3—22no—
424C4×Dic3—22no—
425C4×Dic3C2×D412yes—
426C4×Dic3C2×D412yes—
427C4×Dic3C2412yes—
428C4×Dic3C2412yes—
429#208—24no—
430C2×C3⋊C8C2414yes—
431C2×#41C22×D311yescharacteristic
432C22×Q8—31no—
433C22×Q8—61no—
434C22×Q8—61no—
435C22×D4C22×D311yescharacteristic
436C23×C4—21no—
437C23×C4—62no—
438AGL(1,ℤ/8)Dic618yescomplemented
439C2×SD16C22×D312yes—
440C2×D8C22×D312yes—
441C2×M16—32no—
442C2×M16C22×D311yescharacteristic
443C2×M16C22×D311yescharacteristic
444C4⋊Q8—32no—
445C4⋊Q8—32no—
446C4⋊Q8—32no—
447C4⋊Q8—32no—
448C4⋊Q8—31no—
449C4⋊Q8—31no—
450C4⋊Q8—61no—
451C4⋊Q8—61no—
452C4⋊Q8—62no—
453C4⋊Q8—62no—
454C4⋊Q8—61no—
455C4⋊Q8—61no—
456#125—34no—
457#125—34no—
458#125—32no—
459#125—32no—
460#125—32no—
461#125—62no—
462#125—62no—
463#125—62no—
464#125—62no—
465#125—62no—
466C22⋊Q8—64no—
467C22⋊Q8—64no—
468C22⋊Q8—64no—
469C22⋊Q8—64no—
470C22⋊Q8—62no—
471C22⋊Q8—62no—
472C22⋊Q8—62no—
473C22⋊Q8—62no—
474C22⋊Q8—62no—
475C22⋊Q8—62no—
476C22⋊Q8—61no—
477C22⋊Q8—62no—
478C22⋊Q8—62no—
479C22⋊Q8—62no—
480C22⋊Q8—64no—
481C22⋊Q8—61no—
482C22⋊Q8—61no—
483C22⋊Q8—61no—
484C4×Q8—31no—
485C4×Q8—32no—
486C4×Q8—31no—
487C4×Q8—31no—
488C4×Q8—31no—
489C4×Q8—32no—
490C4×Q8—32no—
491C4×Q8—32no—
492C4×Q8—62no—
493C4×Q8—62no—
494C4×Q8—62no—
495C4×Q8—61no—
496C4×Q8—61no—
497C4×Q8—61no—
498C4×Q8—61no—
499C4×Q8C22×D311yescharacteristic
500C4×Q8C22×D311yescharacteristic
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—34no—
506C4×D4—34no—
507C4×D4—32no—
508C4×D4—32no—
509C4×D4—62no—
510C4×D4—62no—
511C4×D4—62no—
512C4×D4—62no—
513C4×D4C22×D312yes—
514C4×D4C22×D312yes—
515C4×D4C22×D311yescharacteristic
516C4×D4C22×D311yescharacteristic
517#117—21no—
518#117—32no—
519#117—62no—
520#117C22×D311yescharacteristic
521C2×C4⋊C4—31no—
522C2×C4⋊C4—32no—
523C2×C4⋊C4—32no—
524C2×C4⋊C4—62no—
525C2×C4⋊C4—64no—
526C2×C4⋊C4—62no—
527C2×C4⋊C4—62no—
528C2×C4⋊C4—61no—
529C2×C4⋊C4—62no—
530C2×C4⋊C4—62no—
531C2×C4⋊C4—61no—
532C2×C4⋊C4C22×D311yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—62no—
535C2×C42—21no—
536C2×C42—32no—
537C2×C42—62no—
538C2×C42C22×D311yescharacteristic
539#107—34no—
540#107—34no—
541#107—34no—
542#107—34no—
543#107C22×D312yes—
544#106—34no—
545#106—34no—
546#106—34no—
547#106—34no—
548#106C22×D312yes—
549C4⋊C8—34no—
550C4⋊C8—34no—
551C4⋊C8—32no—
552C4⋊C8—32no—
553#103—34no—
554#103C22×D312yes—
555#102—34no—
556#102—34no—
557#102—34no—
558#102C22×D312yes—
559#102C22×D312yes—
560#102C22×D312yes—
561#97—34no—
562#97C22×D312yes—
563C4×C8—34no—
564C4×C8C22×D312yes—
565C23×C3—24no—
566C23×C3—21no—
567C23×C3—22no—
568C23×C3—42no—
569C23×C3—42no—
570C23×C3C22×D411yescharacteristic
571C3×Q8—21no—
572C3×Q8C22×Q812yes—
573C3×D4—24no—
574C3×D4—24no—
575C3×D4—22no—
576C3×D4—21no—
577C3×D4C22×Q812yes—
578C3×D4C22×Q814yes—
579C2×C3×C4—21no—
580C2×C3×C4—24no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—41no—
586C2×C3×C4—44no—
587C2×C3×C4—42no—
588C2×C3×C4—42no—
589C2×C3×C4—44no—
590C2×C3×C4—81no—
591C2×C3×C4C22×D411yescharacteristic
592C2×C3×C4C22×D411yescharacteristic
593C2×C3×C4C22×D411yescharacteristic
594C2×C3×C4C22×D411yescharacteristic
595C2×C3×C4C22×D411yescharacteristic
596C2×C3×C4C22×Q812yes—
