Finite Group Databasebeta

← #25130355

Subgroups — #25130355

Order 11008.

1146 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583613C211yesmaximal, characteristic
2C2×#14583216C211yesmaximal, characteristic, complemented
3C2×#14582938C211yesmaximal, characteristic, complemented
4#19138899C211yesmaximal, characteristic, complemented
5#19135927C211yesmaximal, characteristic, complemented
6#19135926C211yesmaximal, characteristic, complemented
7#19135781C211yesmaximal, characteristic, complemented
8#19135030C211yesmaximal, characteristic, complemented
9#19134889C211yesmaximal, characteristic, complemented
10#19134844C211yesmaximal, characteristic, complemented
11#19134840C211yesmaximal, characteristic, complemented
12#19134796C211yesmaximal, characteristic, complemented
13#19134792C211yesmaximal, characteristic, complemented
14#19134688C211yesmaximal, characteristic, complemented
15C43×#2034C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17#14583613—24no—
18#14583613—24no—
19C2×#13063324C2211yescharacteristic
20C2×#13063312—21no—
21C2×#13063311—21no—
22C2×#13063307—21no—
23C2×#13063297—21no—
24C2×#13063296C2211yescharacteristic
25C2×D4×Dic43C2211yescharacteristic
26C2×C4×C22⋊D43C2211yescharacteristic
27C2×#13063284C2211yescharacteristic
28C2×#13063283C2211yescharacteristic
29C2×#13063281—21no—
30C2×C4⋊C4×D43C2211yescharacteristic
31#14583216—24no—
32#14582938—24no—
33C2×#13063259C2211yescharacteristic
34C2×#13063258C2211yescharacteristic
35C2×#13063257C2211yescharacteristic
36C2×#13063256C2211yescharacteristic
37C2×#13063256C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×(C2×D43)⋊C8C2211yescharacteristic
42#14582833—21no—
43#14582827—21no—
44#14582798C2211yescharacteristic
45#14582795C2211yescharacteristic
46#14582761—21no—
47#14582759C2211yescharacteristic
48#14582756C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×#121×C43C2211yescharacteristic
57C2×#106×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86—21no—
64C22×C22⋊D43—21no—
65C22×C22⋊D43D411yescharacteristic
66C23×Dic43—21no—
67C22×C4×D43—21no—
68C22×C4×D43C2311yescharacteristic
69C2×#10621872—22no—
70C2×#10621872—22no—
71C2×#10621872—22no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063324—22no—
75#13063324—22no—
76#13063312—28no—
77#13063311—28no—
78#13063307—44no—
79#13063297—28no—
80#13063296—22no—
81#13063296D414yes—
82D4×Dic43—22no—
83D4×Dic43—22no—
84C4×C22⋊D43—22no—
85C4×C22⋊D43—22no—
86#13063284—22no—
87#13063284—22no—
88#13063283—22no—
89#13063283D414yes—
90#13063281—28no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4D411yescharacteristic
100C4⋊C4×D43—22no—
101C4⋊C4×D43—22no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43D411yescharacteristic
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4D411yescharacteristic
110C2×C4×Dic43—21no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43C2311yescharacteristic
113#13063259—22no—
114#13063258—22no—
115#13063257—22no—
116#13063256—22no—
117#13063256—22no—
118#13063246—22no—
119#13063246—22no—
120C22⋊(C43⋊C8)—22no—
121(C2×D43)⋊C8—22no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C22×D4×C43—21no—
127C22×D4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131#121×C43—22no—
132#121×C43—22no—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138#106×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141C22⋊C8×C43—22no—
142#95×C43—21no—
143C24×C43—21no—
