Finite Group Databasebeta

← #25098295

Subgroups — #25098295

Order 11008.

1986 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D43C211yesmaximal, characteristic, complemented
2C2×#14583406C211yesmaximal, characteristic
3C2×#14582900C211yesmaximal, characteristic, complemented
4C2×#14582756C211yesmaximal, characteristic, complemented
5#19135030C212yesmaximal, complemented
6#19135025C212yesmaximal, complemented
7#19135020C212yesmaximal, complemented
8#19135015C212yesmaximal, complemented
9#19134315C211yesmaximal, characteristic, complemented
10#19134314C211yesmaximal, characteristic, complemented
11C2×C43×#417C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C22×#10621877C2211yescharacteristic
14C22×#10621872C2212yes—
15C2×M16×D43—24no—
16C2×M16×D43—24no—
17C2×M16×D43—24no—
18C22×C8×D43C2212yes—
19#14583406—24no—
20#14583406C418yescomplemented
21C2×#13063306—21no—
22C2×#13063301C2211yescharacteristic
23C2×#13063301C2211yescharacteristic
24C2×#13063296C2211yescharacteristic
25C2×#13063296C2211yescharacteristic
26C2×#13063293—21no—
27C2×C4×C22⋊D43—21no—
28C2×C4×C22⋊D43—21no—
29C2×#13063284C2211yescharacteristic
30C22×C4⋊Dic43C2211yescharacteristic
31C22×(C2×D43)⋊C4—21no—
32#14582900—24no—
33C2×#13063249C2212yescomplemented
34C2×#13063246C2212yescomplemented
35#14582756—21no—
36#14582756—21no—
37#14582756C2212yes—
38#14582756C2212yes—
39C2×C43⋊#95—21no—
40#14582662C2212yescomplemented
41#14582662C2212yescomplemented
42#14582661C2212yescomplemented
43#14582661C2212yescomplemented
44C22×#41×C43C2211yescharacteristic
45C22×M16×C43C2211yescharacteristic
46C22×C4⋊C4×C43C2211yescharacteristic
47C43×#417—24no—
48C2×#103×C43C2212yescomplemented
49C2×#102×C43C2212yescomplemented
50C24×D43D411yescharacteristic
51C22×C22⋊D43—21no—
52C22×C22⋊D43—21no—
53C23×Dic43—21no—
54C23×Dic43D411yescharacteristic
55C22×C4×D43—22no—
56C22×C4×D43—22no—
57C22×C4×D43—22no—
58C22×C4×D43—22no—
59C22×C4×D43C2×C414yes—
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43D414yes—
63C22×C4×D43C2311yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C2×#10621877—22no—
66C2×#10621877—22no—
67C2×#10621877D414yescomplemented
68C2×#10621872—24no—
69C2×#10621872—24no—
70C2×#10621872—24no—
71M16×D43—232no—
72C22×C43⋊C8C2312yes—
73C2×C8×D43—24no—
74C2×C8×D43—24no—
75C2×C8×D43—24no—
76#13063306—28no—
77#13063301—22no—
78#13063301—22no—
79#13063301C2×C414yescomplemented
80#13063301C2×C414yescomplemented
81#13063296—22no—
82#13063296—22no—
83#13063296C2×C414yescomplemented
84#13063296C2×C414yescomplemented
85#13063293—28no—
86C4×C22⋊D43—28no—
87C4×C22⋊D43—28no—
88#13063284—22no—
89#13063284C2×C414yes—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43C2312yes—
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—22no—
104C2×(C2×D43)⋊C4—22no—
105C2×(C2×D43)⋊C4—44no—
106C2×C4×Dic43—21no—
107#13063249—24no—
108#13063246—24no—
109C43⋊#95—22no—
110C43⋊#95—22no—
111C2×#41×C43—22no—
112C2×#41×C43—22no—
113C2×#41×C43—22no—
114C2×#41×C43—22no—
115C2×#41×C43—22no—
116C2×#41×C43C2×C414yes—
117C22×Q8×C43C2311yescharacteristic
118C22×D4×C43—21no—
119C22×D4×C43C2311yescharacteristic
120C23×C4×C43—21no—
121C23×C4×C43—21no—
122C23×C4×C43C2311yescharacteristic
123C2×M16×C43—22no—
124C2×M16×C43—22no—
125C2×M16×C43D414yescomplemented
126C22×C8×C43C2312yes—
