Finite Group Databasebeta

← C43×#24432 #24944449

Subgroups — C43×#24432 #24944449

Order 11008.

1922 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C43C211yesmaximal, characteristic
2C2×C43×#465C211yesmaximal, characteristic, complemented
3C2×C43×#450C211yesmaximal, characteristic, complemented
4C2×C43×#450C211yesmaximal, characteristic, complemented
5C22×#102×C43C211yesmaximal, characteristic, complemented
6C43×#2417C211yesmaximal, characteristic, complemented
7C43×#2041C211yesmaximal, characteristic, complemented
8C43×#2034C211yesmaximal, characteristic, complemented
9C43×#2014C211yesmaximal, characteristic, complemented
10C43×#2000C211yesmaximal, characteristic, complemented
11C43×#1877C211yesmaximal, characteristic, complemented
12C43×#1874C211yesmaximal, characteristic, complemented
13C43×#1869C211yesmaximal, characteristic, complemented
14C43×#1864C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C43—21no—
17C23×D4×C43C2211yescharacteristic
18C23×D4×C43C2211yescharacteristic
19C22×SD16×C43C2211yescharacteristic
20C22×SD16×C43C2211yescharacteristic, complemented
21C22×SD16×C43C2211yescharacteristic, complemented
22C23×C8×C43C2211yescharacteristic, complemented
23D42×C43—24no—
24D42×C43—24no—
25C2×#127×C43C2211yescharacteristic
26C2×C22⋊Q8×C43C2211yescharacteristic, complemented
27C2×C22⋊Q8×C43C2211yescharacteristic, complemented
28C2×#121×C43—21no—
29C2×#121×C43C2211yescharacteristic
30C2×#121×C43C2211yescharacteristic
31C2×#120×C43—21no—
32C2×#120×C43—21no—
33C2×C4×D4×C43C2211yescharacteristic
34C2×C4×D4×C43C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic, complemented
36C43×#465—24no—
37C43×#450—24no—
38C43×#450—24no—
39C2×#106×C43C2211yescharacteristic, complemented
40C2×#103×C43C2211yescharacteristic, complemented
41C2×#102×C43—24no—
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×#102×C43C2211yescharacteristic, complemented
46C2×#102×C43C2211yescharacteristic, complemented
47C2×#102×C43C2211yescharacteristic, complemented
48C2×#102×C43C2211yescharacteristic, complemented
49C2×#102×C43C2211yescharacteristic, complemented
50C2×#102×C43C2211yescharacteristic, complemented
51C2×C22⋊C8×C43C2211yescharacteristic, complemented
52C2×C22⋊C8×C43C2211yescharacteristic, complemented
53C2×C22⋊C8×C43C2211yescharacteristic, complemented
54C43×#398—21no—
55C43×#396—21no—
56C43×#391C2211yescharacteristic, complemented
57C43×#389C2211yescharacteristic, complemented
58C43×#386—21no—
59C43×#380—21no—
60C43×#380C2211yescharacteristic, complemented
61C43×#340C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C43×#336C2211yescharacteristic, complemented
64C43×#336C2211yescharacteristic, complemented
65C25×C43—21no—
66C25×C43—21no—
67C22×Q8×C43C2311yescharacteristic
68C22×D4×C43—22no—
69C22×D4×C43—22no—
70C22×D4×C43—28no—
71C22×D4×C43—21no—
72C22×D4×C43—21no—
73C22×D4×C43—22no—
74C22×D4×C43—22no—
75C22×D4×C43—22no—
76C22×D4×C43—22no—
77C22×D4×C43—21no—
78C22×D4×C43—21no—
79C22×D4×C43—21no—
80C22×D4×C43—22no—
81C22×D4×C43—21no—
82C22×D4×C43—41no—
83C22×D4×C43—41no—
84C22×D4×C43—41no—
85C22×D4×C43—41no—
86C22×D4×C43—44no—
87C22×D4×C43—44no—
88C22×D4×C43D411yescharacteristic
89C22×D4×C43D414yes—
