Finite Group Databasebeta

← C43×#24524 #24944541

Subgroups — C43×#24524 #24944541

Order 11008.

884 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3094C211yesmaximal, characteristic, complemented
2C2×C43×#449C211yesmaximal, characteristic
3C43×#2924C211yesmaximal, characteristic, complemented
4C43×#2896C211yesmaximal, characteristic, complemented
5C43×#2064C211yesmaximal, characteristic, complemented
6C43×#2063C211yesmaximal, characteristic, complemented
7C43×#2046C211yesmaximal, characteristic, complemented
8C43×#2045C211yesmaximal, characteristic, complemented
9C43×#1978C211yesmaximal, characteristic, complemented
10C43×#1977C211yesmaximal, characteristic, complemented
11C43×#1931C211yesmaximal, characteristic, complemented
12C43×#1930C211yesmaximal, characteristic, complemented
13C43×#1900C211yesmaximal, characteristic, complemented
14C43×#1855C211yesmaximal, characteristic, complemented
15C43×#1785C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C22×M16×C43C2211yescharacteristic
20C2×#121×C43C2211yescharacteristic
21C2×#117×C43C2211yescharacteristic
22C43×#482—21no—
23C43×#482—21no—
24C43×#481—21no—
25C43×#480—21no—
26C43×#449—21no—
27C43×#449—21no—
28C43×#449—21no—
29C43×#449—21no—
30C43×#433—21no—
31C43×#433—21no—
32C43×#432—21no—
33C43×#431—21no—
34C2×#108×C43C2211yescharacteristic
35C2×#108×C43C2211yescharacteristic
36C43×#428C2211yescharacteristic
37C43×#428C2211yescharacteristic
38C43×#424C2211yescharacteristic
39C43×#424C2211yescharacteristic
40C43×#419C2211yescharacteristic
41C43×#419C2211yescharacteristic
42C43×#418C2211yescharacteristic
43C43×#418C2211yescharacteristic
44C43×#418C2211yescharacteristic
45C43×#418C2211yescharacteristic
46C43×#417—21no—
47C43×#417—21no—
48C43×#416—21no—
49C43×#416—21no—
50C2×#103×C43C2211yescharacteristic
51C2×#102×C43C2211yescharacteristic
52C2×#101×C43C2211yescharacteristic
53C2×#101×C43C2211yescharacteristic
54C2×#100×C43C2211yescharacteristic
55C2×#100×C43C2211yescharacteristic
56C2×#100×C43C2211yescharacteristic
57C2×#100×C43C2211yescharacteristic
58C43×#407C2211yescharacteristic
59C43×#407C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#405C2211yescharacteristic
62C43×#405C2211yescharacteristic
63C43×#343C2211yescharacteristic
64C43×#343C2211yescharacteristic
65C43×#341C2211yescharacteristic
66C43×#341C2211yescharacteristic
67C2×#41×C43—22no—
68C2×#41×C43—22no—
69C2×#41×C43—21no—
70C2×#41×C43—21no—
71C2×#41×C43—21no—
72C2×#41×C43—21no—
73C2×#41×C43—41no—
74C2×#41×C43—41no—
75C22×Q8×C43C2311yescharacteristic
76C22×D4×C43—21no—
77C22×D4×C43—21no—
78C22×D4×C43C2311yescharacteristic
79C22×D4×C43C2311yescharacteristic
80C23×C4×C43—21no—
81C23×C4×C43C2311yescharacteristic
82C2×SD16×C43—22no—
83C2×SD16×C43—21no—
84C2×SD16×C43—21no—
85C2×SD16×C43—41no—
86C2×D8×C43—22no—
87C2×D8×C43—21no—
88C2×D8×C43—21no—
89C2×D8×C43—41no—
90C2×M16×C43—21no—
91C2×M16×C43—41no—
92C2×M16×C43—41no—
93C2×M16×C43C2311yescharacteristic
94C2×M16×C43C2311yescharacteristic
95C2×M16×C43C2311yescharacteristic
96C2×M16×C43C2311yescharacteristic
97C2×M16×C43C2311yescharacteristic
98C2×M16×C43C2311yescharacteristic
99C22×C8×C43—21no—
100C22×C8×C43C2311yescharacteristic
101C22×C8×C43C2311yescharacteristic
