Finite Group Databasebeta

← C43×#24434 #24944451

Subgroups — C43×#24434 #24944451

Order 11008.

1674 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#546C211yesmaximal, characteristic, complemented
2C2×C43×#465C211yesmaximal, characteristic, complemented
3C2×C43×#449C211yesmaximal, characteristic, complemented
4C2×C43×#447C211yesmaximal, characteristic, complemented
5C22×#102×C43C211yesmaximal, characteristic, complemented
6C43×#2416C211yesmaximal, characteristic, complemented
7C43×#2042C211yesmaximal, characteristic, complemented
8C43×#2034C211yesmaximal, characteristic, complemented
9C43×#2012C211yesmaximal, characteristic, complemented
10C43×#1999C211yesmaximal, characteristic, complemented
11C43×#1879C211yesmaximal, characteristic, complemented
12C43×#1872C211yesmaximal, characteristic, complemented
13C43×#1869C211yesmaximal, characteristic, complemented
14C43×#1864C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C23×D4×C43C2211yescharacteristic
18C22×SD16×C43C2211yescharacteristic, complemented
19C22×D8×C43C2211yescharacteristic
20C22×D8×C43C2211yescharacteristic
21C23×C8×C43C2211yescharacteristic
22C43×#546—24no—
23C43×#546—24no—
24C2×#124×C43C2211yescharacteristic
25C2×#123×C43—21no—
26C2×C22⋊Q8×C43C2211yescharacteristic
27C2×#121×C43—21no—
28C2×#121×C43—21no—
29C2×#121×C43C2211yescharacteristic
30C2×#121×C43C2211yescharacteristic
31C2×#121×C43C2211yescharacteristic, complemented
32C2×#120×C43—21no—
33C2×C4×D4×C43C2211yescharacteristic
34C2×C4×D4×C43C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C22⋊C4×C43—21no—
37C43×#465—24no—
38C43×#449—24no—
39C43×#447—24no—
40C2×#106×C43C2211yescharacteristic, complemented
41C2×#103×C43C2211yescharacteristic, complemented
42C2×#103×C43C2211yescharacteristic, complemented
43C2×#103×C43C2211yescharacteristic, complemented
44C2×#102×C43—24no—
45C2×#102×C43C2211yescharacteristic
46C2×#102×C43C2211yescharacteristic
47C2×#102×C43C2211yescharacteristic
48C2×#102×C43C2211yescharacteristic
49C2×#102×C43C2211yescharacteristic
50C2×#102×C43C2211yescharacteristic
51C2×#102×C43C2211yescharacteristic, complemented
52C2×C22⋊C8×C43C2211yescharacteristic
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—
66C2×#41×C43—22no—
67C2×#41×C43—22no—
68C2×#41×C43—22no—
69C2×#41×C43—22no—
70C2×#41×C43—41no—
71C2×#41×C43—41no—
72C22×Q8×C43C2311yescharacteristic
73C22×D4×C43—22no—
74C22×D4×C43—22no—
75C22×D4×C43—21no—
76C22×D4×C43—21no—
77C22×D4×C43—21no—
78C22×D4×C43—21no—
79C22×D4×C43—21no—
80C22×D4×C43—22no—
81C22×D4×C43—41no—
82C22×D4×C43—41no—
83C22×D4×C43D411yescharacteristic
84C22×D4×C43D414yescomplemented
85C22×D4×C43C2311yescharacteristic
86C22×D4×C43C2311yescharacteristic
87C22×D4×C43C2311yescharacteristic
88C23×C4×C43—21no—
89C23×C4×C43—21no—
90C23×C4×C43—21no—
91C23×C4×C43C2311yescharacteristic
92C23×C4×C43C2311yescharacteristic
93C2×SD16×C43—22no—
94C2×SD16×C43—22no—
95C2×SD16×C43—41no—
96C2×D8×C43—22no—
97C2×D8×C43—22no—
98C2×D8×C43—22no—
99C2×D8×C43—22no—
100C2×D8×C43—41no—
101C2×D8×C43—41no—
102C22×C8×C43—22no—
103C22×C8×C43—22no—
104C22×C8×C43—41no—
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109#124×C43—22no—
110#124×C43—22no—
111#123×C43—28no—
112C22⋊Q8×C43—22no—
113C22⋊Q8×C43D414yescomplemented
114#121×C43—28no—
115#121×C43—22no—
116#121×C43—22no—
117#121×C43—22no—
118#121×C43—22no—
