Finite Group Databasebeta

← C43×#15982 #24935999

Subgroups — C43×#15982 #24935999

Order 11008.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C43C211yesmaximal, characteristic
2C2×C43×#386C211yesmaximal, characteristic
3C2×C43×#385C211yesmaximal, characteristic, complemented
4C2×C43×#381C211yesmaximal, characteristic, complemented
5C43×#1442C212yesmaximal, complemented
6C43×#1441C212yesmaximal, complemented
7C43×#1440C211yesmaximal, characteristic, complemented
8C43×#1440C211yesmaximal, characteristic, complemented
9C43×#1439C212yesmaximal, complemented
10C43×#1438C211yesmaximal, characteristic
11C43×C22⋊#95C212yesmaximal, complemented
12C23×D4×C43C2211yescharacteristic
13C24×C4×C43C2211yescharacteristic
14C24×C4×C43C2211yescharacteristic
15C2×#123×C43—24no—
16C2×#123×C43—24no—
17C2×#123×C43—24no—
18C22×C4⋊C4×C43C2211yescharacteristic
19C22×C4⋊C4×C43C2211yescharacteristic
20C22×C4⋊C4×C43C2212yes—
21C22×C22⋊C4×C43C2211yescharacteristic
22C22×C22⋊C4×C43C2211yescharacteristic
23C22×C22⋊C4×C43C2212yes—
24C22×C22⋊C4×C43C2212yes—
25C22×C22⋊C4×C43C2211yescharacteristic
26C22×C22⋊C4×C43C2211yescharacteristic
27C22×C22⋊C4×C43C2211yescharacteristic
28C22×C22⋊C4×C43C2211yescharacteristic
29C43×#386—24no—
30C43×#385—24no—
31C43×#381—24no—
32C2×#95×C43C2212yes—
33C2×#95×C43C2212yes—
34C2×#95×C43C2212yes—
35C2×#95×C43C2212yes—
36C2×#95×C43C2212yes—
37C2×#95×C43C2212yes—
38C2×#95×C43C2212yes—
39C2×#95×C43C2212yes—
40C2×#95×C43C2212yes—
41C25×C43C2311yescharacteristic
42C25×C43C2311yescharacteristic
43C22×D4×C43—22no—
44C22×D4×C43—22no—
45C22×D4×C43—24no—
46C22×D4×C43—42no—
47C22×D4×C43D414yes—
48C23×C4×C43—22no—
49C23×C4×C43—22no—
50C23×C4×C43—22no—
51C23×C4×C43—22no—
52C23×C4×C43—24no—
53C23×C4×C43—22no—
54C23×C4×C43—22no—
55C23×C4×C43—24no—
56C23×C4×C43—42no—
57C23×C4×C43—42no—
58C23×C4×C43C2312yes—
59C23×C4×C43C2312yes—
60C23×C4×C43C2311yescharacteristic
61C23×C4×C43C2311yescharacteristic
62C23×C4×C43C2311yescharacteristic
63C23×C4×C43C2311yescharacteristic
64C23×C4×C43C2311yescharacteristic
65C23×C4×C43C2312yes—
66C23×C4×C43C2312yes—
67#123×C43—232no—
68C2×C4⋊C4×C43—22no—
69C2×C4⋊C4×C43—22no—
70C2×C4⋊C4×C43—22no—
71C2×C4⋊C4×C43—22no—
72C2×C4⋊C4×C43—22no—
73C2×C4⋊C4×C43—22no—
74C2×C4⋊C4×C43—24no—
75C2×C4⋊C4×C43—24no—
76C2×C4⋊C4×C43—42no—
77C2×C22⋊C4×C43—22no—
78C2×C22⋊C4×C43—22no—
79C2×C22⋊C4×C43—22no—
80C2×C22⋊C4×C43—22no—
81C2×C22⋊C4×C43—22no—
82C2×C22⋊C4×C43—22no—
83C2×C22⋊C4×C43—22no—
84C2×C22⋊C4×C43—22no—
85C2×C22⋊C4×C43—24no—
86C2×C22⋊C4×C43—22no—
87C2×C22⋊C4×C43—24no—
88C2×C22⋊C4×C43—22no—
89C2×C22⋊C4×C43—24no—
90C2×C22⋊C4×C43—24no—
91C2×C22⋊C4×C43—24no—
92C2×C22⋊C4×C43—42no—
93C2×C22⋊C4×C43—42no—
94C2×C22⋊C4×C43—42no—
95C2×C22⋊C4×C43—42no—
96C2×C22⋊C4×C43D414yes—
97C2×C22⋊C4×C43D414yes—
98#95×C43—24no—
99#95×C43—24no—
100#95×C43—24no—
101#95×C43—24no—
102#95×C43—24no—
103#95×C43—42no—
104#95×C43—42no—
105#95×C43—42no—
106#95×C43—42no—
107C24×C43—21no—
108C24×C43—21no—
109C24×C43—22no—
110C24×C43—22no—
111C24×C43—22no—
112C24×C43—22no—
113C24×C43—22no—
114C24×C43—22no—
115C24×C43—22no—
116C24×C43—22no—
117C24×C43—22no—
118C24×C43—22no—
119C24×C43—22no—
120C24×C43C2×D412yes—
121C24×C43C2×D412yes—
122C24×C43C2×D412yes—
123C24×C43C2×D412yes—
