Finite Group Databasebeta

← C43×#19000 #24939017

Subgroups — C43×#19000 #24939017

Order 11008.

896 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3529C211yesmaximal, characteristic
2C43×#3238C211yesmaximal, characteristic, complemented
3C43×#3218C211yesmaximal, characteristic, complemented
4C43×#3141C211yesmaximal, characteristic, complemented
5C43×#1664C212yesmaximal, complemented
6C43×#1662C212yesmaximal, complemented
7C43×#1661C212yesmaximal, complemented
8C43×#1659C212yesmaximal, complemented
9C43×#1536C211yesmaximal, characteristic, complemented
10C43×#1529C211yesmaximal, characteristic, complemented
11C43×#1529C211yesmaximal, characteristic, complemented
12C43×#563—21no—
13C43×#563C2211yescharacteristic
14C43×#562—21no—
15C43×#562—21no—
16C43×#562C2211yescharacteristic
17C43×#562C2211yescharacteristic
18C43×H(3,𝔽4)C2211yescharacteristic
19C43×#560—21no—
20C43×#560—21no—
21C43×#560—21no—
22C43×#532—21no—
23C43×#532C2211yescharacteristic
24C2×C4⋊Q8×C43C2211yescharacteristic, complemented
25C43×#529—21no—
26C43×#529—21no—
27C43×#529C2211yescharacteristic
28C43×#529C2211yescharacteristic
29C43×#525—21no—
30C43×#525—21no—
31C43×#525—21no—
32C43×#501C2212yescomplemented
33C43×#497C2212yes—
34C43×#491C2212yescomplemented
35C43×#489C2212yes—
36C43×#489C2212yes—
37C43×#489C2212yescomplemented
38C43×#487—21no—
39C43×#486—21no—
40C43×#483—21no—
41C43×#480—21no—
42C43×#477—21no—
43C43×#476—21no—
44C43×#462—21no—
45C43×#461—21no—
46C43×#451—21no—
47C43×#448—21no—
48C43×#432C2211yescharacteristic, complemented
49C43×#432C2211yescharacteristic, complemented
50C43×#417—21no—
51C43×#417—21no—
52C4×M16×C43C2211yescharacteristic, complemented
53C43×#330C2212yescomplemented
54C43×#330C2212yescomplemented
55C43×#329C2212yes—
56C43×#329C2212yes—
57C43×#329C2212yes—
58C43×#329C2212yescomplemented
59C2×#41×C43—21no—
60C2×#41×C43D411yescharacteristic
61C2×#41×C43D411yescharacteristic
62C22×Q8×C43—21no—
63C23×C4×C43—21no—
64C2×Q16×C43—22no—
65C2×SD16×C43—22no—
66C2×M16×C43—21no—
67C4⋊Q8×C43—21no—
68C4⋊Q8×C43—21no—
69C4⋊Q8×C43—21no—
70C4⋊Q8×C43—21no—
71C4⋊Q8×C43D411yescharacteristic
72C4⋊Q8×C43C2312yes—
73#127×C43—21no—
74#127×C43D411yescharacteristic
75#126×C43—21no—
76#126×C43—21no—
77#126×C43—21no—
78#126×C43—21no—
79#126×C43—21no—
80#126×C43—21no—
81#125×C43—21no—
82#125×C43—21no—
83#125×C43C2311yescharacteristic
84#125×C43C2311yescharacteristic
85#124×C43—21no—
86#124×C43—21no—
87#124×C43—21no—
88#124×C43—21no—
89#124×C43C2311yescharacteristic
90#124×C43C2311yescharacteristic
91#124×C43C2311yescharacteristic
92#124×C43C2311yescharacteristic
93#123×C43—21no—
94#123×C43—21no—
95#123×C43—21no—
96#123×C43—21no—
97#123×C43—21no—
98#123×C43—21no—
99#123×C43—21no—
100#123×C43—21no—
101#123×C43—21no—
102#123×C43—21no—
103#123×C43—21no—
104#123×C43—21no—
105C22⋊Q8×C43—21no—
106C22⋊Q8×C43—21no—
107C22⋊Q8×C43—21no—
108C22⋊Q8×C43—21no—
109C22⋊Q8×C43—21no—
110C22⋊Q8×C43—21no—