119#121×C43—22no—
120#121×C43—41no—
121#121×C43—44no—
122#120×C43—28no—
123C4×D4×C43—22no—
124C4×D4×C43—22no—
125C4×D4×C43—22no—
126C4×D4×C43—22no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43—22no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—41no—
132C2×C4⋊C4×C43D411yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C22⋊C4×C43—28no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
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×C43—21no—
148C2×C22⋊C4×C43D411yescharacteristic
149C2×C22⋊C4×C43D411yescharacteristic
150C2×C42×C43C2311yescharacteristic
151#106×C43—22no—
152#103×C43—22no—
153#103×C43—22no—
154#103×C43—41no—
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×C43D414yescomplemented
162C22⋊C8×C43—22no—
163C22⋊C8×C43—22no—
164C22⋊C8×C43—41no—
165#95×C43—21no—
166#95×C43—21no—
167C24×C43—21no—
168C24×C43—21no—
169C24×C43—24no—
170C24×C43—21no—
171C24×C43—42no—
172C24×C43—42no—
173C24×C43—42no—
174C24×C43—42no—
175C24×C43—81no—
176C24×C43—81no—
177C24×C43C2×D411yescharacteristic
178C24×C43C2×D411yescharacteristic
179#41×C43—44no—
180#41×C43—44no—
181#41×C43—44no—
182#41×C43—44no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—21no—
187C2×Q8×C43—21no—
188C2×Q8×C43C2×D412yes—
189C2×D4×C43—24no—
190C2×D4×C43—24no—
191C2×D4×C43—24no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—22no—
197C2×D4×C43—22no—
198C2×D4×C43—22no—
199C2×D4×C43—28no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
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—42no—
211C2×D4×C43—42no—
212C2×D4×C43—42no—
213C2×D4×C43—42no—
214C2×D4×C43—42no—
215C2×D4×C43—42no—
216C2×D4×C43—44no—
217C2×D4×C43—44no—
218C2×D4×C43—44no—
219C2×D4×C43—42no—
220C2×D4×C43—42no—
221C2×D4×C43—42no—
222C2×D4×C43—81no—
223C2×D4×C43—81no—
224C2×D4×C43—81no—
225C2×D4×C43C2×D412yes—
226C2×D4×C43C2×D412yes—
227C2×D4×C43C2×D412yes—
228C2×D4×C43#4112yes—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—24no—
234C22×C4×C43—24no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—21no—
245C22×C4×C43—21no—
246C22×C4×C43—42no—
247C22×C4×C43—42no—
248C22×C4×C43—42no—
249C22×C4×C43—42no—
250C22×C4×C43—81no—
251C22×C4×C43—81no—
252C22×C4×C43—81no—
253C22×C4×C43C2×D412yes—
254C22×C4×C43C2×D412yes—
255C22×C4×C43C2×D411yescharacteristic
256C22×C4×C43C2×D411yescharacteristic
257C22×C4×C43C2×D411yescharacteristic
258C22×C4×C43C2×D411yescharacteristic
259C22×C4×C43C2411yescharacteristic
260SD16×C43—44no—
261D8×C43—44no—
262D8×C43—44no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C2×C8×C43—21no—
268C2×C8×C43—21no—
269C2×C8×C43—21no—
270C2×C8×C43—21no—
271C2×C8×C43—21no—
272C2×C8×C43—21no—
273C2×C8×C43—21no—
274C2×C8×C43—44no—
275C2×C8×C43C2×D412yes—
276C4⋊C4×C43—24no—
277C4⋊C4×C43—22no—
278C4⋊C4×C43—21no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43—21no—
281C4⋊C4×C43—21no—
282C4⋊C4×C43—21no—
283C4⋊C4×C43—21no—
284C4⋊C4×C43—42no—
285C4⋊C4×C43—42no—
286C4⋊C4×C43C2×D412yes—
287C4⋊C4×C43C2×D412yes—
288C22⋊C4×C43—24no—
289C22⋊C4×C43—24no—
290C22⋊C4×C43—24no—
291C22⋊C4×C43—24no—
292C22⋊C4×C43—22no—
293C22⋊C4×C43—22no—
294C22⋊C4×C43—24no—
295C22⋊C4×C43—42no—
296C22⋊C4×C43—42no—
297C22⋊C4×C43—42no—
298C22⋊C4×C43—42no—
299C22⋊C4×C43—81no—
300C42×C43—21no—
301C42×C43—21no—
302C23×C43—21no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—21no—
