Finite Group Databasebeta

← #11659398

Subgroups — #11659398

Order 768.

2742 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5748C211yesmaximal, characteristic
2#85731C211yesmaximal, characteristic, complemented
3C2×#5523C211yesmaximal, characteristic, complemented
4C3×#2873C211yesmaximal, characteristic, complemented
5#83768C211yesmaximal, characteristic, complemented
6C2×#5133C211yesmaximal, characteristic, complemented
7C2×#5121C211yesmaximal, characteristic, complemented
8#78574C214yesmaximal, complemented
9#78571C214yesmaximal, complemented
10#78562C214yesmaximal, complemented
11#78560C214yesmaximal, complemented
12C4×#909C214yesmaximal, complemented
13C4×#908C214yesmaximal, complemented
14#60170—31nomaximal, Sylow
15C22×#235C2211yescharacteristic
16C22×#235C2211yescharacteristic
17C22×C3×M16C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C2×C3×#117C2211yescharacteristic
20C2×#926C2211yescharacteristic
21C22×C4⋊Dic3C2211yescharacteristic
22#5748C4116yescomplemented
23C2×#909C2212yes—
24C2×#909C2212yes—
25C2×#908C2212yes—
26C2×#908C2212yes—
27C2×#904C2214yes—
28#5523—22no—
29#5523—22no—
30#5523C2214yes—
31#5523C2212yescomplemented
32#5523C2214yescomplemented
33#5523C2212yescomplemented
34#5522—22no—
35#5521C2212yescomplemented
36D3×#117—22no—
37#5516C2212yescomplemented
38#5504—21no—
39#5504—21no—
40C2×#892—21no—
41C2×D3×C4⋊C4—21no—
42#5486—22no—
43C2×#67⋊C4—22no—
44C4×#235C2214yes—
45C2×C4×D12C2212yescomplemented
46C2×C4×Dic6C2212yescomplemented
47C3×#405C2214yescomplemented
48C3×#405C2214yescomplemented
49C3×C4×M16C2214yescomplemented
50#5133C2214yes—
51#5133C2214yescomplemented
52#5133C2212yescomplemented
53#5133C2212yescomplemented
54#5131C2212yescomplemented
55#5121C2214yescomplemented
56#5121C2214yescomplemented
57#5120C2212yescomplemented
58#5113C2214yes—
59C2×#821C2212yescomplemented
60C2×#818C2212yescomplemented
61C2×#817C2212yescomplemented
62C2×#816C2212yescomplemented
63#4716C2218yescomplemented
64#4711C2218yescomplemented
65#4710C2218yescomplemented
66#4710C2218yescomplemented
67C4×Dic12C2218yescomplemented
68C4×D24C2218yescomplemented
69C4×#204C2218yescomplemented
70C4×#204C2218yescomplemented
71C2×#575—31no—
72#3428—31no—
73C2×#520—31no—
74#2952—34no—
75#2951—34no—
76#2947—34no—
77#2946—34no—
78C4×#137—34no—
79C4×AGL(1,ℤ/8)—34no—
80C2×#428—31no—
81#2896—31no—
82C2×#417—31no—
83#2873D311yescharacteristic, complemented
84C23×C3×C4C2311yescharacteristic
85C22×#67—21no—
86C22×#67—21no—
87C23×Dic3—21no—
88C2×#235—21no—
89C2×#235—21no—
90C2×#235—21no—
91C2×#235—21no—
92C2×#235—24no—
93C2×#235—24no—
94C2×#235C2×C418yescomplemented
95C2×#235C2×C418yescomplemented
96C2×#235C2312yes—
97C2×#235C2312yes—
98C2×#235C2312yes—
99C2×#235C2312yes—
100C22×D12C2311yescharacteristic
101C22×D12C2311yescharacteristic
102C22×C4×D3—21no—
103C22×C4×D3—21no—
104C22×C4×D3—22no—
105C22×Dic6C2311yescharacteristic
