Finite Group Databasebeta

← #11662142

Subgroups — #11662142

Order 768.

2714 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#575C211yesmaximal, characteristic, complemented
2#87268C211yesmaximal, characteristic, complemented
3#87260C211yesmaximal, characteristic, complemented
4C22×#950C211yesmaximal, characteristic, complemented
5C2×#5233C211yesmaximal, characteristic, complemented
6#83971C214yesmaximal, complemented
7#83970C212yesmaximal, complemented
8#83969C212yesmaximal, complemented
9#83936C214yesmaximal, complemented
10#83935C212yesmaximal, complemented
11#83934C212yesmaximal, complemented
12#83900C218yesmaximal, complemented
13#83768C211yesmaximal, characteristic, complemented
14C2×#5119C211yesmaximal, characteristic, complemented
15#60422—31nomaximal, Sylow
16C22×C3×#41C2211yescharacteristic
17C22×C3×#41C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C3×#575—28no—
20C2×C3×#137C2212yes—
21C2×C3×#137C2212yescomplemented
22C2×C3×AGL(1,ℤ/8)C2212yes—
23C2×C3×AGL(1,ℤ/8)C2212yescomplemented
24C2×C3×#135C2214yescomplemented
25C22×C3×M16C2211yescharacteristic
26#5833—22no—
27#5832C2214yescomplemented
28#5830C2212yes—
29#5828—22no—
30#5827—22no—
31#5827C2214yescomplemented
32Dic3×#41—22no—
33Dic3×#41C2214yescomplemented
34#5825C2212yes—
35C2×#950—28no—
36C2×#950C2214yes—
37C2×#950C2214yescomplemented
38#5816C2212yescomplemented
39#5812C2212yescomplemented
40C22×#216C2211yescharacteristic, complemented
41C22×#215C2211yescharacteristic, complemented
42#5805C2212yescomplemented
43#5804—22no—
44#5798—22no—
45#5798C2212yescomplemented
46C22×#214C2211yescharacteristic, complemented
47C22×#213C2211yescharacteristic, complemented
48#5791—22no—
49C2×#926—22no—
50C2×#926C2211yescharacteristic
51C2×#926C2211yescharacteristic
52C23×C3⋊C8C2211yescharacteristic
53#5233C2212yes—
54#5233C2212yes—
55#5233C2214yescomplemented
56C2×#835C2212yescomplemented
57C2×#832C2212yescomplemented
58#5185C2218yescomplemented
59#5182C2218yescomplemented
60#5166C2218yescomplemented
61#5165C2218yescomplemented
62#5163C2218yescomplemented
63#5162C2218yescomplemented
64#5153C2218yescomplemented
65#5150C2218yescomplemented
66#5133C2214yescomplemented
67#5131C2212yescomplemented
68#5120C2212yescomplemented
69#5119C2212yescomplemented
70#5119C2212yescomplemented
71#5119C2214yescomplemented
72#5113C2214yescomplemented
73C2×Dic3⋊C8C2214yescomplemented
74C2×#575D311yescharacteristic, complemented
75C22×#135—31no—
76#3449—31no—
77#3428—31no—
78#3046—34no—
79#3045—34no—
80#3044—32no—
81#3043—32no—
82#3042—32no—
83#3041—32no—
84#3035—38no—
85C2×#424—31no—
86#2896—31no—
87C2×#416—31no—
88C2×C3×#41—21no—
89C2×C3×#41—21no—
90C2×C3×#41—21no—
91C2×C3×#41—21no—
92C2×C3×#41—24no—
93C2×C3×#41—24no—
94C2×C3×#41—24no—
95C2×C3×#41D418yescomplemented
96C2×C3×#41C2312yes—
97C2×C3×#41C2312yes—
98C2×C3×#41C2312yes—
