Finite Group Databasebeta

← #25140513

Subgroups — #25140513

Order 11008.

1148 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic43C211yesmaximal, characteristic, complemented
2#19138094C211yesmaximal, characteristic, complemented
3D4×C22⋊Dic43C211yesmaximal, characteristic
4#19136118C211yesmaximal, characteristic, complemented
5#19136028C211yesmaximal, characteristic, complemented
6#19135908C211yesmaximal, characteristic, complemented
7#19135795C211yesmaximal, characteristic, complemented
8#19135275C211yesmaximal, characteristic, complemented
9#19135198C211yesmaximal, characteristic, complemented
10#19134952C211yesmaximal, characteristic, complemented
11#19134931C211yesmaximal, characteristic, complemented
12#19134840C211yesmaximal, characteristic, complemented
13#19134603C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic
15C2×C43×#450C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic, complemented
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C22×C22⋊Dic43—21no—
20SD16×Dic43—24no—
21C2×#13063258C2211yescharacteristic, complemented
22C2×#13063257C2211yescharacteristic, complemented
23C2×Dic43⋊C8C2211yescharacteristic, complemented
24C2×#13063249C2211yescharacteristic, complemented
25C2×#13063249C2211yescharacteristic, complemented
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic, complemented
32#14582838—21no—
33#14582824—21no—
34#14582806C2211yescharacteristic, complemented
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582795C2211yescharacteristic, complemented
38#14582787—21no—
39#14582780—21no—
40#14582779—21no—
41#14582779—21no—
42#14582764C2211yescharacteristic, complemented
43#14582759C2211yescharacteristic
44#14582759C2211yescharacteristic
45#14582755—21no—
46C4×C22⋊Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic, complemented
48#14582662C2211yescharacteristic, complemented
49#14582662C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582653C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53C23×D4×C43C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C22×SD16×C43C2211yescharacteristic
56C2×C22⋊Q8×C43C2211yescharacteristic
57C43×#450—24no—
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C23×Dic43—21no—
62C23×Dic43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65Q8×Dic43—22no—
66Q8×Dic43—41no—
67D4×Dic43—22no—
68D4×Dic43—22no—
69D4×Dic43—41no—
70D4×Dic43—41no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—44no—
86C2×C22⋊Dic43D411yescharacteristic
87C2×C22⋊Dic43D411yescharacteristic
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063258—41no—
92#13063257—22no—
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
111C25×C43—21no—
112C22×Q8×C43C2311yescharacteristic
113C22×D4×C43—22no—
114C22×D4×C43—22no—
115C22×D4×C43—22no—
116C22×D4×C43—22no—
117C22×D4×C43—21no—
118C22×D4×C43—41no—
119C22×D4×C43—41no—
120C22×D4×C43C2311yescharacteristic
121C22×D4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C2×SD16×C43—22no—
124C2×SD16×C43—22no—
125C2×SD16×C43—22no—
126C2×SD16×C43—22no—
127C2×SD16×C43—41no—
128C2×SD16×C43D414yes—
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C22⋊Q8×C43—22no—
132C22⋊Q8×C43—41no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C22⋊C4×C43—21no—
136#102×C43—22no—
137#102×C43—22no—
138C22⋊C8×C43—22no—
139C24×C43—21no—
140C24×C43—24no—
141C24×C43—21no—
142C24×C43—42no—
143C24×C43—42no—
144C24×C43—42no—
145C24×C43—42no—
146C24×C43—81no—
