Finite Group Databasebeta

← C43×#18704 #24938721

Subgroups — C43×#18704 #24938721

Order 11008.

972 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3546C211yesmaximal, characteristic, complemented
2C43×#3251C211yesmaximal, characteristic, complemented
3C43×#3214C211yesmaximal, characteristic, complemented
4C43×#3169C211yesmaximal, characteristic, complemented
5C43×#1650C211yesmaximal, characteristic, complemented
6C43×#1647C211yesmaximal, characteristic, complemented
7C43×#1642C211yesmaximal, characteristic, complemented
8C43×#1639C211yesmaximal, characteristic, complemented
9C43×#1628C211yesmaximal, characteristic, complemented
10C43×#1625C211yesmaximal, characteristic, complemented
11C43×#1621C211yesmaximal, characteristic, complemented
12C43×#1619C211yesmaximal, characteristic, complemented
13C43×#1557C211yesmaximal, characteristic, complemented
14C43×#1494C211yesmaximal, characteristic, complemented
15C43×#1492C211yesmaximal, characteristic, complemented
16C43×#560—22no—
17C43×#556C2211yescharacteristic
18C43×#553—21no—
19C43×#550—21no—
20C43×#550C2211yescharacteristic
21C43×#547C2211yescharacteristic
22C43×#546—21no—
23C43×#546—21no—
24D42×C43C2211yescharacteristic
25C43×#542—21no—
26C43×#538—22no—
27C43×#537—21no—
28C43×#535—21no—
29C43×#535—21no—
30C43×#532C2211yescharacteristic
31C43×#532C2211yescharacteristic
32C43×#532C2211yescharacteristic, complemented
33C43×#529C2211yescharacteristic
34C43×#500C2211yescharacteristic, complemented
35C43×#496—21no—
36C43×#493C2211yescharacteristic
37C43×#489—21no—
38C43×#486C2211yescharacteristic
39C43×#486C2211yescharacteristic, complemented
40C43×#478—21no—
41C43×#475C2211yescharacteristic, complemented
42C43×#474C2211yescharacteristic
43C43×#469—21no—
44C43×#468—21no—
45C43×#466—22no—
46C43×#463—21no—
47C43×#461C2211yescharacteristic
48C43×#461C2211yescharacteristic, complemented
49C43×#460C2211yescharacteristic, complemented
50C43×#459C2211yescharacteristic
51C43×#459C2211yescharacteristic
52C43×#459C2211yescharacteristic, complemented
53C43×#449—21no—
54C43×#449—21no—
55C4×D8×C43—22no—
56C43×#432C2211yescharacteristic, complemented
57C43×#423C2211yescharacteristic, complemented
58C2×C4×C8×C43C2211yescharacteristic, complemented
59C43×#332C2211yescharacteristic, complemented
60C43×#332C2211yescharacteristic, complemented
61C43×#331C2211yescharacteristic
62C43×#331C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic, complemented
64C43×Q8⋊C8C2211yescharacteristic, complemented
65C43×D4⋊C8C2211yescharacteristic
66C43×D4⋊C8C2211yescharacteristic
67C43×D4⋊C8C2211yescharacteristic
68C43×D4⋊C8C2211yescharacteristic
69C43×D4⋊C8C2211yescharacteristic, complemented
70C43×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C43—21no—
72C2×#41×C43—21no—
73C2×#41×C43—21no—
74C2×#41×C43—21no—
75C2×#41×C43—21no—
76C22×D4×C43—21no—
77C22×D4×C43—21no—
78C2×SD16×C43—21no—
79C2×SD16×C43—21no—
80C2×SD16×C43—21no—
81C2×D8×C43—22no—
82C2×D8×C43—21no—
83C2×D8×C43—21no—
84C2×D8×C43—21no—
85C2×M16×C43—21no—