111C22⋊Q8×C43—21no—
112C22⋊Q8×C43—21no—
113C22⋊Q8×C43D411yescharacteristic
114C22⋊Q8×C43D411yescharacteristic
115#121×C43—21no—
116#121×C43—21no—
117#121×C43—21no—
118#121×C43—21no—
119#121×C43—21no—
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×C43—21no—
128#121×C43—21no—
129#121×C43D411yescharacteristic
130#121×C43D411yescharacteristic
131#120×C43—21no—
132#120×C43—21no—
133#120×C43—21no—
134#120×C43—21no—
135#120×C43—21no—
136#120×C43—21no—
137C4×Q8×C43D411yescharacteristic
138C4×Q8×C43D411yescharacteristic
139C4×D4×C43—21no—
140C4×D4×C43—21no—
141C4×D4×C43—21no—
142C4×D4×C43—21no—
143C4×D4×C43—21no—
144C4×D4×C43—21no—
145C4×D4×C43—21no—
146C4×D4×C43—21no—
147C4×D4×C43D411yescharacteristic
148C4×D4×C43D411yescharacteristic
149#117×C43—21no—
150#117×C43—21no—
151#117×C43—21no—
152C2×C4⋊C4×C43—21no—
153C2×C4⋊C4×C43—21no—
154C2×C42×C43—21no—
155C2×C42×C43C2311yescharacteristic
156#107×C43—22no—
157#106×C43—22no—
158C4⋊C8×C43—21no—
159C4⋊C8×C43—21no—
160#103×C43—22no—
161#103×C43—22no—
162#103×C43—22no—
163#103×C43—22no—
164#103×C43—22no—
165#102×C43—22no—
166#102×C43—22no—
167#102×C43—22no—
168C22⋊C8×C43—21no—
169C22⋊C8×C43—21no—
170#97×C43C2312yes—
171#97×C43C2312yes—
172#97×C43C2312yes—
173C4×C8×C43—21no—
174C24×C43—21no—
175#41×C43—42no—
176#41×C43—42no—
177#41×C43—82no—
178C2×Q8×C43—21no—
179C2×Q8×C43—22no—
180C2×Q8×C43—41no—
181C2×Q8×C43—82no—
182C2×Q8×C43C2×D411yescharacteristic
183C2×Q8×C43C2×D411yescharacteristic
184C2×Q8×C43C2×D411yescharacteristic
185C2×Q8×C43C2×D411yescharacteristic
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—21no—
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43C2×D411yescharacteristic
200C2×D4×C43C2×D411yescharacteristic
201C2×D4×C43C2×D411yescharacteristic
202C2×D4×C43C2×D411yescharacteristic
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—41no—
213C22×C4×C43—82no—
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217Q16×C43—82no—
218SD16×C43—82no—
219M16×C43—42no—
220C2×C8×C43—22no—
221C2×C8×C43—22no—
222C2×C8×C43—22no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—22no—
240C4⋊C4×C43—22no—
241C4⋊C4×C43—41no—
242C4⋊C4×C43—41no—
243C4⋊C4×C43C2×D411yescharacteristic
244C4⋊C4×C43C2×D411yescharacteristic
245C4⋊C4×C43C2×D411yescharacteristic
246C4⋊C4×C43C2×D411yescharacteristic
247C22⋊C4×C43—21no—
248C22⋊C4×C43—21no—
249C22⋊C4×C43—21no—
250C22⋊C4×C43—21no—
251C22⋊C4×C43—21no—
252C22⋊C4×C43—21no—
253C22⋊C4×C43—21no—
254C22⋊C4×C43—21no—
255C22⋊C4×C43—21no—
256C22⋊C4×C43—21no—
257C22⋊C4×C43—21no—
258C22⋊C4×C43—21no—
259C22⋊C4×C43—21no—
260C22⋊C4×C43—21no—
261C22⋊C4×C43—21no—
262C22⋊C4×C43—21no—
263C22⋊C4×C43—21no—
264C22⋊C4×C43—21no—
265C22⋊C4×C43—21no—
266C22⋊C4×C43—21no—
267C22⋊C4×C43—21no—
268C22⋊C4×C43—21no—
269C22⋊C4×C43—21no—
270C22⋊C4×C43—21no—
271C42×C43—21no—
272C42×C43—21no—
273C42×C43—21no—
274C42×C43—21no—
275C42×C43C2×D411yescharacteristic
276C42×C43C2×D411yescharacteristic
