Finite Group Databasebeta

← #25107740

Subgroups — #25107740

Order 11008.

1092 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583036C211yesmaximal, characteristic
2#19137111C211yesmaximal, characteristic
3#391×D43C211yesmaximal, characteristic, complemented
4#19135448C211yesmaximal, characteristic, complemented
5#19135274C211yesmaximal, characteristic, complemented
6#19135271C211yesmaximal, characteristic, complemented
7#19135232C211yesmaximal, characteristic, complemented
8#19135228C211yesmaximal, characteristic, complemented
9#19134931C211yesmaximal, characteristic, complemented
10#19134927C211yesmaximal, characteristic, complemented
11#19134909C211yesmaximal, characteristic
12#19134786C211yesmaximal, characteristic, complemented
13#19134528C211yesmaximal, characteristic, complemented
14C4×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
15C43×#1968C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063296C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C2×(C22⋊D43)⋊C4—21no—
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C42×D43C2211yescharacteristic
23#14583036C418yescomplemented
24C2×#13063256C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582806C2211yescharacteristic
35#14582805C2211yescharacteristic
36#14582804C2211yescharacteristic
37#14582803—21no—
38#14582803—21no—
39#14582797C2211yescharacteristic
40#14582793—21no—
41#14582775—21no—
42#14582756C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C22⋊C4×Dic43—21no—
45#95×D43—21no—
46#95×D43—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C22×Dic86—21no—
61C22×Dic86C2311yescharacteristic
62C2×Q8×D43—22no—
63C2×Q8×D43—41no—
64C2×Q8×D43—41no—
65C2×Q8×D43—41no—
66C2×Q8×D43—41no—
67C2×Q8×D43C2×C414yescomplemented
68C22×C22⋊D43—21no—
69C23×Dic43—21no—
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43D411yescharacteristic
73C22×C4×D43D411yescharacteristic
74C22×C4×D43C2311yescharacteristic
75C2×#10621883—41no—
76C2×#10621883—41no—
77C2×#10621883C2×C414yescomplemented
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80#13063296—22no—
81#13063296C2×C414yes—
82D4×Dic43—41no—
83D4×Dic43—41no—
84(C22⋊D43)⋊C4—44no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C4⋊C4×D43—41no—
91C4⋊C4×D43—41no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43D411yescharacteristic
97C2×C4×Dic43D411yescharacteristic
98C2×C4×Dic43C2311yescharacteristic
99C42×D43—41no—
100C42×D43—41no—
101#13063256—41no—
102#13063250—41no—
103#13063250C2×C414yescomplemented
104#13063249—41no—
105#13063249C2×C414yescomplemented
106#13063248—41no—
107#13063246—41no—
108(C2×D43)⋊C8—22no—
109(C2×D43)⋊C8C2×C414yescomplemented
110C4×C43⋊C8—41no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C22×Q8×C43C2311yescharacteristic
121C22×D4×C43C2311yescharacteristic
122C2×SD16×C43—41no—
123C2×SD16×C43—41no—
124C2×SD16×C43C2×C414yescomplemented
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C42×C43C2311yescharacteristic
132#106×C43—41no—
133#103×C43—41no—
134#102×C43—41no—
135C4×C8×C43—41no—
136#95×C43—21no—
137#95×C43—21no—
138C24×C43—21no—
139C23×D43C2×D411yescharacteristic
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43C22×C412yes—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43C22×C412yes—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2411yescharacteristic
158C2×C22⋊D43—24no—
159C2×C22⋊D43—42no—
160C2×C22⋊D43—42no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—42no—
166C22×Dic43—42no—
167C22×Dic43—42no—
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171Q8×D43—44no—