99C2×C3×#41C2312yes—
100C22×C3×Q8C2311yescharacteristic
101C22×C3×Q8C2311yescharacteristic
102C22×C3×D4—21no—
103C22×C3×D4—21no—
104C22×C3×D4C2311yescharacteristic
105C22×C3×D4C2311yescharacteristic
106C23×C3×C4—21no—
107C23×C3×C4—21no—
108C23×C3×C4C2311yescharacteristic
109C22×#67—21no—
110C2×#235—21no—
111C2×#235—21no—
112C2×#235—24no—
113C2×#235—24no—
114C2×#235C2312yes—
115C2×#235C2312yes—
116C22×D12C2311yescharacteristic
117C22×C4×D3—21no—
118C22×Dic6C2311yescharacteristic
119C3×#137—28no—
120C3×#137—28no—
121C3×AGL(1,ℤ/8)—28no—
122C3×AGL(1,ℤ/8)—28no—
123C3×#135—216no—
124C2×C3×Q16C2314yes—
125C2×C3×SD16C2314yes—
126C2×C3×SD16C2314yes—
127C2×C3×D8C2314yes—
128C2×C3×M16—24no—
129C2×C3×M16C2312yes—
130C2×C3×M16C2312yes—
131C22×C3×C8C2312yes—
132#953—24no—
133C2×#217—21no—
134C2×#217—24no—
135C2×#217D412yes—
136#950—216no—
137#950—216no—
138#947C2314yes—
139#946—24no—
140Q8×Dic3—24no—
141Q8×Dic3C2318yes—
142#944C2314yes—
143C2×#216—24no—
144C2×#216C2314yes—
145C2×#215—24no—
146C2×#215C2314yes—
147#940C2314yes—
148#939—28no—
149#938—24no—
150#937—24no—
151#936C2314yes—
152#935—24no—
153D4×Dic3—28no—
154D4×Dic3—28no—
155D4×Dic3—24no—
156D4×Dic3C2318yes—
157C2×#214—24no—
158C2×#214C2314yes—
159C2×#213—24no—
160C2×#213C2314yes—
161#930—24no—
162#929—24no—
163C4×#67—28no—
164#926—21no—
165#926—21no—
166#926—24no—
167#926—24no—
168#926—24no—
169#926D412yes—
170#926D412yes—
171#926C2312yes—
172#926C2312yes—
173#926C2312yes—
174#926C2312yes—
175C2×C4⋊Dic3—24no—
176C2×C4⋊Dic3D412yes—
177C2×C4⋊Dic3C2312yes—
178#924—24no—
179C2×C4×Dic3—21no—
180C2×C4×Dic3—24no—
181C2×C4×Dic3C2312yes—
182C22×C3⋊C8—24no—
183C22×C3⋊C8C2312yes—
184C22×C3⋊C8C2311yescharacteristic
185C22×C3⋊C8C2311yescharacteristic
186C22×C3⋊C8C2312yes—
187#835C2314yes—
188#835C2314yes—
189#832C2314yes—
190#832C2314yes—
191#821C2318yes—
192#816C2318yes—
193Dic3⋊C8C2318yes—
194Dic3⋊C8C2318yes—
195C22×#41—31no—
196C22×#41C2×D311yescharacteristic
197C22×#41C2×D311yescharacteristic
198#575—28no—
199C2×#137C2×D312yes—
200C2×#137C2×D312yescomplemented
201C2×AGL(1,ℤ/8)C2×D312yes—
202C2×AGL(1,ℤ/8)C2×D312yescomplemented
203C2×#135—34no—
204C2×#135—34no—
205C2×#135—68no—
206C2×#135C2×D314yescomplemented
207C22×Q16—31no—
208C22×SD16—31no—
209C22×SD16—31no—
210C22×D8—31no—
211C22×M16C2×D311yescharacteristic
212C23×C8—31no—
213#537—62no—
214#536—32no—
215#536—32no—
216#535—32no—
217#535—32no—
218#534—62no—
219#532—34no—
220#525—62no—
221#525—62no—
222#520—34no—
223#520—62no—
224#519—32no—
225#518—32no—
226#518—62no—
227C4×#41—34no—
228C4×#41—62no—
229C2×#117—31no—
230C2×#117—31no—
231C2×#117—62no—
232#464—38no—
233#464—38no—
234#463—38no—
235#463—38no—
236#462—38no—
237#461—38no—
238#460—38no—
239#459—38no—
240#424—32no—
241#424—32no—
242#424—34no—
243C2×C4⋊C8—34no—
244#419—32no—
245#418—32no—
246#417—34no—
247#416—32no—
248#416—32no—
249#416—34no—