90C22×D4×C43C2311yescharacteristic
91C22×D4×C43C2311yescharacteristic
92C22×D4×C43C2311yescharacteristic
93C23×C4×C43—21no—
94C23×C4×C43—21no—
95C23×C4×C43C2311yescharacteristic
96C23×C4×C43C2311yescharacteristic
97C2×SD16×C43—22no—
98C2×SD16×C43—22no—
99C2×SD16×C43—22no—
100C2×SD16×C43—22no—
101C2×SD16×C43—22no—
102C2×SD16×C43—22no—
103C2×SD16×C43—41no—
104C2×SD16×C43—41no—
105C2×SD16×C43—41no—
106C22×C8×C43—22no—
107C22×C8×C43—22no—
108C22×C8×C43—41no—
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113#127×C43—22no—
114#127×C43—22no—
115C22⋊Q8×C43—22no—
116C22⋊Q8×C43—22no—
117C22⋊Q8×C43—22no—
118C22⋊Q8×C43—41no—
119#121×C43—28no—
120#121×C43—22no—
121#121×C43—22no—
122#121×C43—22no—
123#121×C43D414yes—
124#120×C43—28no—
125#120×C43—28no—
126C4×D4×C43—22no—
127C4×D4×C43—22no—
128C4×D4×C43—22no—
129C4×D4×C43—22no—
130C2×C4⋊C4×C43—22no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43—41no—
136C2×C4⋊C4×C43D411yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43D411yescharacteristic
148C2×C22⋊C4×C43D411yescharacteristic
149C2×C42×C43C2311yescharacteristic
150#106×C43—22no—
151#103×C43—22no—
152#102×C43—22no—
153#102×C43—22no—
154#102×C43—22no—
155#102×C43—22no—
156#102×C43—22no—
157#102×C43—22no—
158#102×C43—22no—
159#102×C43—41no—
160#102×C43D414yescomplemented
161C22⋊C8×C43—22no—
162C22⋊C8×C43—22no—
163C22⋊C8×C43—41no—
164#95×C43—21no—
165#95×C43—21no—
166#95×C43—21no—
167#95×C43—21no—
168C24×C43—21no—
169C24×C43—24no—
170C24×C43—21no—
171C24×C43—21no—
172C24×C43—24no—
173C24×C43—42no—
174C24×C43—42no—
175C24×C43—42no—
176C24×C43—42no—
177C24×C43—42no—
178C24×C43—42no—
179C24×C43—42no—
180C24×C43—42no—
181C24×C43—81no—
182C24×C43—81no—
183C24×C43—81no—
184C24×C43—81no—
185C24×C43C2×D411yescharacteristic
186C24×C43C2×D411yescharacteristic
187C2×Q8×C43—21no—
188C2×Q8×C43—21no—
189C2×Q8×C43—21no—
190C2×Q8×C43—21no—
191C2×Q8×C43—21no—
192C2×Q8×C43—21no—
193C2×D4×C43—24no—
194C2×D4×C43—24no—
195C2×D4×C43—24no—
196C2×D4×C43—24no—
197C2×D4×C43—24no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—22no—
204C2×D4×C43—24no—
205C2×D4×C43—22no—
206C2×D4×C43—28no—
207C2×D4×C43—21no—
208C2×D4×C43—21no—
209C2×D4×C43—21no—
210C2×D4×C43—21no—
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43—21no—
214C2×D4×C43—21no—
215C2×D4×C43—42no—
216C2×D4×C43—42no—
217C2×D4×C43—42no—
218C2×D4×C43—42no—
219C2×D4×C43—42no—
220C2×D4×C43—44no—
221C2×D4×C43—44no—
222C2×D4×C43—44no—
223C2×D4×C43—42no—
224C2×D4×C43—44no—
225C2×D4×C43—44no—
226C2×D4×C43—44no—
227C2×D4×C43—432no—
228C2×D4×C43—44no—
229C2×D4×C43—42no—
230C2×D4×C43—42no—
231C2×D4×C43—42no—
232C2×D4×C43—42no—
233C2×D4×C43—81no—
234C2×D4×C43—81no—
235C2×D4×C43SD1614yescomplemented
236C2×D4×C43C2×D412yes—
237C2×D4×C43C2×D412yes—
238C2×D4×C43C2×D412yes—
239C2×D4×C43C2×D412yes—
240C2×D4×C43#4112yes—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—21no—
245C22×C4×C43—24no—
246C22×C4×C43—21no—
247C22×C4×C43—21no—
248C22×C4×C43—21no—
249C22×C4×C43—21no—
250C22×C4×C43—21no—
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43—21no—
254C22×C4×C43—21no—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—42no—
258C22×C4×C43—42no—
259C22×C4×C43—42no—
260C22×C4×C43—42no—