306C23×C43—22no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—21no—
311C23×C43—21no—
312C23×C43—21no—
313C23×C43—21no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—48no—
318C23×C43—41no—
319C23×C43—41no—
320C23×C43—41no—
321C23×C43—41no—
322C23×C43—41no—
323C23×C43—41no—
324C23×C43—41no—
325C23×C43—41no—
326C23×C43—41no—
327C23×C43—41no—
328C23×C43—48no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43—41no—
332C23×C43—41no—
333C23×C43—41no—
334C23×C43—41no—
335C23×C43—41no—
336C23×C43—84no—
337C23×C43—84no—
338C23×C43—84no—
339C23×C43—84no—
340C23×C43—84no—
341C23×C43#12012yes—
342C23×C43#13512yes—
343C23×C43AGL(1,ℤ/8)12yes—
344C23×C43C22×D411yescharacteristic
345Q8×C43—22no—
346Q8×C43—22no—
347Q8×C43—41no—
348Q8×C43—41no—
349D4×C43—22no—
350D4×C43—22no—
351D4×C43—22no—
352D4×C43—22no—
353D4×C43—22no—
354D4×C43—48no—
355D4×C43—48no—
356D4×C43—44no—
357D4×C43—41no—
358D4×C43—41no—
359D4×C43—41no—
360D4×C43—41no—
361D4×C43—41no—
362D4×C43—41no—
363D4×C43—84no—
364D4×C43—84no—
365D4×C43—84no—
366D4×C43#12114yescomplemented
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—22no—
370C2×C4×C43—22no—
371C2×C4×C43—22no—
372C2×C4×C43—22no—
373C2×C4×C43—21no—
374C2×C4×C43—21no—
375C2×C4×C43—22no—
376C2×C4×C43—21no—
377C2×C4×C43—22no—
378C2×C4×C43—21no—
379C2×C4×C43—22no—
380C2×C4×C43—21no—
381C2×C4×C43—21no—
382C2×C4×C43—21no—
383C2×C4×C43—21no—
384C2×C4×C43—21no—
385C2×C4×C43—48no—
386C2×C4×C43—41no—
387C2×C4×C43—41no—
388C2×C4×C43—41no—
389C2×C4×C43—41no—
390C2×C4×C43—41no—
391C2×C4×C43—41no—
392C2×C4×C43—41no—
393C2×C4×C43—41no—
394C2×C4×C43—41no—
395C2×C4×C43—41no—
396C2×C4×C43—41no—
397C2×C4×C43—41no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43—41no—
402C2×C4×C43—84no—
403C2×C4×C43—84no—
404C2×C4×C43#12012yes—
405C2×C4×C43C22×D411yescharacteristic
406C2×C4×C43C22×D411yescharacteristic
407C2×C4×C43C22×D411yescharacteristic
408C2×C4×C43C2×#4111yescharacteristic
409C2×C4×C43H(5,𝔽2)11yescharacteristic
410C2×C4×C43H(5,𝔽2)11yescharacteristic
411C8×C43—22no—
412C8×C43—41no—
413C8×C43—41no—
414C8×C43—41no—
415#24434C4311yesmaximal, characteristic, direct product factor, Sylow
416C22×C43—22no—
417C22×C43—22no—
418C22×C43—22no—
419C22×C43—22no—
420C22×C43—22no—
421C22×C43—22no—
422C22×C43—24no—
423C22×C43—42no—
424C22×C43—42no—
425C22×C43—42no—
426C22×C43—42no—
427C22×C43—42no—
428C22×C43—42no—
429C22×C43—41no—
430C22×C43—42no—
431C22×C43—41no—
432C22×C43—42no—
433C22×C43—41no—
434C22×C43—41no—
435C22×C43—42no—
436C22×C43—41no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43—816no—
440C22×C43—81no—
441C22×C43—81no—
442C22×C43—81no—
443C22×C43—81no—
444C22×C43—81no—
445C22×C43—81no—
446C22×C43—81no—
447C22×C43—81no—
448C22×C43—81no—
449C22×C43—81no—
450C22×C43—81no—
451C22×C43#44914yescomplemented
452C22×C43C2×#12011yescharacteristic
453C22×C43D4211yescharacteristic
454C22×C43#54611yescharacteristic
455C22×C43C2×#13511yescharacteristic
456C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
457C22×C43#57611yescharacteristic
458C22×C43#57711yescharacteristic
459C4×C43—22no—
460C4×C43—41no—
461C4×C43—42no—
462C4×C43—41no—
463C4×C43—42no—
464C4×C43—41no—
465C4×C43—42no—
466C4×C43—81no—
467C4×C43—81no—
468C4×C43C2×#12111yescharacteristic
469C4×C43#53411yescharacteristic
470C4×C43D4211yescharacteristic
471C4×C43#54611yescharacteristic