86C22×C8×C43—21no—
87C4⋊Q8×C43D411yescharacteristic
88C4⋊Q8×C43C2311yescharacteristic
89C4⋊Q8×C43C2311yescharacteristic
90#127×C43—22no—
91#127×C43—21no—
92#127×C43D411yescharacteristic
93#127×C43C2311yescharacteristic
94#127×C43C2311yescharacteristic
95#126×C43—22no—
96#126×C43—22no—
97#126×C43—21no—
98#125×C43D411yescharacteristic
99#124×C43—22no—
100#124×C43—21no—
101#124×C43—21no—
102#124×C43—21no—
103#124×C43—21no—
104#124×C43D411yescharacteristic
105#123×C43—22no—
106#123×C43—22no—
107#123×C43—21no—
108#123×C43—22no—
109C22⋊Q8×C43—22no—
110C22⋊Q8×C43—21no—
111C22⋊Q8×C43—21no—
112C22⋊Q8×C43D411yescharacteristic
113#121×C43—22no—
114#121×C43—22no—
115#121×C43—22no—
116#121×C43—22no—
117#121×C43—22no—
118#121×C43—21no—
119#121×C43—22no—
120#121×C43—21no—
121#121×C43—21no—
122#121×C43—21no—
123#121×C43—21no—
124#121×C43—21no—
125#121×C43—21no—
126#121×C43—21no—
127#121×C43D411yescharacteristic
128#121×C43D411yescharacteristic
129#121×C43D411yescharacteristic
130#121×C43D412yes—
131#120×C43—22no—
132#120×C43—22no—
133#120×C43—22no—
134#120×C43—22no—
135C4×Q8×C43—21no—
136C4×Q8×C43C2311yescharacteristic
137C4×D4×C43—22no—
138C4×D4×C43—21no—
139C4×D4×C43—21no—
140C4×D4×C43—21no—
141C4×D4×C43—21no—
142C4×D4×C43—21no—
143C4×D4×C43—21no—
144C4×D4×C43D412yes—
145C4×D4×C43C2311yescharacteristic
146C4×D4×C43C2311yescharacteristic
147C4×D4×C43C2311yescharacteristic
148#117×C43—21no—
149#117×C43—21no—
150C2×C4⋊C4×C43—21no—
151C2×C22⋊C4×C43—22no—
152C2×C42×C43C2311yescharacteristic
153#107×C43—22no—
154#107×C43—21no—
155#106×C43—21no—
156C4⋊C8×C43—21no—
157C4⋊C8×C43C2311yescharacteristic
158C4⋊C8×C43C2311yescharacteristic
159C4⋊C8×C43C2311yescharacteristic
160C4⋊C8×C43C2311yescharacteristic
161#103×C43—21no—
162#103×C43—21no—
163#103×C43—21no—
164#102×C43—22no—
165#102×C43—21no—
166#102×C43—22no—
167#102×C43—21no—
168#102×C43—21no—
169#102×C43—21no—
170#102×C43—21no—
171C22⋊C8×C43—21no—
172#97×C43—21no—
173C4×C8×C43—21no—
174C4×C8×C43C2311yescharacteristic
175C4×C8×C43C2311yescharacteristic
176C24×C43—22no—
177#41×C43—81no—
178#41×C43—81no—
179#41×C43—81no—
180#41×C43—81no—
181#41×C43—81no—
182#41×C43—81no—
183#41×C43—81no—
184#41×C43—81no—
185#41×C43—81no—
186#41×C43—81no—
187C2×Q8×C43—21no—
188C2×Q8×C43—21no—
189C2×Q8×C43—21no—
190C2×Q8×C43C2×D411yescharacteristic
191C2×D4×C43—22no—
192C2×D4×C43—22no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43—21no—
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—22no—
203C2×D4×C43—21no—
204C2×D4×C43—21no—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43—41no—
208C2×D4×C43—81no—
209C2×D4×C43—81no—
210C2×D4×C43—81no—
211C2×D4×C43—81no—
212C2×D4×C43C2×D411yescharacteristic
213C2×D4×C43C2×D411yescharacteristic
214C2×D4×C43C2×D411yescharacteristic
215C2×D4×C43C2×D412yes—
216C22×C4×C43—22no—
217C22×C4×C43—22no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—22no—
222C22×C4×C43—41no—
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226SD16×C43—81no—
227SD16×C43—81no—
228SD16×C43—81no—
