Finite Group Databasebeta

← C43×#24424 #24944441

Subgroups — C43×#24424 #24944441

Order 11008.

1992 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C43C211yesmaximal, characteristic, complemented
2C2×C43×#466C211yesmaximal, characteristic, complemented
3C2×C43×#447C211yesmaximal, characteristic, complemented
4C2×C43×#447C211yesmaximal, characteristic, complemented
5C22×#102×C43C211yesmaximal, characteristic, complemented
6C43×#2416C211yesmaximal, characteristic, complemented
7C43×#2041C211yesmaximal, characteristic, complemented
8C43×#2033C211yesmaximal, characteristic, complemented
9C43×#2011C211yesmaximal, characteristic, complemented
10C43×#1999C211yesmaximal, characteristic, complemented
11C43×#1879C211yesmaximal, characteristic, complemented
12C43×#1874C211yesmaximal, characteristic, complemented
13C43×#1869C211yesmaximal, characteristic, complemented
14C43×#1862C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C43—21no—
17C23×D4×C43C2211yescharacteristic
18C23×D4×C43C2211yescharacteristic
19C22×D8×C43C2211yescharacteristic
20C22×D8×C43C2211yescharacteristic, complemented
21C22×D8×C43C2211yescharacteristic, complemented
22C23×C8×C43C2211yescharacteristic, complemented
23D42×C43—24no—
24D42×C43—24no—
25C2×#127×C43C2211yescharacteristic
26C2×#121×C43—21no—
27C2×#121×C43—21no—
28C2×#121×C43C2211yescharacteristic
29C2×#121×C43C2211yescharacteristic
30C2×#121×C43C2211yescharacteristic, complemented
31C2×#121×C43C2211yescharacteristic, complemented
32C2×#120×C43—21no—
33C2×#120×C43—21no—
34C2×C4×D4×C43C2211yescharacteristic
35C2×C4×D4×C43C2211yescharacteristic
36C22×C4⋊C4×C43C2211yescharacteristic, complemented
37C43×#466—24no—
38C43×#447—24no—
39C43×#447—24no—
40C2×#107×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×#102×C43C2211yescharacteristic, complemented
52C2×C22⋊C8×C43C2211yescharacteristic, complemented
53C2×C22⋊C8×C43C2211yescharacteristic, complemented
54C2×C22⋊C8×C43C2211yescharacteristic, complemented
55C43×#396—21no—
56C43×#394—21no—
57C43×#390C2211yescharacteristic, complemented
58C43×#389C2211yescharacteristic, complemented
59C43×#386—21no—
60C43×#380C2211yescharacteristic, complemented
61C43×#340C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C43×#336C2211yescharacteristic, complemented
64C43×#336C2211yescharacteristic, complemented
65C25×C43—21no—
66C25×C43—21no—
67C22×D4×C43—22no—
68C22×D4×C43—22no—
69C22×D4×C43—28no—
70C22×D4×C43—21no—
71C22×D4×C43—21no—
72C22×D4×C43—22no—
73C22×D4×C43—22no—
74C22×D4×C43—22no—
75C22×D4×C43—22no—
76C22×D4×C43—21no—
77C22×D4×C43—21no—
78C22×D4×C43—21no—
79C22×D4×C43—21no—
80C22×D4×C43—21no—
81C22×D4×C43—22no—
82C22×D4×C43—21no—
83C22×D4×C43—41no—
84C22×D4×C43—41no—
85C22×D4×C43—41no—
86C22×D4×C43—41no—
87C22×D4×C43—44no—
88C22×D4×C43—44no—
89C22×D4×C43D411yescharacteristic
90C22×D4×C43D414yescomplemented
91C22×D4×C43C2311yescharacteristic
92C22×D4×C43C2311yescharacteristic
93C22×D4×C43C2311yescharacteristic
94C22×D4×C43C2311yescharacteristic
95C23×C4×C43—21no—
96C23×C4×C43—21no—
97C23×C4×C43C2311yescharacteristic
98C23×C4×C43C2311yescharacteristic
99C2×D8×C43—22no—
100C2×D8×C43—22no—
101C2×D8×C43—22no—
102C2×D8×C43—22no—
103C2×D8×C43—22no—
104C2×D8×C43—22no—
105C2×D8×C43—41no—
