Finite Group Databasebeta

← #11659397

Subgroups — #11659397

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×C3×#575C211yesmaximal, characteristic
2#87260C211yesmaximal, characteristic, complemented
3C2×#5827C211yesmaximal, characteristic, complemented
4#84072C211yesmaximal, characteristic, complemented
5C2×#5232C211yesmaximal, characteristic, complemented
6#83965C214yesmaximal, complemented
7Dic3×#137C214yesmaximal, complemented
8#83930C214yesmaximal, complemented
9Dic3×AGL(1,ℤ/8)C214yesmaximal, complemented
10#83899C214yesmaximal, complemented
11#83898C214yesmaximal, complemented
12C2×#5121C211yesmaximal, characteristic, complemented
13#83747C211yesmaximal, characteristic, complemented
14#60170—31nomaximal, Sylow
15C22×C3×#41C2211yescharacteristic
16C22×C3×#41C2211yescharacteristic
17C3×#575C4116yescomplemented
18C2×C3×#137C2212yes—
19C2×C3×#137C2212yes—
20C2×C3×AGL(1,ℤ/8)C2212yes—
21C2×C3×AGL(1,ℤ/8)C2212yes—
22C2×C3×#135C2214yes—
23C22×C3×M16C2211yescharacteristic
24#5827—22no—
25#5827—22no—
26#5827—21no—
27#5827—21no—
28#5827C2214yes—
29#5827C2212yescomplemented
30#5827C2214yescomplemented
31#5827C2212yescomplemented
32Dic3×#41—22no—
33Dic3×#41C2214yes—
34#5812C2212yescomplemented
35C2×Q8×Dic3C2212yescomplemented
36#5798—22no—
37#5798C2212yescomplemented
38C2×D4×Dic3—22no—
39C2×D4×Dic3C2212yescomplemented
40C2×#926—22no—
41C2×#926—21no—
42C2×#926C2211yescharacteristic
43C2×#926C2211yescharacteristic
44C22×C4⋊Dic3—21no—
45C22×C4⋊Dic3C2211yescharacteristic
46C22×#208C2211yescharacteristic
47#5233C2214yes—
48#5232C2214yes—
49#5232C2214yescomplemented
50#5232C2212yescomplemented
51#5232C2212yescomplemented
52#5225C2212yescomplemented
53C2×#835C2212yescomplemented
54#5215C2212yescomplemented
55C2×#832C2212yescomplemented
56#5184C2218yescomplemented
57Dic3×Q16C2218yescomplemented
58#5164C2218yescomplemented
59#5164C2218yescomplemented
60Dic3×SD16C2218yescomplemented
61Dic3×SD16C2218yescomplemented
62#5152C2218yescomplemented
63Dic3×D8C2218yescomplemented
64#5122C2214yescomplemented
65#5121C2214yescomplemented
66#5121C2214yescomplemented
67Dic3×M16C2214yescomplemented
68C2×#818C2212yescomplemented
69C2×#817C2212yescomplemented
70#5101C2214yescomplemented
71C2×#575D311yescharacteristic
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#2873—31no—
84C2×C3×#41—21no—
85C2×C3×#41—21no—
86C2×C3×#41—21no—
87C2×C3×#41—21no—
88C2×C3×#41—24no—
89C2×C3×#41—24no—
90C2×C3×#41C2×C418yescomplemented
91C2×C3×#41C2×C418yescomplemented
92C2×C3×#41C2312yes—
93C2×C3×#41C2312yes—
94C2×C3×#41C2312yes—
95C2×C3×#41C2312yes—
96C22×C3×Q8C2311yescharacteristic
97C22×C3×Q8C2311yescharacteristic
98C22×C3×D4—21no—
99C22×C3×D4—21no—
100C22×C3×D4C2311yescharacteristic
101C22×C3×D4C2311yescharacteristic
102C23×C3×C4—21no—
103C23×C3×C4—21no—
104C23×C3×C4C2311yescharacteristic
105C23×Dic3—21no—
106C23×Dic3—22no—
107C3×#137C2×C4116yescomplemented