229D8×C43—44no—
230D8×C43—81no—
231D8×C43—81no—
232D8×C43—81no—
233M16×C43—81no—
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—42no—
241C4⋊C4×C43—22no—
242C4⋊C4×C43—22no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43C2×D411yescharacteristic
252C4⋊C4×C43C2×D411yescharacteristic
253C4⋊C4×C43C2×D411yescharacteristic
254C4⋊C4×C43C2×D411yescharacteristic
255C4⋊C4×C43C2×D412yes—
256C22⋊C4×C43—22no—
257C22⋊C4×C43—22no—
258C22⋊C4×C43—22no—
259C22⋊C4×C43—22no—
260C22⋊C4×C43—22no—
261C22⋊C4×C43—21no—
262C22⋊C4×C43—21no—
263C22⋊C4×C43—21no—
264C22⋊C4×C43—21no—
265C22⋊C4×C43—21no—
266C22⋊C4×C43—22no—
267C22⋊C4×C43—22no—
268C22⋊C4×C43—21no—
269C22⋊C4×C43—21no—
270C22⋊C4×C43—21no—
271C22⋊C4×C43—21no—
272C22⋊C4×C43—41no—
273C22⋊C4×C43—41no—
274C42×C43—22no—
275C42×C43—21no—
276C42×C43C2×D411yescharacteristic
277C42×C43C2×D411yescharacteristic
278C42×C43C2×D411yescharacteristic
279C42×C43C2411yescharacteristic
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—22no—
283C23×C43—21no—
284C23×C43—41no—
285C23×C43—82no—
286C23×C43—82no—
287C23×C43—82no—
288C23×C43#12011yescharacteristic
289Q8×C43—21no—
290Q8×C43—21no—
291Q8×C43—41no—
292Q8×C43—41no—
293Q8×C43—41no—
294Q8×C43—41no—
295Q8×C43—81no—
296D4×C43—21no—
297D4×C43—21no—
298D4×C43—21no—
299D4×C43—21no—
300D4×C43—21no—
301D4×C43—21no—
302D4×C43—42no—
303D4×C43—42no—
304D4×C43—41no—
305D4×C43—41no—
306D4×C43—41no—
307D4×C43—41no—
308D4×C43—41no—
309D4×C43—41no—
310D4×C43—41no—
311D4×C43—41no—
312D4×C43—81no—
313D4×C43—81no—
314D4×C43—81no—
315D4×C43—82no—
316D4×C43—81no—
317D4×C43—81no—
318D4×C43—82no—
319D4×C43—82no—
320D4×C43—82no—
321D4×C43—82no—
322D4×C43—82no—
323D4×C43—82no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—22no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—82no—
343C2×C4×C43—82no—
344C2×C4×C43—82no—
345C2×C4×C43—82no—
346C2×C4×C43#12011yescharacteristic
347C2×C4×C43#12011yescharacteristic
348C2×C4×C43#12011yescharacteristic
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C22×D411yescharacteristic
352C8×C43—22no—
353C8×C43—41no—
354C8×C43—41no—
355C8×C43—41no—
356C8×C43—41no—
357C8×C43—41no—
358#18704C4311yesmaximal, characteristic, direct product factor, Sylow
359C22×C43—21no—
360C22×C43—21no—
361C22×C43—21no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—42no—
365C22×C43—41no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43—42no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—42no—
373C22×C43—41no—
374C22×C43—81no—
375C22×C43—81no—
376C22×C43—81no—
377C22×C43—164no—
378C22×C43C2×#12011yescharacteristic
379C4×C43—21no—
380C4×C43—21no—
381C4×C43—21no—
382C4×C43—21no—
383C4×C43—41no—
384C4×C43—42no—
385C4×C43—41no—
386C4×C43—41no—
387C4×C43—41no—
388C4×C43—41no—
389C4×C43—81no—
390C4×C43#57611yescharacteristic
391C4×C43#57611yescharacteristic
392C4×C43#57611yescharacteristic
393C4×C43#57711yescharacteristic
394#3546C2×C4311yescharacteristic, complemented
395#3251C2×C4311yescharacteristic, complemented
396#3214C2×C4311yescharacteristic, complemented