106C2×D8×C43—41no—
107C2×D8×C43—41no—
108C22×C8×C43—22no—
109C22×C8×C43—22no—
110C22×C8×C43—41no—
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115#127×C43—22no—
116#127×C43—22no—
117#121×C43—28no—
118#121×C43—22no—
119#121×C43—22no—
120#121×C43—22no—
121#121×C43—22no—
122#121×C43—22no—
123#121×C43—22no—
124#121×C43—41no—
125#121×C43—44no—
126#121×C43D414yescomplemented
127#120×C43—28no—
128#120×C43—28no—
129C4×D4×C43—22no—
130C4×D4×C43—22no—
131C4×D4×C43—22no—
132C4×D4×C43—22no—
133C2×C4⋊C4×C43—22no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43—41no—
137C2×C4⋊C4×C43D411yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
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×C43—21no—
148C2×C22⋊C4×C43—21no—
149C2×C22⋊C4×C43—21no—
150C2×C22⋊C4×C43D411yescharacteristic
151C2×C22⋊C4×C43D411yescharacteristic
152C2×C42×C43C2311yescharacteristic
153#107×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—22no—
160#102×C43—22no—
161#102×C43—22no—
162#102×C43—41no—
163#102×C43D414yescomplemented
164C22⋊C8×C43—22no—
165C22⋊C8×C43—22no—
166C22⋊C8×C43—41no—
167#95×C43—21no—
168#95×C43—21no—
169C24×C43—21no—
170C24×C43—24no—
171C24×C43—21no—
172C24×C43—21no—
173C24×C43—24no—
174C24×C43—21no—
175C24×C43—42no—
176C24×C43—42no—
177C24×C43—42no—
178C24×C43—42no—
179C24×C43—42no—
180C24×C43—42no—
181C24×C43—42no—
182C24×C43—42no—
183C24×C43—81no—
184C24×C43—81no—
185C24×C43—81no—
186C24×C43—81no—
187C24×C43C2×D411yescharacteristic
188C24×C43C2×D411yescharacteristic
189C2×D4×C43—24no—
190C2×D4×C43—24no—
191C2×D4×C43—24no—
192C2×D4×C43—24no—
193C2×D4×C43—24no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—21no—
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—22no—
200C2×D4×C43—24no—
201C2×D4×C43—22no—
202C2×D4×C43—28no—
203C2×D4×C43—21no—
204C2×D4×C43—21no—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
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—21no—
216C2×D4×C43—21no—
217C2×D4×C43—42no—
218C2×D4×C43—42no—
219C2×D4×C43—42no—
220C2×D4×C43—42no—
221C2×D4×C43—42no—
222C2×D4×C43—42no—
223C2×D4×C43—44no—
224C2×D4×C43—44no—
225C2×D4×C43—44no—
226C2×D4×C43—42no—
227C2×D4×C43—44no—
228C2×D4×C43—44no—
229C2×D4×C43—44no—
230C2×D4×C43—432no—
231C2×D4×C43—44no—
232C2×D4×C43—42no—
233C2×D4×C43—42no—
234C2×D4×C43—42no—
235C2×D4×C43—42no—
236C2×D4×C43—42no—
237C2×D4×C43—42no—
238C2×D4×C43—42no—
239C2×D4×C43—42no—
240C2×D4×C43—81no—
241C2×D4×C43—81no—
242C2×D4×C43—81no—
243C2×D4×C43D814yescomplemented
244C2×D4×C43C2×D412yes—
245C2×D4×C43C2×D412yes—
246C2×D4×C43C2×D412yes—
247C2×D4×C43C2×D412yes—
248C2×D4×C43#4112yes—
249C22×C4×C43—21no—
250C22×C4×C43—21no—
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43—24no—
254C22×C4×C43—21no—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—21no—
258C22×C4×C43—21no—
259C22×C4×C43—21no—
260C22×C4×C43—21no—
261C22×C4×C43—21no—
262C22×C4×C43—21no—
263C22×C4×C43—21no—
264C22×C4×C43—42no—
265C22×C4×C43—42no—
266C22×C4×C43—42no—
267C22×C4×C43—42no—
268C22×C4×C43—81no—
269C22×C4×C43C2×D412yes—
270C22×C4×C43C2×D412yes—
271C22×C4×C43C2×D411yescharacteristic
272C22×C4×C43C2×D411yescharacteristic
273C22×C4×C43C2×D411yescharacteristic
274C22×C4×C43C2×D411yescharacteristic
275C22×C4×C43C2411yescharacteristic
276D8×C43—44no—