106C22×Dic6C2311yescharacteristic
107C2×C3×M16—24no—
108C2×C3×M16C2×C418yescomplemented
109C2×C3×M16C2312yes—
110C2×C3×M16C2312yes—
111C2×C3×M16C2312yes—
112C2×C3×M16C2312yes—
113C22×C3×C8C2312yes—
114C22×C3×C8C2312yes—
115C3×#117D412yes—
116C3×#117D412yes—
117C3×#117C2312yes—
118C3×#117C2312yes—
119C2×C3×C4⋊C4D411yescharacteristic
120C2×C3×C4⋊C4D411yescharacteristic
121C2×C3×C22⋊C4D412yes—
122C2×C3×C42C2312yes—
123C2×#217—21no—
124C4×#67—24no—
125C4×#67—24no—
126C2×(C2×D3)⋊C4—22no—
127#926—21no—
128#926—21no—
129#926C2312yes—
130#926C2312yes—
131C2×C4⋊Dic3—21no—
132C2×C4⋊Dic3—21no—
133C2×C4⋊Dic3—21no—
134C2×C4⋊Dic3C2312yes—
135C2×C4⋊Dic3C2312yes—
136C2×C4⋊Dic3C2312yes—
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×Dic3⋊C4—22no—
140C2×C4×Dic3—22no—
141C2×C4×Dic3—21no—
142#909C2×C4116yescomplemented
143#909C2×C4116yescomplemented
144#908C2×C4116yescomplemented
145#908C2×C4116yescomplemented
146C2×Dic12C2314yes—
147#904C2×C4132yescomplemented
148C2×D24C2314yes—
149C2×#204C2314yes—
150C2×#204C2314yes—
151#893—22no—
152#893—22no—
153#892—24no—
154#892—24no—
155#892—22no—
156#892—22no—
157D3×C4⋊C4—24no—
158D3×C4⋊C4—24no—
159D3×C4⋊C4—22no—
160D3×C4⋊C4—22no—
161#887—22no—
162#887—22no—
163#67⋊C4—28no—
164#67⋊C4—28no—
165#67⋊C4—24no—
166#67⋊C4—24no—
167D3×C22⋊C4—24no—
168#877—24no—
169C4×D12—24no—
170C4×D12C2314yes—
171C4×D12C2318yes—
172C4×D12C2314yes—
173#872—24no—
174C42×D3—24no—
175C4×Dic6—24no—
176C4×Dic6C2314yes—
177C4×Dic6C2318yes—
178C4×Dic6C2314yes—
179C3×#97C2318yes—
180C3×C4×C8C2318yes—
181#821C2314yes—
182#821C2314yes—
183#821C2318yes—
184#818C2318yes—
185#817C2318yes—
186#816C2314yes—
187#816C2314yes—
188#816C2318yes—
189C22×#41—31no—
190C22×#41—31no—
191#575—316no—
192C2×#137—32no—
193C2×#137—32no—
194C2×AGL(1,ℤ/8)—32no—
195C2×AGL(1,ℤ/8)—32no—
196C2×#135—34no—
197C22×M16C2×D311yescharacteristic
198C22×M16C2×D311yescharacteristic
199#520—34no—
200#520—34no—
201#520—32no—
202#520—32no—
203#520—62no—
204#520—62no—
205#520—61no—
206#520—61no—
207#519—32no—
208#518—32no—
209#518—62no—
210C4×#41—34no—
211C4×#41—62no—
212C2×C4×Q8—32no—
213C2×C4×D4—32no—
214C2×C4×D4—62no—
215C2×#117—31no—
216C2×#117—62no—
217C2×#117—61no—
218C2×#117C2×D311yescharacteristic
219C22×C4⋊C4—31no—
220C22×C4⋊C4—61no—
221#442—38no—
222#441—38no—
223#440—38no—
224#440—38no—
225C4×Q16—38no—
226C4×SD16—38no—
227C4×SD16—38no—
228C4×D8—38no—
229#428—34no—
230#428—34no—
231C2×#107—32no—
232C2×#106—32no—
233#419—32no—
234#418—32no—
235#417—34no—
236#417—34no—
237#417—32no—
238#417—32no—
239#416—34no—
240C2×#103—32no—
241C2×#102—32no—
242#405C2×D314yescomplemented
243#405C2×D314yescomplemented
244C4×M16C2×D314yescomplemented
245C24×C3C2×D411yescharacteristic
246C23×D3—21no—
247C23×D3—21no—
248C22×C3×C4C22×C414yes—
249C22×C3×C4C2×D412yes—
250C22×C3×C4C2×D412yes—
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4#4114yes—
255C22×C3×C4C2411yescharacteristic