397#3169C2×C4311yescharacteristic, complemented
398#1650C2×C4311yescharacteristic, complemented
399#1647C2×C4311yescharacteristic, complemented
400#1642C2×C4311yescharacteristic, complemented
401#1639C2×C4311yescharacteristic, complemented
402#1628C2×C4311yescharacteristic, complemented
403#1625C2×C4311yescharacteristic, complemented
404#1621C2×C4311yescharacteristic, complemented
405#1619C2×C4311yescharacteristic, complemented
406#1557C2×C4311yescharacteristic, complemented
407#1494C2×C4311yescharacteristic, complemented
408#1492C2×C4311yescharacteristic, complemented
409C2×C43—41no—
410C2×C43—81no—
411C2×C43—82no—
412C2×C43—81no—
413C2×C43—81no—
414C2×C43—161no—
415C2×C43#300811yescharacteristic
416C2×C43#301211yescharacteristic
417C2×C43#301811yescharacteristic
418#560—22no—
419#556C22×C4311yescharacteristic
420#553—21no—
421#550—21no—
422#550C22×C4311yescharacteristic
423#547C22×C4311yescharacteristic
424#546—21no—
425#546—21no—
426D42C22×C4311yescharacteristic
427#542—21no—
428#538—22no—
429#537—21no—
430#535—21no—
431#535—21no—
432#532C22×C4311yescharacteristic
433#532C22×C4311yescharacteristic
434#532C22×C4311yescharacteristic, complemented
435#529C22×C4311yescharacteristic
436#500C22×C4311yescharacteristic, complemented
437#496—21no—
438#493C22×C4311yescharacteristic
439#489—21no—
440#486C22×C4311yescharacteristic
441#486C22×C4311yescharacteristic, complemented
442#478—21no—
443#475C22×C4311yescharacteristic, complemented
444#474C22×C4311yescharacteristic
445#469—21no—
446#468—21no—
447#466—22no—
448#463—21no—
449#461C22×C4311yescharacteristic
450#461C22×C4311yescharacteristic, complemented
451#460C22×C4311yescharacteristic, complemented
452#459C22×C4311yescharacteristic
453#459C22×C4311yescharacteristic
454#459C22×C4311yescharacteristic, complemented
455#449—21no—
456#449—21no—
457C4×D8—22no—
458#432C22×C4311yescharacteristic, complemented
459#423C22×C4311yescharacteristic, complemented
460C2×C4×C8C22×C4311yescharacteristic, complemented
461#332C22×C4311yescharacteristic, complemented
462#332C22×C4311yescharacteristic, complemented
463#331C22×C4311yescharacteristic
464#331C22×C4311yescharacteristic
465Q8⋊C8C22×C4311yescharacteristic, complemented
466Q8⋊C8C22×C4311yescharacteristic, complemented
467D4⋊C8C22×C4311yescharacteristic
468D4⋊C8C22×C4311yescharacteristic
469D4⋊C8C22×C4311yescharacteristic
470D4⋊C8C22×C4311yescharacteristic
471D4⋊C8C22×C4311yescharacteristic, complemented
472D4⋊C8C22×C4311yescharacteristic, complemented
473C43#1870411yescharacteristic, direct product factor, Sylow
474C2×#41—21no—
475C2×#41—21no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C22×D4—21no—
480C22×D4—21no—
481C2×SD16—21no—
482C2×SD16—21no—
483C2×SD16—21no—
484C2×D8—22no—
485C2×D8—21no—
486C2×D8—21no—
487C2×D8—21no—
488C2×M16—21no—
489C22×C8—21no—
490C4⋊Q8D4×C4311yescharacteristic
491C4⋊Q8C23×C4311yescharacteristic
492C4⋊Q8C23×C4311yescharacteristic
493#127—22no—
494#127—21no—
495#127D4×C4311yescharacteristic
496#127C23×C4311yescharacteristic