147C24×C43—81no—
148C24×C43C2×D411yescharacteristic
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43C2×D412yes—
155C2×D4×C43—24no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—44no—
167C2×D4×C43—44no—
168C2×D4×C43—44no—
169C2×D4×C43—44no—
170C2×D4×C43C2×D412yes—
171C2×D4×C43#4112yes—
172C2×D4×C43#4112yes—
173C2×D4×C43#4112yes—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2411yescharacteristic
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—42no—
189C22×Dic43—42no—
190C22×Dic43—42no—
191C22×Dic43—42no—
192C22×Dic43—81no—
193C22×Dic43—81no—
194C22×Dic43C2×D411yescharacteristic
195C22×Dic43C2×D411yescharacteristic
196C22×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198SD16×C43—28no—
199SD16×C43—44no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43C2×D412yes—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—42no—
209C22⋊C4×C43—42no—
210C22⋊Dic43—22no—
211C22⋊Dic43—22no—
212C22⋊Dic43—42no—
213C22⋊Dic43—42no—
214C22⋊Dic43—42no—
215C22⋊Dic43—42no—
216C22⋊Dic43—42no—
217C22⋊Dic43—42no—
218C22⋊Dic43—81no—
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—
228C4⋊Dic43—42no—
229Dic43⋊C4—42no—
230C4×Dic43—21no—
231C4×Dic43—21no—
232C4×Dic43—21no—
233C4×Dic43—21no—
234C4×Dic43—42no—
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—21no—
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—22no—
251C23×C43—48no—
252C23×C43—48no—
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×C43—41no—
263C23×C43—84no—
264C23×C43—84no—
265C23×C43—84no—
266C23×C43—84no—
267C23×C43—84no—
268C23×C43#13512yes—
269C23×C43C22×D411yescharacteristic
270Q8×C43—22no—
271Q8×C43—22no—
272Q8×C43—41no—
273Q8×C43—41no—
274D4×C43—22no—
275D4×C43—22no—
276D4×C43—22no—
277D4×C43—22no—
278D4×C43—22no—
279D4×C43—48no—
280D4×C43—41no—
281D4×C43—41no—
282D4×C43#12314yes—
283C2×C4×C43—21no—
284C2×C4×C43—22no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C2×C4×C43C2×#4111yescharacteristic
300C2×C4×C43H(5,𝔽2)11yescharacteristic
301C2×C4×C43H(5,𝔽2)11yescharacteristic
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—84no—
326C2×Dic43—84no—
327C2×Dic43AGL(1,ℤ/8)12yes—
328C8×C43—22no—
329C8×C43—41no—
330C43⋊C8—41no—
331C43⋊C8—41no—
332#24905—431nomaximal, Sylow
333C22×C43—22no—
334C22×C43—24no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—42no—
338C22×C43—41no—
339C22×C43—42no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—41no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—816no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43#52511yescharacteristic
356C22×C43D4211yescharacteristic
357C22×C43#54611yescharacteristic
358C22×C43C2×#13511yescharacteristic
359C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
360C22×C43#57711yescharacteristic
361C22×C43#57711yescharacteristic
362C4×C43—41no—
363C4×C43—42no—
364C4×C43—81no—
365C4×C43C2×#12311yescharacteristic
366C4×C43#53811yescharacteristic
367C4×C43#54611yescharacteristic
368C4×C43#55111yescharacteristic
369Dic43—22no—
370Dic43—41no—
371Dic43—41no—
372Dic43—41no—
373Dic43—81no—
374Dic43—81no—
375Dic43—81no—
376Dic43—81no—
377C2×#450D4311yescharacteristic
378C2×C4×SD16—431no—
379#2421—431no—
380D4×C22⋊C4—431no—
381#2092—431no—
382#2077—431no—
383#2055—431no—
384#2036—431no—
385#1934—431no—
386#1923—431no—
387#1880—431no—
388#1877—431no—
389#1862—431no—
390#1804—431no—
391#1786—431no—
392C2×C43—42no—
393C2×C43—44no—
394C2×C43—82no—
395C2×C43#241811yescharacteristic