277D8×C43—44no—
278D8×C43—44no—
279C2×C8×C43—21no—
280C2×C8×C43—21no—
281C2×C8×C43—21no—
282C2×C8×C43—21no—
283C2×C8×C43—21no—
284C2×C8×C43—21no—
285C2×C8×C43—21no—
286C2×C8×C43—21no—
287C2×C8×C43—21no—
288C2×C8×C43—21no—
289C2×C8×C43—21no—
290C2×C8×C43—44no—
291C2×C8×C43C2×D412yescomplemented
292C4⋊C4×C43—22no—
293C4⋊C4×C43—21no—
294C4⋊C4×C43—21no—
295C4⋊C4×C43—21no—
296C4⋊C4×C43—21no—
297C4⋊C4×C43—21no—
298C4⋊C4×C43—21no—
299C4⋊C4×C43—42no—
300C4⋊C4×C43—42no—
301C4⋊C4×C43C2×D412yes—
302C4⋊C4×C43C2×D412yescomplemented
303C22⋊C4×C43—24no—
304C22⋊C4×C43—24no—
305C22⋊C4×C43—24no—
306C22⋊C4×C43—22no—
307C22⋊C4×C43—22no—
308C22⋊C4×C43—42no—
309C22⋊C4×C43—42no—
310C22⋊C4×C43—42no—
311C22⋊C4×C43—42no—
312C22⋊C4×C43—81no—
313C42×C43—21no—
314C42×C43—21no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—21no—
318C23×C43—21no—
319C23×C43—21no—
320C23×C43—22no—
321C23×C43—21no—
322C23×C43—22no—
323C23×C43—21no—
324C23×C43—22no—
325C23×C43—21no—
326C23×C43—21no—
327C23×C43—21no—
328C23×C43—22no—
329C23×C43—22no—
330C23×C43—48no—
331C23×C43—48no—
332C23×C43—48no—
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—41no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—41no—
348C23×C43—41no—
349C23×C43—48no—
350C23×C43—41no—
351C23×C43—41no—
352C23×C43—41no—
353C23×C43—41no—
354C23×C43—41no—
355C23×C43—41no—
356C23×C43—41no—
357C23×C43—84no—
358C23×C43—84no—
359C23×C43—84no—
360C23×C43—84no—
361C23×C43—84no—
362C23×C43—84no—
363C23×C43—84no—
364C23×C43—84no—
365C23×C43—84no—
366C23×C43—84no—
367C23×C43#12012yes—
368C23×C43C2×D812yes—
369C23×C43C2×D812yes—
370C23×C43AGL(1,ℤ/8)12yes—
371C23×C43C22×D411yescharacteristic
372D4×C43—28no—
373D4×C43—22no—
374D4×C43—22no—
375D4×C43—22no—
376D4×C43—22no—
377D4×C43—22no—
378D4×C43—22no—
379D4×C43—22no—
380D4×C43—48no—
381D4×C43—48no—
382D4×C43—48no—
383D4×C43—48no—
384D4×C43—48no—
385D4×C43—41no—
386D4×C43—41no—
387D4×C43—41no—
388D4×C43—41no—
389D4×C43—41no—
390D4×C43—41no—
391D4×C43—41no—
392D4×C43—41no—
393D4×C43—84no—
394D4×C43—84no—
395D4×C43—84no—
396D4×C43#12114yescomplemented
397C2×C4×C43—21no—
398C2×C4×C43—21no—
399C2×C4×C43—21no—
400C2×C4×C43—21no—
401C2×C4×C43—22no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—22no—
405C2×C4×C43—21no—
406C2×C4×C43—21no—
407C2×C4×C43—22no—
408C2×C4×C43—21no—
409C2×C4×C43—22no—
410C2×C4×C43—21no—
411C2×C4×C43—21no—
412C2×C4×C43—21no—
413C2×C4×C43—48no—
414C2×C4×C43—41no—
415C2×C4×C43—41no—
416C2×C4×C43—41no—
417C2×C4×C43—41no—
418C2×C4×C43—41no—
419C2×C4×C43—41no—
420C2×C4×C43—41no—
421C2×C4×C43—41no—
422C2×C4×C43—41no—
423C2×C4×C43—41no—
424C2×C4×C43—41no—
425C2×C4×C43—41no—
426C2×C4×C43—41no—
427C2×C4×C43—41no—
428C2×C4×C43—84no—
429C2×C4×C43#12012yes—
430C2×C4×C43C2×D812yes—
431C2×C4×C43C22×D411yescharacteristic
432C2×C4×C43C22×D411yescharacteristic
433C2×C4×C43C22×D411yescharacteristic
434C2×C4×C43C2×#4111yescharacteristic
435C2×C4×C43H(5,𝔽2)11yescharacteristic
436C2×C4×C43H(5,𝔽2)11yescharacteristic
437C8×C43—22no—
438C8×C43—41no—
439C8×C43—41no—
440C8×C43—41no—
441#24424C4311yesmaximal, characteristic, direct product factor, Sylow
442C22×C43—22no—
443C22×C43—22no—
444C22×C43—22no—
445C22×C43—22no—
446C22×C43—22no—
447C22×C43—22no—
448C22×C43—24no—
449C22×C43—22no—
