Finite Group Databasebeta

← #25110367

Subgroups — #25110367

Order 11008.

1054 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583270C211yesmaximal, characteristic
2C4×#13063323C211yesmaximal, characteristic, complemented
3#19137159C211yesmaximal, characteristic
4#19135399C211yesmaximal, characteristic
5#19135395C211yesmaximal, characteristic, complemented
6#19134953C211yesmaximal, characteristic, complemented
7#19134950C211yesmaximal, characteristic, complemented
8#19134949C211yesmaximal, characteristic, complemented
9#19134931C211yesmaximal, characteristic, complemented
10#19134930C211yesmaximal, characteristic, complemented
11#19134927C211yesmaximal, characteristic, complemented
12#19134926C211yesmaximal, characteristic, complemented
13#19134721C211yesmaximal, characteristic, complemented
14#19134339C211yesmaximal, characteristic, complemented
15C43×#1880C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C2×#13063323C2211yescharacteristic
20C2×#13063321C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22C2×D4×Dic43C2211yescharacteristic
23C2×#13063287C2211yescharacteristic
24C2×(C22⋊D43)⋊C4—21no—
25C2×(C22⋊D43)⋊C4—21no—
26#14583270C418yescomplemented
27C2×#13063250C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34C2×C8×Dic43C2211yescharacteristic
35#14582806C2211yescharacteristic
36#14582804C2211yescharacteristic
37#14582801C2211yescharacteristic
38#14582799—21no—
39#14582799—21no—
40#14582794—21no—
41#14582794—21no—
42#14582768C2211yescharacteristic
43#14582768C2211yescharacteristic
44C4×Dic43⋊C4—21no—
45C4×Dic43⋊C4—21no—
46C42×Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C22×C22⋊D43—21no—
64C23×Dic43—21no—
65C22×C4×D43—21no—
66C2×#10621873—41no—
67C2×#10621873—41no—
68C2×#10621873C2×C414yescomplemented
69C2×#10621883—41no—
70C2×#10621883—41no—
71C2×#10621883C2×C414yescomplemented
72C2×#10621884—41no—
73C2×#10621884—41no—
74C2×#10621884C2×C414yescomplemented
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063323—22no—
78#13063323C2×C414yescomplemented
79#13063321—22no—
80#13063321C2×C414yes—
81C4×Dic86—41no—
82C4×Dic86—41no—
83D4×Dic43—41no—
84D4×Dic43—41no—
85#13063287—41no—
86#13063287—41no—
87(C22⋊D43)⋊C4—44no—
88(C22⋊D43)⋊C4—44no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×C22⋊Dic43—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43D411yescharacteristic
104C2×C4×Dic43D411yescharacteristic
105C2×C4×Dic43D411yescharacteristic
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43C2311yescharacteristic
108C2×C4×Dic43C2311yescharacteristic
109#13063250—41no—
110#13063249—41no—
111#13063248—41no—
112#13063247—41no—
113#13063246—41no—
114#13063245—41no—
115C8×Dic43—22no—
116C8×Dic43C2×C414yescomplemented
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C22×Q8×C43C2311yescharacteristic
122C22×D4×C43C2311yescharacteristic
123C2×SD16×C43—41no—
124C2×SD16×C43—41no—
125C2×SD16×C43C2×C414yescomplemented
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C4×Q8×C43—41no—
129C4×Q8×C43—41no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43—21no—
135C2×C42×C43—21no—
136C2×C42×C43C2311yescharacteristic
137#103×C43—41no—
138#102×C43—41no—
139C24×C43—21no—
140C23×D43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C22×C412yes—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43C22×C412yes—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—24no—
160C2×C22⋊D43—24no—
161C2×C22⋊D43—42no—
162C2×C22⋊D43—42no—
163C2×C22⋊D43—42no—