396C2×C43#310511yescharacteristic
397C2×C43#312311yescharacteristic
398C2×C43#326511yescharacteristic
399C2×C43#328211yescharacteristic
400C2×C43#329611yescharacteristic
401C2×C43#332411yescharacteristic
402C23×D4C2×D4311yescharacteristic
403C22×SD16C2×D4311yescharacteristic
404C22×SD16C2×D4311yescharacteristic
405C2×C22⋊Q8C2×D4311yescharacteristic
406C2×C4×Q8—431no—
407C2×C4×D4—431no—
408C2×C4×D4—431no—
409C22×C22⋊C4—861no—
410#450—24no—
411C4×SD16—864no—
412C2×#107—431no—
413C2×#106—431no—
414C2×C4⋊C8—431no—
415C2×#103—431no—
416C2×#103—431no—
417C2×#102—431no—
418C2×#102—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102C2×D4311yescharacteristic
422C2×#102C2×D4311yescharacteristic
423C2×C22⋊C8—431no—
424C2×C22⋊C8C2×D4311yescharacteristic
425C2×C4×C8—431no—
426#400—861no—
427#397—861no—
428#391—431no—
429#390—431no—
430#390—431no—
431#389—431no—
432#388—861no—
433#387—861no—
434#386—861no—
435#386—861no—
436#382—431no—
437#380—431no—
438#380—431no—
439#379—861no—
440C4×C22⋊C4—431no—
441#340—431no—
442#340—431no—
443#340—431no—
444#340—431no—
445#336—431no—
446#336—431no—
447C43#2490511yescharacteristic, complemented, Sylow
448C25—21no—
449C22×Q8C22×D4311yescharacteristic
450C22×D4—22no—
451C22×D4—22no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—21no—
455C22×D4—41no—
456C22×D4—41no—
457C22×D4C22×D4311yescharacteristic
458C22×D4C22×D4311yescharacteristic
459C23×C4—861no—
460C23×C4—861no—
461C23×C4C22×D4311yescharacteristic
462C2×SD16—22no—
463C2×SD16—22no—
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—41no—
467C2×SD16C22⋊D4314yes—
468C22×C8—431no—
469C22×C8—431no—
470C22×C8C22×D4311yescharacteristic
471C22×C8C22×D4311yescharacteristic
472C22⋊Q8—22no—
473C22⋊Q8—41no—
474C4×Q8—862no—
475C4×Q8—1721no—
476C4×D4—862no—
477C4×D4—862no—
478C4×D4—1721no—
479C4×D4—1721no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—431no—
483C2×C4⋊C4—431no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4C22×D4311yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—431no—
490C2×C22⋊C4—431no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—1724no—
500C2×C42—431no—
501C2×C42—431no—
502C2×C42—861no—
503#107—1721no—
504#106—862no—
505C4⋊C8—1721no—
506#103—862no—
507#103—1721no—
508#102—22no—
509#102—22no—
510#102—862no—
511#102—862no—
512#102—862no—
513#102—1721no—
514C22⋊C8—22no—
515C22⋊C8—1721no—
516C4×C8—862no—
517#95—431no—
518#95—431no—
519#95—861no—
520#95—861no—
521#95—861no—
522#95—861no—
523#95—861no—
524#95—861no—
525#95—861no—
526C24—21no—
527C24—24no—
528C24—21no—
529C24—42no—
530C24—42no—
531C24—42no—
532C24—42no—
533C24—81no—
534C24—81no—
535C24D4×D4311yescharacteristic
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8C2×C22⋊D4312yes—
542C2×D4—24no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4#1062190012yes—
558C2×D4#1062190012yes—
559C2×D4#1062190012yes—
560C2×D4C2×C22⋊D4312yes—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—431no—
570C22×C4—431no—
571C22×C4—431no—
572C22×C4—431no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—3441no—
578C22×C4—3441no—
579C22×C4—1722no—
580C22×C4—1722no—
581C22×C4—1722no—
582C22×C4—1722no—
583C22×C4D4×D4311yescharacteristic
584C22×C4C23×D4311yescharacteristic
585SD16—28no—
586SD16—44no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8C2×C22⋊D4312yes—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—42no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—861no—
608C4⋊C4—861no—