472C2×#546C2×C4311yescharacteristic, complemented
473C2×#465C2×C4311yescharacteristic, complemented
474C2×#449C2×C4311yescharacteristic, complemented
475C2×#447C2×C4311yescharacteristic, complemented
476C22×#102C2×C4311yescharacteristic, complemented
477#2416C2×C4311yescharacteristic, complemented
478#2042C2×C4311yescharacteristic, complemented
479#2034C2×C4311yescharacteristic, complemented
480#2012C2×C4311yescharacteristic, complemented
481#1999C2×C4311yescharacteristic, complemented
482#1879C2×C4311yescharacteristic, complemented
483#1872C2×C4311yescharacteristic, complemented
484#1869C2×C4311yescharacteristic, complemented
485#1864C2×C4311yescharacteristic, complemented
486#1788C2×C4311yescharacteristic, complemented
487C2×C43—24no—
488C2×C43—44no—
489C2×C43—81no—
490C2×C43—82no—
491C2×C43—161no—
492C2×C43#241011yescharacteristic
493C2×C43C2×#44911yescharacteristic
494C2×C43#301211yescharacteristic
495C2×C43#326411yescharacteristic
496C2×C43#328211yescharacteristic
497C2×C43#329711yescharacteristic
498C2×C43#330611yescharacteristic
499C22×#41C22×C4311yescharacteristic
500C23×D4C22×C4311yescharacteristic
501C22×SD16C22×C4311yescharacteristic, complemented
502C22×D8C22×C4311yescharacteristic
503C22×D8C22×C4311yescharacteristic
504C23×C8C22×C4311yescharacteristic
505#546—24no—
506#546—24no—
507C2×#124C22×C4311yescharacteristic
508C2×#123—21no—
509C2×C22⋊Q8C22×C4311yescharacteristic
510C2×#121—21no—
511C2×#121—21no—
512C2×#121C22×C4311yescharacteristic
513C2×#121C22×C4311yescharacteristic
514C2×#121C22×C4311yescharacteristic, complemented
515C2×#120—21no—
516C2×C4×D4C22×C4311yescharacteristic
517C2×C4×D4C22×C4311yescharacteristic
518C22×C4⋊C4C22×C4311yescharacteristic
519C22×C22⋊C4—21no—
520#465—24no—
521#449—24no—
522#447—24no—
523C2×#106C22×C4311yescharacteristic, complemented
524C2×#103C22×C4311yescharacteristic, complemented
525C2×#103C22×C4311yescharacteristic, complemented
526C2×#103C22×C4311yescharacteristic, complemented
527C2×#102—24no—
528C2×#102C22×C4311yescharacteristic
529C2×#102C22×C4311yescharacteristic
530C2×#102C22×C4311yescharacteristic
531C2×#102C22×C4311yescharacteristic
532C2×#102C22×C4311yescharacteristic
533C2×#102C22×C4311yescharacteristic
534C2×#102C22×C4311yescharacteristic, complemented
535C2×C22⋊C8C22×C4311yescharacteristic
536C2×C22⋊C8C22×C4311yescharacteristic, complemented
537C2×C22⋊C8C22×C4311yescharacteristic, complemented
538#396—21no—
539#394—21no—
540#390C22×C4311yescharacteristic, complemented
541#389C22×C4311yescharacteristic, complemented
542#386—21no—
543#380C22×C4311yescharacteristic, complemented
544#340C22×C4311yescharacteristic, complemented
545#340C22×C4311yescharacteristic, complemented
546#336C22×C4311yescharacteristic, complemented
547#336C22×C4311yescharacteristic, complemented
548C43#2443411yescharacteristic, direct product factor, Sylow
549C25—21no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—41no—
555C2×#41—41no—
556C22×Q8C23×C4311yescharacteristic
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—22no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C4311yescharacteristic
568C22×D4D4×C4314yescomplemented
569C22×D4C23×C4311yescharacteristic
570C22×D4C23×C4311yescharacteristic
571C22×D4C23×C4311yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4—21no—
575C23×C4C23×C4311yescharacteristic