144C24×C43C2×D411yescharacteristic
145C23×D43C2×D411yescharacteristic
146C2×D4×C43—24no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—81no—
153C2×D4×C43—81no—
154C2×D4×C43C2×D412yes—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2411yescharacteristic
166C2×C22⋊D43—22no—
167C2×C22⋊D43—22no—
168C2×C22⋊D43—24no—
169C2×C22⋊D43—41no—
170C2×C22⋊D43—81no—
171C2×C22⋊D43—81no—
172C22×Dic43—24no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—42no—
178C22×Dic43—42no—
179C22×Dic43C2×D411yescharacteristic
180C22×Dic43C2×D411yescharacteristic
181C22×Dic43C2×D411yescharacteristic
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—42no—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43C2×D412yes—
190C2×C4×D43C2×D412yes—
191C2×Dic86—24no—
192C2×Dic86—81no—
193C2×Dic86—81no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43#4112yes—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43C2×D412yes—
206C22⋊C4×C43—24no—
207C22⋊C4×C43—42no—
208C22⋊Dic43—24no—
209C22⋊Dic43—24no—
210C22⋊Dic43—24no—
211C22⋊Dic43—22no—
212C22⋊Dic43—42no—
213(C2×D43)⋊C4—24no—
214(C2×D43)⋊C4—22no—
215(C2×D43)⋊C4—42no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—42no—
223C4⋊Dic43C2×D412yes—
224C4⋊Dic43C2×D412yes—
225Dic43⋊C4—24no—
226Dic43⋊C4—22no—
227Dic43⋊C4—42no—
228Dic43⋊C4—42no—
229C4×Dic43—24no—
230C4×Dic43—21no—
231C4×Dic43—21no—
232C4×Dic43—24no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8#4112yes—
239#10621872—28no—
240C23×C43—21no—
241C23×C43—22no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43C22×D411yescharacteristic
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43#12012yes—
262D4×C43—22no—
263D4×C43—22no—
264D4×C43—41no—
265D4×C43—41no—
266D4×C43—84no—
267C2×C4×C43—21no—
268C2×C4×C43—22no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43C22×D411yescharacteristic
284C2×C4×C43C22×D411yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C432−1+411yescharacteristic
288C2×C4×C432−1+411yescharacteristic
289C22⋊D43—44no—
290C22⋊D43—84no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—48no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43#12012yes—
312C2×Dic43AGL(1,ℤ/8)12yes—
313C4×D43—22no—
314C4×D43—22no—
315C4×D43—22no—
316C4×D43—22no—
317C4×D43—84no—
318Dic86—84no—
319C8×C43—22no—
320C8×C43—41no—
321C43⋊C8—22no—
322C43⋊C8—41no—
323#24104—431nomaximal, Sylow
324C22×C43—41no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—42no—
330C22×C43—41no—
331C22×C43—42no—
332C22×C43—41no—
333C22×C43—42no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43C2×#12011yescharacteristic
339C22×C43#54711yescharacteristic
340C22×C43#54711yescharacteristic
341C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
342C22×C43#57511yescharacteristic
343C22×C43#57711yescharacteristic
344C22×C43#57711yescharacteristic
345C2×D43—22no—
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—41no—
349C2×D43—41no—
350C2×D43—41no—
351C2×D43—41no—
352C4×C43—41no—
353C4×C43—42no—
354C4×C43—81no—
355C4×C43—81no—
356C4×C43#52511yescharacteristic
357C4×C43#53611yescharacteristic
358C4×C43#54711yescharacteristic
359C4×C43#54711yescharacteristic
360Dic43—22no—
361Dic43—22no—
362Dic43—42no—
363Dic43—41no—
364Dic43—42no—
365Dic43—81no—
366Dic43—81no—
367C2×#555—431no—
368C2×#481—431no—
369C2×#428—431no—
370#2486—431no—
371#2058—431no—
372#2058—431no—
373#2034—431no—
374#2034D4311yescharacteristic, complemented
