Finite Group Databasebeta

← C43×#23972 #24943989

Subgroups — C43×#23972 #24943989

Order 11008.

1516 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#547C211yesmaximal, characteristic, complemented
2C2×C43×#449C211yesmaximal, characteristic, complemented
3C2×C43×#417C211yesmaximal, characteristic, complemented
4C43×#2407C211yesmaximal, characteristic, complemented
5C43×#2024C211yesmaximal, characteristic, complemented
6C43×#2023C211yesmaximal, characteristic, complemented
7C43×#2000C211yesmaximal, characteristic, complemented
8C43×#1999C211yesmaximal, characteristic, complemented
9C43×#1895C211yesmaximal, characteristic, complemented
10C43×#1879C211yesmaximal, characteristic, complemented
11C43×#1877C211yesmaximal, characteristic, complemented
12C43×#1874C211yesmaximal, characteristic, complemented
13C43×#1872C211yesmaximal, characteristic, complemented
14C43×#1870C211yesmaximal, characteristic, complemented
15C43×#1824C211yesmaximal, characteristic, complemented
16C22×#41×C43—21no—
17C22×#41×C43C2211yescharacteristic
18C22×SD16×C43C2211yescharacteristic
19C22×D8×C43C2211yescharacteristic
20C22×M16×C43C2211yescharacteristic
21C43×#547—24no—
22C43×#547—24no—
23C2×C4⋊Q8×C43C2211yescharacteristic
24C2×#123×C43—21no—
25C2×#123×C43—21no—
26C2×C22⋊Q8×C43—21no—
27C2×C22⋊Q8×C43C2211yescharacteristic
28C2×#121×C43C2211yescharacteristic
29C2×#121×C43C2211yescharacteristic
30C2×#121×C43C2211yescharacteristic
31C2×C4×D4×C43C2211yescharacteristic
32C2×C4×D4×C43C2211yescharacteristic
33C22×C4⋊C4×C43C2211yescharacteristic
34C22×C4⋊C4×C43C2211yescharacteristic
35C43×#449—24no—
36C43×#417—24no—
37C2×#103×C43C2211yescharacteristic
38C2×#103×C43C2211yescharacteristic
39C2×#103×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×C22⋊C8×C43C2211yescharacteristic
46C2×C22⋊C8×C43C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C43×#394—21no—
49C43×#392—21no—
50C43×#391C2211yescharacteristic
51C43×#390C2211yescharacteristic
52C43×#386—21no—
53C43×#385—21no—
54C43×#380C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C2×#41×C43—28no—
64C2×#41×C43—22no—
65C2×#41×C43—22no—
66C2×#41×C43—22no—
67C2×#41×C43—22no—
68C2×#41×C43—41no—
69C2×#41×C43—41no—
70C2×#41×C43—44no—
71C2×#41×C43—44no—
72C22×Q8×C43—21no—
73C22×Q8×C43C2311yescharacteristic
74C22×D4×C43—21no—
75C22×D4×C43—21no—
76C22×D4×C43—21no—
77C22×D4×C43—21no—
78C22×D4×C43D411yescharacteristic
79C22×D4×C43C2311yescharacteristic
80C22×D4×C43C2311yescharacteristic
81C23×C4×C43—21no—
82C23×C4×C43—21no—
83C23×C4×C43—21no—
84C23×C4×C43—21no—
85C23×C4×C43C2311yescharacteristic
86C23×C4×C43C2311yescharacteristic
87C2×SD16×C43—22no—
88C2×SD16×C43—22no—
89C2×SD16×C43—41no—
90C2×D8×C43—22no—
91C2×D8×C43—22no—
92C2×D8×C43—41no—
93C2×M16×C43—22no—
94C2×M16×C43—41no—
95C2×M16×C43—41no—
96C22×C8×C43C2311yescharacteristic
97C22×C8×C43C2311yescharacteristic
98C22×C8×C43C2311yescharacteristic
99C22×C8×C43C2311yescharacteristic
100C4⋊Q8×C43—22no—
101C4⋊Q8×C43—22no—
102#123×C43—28no—
103#123×C43—28no—
104C22⋊Q8×C43—28no—
105C22⋊Q8×C43—22no—
106C22⋊Q8×C43—41no—
107#121×C43—22no—
108#121×C43—22no—
109#121×C43—22no—
110#121×C43—22no—
111#121×C43—41no—