256C22×C3×C4C2411yescharacteristic
257C22×C3×C4C2411yescharacteristic
258C2×#67—28no—
259C2×#67—28no—
260C2×#67—22no—
261C2×#67—22no—
262C2×#67—22no—
263C2×#67—22no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—22no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—22no—
270C22×Dic3—22no—
271C22×Dic3—82no—
272#235—28no—
273#235—28no—
274#235—28no—
275#235—28no—
276#235—24no—
277#235—24no—
278#235—24no—
279#235—24no—
280#235C22×C418yes—
281#235C22×C418yes—
282#235C22×C418yes—
283#235C22×C418yescomplemented
284C2×D12—21no—
285C2×D12—21no—
286C2×D12—22no—
287C2×D12—22no—
288C2×D12C22×C414yes—
289C2×D12C22×C414yescomplemented
290C2×D12C2412yes—
291C2×D12C2412yes—
292C2×C4×D3—28no—
293C2×C4×D3—28no—
294C2×C4×D3—22no—
295C2×C4×D3—22no—
296C2×C4×D3—22no—
297C2×C4×D3—22no—
298C2×C4×D3—24no—
299C2×C4×D3—24no—
300C2×C4×D3—28no—
301C2×C4×D3—84no—
302C2×Dic6—21no—
303C2×Dic6—21no—
304C2×Dic6—22no—
305C2×Dic6—22no—
306C2×Dic6C22×C414yes—
307C2×Dic6C22×C414yescomplemented
308C2×Dic6C2412yes—
309C2×Dic6C2412yes—
310C3×M16—24no—
311C3×M16—24no—
312C3×M16C22×C418yes—
313C3×M16C22×C418yescomplemented
314C2×C3×C8—24no—
315C2×C3×C8C22×C418yescomplemented
316C2×C3×C8C2414yes—
317C2×C3×C8C2414yes—
318C3×C4⋊C4C2×D412yes—
319C3×C4⋊C4C2×D412yes—
320C3×C4⋊C4C2×D412yes—
321C3×C4⋊C4C2×D412yes—
322C3×C22⋊C4C2×D414yes—
323C3×C22⋊C4C2×D414yes—
324C3×C42C2×D414yes—
325C3×C42C2414yes—
326#217—22no—
327#217—22no—
328(C2×D3)⋊C4—24no—
329(C2×D3)⋊C4—24no—
330(C2×D3)⋊C4—28no—
331C4⋊Dic3—22no—
332C4⋊Dic3—22no—
333C4⋊Dic3—22no—
334C4⋊Dic3—21no—
335C4⋊Dic3—21no—
336C4⋊Dic3C2412yes—
337C4⋊Dic3C2414yes—
338C4⋊Dic3C2412yes—
339Dic3⋊C4—28no—
340Dic3⋊C4—24no—
341Dic3⋊C4—24no—
342C4×Dic3—28no—
343C4×Dic3—24no—
344C4×Dic3—24no—
345C4×Dic3—22no—
346C4×Dic3—22no—
347Dic12C22×C4116yescomplemented
348D24C22×C4116yescomplemented
349#204C22×C4116yescomplemented
350#204C22×C4116yescomplemented
351C2×#41—38no—
352C2×#41—38no—
353C2×#41—32no—
354C2×#41—32no—
355C2×#41—32no—
356C2×#41—32no—
357C2×#41—61no—
358C2×#41—61no—
359C2×#41—61no—
360C2×#41—61no—
361C2×#41—64no—
362C2×#41—64no—
363C22×Q8—31no—
364C22×Q8—31no—
365C22×D4—31no—
366C22×D4—31no—
367C22×D4—61no—
368C22×D4—61no—
369C23×C4—61no—
370C23×C4—61no—
371C23×C4—61no—
372C23×C4—62no—
373C23×C4C22×D311yescharacteristic
374#137—316no—
375#137—316no—
376AGL(1,ℤ/8)—316no—
377AGL(1,ℤ/8)—316no—
378#135—332no—
379C2×Q16—34no—
380C2×SD16—34no—
381C2×SD16—34no—
382C2×D8—34no—
383C2×M16—24no—
384C2×M16C4×D318yescomplemented
385C2×M16C22×D312yes—
386C2×M16C22×D312yes—
387C2×M16C22×D312yes—
388C2×M16C22×D312yes—
389C22×C8C22×D312yes—
390C22×C8C22×D312yes—
391C4×Q8—38no—
392C4×Q8—34no—
393C4×Q8—34no—
394C4×Q8—62no—
395C4×Q8—62no—
396C4×Q8—64no—
397C4×D4—38no—
398C4×D4—34no—
399C4×D4—34no—
400C4×D4—64no—
401C4×D4—64no—
402C4×D4—62no—
403C4×D4—62no—
404C4×D4—68no—
405C4×D4—68no—
406C4×D4—64no—
407C4×D4—64no—
408C4×D4—64no—
409#117—32no—
410#117—32no—