172Q8×D43—44no—
173Q8×D43—44no—
174Q8×D43—44no—
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—22no—
180C2×C4×D43—24no—
181C2×C4×D43—22no—
182C2×C4×D43—41no—
183C2×C4×D43—41no—
184C2×C4×D43—41no—
185C2×C4×D43—42no—
186C2×C4×D43—42no—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×C4×D43SD1614yescomplemented
191C2×C4×D43C22×C412yes—
192C2×C4×D43#4112yes—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—24no—
199C2×Dic86—42no—
200C2×Dic86—42no—
201C2×Dic86C22×C412yes—
202SD16×C43—44no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43C22×C412yes—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C22⋊C4×C43—42no—
214C22⋊C4×C43—42no—
215C42×C43—21no—
216C42×C43—21no—
217C22⋊Dic43—24no—
218C22⋊Dic43—42no—
219#10621883—44no—
220(C2×D43)⋊C4—42no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43C22×C412yes—
227Dic43⋊C4—42no—
228Dic43⋊C4—42no—
229C4×Dic43—21no—
230C4×Dic43—21no—
231C4×Dic43—41no—
232C4×Dic43—41no—
233C4×Dic43—42no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8C22×C412yes—
240C23×C43—22no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43C22×D411yescharacteristic
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—21no—
252C22×D43C4×D412yes—
253C22×D43C2×SD1612yes—
254C22×D43#13512yes—
255Q8×C43—22no—
256Q8×C43—22no—
257Q8×C43—41no—
258Q8×C43—41no—
259D4×C43—22no—
260D4×C43—22no—
261D4×C43—41no—
262D4×C43—41no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—22no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43C2×SD1612yes—
277C2×C4×C43#13712yes—
278C2×C4×C43C23×C411yescharacteristic
279C2×C4×C43C2×#4111yescharacteristic
280C2×C4×C43H(5,𝔽2)11yescharacteristic
281C2×C4×C43H(5,𝔽2)11yescharacteristic
282C2×C4×C43H(5,𝔽2)11yescharacteristic
283C2×C4×C43H(5,𝔽2)11yescharacteristic
284C22⋊D43—48no—
285C2×Dic43—21no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—84no—
305C2×Dic43C4×D412yes—
306C2×Dic43C2×SD1612yes—
307C4×D43—22no—
308C4×D43—22no—
309C4×D43—22no—
310C4×D43—22no—
311C4×D43—44no—
312C4×D43—44no—
313C4×D43—48no—
314C4×D43—84no—
315Dic86—22no—
316Dic86—22no—
317Dic86—48no—
318Dic86—41no—
319Dic86—41no—
320C8×C43—22no—
321C8×C43—41no—
322C43⋊C8—22no—
323C43⋊C8—41no—
324#22041—431nomaximal, Sylow
325C22×C43—42no—
326C22×C43—42no—
327C22×C43—42no—
328C22×C43—81no—
329C22×C43—81no—
330C22×C43—81no—
331C22×C43—81no—
332C22×C43C2×C4×D411yescharacteristic
333C22×C43#53411yescharacteristic
334C22×C43#53511yescharacteristic
335C22×C43C22×SD1611yescharacteristic
336C22×C43C2×#13511yescharacteristic
337C22×C43C2×#13711yescharacteristic
338C22×C43#57511yescharacteristic
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—22no—
343C2×D43—22no—
344C2×D43—22no—
345C2×D43C4×SD1614yes—
346C4×C43—22no—
347C4×C43—22no—
348C4×C43—42no—
349C4×C43—81no—
350C4×C43—81no—
351C4×C43#51811yescharacteristic
352C4×C43#51811yescharacteristic
353C4×C43#53811yescharacteristic
354C4×C43#53811yescharacteristic
355Dic43—22no—
356Dic43—22no—
357Dic43—42no—
358Dic43—41no—
359Dic43—42no—
360Dic43—81no—
361Dic43—81no—
362C2×#448—431no—
363C4×#121—431no—
364C2×#391—431no—
365#1968—431no—
366#1968D4311yescharacteristic, complemented
367#1933—431no—
368#1933—431no—
369#1927—431no—
370#1927—431no—
371#1877—431no—
372#1877—431no—
373#1874—431no—
374#1853—431no—
375#1787—431no—
376C4×C22⋊C8—431no—
377C2×C43—82no—
378C2×C43#232111yescharacteristic
379C2×C43C2×C4×SD1611yescharacteristic
380C2×C43C4×#13711yescharacteristic
381C2×C43#318711yescharacteristic
382C2×C43#319011yescharacteristic
383C2×C43#320611yescharacteristic