375#1895—431no—
376#1870—431no—
377#1862—431no—
378#1862—431no—
379#1854—431no—
380#1854—431no—
381#1825—431no—
382C2×C43—81no—
383C2×C43—82no—
384C2×C43#240611yescharacteristic
385C2×C43#300611yescharacteristic
386C2×C43#300911yescharacteristic
387C2×C43#334811yescharacteristic
388C2×C43#334811yescharacteristic
389C2×C43#335411yescharacteristic
390C2×C43#335411yescharacteristic
391D43—42no—
392C22×M16—431no—
393#555—864no—
394#555—864no—
395C2×C4⋊Q8—431no—
396C2×#124—861no—
397C2×#124—861no—
398C2×#123—861no—
399C2×#121—431no—
400C2×#121—861no—
401C2×#121C2×D4311yescharacteristic
402C2×C4×D4—431no—
403C2×C4×D4—431no—
404C2×#117—431no—
405C2×#117—431no—
406C2×#117—861no—
407C22×C4⋊C4—431no—
408#481—864no—
409#428—864no—
410C2×#107—431no—
411C2×#107—431no—
412C2×#106—431no—
413C2×#106—431no—
414C2×#106—431no—
415C2×#106C2×D4311yescharacteristic
416C2×#102—431no—
417C2×#102—431no—
418C2×#102C2×D4311yescharacteristic
419C2×#102C2×D4311yescharacteristic
420C2×C22⋊C8—431no—
421C2×C22⋊C8—431no—
422C2×C22⋊C8C2×D4311yescharacteristic
423#398—861no—
424#397—861no—
425#389—431no—
426#389—431no—
427#381—861no—
428#380—431no—
429#380—431no—
430#380C2×D4311yescharacteristic
431#340—431no—
432#340—431no—
433#340—431no—
434#340—431no—
435#340—431no—
436#340C2×D4311yescharacteristic
437#336—431no—
438#336—431no—
439C43#2410411yescharacteristic, complemented, Sylow
440C22×Q8—861no—
441C22×D4—21no—
442C22×D4—431no—
443C22×D4—861no—
444C22×D4C22×D4311yescharacteristic
445C23×C4—431no—
446C23×C4—861no—
447C23×C4—861no—
448C23×C4C22×D4311yescharacteristic
449C2×M16—862no—
450C2×M16—862no—
451C2×M16—862no—
452C22×C8—431no—
453C22×C8—431no—
454C22×C8C22×D4311yescharacteristic
455C22×C8C22×D4311yescharacteristic
456C4⋊Q8—862no—
457C4⋊Q8—862no—
458#124—868no—
459#124—868no—
460#123—1724no—
461#121—22no—
462#121—22no—
463#121—434no—
464#121—862no—
465#121—868no—
466C4×D4—862no—
467C4×D4—862no—
468C4×D4—862no—
469C4×D4—862no—
470#117—434no—
471#117—868no—
472#117—862no—
473#117—862no—
474#117—862no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—862no—
481C2×C4⋊C4—862no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4C22×D4311yescharacteristic
487C2×C4⋊C4C22×D4311yescharacteristic
488C2×C4⋊C4C22×D4311yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—431no—
492C2×C22⋊C4—431no—
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×C42—431no—
500C2×C42—861no—
501C2×C42—861no—
502#107—862no—
503#107—862no—
504#106—22no—
505#106—862no—
506#106—862no—
507#106—862no—
508#102—22no—
509#102—22no—
510#102—862no—
511#102—862no—
512C22⋊C8—22no—
513C22⋊C8—862no—
514C22⋊C8—862no—
515#95—21no—
516#95—861no—
517#95—861no—
518#95—861no—
519#95—861no—
520C24—21no—
521C24—431no—
522C24D4×D4311yescharacteristic
523C2×Q8—864no—
524C2×Q8—3441no—
525C2×Q8—3441no—
526C2×D4—24no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—81no—
533C2×D4—81no—
534C2×D4—862no—
535C2×D4—864no—
536C2×D4—862no—
537C2×D4—3441no—
538C2×D4—3441no—
539C2×D4—1721no—
540C2×D4D4×D4312yes—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—431no—
551C22×C4—431no—
552C22×C4—432no—
553C22×C4—432no—
554C22×C4—431no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—864no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—1722no—
565C22×C4—1722no—
566C22×C4—1722no—
567C22×C4—1722no—
568C22×C4—1722no—
569C22×C4D4×D4311yescharacteristic
570C22×C4C23×D4311yescharacteristic