112#121×C43D414yescomplemented
113C4×D4×C43—22no—
114C4×D4×C43—22no—
115C4×D4×C43—22no—
116C4×D4×C43—22no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43—22no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43—22no—
122C2×C4⋊C4×C43—22no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43D411yescharacteristic
125C2×C4⋊C4×C43D414yescomplemented
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43D411yescharacteristic
140C2×C22⋊C4×C43D411yescharacteristic
141C2×C42×C43C2311yescharacteristic
142#103×C43—22no—
143#103×C43—22no—
144#103×C43—22no—
145#102×C43—22no—
146#102×C43—22no—
147#102×C43—22no—
148#102×C43—41no—
149#102×C43—41no—
150C22⋊C8×C43—22no—
151C22⋊C8×C43—41no—
152C22⋊C8×C43—41no—
153#95×C43—21no—
154#95×C43—21no—
155#95×C43—21no—
156C24×C43—21no—
157C24×C43—21no—
158C24×C43C2×D411yescharacteristic
159C24×C43C2×D411yescharacteristic
160#41×C43—28no—
161#41×C43—44no—
162#41×C43—44no—
163#41×C43—44no—
164#41×C43—432no—
165C2×Q8×C43—24no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—42no—
172C2×Q8×C43—42no—
173C2×Q8×C43#4112yescomplemented
174C2×D4×C43—24no—
175C2×D4×C43—22no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—22no—
179C2×D4×C43—24no—
180C2×D4×C43—22no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—42no—
190C2×D4×C43—42no—
191C2×D4×C43—42no—
192C2×D4×C43—42no—
193C2×D4×C43—42no—
194C2×D4×C43—42no—
195C2×D4×C43—42no—
196C2×D4×C43—42no—
197C2×D4×C43—42no—
198C2×D4×C43—81no—
199C2×D4×C43C2×D412yes—
200C2×D4×C43#4112yescomplemented
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—24no—
206C22×C4×C43—24no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—24no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—42no—
221C22×C4×C43—42no—
222C22×C4×C43—42no—
223C22×C4×C43—42no—
224C22×C4×C43—42no—
225C22×C4×C43—42no—
226C22×C4×C43—42no—
227C22×C4×C43—42no—
228C22×C4×C43—42no—
229C22×C4×C43C2×D412yes—
230C22×C4×C43C2×D412yes—
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2×D411yescharacteristic
235C22×C4×C43C2411yescharacteristic
236SD16×C43—44no—
237D8×C43—44no—
238M16×C43—44no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43—21no—
251C4⋊C4×C43—24no—
252C4⋊C4×C43—24no—
253C4⋊C4×C43—24no—
254C4⋊C4×C43—22no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—42no—
263C4⋊C4×C43C2×D412yes—
264C4⋊C4×C43C2×D412yes—
265C4⋊C4×C43C2×D412yes—
266C22⋊C4×C43—24no—
267C22⋊C4×C43—24no—
268C22⋊C4×C43—24no—
269C22⋊C4×C43—22no—
270C22⋊C4×C43—22no—
271C22⋊C4×C43—42no—
272C22⋊C4×C43—42no—
273C22⋊C4×C43—42no—
274C22⋊C4×C43—81no—
275C22⋊C4×C43—81no—
276C42×C43—21no—
277C42×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—22no—
291C23×C43—22no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43#12012yes—
305C23×C43AGL(1,ℤ/8)12yes—
306C23×C43C22×D411yescharacteristic
307Q8×C43—22no—
308Q8×C43—22no—
309Q8×C43—48no—
310Q8×C43—41no—
311Q8×C43—41no—
312D4×C43—28no—
313D4×C43—22no—
314D4×C43—22no—
315D4×C43—22no—
316D4×C43—22no—
317D4×C43—48no—
318D4×C43—48no—
319D4×C43—48no—
320D4×C43—41no—
321D4×C43—41no—
322D4×C43—41no—
323D4×C43—41no—
324D4×C43—84no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—21no—
