Finite Group Databasebeta

← C43×#29601 #24949618

Subgroups — C43×#29601 #24949618

Order 11008.

1462 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#525C211yesmaximal, characteristic
2C2×C43×#485C211yesmaximal, characteristic, complemented
3C2×C43×#452C211yesmaximal, characteristic, complemented
4C43×#2848C211yesmaximal, characteristic, complemented
5C43×#2036C211yesmaximal, characteristic, complemented
6C43×#2035C211yesmaximal, characteristic, complemented
7C43×#2034C211yesmaximal, characteristic, complemented
8C43×#2033C211yesmaximal, characteristic, complemented
9C43×#2001C211yesmaximal, characteristic, complemented
10C43×#2001C211yesmaximal, characteristic, complemented
11C43×#2000C211yesmaximal, characteristic, complemented
12C43×#2000C211yesmaximal, characteristic, complemented
13C43×#1825C211yesmaximal, characteristic, complemented
14C43×#1788C211yesmaximal, characteristic, complemented
15C43×#1779C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C24×C4×C43C2211yescharacteristic
18C22×Q16×C43C2211yescharacteristic, complemented
19C22×SD16×C43C2211yescharacteristic, complemented
20C43×#525—24no—
21C43×#525—24no—
22C2×#123×C43—21no—
23C2×C22⋊Q8×C43C2211yescharacteristic
24C2×C22⋊Q8×C43C2211yescharacteristic
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×C22⋊Q8×C43C2211yescharacteristic
27C2×C22⋊Q8×C43C2211yescharacteristic
28C2×#121×C43C2211yescharacteristic
29C2×#121×C43C2211yescharacteristic
30C2×#120×C43—21no—
31C2×C4×D4×C43—21no—
32C2×C4×D4×C43—21no—
33C2×#117×C43C2211yescharacteristic
34C43×#485—24no—
35C43×#452—24no—
36C2×#107×C43C2211yescharacteristic, complemented
37C2×#106×C43C2211yescharacteristic, complemented
38C2×#103×C43C2211yescharacteristic, complemented
39C2×#103×C43C2211yescharacteristic, complemented
40C2×#103×C43C2211yescharacteristic, complemented
41C2×#103×C43C2211yescharacteristic, complemented
42C2×#103×C43C2211yescharacteristic, complemented
43C2×#102×C43C2211yescharacteristic, complemented
44C2×#102×C43C2211yescharacteristic, complemented
45C2×#102×C43C2211yescharacteristic, complemented
46C2×C22⋊C8×C43C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C2×C22⋊C8×C43C2211yescharacteristic
49C2×C22⋊C8×C43C2211yescharacteristic
50C2×C22⋊C8×C43C2211yescharacteristic
51C2×C22⋊C8×C43C2211yescharacteristic
52C43×#385—21no—
53C43×#385—21no—
54C43×#385—21no—
55C43×#380C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#379—21no—
59C43×#340C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C43×#340C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C25×C43D411yescharacteristic
64C2×#41×C43—22no—
65C2×#41×C43—41no—
66C2×#41×C43—41no—
67C2×#41×C43—41no—
68C2×#41×C43—41no—
69C2×#41×C43D414yes—
70C22×Q8×C43C2311yescharacteristic
71C22×Q8×C43C2311yescharacteristic
72C22×D4×C43—21no—
73C22×D4×C43—21no—
74C22×D4×C43—21no—
75C22×D4×C43C2311yescharacteristic
76C23×C4×C43—21no—
77C23×C4×C43—22no—
78C23×C4×C43—22no—
79C23×C4×C43—41no—
80C23×C4×C43—41no—
81C23×C4×C43—41no—
82C23×C4×C43—41no—
83C23×C4×C43D411yescharacteristic
84C23×C4×C43D411yescharacteristic
85C23×C4×C43D411yescharacteristic
86C23×C4×C43C2311yescharacteristic
87C23×C4×C43C2311yescharacteristic
88C23×C4×C43C2311yescharacteristic
89C2×Q16×C43—22no—
90C2×Q16×C43—41no—
91C2×Q16×C43—41no—
92C2×SD16×C43—22no—
93C2×SD16×C43—41no—
94C2×SD16×C43—41no—
95C22×C8×C43C2311yescharacteristic
96C22×C8×C43C2311yescharacteristic
97C22×C8×C43C2311yescharacteristic
98C22×C8×C43C2311yescharacteristic
99#123×C43—28no—
100C22⋊Q8×C43—22no—
101C22⋊Q8×C43—22no—
102C22⋊Q8×C43—22no—
103C22⋊Q8×C43—22no—
104C22⋊Q8×C43—22no—