124C24×C43#4114yes—
125C24×C43C2411yescharacteristic
126C2×D4×C43—28no—
127C2×D4×C43—28no—
128C2×D4×C43—44no—
129C2×D4×C43—48no—
130C2×D4×C43—48no—
131C22×C4×C43—28no—
132C22×C4×C43—28no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43—22no—
175C22×C4×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43—22no—
178C22×C4×C43—22no—
179C22×C4×C43—48no—
180C22×C4×C43—48no—
181C22×C4×C43—48no—
182C22×C4×C43—48no—
183C22×C4×C43—44no—
184C22×C4×C43—44no—
185C22×C4×C43—44no—
186C22×C4×C43—44no—
187C22×C4×C43C2×D412yes—
188C22×C4×C43C2×D412yes—
189C22×C4×C43C2×D412yes—
190C22×C4×C43C2×D412yes—
191C22×C4×C43C2×D412yes—
192C22×C4×C43#4114yes—
193C22×C4×C43#4114yes—
194C4⋊C4×C43—28no—
195C4⋊C4×C43—28no—
196C4⋊C4×C43—48no—
197C22⋊C4×C43—28no—
198C22⋊C4×C43—28no—
199C22⋊C4×C43—28no—
200C22⋊C4×C43—28no—
201C22⋊C4×C43—48no—
202C22⋊C4×C43—48no—
203C22⋊C4×C43—44no—
204C22⋊C4×C43—44no—
205C23×C43—22no—
206C23×C43—22no—
207C23×C43—22no—
208C23×C43—22no—
209C23×C43—24no—
210C23×C43—22no—
211C23×C43—22no—
212C23×C43—22no—
213C23×C43—22no—
214C23×C43—24no—
215C23×C43—24no—
216C23×C43—24no—
217C23×C43—24no—
218C23×C43—24no—
219C23×C43—24no—
220C23×C43—24no—
221C23×C43—24no—
222C23×C43—24no—
223C23×C43—24no—
224C23×C43—24no—
225C23×C43—24no—
226C23×C43—24no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—42no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—42no—
233C23×C43—42no—
234C23×C43—42no—
235C23×C43—42no—
236C23×C43—42no—
237C23×C43—42no—
238C23×C43—42no—
239C23×C43—42no—
240C23×C43—42no—
241C23×C43—42no—
242C23×C43—42no—
243C23×C43—42no—
244C23×C43—42no—
245C23×C43#12014yes—
246C23×C43#12314yes—
247C23×C43C22×D411yescharacteristic
248C23×C43C22×D411yescharacteristic
249C23×C43C22×D411yescharacteristic
250C23×C43C2×#4112yes—
251C23×C43C2×#4112yes—
252C23×C43C2×#4112yes—
253C23×C43H(5,𝔽2)12yes—
254C23×C43H(5,𝔽2)12yes—
255C23×C432−1+412yes—
256D4×C43—416no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—24no—
264C2×C4×C43—24no—
265C2×C4×C43—22no—
266C2×C4×C43—24no—
267C2×C4×C43—24no—
268C2×C4×C43—24no—
269C2×C4×C43—24no—
270C2×C4×C43—24no—
271C2×C4×C43—24no—
272C2×C4×C43—24no—
273C2×C4×C43—24no—
274C2×C4×C43—416no—
275C2×C4×C43—416no—
276C2×C4×C43—42no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—42no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—42no—
286C2×C4×C43—41no—
287C2×C4×C43—42no—
288C2×C4×C43—42no—
289C2×C4×C43—42no—
290C2×C4×C43—42no—
291C2×C4×C43—42no—
292C2×C4×C43—42no—
293C2×C4×C43—42no—
294C2×C4×C43—42no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
304C2×C4×C43—42no—
305C2×C4×C43—42no—
306C2×C4×C43—42no—
307C2×C4×C43—42no—
308C2×C4×C43—42no—
309C2×C4×C43—42no—
310C2×C4×C43—42no—
311C2×C4×C43—42no—
312#15982C4311yesmaximal, characteristic, direct product factor, Sylow
313C22×C43—24no—
314C22×C43—24no—
315C22×C43—24no—
316C22×C43—24no—
317C22×C43—28no—
318C22×C43—42no—
319C22×C43—42no—
320C22×C43—44no—
321C22×C43—44no—
322C22×C43—44no—
323C22×C43—44no—
324C22×C43—44no—
325C22×C43—44no—
326C22×C43—44no—
327C22×C43—44no—
328C22×C43—44no—
329C22×C43—44no—
330C22×C43—44no—
331C22×C43C2×#12011yescharacteristic
332C22×C43C2×#12311yescharacteristic
333C22×C43#52511yescharacteristic
334C22×C43#52511yescharacteristic