339C2×C4×C43—22no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—48no—
344C2×C4×C43—48no—
345C2×C4×C43—48no—
346C2×C4×C43—48no—
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—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43#12012yes—
366C2×C4×C43AGL(1,ℤ/8)12yes—
367C2×C4×C43C22×D411yescharacteristic
368C2×C4×C43C22×D411yescharacteristic
369C2×C4×C43C2×#4111yescharacteristic
370C2×C4×C43C2×#4111yescharacteristic
371C2×C4×C43H(5,𝔽2)11yescharacteristic
372C2×C4×C43H(5,𝔽2)11yescharacteristic
373C8×C43—41no—
374C8×C43—41no—
375C8×C43—41no—
376C8×C43—41no—
377#23972C4311yesmaximal, characteristic, direct product factor, Sylow
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—42no—
393C22×C43—42no—
394C22×C43—42no—
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—81no—
399C22×C43—81no—
400C22×C43—81no—
401C22×C43—81no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43—81no—
406C22×C43C2×#12011yescharacteristic
407C22×C43#54611yescharacteristic
408C22×C43#54611yescharacteristic
409C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
410C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
411C22×C43#57711yescharacteristic
412C22×C43#57811yescharacteristic
413C4×C43—22no—
414C4×C43—22no—
415C4×C43—41no—
416C4×C43—42no—
417C4×C43—42no—
418C4×C43—42no—
419C4×C43—42no—
420C4×C43—41no—
421C4×C43—81no—
422C4×C43—81no—
423C4×C43#52511yescharacteristic
424C4×C43#53511yescharacteristic
425C4×C43#54611yescharacteristic
426C4×C43#54611yescharacteristic
427C2×#547C2×C4311yescharacteristic, complemented
428C2×#449C2×C4311yescharacteristic, complemented
429C2×#417C2×C4311yescharacteristic, complemented
430#2407C2×C4311yescharacteristic, complemented
431#2024C2×C4311yescharacteristic, complemented
432#2023C2×C4311yescharacteristic, complemented
433#2000C2×C4311yescharacteristic, complemented
434#1999C2×C4311yescharacteristic, complemented
435#1895C2×C4311yescharacteristic, complemented
436#1879C2×C4311yescharacteristic, complemented
437#1877C2×C4311yescharacteristic, complemented
438#1874C2×C4311yescharacteristic, complemented
439#1872C2×C4311yescharacteristic, complemented
440#1870C2×C4311yescharacteristic, complemented
441#1824C2×C4311yescharacteristic, complemented
442C2×C43—42no—
443C2×C43—42no—
444C2×C43—82no—
445C2×C43—82no—
446C2×C43#240411yescharacteristic
447C2×C43#300311yescharacteristic
448C2×C43#301311yescharacteristic
449C2×C43#330611yescharacteristic
450C2×C43#330811yescharacteristic
451C2×C43#333011yescharacteristic
452C2×C43#333211yescharacteristic
453C22×#41—21no—
454C22×#41C22×C4311yescharacteristic
455C22×SD16C22×C4311yescharacteristic
456C22×D8C22×C4311yescharacteristic
457C22×M16C22×C4311yescharacteristic
458#547—24no—
459#547—24no—
460C2×C4⋊Q8C22×C4311yescharacteristic
461C2×#123—21no—
462C2×#123—21no—
463C2×C22⋊Q8—21no—
464C2×C22⋊Q8C22×C4311yescharacteristic
465C2×#121C22×C4311yescharacteristic
466C2×#121C22×C4311yescharacteristic
467C2×#121C22×C4311yescharacteristic
468C2×C4×D4C22×C4311yescharacteristic
469C2×C4×D4C22×C4311yescharacteristic
470C22×C4⋊C4C22×C4311yescharacteristic
471C22×C4⋊C4C22×C4311yescharacteristic
472#449—24no—
473#417—24no—
474C2×#103C22×C4311yescharacteristic
