Finite Group Databasebeta

← #11675524

Subgroups — #11675524

Order 768.

1846 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#85828C211yesmaximal, characteristic, complemented
2#85788C211yesmaximal, characteristic, complemented
3C3×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
4#83936C212yesmaximal, complemented
5#82525C211yesmaximal, characteristic, complemented
6C2×#5008C211yesmaximal, characteristic, complemented
7#79853C214yesmaximal, complemented
8#79754C214yesmaximal, complemented
9#79626C212yesmaximal, complemented
10#79622C212yesmaximal, complemented
11#79570C212yesmaximal, complemented
12#79568C212yesmaximal, complemented
13#79244C212yesmaximal, complemented
14#78920C212yesmaximal, complemented
15#78869C212yesmaximal, complemented
16#78528C211yesmaximal, characteristic, complemented
17#78508C211yesmaximal, characteristic, complemented
18#61347—31nomaximal, Sylow
19C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
20C3×C4×#41C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22#5827C2212yes—
23C2×#950C2212yes—
24#5805C2212yes—
25#5791—22no—
26#5570C2212yescomplemented
27Q8×Dic6C2212yescomplemented
28#5563—21no—
29#5559C2214yes—
30#5558—22no—
31#5553C2212yes—
32#5551—21no—
33#5543—22no—
34#5543C2212yescomplemented
35#5542C2212yes—
36D4×Dic6—22no—
37D4×Dic6C2212yescomplemented
38#5519—22no—
39#5519C2212yes—
40#5504C2212yes—
41#5494—22no—
42#5477C2211yescharacteristic
43#5470—21no—
44#5470C2211yescharacteristic
45C2×#869—21no—
46C2×#869C2211yescharacteristic
47C3×#442C2212yes—
48C3×#440C2212yes—
49C3×C4×SD16C2212yes—
50C3×C4×D8C2212yes—
51C3×#428C2211yescharacteristic
52C3×#418C2211yescharacteristic
53C3×#417C2211yescharacteristic
54C3×C4×M16C2211yescharacteristic
55C2×#832C2212yes—
56#5166C2214yes—
57#5163C2214yes—
58#5153C2214yes—
59#5150C2214yes—
60#5133C2212yes—
61#5133C2212yes—
62#5122C2212yes—
63#5119C2212yes—
64#5031C2211yescharacteristic, complemented
65#5028C2212yescomplemented
66#5027C2211yescharacteristic, complemented
67#5019C2211yescharacteristic, complemented
68#5016C2212yescomplemented
69#5015C2211yescharacteristic, complemented
70#5008C2212yes—
71#5008C2212yes—
72#5008C2214yes—
73#5002C2212yes—
74C2×#808C2212yes—
75C2×C4⋊(C3⋊C8)C2211yescharacteristic
76#4891C2214yescomplemented
77#4877C2214yescomplemented
78#4870C2214yescomplemented
79#4854C2214yescomplemented
80#4789C2214yescomplemented
81#4788C2214yescomplemented
82#4785C2214yescomplemented
83#4768C2214yes—
84#4765C2214yes—
85#4764C2214yes—
86#4760C2214yes—
87#4758C2214yescomplemented
88#4714C2214yescomplemented
89#4701C2214yescomplemented
90#4694C2212yescomplemented
91#4681C2212yescomplemented
92#4679C2212yescomplemented
93C8×Dic6C2212yescomplemented
94#3506—31no—
95#3503—31no—
96#3373—34no—
97#3371—34no—
98#3369—32no—
99#3366—32no—
100#3362—32no—
101#3360—32no—
102#3141—31no—
103#3136—32no—
104#3084—32no—