102#121×C43—21no—
103#121×C43—21no—
104#121×C43—21no—
105#121×C43—21no—
106#117×C43—21no—
107#117×C43—21no—
108#117×C43D411yescharacteristic
109#117×C43D411yescharacteristic
110#117×C43C2311yescharacteristic
111#117×C43C2311yescharacteristic
112C2×C4⋊C4×C43D411yescharacteristic
113C2×C4⋊C4×C43D411yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C42×C43—21no—
118#108×C43—41no—
119#108×C43—41no—
120#107×C43—21no—
121#107×C43—21no—
122#106×C43—21no—
123#106×C43—21no—
124C4⋊C8×C43—21no—
125C4⋊C8×C43—21no—
126C4⋊C8×C43—21no—
127C4⋊C8×C43—21no—
128#103×C43—21no—
129#103×C43—21no—
130#103×C43—21no—
131#103×C43—21no—
132#103×C43—21no—
133#103×C43—21no—
134#102×C43—21no—
135#102×C43—21no—
136#102×C43—21no—
137#102×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143#102×C43—21no—
144#101×C43—22no—
145#101×C43—41no—
146#100×C43—22no—
147#100×C43—41no—
148#100×C43—41no—
149#100×C43—41no—
150C22⋊C8×C43—21no—
151C22⋊C8×C43—21no—
152C22⋊C8×C43—21no—
153C22⋊C8×C43—21no—
154C22⋊C8×C43D411yescharacteristic
155C22⋊C8×C43D411yescharacteristic
156C22⋊C8×C43D411yescharacteristic
157C22⋊C8×C43D411yescharacteristic
158#97×C43—21no—
159#97×C43—21no—
160C4×C8×C43—21no—
161C4×C8×C43—21no—
162C24×C43—21no—
163C24×C43—21no—
164C24×C43#4111yescharacteristic
165#41×C43—24no—
166#41×C43—24no—
167#41×C43—42no—
168#41×C43—42no—
169#41×C43—42no—
170#41×C43—42no—
171#41×C43—42no—
172#41×C43—42no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43#4112yes—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
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—21no—
190C2×D4×C43—42no—
191C2×D4×C43—42no—
192C2×D4×C43—41no—
193C2×D4×C43—41no—
194C2×D4×C43—41no—
195C2×D4×C43—41no—
196C2×D4×C43—82no—
197C2×D4×C43#4112yes—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—42no—
207C22×C4×C43—42no—
208C22×C4×C43—41no—
209C22×C4×C43—41no—
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43#4111yescharacteristic
215C22×C4×C43C2411yescharacteristic
216SD16×C43—42no—
217SD16×C43—42no—
218D8×C43—42no—
219D8×C43—42no—
220M16×C43—21no—
221M16×C43—21no—
222M16×C43—21no—
223M16×C43—21no—
224M16×C43—21no—
225M16×C43—21no—
226M16×C43—21no—
227M16×C43—21no—
228M16×C43—21no—
229M16×C43—21no—
230M16×C43—21no—
231M16×C43—21no—
232M16×C43—42no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—42no—
244C2×C8×C43C2×D411yescharacteristic
245C2×C8×C43C2×D411yescharacteristic
246C2×C8×C43C2×D411yescharacteristic
247C2×C8×C43C2×D411yescharacteristic
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43C2×D411yescharacteristic
253C4⋊C4×C43C2×D411yescharacteristic
254C4⋊C4×C43C2×D411yescharacteristic
255C4⋊C4×C43C2×D411yescharacteristic
256C22⋊C4×C43—21no—
257C22⋊C4×C43—21no—
258C22⋊C4×C43—21no—
259C22⋊C4×C43—21no—
260C22⋊C4×C43—41no—
261C22⋊C4×C43—41no—
262C42×C43—21no—
263C42×C43—21no—
264C42×C43—21no—
265C42×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—22no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—81no—
277C23×C43—81no—
278C23×C43—81no—
279C23×C43—81no—
280C23×C43#12111yescharacteristic
281C23×C43#12111yescharacteristic
282C23×C43C2×#4111yescharacteristic
283Q8×C43—22no—
284Q8×C43—22no—
285Q8×C43—41no—
286Q8×C43—41no—
287D4×C43—22no—
288D4×C43—22no—