127C2×C4⋊C4×C43—22no—
128C2×C4⋊C4×C43—22no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43C2312yes—
131#103×C43—24no—
132#102×C43—24no—
133C24×C43—21no—
134C24×C43C2×D411yescharacteristic
135C23×D43—22no—
136C23×D43—22no—
137C23×D43—22no—
138C23×D43—22no—
139C23×D43—41no—
140C23×D43—41no—
141C23×D43C22⋊C414yes—
142C23×D43C2×D411yescharacteristic
143C23×D43C2×D411yescharacteristic
144#41×C43—28no—
145#41×C43—28no—
146#41×C43—44no—
147#41×C43—44no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43C22×C412yes—
154C2×D4×C43—21no—
155C2×D4×C43—24no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43C22×C412yes—
163C22×C4×C43—24no—
164C22×C4×C43—21no—
165C22×C4×C43—22no—
166C22×C4×C43—42no—
167C22×C4×C43—42no—
168C22×C4×C43—42no—
169C22×C4×C43—42no—
170C22×C4×C43—42no—
171C22×C4×C43C22×C412yes—
172C22×C4×C43C2×D412yes—
173C22×C4×C43C2×D412yes—
174C22×C4×C43C2×D412yes—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43#4112yes—
177C22×C4×C43#4112yes—
178C22×C4×C43C2411yescharacteristic
179C2×C22⋊D43—24no—
180C2×C22⋊D43—24no—
181C2×C22⋊D43—42no—
182C2×C22⋊D43—42no—
183C2×C22⋊D43—42no—
184C2×C22⋊D43—42no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—22no—
190C22×Dic43—42no—
191C22×Dic43—42no—
192C22×Dic43—42no—
193C22×Dic43C22⋊C414yes—
194C22×Dic43C2×D411yescharacteristic
195C22×Dic43C2×D411yescharacteristic
196C2×C4×D43—28no—
197C2×C4×D43—28no—
198C2×C4×D43—28no—
199C2×C4×D43—22no—
200C2×C4×D43—22no—
201C2×C4×D43—22no—
202C2×C4×D43—22no—
203C2×C4×D43—28no—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—21no—
212C2×C4×D43C22⋊C414yes—
213C2×C4×D43C22⋊C414yes—
214C2×C4×D43C22×C412yes—
215C2×C4×D43C22×C412yes—
216C2×C4×D43C2×D412yes—
217C2×C4×D43C2×D412yes—
218M16×C43—28no—
219C2×C8×C43—22no—
220C2×C8×C43—22no—
221C2×C8×C43C2×D414yes—
222C4⋊C4×C43—22no—
223C4⋊C4×C43—22no—
224C4⋊C4×C43—42no—
225C22⋊Dic43—24no—
226C22⋊Dic43—24no—
227C22⋊Dic43—24no—
228(C2×D43)⋊C4—24no—
229(C2×D43)⋊C4—24no—
230(C2×D43)⋊C4—44no—
231(C2×D43)⋊C4—44no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—22no—
235C4⋊Dic43—22no—
236C4⋊Dic43—42no—
237C4⋊Dic43C22×C412yes—
238C4⋊Dic43C22×C412yes—
239Dic43⋊C4—24no—
240Dic43⋊C4—24no—
241C4×Dic43—24no—
242#10621877—28no—
243C2×C43⋊C8—22no—
244C2×C43⋊C8—22no—
245C2×C43⋊C8C2×D414yes—
246#10621872—216no—
247C8×D43—216no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—22no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43C2×C22⋊C412yes—
260C23×C43#12112yes—
261C23×C43#12112yes—
262C23×C43C22×D411yescharacteristic
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—28no—
274C22×D43—28no—
275C22×D43—44no—
276C22×D43—44no—
277C22×D43—44no—
278C22×D43—44no—
279C22×D43—44no—
280C22×D43C2×C22⋊C412yes—
281C22×D43C2×C22⋊C412yes—
282C22×D43AGL(1,ℤ/8)12yes—
283C22×D43#13712yes—
284Q8×C43—22no—
285Q8×C43—22no—
286Q8×C43—41no—
287Q8×C43—41no—
288D4×C43—22no—
289D4×C43—22no—
290D4×C43—48no—
291D4×C43—41no—
292D4×C43—41no—
293C2×C4×C43—22no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—48no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43—84no—
301C2×C4×C43C2×C22⋊C412yes—
302C2×C4×C43C4×D414yes—
303C2×C4×C43C4×D414yes—
304C2×C4×C43#12014yes—
305C2×C4×C43#12112yes—
306C2×C4×C43#12112yes—
307C2×C4×C43#12314yes—
308C2×C4×C43C23×C411yescharacteristic
