Finite Group Databasebeta

← C43×#24663 #24944680

Subgroups — C43×#24663 #24944680

Order 11008.

912 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#463C211yesmaximal, characteristic, complemented
2C2×C43×#433C211yesmaximal, characteristic, complemented
3C43×#2620C211yesmaximal, characteristic, complemented
4C43×#2324C211yesmaximal, characteristic, complemented
5C43×#2036C211yesmaximal, characteristic, complemented
6C43×#2033C211yesmaximal, characteristic, complemented
7C43×#2000C211yesmaximal, characteristic, complemented
8C43×#1999C211yesmaximal, characteristic
9C43×#1983C211yesmaximal, characteristic, complemented
10C43×#1973C211yesmaximal, characteristic, complemented
11C43×#1970C211yesmaximal, characteristic, complemented
12C43×#1947C211yesmaximal, characteristic, complemented
13C43×#1936C211yesmaximal, characteristic, complemented
14C43×#1933C211yesmaximal, characteristic, complemented
15C43×#1802C211yesmaximal, characteristic, complemented
16C22×SD16×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C2×#124×C43C2211yescharacteristic
19C2×C22⋊Q8×C43C2211yescharacteristic
20C2×#121×C43C2211yescharacteristic
21C2×#121×C43C2211yescharacteristic
22C2×C4×D4×C43C2211yescharacteristic
23C2×#117×C43C2211yescharacteristic
24C43×#463—24no—
25C43×#433—24no—
26C2×#107×C43C2211yescharacteristic
27C2×#107×C43C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×C4⋊C8×C43C2211yescharacteristic
30C2×#103×C43C2211yescharacteristic
31C2×#103×C43C2211yescharacteristic
32C2×#103×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×C22⋊C8×C43C2211yescharacteristic
40C2×#97×C43C2211yescharacteristic
41C2×C4×C8×C43C2211yescharacteristic
42C43×#396—21no—
43C43×#396—21no—
44C43×#394—21no—
45C43×#394—21no—
46C43×#391C2211yescharacteristic
47C43×#390—21no—
48C43×#390C2211yescharacteristic
49C43×#390C2211yescharacteristic
50C43×#389C2211yescharacteristic
51C43×#388—21no—
52C43×#386—21no—
53C43×#385—21no—
54C43×#384C2211yescharacteristic
55C43×#380C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Q8×C43C2311yescharacteristic
62C22×D4×C43—21no—
63C22×D4×C43—21no—
64C22×D4×C43C2311yescharacteristic
65C22×D4×C43C2311yescharacteristic
66C23×C4×C43—21no—
67C23×C4×C43C2311yescharacteristic
68C2×SD16×C43—22no—
69C2×SD16×C43—22no—
70C2×SD16×C43—41no—
71C2×D8×C43—22no—
72C2×D8×C43—22no—
73C2×D8×C43—41no—
74C22×C8×C43C2311yescharacteristic
75C22×C8×C43C2311yescharacteristic
76C22×C8×C43C2311yescharacteristic
77C22×C8×C43C2311yescharacteristic
78#124×C43—22no—
79#124×C43—22no—
80C22⋊Q8×C43—41no—
81C22⋊Q8×C43—41no—
82#121×C43—22no—
83#121×C43—22no—
84#121×C43—41no—
85#121×C43—41no—
86C4×D4×C43—22no—
87C4×D4×C43—22no—
88#117×C43—22no—
89#117×C43—22no—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43D411yescharacteristic
95C2×C4⋊C4×C43D411yescharacteristic
96C2×C4⋊C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43D411yescharacteristic
113C2×C22⋊C4×C43D411yescharacteristic
114C2×C42×C43—21no—
115C2×C42×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117#107×C43—41no—
118#107×C43—41no—
119C4⋊C8×C43—22no—
120C4⋊C8×C43D414yescomplemented
121#103×C43—22no—
122#103×C43—22no—
123#103×C43—41no—
124#102×C43—22no—
125#102×C43—22no—
126#102×C43—41no—
127#102×C43—41no—
128#102×C43—41no—
129C22⋊C8×C43—22no—
130C22⋊C8×C43—22no—
131#97×C43—22no—
132C4×C8×C43—22no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138C24×C43—21no—
139C24×C43—21no—