105C2×#476—31no—
106#3045—32no—
107#3035—31no—
108#2962—31no—
109#2952—32no—
110C4×AGL(1,ℤ/8)D311yescharacteristic, complemented
111C2×C3×#41C2311yescharacteristic
112C22×C3×D4C2311yescharacteristic
113C23×C3×C4—21no—
114C2×#235—22no—
115C2×#235C2312yes—
116C22×Dic6—21no—
117C22×Dic6—22no—
118C3×AGL(1,ℤ/8)—24no—
119C2×C3×SD16C2312yes—
120C2×C3×D8C2312yes—
121C2×C3×M16C2311yescharacteristic
122C2×C3×M16C2311yescharacteristic
123C3×C4×Q8C2311yescharacteristic
124C3×C4×Q8C2311yescharacteristic
125C3×C4×D4—21no—
126C3×C4×D4—21no—
127C3×C4×D4—21no—
128C3×C4×D4—21no—
129C3×C4×D4C2312yes—
130C3×C4×D4C2312yes—
131C3×C4×D4C2311yescharacteristic
132C3×C4×D4C2311yescharacteristic
133C3×#117—21no—
134C3×#117C2311yescharacteristic
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C22⋊C4—21no—
137C2×C3×C42—21no—
138C2×C3×C42C2311yescharacteristic
139#953—24no—
140#950—28no—
141Q8×Dic3C2314yes—
142C2×#216C2312yes—
143C2×#215C2312yes—
144#940C2314yes—
145#938—22no—
146#938—22no—
147#936C2314yes—
148D4×Dic3—24no—
149D4×Dic3C2314yes—
150C2×#214C2312yes—
151C2×#213C2312yes—
152#930—21no—
153#930—21no—
154#930—22no—
155#929—24no—
156C4×#67—24no—
157C4×#67—24no—
158#926—22no—
159#926—22no—
160#926C2312yes—
161C2×C4⋊Dic3—21no—
162C2×C4⋊Dic3—22no—
163C2×C4⋊Dic3—22no—
164C2×C4⋊Dic3C2312yes—
165#924—22no—
166#924—22no—
167#924—22no—
168#924D412yes—
169#924D412yes—
170C22×C3⋊C8C2312yes—
171#893C2314yes—
172#892—22no—
173D3×C4⋊C4—22no—
174#890—24no—
175#890C2314yes—
176#888—24no—
177#888C2314yes—
178#887C2314yes—
179#885—24no—
180#884—24no—
181#883—24no—
182#879—24no—
183#878—24no—
184#878—24no—
185#878—24no—
186#875C2312yes—
187#874C2311yescharacteristic
188C4×D12—21no—
189C4×D12—21no—
190#870—22no—
191#870D412yes—
192#869—22no—
193#869—21no—
194#869—21no—
195#869—22no—
196#869—22no—
197#869D411yescharacteristic
198#869D411yescharacteristic
199#869C2311yescharacteristic
200#869C2312yes—
201#869C2312yes—
202C4×Dic6—22no—
203C4×Dic6—22no—
204C4×Dic6C2312yes—
205C4×Dic6C2312yes—
206C3×#107C2312yes—
207C3×#106C2312yes—
208C3×#103C2312yes—
209C3×#102C2312yes—
210C3×#102C2312yes—
211C3×#102C2312yes—
212C3×#97C2312yes—
213C3×C4×C8C2312yes—
214#832C2314yes—
215#832C2314yes—
216#821C2314yes—
217#821C2314yes—
218#816C2314yes—
219#816C2314yes—
220#815C2314yes—
221Dic3⋊C8C2314yes—
222Dic3⋊C8C2314yes—
223C8×Dic3C2314yes—
224#810C2312yes—
225#810C2312yes—
226#809C2312yes—
227#809C2312yes—
228#808C2314yes—
229#808C2314yes—
230C4⋊(C3⋊C8)C2311yescharacteristic
231C4⋊(C3⋊C8)C2311yescharacteristic
232C4⋊(C3⋊C8)C2312yes—
233C2×AGL(1,ℤ/8)C2×D311yescharacteristic
234C2×#135—32no—
235#559—34no—
236Q82—32no—
237#557—32no—
238#556—32no—
239#555—61no—
240#554—32no—
241#554—62no—
242#553—62no—
243#550—32no—
244D4×Q8—32no—
245D4×Q8—62no—
246#547—61no—
247#544—32no—
248#544—62no—
249#538—62no—
250#535—32no—
251#533—31no—
252#533—61no—