250#416—34no—
251C2×#103—32no—
252C2×#102—32no—
253C24×C3—21no—
254C24×C3—21no—
255C24×C3C2×D411yescharacteristic
256C23×D3—21no—
257C3×#41—28no—
258C3×#41—28no—
259C3×#41—24no—
260C3×#41—24no—
261C3×#41—24no—
262C3×#41—24no—
263C3×#41—24no—
264C3×#41—24no—
265C3×#41—44no—
266C3×#41—44no—
267C3×#41C2×D418yes—
268C3×#41C2×D418yes—
269C2×C3×Q8—21no—
270C2×C3×Q8—21no—
271C2×C3×Q8—22no—
272C2×C3×Q8—22no—
273C2×C3×Q8—22no—
274C2×C3×Q8C2×D414yes—
275C2×C3×Q8C2412yes—
276C2×C3×Q8C2412yes—
277C2×C3×D4—28no—
278C2×C3×D4—22no—
279C2×C3×D4—22no—
280C2×C3×D4—22no—
281C2×C3×D4—22no—
282C2×C3×D4—21no—
283C2×C3×D4—22no—
284C2×C3×D4—21no—
285C2×C3×D4—22no—
286C2×C3×D4—22no—
287C2×C3×D4—44no—
288C2×C3×D4C2×D414yes—
289C2×C3×D4C2412yes—
290C2×C3×D4C2412yes—
291C22×C3×C4—21no—
292C22×C3×C4—28no—
293C22×C3×C4—22no—
294C22×C3×C4—22no—
295C22×C3×C4—21no—
296C22×C3×C4—22no—
297C22×C3×C4—22no—
298C22×C3×C4—44no—
299C22×C3×C4C2×D411yescharacteristic
300C22×C3×C4C2×D411yescharacteristic
301C22×C3×C4C2×D411yescharacteristic
302C22×C3×C4C2×D414yes—
303C22×C3×C4#4114yes—
304C22×C3×C4C2411yescharacteristic
305C22×C3×C4C2411yescharacteristic
306C22×C3×C4C2411yescharacteristic
307C2×#67—22no—
308C2×#67—22no—
309C2×#67—28no—
310C2×#67—44no—
311C22×Dic3—21no—
312C22×Dic3—22no—
313C22×Dic3—28no—
314C22×Dic3C2×D414yes—
315#235—24no—
316#235—24no—
317#235—24no—
318#235—24no—
319#235—44no—
320#235—44no—
321C2×D12—22no—
322C2×D12—22no—
323C2×D12—21no—
324C2×D12C2412yes—
325C2×C4×D3—22no—
326C2×C4×D3—22no—
327C2×C4×D3—44no—
328C2×Dic6—22no—
329C2×Dic6—22no—
330C2×Dic6—21no—
331C2×Dic6C2412yes—
332C3×Q16—28no—
333C3×SD16—28no—
334C3×SD16—28no—
335C3×D8—28no—
336C3×M16—24no—
337C3×M16—24no—
338C2×C3×C8—24no—
339C2×C3×C8C2414yes—
340#217—22no—
341#217—22no—
342#217—28no—
343#217—28no—
344#217C2×D414yes—
345#217C2×D414yes—
346#216—28no—
347#215—28no—
348#214—28no—
349#213—28no—
350(C2×D3)⋊C4—28no—
351C4⋊Dic3—22no—
352C4⋊Dic3—28no—
353C4⋊Dic3C2×D414yes—
354C4⋊Dic3C2×D414yes—
355C4⋊Dic3C2414yes—
356Dic3⋊C4—28no—
357C4×Dic3—22no—
358C4×Dic3—22no—
359C4×Dic3—28no—
360C4×Dic3C2×D414yes—
361C4×Dic3C2414yes—
362C2×C3⋊C8—22no—
363C2×C3⋊C8—22no—
364C2×C3⋊C8—24no—
365C2×C3⋊C8—24no—
366C2×C3⋊C8C2412yes—
367C2×C3⋊C8C2412yes—
368C2×#41—21no—
369C2×#41—21no—
370C2×#41—21no—
371C2×#41—21no—
372C2×#41—24no—
373C2×#41—24no—
374C2×#41—24no—
375C2×#41—32no—
376C2×#41—32no—
377C2×#41—61no—
378C2×#41—61no—
379C2×#41—64no—
380C2×#41—64no—
381C2×#41#6718yescomplemented
382C2×#41C22×D312yes—
383C2×#41C22×D312yes—
384C2×#41C22×D312yes—
385C2×#41C22×D312yes—
386C22×Q8—31no—
387C22×Q8C22×D311yescharacteristic
388C22×Q8C22×D311yescharacteristic
389C22×D4—21no—
390C22×D4—21no—
391C22×D4—31no—
392C22×D4—61no—
393C22×D4C22×D311yescharacteristic
394C22×D4C22×D311yescharacteristic
395C23×C4—21no—
396C23×C4—21no—
397C23×C4—61no—
398C23×C4C22×D311yescharacteristic
