Finite Group Databasebeta

← #25140423

Subgroups — #25140423

Order 11008.

1070 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic43C211yesmaximal, characteristic, complemented
2#19138105C211yesmaximal, characteristic, complemented
3#19137425C211yesmaximal, characteristic, complemented
4#19136131C211yesmaximal, characteristic, complemented
5#19136023C211yesmaximal, characteristic, complemented
6#19135908C211yesmaximal, characteristic, complemented
7#19135774C211yesmaximal, characteristic, complemented
8#19135268C211yesmaximal, characteristic, complemented
9#19135198C211yesmaximal, characteristic, complemented
10#19134945C211yesmaximal, characteristic, complemented
11#19134931C211yesmaximal, characteristic, complemented
12#19134840C211yesmaximal, characteristic, complemented
13#19134593C211yesmaximal, characteristic, complemented
14#19134535C211yesmaximal, characteristic, complemented
15C2×C43×#449C211yesmaximal, characteristic
16C2×#13063306—21no—
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20D8×Dic43—24no—
21C2×#13063259C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582827—21no—
33#14582813—21no—
34#14582806C2211yescharacteristic
35#14582806C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582795C2211yescharacteristic
38#14582779—21no—
39#14582779—21no—
40#14582771—21no—
41#14582768C2211yescharacteristic
42#14582762—21no—
43#14582759C2211yescharacteristic
44#14582759C2211yescharacteristic
45C4×C22⋊Dic43C2211yescharacteristic
46C2×C43⋊#95—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×#41×C43C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C22×D8×C43C2211yescharacteristic
56C2×#121×C43C2211yescharacteristic
57C43×#449—24no—
58C2×#103×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C23×Dic43—21no—
62C23×Dic43—21no—
63C23×Dic43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063306—44no—
67D4×Dic43—22no—
68D4×Dic43—22no—
69D4×Dic43—22no—
70D4×Dic43—41no—
71D4×Dic43—41no—
72D4×Dic43—41no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43D411yescharacteristic
88C2×C22⋊Dic43D411yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063259—22no—
92#13063258—41no—
93Dic43⋊C8—41no—
94#13063249—22no—
95#13063249—41no—
96#13063246—22no—
97#13063246—22no—
98#13063246—22no—
99#13063246—41no—
100C22⋊(C43⋊C8)—41no—
101C8×Dic43—22no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95D411yescharacteristic
110C43⋊#95D411yescharacteristic
111C2×#41×C43—22no—
112C2×#41×C43—22no—
113C2×#41×C43—22no—
114C2×#41×C43—22no—
115C2×#41×C43—41no—
116C2×#41×C43—41no—
117C22×Q8×C43C2311yescharacteristic
118C22×D4×C43—21no—
119C22×D4×C43—21no—
120C22×D4×C43C2311yescharacteristic
121C22×D4×C43C2311yescharacteristic
122C23×C4×C43—21no—
123C23×C4×C43C2311yescharacteristic
124C2×SD16×C43—22no—
125C2×SD16×C43—22no—
126C2×SD16×C43—41no—
127C2×D8×C43—22no—
128C2×D8×C43—22no—
129C2×D8×C43D414yes—
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132#121×C43—22no—
133#121×C43—41no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C22⋊C4×C43—21no—
136#103×C43—22no—
137#102×C43—22no—
138C22⋊C8×C43—22no—
139C24×C43—21no—
140C24×C43—21no—
141C24×C43C2×D411yescharacteristic
142#41×C43—44no—
143#41×C43—44no—
144#41×C43—44no—
145#41×C43—44no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43#4112yes—