253#532—31no—
254C2×C4⋊Q8—31no—
255C2×C4⋊Q8—61no—
256#525—62no—
257#520—32no—
258#520—32no—
259C4×#41C2×D311yescharacteristic
260C2×C4×D4C2×D311yescharacteristic
261#490—34no—
262#489—34no—
263#489—34no—
264#488—34no—
265#487—32no—
266#486—34no—
267#486—32no—
268#479—34no—
269#478—34no—
270#476—32no—
271#476—32no—
272#476—34no—
273#476—34no—
274#475—34no—
275#464—34no—
276#464—32no—
277#463—34no—
278#463—32no—
279#462—31no—
280#461—31no—
281#460—34no—
282#460—31no—
283#459—34no—
284#459—31no—
285#446—34no—
286#446—32no—
287C8×Q8—32no—
288#442—34no—
289#442C2×D312yes—
290#441—34no—
291#440C2×D312yes—
292C4×SD16—34no—
293C4×SD16—34no—
294C4×SD16C2×D312yes—
295C4×D8C2×D312yes—
296#428C2×D311yescharacteristic
297C2×#106—32no—
298#424—32no—
299C2×C4⋊C8—31no—
300#418C2×D311yescharacteristic
301#417—32no—
302#417—32no—
303#417C2×D311yescharacteristic
304#416—32no—
305C2×#102—32no—
306#405—32no—
307C4×M16C2×D311yescharacteristic
308C24×C3—21no—
309C3×#41—22no—
310C3×#41#4114yescomplemented
311C2×C3×Q8C2411yescharacteristic
312C2×C3×D4—21no—
313C2×C3×D4—21no—
314C2×C3×D4—22no—
315C2×C3×D4—22no—
316C2×C3×D4C2412yes—
317C2×C3×D4C2411yescharacteristic
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—22no—
323C22×C3×C4—22no—
324C22×C3×C4—82no—
325C22×C3×C4C2×D411yescharacteristic
326C22×C3×C4C2×D411yescharacteristic
327C22×C3×C4C2411yescharacteristic
328C2×#67—22no—
329C2×#67—24no—
330C2×#67—24no—
331C22×Dic3—22no—
332C22×Dic3—24no—
333#235—24no—
334#235—24no—
335#235—84no—
336C2×D12—21no—
337C2×D12—21no—
338C2×D12C2412yes—
339C2×C4×D3—22no—
340C2×C4×D3—24no—
341C2×Dic6—22no—
342C2×Dic6—22no—
343C2×Dic6—24no—
344C2×Dic6—84no—
345C2×Dic6—82no—
346C2×Dic6C2×D412yes—
347C2×Dic6C2×D412yes—
348C2×Dic6C2412yes—
349C3×SD16—24no—
350C3×D8—24no—
351C3×M16—22no—
352C3×M16—22no—
353C2×C3×C8C2412yes—
354C2×C3×C8C2412yes—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4C2412yes—
359C3×C4⋊C4C2411yescharacteristic
360C3×C4⋊C4C2411yescharacteristic
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—22no—
365C3×C22⋊C4—22no—
366C3×C42—21no—
367C3×C42—21no—
368C3×C42—21no—
369C3×C42C2×D411yescharacteristic
370C3×C42C2×D411yescharacteristic
371C3×C42C2411yescharacteristic
372C3×C42C2411yescharacteristic
373#217—24no—
374#217—24no—
375#217—24no—
376#217C2×D414yes—
377#216—24no—
378#215—24no—
379#214—24no—
380#213—24no—
381(C2×D3)⋊C4—22no—
382(C2×D3)⋊C4—22no—
383(C2×D3)⋊C4—24no—
384C4⋊Dic3—22no—
385C4⋊Dic3—22no—
386C4⋊Dic3—22no—
387C4⋊Dic3—21no—
388C4⋊Dic3—21no—
389C4⋊Dic3—24no—
390C4⋊Dic3—24no—
391C4⋊Dic3C2×D412yes—
392C4⋊Dic3C2×D412yes—
393C4⋊Dic3C2×D412yes—
394C4⋊Dic3C2×D412yes—
395C4⋊Dic3C2414yes—
396Dic3⋊C4—24no—
397Dic3⋊C4—24no—
398Dic3⋊C4—24no—
399Dic3⋊C4C2×D414yes—
400Dic3⋊C4C2×D414yes—
401C4×Dic3—24no—
402C4×Dic3—24no—
403C4×Dic3C2414yes—
404C2×C3⋊C8—24no—
405C2×C3⋊C8C2412yes—
406C2×C3⋊C8C2412yes—
407C2×#41—32no—