399#137—28no—
400#137—28no—
401AGL(1,ℤ/8)—28no—
402AGL(1,ℤ/8)—28no—
403#135—216no—
404#135—616no—
405#135—616no—
406C2×Q16—34no—
407C2×Q16—64no—
408C2×Q16C22×D314yes—
409C2×SD16—34no—
410C2×SD16—34no—
411C2×SD16—64no—
412C2×SD16—64no—
413C2×SD16C22×D314yes—
414C2×SD16C22×D314yes—
415C2×D8—34no—
416C2×D8—64no—
417C2×D8C22×D314yes—
418C2×M16—24no—
419C2×M16C22×D312yes—
420C2×M16C22×D312yes—
421C22×C8—31no—
422C22×C8—31no—
423C22×C8—32no—
424C22×C8—32no—
425C22×C8—64no—
426C22×C8C22×D312yes—
427C4⋊Q8—34no—
428#127—34no—
429#124—34no—
430#124—34no—
431#123—64no—
432#123—64no—
433C22⋊Q8—64no—
434C22⋊Q8—64no—
435#121—64no—
436#121—64no—
437#121—68no—
438#120—64no—
439#120—64no—
440C4×Q8—38no—
441C4×Q8—64no—
442C4×D4—38no—
443C4×D4—68no—
444C4×D4—68no—
445C4×D4—64no—
446C4×D4—68no—
447#117—32no—
448#117—32no—
449#117—32no—
450#117—32no—
451#117—32no—
452#117—32no—
453#117—64no—
454#117—64no—
455#117—64no—
456#117—61no—
457#117—61no—
458C2×C4⋊C4—32no—
459C2×C4⋊C4—32no—
460C2×C4⋊C4—64no—
461C2×C22⋊C4—32no—
462C2×C22⋊C4—64no—
463C2×C22⋊C4—61no—
464C2×C42—32no—
465C2×C42—64no—
466C2×C42—61no—
467C4⋊C8—38no—
468C4⋊C8—38no—
469#103—34no—
470#103—34no—
471#103—38no—
472#102—34no—
473#102—34no—
474#102—38no—
475C23×C3—22no—
476C23×C3—24no—
477C23×C3—22no—
478C23×C3—42no—
479C23×C3—42no—
480C23×C3—82no—
481C23×C3—82no—
482C23×C3#12114yes—
483C23×C3C22×D411yescharacteristic
484C23×C3C22×D411yescharacteristic
485C23×C3C22×D411yescharacteristic
486C22×D3—22no—
487C22×D3—42no—
488C22×D3—82no—
489C3×Q8—24no—
490C3×Q8—22no—
491C3×Q8—22no—
492C3×Q8—22no—
493C3×Q8—42no—
494C3×Q8C22×D414yes—
495C3×D4—28no—
496C3×D4—28no—
497C3×D4—24no—
498C3×D4—22no—
499C3×D4—22no—
500C3×D4—22no—
501C3×D4—44no—
502C3×D4—44no—
503C3×D4—42no—
504C3×D4C22×D414yes—
505C2×C3×C4—24no—
506C2×C3×C4—22no—
507C2×C3×C4—28no—
508C2×C3×C4—28no—
509C2×C3×C4—22no—
510C2×C3×C4—42no—
511C2×C3×C4—44no—
512C2×C3×C4—44no—
513C2×C3×C4#12114yes—
514C2×C3×C4#12114yes—
515C2×C3×C4#12114yes—
516C2×C3×C4C22×D411yescharacteristic
517C2×C3×C4C22×D411yescharacteristic
518C2×C3×C4C22×D411yescharacteristic
519C2×C3×C4C22×D412yes—
520C2×C3×C4C22×D412yes—
521C2×C3×C4C22×D412yes—
522C2×C3×C4C2×#4112yes—
523C2×C3×C4C2×#4112yes—
524C2×C3×C4C2×#4112yes—
525C2×C3×C4C2511yescharacteristic
526#67—44no—
527#67—44no—
528#67—88no—
529C2×Dic3—24no—
530C2×Dic3—22no—
531C2×Dic3—44no—
532C2×Dic3—42no—
533C2×Dic3—88no—
534C2×Dic3—82no—
535C2×Dic3C22×D418yes—
536D12—22no—
537D12—22no—
538D12—42no—
539C4×D3—44no—
540C4×D3—44no—
541Dic6—22no—
542Dic6—22no—
543Dic6—42no—
544C3×C8—24no—
545C3⋊C8—22no—
546C3⋊C8—22no—
547C24—21no—
548C24—21no—
549C24—61no—
550C24D3×D411yescharacteristic
551#41—28no—
552#41—28no—
553#41—24no—
554#41—24no—
555#41—24no—
556#41—24no—
557#41—24no—
558#41—24no—
559#41—44no—
560#41—44no—
561#41—64no—
562#41—64no—
563#41—64no—
