Finite Group Databasebeta

← #25131441

Subgroups — #25131441

Order 11008.

1122 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583622C211yesmaximal, characteristic, complemented
2C2×#14583114C211yesmaximal, characteristic
3C2×C4×#10621883C211yesmaximal, characteristic, complemented
4#19135841C211yesmaximal, characteristic, complemented
5#19135836C211yesmaximal, characteristic, complemented
6#19135677C211yesmaximal, characteristic, complemented
7#19135671C211yesmaximal, characteristic
8#19135532C211yesmaximal, characteristic, complemented
9#19135404C211yesmaximal, characteristic, complemented
10#19134953C211yesmaximal, characteristic, complemented
11#19134946C211yesmaximal, characteristic
12#19134862C211yesmaximal, characteristic, complemented
13#19134855C211yesmaximal, characteristic, complemented
14#19134607C211yesmaximal, characteristic, complemented
15C43×#2580C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19#14583622—24no—
20#14583622—24no—
21C2×#13063325C2211yescharacteristic
22C2×#13063320—21no—
23C2×#13063320—21no—
24C2×#13063313C2211yescharacteristic
25C2×#13063313C2211yescharacteristic
26C2×#13063301—21no—
27C2×C4×Dic86C2211yescharacteristic
28C2×C4×Dic86C2211yescharacteristic
29C2×C4×D172C2211yescharacteristic
30C2×#13063283—21no—
31#14583114—24no—
32C4×#10621883—24no—
33C2×#13063256C2211yescharacteristic
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×#13063245C2211yescharacteristic
45C2×C4×C43⋊C8C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×C4×Q8×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C43×#399—21no—
55C43×#393—21no—
56C43×#390C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#385—21no—
61C43×#385—21no—
62C43×#382C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×Dic86C2311yescharacteristic
65C22×D172C2311yescharacteristic
66C22×C4×D43—21no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—22no—
70C2×#10621883—22no—
71C2×#10621883—22no—
72C2×#10621883—41no—
73C2×#10621882—22no—
74C2×#10621882—22no—
75C2×#10621882—41no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80#13063325—22no—
81#13063325—22no—
82#13063320—28no—
83#13063320—28no—
84#13063313—22no—
85#13063313—22no—
86#13063313—22no—
87#13063313D414yes—
88#13063301—28no—
89C4×Dic86—22no—
90C4×Dic86—22no—
91C4×Dic86—22no—
92C4×Dic86D414yes—
93C4×D172—22no—
94C4×D172—22no—
95#13063283—28no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43—21no—
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—21no—
108#13063256—22no—
109C4⋊(C43⋊C8)—22no—
110#13063248—22no—
111#13063248—22no—
112#13063248—22no—
113#13063248—41no—
114#13063248—41no—
115#13063248—41no—
116#13063246—22no—
117#13063245—22no—
118#13063245—22no—
119#13063245—41no—
120C4×C43⋊C8—22no—
121C22×Q8×C43D411yescharacteristic
122C22×D4×C43C2311yescharacteristic
123C23×C4×C43—21no—
124C4×Q8×C43—22no—
125C4×Q8×C43—22no—
126C4×D4×C43—22no—
127C4×D4×C43—22no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43D411yescharacteristic
131C2×C4⋊C4×C43D411yescharacteristic
132C2×C4⋊C4×C43D411yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C42×C43C2311yescharacteristic
142C2×C42×C43C2311yescharacteristic
143C2×C42×C43C2311yescharacteristic
144#95×C43—21no—
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148C24×C43—21no—
149C23×D43—21no—
150C2×Q8×C43—22no—
151C2×Q8×C43—22no—