164C2×C22⋊D43—42no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—42no—
169C22×Dic43—42no—
170C22×Dic43—42no—
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172C22×C412yes—
181C2×C4×D43—42no—
182C2×C4×D43—42no—
183C2×C4×D43—42no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86C22×C412yes—
190SD16×C43—44no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43C22×C412yes—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—42no—
202C22⋊C4×C43—42no—
203C22⋊C4×C43—42no—
204C42×C43—21no—
205C42×C43—21no—
206C42×C43—42no—
207C22⋊Dic43—42no—
208#10621884—44no—
209#10621883—44no—
210(C2×D43)⋊C4—42no—
211(C2×D43)⋊C4—42no—
212(C2×D43)⋊C4—42no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217Dic43⋊C4—24no—
218Dic43⋊C4—24no—
219Dic43⋊C4—42no—
220Dic43⋊C4—42no—
221Dic43⋊C4—42no—
222Dic43⋊C4—42no—
223Dic43⋊C4—42no—
224C4×Dic43—21no—
225C4×Dic43—21no—
226C4×Dic43—22no—
227C4×Dic43—22no—
228C4×Dic43—22no—
229C4×Dic43—42no—
230C4×Dic43SD1614yescomplemented
231C4×Dic43C22×C412yes—
232C4×Dic43#4112yes—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8C22×C412yes—
239#10621873—44no—
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—22no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—41no—
253C22×D43—41no—
254C22×D43—41no—
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—22no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
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×C43—41no—
277C2×C4×C43C2×SD1612yes—
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—
285C22⋊D43—48no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—22no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—84no—
301C2×Dic43C4×D412yes—
302C2×Dic43C4×D412yes—
303C2×Dic43C2×SD1612yes—
304C2×Dic43C2×SD1612yes—
305C2×Dic43#13512yes—
306C2×Dic43AGL(1,ℤ/8)12yes—
307C2×Dic43#13712yes—
308D172—22no—
309D172—22no—
310D172—41no—
311D172—41no—
312C4×D43—84no—
313Dic86—22no—
314Dic86—22no—
315Dic86—41no—
316Dic86—41no—
317C8×C43—22no—
318C8×C43—41no—
319C43⋊C8—22no—
320C43⋊C8—41no—
321#22268—431nomaximal, Sylow
322C22×C43—42no—
323C22×C43—42no—
324C22×C43—42no—
325C22×C43—81no—
326C22×C43—81no—
327C22×C43—81no—
328C22×C43—81no—
329C22×C43C2×C4×D411yescharacteristic
330C22×C43#53511yescharacteristic
331C22×C43#53511yescharacteristic
332C22×C43C22×SD1611yescharacteristic
333C22×C43C2×#13511yescharacteristic
334C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
335C22×C43C2×#13711yescharacteristic
336C2×D43—42no—
337C2×D43—42no—
338C2×D43—42no—
339C2×D43—81no—
340C2×D43—81no—
341C2×D43—81no—
342C2×D43—81no—
343C4×C43—22no—
344C4×C43—42no—
345C4×C43—41no—
346C4×C43—81no—
347C4×C43—81no—
348C4×C43#51811yescharacteristic
349C4×C43#51811yescharacteristic
350C4×C43#54011yescharacteristic
351C4×C43#54011yescharacteristic
352Dic43—22no—
353Dic43—42no—
354Dic43—41no—
355Dic43—81no—
356Dic43—81no—
357Dic43C4×SD1614yes—
358Dic43#44014yes—
359C2×#492—431no—
360C4×C4⋊Q8—431no—
361C4×#127—431no—
362#1957—431no—
363#1956—431no—
364#1880—431no—
365#1880—431no—
366#1880—431no—
367#1880D4311yescharacteristic, complemented
368#1877—431no—
369#1877—431no—
370#1877—431no—
371#1877—431no—
372#1834—431no—
373#1744—431no—
374C2×C43—82no—
375C2×C43#232811yescharacteristic
376C2×C43C2×C4×SD1611yescharacteristic
377C2×C43C2×#44011yescharacteristic
378C2×C43#320611yescharacteristic
379C2×C43#320711yescharacteristic
380C2×C43#320811yescharacteristic
381C2×C43#321011yescharacteristic
382D43—82no—
383C22×SD16—431no—
384C22×SD16—431no—
