Finite Group Databasebeta

← C43×#24891 #24944908

Subgroups — C43×#24891 #24944908

Order 11008.

1006 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#485C211yesmaximal, characteristic, complemented
2C2×C43×#417C211yesmaximal, characteristic, complemented
3C43×#2407C211yesmaximal, characteristic
4C43×#2352C211yesmaximal, characteristic, complemented
5C43×#2092C211yesmaximal, characteristic, complemented
6C43×#2074C211yesmaximal, characteristic, complemented
7C43×#2035C211yesmaximal, characteristic, complemented
8C43×#2034C211yesmaximal, characteristic, complemented
9C43×#1927C211yesmaximal, characteristic, complemented
10C43×#1926C211yesmaximal, characteristic, complemented
11C43×#1875C211yesmaximal, characteristic, complemented
12C43×#1870C211yesmaximal, characteristic, complemented
13C43×#1853C211yesmaximal, characteristic, complemented
14C43×#1809C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C22×M16×C43C2211yescharacteristic
18C2×C22⋊Q8×C43C2211yescharacteristic
19C2×#121×C43C2211yescharacteristic
20C2×C4×D4×C43C2211yescharacteristic
21C2×#117×C43C2211yescharacteristic
22C22×C4⋊C4×C43C2211yescharacteristic
23C43×#485—24no—
24C2×#107×C43C2211yescharacteristic
25C2×#106×C43C2211yescharacteristic
26C2×#106×C43C2211yescharacteristic
27C2×#106×C43C2211yescharacteristic
28C43×#417—24no—
29C2×#103×C43C2211yescharacteristic
30C2×#103×C43C2211yescharacteristic
31C2×#103×C43C2211yescharacteristic
32C2×#103×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic
37C2×C22⋊C8×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×C22⋊C8×C43C2211yescharacteristic
40C43×#394—21no—
41C43×#392—21no—
42C43×#391C2211yescharacteristic
43C43×#390C2211yescharacteristic
44C43×#388—21no—
45C43×#387—21no—
46C43×#386—21no—
47C43×#386—21no—
48C43×#385—21no—
49C43×#382C2211yescharacteristic
50C43×#380C2211yescharacteristic
51C43×#380C2211yescharacteristic
52C43×#380C2211yescharacteristic
53C4×C4⋊C4×C43C2211yescharacteristic
54C4×C22⋊C4×C43—21no—
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C2×#41×C43—22no—
62C2×#41×C43—22no—
63C2×#41×C43—22no—
64C2×#41×C43—22no—
65C2×#41×C43—41no—
66C2×#41×C43—41no—
67C22×Q8×C43C2311yescharacteristic
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70C22×D4×C43D411yescharacteristic
71C22×D4×C43C2311yescharacteristic
72C23×C4×C43—21no—
73C23×C4×C43—21no—
74C23×C4×C43C2311yescharacteristic
75C23×C4×C43C2311yescharacteristic
76C2×M16×C43—22no—
77C2×M16×C43—22no—
78C2×M16×C43—41no—
79C22×C8×C43C2311yescharacteristic
80C22×C8×C43C2311yescharacteristic
81C22×C8×C43C2311yescharacteristic
82C22×C8×C43C2311yescharacteristic
83C22⋊Q8×C43—22no—
84C22⋊Q8×C43—41no—
85#121×C43—22no—
86#121×C43—41no—
87C4×D4×C43—22no—
88C4×D4×C43—22no—
89#117×C43—22no—
90#117×C43—41no—
91C2×C4⋊C4×C43—22no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—41no—
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×C4⋊C4×C43C2311yescharacteristic
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×C43D411yescharacteristic
111C2×C22⋊C4×C43D411yescharacteristic
112C2×C42×C43—21no—
113C2×C42×C43—21no—
114C2×C42×C43C2311yescharacteristic
115#107×C43—22no—
116#106×C43—22no—
117#106×C43—41no—
118#106×C43—41no—
119#103×C43—22no—
120#103×C43—22no—
121#103×C43—41no—
122#103×C43D414yescomplemented
123#102×C43—22no—
124#102×C43—22no—
125#102×C43—22no—
126#102×C43—41no—
127C22⋊C8×C43—22no—
128C22⋊C8×C43—22no—
129C22⋊C8×C43—41no—
130#95×C43—21no—
131#95×C43—21no—
132#95×C43—21no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138C24×C43—21no—