152C2×D4×C43—24no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43—81no—
166C2×D4×C43C2×D412yes—
167C2×D4×C43C2×D412yes—
168C2×D4×C43#4112yes—
169C2×D4×C43#4112yes—
170C22×C4×C43—24no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—42no—
180C22×C4×C43—42no—
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2411yescharacteristic
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—42no—
188C22×Dic43—42no—
189C22×Dic43—42no—
190C22×Dic43—42no—
191C22×Dic43—42no—
192C22×Dic43—42no—
193C22×Dic43—81no—
194C22×Dic43—81no—
195C22×Dic43—81no—
196C22×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198C22×Dic43C2×D411yescharacteristic
199C22×Dic43C2×D411yescharacteristic
200SD16×C43—44no—
201D8×C43—28no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43C2×D412yes—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C22⋊C4×C43—42no—
211C22⋊Dic43—22no—
212C22⋊Dic43—22no—
213C22⋊Dic43—42no—
214C22⋊Dic43—42no—
215C22⋊Dic43—42no—
216C22⋊Dic43—42no—
217C22⋊Dic43—42no—
218C22⋊Dic43—42no—
219C22⋊Dic43—81no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228Dic43⋊C4—42no—
229Dic43⋊C4—42no—
230Dic43⋊C4—81no—
231C4×Dic43—21no—
232C4×Dic43—21no—
233C4×Dic43—21no—
234C4×Dic43—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C23×C43—22no—
242C23×C43—22no—
243C23×C43—22no—
244C23×C43—21no—
245C23×C43—22no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43C22×D411yescharacteristic
263Q8×C43—22no—
264Q8×C43—22no—
265Q8×C43—41no—
266Q8×C43—41no—
267D4×C43—22no—
268D4×C43—22no—
269D4×C43—22no—
270D4×C43—22no—
271D4×C43—22no—
272D4×C43—48no—
273D4×C43—41no—
274D4×C43—41no—
275D4×C43—84no—
276D4×C43#12314yescomplemented
277C2×C4×C43—21no—
278C2×C4×C43—22no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—48no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43C2×#4111yescharacteristic
295C2×C4×C43H(5,𝔽2)11yescharacteristic
296C2×C4×C43H(5,𝔽2)11yescharacteristic
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—84no—
320C2×Dic43—84no—
321C2×Dic43—84no—
322C2×Dic43#13512yes—
323C2×Dic43AGL(1,ℤ/8)12yes—
324C8×C43—22no—
325C8×C43—41no—
326C43⋊C8—41no—
327C43⋊C8—41no—
328#24899—431nomaximal, Sylow
329C22×C43—24no—
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—42no—
336C22×C43—41no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—42no—
341C22×C43—41no—
342C22×C43—42no—
343C22×C43—41no—
344C22×C43—42no—
345C22×C43—41no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43#52511yescharacteristic
351C22×C43D4211yescharacteristic
352C22×C43#54611yescharacteristic
353C22×C43C2×#13511yescharacteristic
354C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C43#57611yescharacteristic
356C22×C43#57811yescharacteristic
357C4×C43—41no—
358C4×C43—42no—
359C4×C43—81no—
360C4×C43C2×#12311yescharacteristic
361C4×C43#53811yescharacteristic
362C4×C43#54611yescharacteristic
363C4×C43#55111yescharacteristic
364Dic43—22no—
365Dic43—22no—
366Dic43—41no—
367Dic43—41no—
368Dic43—81no—
369Dic43—81no—
370Dic43—81no—
371Dic43—81no—
372C2×#449D4311yescharacteristic
373C2×C4×D8—431no—
374#2422—431no—
375#2339—431no—
376#2095—431no—
377#2076—431no—
378#2055—431no—
379#2033—431no—
380#1933—431no—
381#1923—431no—
382#1879—431no—
383#1877—431no—
384#1862—431no—
385#1802—431no—
386#1788—431no—
387C2×C43—44no—