277C42×C43C2×D411yescharacteristic
278C42×C43C2411yescharacteristic
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—81no—
284C23×C43—81no—
285C23×C43—81no—
286C23×C43#12011yescharacteristic
287Q8×C43—41no—
288Q8×C43—41no—
289Q8×C43—41no—
290Q8×C43—41no—
291Q8×C43—42no—
292Q8×C43—42no—
293Q8×C43—82no—
294Q8×C43—81no—
295D4×C43—41no—
296D4×C43—41no—
297D4×C43—41no—
298D4×C43—41no—
299D4×C43—81no—
300D4×C43—81no—
301D4×C43—81no—
302D4×C43—81no—
303D4×C43—81no—
304D4×C43—81no—
305D4×C43—81no—
306D4×C43—81no—
307D4×C43—81no—
308D4×C43—81no—
309D4×C43—81no—
310D4×C43—81no—
311D4×C43—81no—
312C2×C4×C43—22no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—42no—
324C2×C4×C43—42no—
325C2×C4×C43—42no—
326C2×C4×C43—42no—
327C2×C4×C43—42no—
328C2×C4×C43—81no—
329C2×C4×C43—81no—
330C2×C4×C43—81no—
331C2×C4×C43—81no—
332C2×C4×C43—81no—
333C2×C4×C43—82no—
334C2×C4×C43#12011yescharacteristic
335C2×C4×C43#12011yescharacteristic
336C2×C4×C43#12011yescharacteristic
337C2×C4×C43C22×D411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C8×C43—42no—
341C8×C43—42no—
342C8×C43—42no—
343#19000C4311yesmaximal, characteristic, direct product factor, Sylow
344C22×C43—21no—
345C22×C43—21no—
346C22×C43—21no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—84no—
360C22×C43C2×#12011yescharacteristic
361C4×C43—21no—
362C4×C43—21no—
363C4×C43—21no—
364C4×C43—21no—
365C4×C43—21no—
366C4×C43—41no—
367C4×C43—41no—
368C4×C43—41no—
369C4×C43—41no—
370C4×C43—41no—
371C4×C43—41no—
372C4×C43—41no—
373C4×C43—41no—
374C4×C43—82no—
375C4×C43#45512yes—
376#3529C2×C4311yescharacteristic
377#3238C2×C4311yescharacteristic, complemented
378#3218C2×C4311yescharacteristic, complemented
379#3141C2×C4311yescharacteristic, complemented
380#1664C2×C4312yescomplemented
381#1662C2×C4312yescomplemented
382#1661C2×C4312yescomplemented
383#1659C2×C4312yescomplemented
384#1536C2×C4311yescharacteristic, complemented
385#1529C2×C4311yescharacteristic, complemented
386#1529C2×C4311yescharacteristic, complemented
387C2×C43—41no—
388C2×C43—81no—
389C2×C43—81no—
390C2×C43—81no—
391C2×C43—81no—
392C2×C43C2×#45511yescharacteristic
393C2×C43#302111yescharacteristic
394C2×C43#302211yescharacteristic
395#563—21no—
396#563C22×C4311yescharacteristic
397#562—21no—
398#562—21no—
399#562C22×C4311yescharacteristic
400#562C22×C4311yescharacteristic
401H(3,𝔽4)C22×C4311yescharacteristic
402#560—21no—
403#560—21no—
404#560—21no—
405#532—21no—
406#532C22×C4311yescharacteristic
407C2×C4⋊Q8C22×C4311yescharacteristic, complemented
408#529—21no—
409#529—21no—
410#529C22×C4311yescharacteristic
411#529C22×C4311yescharacteristic
412#525—21no—
413#525—21no—
414#525—21no—
415#501C22×C4312yescomplemented
416#497C22×C4312yes—
417#491C22×C4312yescomplemented
418#489C22×C4312yes—
419#489C22×C4312yes—
420#489C22×C4312yescomplemented
421#487—21no—
422#486—21no—
423#483—21no—
424#480—21no—
425#477—21no—
426#476—21no—
427#462—21no—
428#461—21no—
429#451—21no—