335C22×C43#52912yes—
336C22×C43#53411yescharacteristic
337C22×C43#53511yescharacteristic
338C22×C43#53611yescharacteristic
339C22×C43#53912yes—
340C22×C43#54012yes—
341C22×C43#54212yes—
342C22×C43#54612yes—
343C22×C43#54612yes—
344C22×C43#54612yes—
345C22×C43#54612yes—
346C22×C43#54712yes—
347C22×C43#54712yes—
348C22×C43#55112yes—
349C22×C43#55212yes—
350C22×C43#55312yes—
351C22×C43#56212yes—
352C4×C43—42no—
353C4×C43—44no—
354C4×C43—42no—
355C4×C43—42no—
356C4×C43—42no—
357C4×C43—42no—
358C4×C43—44no—
359C4×C43—82no—
360C4×C43—82no—
361C22×#123C2×C4311yescharacteristic
362C2×#386C2×C4311yescharacteristic
363C2×#385C2×C4311yescharacteristic, complemented
364C2×#381C2×C4311yescharacteristic, complemented
365#1442C2×C4312yescomplemented
366#1441C2×C4312yescomplemented
367#1440C2×C4311yescharacteristic, complemented
368#1440C2×C4311yescharacteristic, complemented
369#1439C2×C4312yescomplemented
370#1438C2×C4311yescharacteristic
371C22⋊#95C2×C4312yescomplemented
372C2×C43—44no—
373C2×C43—44no—
374C2×C43#240411yescharacteristic
375C2×C43#240511yescharacteristic
376C2×C43#240611yescharacteristic
377C2×C43#241912yes—
378C2×C43#245712yes—
379C2×C43#247012yes—
380C2×C43#268712yes—
381C2×C43#270112yes—
382C2×C43#270612yes—
383C23×D4C22×C4311yescharacteristic
384C24×C4C22×C4311yescharacteristic
385C24×C4C22×C4311yescharacteristic
386C2×#123—24no—
387C2×#123—24no—
388C2×#123—24no—
389C22×C4⋊C4C22×C4311yescharacteristic
390C22×C4⋊C4C22×C4311yescharacteristic
391C22×C4⋊C4C22×C4312yes—
392C22×C22⋊C4C22×C4311yescharacteristic
393C22×C22⋊C4C22×C4311yescharacteristic
394C22×C22⋊C4C22×C4312yes—
395C22×C22⋊C4C22×C4312yes—
396C22×C22⋊C4C22×C4311yescharacteristic
397C22×C22⋊C4C22×C4311yescharacteristic
398C22×C22⋊C4C22×C4311yescharacteristic
399C22×C22⋊C4C22×C4311yescharacteristic
400#386—24no—
401#385—24no—
402#381—24no—
403C2×#95C22×C4312yes—
404C2×#95C22×C4312yes—
405C2×#95C22×C4312yes—
406C2×#95C22×C4312yes—
407C2×#95C22×C4312yes—
408C2×#95C22×C4312yes—
409C2×#95C22×C4312yes—
410C2×#95C22×C4312yes—
411C2×#95C22×C4312yes—
412C43#1598211yescharacteristic, direct product factor, Sylow
413C25C23×C4311yescharacteristic
414C25C23×C4311yescharacteristic
415C22×D4—22no—
416C22×D4—22no—
417C22×D4—24no—
418C22×D4—42no—
419C22×D4D4×C4314yes—
420C23×C4—22no—
421C23×C4—22no—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—24no—
425C23×C4—22no—
426C23×C4—22no—
427C23×C4—24no—
428C23×C4—42no—
429C23×C4—42no—
430C23×C4C23×C4312yes—
431C23×C4C23×C4312yes—
432C23×C4C23×C4311yescharacteristic
433C23×C4C23×C4311yescharacteristic
434C23×C4C23×C4311yescharacteristic
435C23×C4C23×C4311yescharacteristic
436C23×C4C23×C4311yescharacteristic
437C23×C4C23×C4312yes—
438C23×C4C23×C4312yes—
439#123—232no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—42no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—42no—
466C2×C22⋊C4—42no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4D4×C4314yes—
469C2×C22⋊C4D4×C4314yes—
470#95—24no—
471#95—24no—
472#95—24no—
473#95—24no—
474#95—24no—
475#95—42no—
476#95—42no—
477#95—42no—
478#95—42no—
479C24—21no—
480C24—21no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24C2×D4×C4312yes—
493C24C2×D4×C4312yes—
494C24C2×D4×C4312yes—
495C24C2×D4×C4312yes—