475C2×#103C22×C4311yescharacteristic
476C2×#103C22×C4311yescharacteristic
477C2×#102C22×C4311yescharacteristic
478C2×#102C22×C4311yescharacteristic
479C2×#102C22×C4311yescharacteristic
480C2×#102C22×C4311yescharacteristic
481C2×#102C22×C4311yescharacteristic
482C2×C22⋊C8C22×C4311yescharacteristic
483C2×C22⋊C8C22×C4311yescharacteristic
484C2×C22⋊C8C22×C4311yescharacteristic
485#394—21no—
486#392—21no—
487#391C22×C4311yescharacteristic
488#390C22×C4311yescharacteristic
489#386—21no—
490#385—21no—
491#380C22×C4311yescharacteristic
492#340C22×C4311yescharacteristic
493#340C22×C4311yescharacteristic
494#340C22×C4311yescharacteristic
495#340C22×C4311yescharacteristic
496#340C22×C4311yescharacteristic
497#340C22×C4311yescharacteristic
498#336C22×C4311yescharacteristic
499#336C22×C4311yescharacteristic
500C43#2397211yescharacteristic, direct product factor, Sylow
501C2×#41—28no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—44no—
509C2×#41—44no—
510C22×Q8—21no—
511C22×Q8C23×C4311yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4D4×C4311yescharacteristic
517C22×D4C23×C4311yescharacteristic
518C22×D4C23×C4311yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C23×C4311yescharacteristic
524C23×C4C23×C4311yescharacteristic
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—41no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—41no—
531C2×M16—22no—
532C2×M16—41no—
533C2×M16—41no—
534C22×C8C23×C4311yescharacteristic
535C22×C8C23×C4311yescharacteristic
536C22×C8C23×C4311yescharacteristic
537C22×C8C23×C4311yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540#123—28no—
541#123—28no—
542C22⋊Q8—28no—
543C22⋊Q8—22no—
544C22⋊Q8—41no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—22no—
549#121—41no—
550#121D4×C4314yescomplemented
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4D4×C4311yescharacteristic
563C2×C4⋊C4D4×C4314yescomplemented
564C2×C4⋊C4C23×C4311yescharacteristic
565C2×C4⋊C4C23×C4311yescharacteristic
566C2×C4⋊C4C23×C4311yescharacteristic
567C2×C4⋊C4C23×C4311yescharacteristic
568C2×C4⋊C4C23×C4311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4D4×C4311yescharacteristic
578C2×C22⋊C4D4×C4311yescharacteristic
579C2×C42C23×C4311yescharacteristic
580#103—22no—
581#103—22no—
582#103—22no—
583#102—22no—
584#102—22no—
585#102—22no—
586#102—41no—
587#102—41no—
588C22⋊C8—22no—
589C22⋊C8—41no—
590C22⋊C8—41no—
591#95—21no—
592#95—21no—
593#95—21no—
594C24—21no—
595C24—21no—
596C24C2×D4×C4311yescharacteristic
597C24C2×D4×C4311yescharacteristic
598#41—28no—
599#41—44no—
600#41—44no—
601#41—44no—
602#41—432no—
603C2×Q8—24no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8#41×C4312yescomplemented
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—81no—
637C2×D4C2×D4×C4312yes—
638C2×D4#41×C4312yescomplemented
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C2×D4×C4311yescharacteristic
668C22×C4C2×D4×C4311yescharacteristic
669C22×C4C2×D4×C4311yescharacteristic
670C22×C4C2×D4×C4312yes—
671C22×C4C2×D4×C4312yes—
672C22×C4C2×D4×C4311yescharacteristic
673C22×C4C24×C4311yescharacteristic
674SD16—44no—
675D8—44no—