388C2×C43—81no—
389C2×C43—82no—
390C2×C43#241811yescharacteristic
391C2×C43#310611yescharacteristic
392C2×C43#312411yescharacteristic
393C2×C43#326411yescharacteristic
394C2×C43#328311yescharacteristic
395C2×C43#329711yescharacteristic
396C2×C43#333011yescharacteristic
397C22×#41C2×D4311yescharacteristic
398C22×SD16C2×D4311yescharacteristic
399C22×D8C2×D4311yescharacteristic
400C2×#123—861no—
401C2×#121C2×D4311yescharacteristic
402C2×C4×D4—431no—
403C2×C4×D4—431no—
404C2×C4×D4—431no—
405#449—24no—
406C4×D8—864no—
407C2×#107—431no—
408C2×#107—431no—
409C2×C4⋊C8—431no—
410C2×#103—431no—
411C2×#103—431no—
412C2×#103C2×D4311yescharacteristic
413C2×#102—431no—
414C2×#102—431no—
415C2×#102—431no—
416C2×#102—431no—
417C2×#102C2×D4311yescharacteristic
418C2×C22⋊C8—431no—
419C2×C22⋊C8C2×D4311yescharacteristic
420C2×C4×C8—431no—
421#397—861no—
422#394—861no—
423#391—431no—
424#391—431no—
425#390—431no—
426#389—431no—
427#386—861no—
428#386—861no—
429#385—861no—
430#384—431no—
431#381—861no—
432#380—431no—
433#380—431no—
434C4×C22⋊C4—431no—
435C2×#95—861no—
436#340—431no—
437#340—431no—
438#340—431no—
439#340—431no—
440#336—431no—
441#336—431no—
442C43#2489911yescharacteristic, complemented, Sylow
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—41no—
448C2×#41—41no—
449C22×Q8C22×D4311yescharacteristic
450C22×D4—21no—
451C22×D4—21no—
452C22×D4C22×D4311yescharacteristic
453C22×D4C22×D4311yescharacteristic
454C23×C4—21no—
455C23×C4—861no—
456C23×C4—861no—
457C23×C4—861no—
458C23×C4C22×D4311yescharacteristic
459C2×SD16—22no—
460C2×SD16—22no—
461C2×SD16—41no—
462C2×D8—22no—
463C2×D8—22no—
464C2×D8C22⋊D4314yes—
465C22×C8—431no—
466C22×C8—431no—
467C22×C8C22×D4311yescharacteristic
468C22×C8C22×D4311yescharacteristic
469#123—1724no—
470#121—22no—
471#121—41no—
472C4×D4—862no—
473C4×D4—862no—
474C4×D4—862no—
475C4×D4—1721no—
476C4×D4—1721no—
477C4×D4—1721no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4C22×D4311yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—431no—
488C2×C22⋊C4—431no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C42—431no—
497C2×C42—431no—
498#107—862no—
499#107—1721no—
500C4⋊C8—1721no—
501#103—22no—
502#103—862no—
503#103—1721no—
504#102—22no—
505#102—862no—
506#102—862no—
507#102—862no—
508#102—1721no—
509C22⋊C8—22no—
510C22⋊C8—1721no—
511C4×C8—862no—
512#95—431no—
513#95—431no—
514#95—861no—
515#95—861no—
516#95—861no—
517#95—861no—
518#95—861no—
519#95—861no—
520#95—861no—
521C24—21no—
522C24—21no—
523C24D4×D4311yescharacteristic
524#41—44no—
525#41—44no—
526#41—44no—
527#41—44no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8#1062190012yes—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—81no—
548C2×D4#1062190012yes—
549C2×D4#1062190012yes—
550C2×D4C2×C22⋊D4312yes—
551C2×D4C2×C22⋊D4312yes—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—431no—
564C22×C4—431no—
565C22×C4—431no—
566C22×C4—431no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—3441no—
572C22×C4—3441no—
573C22×C4—3441no—
574C22×C4—1722no—
575C22×C4—1722no—
576C22×C4—1722no—
577C22×C4—1722no—
578C22×C4—1722no—
579C22×C4—1722no—
580C22×C4D4×D4311yescharacteristic
581C22×C4C23×D4311yescharacteristic
582SD16—44no—
583D8—28no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—861no—
590C2×C8—861no—