408C2×#41—62no—
409C2×#41C22×D311yescharacteristic
410C22×Q8—62no—
411C22×Q8—61no—
412C22×D4C22×D311yescharacteristic
413C23×C4—21no—
414AGL(1,ℤ/8)—24no—
415#135—68no—
416C2×Q16—32no—
417C2×SD16—32no—
418C2×SD16—32no—
419C2×SD16C22×D312yes—
420C2×D8—32no—
421C2×D8C22×D312yes—
422C2×M16C22×D311yescharacteristic
423C2×M16C22×D311yescharacteristic
424C22×C8—32no—
425C4⋊Q8—34no—
426C4⋊Q8—31no—
427C4⋊Q8—31no—
428C4⋊Q8—32no—
429C4⋊Q8—32no—
430C4⋊Q8—31no—
431C4⋊Q8—62no—
432C4⋊Q8—62no—
433C4⋊Q8—62no—
434C4⋊Q8—64no—
435C4⋊Q8—61no—
436C4⋊Q8—61no—
437#127—34no—
438#127—31no—
439#126—64no—
440#125—34no—
441#125—32no—
442#125—62no—
443#125—64no—
444#124—34no—
445#124—32no—
446#124—64no—
447#123—64no—
448#123—64no—
449C22⋊Q8—32no—
450C22⋊Q8—32no—
451C22⋊Q8—64no—
452C22⋊Q8—64no—
453C22⋊Q8—64no—
454C22⋊Q8—62no—
455C22⋊Q8—62no—
456C22⋊Q8—62no—
457#121—64no—
458#121—62no—
459#121—62no—
460#121—62no—
461#121—61no—
462#121—61no—
463#120—64no—
464C4×Q8—32no—
465C4×Q8—32no—
466C4×Q8—34no—
467C4×Q8—34no—
468C4×Q8—62no—
469C4×Q8—62no—
470C4×Q8C22×D311yescharacteristic
471C4×Q8C22×D311yescharacteristic
472C4×D4—21no—
473C4×D4—21no—
474C4×D4—21no—
475C4×D4—21no—
476C4×D4—34no—
477C4×D4—34no—
478C4×D4—64no—
479C4×D4—64no—
480C4×D4—64no—
481C4×D4—61no—
482C4×D4—61no—
483C4×D4C22×D312yes—
484C4×D4C22×D312yes—
485C4×D4C22×D311yescharacteristic
486C4×D4C22×D311yescharacteristic
487#117—21no—
488#117—32no—
489#117—62no—
490#117—62no—
491#117—62no—
492#117C22×D311yescharacteristic
493C2×C4⋊C4—32no—
494C2×C4⋊C4—62no—
495C2×C4⋊C4—62no—
496C2×C4⋊C4—62no—
497C2×C4⋊C4—61no—
498C2×C4⋊C4C22×D311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C42—21no—
501C2×C42C22×D311yescharacteristic
502#107C22×D312yes—
503#106—34no—
504#106—34no—
505#106C22×D312yes—
506C4⋊C8—34no—
507C4⋊C8—34no—
508C4⋊C8—31no—
509C4⋊C8—31no—
510C4⋊C8—32no—
511#103—34no—
512#103—34no—
513#103—32no—
514#103—32no—
515#103C22×D312yes—
516#102—34no—
517#102—34no—
518#102—34no—
519#102—34no—
520#102—32no—
521#102—32no—
522#102C22×D312yes—
523#102C22×D312yes—
524#102C22×D312yes—
525#97—34no—
526#97C22×D312yes—
527C4×C8—34no—
528C4×C8C22×D312yes—
529C23×C3—21no—
530C23×C3—22no—
531C23×C3—42no—
532C23×C3—81no—
533C23×C3—81no—
534C23×C3C22×D411yescharacteristic
535C22×D3—22no—
536C3×Q8—21no—
537C3×Q8C2×#4112yes—
538C3×D4—24no—
539C3×D4—22no—
540C3×D4—21no—
541C3×D4—22no—
542C3×D4—42no—
543C3×D4C2×#4112yes—
544C2×C3×C4—21no—
545C2×C3×C4—24no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—41no—
551C2×C3×C4—42no—
552C2×C3×C4—44no—
553C2×C3×C4—42no—
554C2×C3×C4—82no—
555C2×C3×C4—81no—
556C2×C3×C4C22×D411yescharacteristic
557C2×C3×C4C22×D411yescharacteristic
558C2×C3×C4C22×D411yescharacteristic
559C2×C3×C4C22×D411yescharacteristic
560C2×C3×C4C22×D411yescharacteristic
561C2×C3×C4C2×#4112yes—
562C2×C3×C42−1+412yes—
563C2×C3×C4C2511yescharacteristic
564#67—44no—
565#67—84no—