411#117—61no—
412#117—61no—
413#117—64no—
414#117—64no—
415#117—62no—
416#117—62no—
417#117—64no—
418#117—64no—
419#117D1212yes—
420#117D1212yes—
421#117C22×D312yes—
422#117C22×D312yes—
423C2×C4⋊C4—32no—
424C2×C4⋊C4—32no—
425C2×C4⋊C4—32no—
426C2×C4⋊C4—31no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—61no—
429C2×C4⋊C4—61no—
430C2×C4⋊C4—61no—
431C2×C4⋊C4—62no—
432C2×C4⋊C4—64no—
433C2×C4⋊C4—64no—
434C2×C4⋊C4—62no—
435C2×C4⋊C4—62no—
436C2×C4⋊C4D1211yescharacteristic
437C2×C4⋊C4D1211yescharacteristic
438C2×C22⋊C4—61no—
439C2×C22⋊C4—62no—
440C2×C22⋊C4—64no—
441C2×C22⋊C4D1212yes—
442C2×C42—61no—
443C2×C42—62no—
444C2×C42—64no—
445C2×C42C22×D312yes—
446#107—38no—
447#106—38no—
448#103—38no—
449#103—34no—
450#103—34no—
451#102—38no—
452#102—34no—
453#102—34no—
454#97C22×D318yes—
455C4×C8C22×D318yes—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3C4×D414yes—
459C23×C3C22×D411yescharacteristic
460C23×C3C22×D411yescharacteristic
461C23×C3C22×D411yescharacteristic
462C22×D3—24no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—24no—
466C22×D3—42no—
467C22×D3—42no—
468C22×D3—81no—
469C22×D3—81no—
470C2×C3×C4—42no—
471C2×C3×C4—42no—
472C2×C3×C4C4×D414yes—
473C2×C3×C4C4×D414yes—
474C2×C3×C4C4×D414yes—
475C2×C3×C4C23×C412yes—
476C2×C3×C4C23×C412yes—
477C2×C3×C4C23×C412yes—
478C2×C3×C4C22×D414yes—
479C2×C3×C4C22×D414yes—
480C2×C3×C4C22×D411yescharacteristic
481C2×C3×C4C22×D411yescharacteristic
482C2×C3×C4C22×D411yescharacteristic
483C2×C3×C4C2×#4112yes—
484C2×C3×C4C2×#4112yes—
485C2×C3×C4C2×#4112yes—
486C2×C3×C4C2511yescharacteristic
487#67—28no—
488#67—28no—
489#67—28no—
490#67—28no—
491C2×Dic3—24no—
492C2×Dic3—24no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—24no—
498C2×Dic3—44no—
499C2×Dic3—81no—
500C2×Dic3—81no—
501C2×Dic3—82no—
502C2×Dic3—82no—
503D12—24no—
504D12—24no—
505D12—22no—
506D12—22no—
507D12C23×C414yes—
508D12C23×C414yes—
509C4×D3—28no—
510C4×D3—28no—
511C4×D3—28no—
512C4×D3—28no—
513C4×D3—84no—
514C4×D3—84no—
515C4×D3—88no—
516Dic6—24no—
517Dic6—24no—
518Dic6—22no—
519Dic6—22no—
520Dic6C23×C414yes—
521Dic6C23×C414yes—
522C3×C8—24no—
523C3×C8C23×C418yes—
524C24—61no—
525C24—61no—
526C24C2×D1211yescharacteristic
527#41—38no—
528#41—38no—
529#41—38no—
530#41—38no—
531#41—68no—
532#41—68no—
533#41—68no—
534#41—68no—
535#41—64no—
536#41—64no—
537#41—64no—
538#41—64no—
539C2×Q8—34no—
540C2×Q8—34no—
541C2×Q8—32no—
542C2×Q8—32no—
543C2×Q8—61no—
544C2×Q8—61no—
545C2×Q8—62no—
546C2×Q8—62no—
547C2×D4—34no—
548C2×D4—34no—
549C2×D4—32no—
550C2×D4—32no—
551C2×D4—68no—
552C2×D4—68no—
553C2×D4—62no—
554C2×D4—62no—
555C2×D4—62no—
556C2×D4—62no—
557C2×D4—61no—
558C2×D4—61no—
559C2×D4—62no—
560C2×D4—62no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—68no—
564C22×C4—68no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4—64no—
575C22×C4—64no—
576C22×C4—68no—
577C22×C4—244no—
578C22×C4—242no—
579C22×C4C2×C4×D314yes—