571M16—868no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—432no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8#1062190012yes—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—432no—
590C4⋊C4—432no—
591C4⋊C4—862no—
592C4⋊C4—864no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—1722no—
600C4⋊C4—1722no—
601C4⋊C4—1722no—
602C4⋊C4D4×D4312yes—
603C22⋊C4—24no—
604C22⋊C4—42no—
605C22⋊C4—862no—
606C22⋊C4—864no—
607C22⋊C4—862no—
608C22⋊C4—864no—
609C22⋊C4—864no—
610C22⋊C4—864no—
611C22⋊C4—1722no—
612C22⋊C4—1722no—
613C42—864no—
614C42—864no—
615C42—861no—
616C42—861no—
617C23—22no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—432no—
632C23—861no—
633C23—861no—
634C23—861no—
635C23—861no—
636C23—861no—
637C23—861no—
638C23C2×D4×D4311yescharacteristic
639Q8—3444no—
640D4—22no—
641D4—22no—
642D4—41no—
643D4—41no—
644D4—84no—
645D4—3444no—
646D4—1724no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—432no—
664C2×C4—432no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—861no—
675C2×C4—862no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—3444no—
679C2×C4—1728no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4C2×D4×D4311yescharacteristic
691C2×C4C2×D4×D4311yescharacteristic
692C2×C4#41×D4311yescharacteristic
693C2×C4C2×#1062190011yescharacteristic
694C2×C4#1306337211yescharacteristic
695C2×C4#1306337211yescharacteristic
696C8—22no—
697C8—41no—
698C8—862no—
699C8—1721no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—42no—
704C22—42no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—862no—
715C22—862no—
716C22—862no—
717C22—1721no—
718C22—1721no—
719C22—1721no—
720C22—1721no—
721C22#120×D4311yescharacteristic
722C22#1458354711yescharacteristic
723C22#1458354911yescharacteristic
724C22AGL(1,ℤ/8)×D4311yescharacteristic
725C22#1458369611yescharacteristic
726C22#1458370511yescharacteristic
727C22#1458370911yescharacteristic
728C4—41no—
729C4—42no—
730C4—81no—
731C4—81no—
732C4—862no—
733C4—862no—
734C4—3441no—
735C4—3441no—
736C4—1722no—
737C4—1721no—
738C4—1722no—
739C4#1458340911yescharacteristic
740C4#1458346911yescharacteristic
741C4#1458354711yescharacteristic
742C4#1458354911yescharacteristic
743C2—81no—
744C2—82no—
745C2—1722no—
746C2#1913792511yescharacteristic
747C2#1914384411yescharacteristic
748C2#1914386711yescharacteristic
749C2#1914710811yescharacteristic
750C2#1914711611yescharacteristic
751C2#1914718311yescharacteristic
752C2#1914718511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2034C2
socleC23×C43C22×D4
prime radicalC2×#14583613C2
hypercenter#2034D43
hypocenterC43#24104
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2034

Complements

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

NH ≅ G/Ntype
2. C2×#14583216C2semidirect
3. C2×#14582938C2semidirect
4. #19138899C2semidirect
5. #19135927C2semidirect
6. #19135926C2semidirect
7. #19135781C2semidirect
8. #19135030C2semidirect
9. #19134889C2semidirect
10. #19134844C2semidirect
11. #19134840C2semidirect
12. #19134796C2semidirect
13. #19134792C2semidirect
14. #19134688C2semidirect
15. C43×#2034C2semidirect
374. #2034D43semidirect
439. C43#24104semidirect

Maximal subgroups

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

subgroupindex
C2×#145836132
C2×#145832162
C2×#145829382
#191388992
#191359272
#191359262
#191357812
#191350302
#191348892
#191348442
#191348402
#191347962
#191347922
#191346882
C43×#20342
#2410443