261C22×C4×C43—81no—
262C22×C4×C43C2×D412yes—
263C22×C4×C43C2×D412yes—
264C22×C4×C43C2×D411yescharacteristic
265C22×C4×C43C2×D411yescharacteristic
266C22×C4×C43C2×D411yescharacteristic
267C22×C4×C43C2×D411yescharacteristic
268C22×C4×C43C2411yescharacteristic
269SD16×C43—44no—
270SD16×C43—44no—
271SD16×C43—44no—
272C2×C8×C43—21no—
273C2×C8×C43—21no—
274C2×C8×C43—21no—
275C2×C8×C43—21no—
276C2×C8×C43—21no—
277C2×C8×C43—21no—
278C2×C8×C43—21no—
279C2×C8×C43—21no—
280C2×C8×C43—21no—
281C2×C8×C43—21no—
282C2×C8×C43—21no—
283C2×C8×C43—44no—
284C2×C8×C43C2×D412yescomplemented
285C4⋊C4×C43—22no—
286C4⋊C4×C43—21no—
287C4⋊C4×C43—21no—
288C4⋊C4×C43—21no—
289C4⋊C4×C43—21no—
290C4⋊C4×C43—21no—
291C4⋊C4×C43—21no—
292C4⋊C4×C43—42no—
293C4⋊C4×C43—42no—
294C4⋊C4×C43—42no—
295C4⋊C4×C43—81no—
296C4⋊C4×C43C2×D412yes—
297C4⋊C4×C43C2×D412yescomplemented
298C22⋊C4×C43—24no—
299C22⋊C4×C43—24no—
300C22⋊C4×C43—24no—
301C22⋊C4×C43—22no—
302C22⋊C4×C43—22no—
303C22⋊C4×C43—42no—
304C22⋊C4×C43—42no—
305C22⋊C4×C43—81no—
306C42×C43—21no—
307C42×C43—21no—
308C23×C43—21no—
309C23×C43—21no—
310C23×C43—21no—
311C23×C43—21no—
312C23×C43—21no—
313C23×C43—22no—
314C23×C43—21no—
315C23×C43—22no—
316C23×C43—21no—
317C23×C43—22no—
318C23×C43—21no—
319C23×C43—21no—
320C23×C43—21no—
321C23×C43—22no—
322C23×C43—22no—
323C23×C43—48no—
324C23×C43—48no—
325C23×C43—48no—
326C23×C43—41no—
327C23×C43—41no—
328C23×C43—41no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43—41no—
332C23×C43—41no—
333C23×C43—41no—
334C23×C43—41no—
335C23×C43—41no—
336C23×C43—41no—
337C23×C43—41no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—41no—
342C23×C43—48no—
343C23×C43—84no—
344C23×C43—84no—
345C23×C43—84no—
346C23×C43—84no—
347C23×C43—84no—
348C23×C43—84no—
349C23×C43—84no—
350C23×C43—84no—
351C23×C43—84no—
352C23×C43—84no—
353C23×C43#12012yes—
354C23×C43C2×SD1612yes—
355C23×C43C2×SD1612yes—
356C23×C43AGL(1,ℤ/8)12yes—
357C23×C43C22×D411yescharacteristic
358Q8×C43—41no—
359Q8×C43—41no—
360Q8×C43—41no—
361Q8×C43—41no—
362D4×C43—28no—
363D4×C43—22no—
364D4×C43—22no—
365D4×C43—22no—
366D4×C43—22no—
367D4×C43—22no—
368D4×C43—22no—
369D4×C43—22no—
370D4×C43—48no—
371D4×C43—48no—
372D4×C43—48no—
373D4×C43—48no—
374D4×C43—48no—
375D4×C43—41no—
376D4×C43—41no—
377D4×C43—41no—
378D4×C43—41no—
379D4×C43—84no—
380D4×C43#12114yes—
381C2×C4×C43—21no—
382C2×C4×C43—21no—
383C2×C4×C43—21no—
384C2×C4×C43—21no—
385C2×C4×C43—22no—
386C2×C4×C43—22no—
387C2×C4×C43—22no—
388C2×C4×C43—22no—
389C2×C4×C43—21no—
390C2×C4×C43—21no—
391C2×C4×C43—22no—
392C2×C4×C43—22no—
393C2×C4×C43—21no—
394C2×C4×C43—21no—
395C2×C4×C43—21no—
396C2×C4×C43—21no—
397C2×C4×C43—48no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43—41no—
402C2×C4×C43—41no—
403C2×C4×C43—41no—
404C2×C4×C43—41no—
405C2×C4×C43—41no—
406C2×C4×C43—41no—
407C2×C4×C43—41no—
408C2×C4×C43—41no—
409C2×C4×C43—41no—
410C2×C4×C43—41no—
411C2×C4×C43—41no—
412C2×C4×C43—41no—
413C2×C4×C43—41no—
414C2×C4×C43—41no—
415C2×C4×C43—84no—
416C2×C4×C43#12012yes—
417C2×C4×C43C2×SD1612yes—
418C2×C4×C43C22×D411yescharacteristic
419C2×C4×C43C22×D411yescharacteristic
420C2×C4×C43C22×D411yescharacteristic
421C2×C4×C43C2×#4111yescharacteristic