384C2×C43#321111yescharacteristic
385D43—24no—
386C23×Q8—431no—
387C22×SD16—431no—
388C22×SD16C2×D4311yescharacteristic
389C2×#121—431no—
390C2×C4×D4—431no—
391C2×C4×D4—861no—
392C22×C4⋊C4—431no—
393C22×C42—431no—
394#448—438no—
395C2×#106—431no—
396C2×#106C2×D4311yescharacteristic
397C2×#103—431no—
398C2×#103—431no—
399C2×#103—431no—
400C2×#103—431no—
401C2×#103—431no—
402C2×#103C2×D4311yescharacteristic
403C2×#102—431no—
404C2×#102C2×D4311yescharacteristic
405C2×C22⋊C8—431no—
406C2×C22⋊C8—431no—
407C2×C4×C8—431no—
408C2×C4×C8C2×D4311yescharacteristic
409#391—431no—
410#391—431no—
411#391—431no—
412#391—861no—
413#391—861no—
414#391C2×D4311yescharacteristic
415#390C2×D4311yescharacteristic
416#389—431no—
417#388—861no—
418#386—861no—
419#380—431no—
420C4×C4⋊C4—431no—
421C4×C22⋊C4—861no—
422C2×#95—861no—
423C2×#95—861no—
424#340—431no—
425#340—431no—
426#340—431no—
427#340—431no—
428#336—431no—
429#336—431no—
430C43#2204111yescharacteristic, complemented, Sylow
431C22×Q8—434no—
432C22×Q8—431no—
433C22×Q8—861no—
434C22×Q8—862no—
435C22×Q8—1721no—
436C22×Q8—1721no—
437C22×Q8—1721no—
438C22×Q8—1721no—
439C22×Q8C22×D4311yescharacteristic
440C22×D4—861no—
441C22×D4C22×D4311yescharacteristic
442C23×C4—431no—
443C23×C4—431no—
444C23×C4—431no—
445C23×C4—861no—
446C23×C4—861no—
447C23×C4—861no—
448C2×SD16—41no—
449C2×SD16—41no—
450C2×SD16—434no—
451C2×SD16—1721no—
452C2×SD16—1721no—
453C2×SD16C4×D4314yescomplemented
454C22×C8—431no—
455C22×C8—431no—
456C22×C8C22×D4311yescharacteristic
457C22×C8C22×D4311yescharacteristic
458#121—434no—
459#121—862no—
460C4×D4—1721no—
461C4×D4—1721no—
462C4×D4—1724no—
463C2×C4⋊C4—431no—
464C2×C4⋊C4—431no—
465C2×C4⋊C4—431no—
466C2×C4⋊C4—861no—
467C2×C4⋊C4—861no—
468C2×C4⋊C4—1721no—
469C2×C4⋊C4—1721no—
470C2×C4⋊C4C22×D4311yescharacteristic
471C2×C4⋊C4C22×D4311yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—861no—
475C2×C22⋊C4—861no—
476C2×C22⋊C4—861no—
477C2×C42—431no—
478C2×C42—431no—
479C2×C42—431no—
480C2×C42—861no—
481C2×C42—1721no—
482C2×C42—1721no—
483C2×C42C22×D4311yescharacteristic
484#106—41no—
485#106—1721no—
486#103—41no—
487#103—434no—
488#103—434no—
489#103—1721no—
490#103—1721no—
491#103—1721no—
492#102—41no—
493#102—1721no—
494C22⋊C8—434no—
495C22⋊C8—862no—
496C4×C8—41no—
497C4×C8—1721no—
498#95—21no—
499#95—21no—
500#95—861no—
501#95—861no—
502#95—861no—
503#95—861no—
504#95—861no—
505#95—861no—
506#95—861no—
507#95—861no—
508#95—861no—
509C24—21no—
510C24—431no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—432no—
517C2×Q8—864no—
518C2×Q8—861no—
519C2×Q8—861no—
520C2×Q8—861no—
521C2×Q8—861no—
522C2×Q8—861no—
523C2×Q8—1722no—
524C2×Q8—1722no—
525C2×Q8—1724no—
526C2×Q8—1724no—
527C2×Q8—1724no—
528C2×Q8—1724no—
529C2×Q8C2×C4×D4312yes—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—864no—
536C2×D4—1722no—
537C2×D4—1722no—
538C2×D4C2×C4×D4312yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—431no—
543C22×C4—431no—
544C22×C4—432no—
545C22×C4—432no—
546C22×C4—434no—
547C22×C4—431no—
548C22×C4—862no—
549C22×C4—864no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—862no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—1721no—
560C22×C4—1721no—
561C22×C4—1721no—
562C22×C4—1722no—
563C22×C4—1722no—
564C22×C4—1722no—
565C22×C4—1722no—
566C22×C4—1722no—
567C22×C4—1722no—
568C22×C4—1722no—
569C22×C4—1722no—
570C22×C4D4×D4311yescharacteristic
571C22×C4D4×D4311yescharacteristic
572C22×C4C23×D4311yescharacteristic
573SD16—44no—