105C22⋊Q8×C43—22no—
106C22⋊Q8×C43—41no—
107C22⋊Q8×C43—41no—
108C22⋊Q8×C43—41no—
109C22⋊Q8×C43—41no—
110#121×C43—22no—
111#121×C43—22no—
112#121×C43—22no—
113#121×C43—22no—
114#120×C43—28no—
115C4×D4×C43—28no—
116C4×D4×C43—28no—
117#117×C43—22no—
118#117×C43D414yes—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
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×C43—21no—
140C2×C42×C43—21no—
141#107×C43—22no—
142#106×C43—22no—
143#103×C43—22no—
144#103×C43—22no—
145#103×C43—22no—
146#103×C43—41no—
147#103×C43—41no—
148#102×C43—22no—
149#102×C43—41no—
150#102×C43—41no—
151C22⋊C8×C43—22no—
152C22⋊C8×C43—22no—
153C22⋊C8×C43—41no—
154C22⋊C8×C43—41no—
155C22⋊C8×C43—41no—
156C22⋊C8×C43—41no—
157#95×C43—21no—
158#95×C43—21no—
159#95×C43—21no—
160C24×C43—22no—
161C24×C43—22no—
162C24×C43—22no—
163C24×C43—21no—
164C24×C43—41no—
165C24×C43—41no—
166C24×C43—41no—
167C24×C43—41no—
168C24×C43C2×D411yescharacteristic
169C24×C43C2×D411yescharacteristic
170C24×C43C2×D411yescharacteristic
171#41×C43—44no—
172#41×C43—44no—
173#41×C43—44no—
174#41×C43—44no—
175C2×Q8×C43—21no—
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43—21no—
179C2×Q8×C43—21no—
180C2×Q8×C43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43C2×D412yes—
187C2×D4×C43—24no—
188C2×D4×C43—24no—
189C2×D4×C43—21no—
190C2×D4×C43—24no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—42no—
196C2×D4×C43—42no—
197C2×D4×C43—42no—
198C2×D4×C43—42no—
199C2×D4×C43—42no—
200C2×D4×C43—42no—
201C2×D4×C43C2×D412yes—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—22no—
207C22×C4×C43—22no—
208C22×C4×C43—24no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
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—21no—
221C22×C4×C43—22no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—41no—
230C22×C4×C43—41no—
231C22×C4×C43—41no—
232C22×C4×C43—41no—
233C22×C4×C43—41no—
234C22×C4×C43—41no—
235C22×C4×C43—44no—
236C22×C4×C43—44no—
237C22×C4×C43—44no—
238C22×C4×C43—44no—
239C22×C4×C43—42no—
240C22×C4×C43—42no—
241C22×C4×C43C2×D412yes—
242C22×C4×C43C2×D412yes—
243C22×C4×C43C2×D411yescharacteristic
244C22×C4×C43C2×D411yescharacteristic
245C22×C4×C43C2×D411yescharacteristic
246C22×C4×C43C2411yescharacteristic
247Q16×C43—44no—
248SD16×C43—44no—
249C2×C8×C43—21no—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—21no—
261C4⋊C4×C43—24no—
262C4⋊C4×C43—24no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43—42no—
272C4⋊C4×C43—42no—
273C4⋊C4×C43—42no—
274C4⋊C4×C43C2×D412yes—
275C4⋊C4×C43C2×D412yes—
276C22⋊C4×C43—24no—
277C22⋊C4×C43—24no—
278C22⋊C4×C43—24no—
279C22⋊C4×C43—24no—
280C22⋊C4×C43—24no—
281C22⋊C4×C43—42no—
282C22⋊C4×C43—42no—
283C22⋊C4×C43—42no—
284C22⋊C4×C43—42no—
285C22⋊C4×C43—42no—
286C22⋊C4×C43—42no—
287C42×C43—24no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43—21no—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—21no—
306C23×C43—22no—
307C23×C43—44no—
308C23×C43—44no—
309C23×C43—44no—
310C23×C43—44no—
311C23×C43—44no—
312C23×C43—44no—
313C23×C43—44no—
314C23×C43—41no—
315C23×C43—41no—
316C23×C43—41no—
317C23×C43—41no—
318C23×C43—41no—
319C23×C43—41no—
320C23×C43#12012yes—
321C23×C43#13512yes—
322C23×C43#13712yes—
323C23×C43C22×D411yescharacteristic
324Q8×C43—22no—
325Q8×C43—22no—
326Q8×C43—41no—
327Q8×C43—41no—
328Q8×C43—41no—
329Q8×C43—41no—
330Q8×C43—41no—
331Q8×C43—41no—
332D4×C43—22no—
333D4×C43—22no—
334D4×C43—48no—
335D4×C43—48no—
336D4×C43—48no—
337D4×C43—41no—
338D4×C43—41no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—22no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—44no—
