Finite Group Databasebeta

← C43×#25160 #24945177

Subgroups — C43×#25160 #24945177

Order 11008.

1316 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#463C211yesmaximal, characteristic, complemented
2C2×C43×#450C211yesmaximal, characteristic, complemented
3C2×C43×#447C211yesmaximal, characteristic
4C2×C4×D8×C43C211yesmaximal, characteristic, complemented
5C43×#2427C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
7C43×#2067C211yesmaximal, characteristic, complemented
8C43×#2036C211yesmaximal, characteristic, complemented
9C43×#2034C211yesmaximal, characteristic, complemented
10C43×#2012C211yesmaximal, characteristic, complemented
11C43×#1968C211yesmaximal, characteristic, complemented
12C43×#1923C211yesmaximal, characteristic, complemented
13C43×#1879C211yesmaximal, characteristic, complemented
14C43×#1877C211yesmaximal, characteristic, complemented
15C43×#1864C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×SD16×C43C2211yescharacteristic
19C22×D8×C43C2211yescharacteristic
20C22×D8×C43C2211yescharacteristic
21C2×#124×C43C2211yescharacteristic, complemented
22C2×C22⋊Q8×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×C4×D4×C43C2211yescharacteristic
25C2×C4×D4×C43C2211yescharacteristic
26C2×C4×D4×C43C2211yescharacteristic, complemented
27C22×C22⋊C4×C43—21no—
28C43×#463—24no—
29C43×#450—24no—
30C43×#447—24no—
31C4×D8×C43—24no—
32C2×#107×C43C2211yescharacteristic, complemented
33C2×#106×C43C2211yescharacteristic, complemented
34C2×C4⋊C8×C43C2211yescharacteristic, complemented
35C2×#103×C43C2211yescharacteristic, complemented
36C2×#103×C43C2211yescharacteristic, complemented
37C2×#102×C43C2211yescharacteristic
38C2×#102×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic, complemented
42C2×#102×C43C2211yescharacteristic, complemented
43C2×C22⋊C8×C43C2211yescharacteristic
44C2×C22⋊C8×C43C2211yescharacteristic
45C2×C4×C8×C43C2211yescharacteristic, complemented
46C43×#397—21no—
47C43×#394—21no—
48C43×#391C2211yescharacteristic, complemented
49C43×#390C2211yescharacteristic
50C43×#390C2211yescharacteristic
51C43×#389C2211yescharacteristic, complemented
52C43×#386—21no—
53C43×#386—21no—
54C43×#386—21no—
55C43×#380—21no—
56C43×#380C2211yescharacteristic
57C43×#379—21no—
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C43×#336C2211yescharacteristic, complemented
62C43×#336C2211yescharacteristic, complemented
63C25×C43—21no—
64C22×Q8×C43C2311yescharacteristic
65C22×D4×C43—22no—
66C22×D4×C43—22no—
67C22×D4×C43—22no—
68C22×D4×C43—22no—
69C22×D4×C43—21no—
70C22×D4×C43—21no—
71C22×D4×C43—41no—
72C22×D4×C43—41no—
73C22×D4×C43C2311yescharacteristic
74C22×D4×C43C2311yescharacteristic
75C22×D4×C43C2311yescharacteristic
76C23×C4×C43—21no—
77C23×C4×C43—21no—
78C23×C4×C43—21no—
79C23×C4×C43C2311yescharacteristic
80C2×SD16×C43—22no—
81C2×SD16×C43—22no—
82C2×SD16×C43—22no—
83C2×SD16×C43—22no—
84C2×SD16×C43—22no—
85C2×SD16×C43—41no—
86C2×D8×C43—22no—
87C2×D8×C43—22no—
88C2×D8×C43—22no—
89C2×D8×C43—22no—
90C2×D8×C43—41no—
91C2×D8×C43D414yes—
92C22×C8×C43C2311yescharacteristic
93C22×C8×C43C2311yescharacteristic
94C22×C8×C43C2311yescharacteristic
95C22×C8×C43C2311yescharacteristic
96#124×C43—22no—
97#124×C43—41no—
98C22⋊Q8×C43—22no—
99C22⋊Q8×C43—41no—
100#121×C43—22no—
101#121×C43—41no—
102C4×D4×C43—22no—
103C4×D4×C43—22no—
104C4×D4×C43—22no—
105C4×D4×C43—41no—
106C4×D4×C43—41no—