140C24×C43C2×D411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×D4×C43—24no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—42no—
160C2×D4×C43—81no—
161C2×D4×C43—81no—
162C2×D4×C43—81no—
163C2×D4×C43—81no—
164C2×D4×C43#4112yes—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—42no—
178C22×C4×C43—81no—
179C22×C4×C43—81no—
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2411yescharacteristic
186SD16×C43—44no—
187D8×C43—44no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43C2×D412yes—
199C2×C8×C43C2×D412yes—
200C4⋊C4×C43—22no—
201C4⋊C4×C43—22no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—42no—
212C4⋊C4×C43—81no—
213C4⋊C4×C43—81no—
214C4⋊C4×C43—81no—
215C4⋊C4×C43#4112yes—
216C22⋊C4×C43—24no—
217C22⋊C4×C43—22no—
218C22⋊C4×C43—22no—
219C22⋊C4×C43—42no—
220C22⋊C4×C43—42no—
221C22⋊C4×C43—42no—
222C22⋊C4×C43—42no—
223C22⋊C4×C43—42no—
224C22⋊C4×C43—81no—
225C22⋊C4×C43—81no—
226C22⋊C4×C43—81no—
227C22⋊C4×C43—81no—
228C22⋊C4×C43—81no—
229C42×C43—21no—
230C42×C43—21no—
231C42×C43—81no—
232C42×C43C2×D412yes—
233C42×C43#4112yes—
234C23×C43—21no—
235C23×C43—22no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43C22×D411yescharacteristic
256Q8×C43—41no—
257Q8×C43—41no—
258Q8×C43—41no—
259Q8×C43—41no—
260D4×C43—22no—
261D4×C43—22no—
262D4×C43—41no—
263D4×C43—41no—
264D4×C43—41no—
265D4×C43—41no—
266D4×C43—41no—
267D4×C43—41no—
268D4×C43—84no—
269D4×C43—84no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—22no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—84no—
306C2×C4×C43#12112yes—
307C2×C4×C43#12112yes—
308C2×C4×C43C22×D411yescharacteristic
309C2×C4×C43C2×#4111yescharacteristic
310C2×C4×C43C2×#4111yescharacteristic
311C2×C4×C43C2×#4111yescharacteristic
312C2×C4×C43H(5,𝔽2)11yescharacteristic
313C2×C4×C43H(5,𝔽2)11yescharacteristic
314C8×C43—22no—
315C8×C43—22no—
316C8×C43—41no—
317C8×C43—41no—
318#24663C4311yesmaximal, characteristic, direct product factor, Sylow
319C22×C43—41no—
320C22×C43—42no—
321C22×C43—41no—
322C22×C43—42no—
323C22×C43—41no—
324C22×C43—42no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—81no—
330C22×C43—81no—
331C22×C43—81no—
332C22×C43—81no—
333C22×C43—81no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43—81no—
340C22×C43C2×#12111yescharacteristic
341C22×C43#52511yescharacteristic
342C22×C43#53511yescharacteristic
343C22×C43#57611yescharacteristic
344C22×C43#57611yescharacteristic
345C22×C43#57711yescharacteristic
346C22×C43#57811yescharacteristic
347C4×C43—22no—
348C4×C43—22no—
349C4×C43—42no—
350C4×C43—41no—
351C4×C43—41no—
352C4×C43—41no—
353C4×C43—81no—
354C4×C43—81no—
355C4×C43—81no—
356C4×C43—81no—
357C4×C43—81no—
358C4×C43#54611yescharacteristic
359C4×C43#55011yescharacteristic
360C4×C43#55311yescharacteristic
361C4×C43#55511yescharacteristic
362C2×#463C2×C4311yescharacteristic, complemented
363C2×#433C2×C4311yescharacteristic, complemented
364#2620C2×C4311yescharacteristic, complemented
365#2324C2×C4311yescharacteristic, complemented
366#2036C2×C4311yescharacteristic, complemented
367#2033C2×C4311yescharacteristic, complemented
368#2000C2×C4311yescharacteristic, complemented
369#1999C2×C4311yescharacteristic
370#1983C2×C4311yescharacteristic, complemented
371#1973C2×C4311yescharacteristic, complemented
372#1970C2×C4311yescharacteristic, complemented
373#1947C2×C4311yescharacteristic, complemented
374#1936C2×C4311yescharacteristic, complemented
375#1933C2×C4311yescharacteristic, complemented
376#1802C2×C4311yescharacteristic, complemented