496C24#41×C4314yes—
497C24C24×C4311yescharacteristic
498C2×D4—28no—
499C2×D4—28no—
500C2×D4—44no—
501C2×D4—48no—
502C2×D4—48no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—48no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4C2×D4×C4312yes—
560C22×C4C2×D4×C4312yes—
561C22×C4C2×D4×C4312yes—
562C22×C4C2×D4×C4312yes—
563C22×C4C2×D4×C4312yes—
564C22×C4#41×C4314yes—
565C22×C4#41×C4314yes—
566C4⋊C4—28no—
567C4⋊C4—28no—
568C4⋊C4—48no—
569C22⋊C4—28no—
570C22⋊C4—28no—
571C22⋊C4—28no—
572C22⋊C4—28no—
573C22⋊C4—48no—
574C22⋊C4—48no—
575C22⋊C4—44no—
576C22⋊C4—44no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—24no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—41no—
600C23—41no—
601C23—42no—
602C23—41no—
603C23—41no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23#120×C4314yes—
618C23#123×C4314yes—
619C23C22×D4×C4311yescharacteristic
620C23C22×D4×C4311yescharacteristic
621C23C22×D4×C4311yescharacteristic
622C23C2×#41×C4312yes—
623C23C2×#41×C4312yes—
624C23C2×#41×C4312yes—
625C23H(5,𝔽2)×C4312yes—
626C23H(5,𝔽2)×C4312yes—
627C232−1+4×C4312yes—
628D4—416no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—416no—
647C2×C4—416no—
648C2×C4—42no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—42no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C22—24no—
685C22—24no—
686C22—24no—
687C22—24no—
688C22—28no—
689C22—42no—
690C22—42no—
691C22—44no—
692C22—44no—
693C22—44no—
694C22—44no—
695C22—44no—
696C22—44no—
697C22—44no—
698C22—44no—
699C22—44no—
700C22—44no—
701C22—44no—
702C22C2×#120×C4311yescharacteristic
703C22C2×#123×C4311yescharacteristic
704C22C43×#52511yescharacteristic
705C22C43×#52511yescharacteristic
706C22C43×#52912yes—
707C22C43×#53411yescharacteristic
708C22C43×#53511yescharacteristic
709C22C43×#53611yescharacteristic
710C22C43×#53912yes—
711C22C43×#54012yes—
712C22C43×#54212yes—
713C22C43×#54612yes—
714C22C43×#54612yes—
715C22C43×#54612yes—
716C22C43×#54612yes—
717C22C43×#54712yes—
718C22C43×#54712yes—
719C22C43×#55112yes—
720C22C43×#55212yes—
721C22C43×#55312yes—
722C22C43×#56212yes—
723C4—44no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—44no—
730C4—82no—
731C4—82no—
732C2—44no—
733C2—44no—
734C2C43×#240411yescharacteristic
735C2C43×#240511yescharacteristic
736C2C43×#240611yescharacteristic
737C2C43×#241912yes—
738C2C43×#245712yes—
739C2C43×#247012yes—
740C2C43×#268712yes—
741C2C43×#270112yes—
742C2C43×#270612yes—
subgroupG/H
center, socleC24×C43C24
commutator, Frattini, cosocleC24C24×C43
prime radicalC23×D4×C43C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C43×#385C2semidirect
4. C2×C43×#381C2semidirect
5. C43×#1442C2semidirect
6. C43×#1441C2semidirect
7. C43×#1440C2semidirect
8. C43×#1440C2semidirect
9. C43×#1439C2semidirect
11. C43×C22⋊#95C2semidirect
312. #15982C43direct (N × H)
363. C2×#385C2×C43semidirect
364. C2×#381C2×C43semidirect
365. #1442C2×C43semidirect
366. #1441C2×C43semidirect
367. #1440C2×C43semidirect
368. #1440C2×C43semidirect
369. #1439C2×C43semidirect
371. C22⋊#95C2×C43semidirect
412. C43#15982direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#123×C432
C2×C43×#3862
C2×C43×#3852
C2×C43×#3812
C43×#14422
C43×#14412
C43×#14402
C43×#14392
C43×#14382
C43×C22⋊#952
#1598243