107C4×D4×C43—41no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—44no—
127C2×C22⋊C4×C43D411yescharacteristic
128C2×C22⋊C4×C43D411yescharacteristic
129C2×C42×C43C2311yescharacteristic
130C2×C42×C43C2311yescharacteristic
131#107×C43—22no—
132#106×C43—41no—
133C4⋊C8×C43—22no—
134#103×C43—22no—
135#103×C43—41no—
136#102×C43—22no—
137#102×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#102×C43D414yescomplemented
142C22⋊C8×C43—22no—
143C22⋊C8×C43—22no—
144C4×C8×C43—22no—
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43—21no—
149#95×C43D411yescharacteristic
150#95×C43D411yescharacteristic
151C24×C43—21no—
152C24×C43—24no—
153C24×C43—21no—
154C24×C43—21no—
155C24×C43—42no—
156C24×C43—42no—
157C24×C43—42no—
158C24×C43—42no—
159C24×C43—81no—
160C24×C43—81no—
161C24×C43C2×D411yescharacteristic
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×D4×C43—24no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—42no—
183C2×D4×C43—42no—
184C2×D4×C43—42no—
185C2×D4×C43—44no—
186C2×D4×C43—44no—
187C2×D4×C43—44no—
188C2×D4×C43—44no—
189C2×D4×C43—42no—
190C2×D4×C43—81no—
191C2×D4×C43C2×D412yes—
192C2×D4×C43C2×D412yes—
193C2×D4×C43C2×D412yes—
194C2×D4×C43#4112yes—
195C2×D4×C43#4112yes—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—42no—
208C22×C4×C43—42no—
209C22×C4×C43—42no—
210C22×C4×C43—42no—
211C22×C4×C43—42no—
212C22×C4×C43—42no—
213C22×C4×C43—81no—
214C22×C4×C43—81no—
215C22×C4×C43—81no—
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2411yescharacteristic
222SD16×C43—44no—
223SD16×C43—44no—
224D8×C43—28no—
225D8×C43—44no—
226C2×C8×C43—21no—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43C2×D412yes—
237C2×C8×C43C2×D412yes—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—42no—
246C4⋊C4×C43—81no—
247C4⋊C4×C43C2×D412yes—
248C22⋊C4×C43—22no—
249C22⋊C4×C43—22no—
250C22⋊C4×C43—42no—
251C22⋊C4×C43—42no—
252C22⋊C4×C43—42no—
253C22⋊C4×C43—42no—
254C22⋊C4×C43—42no—
255C22⋊C4×C43—42no—
256C22⋊C4×C43—42no—
257C22⋊C4×C43—42no—
258C22⋊C4×C43—42no—
259C22⋊C4×C43—42no—
260C22⋊C4×C43—81no—
261C22⋊C4×C43—81no—
262C42×C43—21no—
263C42×C43—21no—
264C42×C43—21no—
265C42×C43—21no—
266C23×C43—21no—
267C23×C43—22no—
268C23×C43—21no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—48no—
278C23×C43—48no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—84no—
296C23×C43—84no—
297C23×C43—84no—
298C23×C43—84no—
299C23×C43—84no—
300C23×C43#13512yes—
301C23×C43C22×D411yescharacteristic
302Q8×C43—41no—
303Q8×C43—41no—
304Q8×C43—41no—
305Q8×C43—41no—
306D4×C43—22no—
307D4×C43—22no—
308D4×C43—22no—
309D4×C43—22no—
310D4×C43—22no—
311D4×C43—22no—
312D4×C43—22no—
313D4×C43—48no—
314D4×C43—41no—
315D4×C43—41no—
316D4×C43—41no—
317D4×C43—41no—
318D4×C43—84no—
319D4×C43#12114yes—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—22no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—84no—
354C2×C4×C43—84no—
355C2×C4×C43—84no—
356C2×C4×C43AGL(1,ℤ/8)12yes—
357C2×C4×C43C22×D411yescharacteristic
358C2×C4×C43C22×D411yescharacteristic
359C2×C4×C43C2×#4111yescharacteristic
360C2×C4×C43C2×#4111yescharacteristic
361C2×C4×C43H(5,𝔽2)11yescharacteristic
362C2×C4×C43H(5,𝔽2)11yescharacteristic
363C8×C43—22no—
364C8×C43—22no—
365C8×C43—41no—
366C8×C43—41no—
367#25160C4311yesmaximal, characteristic, direct product factor, Sylow
368C22×C43—22no—