566#67—84no—
567C2×Dic3—22no—
568C2×Dic3—24no—
569C2×Dic3—84no—
570C2×Dic3—82no—
571C2×Dic3C22×D414yes—
572C2×Dic3C22×D414yes—
573D12—22no—
574D12—22no—
575D12—42no—
576D12—81no—
577C4×D3—44no—
578C4×D3—84no—
579Dic6—24no—
580Dic6—22no—
581Dic6—22no—
582Dic6—42no—
583Dic6—44no—
584Dic6—84no—
585Dic6—82no—
586C3×C8—22no—
587C3×C8—22no—
588C3⋊C8—22no—
589C3⋊C8—22no—
590C24—21no—
591#41—22no—
592#41—64no—
593#41—64no—
594#41—244no—
595#41#23514yescomplemented
596C2×Q8—32no—
597C2×Q8—32no—
598C2×Q8—32no—
599C2×Q8—64no—
600C2×Q8—62no—
601C2×Q8—62no—
602C2×Q8—242no—
603C2×Q8—244no—
604C2×Q8C23×D311yescharacteristic
605C2×D4—21no—
606C2×D4—22no—
607C2×D4—21no—
608C2×D4—22no—
609C2×D4—32no—
610C2×D4—64no—
611C2×D4—64no—
612C2×D4—62no—
613C2×D4—61no—
614C2×D4—61no—
615C2×D4C23×D312yes—
616C2×D4C23×D311yescharacteristic
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—64no—
624C22×C4—64no—
625C22×C4—62no—
626C22×C4—62no—
627C22×C4—82no—
628C22×C4D3×D411yescharacteristic
629C22×C4D3×D411yescharacteristic
630C22×C4C23×D311yescharacteristic
631Q16—64no—
632SD16—24no—
633SD16—64no—
634SD16—64no—
635D8—24no—
636D8—64no—
637M16—22no—
638M16—22no—
639C2×C8—32no—
640C2×C8—32no—
641C2×C8—64no—
642C2×C8C23×D312yes—
643C2×C8C23×D312yes—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—32no—
648C4⋊C4—32no—
649C4⋊C4—32no—
650C4⋊C4—34no—
651C4⋊C4—32no—
652C4⋊C4—34no—
653C4⋊C4—34no—
654C4⋊C4—64no—
655C4⋊C4—64no—
656C4⋊C4—64no—
657C4⋊C4—64no—
658C4⋊C4—64no—
659C4⋊C4—62no—
660C4⋊C4—62no—
661C4⋊C4—62no—
662C4⋊C4—61no—
663C4⋊C4—61no—
664C4⋊C4C23×D311yescharacteristic
665C4⋊C4C23×D311yescharacteristic
666C4⋊C4C23×D312yes—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—34no—
673C22⋊C4—64no—
674C22⋊C4—64no—
675C22⋊C4—64no—
676C22⋊C4—64no—
677C22⋊C4—62no—
678C22⋊C4—62no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—34no—
683C42—64no—
684C42—64no—
685C42D3×D411yescharacteristic
686C42D3×D411yescharacteristic
687C42C23×D311yescharacteristic
688C42C23×D311yescharacteristic
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—22no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3—84no—
698C22×C3#54812yes—
699C22×C3C23×D411yescharacteristic
700C2×D3—42no—
701C2×D3—42no—
702C2×D3—42no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—22no—
706C3×C4—21no—
707C3×C4—41no—
708C3×C4—42no—
709C3×C4—41no—
710C3×C4#54812yes—
711C3×C4#57712yes—
712C3×C4C22×#4111yescharacteristic
713C3×C4C2×2−1+411yescharacteristic
714Dic3—24no—
715Dic3—24no—
716Dic3—44no—
717Dic3—42no—
718C23—21no—
719C23—22no—
720C23—42no—
721C23—62no—
722C23—81no—
723C23—81no—
724C23C2×D3×D411yescharacteristic
725Q8—21no—
726Q8—64no—
727Q8—62no—
728Q8—62no—
729Q8—122no—
730Q8—124no—
731Q8—242no—
732Q8—244no—
733Q8C2×#23512yes—
734D4—24no—
735D4—22no—
736D4—21no—
737D4—22no—
738D4—42no—
739D4—62no—
740D4—62no—
741D4—124no—
742D4—122no—
743D4—241no—