564#41—64no—
565#41—124no—
566#41—124no—
567#41C2×#6718yes—
568#41C2×#6718yes—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—32no—
575C2×Q8—61no—
576C2×Q8—62no—
577C2×Q8—62no—
578C2×Q8C2×#6714yes—
579C2×Q8C23×D312yes—
580C2×Q8C23×D312yes—
581C2×D4—28no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—32no—
592C2×D4—44no—
593C2×D4—68no—
594C2×D4—62no—
595C2×D4—62no—
596C2×D4—61no—
597C2×D4—62no—
598C2×D4—62no—
599C2×D4—124no—
600C2×D4C2×#6714yes—
601C2×D4C23×D312yes—
602C2×D4C23×D312yes—
603C22×C4—21no—
604C22×C4—28no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—34no—
611C22×C4—44no—
612C22×C4—68no—
613C22×C4—61no—
614C22×C4—62no—
615C22×C4—62no—
616C22×C4—62no—
617C22×C4—124no—
618C22×C4D3×D411yescharacteristic
619C22×C4D3×D411yescharacteristic
620C22×C4D3×D411yescharacteristic
621C22×C4#23714yes—
622C22×C4C2×#6714yes—
623C22×C4C23×D311yescharacteristic
624C22×C4C23×D311yescharacteristic
625C22×C4C23×D311yescharacteristic
626Q16—28no—
627Q16—68no—
628SD16—28no—
629SD16—28no—
630SD16—68no—
631SD16—68no—
632D8—28no—
633D8—68no—
634M16—24no—
635M16—24no—
636C2×C8—24no—
637C2×C8—32no—
638C2×C8—32no—
639C2×C8—62no—
640C2×C8—62no—
641C2×C8—64no—
642C2×C8—64no—
643C2×C8C23×D314yes—
644C4⋊C4—34no—
645C4⋊C4—34no—
646C4⋊C4—34no—
647C4⋊C4—68no—
648C4⋊C4—68no—
649C4⋊C4—62no—
650C22⋊C4—34no—
651C22⋊C4—34no—
652C22⋊C4—68no—
653C22⋊C4—68no—
654C22⋊C4—68no—
655C22⋊C4—62no—
656C22⋊C4—62no—
657C42—34no—
658C42—34no—
659C42—68no—
660C42—62no—
661C42—62no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—24no—
666C22×C3—44no—
667C22×C3—44no—
668C22×C3—44no—
669C22×C3—42no—
670C22×C3—84no—
671C22×C3—84no—
672C22×C3C2×#12112yes—
673C22×C3C2×#12112yes—
674C22×C3C2×#12112yes—
675C22×C3C23×D411yescharacteristic
676C2×D3—44no—
677C2×D3—42no—
678C2×D3—84no—
679C3×C4—24no—
680C3×C4—42no—
681C3×C4C2×#12112yes—
682C3×C4C2×#12112yes—
683C3×C4C2×#12112yes—
684C3×C4C23×D411yescharacteristic
685C3×C4C22×#4111yescharacteristic
686Dic3—28no—
687Dic3—44no—
688Dic3—42no—
689C23—22no—
690C23—24no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—62no—
695C23—82no—
696C23—82no—
697C23—122no—
698C23—242no—
699C23#93914yes—
700C23C2×D3×D411yescharacteristic
701C23C2×D3×D411yescharacteristic
702C23C2×D3×D411yescharacteristic
703Q8—22no—
704Q8—24no—
705Q8—22no—
706Q8—22no—
707Q8—42no—
708Q8—62no—
709Q8—62no—
710Q8—122no—
711Q8C22×#6714yes—
712D4—28no—
713D4—28no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—24no—
718D4—44no—
719D4—44no—
720D4—42no—
721D4—62no—
722D4—62no—
723D4—124no—
724D4—124no—
725D4—122no—
726D4—248no—
727D4C22×#6714yes—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—28no—
731C2×C4—28no—
732C2×C4—22no—
733C2×C4—38no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—64no—
738C2×C4—62no—
739C2×C4—124no—
740C2×C4—122no—
741C2×C4—124no—
742C2×C4—124no—
743C2×C4—248no—