139C24×C43C2×D411yescharacteristic
140C24×C43C2×D411yescharacteristic
141#41×C43—28no—
142#41×C43—44no—
143#41×C43—44no—
144#41×C43—44no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43C2×D412yes—
151C2×D4×C43—21no—
152C2×D4×C43—22no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—41no—
158C2×D4×C43—41no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—81no—
165C2×D4×C43#4112yes—
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—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—42no—
184C22×C4×C43—42no—
185C22×C4×C43—42no—
186C22×C4×C43—42no—
187C22×C4×C43—42no—
188C22×C4×C43—81no—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43#4112yes—
194C22×C4×C43#4112yes—
195C22×C4×C43C2411yescharacteristic
196M16×C43—44no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43C2×D412yes—
209C4⋊C4×C43—22no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—42no—
222C4⋊C4×C43—42no—
223C4⋊C4×C43C2×D412yes—
224C22⋊C4×C43—22no—
225C22⋊C4×C43—22no—
226C22⋊C4×C43—42no—
227C22⋊C4×C43—42no—
228C22⋊C4×C43—42no—
229C22⋊C4×C43—42no—
230C22⋊C4×C43—42no—
231C22⋊C4×C43—81no—
232C22⋊C4×C43—81no—
233C22⋊C4×C43—81no—
234C42×C43—21no—
235C42×C43—21no—
236C42×C43—42no—
237C42×C43—81no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—22no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43#12312yes—
259C23×C43C22×D411yescharacteristic
260Q8×C43—22no—
261Q8×C43—22no—
262Q8×C43—41no—
263Q8×C43—41no—
264D4×C43—22no—
265D4×C43—22no—
266D4×C43—44no—
267D4×C43—48no—
268D4×C43—41no—
269D4×C43—41no—
270D4×C43—84no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—48no—
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—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—84no—
313C2×C4×C43#12312yes—
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×C4×C43C2×#4111yescharacteristic
318C2×C4×C43H(5,𝔽2)11yescharacteristic
319C2×C4×C43H(5,𝔽2)11yescharacteristic
320C8×C43—22no—
321C8×C43—41no—
322C8×C43—41no—
323C8×C43—41no—
324#24891C4311yesmaximal, characteristic, direct product factor, Sylow
325C22×C43—22no—
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—42no—
336C22×C43—41no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—42no—
340C22×C43—41no—
341C22×C43—42no—
342C22×C43—81no—
343C22×C43—81no—
344C22×C43—81no—
345C22×C43—81no—
346C22×C43C2×#12311yescharacteristic
347C22×C43D4211yescharacteristic
348C22×C43#54611yescharacteristic
349C22×C43#57511yescharacteristic
350C22×C43#57511yescharacteristic
351C22×C43#57711yescharacteristic
352C22×C43#57711yescharacteristic
353C4×C43—22no—
354C4×C43—41no—
355C4×C43—41no—
356C4×C43—41no—
357C4×C43—42no—
358C4×C43—42no—
359C4×C43—81no—
360C4×C43—81no—
361C4×C43—81no—
362C4×C43—81no—
363C4×C43—81no—
364C4×C43#52511yescharacteristic
365C4×C43#53811yescharacteristic
366C4×C43#54611yescharacteristic
367C4×C43#55111yescharacteristic
368C2×#485C2×C4311yescharacteristic, complemented
369C2×#417C2×C4311yescharacteristic, complemented
370#2407C2×C4311yescharacteristic
371#2352C2×C4311yescharacteristic, complemented
372#2092C2×C4311yescharacteristic, complemented
373#2074C2×C4311yescharacteristic, complemented
374#2035C2×C4311yescharacteristic, complemented
375#2034C2×C4311yescharacteristic, complemented
376#1927C2×C4311yescharacteristic, complemented
377#1926C2×C4311yescharacteristic, complemented
378#1875C2×C4311yescharacteristic, complemented
379#1870C2×C4311yescharacteristic, complemented
380#1853C2×C4311yescharacteristic, complemented