369C22×C43—24no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—42no—
373C22×C43—41no—
374C22×C43—42no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—42no—
378C22×C43—41no—
379C22×C43—42no—
380C22×C43—42no—
381C22×C43—42no—
382C22×C43—42no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—42no—
386C22×C43—42no—
387C22×C43—42no—
388C22×C43—816no—
389C22×C43—81no—
390C22×C43—81no—
391C22×C43—81no—
392C22×C43—81no—
393C22×C43—81no—
394C22×C43—81no—
395C22×C43—81no—
396C22×C43—81no—
397C22×C43#52511yescharacteristic
398C22×C43D4211yescharacteristic
399C22×C43D4211yescharacteristic
400C22×C43C2×#13511yescharacteristic
401C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
402C22×C43#57611yescharacteristic
403C22×C43#57711yescharacteristic
404C4×C43—22no—
405C4×C43—41no—
406C4×C43—42no—
407C4×C43—41no—
408C4×C43—41no—
409C4×C43—41no—
410C4×C43—81no—
411C4×C43—81no—
412C4×C43—81no—
413C4×C43—81no—
414C4×C43C2×#12111yescharacteristic
415C4×C43#53811yescharacteristic
416C4×C43#54611yescharacteristic
417C4×C43#54611yescharacteristic
418C2×#463C2×C4311yescharacteristic, complemented
419C2×#450C2×C4311yescharacteristic, complemented
420C2×#447C2×C4311yescharacteristic
421C2×C4×D8C2×C4311yescharacteristic, complemented
422#2427C2×C4311yescharacteristic, complemented
423D4×C22⋊C4C2×C4311yescharacteristic, complemented
424#2067C2×C4311yescharacteristic, complemented
425#2036C2×C4311yescharacteristic, complemented
426#2034C2×C4311yescharacteristic, complemented
427#2012C2×C4311yescharacteristic, complemented
428#1968C2×C4311yescharacteristic, complemented
429#1923C2×C4311yescharacteristic, complemented
430#1879C2×C4311yescharacteristic, complemented
431#1877C2×C4311yescharacteristic, complemented
432#1864C2×C4311yescharacteristic, complemented
433C2×C43—42no—
434C2×C43—44no—
435C2×C43—82no—
436C2×C43—82no—
437C2×C43#242411yescharacteristic
438C2×C43#310511yescharacteristic
439C2×C43#311811yescharacteristic
440C2×C43#326411yescharacteristic
441C2×C43#327211yescharacteristic
442C2×C43#328011yescharacteristic
443C2×C43#328211yescharacteristic
444C23×D4C22×C4311yescharacteristic
445C22×SD16C22×C4311yescharacteristic
446C22×SD16C22×C4311yescharacteristic
447C22×D8C22×C4311yescharacteristic
448C22×D8C22×C4311yescharacteristic
449C2×#124C22×C4311yescharacteristic, complemented
450C2×C22⋊Q8C22×C4311yescharacteristic
451C2×#121C22×C4311yescharacteristic
452C2×C4×D4C22×C4311yescharacteristic
453C2×C4×D4C22×C4311yescharacteristic
454C2×C4×D4C22×C4311yescharacteristic, complemented
455C22×C22⋊C4—21no—
456#463—24no—
457#450—24no—
458#447—24no—
459C4×D8—24no—
460C2×#107C22×C4311yescharacteristic, complemented
461C2×#106C22×C4311yescharacteristic, complemented
462C2×C4⋊C8C22×C4311yescharacteristic, complemented
463C2×#103C22×C4311yescharacteristic, complemented
464C2×#103C22×C4311yescharacteristic, complemented
465C2×#102C22×C4311yescharacteristic
466C2×#102C22×C4311yescharacteristic
467C2×#102C22×C4311yescharacteristic
468C2×#102C22×C4311yescharacteristic
469C2×#102C22×C4311yescharacteristic, complemented
470C2×#102C22×C4311yescharacteristic, complemented
471C2×C22⋊C8C22×C4311yescharacteristic
472C2×C22⋊C8C22×C4311yescharacteristic
473C2×C4×C8C22×C4311yescharacteristic, complemented
474#397—21no—
475#394—21no—
476#391C22×C4311yescharacteristic, complemented
477#390C22×C4311yescharacteristic
478#390C22×C4311yescharacteristic