430#448—21no—
431#432C22×C4311yescharacteristic, complemented
432#432C22×C4311yescharacteristic, complemented
433#417—21no—
434#417—21no—
435C4×M16C22×C4311yescharacteristic, complemented
436#330C22×C4312yescomplemented
437#330C22×C4312yescomplemented
438#329C22×C4312yes—
439#329C22×C4312yes—
440#329C22×C4312yes—
441#329C22×C4312yescomplemented
442C43#1900011yescharacteristic, direct product factor, Sylow
443C2×#41—21no—
444C2×#41D4×C4311yescharacteristic
445C2×#41D4×C4311yescharacteristic
446C22×Q8—21no—
447C23×C4—21no—
448C2×Q16—22no—
449C2×SD16—22no—
450C2×M16—21no—
451C4⋊Q8—21no—
452C4⋊Q8—21no—
453C4⋊Q8—21no—
454C4⋊Q8—21no—
455C4⋊Q8D4×C4311yescharacteristic
456C4⋊Q8C23×C4312yes—
457#127—21no—
458#127D4×C4311yescharacteristic
459#126—21no—
460#126—21no—
461#126—21no—
462#126—21no—
463#126—21no—
464#126—21no—
465#125—21no—
466#125—21no—
467#125C23×C4311yescharacteristic
468#125C23×C4311yescharacteristic
469#124—21no—
470#124—21no—
471#124—21no—
472#124—21no—
473#124C23×C4311yescharacteristic
474#124C23×C4311yescharacteristic
475#124C23×C4311yescharacteristic
476#124C23×C4311yescharacteristic
477#123—21no—
478#123—21no—
479#123—21no—
480#123—21no—
481#123—21no—
482#123—21no—
483#123—21no—
484#123—21no—
485#123—21no—
486#123—21no—
487#123—21no—
488#123—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C4311yescharacteristic
498C22⋊Q8D4×C4311yescharacteristic
499#121—21no—
500#121—21no—
501#121—21no—
502#121—21no—
503#121—21no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121D4×C4311yescharacteristic
514#121D4×C4311yescharacteristic
515#120—21no—
516#120—21no—
517#120—21no—
518#120—21no—
519#120—21no—
520#120—21no—
521C4×Q8D4×C4311yescharacteristic
522C4×Q8D4×C4311yescharacteristic
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4D4×C4311yescharacteristic
532C4×D4D4×C4311yescharacteristic
533#117—21no—
534#117—21no—
535#117—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C42—21no—
539C2×C42C23×C4311yescharacteristic
540#107—22no—
541#106—22no—
542C4⋊C8—21no—
543C4⋊C8—21no—
544#103—22no—
545#103—22no—
546#103—22no—
547#103—22no—
548#103—22no—
549#102—22no—
550#102—22no—
551#102—22no—
552C22⋊C8—21no—
553C22⋊C8—21no—
554#97C23×C4312yes—
555#97C23×C4312yes—
556#97C23×C4312yes—
557C4×C8—21no—
558C24—21no—
559#41—42no—
560#41—42no—
561#41—82no—
562C2×Q8—21no—
563C2×Q8—22no—
564C2×Q8—41no—
565C2×Q8—82no—
566C2×Q8C2×D4×C4311yescharacteristic
567C2×Q8C2×D4×C4311yescharacteristic
568C2×Q8C2×D4×C4311yescharacteristic
569C2×Q8C2×D4×C4311yescharacteristic
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4C2×D4×C4311yescharacteristic
584C2×D4C2×D4×C4311yescharacteristic
585C2×D4C2×D4×C4311yescharacteristic
586C2×D4C2×D4×C4311yescharacteristic
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—41no—
597C22×C4—82no—
598C22×C4C2×D4×C4311yescharacteristic
599C22×C4C2×D4×C4311yescharacteristic
600C22×C4C2×D4×C4311yescharacteristic
601Q16—82no—
602SD16—82no—