309C2×C4×C43C22×D411yescharacteristic
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C2×#4111yescharacteristic
313C2×C4×C43C2×#4111yescharacteristic
314C22⋊D43—48no—
315C22⋊D43—48no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—28no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329C2×Dic43—42no—
330C2×Dic43—84no—
331C2×Dic43C2×C22⋊C412yes—
332C2×Dic43C2×C22⋊C412yes—
333C4×D43—22no—
334C4×D43—22no—
335C4×D43—22no—
336C4×D43—22no—
337C4×D43—22no—
338C4×D43—22no—
339C4×D43—22no—
340C4×D43—22no—
341C4×D43—28no—
342C4×D43—28no—
343C8×C43—24no—
344C43⋊C8—24no—
345#20971—431nomaximal, Sylow
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—22no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43#38614yes—
360C22×C43C22×C22⋊C411yescharacteristic
361C22×C43C2×#12111yescharacteristic
362C22×C43C2×#12111yescharacteristic
363C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
364C22×C43C2×#13711yescharacteristic
365C22×C43#57511yescharacteristic
366C22×C43#57511yescharacteristic
367C2×D43—22no—
368C2×D43—22no—
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—22no—
372C2×D43—22no—
373C2×D43—22no—
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—416no—
377C2×D43—41no—
378C2×D43—41no—
379C2×D43—41no—
380C2×D43—41no—
381C2×D43#41714yescomplemented
382C4×C43—42no—
383C4×C43—82no—
384C4×C43#38614yes—
385C4×C43C2×C4×D411yescharacteristic
386C4×C43C2×C4×D411yescharacteristic
387C4×C43C2×#12011yescharacteristic
388C4×C43C2×#12311yescharacteristic
389Dic43—22no—
390Dic43—22no—
391Dic43—42no—
392Dic43—42no—
393Dic43—82no—
394C23×M16—431no—
395C2×#525—431no—
396C2×#417—431no—
397C2×#417D4311yescharacteristic, complemented
398C2×#380—431no—
399#1895—432no—
400#1894—432no—
401#1893—432no—
402#1892—432no—
403#1736—431no—
404#1736—431no—
405C2×C43—24no—
406C2×C43—82no—
407C2×C43C2×#38611yescharacteristic
408C2×C43C2×#41711yescharacteristic
409C2×C43#289611yescharacteristic
410C2×C43#305511yescharacteristic
411C2×C43#305511yescharacteristic
412C2×C43#305611yescharacteristic
413C2×C43#305611yescharacteristic
414D43—24no—
415D43—42no—
416C22×#41C2×D4311yescharacteristic
417C24×C4—431no—
418C22×M16—431no—
419C22×M16—432no—
420C22×M16—864no—
421C22×M16—864no—
422C22×M16—864no—
423C22×M16C2×D4311yescharacteristic
424C23×C8—432no—
425#525—438no—
426#525—864no—
427C2×#123—861no—
428C2×C22⋊Q8—431no—
429C2×C22⋊Q8—431no—
430C2×#121—431no—
431C2×#121—431no—
432C2×#120—861no—
433C2×C4×D4—861no—
434C2×C4×D4—861no—
435C2×#117—431no—
436C22×C4⋊C4—431no—
437C22×C4⋊C4C2×D4311yescharacteristic
438C22×C22⋊C4—861no—
439#417—24no—
440#417—864no—
441C2×#103—432no—
442C2×#103C2×D4312yescomplemented
443C2×#102—432no—
444C2×#102C2×D4312yescomplemented
445#380—432no—
446#380—432no—
447#380—861no—
448#380—861no—
449C2×#95—861no—
450#340—432no—
451#340—432no—
452#340—432no—
453#340—432no—
454C43#2097111yescharacteristic, complemented, Sylow
455C25—431no—
456C2×#41—22no—
457C2×#41—22no—
458C2×#41—22no—
459C2×#41—22no—
460C2×#41—22no—
461C2×#41C4×D4314yes—
462C22×Q8C22×D4311yescharacteristic
463C22×D4—21no—
464C22×D4—861no—
465C22×D4—861no—
466C22×D4C22×D4311yescharacteristic
467C23×C4—21no—
468C23×C4—21no—
469C23×C4—431no—
470C23×C4—434no—
471C23×C4—431no—
472C23×C4—431no—
473C23×C4—434no—
474C23×C4—431no—
475C23×C4—431no—
476C23×C4—862no—