385C22×SD16—431no—
386C22×SD16C2×D4311yescharacteristic
387C2×C4⋊Q8—431no—
388C2×#127—431no—
389C2×C4×Q8—431no—
390C2×C4×Q8C2×D4311yescharacteristic
391C2×C4×D4—431no—
392C2×C4×D4—431no—
393C2×C4×D4—861no—
394C2×C4×D4—861no—
395#492—438no—
396C2×#103—431no—
397C2×#103—431no—
398C2×#103—431no—
399C2×#103C2×D4311yescharacteristic
400C2×#102—431no—
401C2×#102—431no—
402C2×#102—431no—
403C2×#102C2×D4311yescharacteristic
404C2×C4×C8—431no—
405C2×C4×C8—431no—
406#391—431no—
407#391—431no—
408#390—431no—
409#390—861no—
410#390—861no—
411#390C2×D4311yescharacteristic
412#389—861no—
413#389—861no—
414#384—431no—
415#384—431no—
416C4×C4⋊C4—861no—
417C4×C4⋊C4—861no—
418C43—431no—
419#340—431no—
420#340—431no—
421#340—431no—
422#340C2×D4311yescharacteristic
423#336—431no—
424#336—431no—
425#336—431no—
426#336C2×D4311yescharacteristic
427C43#2226811yescharacteristic, complemented, Sylow
428C22×Q8—431no—
429C22×Q8C22×D4311yescharacteristic
430C22×D4—431no—
431C22×D4—861no—
432C22×D4—861no—
433C22×D4C22×D4311yescharacteristic
434C23×C4—861no—
435C23×C4—861no—
436C2×SD16—41no—
437C2×SD16—41no—
438C2×SD16—434no—
439C2×SD16—434no—
440C2×SD16—434no—
441C2×SD16—1721no—
442C2×SD16—1721no—
443C2×SD16—1721no—
444C2×SD16—1721no—
445C2×SD16—1721no—
446C2×SD16—1721no—
447C2×SD16C4×D4314yescomplemented
448C22×C8—431no—
449C22×C8—431no—
450C22×C8C22×D4311yescharacteristic
451C22×C8C22×D4311yescharacteristic
452C4⋊Q8—434no—
453C4⋊Q8—862no—
454#127—434no—
455#127—862no—
456C4×Q8—41no—
457C4×Q8—41no—
458C4×Q8—1721no—
459C4×Q8—1721no—
460C4×D4—1724no—
461C4×D4—1724no—
462C4×D4—1721no—
463C4×D4—1721no—
464C4×D4—1721no—
465C4×D4—1721no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—431no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—861no—
470C2×C4⋊C4—861no—
471C2×C4⋊C4—861no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4C22×D4311yescharacteristic
477C2×C4⋊C4C22×D4311yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—861no—
481C2×C22⋊C4—861no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C42—21no—
485C2×C42—431no—
486C2×C42—431no—
487C2×C42—431no—
488C2×C42—431no—
489C2×C42—431no—
490C2×C42—431no—
491C2×C42—861no—
492C2×C42C22×D4311yescharacteristic
493#103—41no—
494#103—1721no—
495#103—1721no—
496#103—1721no—
497#102—41no—
498#102—1721no—
499#102—1721no—
500#102—1721no—
501C4×C8—434no—
502C4×C8—862no—
503#95—861no—
504#95—861no—
505#95—861no—
506#95—861no—
507C24—21no—
508C24—861no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—432no—
515C2×Q8—861no—
516C2×Q8—861no—
517C2×Q8—861no—
518C2×Q8—861no—
519C2×Q8—861no—
520C2×Q8C2×C4×D4312yes—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—432no—
527C2×D4—864no—
528C2×D4—864no—
529C2×D4—861no—
530C2×D4—861no—
531C2×D4—861no—
532C2×D4—861no—
533C2×D4—861no—
534C2×D4—1722no—
535C2×D4—1722no—
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—431no—
545C22×C4—431no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—1722no—
550C22×C4—1722no—
551C22×C4—1722no—
552C22×C4—1722no—
553C22×C4—1722no—
554C22×C4—1722no—
555C22×C4D4×D4311yescharacteristic
556C22×C4D4×D4311yescharacteristic
557C22×C4C23×D4311yescharacteristic
558SD16—44no—
559SD16—1724no—
560SD16—1724no—
561SD16—1724no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—432no—
568C2×C8—861no—
569C2×C8—861no—
570C2×C8—861no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8C2×C4×D4312yes—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—42no—
579C4⋊C4—864no—
580C4⋊C4—864no—
581C4⋊C4—861no—