450C22×C43—22no—
451C22×C43—22no—
452C22×C43—41no—
453C22×C43—42no—
454C22×C43—41no—
455C22×C43—42no—
456C22×C43—41no—
457C22×C43—42no—
458C22×C43—42no—
459C22×C43—42no—
460C22×C43—41no—
461C22×C43—42no—
462C22×C43—42no—
463C22×C43—42no—
464C22×C43—42no—
465C22×C43—42no—
466C22×C43—42no—
467C22×C43—42no—
468C22×C43—816no—
469C22×C43—816no—
470C22×C43—81no—
471C22×C43—81no—
472C22×C43—81no—
473C22×C43—81no—
474C22×C43—81no—
475C22×C43—81no—
476C22×C43—81no—
477C22×C43—81no—
478C22×C43—81no—
479C22×C43—81no—
480C22×C43—81no—
481C22×C43—81no—
482C22×C43—81no—
483C22×C43—81no—
484C22×C43—81no—
485C22×C43#44714yescomplemented
486C22×C43C2×#12011yescharacteristic
487C22×C43D4211yescharacteristic
488C22×C43#54611yescharacteristic
489C22×C43C22×D811yescharacteristic
490C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
491C22×C43#57611yescharacteristic
492C22×C43#57711yescharacteristic
493C4×C43—22no—
494C4×C43—22no—
495C4×C43—41no—
496C4×C43—42no—
497C4×C43—41no—
498C4×C43—42no—
499C4×C43—81no—
500C4×C43—81no—
501C4×C43C2×#12111yescharacteristic
502C4×C43#53411yescharacteristic
503C4×C43D4211yescharacteristic
504C4×C43#54611yescharacteristic
505C2×D42C2×C4311yescharacteristic, complemented
506C2×#466C2×C4311yescharacteristic, complemented
507C2×#447C2×C4311yescharacteristic, complemented
508C2×#447C2×C4311yescharacteristic, complemented
509C22×#102C2×C4311yescharacteristic, complemented
510#2416C2×C4311yescharacteristic, complemented
511#2041C2×C4311yescharacteristic, complemented
512#2033C2×C4311yescharacteristic, complemented
513#2011C2×C4311yescharacteristic, complemented
514#1999C2×C4311yescharacteristic, complemented
515#1879C2×C4311yescharacteristic, complemented
516#1874C2×C4311yescharacteristic, complemented
517#1869C2×C4311yescharacteristic, complemented
518#1862C2×C4311yescharacteristic, complemented
519#1786C2×C4311yescharacteristic, complemented
520C2×C43—24no—
521C2×C43—42no—
522C2×C43—44no—
523C2×C43—82no—
524C2×C43—82no—
525C2×C43—161no—
526C2×C43#241011yescharacteristic
527C2×C43C2×#44711yescharacteristic
528C2×C43#301211yescharacteristic
529C2×C43#326511yescharacteristic
530C2×C43D4×D811yescharacteristic
531C2×C43#329411yescharacteristic
532C2×C43#331811yescharacteristic
533C23×D4—21no—
534C23×D4C22×C4311yescharacteristic
535C23×D4C22×C4311yescharacteristic
536C22×D8C22×C4311yescharacteristic
537C22×D8C22×C4311yescharacteristic, complemented
538C22×D8C22×C4311yescharacteristic, complemented
539C23×C8C22×C4311yescharacteristic, complemented
540D42—24no—
541D42—24no—
542C2×#127C22×C4311yescharacteristic
543C2×#121—21no—
544C2×#121—21no—
545C2×#121C22×C4311yescharacteristic
546C2×#121C22×C4311yescharacteristic
547C2×#121C22×C4311yescharacteristic, complemented
548C2×#121C22×C4311yescharacteristic, complemented
549C2×#120—21no—
550C2×#120—21no—
551C2×C4×D4C22×C4311yescharacteristic
552C2×C4×D4C22×C4311yescharacteristic
553C22×C4⋊C4C22×C4311yescharacteristic, complemented
554#466—24no—
555#447—24no—
556#447—24no—
557C2×#107C22×C4311yescharacteristic, complemented
558C2×#102—24no—
559C2×#102C22×C4311yescharacteristic
560C2×#102C22×C4311yescharacteristic
561C2×#102C22×C4311yescharacteristic
562C2×#102C22×C4311yescharacteristic, complemented