355C2×C4×C43—44no—
356C2×C4×C43—48no—
357C2×C4×C43—44no—
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—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43#12012yes—
385C2×C4×C43C22×D411yescharacteristic
386C2×C4×C43C22×D411yescharacteristic
387C2×C4×C43H(5,𝔽2)11yescharacteristic
388C2×C4×C43H(5,𝔽2)11yescharacteristic
389C2×C4×C43H(5,𝔽2)11yescharacteristic
390C2×C4×C43H(5,𝔽2)11yescharacteristic
391C8×C43—41no—
392C8×C43—41no—
393C8×C43—41no—
394C8×C43—41no—
395#29601C4311yesmaximal, characteristic, direct product factor, Sylow
396C22×C43—22no—
397C22×C43—22no—
398C22×C43—22no—
399C22×C43—22no—
400C22×C43—22no—
401C22×C43—22no—
402C22×C43—22no—
403C22×C43—22no—
404C22×C43—22no—
405C22×C43—416no—
406C22×C43—41no—
407C22×C43—41no—
408C22×C43—41no—
409C22×C43—41no—
410C22×C43—41no—
411C22×C43—41no—
412C22×C43—41no—
413C22×C43—41no—
414C22×C43—41no—
415C22×C43—41no—
416C22×C43—41no—
417C22×C43—41no—
418C22×C43—42no—
419C22×C43—42no—
420C22×C43—42no—
421C22×C43—81no—
422C22×C43—81no—
423C22×C43—81no—
424C22×C43—81no—
425C22×C43C2×#12011yescharacteristic
426C22×C43#53411yescharacteristic
427C22×C43#53411yescharacteristic
428C22×C43C2×#13511yescharacteristic
429C22×C43C2×#13711yescharacteristic
430C22×C43#57511yescharacteristic
431C22×C43#57511yescharacteristic
432C4×C43—22no—
433C4×C43—41no—
434C4×C43—41no—
435C4×C43—42no—
436C4×C43—42no—
437C4×C43—42no—
438C4×C43—81no—
439C4×C43—81no—
440C4×C43—81no—
441C4×C43—81no—
442C4×C43#53411yescharacteristic
443C4×C43#53411yescharacteristic
444C4×C43#53511yescharacteristic
445C4×C43#53511yescharacteristic
446C2×#525C2×C4311yescharacteristic
447C2×#485C2×C4311yescharacteristic, complemented
448C2×#452C2×C4311yescharacteristic, complemented
449#2848C2×C4311yescharacteristic, complemented
450#2036C2×C4311yescharacteristic, complemented
451#2035C2×C4311yescharacteristic, complemented
452#2034C2×C4311yescharacteristic, complemented
453#2033C2×C4311yescharacteristic, complemented
454#2001C2×C4311yescharacteristic, complemented
455#2001C2×C4311yescharacteristic, complemented
456#2000C2×C4311yescharacteristic, complemented
457#2000C2×C4311yescharacteristic, complemented
458#1825C2×C4311yescharacteristic, complemented
459#1788C2×C4311yescharacteristic, complemented
460#1779C2×C4311yescharacteristic, complemented
461C2×C43—42no—
462C2×C43—42no—
463C2×C43—42no—
464C2×C43—82no—
465C2×C43#261311yescharacteristic
466C2×C43#300211yescharacteristic
467C2×C43#300711yescharacteristic
468C2×C43#319011yescharacteristic
469C2×C43#319111yescharacteristic
470C2×C43#319611yescharacteristic
471C2×C43#319711yescharacteristic
472C22×#41C22×C4311yescharacteristic
473C24×C4C22×C4311yescharacteristic
474C22×Q16C22×C4311yescharacteristic, complemented
475C22×SD16C22×C4311yescharacteristic, complemented
476#525—24no—
477#525—24no—
478C2×#123—21no—
479C2×C22⋊Q8C22×C4311yescharacteristic
480C2×C22⋊Q8C22×C4311yescharacteristic
481C2×C22⋊Q8C22×C4311yescharacteristic
482C2×C22⋊Q8C22×C4311yescharacteristic
483C2×C22⋊Q8C22×C4311yescharacteristic
484C2×#121C22×C4311yescharacteristic
485C2×#121C22×C4311yescharacteristic
486C2×#120—21no—
487C2×C4×D4—21no—
488C2×C4×D4—21no—
489C2×#117C22×C4311yescharacteristic
490#485—24no—
491#452—24no—
492C2×#107C22×C4311yescharacteristic, complemented
493C2×#106C22×C4311yescharacteristic, complemented
494C2×#103C22×C4311yescharacteristic, complemented
495C2×#103C22×C4311yescharacteristic, complemented
496C2×#103C22×C4311yescharacteristic, complemented
497C2×#103C22×C4311yescharacteristic, complemented
498C2×#103C22×C4311yescharacteristic, complemented