477C23×C4—862no—
478C23×C4—862no—
479C23×C4—862no—
480C23×C4—861no—
481C23×C4C22×D4311yescharacteristic
482C2×M16—22no—
483C2×M16—22no—
484C2×M16—434no—
485C2×M16—864no—
486C2×M16—864no—
487C2×M16—8632no—
488C2×M16—862no—
489C2×M16—862no—
490C2×M16—864no—
491C2×M16C22⋊D4314yescomplemented
492C22×C8—432no—
493C22×C8—864no—
494C22×C8—864no—
495C22×C8—864no—
496C22×C8C22×D4312yes—
497#123—868no—
498C22⋊Q8—434no—
499C22⋊Q8—434no—
500C22⋊Q8—862no—
501C22⋊Q8—862no—
502#121—434no—
503#121—434no—
504#121—862no—
505#121—862no—
506#120—868no—
507C4×D4—868no—
508C4×D4—868no—
509#117—434no—
510#117—862no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—432no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—862no—
520C2×C4⋊C4—862no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4C22×D4312yes—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—862no—
529C2×C22⋊C4—862no—
530C2×C22⋊C4—1724no—
531C2×C42—861no—
532#103—24no—
533#103—864no—
534#102—24no—
535#102—864no—
536#95—862no—
537#95—862no—
538C24—21no—
539C24—431no—
540C24—431no—
541C24—434no—
542C24—862no—
543C24—862no—
544C24—862no—
545C24—862no—
546C24—1721no—
547C24—1721no—
548C24D4×D4311yescharacteristic
549#41—28no—
550#41—28no—
551#41—44no—
552#41—44no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8C2×C4×D4312yes—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—864no—
568C2×D4—864no—
569C2×D4—1722no—
570C2×D4—1722no—
571C2×D4—1722no—
572C2×D4—1722no—
573C2×D4C2×C4×D4312yes—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—434no—
583C22×C4—431no—
584C22×C4—431no—
585C22×C4—434no—
586C22×C4—434no—
587C22×C4—432no—
588C22×C4—432no—
589C22×C4—432no—
590C22×C4—432no—
591C22×C4—862no—
592C22×C4—862no—
593C22×C4—868no—
594C22×C4—868no—
595C22×C4—868no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—862no—
600C22×C4—868no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—862no—
612C22×C4—1722no—
613C22×C4—1722no—
614C22×C4—1722no—
615C22×C4C2×C4×D4312yes—
616C22×C4#1062189812yes—
617C22×C4D4×D4311yescharacteristic
618C22×C4D4×D4312yes—
619C22×C4D4×D4312yes—
620C22×C4#1062190012yes—
621C22×C4C2×C22⋊D4312yes—
622C22×C4C23×D4311yescharacteristic
623M16—28no—
624M16—8616no—
625M16—868no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—434no—
629C2×C8—8616no—
630C2×C8—862no—
631C2×C8—862no—
632C2×C8C2×C22⋊D4314yes—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—42no—
636C4⋊C4—432no—
637C4⋊C4—432no—
638C4⋊C4—864no—
639C4⋊C4—864no—
640C4⋊C4—861no—
641C4⋊C4—861no—
642C4⋊C4—862no—
643C4⋊C4—862no—
644C4⋊C4—1722no—
645C22⋊C4—864no—
646C22⋊C4—864no—
647C22⋊C4—864no—
648C22⋊C4—864no—
649C22⋊C4—864no—
650C22⋊C4—1724no—
651C22⋊C4—1724no—
652C42—864no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—22no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—432no—
665C23—432no—
666C23—432no—
667C23—432no—
668C23—868no—
669C23—861no—
670C23—861no—
671C23—861no—
672C23—861no—
673C23—861no—
674C23—861no—
675C23—861no—
676C23—861no—
677C23—861no—
678C23—861no—
679C23—868no—
680C23—1724no—
681C23—1724no—
682C23—1724no—
683C23—1724no—
684C23—1724no—
685C23C22⋊C4×D4312yes—
686C23#1306329612yes—
687C23#1306329812yes—
688C23C2×D4×D4311yescharacteristic
689Q8—22no—
690Q8—22no—
691Q8—41no—
692Q8—41no—
693D4—22no—
694D4—22no—
695D4—48no—
696D4—41no—