289D4×C43—44no—
290D4×C43—44no—
291D4×C43—41no—
292D4×C43—41no—
293D4×C43—41no—
294D4×C43—41no—
295D4×C43—41no—
296D4×C43—41no—
297D4×C43—82no—
298D4×C43—82no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—22no—
314C2×C4×C43—44no—
315C2×C4×C43—44no—
316C2×C4×C43—42no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—81no—
321C2×C4×C43—81no—
322C2×C4×C43#12111yescharacteristic
323C2×C4×C43#12111yescharacteristic
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C2×#4111yescharacteristic
327C2×C4×C43C2×#4111yescharacteristic
328C2×C4×C43H(5,𝔽2)11yescharacteristic
329C2×C4×C43H(5,𝔽2)11yescharacteristic
330C8×C43—21no—
331C8×C43—21no—
332C8×C43—21no—
333C8×C43—21no—
334C8×C43—41no—
335C8×C43—41no—
336C8×C43—41no—
337C8×C43—41no—
338C8×C43—41no—
339C8×C43—41no—
340#24524C4311yesmaximal, characteristic, direct product factor, Sylow
341C22×C43—21no—
342C22×C43—21no—
343C22×C43—21no—
344C22×C43—21no—
345C22×C43—21no—
346C22×C43—21no—
347C22×C43—21no—
348C22×C43—21no—
349C22×C43—42no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—82no—
353C22×C43—82no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—161no—
360C22×C43—161no—
361C22×C43C2×#12111yescharacteristic
362C22×C43#55111yescharacteristic
363C22×C43#55111yescharacteristic
364C4×C43—21no—
365C4×C43—21no—
366C4×C43—42no—
367C4×C43—41no—
368C4×C43—41no—
369C4×C43—41no—
370C4×C43—41no—
371C4×C43—81no—
372C4×C43#52511yescharacteristic
373C4×C43#53511yescharacteristic
374C4×C43#54611yescharacteristic
375C4×C43#54611yescharacteristic
376#3094C2×C4311yescharacteristic, complemented
377C2×#449C2×C4311yescharacteristic
378#2924C2×C4311yescharacteristic, complemented
379#2896C2×C4311yescharacteristic, complemented
380#2064C2×C4311yescharacteristic, complemented
381#2063C2×C4311yescharacteristic, complemented
382#2046C2×C4311yescharacteristic, complemented
383#2045C2×C4311yescharacteristic, complemented
384#1978C2×C4311yescharacteristic, complemented
385#1977C2×C4311yescharacteristic, complemented
386#1931C2×C4311yescharacteristic, complemented
387#1930C2×C4311yescharacteristic, complemented
388#1900C2×C4311yescharacteristic, complemented
389#1855C2×C4311yescharacteristic, complemented
390#1785C2×C4311yescharacteristic, complemented
391C2×C43—21no—
392C2×C43—21no—
393C2×C43—41no—
394C2×C43—41no—
395C2×C43—82no—
396C2×C43—161no—
397C2×C43#241111yescharacteristic
398C2×C43#306711yescharacteristic
399C2×C43#306811yescharacteristic
400C22×#41C22×C4311yescharacteristic
401C22×SD16C22×C4311yescharacteristic
402C22×D8C22×C4311yescharacteristic
403C22×M16C22×C4311yescharacteristic
404C2×#121C22×C4311yescharacteristic
405C2×#117C22×C4311yescharacteristic
406#482—21no—
407#482—21no—
408#481—21no—
409#480—21no—
410#449—21no—
411#449—21no—
412#449—21no—
413#449—21no—
414#433—21no—
415#433—21no—
416#432—21no—
417#431—21no—
418C2×#108C22×C4311yescharacteristic
419C2×#108C22×C4311yescharacteristic
420#428C22×C4311yescharacteristic
421#428C22×C4311yescharacteristic
422#424C22×C4311yescharacteristic
423#424C22×C4311yescharacteristic
424#419C22×C4311yescharacteristic
425#419C22×C4311yescharacteristic
426#418C22×C4311yescharacteristic
427#418C22×C4311yescharacteristic
428#418C22×C4311yescharacteristic