499C2×#102C22×C4311yescharacteristic, complemented
500C2×#102C22×C4311yescharacteristic, complemented
501C2×#102C22×C4311yescharacteristic, complemented
502C2×C22⋊C8C22×C4311yescharacteristic
503C2×C22⋊C8C22×C4311yescharacteristic
504C2×C22⋊C8C22×C4311yescharacteristic
505C2×C22⋊C8C22×C4311yescharacteristic
506C2×C22⋊C8C22×C4311yescharacteristic
507C2×C22⋊C8C22×C4311yescharacteristic
508#385—21no—
509#385—21no—
510#385—21no—
511#380C22×C4311yescharacteristic
512#380C22×C4311yescharacteristic
513#380C22×C4311yescharacteristic
514#379—21no—
515#340C22×C4311yescharacteristic, complemented
516#340C22×C4311yescharacteristic, complemented
517#340C22×C4311yescharacteristic, complemented
518#340C22×C4311yescharacteristic, complemented
519C43#2960111yescharacteristic, direct product factor, Sylow
520C25D4×C4311yescharacteristic
521C2×#41—22no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41—41no—
525C2×#41—41no—
526C2×#41D4×C4314yes—
527C22×Q8C23×C4311yescharacteristic
528C22×Q8C23×C4311yescharacteristic
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4C23×C4311yescharacteristic
533C23×C4—21no—
534C23×C4—22no—
535C23×C4—22no—
536C23×C4—41no—
537C23×C4—41no—
538C23×C4—41no—
539C23×C4—41no—
540C23×C4D4×C4311yescharacteristic
541C23×C4D4×C4311yescharacteristic
542C23×C4D4×C4311yescharacteristic
543C23×C4C23×C4311yescharacteristic
544C23×C4C23×C4311yescharacteristic
545C23×C4C23×C4311yescharacteristic
546C2×Q16—22no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×SD16—22no—
550C2×SD16—41no—
551C2×SD16—41no—
552C22×C8C23×C4311yescharacteristic
553C22×C8C23×C4311yescharacteristic
554C22×C8C23×C4311yescharacteristic
555C22×C8C23×C4311yescharacteristic
556#123—28no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#120—28no—
572C4×D4—28no—
573C4×D4—28no—
574#117—22no—
575#117D4×C4314yes—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4C23×C4311yescharacteristic
582C2×C4⋊C4C23×C4311yescharacteristic
583C2×C4⋊C4C23×C4311yescharacteristic
584C2×C4⋊C4C23×C4311yescharacteristic
585C2×C4⋊C4C23×C4311yescharacteristic
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C42—21no—
598#107—22no—
599#106—22no—
600#103—22no—
601#103—22no—
602#103—22no—
603#103—41no—
604#103—41no—
605#102—22no—
606#102—41no—
607#102—41no—
608C22⋊C8—22no—
609C22⋊C8—22no—
610C22⋊C8—41no—
611C22⋊C8—41no—
612C22⋊C8—41no—
613C22⋊C8—41no—
614#95—21no—
615#95—21no—
616#95—21no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—21no—
621C24—41no—
622C24—41no—
623C24—41no—
624C24—41no—
625C24C2×D4×C4311yescharacteristic
626C24C2×D4×C4311yescharacteristic
627C24C2×D4×C4311yescharacteristic
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×D4×C4312yes—
644C2×D4—24no—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4C2×D4×C4312yes—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—24no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—41no—
687C22×C4—41no—
688C22×C4—41no—
689C22×C4—41no—
690C22×C4—41no—
691C22×C4—41no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4C2×D4×C4311yescharacteristic
699C22×C4C2×D4×C4311yescharacteristic
700C22×C4C2×D4×C4311yescharacteristic
701C22×C4C2×D4×C4312yes—
702C22×C4C2×D4×C4312yes—
703C22×C4C24×C4311yescharacteristic
704Q16—44no—
705SD16—44no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C4⋊C4—24no—
719C4⋊C4—24no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—42no—
729C4⋊C4—42no—
730C4⋊C4—42no—
731C4⋊C4C2×D4×C4312yes—
732C4⋊C4C2×D4×C4312yes—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—24no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—42no—