377C2×C43—81no—
378C2×C43—82no—
379C2×C43—161no—
380C2×C43#241411yescharacteristic
381C2×C43#306111yescharacteristic
382C2×C43#306211yescharacteristic
383C2×C43#311811yescharacteristic
384C2×C43#312411yescharacteristic
385C2×C43#322011yescharacteristic
386C2×C43#322511yescharacteristic
387C22×SD16C22×C4311yescharacteristic
388C22×D8C22×C4311yescharacteristic
389C2×#124C22×C4311yescharacteristic
390C2×C22⋊Q8C22×C4311yescharacteristic
391C2×#121C22×C4311yescharacteristic
392C2×#121C22×C4311yescharacteristic
393C2×C4×D4C22×C4311yescharacteristic
394C2×#117C22×C4311yescharacteristic
395#463—24no—
396#433—24no—
397C2×#107C22×C4311yescharacteristic
398C2×#107C22×C4311yescharacteristic
399C2×C4⋊C8C22×C4311yescharacteristic
400C2×C4⋊C8C22×C4311yescharacteristic
401C2×#103C22×C4311yescharacteristic
402C2×#103C22×C4311yescharacteristic
403C2×#103C22×C4311yescharacteristic
404C2×#102C22×C4311yescharacteristic
405C2×#102C22×C4311yescharacteristic
406C2×#102C22×C4311yescharacteristic
407C2×#102C22×C4311yescharacteristic
408C2×#102C22×C4311yescharacteristic
409C2×C22⋊C8C22×C4311yescharacteristic
410C2×C22⋊C8C22×C4311yescharacteristic
411C2×#97C22×C4311yescharacteristic
412C2×C4×C8C22×C4311yescharacteristic
413#396—21no—
414#396—21no—
415#394—21no—
416#394—21no—
417#391C22×C4311yescharacteristic
418#390—21no—
419#390C22×C4311yescharacteristic
420#390C22×C4311yescharacteristic
421#389C22×C4311yescharacteristic
422#388—21no—
423#386—21no—
424#385—21no—
425#384C22×C4311yescharacteristic
426#380C22×C4311yescharacteristic
427C4×C4⋊C4C22×C4311yescharacteristic
428#340C22×C4311yescharacteristic
429#340C22×C4311yescharacteristic
430#340C22×C4311yescharacteristic
431#340C22×C4311yescharacteristic
432C43#2466311yescharacteristic, direct product factor, Sylow
433C22×Q8C23×C4311yescharacteristic
434C22×D4—21no—
435C22×D4—21no—
436C22×D4C23×C4311yescharacteristic
437C22×D4C23×C4311yescharacteristic
438C23×C4—21no—
439C23×C4C23×C4311yescharacteristic
440C2×SD16—22no—
441C2×SD16—22no—
442C2×SD16—41no—
443C2×D8—22no—
444C2×D8—22no—
445C2×D8—41no—
446C22×C8C23×C4311yescharacteristic
447C22×C8C23×C4311yescharacteristic
448C22×C8C23×C4311yescharacteristic
449C22×C8C23×C4311yescharacteristic
450#124—22no—
451#124—22no—
452C22⋊Q8—41no—
453C22⋊Q8—41no—
454#121—22no—
455#121—22no—
456#121—41no—
457#121—41no—
458C4×D4—22no—
459C4×D4—22no—
460#117—22no—
461#117—22no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4D4×C4311yescharacteristic
467C2×C4⋊C4D4×C4311yescharacteristic
468C2×C4⋊C4C23×C4311yescharacteristic
469C2×C4⋊C4C23×C4311yescharacteristic
470C2×C4⋊C4C23×C4311yescharacteristic
471C2×C4⋊C4C23×C4311yescharacteristic
472C2×C4⋊C4C23×C4311yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4D4×C4311yescharacteristic
485C2×C22⋊C4D4×C4311yescharacteristic
486C2×C42—21no—
487C2×C42C23×C4311yescharacteristic
488C2×C42C23×C4311yescharacteristic
489#107—41no—
490#107—41no—
491C4⋊C8—22no—
492C4⋊C8D4×C4314yescomplemented
493#103—22no—
494#103—22no—
495#103—41no—
496#102—22no—
497#102—22no—
498#102—41no—
499#102—41no—
500#102—41no—
501C22⋊C8—22no—
502C22⋊C8—22no—
503#97—22no—
504C4×C8—22no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510C24—21no—
511C24—21no—
512C24C2×D4×C4311yescharacteristic
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×D4—24no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—42no—
532C2×D4—81no—
533C2×D4—81no—
534C2×D4—81no—
535C2×D4—81no—
536C2×D4#41×C4312yes—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—42no—