580C22×C4C2×D1212yes—
581C22×C4C2×D1212yes—
582C22×C4C2×D1211yescharacteristic
583C22×C4C2×D1211yescharacteristic
584C22×C4C2×D1211yescharacteristic
585C22×C4#23514yes—
586C22×C4C23×D311yescharacteristic
587C22×C4C23×D311yescharacteristic
588C22×C4C23×D311yescharacteristic
589Q16—316no—
590SD16—316no—
591SD16—316no—
592D8—316no—
593M16—24no—
594M16—24no—
595M16C2×C4×D318yes—
596M16C2×C4×D318yescomplemented
597C2×C8—24no—
598C2×C8C2×C4×D318yescomplemented
599C2×C8C23×D314yes—
600C2×C8C23×D314yes—
601C4⋊C4—32no—
602C4⋊C4—34no—
603C4⋊C4—32no—
604C4⋊C4—62no—
605C4⋊C4—62no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—62no—
609C4⋊C4—68no—
610C4⋊C4—64no—
611C4⋊C4—64no—
612C4⋊C4C2×D1212yes—
613C4⋊C4C2×D1212yes—
614C4⋊C4C2×D1212yes—
615C4⋊C4C2×D1212yes—
616C22⋊C4—62no—
617C22⋊C4—62no—
618C22⋊C4—64no—
619C22⋊C4—64no—
620C22⋊C4—68no—
621C22⋊C4C2×D1214yes—
622C22⋊C4C2×D1214yes—
623C42—62no—
624C42—62no—
625C42—64no—
626C42—64no—
627C42—68no—
628C42C2×D1214yes—
629C42C23×D314yes—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—44no—
637C22×C3C2×C4×D412yes—
638C22×C3C2×C4×D412yes—
639C22×C3C2×C4×D412yes—
640C22×C3C23×D411yescharacteristic
641C2×D3—24no—
642C2×D3—24no—
643C2×D3—48no—
644C2×D3—42no—
645C2×D3—42no—
646C2×D3—42no—
647C2×D3—42no—
648C2×D3—84no—
649C3×C4—24no—
650C3×C4—24no—
651C3×C4C2×C4×D412yes—
652C3×C4C2×C4×D412yes—
653C3×C4C2×C4×D412yes—
654C3×C4C24×C411yescharacteristic
655C3×C4C22×#4111yescharacteristic
656Dic3—24no—
657Dic3—24no—
658Dic3—44no—
659Dic3—42no—
660Dic3—42no—
661C23—41no—
662C23—41no—
663C23—62no—
664C23—62no—
665C23—64no—
666C23—64no—
667C23—122no—
668C23—122no—
669C23—241no—
670C23—241no—
671C23C4×D1214yes—
672C23C22×D1211yescharacteristic
673C23C22×D1211yescharacteristic
674C23C22×D1211yescharacteristic
675Q8—34no—
676Q8—34no—
677Q8—62no—
678Q8—62no—
679Q8—64no—
680Q8—64no—
681D4—34no—
682D4—34no—
683D4—68no—
684D4—68no—
685D4—68no—
686D4—68no—
687D4—62no—
688D4—62no—
689D4—64no—
690D4—64no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—64no—
696C2×C4—64no—
697C2×C4—68no—
698C2×C4—68no—
699C2×C4—68no—
700C2×C4—68no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—64no—
704C2×C4—124no—
705C2×C4—248no—
706C2×C4—244no—
707C2×C4—244no—
708C2×C4—242no—
709C2×C4—242no—
710C2×C4—241no—
711C2×C4—241no—
712C2×C4C4×D1214yes—
713C2×C4C4×D1214yes—
714C2×C4C4×D1214yes—
715C2×C4C22×C4×D312yes—
716C2×C4C22×C4×D312yes—
717C2×C4C22×C4×D312yes—
718C2×C4C22×D1214yes—
719C2×C4C22×D1214yes—
720C2×C4C22×D1211yescharacteristic
721C2×C4C22×D1211yescharacteristic
722C2×C4C22×D1211yescharacteristic
723C2×C4C2×#23512yes—
724C2×C4C2×#23512yes—
725C2×C4C2×#23512yes—
726C2×C4C24×D311yescharacteristic
727C8—24no—
728C8C22×C4×D318yes—
729C2×C3—22no—
730C2×C3—22no—
731C2×C3—22no—
732C2×C3C22×C4×D411yescharacteristic
733C2×C3#358511yescharacteristic
734C2×C3#358611yescharacteristic
735D3—44no—