381#1809C2×C4311yescharacteristic, complemented
382#1788C2×C4311yescharacteristic, complemented
383C2×C43—42no—
384C2×C43—81no—
385C2×C43—82no—
386C2×C43#241811yescharacteristic
387C2×C43#309311yescharacteristic
388C2×C43#309911yescharacteristic
389C2×C43#327111yescharacteristic
390C2×C43#327511yescharacteristic
391C2×C43#330711yescharacteristic
392C2×C43#332311yescharacteristic
393C22×#41C22×C4311yescharacteristic
394C22×M16C22×C4311yescharacteristic
395C2×C22⋊Q8C22×C4311yescharacteristic
396C2×#121C22×C4311yescharacteristic
397C2×C4×D4C22×C4311yescharacteristic
398C2×#117C22×C4311yescharacteristic
399C22×C4⋊C4C22×C4311yescharacteristic
400#485—24no—
401C2×#107C22×C4311yescharacteristic
402C2×#106C22×C4311yescharacteristic
403C2×#106C22×C4311yescharacteristic
404C2×#106C22×C4311yescharacteristic
405#417—24no—
406C2×#103C22×C4311yescharacteristic
407C2×#103C22×C4311yescharacteristic
408C2×#103C22×C4311yescharacteristic
409C2×#103C22×C4311yescharacteristic
410C2×#102C22×C4311yescharacteristic
411C2×#102C22×C4311yescharacteristic
412C2×#102C22×C4311yescharacteristic
413C2×#102C22×C4311yescharacteristic
414C2×C22⋊C8C22×C4311yescharacteristic
415C2×C22⋊C8C22×C4311yescharacteristic
416C2×C22⋊C8C22×C4311yescharacteristic
417#394—21no—
418#392—21no—
419#391C22×C4311yescharacteristic
420#390C22×C4311yescharacteristic
421#388—21no—
422#387—21no—
423#386—21no—
424#386—21no—
425#385—21no—
426#382C22×C4311yescharacteristic
427#380C22×C4311yescharacteristic
428#380C22×C4311yescharacteristic
429#380C22×C4311yescharacteristic
430C4×C4⋊C4C22×C4311yescharacteristic
431C4×C22⋊C4—21no—
432#340C22×C4311yescharacteristic
433#340C22×C4311yescharacteristic
434#340C22×C4311yescharacteristic
435#340C22×C4311yescharacteristic
436#336C22×C4311yescharacteristic
437#336C22×C4311yescharacteristic
438C43#2489111yescharacteristic, direct product factor, Sylow
439C2×#41—22no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—41no—
444C2×#41—41no—
445C22×Q8C23×C4311yescharacteristic
446C22×D4—21no—
447C22×D4—21no—
448C22×D4D4×C4311yescharacteristic
449C22×D4C23×C4311yescharacteristic
450C23×C4—21no—
451C23×C4—21no—
452C23×C4C23×C4311yescharacteristic
453C23×C4C23×C4311yescharacteristic
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—41no—
457C22×C8C23×C4311yescharacteristic
458C22×C8C23×C4311yescharacteristic
459C22×C8C23×C4311yescharacteristic
460C22×C8C23×C4311yescharacteristic
461C22⋊Q8—22no—
462C22⋊Q8—41no—
463#121—22no—
464#121—41no—
465C4×D4—22no—
466C4×D4—22no—
467#117—22no—
468#117—41no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—41no—
473C2×C4⋊C4D4×C4311yescharacteristic
474C2×C4⋊C4C23×C4311yescharacteristic
475C2×C4⋊C4C23×C4311yescharacteristic
476C2×C4⋊C4C23×C4311yescharacteristic
477C2×C4⋊C4C23×C4311yescharacteristic
478C2×C4⋊C4C23×C4311yescharacteristic
479C2×C4⋊C4C23×C4311yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4D4×C4311yescharacteristic
489C2×C22⋊C4D4×C4311yescharacteristic
490C2×C42—21no—
491C2×C42—21no—
492C2×C42C23×C4311yescharacteristic
493#107—22no—
494#106—22no—
495#106—41no—
496#106—41no—
497#103—22no—
498#103—22no—
499#103—41no—
500#103D4×C4314yescomplemented
501#102—22no—
502#102—22no—
503#102—22no—
504#102—41no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8—41no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516C24—21no—
517C24C2×D4×C4311yescharacteristic
518C24C2×D4×C4311yescharacteristic
519#41—28no—
520#41—44no—
521#41—44no—
522#41—44no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8C2×D4×C4312yes—