744D4—244no—
745D4—244no—
746D4C2×#23512yes—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—22no—
753C2×C4—34no—
754C2×C4—34no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—62no—
760C2×C4—64no—
761C2×C4—82no—
762C2×C4—81no—
763C2×C4—124no—
764C2×C4—244no—
765C2×C4—244no—
766C2×C4—242no—
767C2×C4C2×#23512yes—
768C2×C4C2×D3×D411yescharacteristic
769C2×C4C2×D3×D411yescharacteristic
770C2×C4C2×D3×D411yescharacteristic
771C2×C4C2×D3×D411yescharacteristic
772C2×C4C2×D3×D411yescharacteristic
773C2×C4#101012yes—
774C2×C4C24×D311yescharacteristic
775C8—22no—
776C8—22no—
777C8—62no—
778C8—62no—
779C2×C3—22no—
780C2×C3—42no—
781C2×C3—82no—
782C2×C3C2×#54811yescharacteristic
783C2×C3C2×#57711yescharacteristic
784C2×C3#358511yescharacteristic
785D3—82no—
786C22—21no—
787C22—21no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—84no—
795C22—122no—
796C22—122no—
797C22—122no—
798C22#555212yes—
799C22C22×D3×D411yescharacteristic
800C4—21no—
801C4—21no—
802C4—21no—
803C4—22no—
804C4—42no—
805C4—41no—
806C4—41no—
807C4—64no—
808C4—64no—
809C4—124no—
810C4—122no—
811C4#555212yes—
812C4#577512yes—
813C4C22×#23511yescharacteristic
814C4C2×#101011yescharacteristic
815C3#6134711yescharacteristic, complemented, Sylow
816C2—22no—
817C2—42no—
818C2—82no—
819C2—242no—
820C2C2×#555211yescharacteristic
821C2C2×#577511yescharacteristic
822C2#8720011yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×C4×AGL(1,ℤ/8)C2
socleC22×C3C23×D4
hypercenterC4×AGL(1,ℤ/8)D3
hypocenterC3#61347
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. #85828C2semidirect
2. #85788C2semidirect
3. C3×C4×AGL(1,ℤ/8)C2semidirect
4. #83936C2semidirect
5. #82525C2semidirect
6. C2×#5008C2semidirect
7. #79853C2semidirect
8. #79754C2semidirect
9. #79626C2semidirect
10. #79622C2semidirect
11. #79570C2semidirect
12. #79568C2semidirect
13. #79244C2semidirect
14. #78920C2semidirect
15. #78869C2semidirect
16. #78528C2semidirect
17. #78508C2semidirect
26. #5570C22semidirect
27. Q8×Dic6C22semidirect
34. #5543C22semidirect
37. D4×Dic6C22semidirect
64. #5031C22semidirect
65. #5028C22semidirect
66. #5027C22semidirect
67. #5019C22semidirect
68. #5016C22semidirect
69. #5015C22semidirect
76. #4891C22semidirect
77. #4877C22semidirect
78. #4870C22semidirect
79. #4854C22semidirect
80. #4789C22semidirect
81. #4788C22semidirect
82. #4785C22semidirect
87. #4758C22semidirect
88. #4714C22semidirect
89. #4701C22semidirect
90. #4694C22semidirect
91. #4681C22semidirect
92. #4679C22semidirect
93. C8×Dic6C22semidirect
110. C4×AGL(1,ℤ/8)D3semidirect
310. C3×#41#41semidirect
595. #41#235semidirect
815. C3#61347semidirect

Maximal subgroups

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

subgroupindex
#858282
#857882
C3×C4×AGL(1,ℤ/8)2
#839362
#825252
C2×#50082
#798532
#797542
#796262
#796222
#795702
#795682
#792442
#789202
#788692
#785282
#785082
#613473