422C2×C4×C43H(5,𝔽2)11yescharacteristic
423C2×C4×C43H(5,𝔽2)11yescharacteristic
424C8×C43—22no—
425C8×C43—41no—
426C8×C43—41no—
427C8×C43—41no—
428#24432C4311yesmaximal, characteristic, direct product factor, Sylow
429C22×C43—22no—
430C22×C43—22no—
431C22×C43—22no—
432C22×C43—22no—
433C22×C43—22no—
434C22×C43—22no—
435C22×C43—24no—
436C22×C43—22no—
437C22×C43—22no—
438C22×C43—22no—
439C22×C43—41no—
440C22×C43—42no—
441C22×C43—41no—
442C22×C43—42no—
443C22×C43—41no—
444C22×C43—42no—
445C22×C43—42no—
446C22×C43—42no—
447C22×C43—41no—
448C22×C43—42no—
449C22×C43—42no—
450C22×C43—42no—
451C22×C43—42no—
452C22×C43—42no—
453C22×C43—42no—
454C22×C43—42no—
455C22×C43—816no—
456C22×C43—816no—
457C22×C43—81no—
458C22×C43—81no—
459C22×C43—81no—
460C22×C43—81no—
461C22×C43—81no—
462C22×C43—81no—
463C22×C43—81no—
464C22×C43—81no—
465C22×C43#45014yescomplemented
466C22×C43C2×#12011yescharacteristic
467C22×C43D4211yescharacteristic
468C22×C43#54611yescharacteristic
469C22×C43C22×SD1611yescharacteristic
470C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
471C22×C43#57611yescharacteristic
472C22×C43#57711yescharacteristic
473C4×C43—22no—
474C4×C43—22no—
475C4×C43—41no—
476C4×C43—42no—
477C4×C43—42no—
478C4×C43—41no—
479C4×C43—81no—
480C4×C43—81no—
481C4×C43—81no—
482C4×C43C2×#12111yescharacteristic
483C4×C43#53411yescharacteristic
484C4×C43D4211yescharacteristic
485C4×C43#54611yescharacteristic
486C2×D42C2×C4311yescharacteristic
487C2×#465C2×C4311yescharacteristic, complemented
488C2×#450C2×C4311yescharacteristic, complemented
489C2×#450C2×C4311yescharacteristic, complemented
490C22×#102C2×C4311yescharacteristic, complemented
491#2417C2×C4311yescharacteristic, complemented
492#2041C2×C4311yescharacteristic, complemented
493#2034C2×C4311yescharacteristic, complemented
494#2014C2×C4311yescharacteristic, complemented
495#2000C2×C4311yescharacteristic, complemented
496#1877C2×C4311yescharacteristic, complemented
497#1874C2×C4311yescharacteristic, complemented
498#1869C2×C4311yescharacteristic, complemented
499#1864C2×C4311yescharacteristic, complemented
500#1786C2×C4311yescharacteristic, complemented
501C2×C43—24no—
502C2×C43—42no—
503C2×C43—44no—
504C2×C43—82no—
505C2×C43—82no—
506C2×C43#241011yescharacteristic
507C2×C43C2×#45011yescharacteristic
508C2×C43#301211yescharacteristic
509C2×C43#326411yescharacteristic
510C2×C43D4×SD1611yescharacteristic
511C2×C43#329511yescharacteristic
512C2×C43#331011yescharacteristic
513C23×D4—21no—
514C23×D4C22×C4311yescharacteristic
515C23×D4C22×C4311yescharacteristic
516C22×SD16C22×C4311yescharacteristic
517C22×SD16C22×C4311yescharacteristic, complemented
518C22×SD16C22×C4311yescharacteristic, complemented
519C23×C8C22×C4311yescharacteristic, complemented
520D42—24no—
521D42—24no—
522C2×#127C22×C4311yescharacteristic
523C2×C22⋊Q8C22×C4311yescharacteristic, complemented
524C2×C22⋊Q8C22×C4311yescharacteristic, complemented
525C2×#121—21no—
526C2×#121C22×C4311yescharacteristic
527C2×#121C22×C4311yescharacteristic
528C2×#120—21no—
529C2×#120—21no—
530C2×C4×D4C22×C4311yescharacteristic
531C2×C4×D4C22×C4311yescharacteristic
532C22×C4⋊C4C22×C4311yescharacteristic, complemented
533#465—24no—
534#450—24no—
535#450—24no—