597C2×C3×C42−1+412yes—
598C2×C3×C4C2511yescharacteristic
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—24no—
602C2×Dic3—42no—
603C2×Dic3—42no—
604C2×Dic3—44no—
605C2×Dic3—44no—
606C2×Dic3—82no—
607C2×Dic3—84no—
608C2×Dic3—84no—
609C2×Dic3C22×D412yes—
610C2×Dic3C22×D412yes—
611C2×Dic3C22×D412yes—
612C2×Dic3C22×D412yes—
613Dic6—22no—
614Dic6—22no—
615Dic6—42no—
616Dic6—44no—
617Dic6—42no—
618Dic6—82no—
619Dic6—81no—
620Dic6—82no—
621Dic6—82no—
622C3×C8—22no—
623C3×C8C22×Q814yes—
624C3⋊C8—24no—
625C24—21no—
626#41—22no—
627#41C2×Dic614yes—
628C2×Q8—31no—
629C2×Q8—31no—
630C2×Q8—32no—
631C2×Q8—62no—
632C2×Q8—62no—
633C2×Q8—61no—
634C2×Q8—61no—
635C2×Q8—62no—
636C2×Q8—62no—
637C2×Q8—122no—
638C2×Q8—124no—
639C2×Q8—242no—
640C2×Q8C23×D311yescharacteristic
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—22no—
644C2×D4C2×Dic614yescomplemented
645C2×D4C23×D311yescharacteristic
646C2×D4C23×D312yes—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—21no—
653C22×C4—32no—
654C22×C4—32no—
655C22×C4—44no—
656C22×C4—62no—
657C22×C4—62no—
658C22×C4—64no—
659C22×C4—64no—
660C22×C4—62no—
661C22×C4—244no—
662C22×C4D3×D411yescharacteristic
663C22×C4D3×D411yescharacteristic
664C22×C4C23×D311yescharacteristic
665SD16C2×Dic618yescomplemented
666D8C2×Dic618yescomplemented
667M16—22no—
668M16—64no—
669M16C2×Dic614yescomplemented
670C2×C8—34no—
671C2×C8C23×D312yes—
672C2×C8C23×D312yes—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—31no—
677C4⋊C4—32no—
678C4⋊C4—31no—
679C4⋊C4—32no—
680C4⋊C4—32no—
681C4⋊C4—32no—
682C4⋊C4—32no—
683C4⋊C4—32no—
684C4⋊C4—32no—
685C4⋊C4—34no—
686C4⋊C4—64no—
687C4⋊C4—64no—
688C4⋊C4—62no—
689C4⋊C4—62no—
690C4⋊C4—62no—
691C4⋊C4—64no—
692C4⋊C4—64no—
693C4⋊C4—62no—
694C4⋊C4—62no—
695C4⋊C4—62no—
696C4⋊C4—62no—
697C4⋊C4—62no—
698C4⋊C4—62no—
699C4⋊C4—62no—
700C4⋊C4—62no—
701C4⋊C4—62no—
702C4⋊C4—61no—
703C4⋊C4—62no—
704C4⋊C4—61no—
705C4⋊C4C23×D311yescharacteristic
706C4⋊C4C23×D311yescharacteristic
707C4⋊C4C23×D312yes—
708C22⋊C4—21no—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—64no—
714C22⋊C4—64no—
715C22⋊C4—62no—
716C22⋊C4—62no—
717C22⋊C4—62no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—32no—
722C42—32no—
723C42—32no—
724C42—32no—
725C42—62no—
726C42—62no—
727C42—62no—
728C42D3×D411yescharacteristic
729C42D3×D411yescharacteristic
730C42C23×D311yescharacteristic
731C42C23×D311yescharacteristic
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—22no—
735C22×C3—24no—
736C22×C3—48no—
737C22×C3—42no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—42no—
741C22×C3D4×Q812yes—
742C22×C3C23×D411yescharacteristic
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—22no—
746C3×C4—21no—
747C3×C4—41no—
748C3×C4—41no—
749C3×C4—42no—
750C3×C4D4×Q812yes—
751C3×C4#57512yes—
752C3×C4C23×Q811yescharacteristic
753C3×C4C2×2−1+411yescharacteristic
754Dic3—22no—
755Dic3—22no—
756Dic3—22no—
757Dic3—22no—
758Dic3—44no—
759Dic3—42no—
760Dic3—42no—
761C23—21no—
762C23—22no—
763C23—24no—
764C23—42no—
765C23—42no—
766C23C2×D3×D411yescharacteristic
767Q8—21no—
768Q8—62no—
769Q8—62no—
770Q8—122no—
771Q8—124no—
772Q8—122no—
773Q8—242no—
774Q8—242no—