108C3×#137C2×C4116yescomplemented
109C3×AGL(1,ℤ/8)C2×C4116yescomplemented
110C3×AGL(1,ℤ/8)C2×C4116yescomplemented
111C3×#135C2×C4132yescomplemented
112C2×C3×Q16C2314yes—
113C2×C3×SD16C2314yes—
114C2×C3×SD16C2314yes—
115C2×C3×D8C2314yes—
116C2×C3×M16C2×C418yescomplemented
117C2×C3×M16C2312yes—
118C2×C3×M16C2312yes—
119C22×C3×C8C2312yes—
120C2×#217—21no—
121C2×#217—22no—
122C2×#217—24no—
123C2×#217D412yes—
124Q8×Dic3—22no—
125Q8×Dic3—22no—
126Q8×Dic3—24no—
127Q8×Dic3C2314yes—
128Q8×Dic3C2318yes—
129Q8×Dic3C2314yes—
130D4×Dic3—24no—
131D4×Dic3—24no—
132D4×Dic3—28no—
133D4×Dic3—28no—
134D4×Dic3—24no—
135D4×Dic3—24no—
136D4×Dic3—22no—
137D4×Dic3—22no—
138D4×Dic3—24no—
139D4×Dic3C2314yes—
140D4×Dic3C2318yes—
141D4×Dic3C2314yes—
142#926—21no—
143#926—21no—
144#926—24no—
145#926—24no—
146#926—24no—
147#926—22no—
148#926—22no—
149#926—24no—
150#926D412yes—
151#926D412yes—
152#926C2312yes—
153#926C2312yes—
154#926C2312yes—
155#926C2312yes—
156C2×C4⋊Dic3—21no—
157C2×C4⋊Dic3—21no—
158C2×C4⋊Dic3—21no—
159C2×C4⋊Dic3—22no—
160C2×C4⋊Dic3—24no—
161C2×C4⋊Dic3—24no—
162C2×C4⋊Dic3—22no—
163C2×C4⋊Dic3—22no—
164C2×C4⋊Dic3D411yescharacteristic
165C2×C4⋊Dic3D411yescharacteristic
166C2×C4⋊Dic3C2312yes—
167C2×C4⋊Dic3C2312yes—
168C2×C4⋊Dic3C2312yes—
169C2×C4⋊Dic3C2311yescharacteristic
170C2×C4⋊Dic3C2311yescharacteristic
171C2×C4×Dic3—21no—
172C2×C4×Dic3—22no—
173C2×C4×Dic3—24no—
174C2×C4×Dic3C2312yes—
175C2×#208—24no—
176C2×#208C2312yes—
177C2×#208C2312yes—
178C22×C3⋊C8C2312yes—
179#835C2314yes—
180#835C2318yes—
181#835C2314yes—
182#832C2314yes—
183#832C2318yes—
184#832C2314yes—
185#818C2318yes—
186#817C2318yes—
187#815C2318yes—
188C8×Dic3C2318yes—
189C22×#41C2×D311yescharacteristic
190C22×#41C2×D311yescharacteristic
191#575Dic3116yescomplemented
192C2×#137C2×D312yes—
193C2×#137C2×D312yes—
194C2×AGL(1,ℤ/8)C2×D312yes—
195C2×AGL(1,ℤ/8)C2×D312yes—
196C2×#135C2×D314yes—
197C22×M16—31no—
198C22×M16C2×D311yescharacteristic
199#520—34no—
200#520—34no—
201#520—32no—
202#520—32no—
203#520—61no—
204#520—61no—
205#520—62no—
206#520—62no—
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—31no—
217C2×#117—61no—
218C2×#117—62no—
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#405—34no—
243#405—34no—
244C4×M16—34no—
245C24×C3—21no—
246C24×C3—21no—
247C24×C3C2×D411yescharacteristic
248C3×#41—28no—
249C3×#41—28no—
250C3×#41—28no—
251C3×#41—28no—
252C3×#41—24no—
253C3×#41—24no—
254C3×#41—24no—
255C3×#41—24no—
256C3×#41C22×C418yes—
257C3×#41C22×C418yes—
258C3×#41C22×C418yes—
259C3×#41C22×C418yescomplemented
260C2×C3×Q8—21no—
261C2×C3×Q8—21no—
262C2×C3×Q8—22no—
263C2×C3×Q8—22no—
264C2×C3×Q8C22×C414yes—
265C2×C3×Q8C22×C414yescomplemented
266C2×C3×Q8C2412yes—
267C2×C3×Q8C2412yes—
268C2×C3×D4—28no—
269C2×C3×D4—28no—
270C2×C3×D4—22no—
271C2×C3×D4—22no—
272C2×C3×D4—22no—
273C2×C3×D4—22no—
274C2×C3×D4—21no—
275C2×C3×D4—21no—
276C2×C3×D4—22no—
277C2×C3×D4—22no—