536C2×#106C22×C4311yescharacteristic, complemented
537C2×#103C22×C4311yescharacteristic, complemented
538C2×#102—24no—
539C2×#102C22×C4311yescharacteristic
540C2×#102C22×C4311yescharacteristic
541C2×#102C22×C4311yescharacteristic
542C2×#102C22×C4311yescharacteristic, complemented
543C2×#102C22×C4311yescharacteristic, complemented
544C2×#102C22×C4311yescharacteristic, complemented
545C2×#102C22×C4311yescharacteristic, complemented
546C2×#102C22×C4311yescharacteristic, complemented
547C2×#102C22×C4311yescharacteristic, complemented
548C2×C22⋊C8C22×C4311yescharacteristic, complemented
549C2×C22⋊C8C22×C4311yescharacteristic, complemented
550C2×C22⋊C8C22×C4311yescharacteristic, complemented
551#398—21no—
552#396—21no—
553#391C22×C4311yescharacteristic, complemented
554#389C22×C4311yescharacteristic, complemented
555#386—21no—
556#380—21no—
557#380C22×C4311yescharacteristic, complemented
558#340C22×C4311yescharacteristic, complemented
559#340C22×C4311yescharacteristic, complemented
560#336C22×C4311yescharacteristic, complemented
561#336C22×C4311yescharacteristic, complemented
562C43#2443211yescharacteristic, direct product factor, Sylow
563C25—21no—
564C25—21no—
565C22×Q8C23×C4311yescharacteristic
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—28no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—22no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—22no—
579C22×D4—21no—
580C22×D4—41no—
581C22×D4—41no—
582C22×D4—41no—
583C22×D4—41no—
584C22×D4—44no—
585C22×D4—44no—
586C22×D4D4×C4311yescharacteristic
587C22×D4D4×C4314yes—
588C22×D4C23×C4311yescharacteristic
589C22×D4C23×C4311yescharacteristic
590C22×D4C23×C4311yescharacteristic
591C23×C4—21no—
592C23×C4—21no—
593C23×C4C23×C4311yescharacteristic
594C23×C4C23×C4311yescharacteristic
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—22no—
601C2×SD16—41no—
602C2×SD16—41no—
603C2×SD16—41no—
604C22×C8—22no—
605C22×C8—22no—
606C22×C8—41no—
607C22×C8C23×C4311yescharacteristic
608C22×C8C23×C4311yescharacteristic
609C22×C8C23×C4311yescharacteristic
610C22×C8C23×C4311yescharacteristic
611#127—22no—
612#127—22no—
613C22⋊Q8—22no—
614C22⋊Q8—22no—
615C22⋊Q8—22no—
616C22⋊Q8—41no—
617#121—28no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121D4×C4314yes—
622#120—28no—
623#120—28no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4D4×C4311yescharacteristic
635C2×C4⋊C4C23×C4311yescharacteristic
636C2×C4⋊C4C23×C4311yescharacteristic
637C2×C4⋊C4C23×C4311yescharacteristic
638C2×C4⋊C4C23×C4311yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4D4×C4311yescharacteristic
646C2×C22⋊C4D4×C4311yescharacteristic
647C2×C42C23×C4311yescharacteristic
648#106—22no—
649#103—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—41no—
658#102D4×C4314yescomplemented
659C22⋊C8—22no—
660C22⋊C8—22no—
661C22⋊C8—41no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666C24—21no—
667C24—24no—
668C24—21no—
669C24—21no—
670C24—24no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—42no—
677C24—42no—
678C24—42no—
679C24—81no—
680C24—81no—
681C24—81no—
682C24—81no—
683C24C2×D4×C4311yescharacteristic
684C24C2×D4×C4311yescharacteristic
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—432no—