479#389C22×C4311yescharacteristic, complemented
480#386—21no—
481#386—21no—
482#386—21no—
483#380—21no—
484#380C22×C4311yescharacteristic
485#379—21no—
486C4×C22⋊C4C22×C4311yescharacteristic
487#340C22×C4311yescharacteristic, complemented
488#340C22×C4311yescharacteristic, complemented
489#336C22×C4311yescharacteristic, complemented
490#336C22×C4311yescharacteristic, complemented
491C43#2516011yescharacteristic, direct product factor, Sylow
492C25—21no—
493C22×Q8C23×C4311yescharacteristic
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4C23×C4311yescharacteristic
503C22×D4C23×C4311yescharacteristic
504C22×D4C23×C4311yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C23×C4311yescharacteristic
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—41no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8—41no—
520C2×D8D4×C4314yes—
521C22×C8C23×C4311yescharacteristic
522C22×C8C23×C4311yescharacteristic
523C22×C8C23×C4311yescharacteristic
524C22×C8C23×C4311yescharacteristic
525#124—22no—
526#124—41no—
527C22⋊Q8—22no—
528C22⋊Q8—41no—
529#121—22no—
530#121—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4C23×C4311yescharacteristic
540C2×C4⋊C4C23×C4311yescharacteristic
541C2×C4⋊C4C23×C4311yescharacteristic
542C2×C4⋊C4C23×C4311yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—44no—
556C2×C22⋊C4D4×C4311yescharacteristic
557C2×C22⋊C4D4×C4311yescharacteristic
558C2×C42C23×C4311yescharacteristic
559C2×C42C23×C4311yescharacteristic
560#107—22no—
561#106—41no—
562C4⋊C8—22no—
563#103—22no—
564#103—41no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102D4×C4314yescomplemented
571C22⋊C8—22no—
572C22⋊C8—22no—
573C4×C8—22no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95D4×C4311yescharacteristic
579#95D4×C4311yescharacteristic
580C24—21no—
581C24—24no—
582C24—21no—
583C24—21no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—81no—
589C24—81no—
590C24C2×D4×C4311yescharacteristic
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×D4—24no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4C2×D4×C4312yes—
621C2×D4C2×D4×C4312yes—
622C2×D4C2×D4×C4312yes—
623C2×D4#41×C4312yes—
624C2×D4#41×C4312yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—81no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4C2×D4×C4311yescharacteristic
646C22×C4C2×D4×C4311yescharacteristic
647C22×C4C2×D4×C4311yescharacteristic
648C22×C4C2×D4×C4311yescharacteristic
649C22×C4C2×D4×C4311yescharacteristic
650C22×C4C24×C4311yescharacteristic
651SD16—44no—
652SD16—44no—
653D8—28no—
654D8—44no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8C2×D4×C4312yes—
666C2×C8C2×D4×C4312yes—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—42no—
675C4⋊C4—81no—
676C4⋊C4C2×D4×C4312yes—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—81no—
690C22⋊C4—81no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C23—21no—
696C23—22no—
697C23—21no—
698C23—22no—
699C23—22no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—48no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23#135×C4312yes—
730C23C22×D4×C4311yescharacteristic
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—48no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—84no—
748D4#121×C4314yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—84no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4AGL(1,ℤ/8)×C4312yes—