574SD16—1724no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—432no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8C2×C4×D4312yes—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—432no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—1722no—
598C4⋊C4—1722no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—864no—
602C22⋊C4—1722no—
603C22⋊C4—1722no—
604C42—21no—
605C42—21no—
606C42—861no—
607C42—861no—
608C42—1721no—
609C42—1721no—
610C42—1722no—
611C23—22no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—432no—
619C23—432no—
620C23—432no—
621C23—861no—
622C23—861no—
623C23—861no—
624C23—861no—
625C23C2×D4×D4311yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—41no—
629Q8—41no—
630Q8—862no—
631Q8—862no—
632Q8—1728no—
633Q8—1721no—
634Q8—1721no—
635D4—22no—
636D4—22no—
637D4—41no—
638D4—41no—
639D4—1728no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—432no—
654C2×C4—432no—
655C2×C4—861no—
656C2×C4—861no—
657C2×C4—861no—
658C2×C4—861no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—3444no—
669C2×C4—3444no—
670C2×C4—1724no—
671C2×C4—1724no—
672C2×C4—1728no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4SD16×D4312yes—
684C2×C4#1306335412yes—
685C2×C4C22×C4×D4311yescharacteristic
686C2×C4#41×D4311yescharacteristic
687C2×C4#1306337011yescharacteristic
688C2×C4#1306337011yescharacteristic
689C2×C4#1306337011yescharacteristic
690C2×C4#1306337111yescharacteristic
691C8—22no—
692C8—41no—
693C8—862no—
694C8—1721no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—434no—
703C22—862no—
704C22—862no—
705C22—862no—
706C22—862no—
707C22—862no—
708C22—862no—
709C22C4×D4×D4311yescharacteristic
710C22#1458345711yescharacteristic
711C22#1458346211yescharacteristic
712C22C2×SD16×D4311yescharacteristic
713C22#135×D4311yescharacteristic
714C22C2×#1306335411yescharacteristic
715C22#1458369611yescharacteristic
716C4—22no—
717C4—22no—
718C4—42no—
719C4—81no—
720C4—81no—
721C4—862no—
722C4—862no—
723C4—3441no—
724C4—3441no—
725C4—1721no—
726C4—1722no—
727C4—1722no—
728C4#1458337111yescharacteristic
729C4#1458337211yescharacteristic
730C4#1458348111yescharacteristic
731C4#1458348311yescharacteristic
732C2—82no—
733C2—864no—
734C2#1913725411yescharacteristic
735C2C4×SD16×D4311yescharacteristic
736C2C4×#1306335411yescharacteristic
737C2#1914534711yescharacteristic
738C2#1914537111yescharacteristic
739C2#1914551611yescharacteristic
740C2#1914555511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1968C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
cosocleC22×C4×C43C24
hypercenter#1968D43
hypocenterC43#22041
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1968

Complements

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

NH ≅ G/Ntype
3. #391×D43C2semidirect
4. #19135448C2semidirect
5. #19135274C2semidirect
6. #19135271C2semidirect
7. #19135232C2semidirect
8. #19135228C2semidirect
9. #19134931C2semidirect
10. #19134927C2semidirect
12. #19134786C2semidirect
13. #19134528C2semidirect
14. C4×(C2×D43)⋊C8C2semidirect
15. C43×#1968C2semidirect
23. #14583036C4semidirect
67. C2×Q8×D43C2×C4semidirect
77. C2×#10621883C2×C4semidirect
103. #13063250C2×C4semidirect
105. #13063249C2×C4semidirect
109. (C2×D43)⋊C8C2×C4semidirect
124. C2×SD16×C43C2×C4semidirect
190. C2×C4×D43SD16semidirect
366. #1968D43semidirect
430. C43#22041semidirect
453. C2×SD16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830362
#191371112
#391×D432
#191354482
#191352742
#191352712
#191352322
#191352282
#191349312
#191349272
#191349092
#191347862
#191345282
C4×(C2×D43)⋊C82
C43×#19682
#2204143