744C2×C4—242no—
745C2×C4#93914yes—
746C2×C4#93914yes—
747C2×C4#93914yes—
748C2×C4C2×D3×D411yescharacteristic
749C2×C4C2×D3×D411yescharacteristic
750C2×C4C2×D3×D411yescharacteristic
751C2×C4C2×#23712yes—
752C2×C4C2×#23712yes—
753C2×C4C2×#23712yes—
754C2×C4C22×#6712yes—
755C2×C4C22×#6712yes—
756C2×C4C22×#6712yes—
757C2×C4C24×D311yescharacteristic
758C8—24no—
759C8—62no—
760C8—62no—
761C2×C3—22no—
762C2×C3—22no—
763C2×C3—22no—
764C2×C3—44no—
765C2×C3—82no—
766C2×C3C22×#12111yescharacteristic
767C2×C3#358412yes—
768D3—82no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—24no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—42no—
777C22—84no—
778C22—84no—
779C22—124no—
780C22—122no—
781C22—244no—
782C22C2×#93912yes—
783C22C2×#93912yes—
784C22C2×#93912yes—
785C22C22×D3×D411yescharacteristic
786C4—24no—
787C4—42no—
788C4—68no—
789C4—124no—
790C4—122no—
791C4C2×#93912yes—
792C4C2×#93912yes—
793C4C2×#93912yes—
794C4C22×#23711yescharacteristic
795C4C23×#6711yescharacteristic
796C3#6042211yescharacteristic, complemented, Sylow
797C2—22no—
798C2—22no—
799C2—22no—
800C2—44no—
801C2—82no—
802C2—242no—
803C2#8719912yes—
804C2C22×#93911yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#575C2
socleC22×C3C23×D4
hypercenterC2×#575D3
hypocenterC3#60422
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×C3×#575C2semidirect
2. #87268C2semidirect
3. #87260C2semidirect
4. C22×#950C2semidirect
5. C2×#5233C2semidirect
6. #83971C2semidirect
7. #83970C2semidirect
8. #83969C2semidirect
9. #83936C2semidirect
10. #83935C2semidirect
11. #83934C2semidirect
12. #83900C2semidirect
13. #83768C2semidirect
14. C2×#5119C2semidirect
21. C2×C3×#137C22semidirect
23. C2×C3×AGL(1,ℤ/8)C22semidirect
24. C2×C3×#135C22semidirect
27. #5832C22semidirect
31. #5827C22semidirect
33. Dic3×#41C22semidirect
37. C2×#950C22semidirect
38. #5816C22semidirect
39. #5812C22semidirect
40. C22×#216C22semidirect
41. C22×#215C22semidirect
42. #5805C22semidirect
45. #5798C22semidirect
46. C22×#214C22semidirect
47. C22×#213C22semidirect
55. #5233C22semidirect
56. C2×#835C22semidirect
57. C2×#832C22semidirect
58. #5185C22semidirect
59. #5182C22semidirect
60. #5166C22semidirect
61. #5165C22semidirect
62. #5163C22semidirect
63. #5162C22semidirect
64. #5153C22semidirect
65. #5150C22semidirect
66. #5133C22semidirect
67. #5131C22semidirect
68. #5120C22semidirect
69. #5119C22semidirect
70. #5119C22semidirect
71. #5119C22semidirect
72. #5113C22semidirect
73. C2×Dic3⋊C8C22semidirect
74. C2×#575D3semidirect
95. C2×C3×#41D4semidirect
200. C2×#137C2×D3semidirect
202. C2×AGL(1,ℤ/8)C2×D3semidirect
206. C2×#135C2×D3semidirect
381. C2×#41#67semidirect
796. C3#60422semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5752
#872682
#872602
C22×#9502
C2×#52332
#839712
#839702
#839692
#839362
#839352
#839342
#839002
#837682
C2×#51192
#604223