497#127C23×C4311yescharacteristic
498#126—22no—
499#126—22no—
500#126—21no—
501#125D4×C4311yescharacteristic
502#124—22no—
503#124—21no—
504#124—21no—
505#124—21no—
506#124—21no—
507#124D4×C4311yescharacteristic
508#123—22no—
509#123—22no—
510#123—21no—
511#123—22no—
512C22⋊Q8—22no—
513C22⋊Q8—21no—
514C22⋊Q8—21no—
515C22⋊Q8D4×C4311yescharacteristic
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—21no—
522#121—22no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121D4×C4311yescharacteristic
531#121D4×C4311yescharacteristic
532#121D4×C4311yescharacteristic
533#121D4×C4312yes—
534#120—22no—
535#120—22no—
536#120—22no—
537#120—22no—
538C4×Q8—21no—
539C4×Q8C23×C4311yescharacteristic
540C4×D4—22no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4D4×C4312yes—
548C4×D4C23×C4311yescharacteristic
549C4×D4C23×C4311yescharacteristic
550C4×D4C23×C4311yescharacteristic
551#117—21no—
552#117—21no—
553C2×C4⋊C4—21no—
554C2×C22⋊C4—22no—
555C2×C42C23×C4311yescharacteristic
556#107—22no—
557#107—21no—
558#106—21no—
559C4⋊C8—21no—
560C4⋊C8C23×C4311yescharacteristic
561C4⋊C8C23×C4311yescharacteristic
562C4⋊C8C23×C4311yescharacteristic
563C4⋊C8C23×C4311yescharacteristic
564#103—21no—
565#103—21no—
566#103—21no—
567#102—22no—
568#102—21no—
569#102—22no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574C22⋊C8—21no—
575#97—21no—
576C4×C8—21no—
577C4×C8C23×C4311yescharacteristic
578C4×C8C23×C4311yescharacteristic
579C24—22no—
580#41—81no—
581#41—81no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—81no—
586#41—81no—
587#41—81no—
588#41—81no—
589#41—81no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8C2×D4×C4311yescharacteristic
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4C2×D4×C4311yescharacteristic
616C2×D4C2×D4×C4311yescharacteristic
617C2×D4C2×D4×C4311yescharacteristic
618C2×D4C2×D4×C4312yes—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—41no—
626C22×C4C2×D4×C4311yescharacteristic
627C22×C4C2×D4×C4311yescharacteristic
628C22×C4C2×D4×C4311yescharacteristic
629SD16—81no—
630SD16—81no—
631SD16—81no—
632D8—44no—
633D8—81no—
634D8—81no—
635D8—81no—
636M16—81no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—42no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4C2×D4×C4311yescharacteristic
655C4⋊C4C2×D4×C4311yescharacteristic
656C4⋊C4C2×D4×C4311yescharacteristic
657C4⋊C4C2×D4×C4311yescharacteristic
658C4⋊C4C2×D4×C4312yes—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C42—22no—
678C42—21no—
679C42C2×D4×C4311yescharacteristic
680C42C2×D4×C4311yescharacteristic
681C42C2×D4×C4311yescharacteristic
682C42C24×C4311yescharacteristic
683C23—21no—
684C23—21no—
685C23—22no—
686C23—21no—
687C23—41no—
688C23—82no—
689C23—82no—
690C23—82no—
691C23#120×C4311yescharacteristic
692Q8—21no—
693Q8—21no—
694Q8—41no—
695Q8—41no—
696Q8—41no—
697Q8—41no—
698Q8—81no—
699D4—21no—
700D4—21no—
701D4—21no—
702D4—21no—
703D4—21no—
704D4—21no—
705D4—42no—
706D4—42no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—81no—
716D4—81no—