563C2×#102C22×C4311yescharacteristic, complemented
564C2×#102C22×C4311yescharacteristic, complemented
565C2×#102C22×C4311yescharacteristic, complemented
566C2×#102C22×C4311yescharacteristic, complemented
567C2×#102C22×C4311yescharacteristic, complemented
568C2×#102C22×C4311yescharacteristic, complemented
569C2×C22⋊C8C22×C4311yescharacteristic, complemented
570C2×C22⋊C8C22×C4311yescharacteristic, complemented
571C2×C22⋊C8C22×C4311yescharacteristic, complemented
572#396—21no—
573#394—21no—
574#390C22×C4311yescharacteristic, complemented
575#389C22×C4311yescharacteristic, complemented
576#386—21no—
577#380C22×C4311yescharacteristic, complemented
578#340C22×C4311yescharacteristic, complemented
579#340C22×C4311yescharacteristic, complemented
580#336C22×C4311yescharacteristic, complemented
581#336C22×C4311yescharacteristic, complemented
582C43#2442411yescharacteristic, direct product factor, Sylow
583C25—21no—
584C25—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—28no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—22no—
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—22no—
600C22×D4—21no—
601C22×D4—41no—
602C22×D4—41no—
603C22×D4—41no—
604C22×D4—41no—
605C22×D4—44no—
606C22×D4—44no—
607C22×D4D4×C4311yescharacteristic
608C22×D4D4×C4314yescomplemented
609C22×D4C23×C4311yescharacteristic
610C22×D4C23×C4311yescharacteristic
611C22×D4C23×C4311yescharacteristic
612C22×D4C23×C4311yescharacteristic
613C23×C4—21no—
614C23×C4—21no—
615C23×C4C23×C4311yescharacteristic
616C23×C4C23×C4311yescharacteristic
617C2×D8—22no—
618C2×D8—22no—
619C2×D8—22no—
620C2×D8—22no—
621C2×D8—22no—
622C2×D8—22no—
623C2×D8—41no—
624C2×D8—41no—
625C2×D8—41no—
626C22×C8—22no—
627C22×C8—22no—
628C22×C8—41no—
629C22×C8C23×C4311yescharacteristic
630C22×C8C23×C4311yescharacteristic
631C22×C8C23×C4311yescharacteristic
632C22×C8C23×C4311yescharacteristic
633#127—22no—
634#127—22no—
635#121—28no—
636#121—22no—
637#121—22no—
638#121—22no—
639#121—22no—
640#121—22no—
641#121—22no—
642#121—41no—
643#121—44no—
644#121D4×C4314yescomplemented
645#120—28no—
646#120—28no—
647C4×D4—22no—
648C4×D4—22no—
649C4×D4—22no—
650C4×D4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4D4×C4311yescharacteristic
656C2×C4⋊C4C23×C4311yescharacteristic
657C2×C4⋊C4C23×C4311yescharacteristic
658C2×C4⋊C4C23×C4311yescharacteristic
659C2×C4⋊C4C23×C4311yescharacteristic
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4D4×C4311yescharacteristic
669C2×C22⋊C4D4×C4311yescharacteristic
670C2×C42C23×C4311yescharacteristic
671#107—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—22no—
677#102—22no—
678#102—22no—
679#102—22no—
680#102—41no—
681#102D4×C4314yescomplemented
682C22⋊C8—22no—
683C22⋊C8—22no—
684C22⋊C8—41no—
685#95—21no—
686#95—21no—
687C24—21no—
688C24—24no—
689C24—21no—
690C24—21no—
691C24—24no—
692C24—21no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—42no—
698C24—42no—
699C24—42no—
700C24—42no—
701C24—81no—
702C24—81no—
703C24—81no—
704C24—81no—
705C24C2×D4×C4311yescharacteristic
706C24C2×D4×C4311yescharacteristic
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—28no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—432no—
747C2×D4—44no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—81no—