576C23×C4C23×C4311yescharacteristic
577C2×SD16—22no—
578C2×SD16—22no—
579C2×SD16—41no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—41no—
585C2×D8—41no—
586C22×C8—22no—
587C22×C8—22no—
588C22×C8—41no—
589C22×C8C23×C4311yescharacteristic
590C22×C8C23×C4311yescharacteristic
591C22×C8C23×C4311yescharacteristic
592C22×C8C23×C4311yescharacteristic
593#124—22no—
594#124—22no—
595#123—28no—
596C22⋊Q8—22no—
597C22⋊Q8D4×C4314yescomplemented
598#121—28no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—41no—
605#121—44no—
606#120—28no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4D4×C4311yescharacteristic
617C2×C4⋊C4C23×C4311yescharacteristic
618C2×C4⋊C4C23×C4311yescharacteristic
619C2×C4⋊C4C23×C4311yescharacteristic
620C2×C4⋊C4C23×C4311yescharacteristic
621C2×C22⋊C4—28no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4D4×C4311yescharacteristic
633C2×C22⋊C4D4×C4311yescharacteristic
634C2×C42C23×C4311yescharacteristic
635#106—22no—
636#103—22no—
637#103—22no—
638#103—41no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—22no—
645#102D4×C4314yescomplemented
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—41no—
649#95—21no—
650#95—21no—
651C24—21no—
652C24—21no—
653C24—24no—
654C24—21no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—42no—
659C24—81no—
660C24—81no—
661C24C2×D4×C4311yescharacteristic
662C24C2×D4×C4311yescharacteristic
663#41—44no—
664#41—44no—
665#41—44no—
666#41—44no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8C2×D4×C4312yes—
673C2×D4—28no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4C2×D4×C4312yes—
710C2×D4C2×D4×C4312yes—
711C2×D4C2×D4×C4312yes—
712C2×D4#41×C4312yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—24no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—24no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4—81no—
736C22×C4—81no—
737C22×C4C2×D4×C4311yescharacteristic
738C22×C4C2×D4×C4311yescharacteristic
739C22×C4C2×D4×C4311yescharacteristic
740C22×C4C2×D4×C4311yescharacteristic
741C22×C4C2×D4×C4312yes—
742C22×C4C2×D4×C4312yes—
743C22×C4C24×C4311yescharacteristic
744SD16—44no—
745D8—44no—
746D8—44no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—44no—
759C2×C8C2×D4×C4312yes—
760C4⋊C4—24no—
761C4⋊C4—22no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—42no—
769C4⋊C4—42no—
770C4⋊C4C2×D4×C4312yes—
771C4⋊C4C2×D4×C4312yes—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—24no—
778C22⋊C4—22no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C22⋊C4—42no—
783C22⋊C4—81no—
784C42—21no—
785C42—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—48no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—48no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23#120×C4312yes—
826C23#135×C4312yes—
827C23AGL(1,ℤ/8)×C4312yes—
828C23C22×D4×C4311yescharacteristic
829Q8—22no—
830Q8—22no—
831Q8—41no—
832Q8—41no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—48no—
839D4—48no—
840D4—44no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4#121×C4314yescomplemented
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—48no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—84no—
887C2×C4—84no—
888C2×C4#120×C4312yes—
889C2×C4C22×D4×C4311yescharacteristic
890C2×C4C22×D4×C4311yescharacteristic
891C2×C4C22×D4×C4311yescharacteristic