278C2×C3×D4C22×C414yes—
279C2×C3×D4C22×C414yescomplemented
280C2×C3×D4C2412yes—
281C2×C3×D4C2412yes—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—28no—
285C22×C3×C4—28no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—22no—
289C22×C3×C4—22no—
290C22×C3×C4C22×C414yes—
291C22×C3×C4C2×D411yescharacteristic
292C22×C3×C4C2×D411yescharacteristic
293C22×C3×C4C2×D411yescharacteristic
294C22×C3×C4#4114yes—
295C22×C3×C4C2411yescharacteristic
296C22×C3×C4C2411yescharacteristic
297C22×C3×C4C2411yescharacteristic
298C22×Dic3—22no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—22no—
302C22×Dic3—22no—
303C22×Dic3—24no—
304C22×Dic3—24no—
305C22×Dic3—28no—
306C22×Dic3—84no—
307C22×Dic3—82no—
308C22×Dic3C2×D412yes—
309C22×Dic3C2×D412yes—
310C3×Q16C22×C4116yescomplemented
311C3×SD16C22×C4116yescomplemented
312C3×SD16C22×C4116yescomplemented
313C3×D8C22×C4116yescomplemented
314C3×M16C22×C418yes—
315C3×M16C22×C418yescomplemented
316C2×C3×C8C22×C418yescomplemented
317C2×C3×C8C2414yes—
318#217—22no—
319#217—22no—
320#217—24no—
321#217—24no—
322#217—28no—
323#217C2×D414yes—
324#217C2×D414yes—
325C4⋊Dic3—22no—
326C4⋊Dic3—22no—
327C4⋊Dic3—21no—
328C4⋊Dic3—21no—
329C4⋊Dic3—22no—
330C4⋊Dic3—28no—
331C4⋊Dic3—24no—
332C4⋊Dic3—24no—
333C4⋊Dic3C2×D412yes—
334C4⋊Dic3C2×D412yes—
335C4⋊Dic3C2×D412yes—
336C4⋊Dic3C2×D412yes—
337C4⋊Dic3C2412yes—
338C4⋊Dic3C2414yes—
339C4⋊Dic3C2412yes—
340C4×Dic3—22no—
341C4×Dic3—22no—
342C4×Dic3—24no—
343C4×Dic3—24no—
344C4×Dic3—28no—
345C4×Dic3C2×D414yes—
346C4×Dic3C2414yes—
347#208—24no—
348#208—24no—
349C2×C3⋊C8—24no—
350C2×C3⋊C8C2414yes—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41—21no—
355C2×#41—24no—
356C2×#41—24no—
357C2×#41C2×Dic318yescomplemented
358C2×#41C2×Dic318yescomplemented
359C2×#41C22×D312yes—
360C2×#41C22×D312yes—
361C2×#41C22×D312yes—
362C2×#41C22×D312yes—
363C22×Q8C22×D311yescharacteristic
364C22×Q8C22×D311yescharacteristic
365C22×D4—21no—
366C22×D4—21no—
367C22×D4C22×D311yescharacteristic
368C22×D4C22×D311yescharacteristic
369C23×C4—21no—
370C23×C4—21no—
371C23×C4—62no—
372C23×C4—61no—
373C23×C4C22×D311yescharacteristic
374#137C2×Dic3116yescomplemented
375#137C2×Dic3116yescomplemented
376AGL(1,ℤ/8)C2×Dic3116yescomplemented
377AGL(1,ℤ/8)C2×Dic3116yescomplemented
378#135C2×Dic3132yescomplemented
379C2×Q16C22×D314yes—
380C2×SD16C22×D314yes—
381C2×SD16C22×D314yes—
382C2×D8C22×D314yes—
383C2×M16—32no—
384C2×M16—32no—
385C2×M16—64no—
386C2×M16C2×Dic318yescomplemented
387C2×M16C22×D312yes—
388C2×M16C22×D312yes—
389C22×C8—32no—
390C22×C8C22×D312yes—
391C4×Q8—38no—
392C4×Q8—34no—
393C4×Q8—34no—
394C4×Q8—64no—
395C4×Q8—62no—
396C4×Q8—62no—
397C4×D4—38no—
398C4×D4—34no—
399C4×D4—34no—
400C4×D4—64no—
401C4×D4—68no—
402C4×D4—68no—
403C4×D4—64no—
404C4×D4—64no—
405C4×D4—62no—
406C4×D4—62no—
407C4×D4—64no—
408C4×D4—64no—
409#117—32no—
410#117—32no—
411#117—32no—
412#117—32no—
413#117—32no—