775Q8—241no—
776Q8—242no—
777Q8C22×Dic612yes—
778D4—24no—
779D4—22no—
780D4—21no—
781D4—24no—
782D4C22×Dic612yes—
783D4C22×Dic614yes—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—32no—
791C2×C4—32no—
792C2×C4—32no—
793C2×C4—32no—
794C2×C4—41no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—42no—
799C2×C4—62no—
800C2×C4—62no—
801C2×C4—64no—
802C2×C4—81no—
803C2×C4—122no—
804C2×C4—122no—
805C2×C4—124no—
806C2×C4—124no—
807C2×C4—244no—
808C2×C4—244no—
809C2×C4—242no—
810C2×C4C22×Dic612yes—
811C2×C4C2×D3×D411yescharacteristic
812C2×C4C2×D3×D411yescharacteristic
813C2×C4C2×D3×D411yescharacteristic
814C2×C4C2×D3×D411yescharacteristic
815C2×C4C2×D3×D411yescharacteristic
816C2×C4#101012yes—
817C2×C4C24×D311yescharacteristic
818C8—22no—
819C8—64no—
820C8C22×Dic614yes—
821C2×C3—22no—
822C2×C3—42no—
823C2×C3—44no—
824C2×C3C2×D4×Q811yescharacteristic
825C2×C3C2×#57511yescharacteristic
826C2×C3#358511yescharacteristic
827C22—21no—
828C22—21no—
829C22—22no—
830C22—24no—
831C22—48no—
832C22—42no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22D4×Dic612yes—
837C22C22×D3×D411yescharacteristic
838C4—21no—
839C4—21no—
840C4—21no—
841C4—22no—
842C4—42no—
843C4—41no—
844C4—41no—
845C4—62no—
846C4—62no—
847C4—62no—
848C4—62no—
849C4—122no—
850C4—124no—
851C4—122no—
852C4D4×Dic612yes—
853C4#577312yes—
854C4C23×Dic611yescharacteristic
855C4C2×#101011yescharacteristic
856C3#6136711yescharacteristic, complemented, Sylow
857C2—22no—
858C2—44no—
859C2—42no—
860C2C2×D4×Dic611yescharacteristic
861C2C2×#577311yescharacteristic
862C2#8720011yescharacteristic
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
hypocenterC3#61367
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×#5543C2semidirect
5. #82508C2semidirect
6. #82296C2semidirect
7. #79856C2semidirect
8. #79762C2semidirect
9. #79634C2semidirect
10. #79632C2semidirect
11. #79576C2semidirect
12. #79574C2semidirect
13. #79204C2semidirect
14. #78917C2semidirect
15. #78871C2semidirect
16. M16×Dic6C2semidirect
17. #78506C2semidirect
26. #5570C22semidirect
27. #5569C22semidirect
28. Q8×Dic6C22semidirect
36. #5543C22semidirect
38. #5539C22semidirect
40. D4×Dic6C22semidirect
68. #5021C22semidirect
69. #5020C22semidirect
72. #5008C22semidirect
74. #5007C22semidirect
78. #4878C22semidirect
79. #4876C22semidirect
80. #4858C22semidirect
81. #4856C22semidirect
82. #4799C22semidirect
83. #4796C22semidirect
85. #4766C22semidirect
87. #4763C22semidirect
90. #4702C22semidirect
91. #4701C22semidirect
92. #4682C22semidirect
93. #4680C22semidirect
94. #4679C22semidirect
95. C8×Dic6C22semidirect
120. C3×AGL(1,ℤ/8)Q8semidirect
331. C2×C3×D4C2×Q8semidirect
364. C3×SD16C2×Q8semidirect
365. C3×D8C2×Q8semidirect
367. C3×M16C2×Q8semidirect
438. AGL(1,ℤ/8)Dic6semidirect
644. C2×D4C2×Dic6semidirect
665. SD16C2×Dic6semidirect
666. D8C2×Dic6semidirect
669. M16C2×Dic6semidirect
856. C3#61367semidirect

Maximal subgroups

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

subgroupindex
#41×Dic62
C2×#55432
C3×C4×AGL(1,ℤ/8)2
Dic3×AGL(1,ℤ/8)2
#825082
#822962
#798562
#797622
#796342
#796322
#795762
#795742
#792042
#789172
#788712
M16×Dic62
#785062
#613673