892C2×C4C2×#41×C4311yescharacteristic
893C2×C4H(5,𝔽2)×C4311yescharacteristic
894C2×C4H(5,𝔽2)×C4311yescharacteristic
895C8—22no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—24no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—41no—
913C22—42no—
914C22—41no—
915C22—42no—
916C22—41no—
917C22—41no—
918C22—42no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22C43×#44914yescomplemented
935C22C2×#120×C4311yescharacteristic
936C22D42×C4311yescharacteristic
937C22C43×#54611yescharacteristic
938C22C2×#135×C4311yescharacteristic
939C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
940C22C43×#57611yescharacteristic
941C22C43×#57711yescharacteristic
942C4—22no—
943C4—41no—
944C4—42no—
945C4—41no—
946C4—42no—
947C4—41no—
948C4—42no—
949C4—81no—
950C4—81no—
951C4C2×#121×C4311yescharacteristic
952C4C43×#53411yescharacteristic
953C4D42×C4311yescharacteristic
954C4C43×#54611yescharacteristic
955C2—24no—
956C2—44no—
957C2—81no—
958C2—82no—
959C2—161no—
960C2C43×#241011yescharacteristic
961C2C2×C43×#44911yescharacteristic
962C2C43×#301211yescharacteristic
963C2C43×#326411yescharacteristic
964C2C43×#328211yescharacteristic
965C2C43×#329711yescharacteristic
966C2C43×#330611yescharacteristic
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×C43×#546C2semidirect
2. C2×C43×#465C2semidirect
3. C2×C43×#449C2semidirect
4. C2×C43×#447C2semidirect
5. C22×#102×C43C2semidirect
6. C43×#2416C2semidirect
7. C43×#2042C2semidirect
8. C43×#2034C2semidirect
9. C43×#2012C2semidirect
10. C43×#1999C2semidirect
11. C43×#1879C2semidirect
12. C43×#1872C2semidirect
13. C43×#1869C2semidirect
14. C43×#1864C2semidirect
15. C43×#1788C2semidirect
18. C22×SD16×C43C22semidirect
31. C2×#121×C43C22semidirect
40. C2×#106×C43C22semidirect
41. C2×#103×C43C22semidirect
42. C2×#103×C43C22semidirect
43. C2×#103×C43C22semidirect
51. C2×#102×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
84. C22×D4×C43D4semidirect
113. C22⋊Q8×C43D4semidirect
161. #102×C43D4semidirect
366. D4×C43#121semidirect
415. #24434C43direct (N × H)
451. C22×C43#449semidirect
472. C2×#546C2×C43semidirect
473. C2×#465C2×C43semidirect
474. C2×#449C2×C43semidirect
475. C2×#447C2×C43semidirect
476. C22×#102C2×C43semidirect
477. #2416C2×C43semidirect
478. #2042C2×C43semidirect
479. #2034C2×C43semidirect
480. #2012C2×C43semidirect
481. #1999C2×C43semidirect
482. #1879C2×C43semidirect
483. #1872C2×C43semidirect
484. #1869C2×C43semidirect
485. #1864C2×C43semidirect
486. #1788C2×C43semidirect
501. C22×SD16C22×C43semidirect
514. C2×#121C22×C43semidirect
523. C2×#106C22×C43semidirect
524. C2×#103C22×C43semidirect
525. C2×#103C22×C43semidirect
526. C2×#103C22×C43semidirect
534. C2×#102C22×C43semidirect
536. C2×C22⋊C8C22×C43semidirect
537. C2×C22⋊C8C22×C43semidirect
540. #390C22×C43semidirect
541. #389C22×C43semidirect
543. #380C22×C43semidirect
544. #340C22×C43semidirect
545. #340C22×C43semidirect
546. #336C22×C43semidirect
547. #336C22×C43semidirect
548. C43#24434direct (N × H)
568. C22×D4D4×C43semidirect
597. C22⋊Q8D4×C43semidirect
645. #102D4×C43semidirect
850. D4#121×C43semidirect
934. C22C43×#449semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5462
C2×C43×#4652
C2×C43×#4492
C2×C43×#4472
C22×#102×C432
C43×#24162
C43×#20422
C43×#20342
C43×#20122
C43×#19992
C43×#18792
C43×#18722
C43×#18692
C43×#18642
C43×#17882
#2443443