603M16—42no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4C2×D4×C4311yescharacteristic
628C4⋊C4C2×D4×C4311yescharacteristic
629C4⋊C4C2×D4×C4311yescharacteristic
630C4⋊C4C2×D4×C4311yescharacteristic
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42C2×D4×C4311yescharacteristic
660C42C2×D4×C4311yescharacteristic
661C42C2×D4×C4311yescharacteristic
662C42C24×C4311yescharacteristic
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—81no—
668C23—81no—
669C23—81no—
670C23#120×C4311yescharacteristic
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675Q8—42no—
676Q8—42no—
677Q8—82no—
678Q8—81no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—81no—
684D4—81no—
685D4—81no—
686D4—81no—
687D4—81no—
688D4—81no—
689D4—81no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—81no—
694D4—81no—
695D4—81no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—82no—
718C2×C4#120×C4311yescharacteristic
719C2×C4#120×C4311yescharacteristic
720C2×C4#120×C4311yescharacteristic
721C2×C4C22×D4×C4311yescharacteristic
722C2×C4C22×D4×C4311yescharacteristic
723C2×C4C22×D4×C4311yescharacteristic
724C8—42no—
725C8—42no—
726C8—42no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—84no—
743C22C2×#120×C4311yescharacteristic
744C4—21no—
745C4—21no—
746C4—21no—
747C4—21no—
748C4—21no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—82no—
758C4C43×#45512yes—
759C2—41no—
760C2—81no—
761C2—81no—
762C2—81no—
763C2—81no—
764C2C2×C43×#45511yescharacteristic
765C2C43×#302111yescharacteristic
766C2C43×#302211yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3529C2
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
2. C43×#3238C2semidirect
3. C43×#3218C2semidirect
4. C43×#3141C2semidirect
5. C43×#1664C2semidirect
6. C43×#1662C2semidirect
7. C43×#1661C2semidirect
8. C43×#1659C2semidirect
9. C43×#1536C2semidirect
10. C43×#1529C2semidirect
11. C43×#1529C2semidirect
24. C2×C4⋊Q8×C43C22semidirect
32. C43×#501C22semidirect
34. C43×#491C22semidirect
37. C43×#489C22semidirect
48. C43×#432C22semidirect
49. C43×#432C22semidirect
52. C4×M16×C43C22semidirect
53. C43×#330C22semidirect
54. C43×#330C22semidirect
58. C43×#329C22semidirect
343. #19000C43direct (N × H)
377. #3238C2×C43semidirect
378. #3218C2×C43semidirect
379. #3141C2×C43semidirect
380. #1664C2×C43semidirect
381. #1662C2×C43semidirect
382. #1661C2×C43semidirect
383. #1659C2×C43semidirect
384. #1536C2×C43semidirect
385. #1529C2×C43semidirect
386. #1529C2×C43semidirect
407. C2×C4⋊Q8C22×C43semidirect
415. #501C22×C43semidirect
417. #491C22×C43semidirect
420. #489C22×C43semidirect
431. #432C22×C43semidirect
432. #432C22×C43semidirect
435. C4×M16C22×C43semidirect
436. #330C22×C43semidirect
437. #330C22×C43semidirect
441. #329C22×C43semidirect
442. C43#19000direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35292
C43×#32382
C43×#32182
C43×#31412
C43×#16642
C43×#16622
C43×#16612
C43×#16592
C43×#15362
C43×#15292
#1900043