591C2×C8—861no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8C2×C22⋊D4312yes—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—861no—
599C4⋊C4—861no—
600C4⋊C4—861no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—3441no—
607C4⋊C4—1722no—
608C4⋊C4—1722no—
609C22⋊C4—42no—
610C22⋊C4—862no—
611C22⋊C4—862no—
612C22⋊C4—3441no—
613C22⋊C4—1722no—
614C22⋊C4—1722no—
615C22⋊C4—1722no—
616C22⋊C4—1722no—
617C22⋊C4—1722no—
618C22⋊C4—1722no—
619C42—861no—
620C42—861no—
621C42—861no—
622C42—861no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—21no—
633C23—21no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23C2×D4×D4311yescharacteristic
645Q8—22no—
646Q8—22no—
647Q8—41no—
648Q8—41no—
649D4—22no—
650D4—22no—
651D4—22no—
652D4—22no—
653D4—22no—
654D4—48no—
655D4—41no—
656D4—41no—
657D4—84no—
658D4#1306330614yescomplemented
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—48no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—432no—
674C2×C4—432no—
675C2×C4—861no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—861no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—861no—
684C2×C4—861no—
685C2×C4—3444no—
686C2×C4—3444no—
687C2×C4—3444no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4C22×C22⋊D4311yescharacteristic
701C2×C4C2×#1062190011yescharacteristic
702C2×C4C2×#1062190011yescharacteristic
703C2×C4C2×#1062190011yescharacteristic
704C2×C4#1306337011yescharacteristic
705C2×C4#1306337011yescharacteristic
706C8—22no—
707C8—41no—
708C8—1721no—
709C8—1721no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—41no—
718C22—42no—
719C22—41no—
720C22—42no—
721C22—42no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22#1458340511yescharacteristic
732C22D4×C22⋊D4311yescharacteristic
733C22#1458353611yescharacteristic
734C22#135×D4311yescharacteristic
735C22AGL(1,ℤ/8)×D4311yescharacteristic
736C22#1458370311yescharacteristic
737C22#1458371311yescharacteristic
738C4—41no—
739C4—42no—
740C4—81no—
741C4—862no—
742C4—862no—
743C4—3441no—
744C4—3441no—
745C4—3441no—
746C4—3441no—
747C4—1721no—
748C4—1721no—
749C4C2×#1306330611yescharacteristic
750C4#1458348411yescharacteristic
751C4#1458354311yescharacteristic
752C4#1458358011yescharacteristic
753C2—44no—
754C2—81no—
755C2—82no—
756C2#1913805311yescharacteristic
757C2#1914464811yescharacteristic
758C2#1914485011yescharacteristic
759C2#1914606911yescharacteristic
760C2#1914631111yescharacteristic
761C2#1914643811yescharacteristic
762C2#1914689311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#449C2
socleC23×C43C22×D4
hypercenterC2×#449D43
hypocenterC43#24899
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×D8×Dic43C2semidirect
2. #19138105C2semidirect
3. #19137425C2semidirect
4. #19136131C2semidirect
5. #19136023C2semidirect
6. #19135908C2semidirect
7. #19135774C2semidirect
8. #19135268C2semidirect
9. #19135198C2semidirect
10. #19134945C2semidirect
11. #19134931C2semidirect
12. #19134840C2semidirect
13. #19134593C2semidirect
14. #19134535C2semidirect
276. D4×C43#123semidirect
442. C43#24899semidirect
658. D4#13063306semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic432
#191381052
#191374252
#191361312
#191360232
#191359082
#191357742
#191352682
#191351982
#191349452
#191349312
#191348402
#191345932
#191345352
C2×C43×#4492
#2489943