582C4⋊C4—861no—
583C4⋊C4—861no—
584C4⋊C4—861no—
585C4⋊C4—1722no—
586C4⋊C4—1722no—
587C4⋊C4—1722no—
588C4⋊C4—1722no—
589C4⋊C4—1722no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—1722no—
593C22⋊C4—1722no—
594C22⋊C4—1722no—
595C22⋊C4—1722no—
596C42—21no—
597C42—21no—
598C42—42no—
599C42—434no—
600C42—432no—
601C42—432no—
602C42—862no—
603C42—862no—
604C42—862no—
605C42—861no—
606C42—861no—
607C42—1722no—
608C23—22no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—862no—
616C23—1721no—
617C23—1721no—
618C23—1721no—
619C23—1721no—
620C23—1721no—
621C23—1721no—
622C23C2×D4×D4311yescharacteristic
623Q8—22no—
624Q8—22no—
625Q8—41no—
626Q8—41no—
627Q8—862no—
628Q8—862no—
629Q8—1721no—
630Q8—1721no—
631D4—22no—
632D4—22no—
633D4—41no—
634D4—41no—
635D4—862no—
636D4—862no—
637D4—1728no—
638D4—1728no—
639D4—1721no—
640D4—1721no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—432no—
656C2×C4—432no—
657C2×C4—432no—
658C2×C4—432no—
659C2×C4—432no—
660C2×C4—432no—
661C2×C4—432no—
662C2×C4—861no—
663C2×C4—861no—
664C2×C4—862no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—3444no—
669C2×C4—3444no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4SD16×D4312yes—
679C2×C4C22×C4×D4311yescharacteristic
680C2×C4#41×D4311yescharacteristic
681C2×C4#1306337011yescharacteristic
682C2×C4#1306337011yescharacteristic
683C2×C4#1306337011yescharacteristic
684C2×C4#1306337111yescharacteristic
685C8—22no—
686C8—41no—
687C8—862no—
688C8—1721no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—3441no—
697C22—3441no—
698C22—3441no—
699C22—3441no—
700C22—1722no—
701C22—1722no—
702C22—1722no—
703C22C4×D4×D4311yescharacteristic
704C22#1458346411yescharacteristic
705C22#1458346511yescharacteristic
706C22C2×SD16×D4311yescharacteristic
707C22#135×D4311yescharacteristic
708C22AGL(1,ℤ/8)×D4311yescharacteristic
709C22#137×D4311yescharacteristic
710C4—22no—
711C4—42no—
712C4—41no—
713C4—81no—
714C4—81no—
715C4—434no—
716C4—434no—
717C4—862no—
718C4—3441no—
719C4—3441no—
720C4—1722no—
721C4—1721no—
722C4#1458337111yescharacteristic
723C4#1458337211yescharacteristic
724C4#1458349911yescharacteristic
725C4#1458350111yescharacteristic
726C2—82no—
727C2—3442no—
728C2#1913731611yescharacteristic
729C2C4×SD16×D4311yescharacteristic
730C2#440×D4311yescharacteristic
731C2#1914551811yescharacteristic
732C2#1914552611yescharacteristic
733C2#1914553511yescharacteristic
734C2#1914555011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1880C2
socleC23×C43C22×D4
prime radicalC2×#13063321C22
cosocleC22×C4×C43C24
hypercenter#1880D43
hypocenterC43#22268
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
2. C4×#13063323C2semidirect
5. #19135395C2semidirect
6. #19134953C2semidirect
7. #19134950C2semidirect
8. #19134949C2semidirect
9. #19134931C2semidirect
10. #19134930C2semidirect
11. #19134927C2semidirect
12. #19134926C2semidirect
13. #19134721C2semidirect
14. #19134339C2semidirect
15. C43×#1880C2semidirect
26. #14583270C4semidirect
68. C2×#10621873C2×C4semidirect
71. C2×#10621883C2×C4semidirect
74. C2×#10621884C2×C4semidirect
78. #13063323C2×C4semidirect
116. C8×Dic43C2×C4semidirect
125. C2×SD16×C43C2×C4semidirect
230. C4×Dic43SD16semidirect
367. #1880D43semidirect
427. C43#22268semidirect
447. C2×SD16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832702
C4×#130633232
#191371592
#191353992
#191353952
#191349532
#191349502
#191349492
#191349312
#191349302
#191349272
#191349262
#191347212
#191343392
C43×#18802
#2226843