717D4—82no—
718D4—81no—
719D4—81no—
720D4—81no—
721D4—82no—
722D4—82no—
723D4—82no—
724D4—82no—
725D4—82no—
726D4—82no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—82no—
746C2×C4—82no—
747C2×C4—82no—
748C2×C4—82no—
749C2×C4#120×C4311yescharacteristic
750C2×C4#120×C4311yescharacteristic
751C2×C4#120×C4311yescharacteristic
752C2×C4C22×D4×C4311yescharacteristic
753C2×C4C22×D4×C4311yescharacteristic
754C2×C4C22×D4×C4311yescharacteristic
755C8—22no—
756C8—41no—
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—164no—
780C22C2×#120×C4311yescharacteristic
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—41no—
786C4—42no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4C43×#57611yescharacteristic
793C4C43×#57611yescharacteristic
794C4C43×#57611yescharacteristic
795C4C43×#57711yescharacteristic
796C2—41no—
797C2—81no—
798C2—81no—
799C2—82no—
800C2—81no—
801C2—161no—
802C2C43×#300811yescharacteristic
803C2C43×#301211yescharacteristic
804C2C43×#301811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC42C24×C43
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3546C2semidirect
2. C43×#3251C2semidirect
3. C43×#3214C2semidirect
4. C43×#3169C2semidirect
5. C43×#1650C2semidirect
6. C43×#1647C2semidirect
7. C43×#1642C2semidirect
8. C43×#1639C2semidirect
9. C43×#1628C2semidirect
10. C43×#1625C2semidirect
11. C43×#1621C2semidirect
12. C43×#1619C2semidirect
13. C43×#1557C2semidirect
14. C43×#1494C2semidirect
15. C43×#1492C2semidirect
32. C43×#532C22semidirect
34. C43×#500C22semidirect
39. C43×#486C22semidirect
41. C43×#475C22semidirect
48. C43×#461C22semidirect
49. C43×#460C22semidirect
52. C43×#459C22semidirect
56. C43×#432C22semidirect
57. C43×#423C22semidirect
58. C2×C4×C8×C43C22semidirect
59. C43×#332C22semidirect
60. C43×#332C22semidirect
63. C43×Q8⋊C8C22semidirect
64. C43×Q8⋊C8C22semidirect
69. C43×D4⋊C8C22semidirect
70. C43×D4⋊C8C22semidirect
358. #18704C43direct (N × H)
394. #3546C2×C43semidirect
395. #3251C2×C43semidirect
396. #3214C2×C43semidirect
397. #3169C2×C43semidirect
398. #1650C2×C43semidirect
399. #1647C2×C43semidirect
400. #1642C2×C43semidirect
401. #1639C2×C43semidirect
402. #1628C2×C43semidirect
403. #1625C2×C43semidirect
404. #1621C2×C43semidirect
405. #1619C2×C43semidirect
406. #1557C2×C43semidirect
407. #1494C2×C43semidirect
408. #1492C2×C43semidirect
434. #532C22×C43semidirect
436. #500C22×C43semidirect
441. #486C22×C43semidirect
443. #475C22×C43semidirect
450. #461C22×C43semidirect
451. #460C22×C43semidirect
454. #459C22×C43semidirect
458. #432C22×C43semidirect
459. #423C22×C43semidirect
460. C2×C4×C8C22×C43semidirect
461. #332C22×C43semidirect
462. #332C22×C43semidirect
465. Q8⋊C8C22×C43semidirect
466. Q8⋊C8C22×C43semidirect
471. D4⋊C8C22×C43semidirect
472. D4⋊C8C22×C43semidirect
473. C43#18704direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35462
C43×#32512
C43×#32142
C43×#31692
C43×#16502
C43×#16472
C43×#16422
C43×#16392
C43×#16282
C43×#16252
C43×#16212
C43×#16192
C43×#15572
C43×#14942
C43×#14922
#1870443