152C2×Q8×C43—41no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43#4112yes—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—42no—
163C22×C4×C43—81no—
164C22×C4×C43—81no—
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2411yescharacteristic
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172C2×D412yes—
181C2×C4×D43—24no—
182C2×C4×D43—42no—
183C2×C4×D43—42no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86C2×D412yes—
195C2×Dic86C2×D412yes—
196C4⋊C4×C43—22no—
197C4⋊C4×C43—22no—
198C4⋊C4×C43—22no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—81no—
206C4⋊C4×C43—81no—
207C22⋊C4×C43—42no—
208C22⋊C4×C43—42no—
209C22⋊C4×C43—42no—
210C22⋊C4×C43—81no—
211C22⋊C4×C43—81no—
212C42×C43—21no—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43—21no—
216C42×C43C2×D412yes—
217C42×C43C2×D412yes—
218#10621883—28no—
219#10621883—44no—
220#10621882—44no—
221(C2×D43)⋊C4—24no—
222(C2×D43)⋊C4—24no—
223(C2×D43)⋊C4—24no—
224(C2×D43)⋊C4—24no—
225(C2×D43)⋊C4—24no—
226C4⋊Dic43—24no—
227C4⋊Dic43—24no—
228C4⋊Dic43—21no—
229C4⋊Dic43C2×D412yes—
230Dic43⋊C4—24no—
231Dic43⋊C4—24no—
232C4×Dic43—24no—
233C4×Dic43—24no—
234C2×C43⋊C8—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—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8#4112yes—
246C23×C43—22no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43C22×D411yescharacteristic
254C22×D43—22no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261Q8×C43—44no—
262D4×C43—22no—
263D4×C43—22no—
264D4×C43—41no—
265D4×C43—41no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—41no—
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—84no—
291C2×C4×C43#12012yes—
292C2×C4×C43#12012yes—
293C2×C4×C43#13512yes—
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43H(5,𝔽2)11yescharacteristic
299C2×C4×C432−1+411yescharacteristic
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309D172—22no—
310D172—22no—
311D172—41no—
312D172—41no—
313C4×D43—48no—
314Dic86—22no—
315Dic86—22no—
316Dic86—22no—
317Dic86—22no—
318Dic86—41no—
319Dic86—41no—
320Dic86—41no—
321Dic86—41no—
322C43⋊C8—22no—
323C43⋊C8—41no—
324C43⋊C8—41no—
325C43⋊C8—41no—
326#24193—431nomaximal, Sylow
327C22×C43—42no—
328C22×C43—42no—
329C22×C43—42no—
330C22×C43—81no—
331C22×C43—81no—
332C22×C43—81no—
333C22×C43—81no—
334C22×C43C2×#12011yescharacteristic
335C22×C43#54811yescharacteristic
336C22×C43#55011yescharacteristic
337C22×C43C2×#13511yescharacteristic
338C22×C43#57511yescharacteristic
339C22×C43#57711yescharacteristic
340C22×C43#57711yescharacteristic
341C2×D43—42no—
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—81no—
345C2×D43—81no—
346C2×D43—81no—
347C2×D43—81no—
348C4×C43—22no—
349C4×C43—22no—
350C4×C43—22no—
351C4×C43—41no—
352C4×C43—41no—
353C4×C43—41no—
354C4×C43—81no—
355C4×C43—81no—
356C4×C43—81no—
357C4×C43#52511yescharacteristic
358C4×C43#53711yescharacteristic
359C4×C43#54611yescharacteristic
360C4×C43#54711yescharacteristic
361Dic43—42no—
362Dic43—42no—
363Dic43—42no—
364C2×#556—431no—
365C2×#463—431no—
366C2×C4×SD16—431no—
367#2580D4311yescharacteristic, complemented
368#2043—431no—
369#2042—431no—
370#2013—431no—
371#2012—431no—
372#1984—431no—
373#1958—431no—
374#1880—431no—
375#1879—431no—
376#1865—431no—
377#1864—431no—
378#1805—431no—
379C2×C43—82no—
380C2×C43#240711yescharacteristic
381C2×C43#300211yescharacteristic
382C2×C43#301011yescharacteristic