414#117—32no—
415#117—64no—
416#117—64no—
417#117—62no—
418#117—64no—
419#117—62no—
420#117—64no—
421#117—61no—
422#117—61no—
423C2×C4⋊C4—31no—
424C2×C4⋊C4—31no—
425C2×C4⋊C4—32no—
426C2×C4⋊C4—32no—
427C2×C4⋊C4—32no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—64no—
431C2×C4⋊C4—64no—
432C2×C4⋊C4—62no—
433C2×C4⋊C4—62no—
434C2×C4⋊C4—62no—
435C2×C4⋊C4—61no—
436C2×C4⋊C4—61no—
437C2×C4⋊C4—61no—
438C2×C22⋊C4—32no—
439C2×C22⋊C4—64no—
440C2×C22⋊C4—62no—
441C2×C22⋊C4—61no—
442C2×C42—32no—
443C2×C42—64no—
444C2×C42—62no—
445C2×C42—61no—
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#97—38no—
455C4×C8—38no—
456C23×C3—24no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—24no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—42no—
463C23×C3—42no—
464C23×C3—81no—
465C23×C3—81no—
466C23×C3C4×D414yes—
467C23×C3C22×D411yescharacteristic
468C23×C3C22×D411yescharacteristic
469C23×C3C22×D411yescharacteristic
470C3×Q8—24no—
471C3×Q8—24no—
472C3×Q8—22no—
473C3×Q8—22no—
474C3×Q8C23×C414yes—
475C3×Q8C23×C414yes—
476C3×D4—28no—
477C3×D4—28no—
478C3×D4—28no—
479C3×D4—28no—
480C3×D4—24no—
481C3×D4—24no—
482C3×D4—22no—
483C3×D4—22no—
484C3×D4C23×C414yes—
485C3×D4C23×C414yes—
486C2×C3×C4—24no—
487C2×C3×C4—24no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—28no—
491C2×C3×C4—28no—
492C2×C3×C4—28no—
493C2×C3×C4—28no—
494C2×C3×C4C4×D414yes—
495C2×C3×C4C4×D414yes—
496C2×C3×C4C4×D414yes—
497C2×C3×C4C23×C412yes—
498C2×C3×C4C23×C412yes—
499C2×C3×C4C23×C412yes—
500C2×C3×C4C22×D411yescharacteristic
501C2×C3×C4C22×D411yescharacteristic
502C2×C3×C4C22×D411yescharacteristic
503C2×C3×C4C2×#4112yes—
504C2×C3×C4C2×#4112yes—
505C2×C3×C4C2×#4112yes—
506C2×C3×C4C2511yescharacteristic
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—24no—
510C2×Dic3—42no—
511C2×Dic3—42no—
512C2×Dic3—44no—
513C2×Dic3—84no—
514C2×Dic3—84no—
515C2×Dic3—88no—
516C2×Dic3—81no—
517C2×Dic3—81no—
518C2×Dic3—82no—
519C2×Dic3—82no—
520C2×Dic3C22×D414yes—
521C2×Dic3C22×D414yes—
522C3×C8C23×C418yes—
523C3⋊C8—24no—
524C24—21no—
525C24—21no—
526C24D3×D411yescharacteristic
527#41—28no—
528#41—28no—
529#41—28no—
530#41—28no—
531#41—24no—
532#41—24no—
533#41—24no—
534#41—24no—
535#41C22×Dic318yes—
536#41C22×Dic318yes—
537#41C22×Dic318yes—
538#41C22×Dic318yescomplemented
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8C22×Dic314yes—
544C2×Q8C22×Dic314yescomplemented
545C2×Q8C23×D312yes—
546C2×Q8C23×D312yes—
547C2×D4—28no—
548C2×D4—28no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4C22×Dic314yes—
558C2×D4C22×Dic314yescomplemented
559C2×D4C23×D312yes—
560C2×D4C23×D312yes—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—32no—
570C22×C4—32no—
571C22×C4—64no—
572C22×C4—64no—
573C22×C4—68no—
574C22×C4—62no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—62no—
578C22×C4—62no—
579C22×C4—244no—
580C22×C4—242no—
581C22×C4D3×D411yescharacteristic