676M16—44no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—42no—
701C4⋊C4C2×D4×C4312yes—
702C4⋊C4C2×D4×C4312yes—
703C4⋊C4C2×D4×C4312yes—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—22no—
707C22⋊C4—24no—
708C22⋊C4—22no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—21no—
715C42—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23#120×C4312yes—
743C23AGL(1,ℤ/8)×C4312yes—
744C23C22×D4×C4311yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—48no—
748Q8—41no—
749Q8—41no—
750D4—28no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—48no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—84no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4#120×C4312yes—
804C2×C4AGL(1,ℤ/8)×C4312yes—
805C2×C4C22×D4×C4311yescharacteristic
806C2×C4C22×D4×C4311yescharacteristic
807C2×C4C2×#41×C4311yescharacteristic
808C2×C4C2×#41×C4311yescharacteristic
809C2×C4H(5,𝔽2)×C4311yescharacteristic
810C2×C4H(5,𝔽2)×C4311yescharacteristic
811C8—41no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22C2×#120×C4311yescharacteristic
844C22C43×#54611yescharacteristic
845C22C43×#54611yescharacteristic
846C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
847C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
848C22C43×#57711yescharacteristic
849C22C43×#57811yescharacteristic
850C4—22no—
851C4—22no—
852C4—41no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—41no—
858C4—81no—
859C4—81no—
860C4C43×#52511yescharacteristic
861C4C43×#53511yescharacteristic
862C4C43×#54611yescharacteristic
863C4C43×#54611yescharacteristic
864C2—42no—
865C2—42no—
866C2—82no—
867C2—82no—
868C2C43×#240411yescharacteristic
869C2C43×#300311yescharacteristic
870C2C43×#301311yescharacteristic
871C2C43×#330611yescharacteristic
872C2C43×#330811yescharacteristic
873C2C43×#333011yescharacteristic
874C2C43×#333211yescharacteristic
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×#547C2semidirect
2. C2×C43×#449C2semidirect
3. C2×C43×#417C2semidirect
4. C43×#2407C2semidirect
5. C43×#2024C2semidirect
6. C43×#2023C2semidirect
7. C43×#2000C2semidirect
8. C43×#1999C2semidirect
9. C43×#1895C2semidirect
10. C43×#1879C2semidirect
11. C43×#1877C2semidirect
12. C43×#1874C2semidirect
13. C43×#1872C2semidirect
14. C43×#1870C2semidirect
15. C43×#1824C2semidirect
112. #121×C43D4semidirect
125. C2×C4⋊C4×C43D4semidirect
173. C2×Q8×C43#41semidirect
200. C2×D4×C43#41semidirect
377. #23972C43direct (N × H)
427. C2×#547C2×C43semidirect
428. C2×#449C2×C43semidirect
429. C2×#417C2×C43semidirect
430. #2407C2×C43semidirect
431. #2024C2×C43semidirect
432. #2023C2×C43semidirect
433. #2000C2×C43semidirect
434. #1999C2×C43semidirect
435. #1895C2×C43semidirect
436. #1879C2×C43semidirect
437. #1877C2×C43semidirect
438. #1874C2×C43semidirect
439. #1872C2×C43semidirect
440. #1870C2×C43semidirect
441. #1824C2×C43semidirect
500. C43#23972direct (N × H)
550. #121D4×C43semidirect
563. C2×C4⋊C4D4×C43semidirect
611. C2×Q8#41×C43semidirect
638. C2×D4#41×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5472
C2×C43×#4492
C2×C43×#4172
C43×#24072
C43×#20242
C43×#20232
C43×#20002
C43×#19992
C43×#18952
C43×#18792
C43×#18772
C43×#18742
C43×#18722
C43×#18702
C43×#18242
#2397243