383C2×C43#336011yescharacteristic
384C2×C43#337611yescharacteristic
385C2×C43#339411yescharacteristic
386C2×C43#340111yescharacteristic
387D43—82no—
388C22×SD16—431no—
389C22×SD16—431no—
390C22×D8—431no—
391#556—864no—
392#556—864no—
393C2×C4⋊Q8—431no—
394C2×#126—861no—
395C2×#126—861no—
396C2×#124—431no—
397C2×#124—431no—
398C2×C22⋊Q8—861no—
399C2×C4×Q8—431no—
400C2×C4×Q8—431no—
401C2×C4×Q8C2×D4311yescharacteristic
402C2×C4×D4—431no—
403C2×C4×D4C2×D4311yescharacteristic
404C2×#117—861no—
405#463—864no—
406C4×SD16—864no—
407C2×#106—431no—
408C2×C4⋊C8—431no—
409C2×#103—431no—
410C2×#103—431no—
411C2×#103—431no—
412C2×#103—431no—
413C2×#103—431no—
414C2×#103—431no—
415C2×#102—431no—
416C2×#102—431no—
417C2×#102—431no—
418C2×#102—431no—
419C2×C4×C8—431no—
420#399—21no—
421#393—21no—
422#390C2×D4311yescharacteristic
423#390C2×D4311yescharacteristic
424#389C2×D4311yescharacteristic
425#389C2×D4311yescharacteristic
426#385—21no—
427#385—21no—
428#382C2×D4311yescharacteristic
429#340—431no—
430#340—431no—
431#336—431no—
432#336—431no—
433#336—431no—
434#336—431no—
435C43#2419311yescharacteristic, complemented, Sylow
436C22×Q8—431no—
437C22×Q8—431no—
438C22×Q8C22⋊D4311yescharacteristic
439C22×D4—431no—
440C22×D4C22×D4311yescharacteristic
441C23×C4—21no—
442C23×C4—861no—
443C2×SD16—862no—
444C2×SD16—862no—
445C2×SD16—862no—
446C2×SD16—862no—
447C2×SD16—862no—
448C2×SD16—1721no—
449C2×D8—862no—
450C2×D8—862no—
451C2×D8—1721no—
452C22×C8—431no—
453C22×C8—431no—
454C22×C8—431no—
455C22×C8—431no—
456C4⋊Q8—862no—
457C4⋊Q8—862no—
458#126—868no—
459#126—868no—
460#124—434no—
461#124—862no—
462#124—862no—
463#124—862no—
464C22⋊Q8—868no—
465C4×Q8—22no—
466C4×Q8—22no—
467C4×Q8—434no—
468C4×Q8—862no—
469C4×Q8—862no—
470C4×Q8—862no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—862no—
474C4×D4—862no—
475#117—868no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4C22⋊D4311yescharacteristic
484C2×C4⋊C4C22⋊D4311yescharacteristic
485C2×C4⋊C4C22⋊D4311yescharacteristic
486C2×C4⋊C4C22×D4311yescharacteristic
487C2×C4⋊C4C22×D4311yescharacteristic
488C2×C4⋊C4C22×D4311yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C42—861no—
500C2×C42—861no—
501C2×C42C22×D4311yescharacteristic
502C2×C42C22×D4311yescharacteristic
503C2×C42C22×D4311yescharacteristic
504#106—862no—
505C4⋊C8—862no—
506#103—862no—
507#103—862no—
508#103—862no—
509#103—1721no—
510#103—1721no—
511#103—1721no—
512#102—862no—
513#102—862no—
514#102—862no—
515#102—1721no—
516C4×C8—862no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521C24—21no—
522C24—861no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—41no—
526C2×Q8—432no—
527C2×Q8—432no—
528C2×Q8—861no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×Q8—861no—
535C2×Q8—861no—
536C2×Q8—861no—
537C2×Q8—861no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—432no—
544C2×D4—861no—
545C2×D4—861no—
546C2×D4—861no—
547C2×D4—861no—
548C2×D4—861no—
549C2×D4#1062190212yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—42no—
554C22×C4—81no—
555C22×C4—81no—
556C22×C4—864no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—1722no—
561C22×C4—1722no—
562C22×C4C2×C22⋊D4311yescharacteristic
563C22×C4C2×C22⋊D4311yescharacteristic
564C22×C4C2×C22⋊D4311yescharacteristic
565C22×C4C2×C22⋊D4311yescharacteristic
566C22×C4C2×C22⋊D4311yescharacteristic