582C22×C4D3×D411yescharacteristic
583C22×C4D3×D411yescharacteristic
584C22×C4#23714yes—
585C22×C4C22×Dic314yes—
586C22×C4C23×D311yescharacteristic
587C22×C4C23×D311yescharacteristic
588C22×C4C23×D311yescharacteristic
589Q16C22×Dic3116yescomplemented
590SD16C22×Dic3116yescomplemented
591SD16C22×Dic3116yescomplemented
592D8C22×Dic3116yescomplemented
593M16—64no—
594M16—64no—
595M16C22×Dic318yes—
596M16C22×Dic318yescomplemented
597C2×C8—34no—
598C2×C8—64no—
599C2×C8C22×Dic318yescomplemented
600C2×C8C23×D314yes—
601C4⋊C4—32no—
602C4⋊C4—32no—
603C4⋊C4—32no—
604C4⋊C4—32no—
605C4⋊C4—32no—
606C4⋊C4—34no—
607C4⋊C4—32no—
608C4⋊C4—68no—
609C4⋊C4—64no—
610C4⋊C4—64no—
611C4⋊C4—62no—
612C4⋊C4—62no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—62no—
616C22⋊C4—34no—
617C22⋊C4—34no—
618C22⋊C4—64no—
619C22⋊C4—68no—
620C22⋊C4—64no—
621C22⋊C4—62no—
622C22⋊C4—62no—
623C42—34no—
624C42—34no—
625C42—64no—
626C42—68no—
627C42—64no—
628C42—62no—
629C42—62no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—24no—
637C22×C3—24no—
638C22×C3—44no—
639C22×C3—48no—
640C22×C3—42no—
641C22×C3—42no—
642C22×C3—42no—
643C22×C3—42no—
644C22×C3—84no—
645C22×C3C2×C4×D412yes—
646C22×C3C2×C4×D412yes—
647C22×C3C2×C4×D412yes—
648C22×C3C23×D411yescharacteristic
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—22no—
662C23—22no—
663C23—24no—
664C23—24no—
665C23—41no—
666C23—41no—
667C23—42no—
668C23—42no—
669C23—81no—
670C23—81no—
671C23D4×Dic314yes—
672C23C2×D3×D411yescharacteristic
673C23C2×D3×D411yescharacteristic
674C23C2×D3×D411yescharacteristic
675Q8—22no—
676Q8—22no—
677Q8—24no—
678Q8—24no—
679Q8C23×Dic314yes—
680Q8C23×Dic314yes—
681D4—28no—
682D4—28no—
683D4—28no—
684D4—28no—
685D4—22no—
686D4—22no—
687D4—24no—
688D4—24no—
689D4C23×Dic314yes—
690D4C23×Dic314yes—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—34no—
700C2×C4—34no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—64no—
704C2×C4—122no—
705C2×C4—122no—
706C2×C4—124no—
707C2×C4—248no—
708C2×C4—244no—
709C2×C4—244no—
710C2×C4—242no—
711C2×C4—242no—
712C2×C4—241no—
713C2×C4—241no—
714C2×C4D4×Dic314yes—
715C2×C4D4×Dic314yes—
716C2×C4D4×Dic314yes—
717C2×C4C2×D3×D411yescharacteristic
718C2×C4C2×D3×D411yescharacteristic
719C2×C4C2×D3×D411yescharacteristic
720C2×C4C2×#23712yes—
721C2×C4C2×#23712yes—
722C2×C4C2×#23712yes—
723C2×C4C23×Dic312yes—
724C2×C4C23×Dic312yes—
725C2×C4C23×Dic312yes—
726C2×C4C24×D311yescharacteristic
727C8—64no—
728C8C23×Dic318yes—
729C2×C3—22no—
730C2×C3—22no—
731C2×C3—22no—
732C2×C3—44no—
733C2×C3—44no—
734C2×C3C22×C4×D411yescharacteristic
735C2×C3#358511yescharacteristic
736C2×C3#358611yescharacteristic
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—24no—
744C22—24no—
745C22—44no—
746C22—48no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—84no—
752C22C2×D4×Dic312yes—
753C22C2×D4×Dic312yes—
754C22C2×D4×Dic312yes—
755C22C22×D3×D411yescharacteristic
756C4—24no—