736D3—44no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—44no—
744C22—64no—
745C22—64no—
746C22—128no—
747C22—122no—
748C22—122no—
749C22—122no—
750C22—122no—
751C22—244no—
752C22C2×C4×D1212yes—
753C22C2×C4×D1212yes—
754C22C2×C4×D1212yes—
755C22C23×D1211yescharacteristic
756C4—24no—
757C4—24no—
758C4—64no—
759C4—64no—
760C4—124no—
761C4—122no—
762C4—122no—
763C4C2×C4×D1212yes—
764C4C2×C4×D1212yes—
765C4C2×C4×D1212yes—
766C4C23×C4×D311yescharacteristic
767C4C22×#23511yescharacteristic
768C3#6017011yescharacteristic, complemented, Sylow
769C2—22no—
770C2—22no—
771C2—22no—
772C2—124no—
773C2—124no—
774C2C22×C4×D1211yescharacteristic
775C2#8716711yescharacteristic
776C2#8716811yescharacteristic
subgroupG/H
centerC22C23×D12
commutatorC3×C4C24×C4
FrattiniC2×C4C24×D3
FittingC3×#2873C2
socleC22×C3C23×D4
prime radicalC2×#5748C2
cosocleC2×C3×C4C25
hypercenter#2873D3
hypocenterC3#60170
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2873

Complements

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

NH ≅ G/Ntype
2. #85731C2semidirect
3. C2×#5523C2semidirect
4. C3×#2873C2semidirect
5. #83768C2semidirect
6. C2×#5133C2semidirect
7. C2×#5121C2semidirect
8. #78574C2semidirect
9. #78571C2semidirect
10. #78562C2semidirect
11. #78560C2semidirect
12. C4×#909C2semidirect
13. C4×#908C2semidirect
22. #5748C4semidirect
31. #5523C22semidirect
32. #5523C22semidirect
33. #5523C22semidirect
35. #5521C22semidirect
37. #5516C22semidirect
45. C2×C4×D12C22semidirect
46. C2×C4×Dic6C22semidirect
47. C3×#405C22semidirect
48. C3×#405C22semidirect
49. C3×C4×M16C22semidirect
51. #5133C22semidirect
52. #5133C22semidirect
53. #5133C22semidirect
54. #5131C22semidirect
55. #5121C22semidirect
56. #5121C22semidirect
57. #5120C22semidirect
59. C2×#821C22semidirect
60. C2×#818C22semidirect
61. C2×#817C22semidirect
62. C2×#816C22semidirect
63. #4716C22semidirect
64. #4711C22semidirect
65. #4710C22semidirect
66. #4710C22semidirect
67. C4×Dic12C22semidirect
68. C4×D24C22semidirect
69. C4×#204C22semidirect
70. C4×#204C22semidirect
83. #2873D3semidirect
94. C2×#235C2×C4semidirect
95. C2×#235C2×C4semidirect
108. C2×C3×M16C2×C4semidirect
142. #909C2×C4semidirect
143. #909C2×C4semidirect
144. #908C2×C4semidirect
145. #908C2×C4semidirect
147. #904C2×C4semidirect
242. #405C2×D3semidirect
243. #405C2×D3semidirect
244. C4×M16C2×D3semidirect
283. #235C22×C4semidirect
289. C2×D12C22×C4semidirect
307. C2×Dic6C22×C4semidirect
313. C3×M16C22×C4semidirect
315. C2×C3×C8C22×C4semidirect
347. Dic12C22×C4semidirect
348. D24C22×C4semidirect
349. #204C22×C4semidirect
350. #204C22×C4semidirect
384. C2×M16C4×D3semidirect
596. M16C2×C4×D3semidirect
598. C2×C8C2×C4×D3semidirect
768. C3#60170semidirect

Maximal subgroups

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

subgroupindex
C2×#57482
#857312
C2×#55232
C3×#28732
#837682
C2×#51332
C2×#51212
#785742
#785712
#785622
#785602
C4×#9092
C4×#9082
#601703