550C22×C4—81no—
551C22×C4—81no—
552C22×C4C2×D4×C4311yescharacteristic
553C22×C4C2×D4×C4311yescharacteristic
554C22×C4C2×D4×C4311yescharacteristic
555C22×C4C2×D4×C4311yescharacteristic
556C22×C4C2×D4×C4311yescharacteristic
557C22×C4C24×C4311yescharacteristic
558SD16—44no—
559D8—44no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8C2×D4×C4312yes—
571C2×C8C2×D4×C4312yes—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—42no—
584C4⋊C4—81no—
585C4⋊C4—81no—
586C4⋊C4—81no—
587C4⋊C4#41×C4312yes—
588C22⋊C4—24no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—81no—
597C22⋊C4—81no—
598C22⋊C4—81no—
599C22⋊C4—81no—
600C22⋊C4—81no—
601C42—21no—
602C42—21no—
603C42—81no—
604C42C2×D4×C4312yes—
605C42#41×C4312yes—
606C23—21no—
607C23—22no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23C22×D4×C4311yescharacteristic
628Q8—41no—
629Q8—41no—
630Q8—41no—
631Q8—41no—
632D4—22no—
633D4—22no—
634D4—41no—
635D4—41no—
636D4—41no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—84no—
641D4—84no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—84no—
678C2×C4#121×C4312yes—
679C2×C4#121×C4312yes—
680C2×C4C22×D4×C4311yescharacteristic
681C2×C4C2×#41×C4311yescharacteristic
682C2×C4C2×#41×C4311yescharacteristic
683C2×C4C2×#41×C4311yescharacteristic
684C2×C4H(5,𝔽2)×C4311yescharacteristic
685C2×C4H(5,𝔽2)×C4311yescharacteristic
686C8—22no—
687C8—22no—
688C8—41no—
689C8—41no—
690C22—41no—
691C22—42no—
692C22—41no—
693C22—42no—
694C22—41no—
695C22—42no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22C2×#121×C4311yescharacteristic
712C22C43×#52511yescharacteristic
713C22C43×#53511yescharacteristic
714C22C43×#57611yescharacteristic
715C22C43×#57611yescharacteristic
716C22C43×#57711yescharacteristic
717C22C43×#57811yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—81no—
725C4—81no—
726C4—81no—
727C4—81no—
728C4—81no—
729C4C43×#54611yescharacteristic
730C4C43×#55011yescharacteristic
731C4C43×#55311yescharacteristic
732C4C43×#55511yescharacteristic
733C2—81no—
734C2—82no—
735C2—161no—
736C2C43×#241411yescharacteristic
737C2C43×#306111yescharacteristic
738C2C43×#306211yescharacteristic
739C2C43×#311811yescharacteristic
740C2C43×#312411yescharacteristic
741C2C43×#322011yescharacteristic
742C2C43×#322511yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×#117×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#463C2semidirect
2. C2×C43×#433C2semidirect
3. C43×#2620C2semidirect
4. C43×#2324C2semidirect
5. C43×#2036C2semidirect
6. C43×#2033C2semidirect
7. C43×#2000C2semidirect
9. C43×#1983C2semidirect
10. C43×#1973C2semidirect
11. C43×#1970C2semidirect
12. C43×#1947C2semidirect
13. C43×#1936C2semidirect
14. C43×#1933C2semidirect
15. C43×#1802C2semidirect
120. C4⋊C8×C43D4semidirect
318. #24663C43direct (N × H)
362. C2×#463C2×C43semidirect
363. C2×#433C2×C43semidirect
364. #2620C2×C43semidirect
365. #2324C2×C43semidirect
366. #2036C2×C43semidirect
367. #2033C2×C43semidirect
368. #2000C2×C43semidirect
370. #1983C2×C43semidirect
371. #1973C2×C43semidirect
372. #1970C2×C43semidirect
373. #1947C2×C43semidirect
374. #1936C2×C43semidirect
375. #1933C2×C43semidirect
376. #1802C2×C43semidirect
432. C43#24663direct (N × H)
492. C4⋊C8D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4632
C2×C43×#4332
C43×#26202
C43×#23242
C43×#20362
C43×#20332
C43×#20002
C43×#19992
C43×#19832
C43×#19732
C43×#19702
C43×#19472
C43×#19362
C43×#19332
C43×#18022
#2466343