759C2×D4—81no—
760C2×D4—81no—
761C2×D4D8×C4314yescomplemented
762C2×D4C2×D4×C4312yes—
763C2×D4C2×D4×C4312yes—
764C2×D4C2×D4×C4312yes—
765C2×D4C2×D4×C4312yes—
766C2×D4#41×C4312yes—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—24no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—81no—
787C22×C4C2×D4×C4311yescharacteristic
788C22×C4C2×D4×C4311yescharacteristic
789C22×C4C2×D4×C4311yescharacteristic
790C22×C4C2×D4×C4312yes—
791C22×C4C2×D4×C4312yes—
792C22×C4C2×D4×C4311yescharacteristic
793C22×C4C24×C4311yescharacteristic
794D8—44no—
795D8—44no—
796D8—44no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—44no—
809C2×C8C2×D4×C4312yescomplemented
810C4⋊C4—22no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—42no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C4312yes—
820C4⋊C4C2×D4×C4312yescomplemented
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—22no—
824C22⋊C4—24no—
825C22⋊C4—22no—
826C22⋊C4—42no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C42—21no—
832C42—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—22no—
839C23—21no—
840C23—22no—
841C23—21no—
842C23—22no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—22no—
847C23—22no—
848C23—48no—
849C23—48no—
850C23—48no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—48no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23—84no—
881C23—84no—
882C23—84no—
883C23—84no—
884C23—84no—
885C23#120×C4312yes—
886C23C2×D8×C4312yes—
887C23C2×D8×C4312yes—
888C23AGL(1,ℤ/8)×C4312yes—
889C23C22×D4×C4311yescharacteristic
890D4—28no—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—22no—
897D4—22no—
898D4—48no—
899D4—48no—
900D4—48no—
901D4—48no—
902D4—48no—
903D4—41no—
904D4—41no—
905D4—41no—
906D4—41no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—84no—
912D4—84no—
913D4—84no—
914D4#121×C4314yescomplemented
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—22no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—48no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—84no—
947C2×C4#120×C4312yes—
948C2×C4C2×D8×C4312yes—
949C2×C4C22×D4×C4311yescharacteristic
950C2×C4C22×D4×C4311yescharacteristic
951C2×C4C22×D4×C4311yescharacteristic
952C2×C4C2×#41×C4311yescharacteristic
953C2×C4H(5,𝔽2)×C4311yescharacteristic
954C2×C4H(5,𝔽2)×C4311yescharacteristic
955C8—22no—
956C8—41no—
957C8—41no—
958C8—41no—
959C22—22no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—24no—
966C22—22no—
967C22—22no—
968C22—22no—
969C22—41no—
970C22—42no—
971C22—41no—
972C22—42no—
973C22—41no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—816no—
986C22—816no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22—81no—
996C22—81no—
997C22—81no—
998C22—81no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22C43×#44714yescomplemented
1003C22C2×#120×C4311yescharacteristic
1004C22D42×C4311yescharacteristic
1005C22C43×#54611yescharacteristic
1006C22C22×D8×C4311yescharacteristic
1007C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
1008C22C43×#57611yescharacteristic
1009C22C43×#57711yescharacteristic
1010C4—22no—
1011C4—22no—
1012C4—41no—
1013C4—42no—
1014C4—41no—
1015C4—42no—
1016C4—81no—
1017C4—81no—
1018C4C2×#121×C4311yescharacteristic
1019C4C43×#53411yescharacteristic