697D4—41no—
698D4—1728no—
699D4—1728no—
700C2×C4—22no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—48no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—84no—
708C2×C4—432no—
709C2×C4—432no—
710C2×C4—861no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—861no—
714C2×C4—868no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—868no—
724C2×C4—868no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—3444no—
728C2×C4—1722no—
729C2×C4—1722no—
730C2×C4—1722no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4C22⋊C4×D4312yes—
736C2×C4(C22⋊D43)⋊C414yes—
737C2×C4C4×C22⋊D4314yes—
738C2×C4#1306329314yes—
739C2×C4#1306329612yes—
740C2×C4#1306329812yes—
741C2×C4#1306330714yes—
742C2×C4C22×C4×D4311yescharacteristic
743C2×C4C2×D4×D4311yescharacteristic
744C2×C4C2×D4×D4311yescharacteristic
745C2×C4C22×C22⋊D4311yescharacteristic
746C2×C4C2×#1062190011yescharacteristic
747C2×C4C2×#1062189811yescharacteristic
748C8—24no—
749C8—864no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—434no—
764C22—862no—
765C22—862no—
766C22—862no—
767C22—862no—
768C22—862no—
769C22—862no—
770C22—862no—
771C22—862no—
772C22—862no—
773C22—17216no—
774C22—1721no—
775C22—1721no—
776C22—1721no—
777C22—1721no—
778C22#1458277514yes—
779C22C2×C22⋊C4×D4311yescharacteristic
780C22C2×#1306329611yescharacteristic
781C22C2×#1306329811yescharacteristic
782C22AGL(1,ℤ/8)×D4311yescharacteristic
783C22#137×D4311yescharacteristic
784C22#1458369511yescharacteristic
785C22#1458369811yescharacteristic
786C4—42no—
787C4—82no—
788C4—862no—
789C4—862no—
790C4—3442no—
791C4—1722no—
792C4—1722no—
793C4#1458277514yes—
794C4C2×(C22⋊D43)⋊C411yescharacteristic
795C4C2×C4×C22⋊D4311yescharacteristic
796C4C2×#1306329311yescharacteristic
797C4C2×#1306330711yescharacteristic
798C2—24no—
799C2—82no—
800C2—864no—
801C2—1722no—
802C2C2×#1458277511yescharacteristic
803C2#417×D4311yescharacteristic
804C2#1914311111yescharacteristic
805C2#1914420811yescharacteristic
806C2#1914421711yescharacteristic
807C2#1914421911yescharacteristic
808C2#1914422811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#417C2
socleC23×C43C22×D4
prime radicalC2×#14583406C2
cosocleC22×C4×C43C24
hypercenterC2×#417D43
hypocenterC43#20971
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C22×M16×D43C2semidirect
3. C2×#14582900C2semidirect
4. C2×#14582756C2semidirect
5. #19135030C2semidirect
6. #19135025C2semidirect
7. #19135020C2semidirect
8. #19135015C2semidirect
9. #19134315C2semidirect
10. #19134314C2semidirect
11. C2×C43×#417C2semidirect
20. #14583406C4semidirect
33. C2×#13063249C22semidirect
34. C2×#13063246C22semidirect
40. #14582662C22semidirect
41. #14582662C22semidirect
42. #14582661C22semidirect
43. #14582661C22semidirect
48. C2×#103×C43C22semidirect
49. C2×#102×C43C22semidirect
67. C2×#10621877D4semidirect
79. #13063301C2×C4semidirect
80. #13063301C2×C4semidirect
83. #13063296C2×C4semidirect
84. #13063296C2×C4semidirect
125. C2×M16×C43D4semidirect
381. C2×D43#417semidirect
397. C2×#417D43semidirect
442. C2×#103C2×D43semidirect
444. C2×#102C2×D43semidirect
454. C43#20971semidirect
491. C2×M16C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D432
C2×#145834062
C2×#145829002
C2×#145827562
#191350302
#191350252
#191350202
#191350152
#191343152
#191343142
C2×C43×#4172
#2097143