429#418C22×C4311yescharacteristic
430#417—21no—
431#417—21no—
432#416—21no—
433#416—21no—
434C2×#103C22×C4311yescharacteristic
435C2×#102C22×C4311yescharacteristic
436C2×#101C22×C4311yescharacteristic
437C2×#101C22×C4311yescharacteristic
438C2×#100C22×C4311yescharacteristic
439C2×#100C22×C4311yescharacteristic
440C2×#100C22×C4311yescharacteristic
441C2×#100C22×C4311yescharacteristic
442#407C22×C4311yescharacteristic
443#407C22×C4311yescharacteristic
444C2×C22⋊C8C22×C4311yescharacteristic
445#405C22×C4311yescharacteristic
446#405C22×C4311yescharacteristic
447#343C22×C4311yescharacteristic
448#343C22×C4311yescharacteristic
449#341C22×C4311yescharacteristic
450#341C22×C4311yescharacteristic
451C43#2452411yescharacteristic, direct product factor, Sylow
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—41no—
459C2×#41—41no—
460C22×Q8C23×C4311yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4C23×C4311yescharacteristic
464C22×D4C23×C4311yescharacteristic
465C23×C4—21no—
466C23×C4C23×C4311yescharacteristic
467C2×SD16—22no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—41no—
471C2×D8—22no—
472C2×D8—21no—
473C2×D8—21no—
474C2×D8—41no—
475C2×M16—21no—
476C2×M16—41no—
477C2×M16—41no—
478C2×M16C23×C4311yescharacteristic
479C2×M16C23×C4311yescharacteristic
480C2×M16C23×C4311yescharacteristic
481C2×M16C23×C4311yescharacteristic
482C2×M16C23×C4311yescharacteristic
483C2×M16C23×C4311yescharacteristic
484C22×C8—21no—
485C22×C8C23×C4311yescharacteristic
486C22×C8C23×C4311yescharacteristic
487#121—21no—
488#121—21no—
489#121—21no—
490#121—21no—
491#117—21no—
492#117—21no—
493#117D4×C4311yescharacteristic
494#117D4×C4311yescharacteristic
495#117C23×C4311yescharacteristic
496#117C23×C4311yescharacteristic
497C2×C4⋊C4D4×C4311yescharacteristic
498C2×C4⋊C4D4×C4311yescharacteristic
499C2×C4⋊C4C23×C4311yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C42—21no—
503#108—41no—
504#108—41no—
505#107—21no—
506#107—21no—
507#106—21no—
508#106—21no—
509C4⋊C8—21no—
510C4⋊C8—21no—
511C4⋊C8—21no—
512C4⋊C8—21no—
513#103—21no—
514#103—21no—
515#103—21no—
516#103—21no—
517#103—21no—
518#103—21no—
519#102—21no—
520#102—21no—
521#102—21no—
522#102—21no—
523#102—21no—
524#102—21no—
525#102—21no—
526#102—21no—
527#102—21no—
528#102—21no—
529#101—22no—
530#101—41no—
531#100—22no—
532#100—41no—
533#100—41no—
534#100—41no—
535C22⋊C8—21no—
536C22⋊C8—21no—
537C22⋊C8—21no—
538C22⋊C8—21no—
539C22⋊C8D4×C4311yescharacteristic
540C22⋊C8D4×C4311yescharacteristic
541C22⋊C8D4×C4311yescharacteristic
542C22⋊C8D4×C4311yescharacteristic
543#97—21no—
544#97—21no—
545C4×C8—21no—
546C4×C8—21no—
547C24—21no—
548C24—21no—
549C24#41×C4311yescharacteristic
550#41—24no—
551#41—24no—
552#41—42no—
553#41—42no—
554#41—42no—
555#41—42no—
556#41—42no—
557#41—42no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8#41×C4312yes—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—82no—
582C2×D4#41×C4312yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4C2×D4×C4311yescharacteristic
596C22×C4C2×D4×C4311yescharacteristic
597C22×C4C2×D4×C4311yescharacteristic
598C22×C4C2×D4×C4311yescharacteristic
599C22×C4#41×C4311yescharacteristic
600C22×C4C24×C4311yescharacteristic
601SD16—42no—