757C4—24no—
758C4—64no—
759C4—64no—
760C4—124no—
761C4—122no—
762C4—122no—
763C4C2×D4×Dic312yes—
764C4C2×D4×Dic312yes—
765C4C2×D4×Dic312yes—
766C4C22×#23711yescharacteristic
767C4C24×Dic311yescharacteristic
768C3#6017011yescharacteristic, complemented, Sylow
769C2—22no—
770C2—22no—
771C2—22no—
772C2—44no—
773C2—44no—
774C2#8720011yescharacteristic
775C2#8720111yescharacteristic
776C2C22×D4×Dic311yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutatorC3×C4C24×C4
FrattiniC2×C4C24×D3
Fitting, prime radicalC2×C3×#575C2
socleC22×C3C23×D4
cosocleC2×C3×C4C25
hypercenterC2×#575D3
hypocenterC3#60170
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
2. #87260C2semidirect
3. C2×#5827C2semidirect
4. #84072C2semidirect
5. C2×#5232C2semidirect
6. #83965C2semidirect
7. Dic3×#137C2semidirect
8. #83930C2semidirect
9. Dic3×AGL(1,ℤ/8)C2semidirect
10. #83899C2semidirect
11. #83898C2semidirect
12. C2×#5121C2semidirect
13. #83747C2semidirect
17. C3×#575C4semidirect
29. #5827C22semidirect
30. #5827C22semidirect
31. #5827C22semidirect
34. #5812C22semidirect
35. C2×Q8×Dic3C22semidirect
37. #5798C22semidirect
39. C2×D4×Dic3C22semidirect
49. #5232C22semidirect
50. #5232C22semidirect
51. #5232C22semidirect
52. #5225C22semidirect
53. C2×#835C22semidirect
54. #5215C22semidirect
55. C2×#832C22semidirect
56. #5184C22semidirect
57. Dic3×Q16C22semidirect
58. #5164C22semidirect
59. #5164C22semidirect
60. Dic3×SD16C22semidirect
61. Dic3×SD16C22semidirect
62. #5152C22semidirect
63. Dic3×D8C22semidirect
64. #5122C22semidirect
65. #5121C22semidirect
66. #5121C22semidirect
67. Dic3×M16C22semidirect
68. C2×#818C22semidirect
69. C2×#817C22semidirect
70. #5101C22semidirect
90. C2×C3×#41C2×C4semidirect
91. C2×C3×#41C2×C4semidirect
107. C3×#137C2×C4semidirect
108. C3×#137C2×C4semidirect
109. C3×AGL(1,ℤ/8)C2×C4semidirect
110. C3×AGL(1,ℤ/8)C2×C4semidirect
111. C3×#135C2×C4semidirect
116. C2×C3×M16C2×C4semidirect
191. #575Dic3semidirect
259. C3×#41C22×C4semidirect
265. C2×C3×Q8C22×C4semidirect
279. C2×C3×D4C22×C4semidirect
310. C3×Q16C22×C4semidirect
311. C3×SD16C22×C4semidirect
312. C3×SD16C22×C4semidirect
313. C3×D8C22×C4semidirect
315. C3×M16C22×C4semidirect
316. C2×C3×C8C22×C4semidirect
357. C2×#41C2×Dic3semidirect
358. C2×#41C2×Dic3semidirect
374. #137C2×Dic3semidirect
375. #137C2×Dic3semidirect
376. AGL(1,ℤ/8)C2×Dic3semidirect
377. AGL(1,ℤ/8)C2×Dic3semidirect
378. #135C2×Dic3semidirect
386. C2×M16C2×Dic3semidirect
538. #41C22×Dic3semidirect
544. C2×Q8C22×Dic3semidirect
558. C2×D4C22×Dic3semidirect
589. Q16C22×Dic3semidirect
590. SD16C22×Dic3semidirect
591. SD16C22×Dic3semidirect
592. D8C22×Dic3semidirect
596. M16C22×Dic3semidirect
599. C2×C8C22×Dic3semidirect
768. C3#60170semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5752
#872602
C2×#58272
#840722
C2×#52322
#839652
Dic3×#1372
#839302
Dic3×AGL(1,ℤ/8)2
#838992
#838982
C2×#51212
#837472
#601703