529C2×D4—22no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—81no—
543C2×D4#41×C4312yes—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4C2×D4×C4311yescharacteristic
568C22×C4C2×D4×C4311yescharacteristic
569C22×C4C2×D4×C4311yescharacteristic
570C22×C4C2×D4×C4311yescharacteristic
571C22×C4#41×C4312yes—
572C22×C4#41×C4312yes—
573C22×C4C24×C4311yescharacteristic
574M16—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8C2×D4×C4312yes—
587C4⋊C4—22no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4C2×D4×C4312yes—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C42—21no—
613C42—21no—
614C42—42no—
615C42—81no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23#123×C4312yes—
637C23C22×D4×C4311yescharacteristic
638Q8—22no—
639Q8—22no—
640Q8—41no—
641Q8—41no—
642D4—22no—
643D4—22no—
644D4—44no—
645D4—48no—
646D4—41no—
647D4—41no—
648D4—84no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—48no—
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—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—84no—
691C2×C4#123×C4312yes—
692C2×C4C22×D4×C4311yescharacteristic
693C2×C4C2×#41×C4311yescharacteristic
694C2×C4C2×#41×C4311yescharacteristic
695C2×C4C2×#41×C4311yescharacteristic
696C2×C4H(5,𝔽2)×C4311yescharacteristic
697C2×C4H(5,𝔽2)×C4311yescharacteristic
698C8—22no—
699C8—41no—
700C8—41no—
701C8—41no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—42no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—42no—
717C22—41no—
718C22—42no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22C2×#123×C4311yescharacteristic
724C22D42×C4311yescharacteristic
725C22C43×#54611yescharacteristic
726C22C43×#57511yescharacteristic
727C22C43×#57511yescharacteristic
728C22C43×#57711yescharacteristic
729C22C43×#57711yescharacteristic
730C4—22no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—42no—
735C4—42no—
736C4—81no—
737C4—81no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4C43×#52511yescharacteristic
742C4C43×#53811yescharacteristic
743C4C43×#54611yescharacteristic
744C4C43×#55111yescharacteristic
745C2—42no—
746C2—81no—
747C2—82no—
748C2C43×#241811yescharacteristic
749C2C43×#309311yescharacteristic
750C2C43×#309911yescharacteristic
751C2C43×#327111yescharacteristic
752C2C43×#327511yescharacteristic
753C2C43×#330711yescharacteristic
754C2C43×#332311yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#2407C2
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×#485C2semidirect
2. C2×C43×#417C2semidirect
4. C43×#2352C2semidirect
5. C43×#2092C2semidirect
6. C43×#2074C2semidirect
7. C43×#2035C2semidirect
8. C43×#2034C2semidirect
9. C43×#1927C2semidirect
10. C43×#1926C2semidirect
11. C43×#1875C2semidirect
12. C43×#1870C2semidirect
13. C43×#1853C2semidirect
14. C43×#1809C2semidirect
15. C43×#1788C2semidirect
122. #103×C43D4semidirect
324. #24891C43direct (N × H)
368. C2×#485C2×C43semidirect
369. C2×#417C2×C43semidirect
371. #2352C2×C43semidirect
372. #2092C2×C43semidirect
373. #2074C2×C43semidirect
374. #2035C2×C43semidirect
375. #2034C2×C43semidirect
376. #1927C2×C43semidirect
377. #1926C2×C43semidirect
378. #1875C2×C43semidirect
379. #1870C2×C43semidirect
380. #1853C2×C43semidirect
381. #1809C2×C43semidirect
382. #1788C2×C43semidirect
438. C43#24891direct (N × H)
500. #103D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4852
C2×C43×#4172
C43×#24072
C43×#23522
C43×#20922
C43×#20742
C43×#20352
C43×#20342
C43×#19272
C43×#19262
C43×#18752
C43×#18702
C43×#18532
C43×#18092
C43×#17882
#2489143