609C4⋊C4—861no—
610C4⋊C4—1722no—
611C4⋊C4—1722no—
612C22⋊C4—42no—
613C22⋊C4—862no—
614C22⋊C4—862no—
615C22⋊C4—3441no—
616C22⋊C4—3441no—
617C22⋊C4—1722no—
618C22⋊C4—1722no—
619C22⋊C4—1722no—
620C22⋊C4—1722no—
621C22⋊C4—1722no—
622C22⋊C4—1722no—
623C42—861no—
624C42—861no—
625C42—861no—
626C42—861no—
627C42—1722no—
628C23—21no—
629C23—22no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—22no—
638C23—48no—
639C23—48no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23#1306334612yes—
656C23C2×D4×D4311yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661D4—22no—
662D4—22no—
663D4—22no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—41no—
668D4—41no—
669D4#1306330614yes—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—432no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—861no—
687C2×C4—861no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—861no—
695C2×C4—3444no—
696C2×C4—3444no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4C22×C22⋊D4311yescharacteristic
710C2×C4C2×#1062190011yescharacteristic
711C2×C4C2×#1062190011yescharacteristic
712C2×C4C2×#1062190011yescharacteristic
713C2×C4#1306337011yescharacteristic
714C2×C4#1306337011yescharacteristic
715C8—22no—
716C8—41no—
717C8—1721no—
718C8—1721no—
719C22—24no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—42no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—816no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22#1458340511yescharacteristic
742C22D4×C22⋊D4311yescharacteristic
743C22#1458353611yescharacteristic
744C22C2×#1306334611yescharacteristic
745C22AGL(1,ℤ/8)×D4311yescharacteristic
746C22#1458370511yescharacteristic
747C22#1458370911yescharacteristic
748C4—41no—
749C4—42no—
750C4—81no—
751C4—862no—
752C4—3441no—
753C4—3441no—
754C4—3441no—
755C4—3441no—
756C4—1721no—
757C4—1721no—
758C4—1721no—
759C4C2×#1306330611yescharacteristic
760C4#1458348411yescharacteristic
761C4#1458354311yescharacteristic
762C4#1458358011yescharacteristic
763C2—42no—
764C2—44no—
765C2—82no—
766C2#1913805311yescharacteristic
767C2#1914464311yescharacteristic
768C2#1914484111yescharacteristic
769C2#1914608411yescharacteristic
770C2#1914630211yescharacteristic
771C2#1914643411yescharacteristic
772C2#1914681911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#450C2
socleC23×C43C22×D4
prime radicalC23×D4×C43C22
hypercenterC2×#450D43
hypocenterC43#24905
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×SD16×Dic43C2semidirect
2. #19138094C2semidirect
4. #19136118C2semidirect
5. #19136028C2semidirect
6. #19135908C2semidirect
7. #19135795C2semidirect
8. #19135275C2semidirect
9. #19135198C2semidirect
10. #19134952C2semidirect
11. #19134931C2semidirect
12. #19134840C2semidirect
13. #19134603C2semidirect
16. C2×Q8×Dic43C22semidirect
21. C2×#13063258C22semidirect
22. C2×#13063257C22semidirect
23. C2×Dic43⋊C8C22semidirect
24. C2×#13063249C22semidirect
25. C2×#13063249C22semidirect
31. C2×C8×Dic43C22semidirect
34. #14582806C22semidirect
37. #14582795C22semidirect
42. #14582764C22semidirect
47. #14582662C22semidirect
48. #14582662C22semidirect
49. #14582662C22semidirect
50. #14582661C22semidirect
51. #14582653C22semidirect
52. #14582653C22semidirect
447. C43#24905semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic432
#191380942
D4×C22⋊Dic432
#191361182
#191360282
#191359082
#191357952
#191352752
#191351982
#191349522
#191349312
#191348402
#191346032
#191345262
C2×C43×#4502
#2490543