602SD16—42no—
603D8—42no—
604D8—42no—
605M16—21no—
606M16—21no—
607M16—21no—
608M16—21no—
609M16—21no—
610M16—21no—
611M16—21no—
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—42no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—42no—
629C2×C8C2×D4×C4311yescharacteristic
630C2×C8C2×D4×C4311yescharacteristic
631C2×C8C2×D4×C4311yescharacteristic
632C2×C8C2×D4×C4311yescharacteristic
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4C2×D4×C4311yescharacteristic
638C4⋊C4C2×D4×C4311yescharacteristic
639C4⋊C4C2×D4×C4311yescharacteristic
640C4⋊C4C2×D4×C4311yescharacteristic
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—41no—
646C22⋊C4—41no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—81no—
662C23—81no—
663C23—81no—
664C23—81no—
665C23#121×C4311yescharacteristic
666C23#121×C4311yescharacteristic
667C23C2×#41×C4311yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672D4—22no—
673D4—22no—
674D4—44no—
675D4—44no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—82no—
683D4—82no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4#121×C4311yescharacteristic
708C2×C4#121×C4311yescharacteristic
709C2×C4C22×D4×C4311yescharacteristic
710C2×C4C22×D4×C4311yescharacteristic
711C2×C4C2×#41×C4311yescharacteristic
712C2×C4C2×#41×C4311yescharacteristic
713C2×C4H(5,𝔽2)×C4311yescharacteristic
714C2×C4H(5,𝔽2)×C4311yescharacteristic
715C8—21no—
716C8—21no—
717C8—21no—
718C8—21no—
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8—41no—
724C8—41no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—42no—
734C22—81no—
735C22—81no—
736C22—82no—
737C22—82no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—161no—
744C22—161no—
745C22C2×#121×C4311yescharacteristic
746C22C43×#55111yescharacteristic
747C22C43×#55111yescharacteristic
748C4—21no—
749C4—21no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—81no—
756C4C43×#52511yescharacteristic
757C4C43×#53511yescharacteristic
758C4C43×#54611yescharacteristic
759C4C43×#54611yescharacteristic
760C2—21no—
761C2—21no—
762C2—41no—
763C2—41no—
764C2—82no—
765C2—161no—
766C2C43×#241111yescharacteristic
767C2C43×#306711yescharacteristic
768C2C43×#306811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3094C2semidirect
3. C43×#2924C2semidirect
4. C43×#2896C2semidirect
5. C43×#2064C2semidirect
6. C43×#2063C2semidirect
7. C43×#2046C2semidirect
8. C43×#2045C2semidirect
9. C43×#1978C2semidirect
10. C43×#1977C2semidirect
11. C43×#1931C2semidirect
12. C43×#1930C2semidirect
13. C43×#1900C2semidirect
14. C43×#1855C2semidirect
15. C43×#1785C2semidirect
340. #24524C43direct (N × H)
376. #3094C2×C43semidirect
378. #2924C2×C43semidirect
379. #2896C2×C43semidirect
380. #2064C2×C43semidirect
381. #2063C2×C43semidirect
382. #2046C2×C43semidirect
383. #2045C2×C43semidirect
384. #1978C2×C43semidirect
385. #1977C2×C43semidirect
386. #1931C2×C43semidirect
387. #1930C2×C43semidirect
388. #1900C2×C43semidirect
389. #1855C2×C43semidirect
390. #1785C2×C43semidirect
451. C43#24524direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#30942
C2×C43×#4492
C43×#29242
C43×#28962
C43×#20642
C43×#20632
C43×#20462
C43×#20452
C43×#19782
C43×#19772
C43×#19312
C43×#19302
C43×#19002
C43×#18552
C43×#17852
#2452443