786C2×C4C22×D4×C4311yescharacteristic
787C2×C4C22×D4×C4311yescharacteristic
788C2×C4C2×#41×C4311yescharacteristic
789C2×C4C2×#41×C4311yescharacteristic
790C2×C4H(5,𝔽2)×C4311yescharacteristic
791C2×C4H(5,𝔽2)×C4311yescharacteristic
792C8—22no—
793C8—22no—
794C8—41no—
795C8—41no—
796C22—22no—
797C22—24no—
798C22—22no—
799C22—22no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—816no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22C43×#52511yescharacteristic
826C22D42×C4311yescharacteristic
827C22D42×C4311yescharacteristic
828C22C2×#135×C4311yescharacteristic
829C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
830C22C43×#57611yescharacteristic
831C22C43×#57711yescharacteristic
832C4—22no—
833C4—41no—
834C4—42no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—81no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4C2×#121×C4311yescharacteristic
843C4C43×#53811yescharacteristic
844C4C43×#54611yescharacteristic
845C4C43×#54611yescharacteristic
846C2—42no—
847C2—44no—
848C2—82no—
849C2—82no—
850C2C43×#242411yescharacteristic
851C2C43×#310511yescharacteristic
852C2C43×#311811yescharacteristic
853C2C43×#326411yescharacteristic
854C2C43×#327211yescharacteristic
855C2C43×#328011yescharacteristic
856C2C43×#328211yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C22⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#463C2semidirect
2. C2×C43×#450C2semidirect
4. C2×C4×D8×C43C2semidirect
5. C43×#2427C2semidirect
6. D4×C22⋊C4×C43C2semidirect
7. C43×#2067C2semidirect
8. C43×#2036C2semidirect
9. C43×#2034C2semidirect
10. C43×#2012C2semidirect
11. C43×#1968C2semidirect
12. C43×#1923C2semidirect
13. C43×#1879C2semidirect
14. C43×#1877C2semidirect
15. C43×#1864C2semidirect
21. C2×#124×C43C22semidirect
26. C2×C4×D4×C43C22semidirect
32. C2×#107×C43C22semidirect
33. C2×#106×C43C22semidirect
34. C2×C4⋊C8×C43C22semidirect
35. C2×#103×C43C22semidirect
36. C2×#103×C43C22semidirect
41. C2×#102×C43C22semidirect
42. C2×#102×C43C22semidirect
45. C2×C4×C8×C43C22semidirect
48. C43×#391C22semidirect
51. C43×#389C22semidirect
59. C43×#340C22semidirect
60. C43×#340C22semidirect
61. C43×#336C22semidirect
62. C43×#336C22semidirect
141. #102×C43D4semidirect
367. #25160C43direct (N × H)
418. C2×#463C2×C43semidirect
419. C2×#450C2×C43semidirect
421. C2×C4×D8C2×C43semidirect
422. #2427C2×C43semidirect
423. D4×C22⋊C4C2×C43semidirect
424. #2067C2×C43semidirect
425. #2036C2×C43semidirect
426. #2034C2×C43semidirect
427. #2012C2×C43semidirect
428. #1968C2×C43semidirect
429. #1923C2×C43semidirect
430. #1879C2×C43semidirect
431. #1877C2×C43semidirect
432. #1864C2×C43semidirect
449. C2×#124C22×C43semidirect
454. C2×C4×D4C22×C43semidirect
460. C2×#107C22×C43semidirect
461. C2×#106C22×C43semidirect
462. C2×C4⋊C8C22×C43semidirect
463. C2×#103C22×C43semidirect
464. C2×#103C22×C43semidirect
469. C2×#102C22×C43semidirect
470. C2×#102C22×C43semidirect
473. C2×C4×C8C22×C43semidirect
476. #391C22×C43semidirect
479. #389C22×C43semidirect
487. #340C22×C43semidirect
488. #340C22×C43semidirect
489. #336C22×C43semidirect
490. #336C22×C43semidirect
491. C43#25160direct (N × H)
570. #102D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4632
C2×C43×#4502
C2×C43×#4472
C2×C4×D8×C432
C43×#24272
D4×C22⋊C4×C432
C43×#20672
C43×#20362
C43×#20342
C43×#20122
C43×#19682
C43×#19232
C43×#18792
C43×#18772
C43×#18642
#2516043