567C22×C4C2×C22⋊D4311yescharacteristic
568C22×C4C23×D4311yescharacteristic
569SD16—868no—
570SD16—1724no—
571D8—1724no—
572C2×C8—432no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—81no—
594C4⋊C4—81no—
595C4⋊C4—432no—
596C4⋊C4—864no—
597C4⋊C4—864no—
598C4⋊C4—864no—
599C4⋊C4—864no—
600C4⋊C4—861no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—864no—
607C22⋊C4—864no—
608C22⋊C4—864no—
609C22⋊C4—864no—
610C22⋊C4—864no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—864no—
616C42—864no—
617C42D4×D4312yes—
618C42D4×D4312yes—
619C23—22no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—862no—
627C23—1721no—
628C23—1721no—
629C23—1721no—
630C23—1721no—
631C23—1721no—
632C23—1721no—
633C23C22×C22⋊D4311yescharacteristic
634Q8—44no—
635Q8—862no—
636Q8—862no—
637Q8—862no—
638Q8—862no—
639Q8—1721no—
640Q8—1721no—
641Q8—1721no—
642Q8—1721no—
643D4—22no—
644D4—22no—
645D4—41no—
646D4—41no—
647D4—862no—
648D4—862no—
649D4—1721no—
650D4—1721no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—84no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—1728no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4#1306329312yes—
687C2×C4#1306329312yes—
688C2×C4#1306334512yes—
689C2×C4C2×D4×D4311yescharacteristic
690C2×C4C2×D4×D4311yescharacteristic
691C2×C4#41×D4311yescharacteristic
692C2×C4C2×#1062190211yescharacteristic
693C2×C4#1306337111yescharacteristic
694C2×C4#1306337311yescharacteristic
695C8—862no—
696C8—1721no—
697C8—1721no—
698C8—1721no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—3441no—
707C22—3441no—
708C22—3441no—
709C22—3441no—
710C22—1722no—
711C22—1722no—
712C22—1722no—
713C22C2×#1306329311yescharacteristic
714C22#1458356011yescharacteristic
715C22#1458356811yescharacteristic
716C22C2×#1306334511yescharacteristic
717C22#1458369711yescharacteristic
718C22#1458371011yescharacteristic
719C22#1458371011yescharacteristic
720C4—22no—
721C4—22no—
722C4—22no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—81no—
727C4—81no—
728C4—81no—
729C4—1722no—
730C4—1722no—
731C4—1722no—
732C4#1458341211yescharacteristic
733C4#1458347911yescharacteristic
734C4#1458354011yescharacteristic
735C4#1458355111yescharacteristic
736C2—82no—
737C2—3442no—
738C2#1913794211yescharacteristic
739C2#1914381111yescharacteristic
740C2#1914387911yescharacteristic
741C2#1914724411yescharacteristic
742C2#1914742211yescharacteristic
743C2#1914758711yescharacteristic
744C2#1914765511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2580C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenter#2580D43
hypocenterC43#24193
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2580

Complements

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

NH ≅ G/Ntype
1. C2×#14583622C2semidirect
3. C2×C4×#10621883C2semidirect
4. #19135841C2semidirect
5. #19135836C2semidirect
6. #19135677C2semidirect
8. #19135532C2semidirect
9. #19135404C2semidirect
10. #19134953C2semidirect
12. #19134862C2semidirect
13. #19134855C2semidirect
14. #19134607C2semidirect
15. C43×#2580C2semidirect
367. #2580D43semidirect
435. C43#24193semidirect

Maximal subgroups

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

subgroupindex
C2×#145836222
C2×#145831142
C2×C4×#106218832
#191358412
#191358362
#191356772
#191356712
#191355322
#191354042
#191349532
#191349462
#191348622
#191348552
#191346072
C43×#25802
#2419343