1020C4D42×C4311yescharacteristic
1021C4C43×#54611yescharacteristic
1022C2—24no—
1023C2—42no—
1024C2—44no—
1025C2—82no—
1026C2—82no—
1027C2—161no—
1028C2C43×#241011yescharacteristic
1029C2C2×C43×#44711yescharacteristic
1030C2C43×#301211yescharacteristic
1031C2C43×#326511yescharacteristic
1032C2D4×D8×C4311yescharacteristic
1033C2C43×#329411yescharacteristic
1034C2C43×#331811yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
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
1. C2×D42×C43C2semidirect
2. C2×C43×#466C2semidirect
3. C2×C43×#447C2semidirect
4. C2×C43×#447C2semidirect
5. C22×#102×C43C2semidirect
6. C43×#2416C2semidirect
7. C43×#2041C2semidirect
8. C43×#2033C2semidirect
9. C43×#2011C2semidirect
10. C43×#1999C2semidirect
11. C43×#1879C2semidirect
12. C43×#1874C2semidirect
13. C43×#1869C2semidirect
14. C43×#1862C2semidirect
15. C43×#1786C2semidirect
20. C22×D8×C43C22semidirect
21. C22×D8×C43C22semidirect
22. C23×C8×C43C22semidirect
30. C2×#121×C43C22semidirect
31. C2×#121×C43C22semidirect
36. C22×C4⋊C4×C43C22semidirect
40. C2×#107×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×#102×C43C22semidirect
52. C2×C22⋊C8×C43C22semidirect
53. C2×C22⋊C8×C43C22semidirect
54. C2×C22⋊C8×C43C22semidirect
57. C43×#390C22semidirect
58. C43×#389C22semidirect
60. C43×#380C22semidirect
61. C43×#340C22semidirect
62. C43×#340C22semidirect
63. C43×#336C22semidirect
64. C43×#336C22semidirect
90. C22×D4×C43D4semidirect
126. #121×C43D4semidirect
163. #102×C43D4semidirect
243. C2×D4×C43D8semidirect
291. C2×C8×C43C2×D4semidirect
302. C4⋊C4×C43C2×D4semidirect
396. D4×C43#121semidirect
441. #24424C43direct (N × H)
485. C22×C43#447semidirect
505. C2×D42C2×C43semidirect
506. C2×#466C2×C43semidirect
507. C2×#447C2×C43semidirect
508. C2×#447C2×C43semidirect
509. C22×#102C2×C43semidirect
510. #2416C2×C43semidirect
511. #2041C2×C43semidirect
512. #2033C2×C43semidirect
513. #2011C2×C43semidirect
514. #1999C2×C43semidirect
515. #1879C2×C43semidirect
516. #1874C2×C43semidirect
517. #1869C2×C43semidirect
518. #1862C2×C43semidirect
519. #1786C2×C43semidirect
537. C22×D8C22×C43semidirect
538. C22×D8C22×C43semidirect
539. C23×C8C22×C43semidirect
547. C2×#121C22×C43semidirect
548. C2×#121C22×C43semidirect
553. C22×C4⋊C4C22×C43semidirect
557. C2×#107C22×C43semidirect
562. C2×#102C22×C43semidirect
563. C2×#102C22×C43semidirect
564. C2×#102C22×C43semidirect
565. C2×#102C22×C43semidirect
566. C2×#102C22×C43semidirect
567. C2×#102C22×C43semidirect
568. C2×#102C22×C43semidirect
569. C2×C22⋊C8C22×C43semidirect
570. C2×C22⋊C8C22×C43semidirect
571. C2×C22⋊C8C22×C43semidirect
574. #390C22×C43semidirect
575. #389C22×C43semidirect
577. #380C22×C43semidirect
578. #340C22×C43semidirect
579. #340C22×C43semidirect
580. #336C22×C43semidirect
581. #336C22×C43semidirect
582. C43#24424direct (N × H)
608. C22×D4D4×C43semidirect
644. #121D4×C43semidirect
681. #102D4×C43semidirect
761. C2×D4D8×C43semidirect
809. C2×C8C2×D4×C43semidirect
820. C4⋊C4C2×D4×C43semidirect
914. D4#121×C43semidirect
1002. C22C43×#447semidirect

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×#4662
C2×C43×#4472
C22×#102×C432
C43×#24162
C43×#20412
C43×#20332
C43×#20112
C43×#19992
C43×#18792
C43×#18742
C43×#18692
C43×#18622
C43×#17862
#2442443