724C2×D4—44no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—44no—
730C2×D4—42no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4SD16×C4314yescomplemented
734C2×D4C2×D4×C4312yes—
735C2×D4C2×D4×C4312yes—
736C2×D4C2×D4×C4312yes—
737C2×D4C2×D4×C4312yes—
738C2×D4#41×C4312yes—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—24no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—81no—
760C22×C4C2×D4×C4311yescharacteristic
761C22×C4C2×D4×C4311yescharacteristic
762C22×C4C2×D4×C4311yescharacteristic
763C22×C4C2×D4×C4312yes—
764C22×C4C2×D4×C4312yes—
765C22×C4C2×D4×C4311yescharacteristic
766C22×C4C24×C4311yescharacteristic
767SD16—44no—
768SD16—44no—
769SD16—44no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—44no—
782C2×C8C2×D4×C4312yescomplemented
783C4⋊C4—22no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—42no—
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—81no—
794C4⋊C4C2×D4×C4312yes—
795C4⋊C4C2×D4×C4312yescomplemented
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—22no—
799C22⋊C4—24no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—81no—
804C42—21no—
805C42—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—21no—
813C23—22no—
814C23—21no—
815C23—22no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—22no—
820C23—22no—
821C23—48no—
822C23—48no—
823C23—48no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—48no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23#120×C4312yes—
852C23C2×SD16×C4312yes—
853C23C2×SD16×C4312yes—
854C23AGL(1,ℤ/8)×C4312yes—
855C23C22×D4×C4311yescharacteristic
856Q8—41no—
857Q8—41no—
858Q8—41no—
859Q8—41no—
860D4—28no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—22no—
865D4—22no—
866D4—22no—
867D4—22no—
868D4—48no—
869D4—48no—
870D4—48no—
871D4—48no—
872D4—48no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—84no—
878D4#121×C4314yes—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—48no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—84no—
914C2×C4#120×C4312yes—
915C2×C4C2×SD16×C4312yes—
916C2×C4C22×D4×C4311yescharacteristic
917C2×C4C22×D4×C4311yescharacteristic
918C2×C4C22×D4×C4311yescharacteristic
919C2×C4C2×#41×C4311yescharacteristic
920C2×C4H(5,𝔽2)×C4311yescharacteristic
921C2×C4H(5,𝔽2)×C4311yescharacteristic
922C8—22no—
923C8—41no—
924C8—41no—
925C8—41no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—24no—
933C22—22no—
934C22—22no—
935C22—22no—
936C22—41no—
937C22—42no—
938C22—41no—
939C22—42no—
940C22—41no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—41no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—816no—
953C22—816no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22C43×#45014yescomplemented
963C22C2×#120×C4311yescharacteristic
964C22D42×C4311yescharacteristic
965C22C43×#54611yescharacteristic
966C22C22×SD16×C4311yescharacteristic
967C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
968C22C43×#57611yescharacteristic
969C22C43×#57711yescharacteristic
970C4—22no—
971C4—22no—
972C4—41no—
973C4—42no—
974C4—42no—
975C4—41no—
976C4—81no—
977C4—81no—
978C4—81no—
979C4C2×#121×C4311yescharacteristic
980C4C43×#53411yescharacteristic
981C4D42×C4311yescharacteristic