744C42—24no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23#120×C4312yes—
778C23#135×C4312yes—
779C23#137×C4312yes—
780C23C22×D4×C4311yescharacteristic
781Q8—22no—
782Q8—22no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789D4—22no—
790D4—22no—
791D4—48no—
792D4—48no—
793D4—48no—
794D4—41no—
795D4—41no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—48no—
814C2×C4—44no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4#120×C4312yes—
842C2×C4C22×D4×C4311yescharacteristic
843C2×C4C22×D4×C4311yescharacteristic
844C2×C4H(5,𝔽2)×C4311yescharacteristic
845C2×C4H(5,𝔽2)×C4311yescharacteristic
846C2×C4H(5,𝔽2)×C4311yescharacteristic
847C2×C4H(5,𝔽2)×C4311yescharacteristic
848C8—41no—
849C8—41no—
850C8—41no—
851C8—41no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—416no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22C2×#120×C4311yescharacteristic
882C22C43×#53411yescharacteristic
883C22C43×#53411yescharacteristic
884C22C2×#135×C4311yescharacteristic
885C22C2×#137×C4311yescharacteristic
886C22C43×#57511yescharacteristic
887C22C43×#57511yescharacteristic
888C4—22no—
889C4—41no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4C43×#53411yescharacteristic
899C4C43×#53411yescharacteristic
900C4C43×#53511yescharacteristic
901C4C43×#53511yescharacteristic
902C2—42no—
903C2—42no—
904C2—42no—
905C2—82no—
906C2C43×#261311yescharacteristic
907C2C43×#300211yescharacteristic
908C2C43×#300711yescharacteristic
909C2C43×#319011yescharacteristic
910C2C43×#319111yescharacteristic
911C2C43×#319611yescharacteristic
912C2C43×#319711yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C24×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#485C2semidirect
3. C2×C43×#452C2semidirect
4. C43×#2848C2semidirect
5. C43×#2036C2semidirect
6. C43×#2035C2semidirect
7. C43×#2034C2semidirect
8. C43×#2033C2semidirect
9. C43×#2001C2semidirect
10. C43×#2001C2semidirect
11. C43×#2000C2semidirect
12. C43×#2000C2semidirect
13. C43×#1825C2semidirect
14. C43×#1788C2semidirect
15. C43×#1779C2semidirect
18. C22×Q16×C43C22semidirect
19. C22×SD16×C43C22semidirect
36. C2×#107×C43C22semidirect
37. C2×#106×C43C22semidirect
38. C2×#103×C43C22semidirect
39. C2×#103×C43C22semidirect
40. C2×#103×C43C22semidirect
41. C2×#103×C43C22semidirect
42. C2×#103×C43C22semidirect
43. C2×#102×C43C22semidirect
44. C2×#102×C43C22semidirect
45. C2×#102×C43C22semidirect
59. C43×#340C22semidirect
60. C43×#340C22semidirect
61. C43×#340C22semidirect
62. C43×#340C22semidirect
395. #29601C43direct (N × H)
447. C2×#485C2×C43semidirect
448. C2×#452C2×C43semidirect
449. #2848C2×C43semidirect
450. #2036C2×C43semidirect
451. #2035C2×C43semidirect
452. #2034C2×C43semidirect
453. #2033C2×C43semidirect
454. #2001C2×C43semidirect
455. #2001C2×C43semidirect
456. #2000C2×C43semidirect
457. #2000C2×C43semidirect
458. #1825C2×C43semidirect
459. #1788C2×C43semidirect
460. #1779C2×C43semidirect
474. C22×Q16C22×C43semidirect
475. C22×SD16C22×C43semidirect
492. C2×#107C22×C43semidirect
493. C2×#106C22×C43semidirect
494. C2×#103C22×C43semidirect
495. C2×#103C22×C43semidirect
496. C2×#103C22×C43semidirect
497. C2×#103C22×C43semidirect
498. C2×#103C22×C43semidirect
499. C2×#102C22×C43semidirect
500. C2×#102C22×C43semidirect
501. C2×#102C22×C43semidirect
515. #340C22×C43semidirect
516. #340C22×C43semidirect
517. #340C22×C43semidirect
518. #340C22×C43semidirect
519. C43#29601direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5252
C2×C43×#4852
C2×C43×#4522
C43×#28482
C43×#20362
C43×#20352
C43×#20342
C43×#20332
C43×#20012
C43×#20002
C43×#18252
C43×#17882
C43×#17792
#2960143