982C4C43×#54611yescharacteristic
983C2—24no—
984C2—42no—
985C2—44no—
986C2—82no—
987C2—82no—
988C2C43×#241011yescharacteristic
989C2C2×C43×#45011yescharacteristic
990C2C43×#301211yescharacteristic
991C2C43×#326411yescharacteristic
992C2D4×SD16×C4311yescharacteristic
993C2C43×#329511yescharacteristic
994C2C43×#331011yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×D42×C43C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C4×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#465C2semidirect
3. C2×C43×#450C2semidirect
4. C2×C43×#450C2semidirect
5. C22×#102×C43C2semidirect
6. C43×#2417C2semidirect
7. C43×#2041C2semidirect
8. C43×#2034C2semidirect
9. C43×#2014C2semidirect
10. C43×#2000C2semidirect
11. C43×#1877C2semidirect
12. C43×#1874C2semidirect
13. C43×#1869C2semidirect
14. C43×#1864C2semidirect
15. C43×#1786C2semidirect
20. C22×SD16×C43C22semidirect
21. C22×SD16×C43C22semidirect
22. C23×C8×C43C22semidirect
26. C2×C22⋊Q8×C43C22semidirect
27. C2×C22⋊Q8×C43C22semidirect
35. C22×C4⋊C4×C43C22semidirect
39. C2×#106×C43C22semidirect
40. C2×#103×C43C22semidirect
45. C2×#102×C43C22semidirect
46. C2×#102×C43C22semidirect
47. C2×#102×C43C22semidirect
48. C2×#102×C43C22semidirect
49. C2×#102×C43C22semidirect
50. C2×#102×C43C22semidirect
51. C2×C22⋊C8×C43C22semidirect
52. C2×C22⋊C8×C43C22semidirect
53. C2×C22⋊C8×C43C22semidirect
56. C43×#391C22semidirect
57. C43×#389C22semidirect
60. C43×#380C22semidirect
61. C43×#340C22semidirect
62. C43×#340C22semidirect
63. C43×#336C22semidirect
64. C43×#336C22semidirect
160. #102×C43D4semidirect
235. C2×D4×C43SD16semidirect
284. C2×C8×C43C2×D4semidirect
297. C4⋊C4×C43C2×D4semidirect
428. #24432C43direct (N × H)
465. C22×C43#450semidirect
487. C2×#465C2×C43semidirect
488. C2×#450C2×C43semidirect
489. C2×#450C2×C43semidirect
490. C22×#102C2×C43semidirect
491. #2417C2×C43semidirect
492. #2041C2×C43semidirect
493. #2034C2×C43semidirect
494. #2014C2×C43semidirect
495. #2000C2×C43semidirect
496. #1877C2×C43semidirect
497. #1874C2×C43semidirect
498. #1869C2×C43semidirect
499. #1864C2×C43semidirect
500. #1786C2×C43semidirect
517. C22×SD16C22×C43semidirect
518. C22×SD16C22×C43semidirect
519. C23×C8C22×C43semidirect
523. C2×C22⋊Q8C22×C43semidirect
524. C2×C22⋊Q8C22×C43semidirect
532. C22×C4⋊C4C22×C43semidirect
536. C2×#106C22×C43semidirect
537. C2×#103C22×C43semidirect
542. C2×#102C22×C43semidirect
543. C2×#102C22×C43semidirect
544. C2×#102C22×C43semidirect
545. C2×#102C22×C43semidirect
546. C2×#102C22×C43semidirect
547. C2×#102C22×C43semidirect
548. C2×C22⋊C8C22×C43semidirect
549. C2×C22⋊C8C22×C43semidirect
550. C2×C22⋊C8C22×C43semidirect
553. #391C22×C43semidirect
554. #389C22×C43semidirect
557. #380C22×C43semidirect
558. #340C22×C43semidirect
559. #340C22×C43semidirect
560. #336C22×C43semidirect
561. #336C22×C43semidirect
562. C43#24432direct (N × H)
658. #102D4×C43semidirect
733. C2×D4SD16×C43semidirect
782. C2×C8C2×D4×C43semidirect
795. C4⋊C4C2×D4×C43semidirect
962. C22C43×#450semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C432
C2×C43×#4652
C2×C43×#4502
C22×#102×C432
C43×#24172
C43×#20412
C43×#20342
C43×#20142
C43×#20002
C43×#18772
C43×#18742
C43×#18692
C43×#18642
C43×#17862
#2443243