Finite Group Databasebeta

← C43×#8487 #24928504

Subgroups — C43×#8487 #24928504

Order 11008.

832 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3534C211yesmaximal, characteristic
2C43×#1899C211yesmaximal, characteristic, complemented
3C43×#1897C211yesmaximal, characteristic, complemented
4C43×#1875C211yesmaximal, characteristic, complemented
5C43×#1516C211yesmaximal, characteristic, complemented
6C43×#1510C211yesmaximal, characteristic, complemented
7C43×#1468C211yesmaximal, characteristic, complemented
8C43×#562—21no—
9C43×#560—21no—
10C43×#553—21no—
11C43×#551—21no—
12C43×#546—21no—
13C43×#546—21no—
14C43×#546—21no—
15D42×C43—21no—
16C43×#540—21no—
17C43×#539—21no—
18C43×#539C411yescharacteristic, complemented
19C43×#538—21no—
20C43×#538C411yescharacteristic, complemented
21C43×#537C411yescharacteristic, complemented
22C43×#534—21no—
23C43×#534C411yescharacteristic, complemented
24C43×#525C2211yescharacteristic
25C2×#123×C43C2211yescharacteristic
26C2×#121×C43C2211yescharacteristic
27C2×#117×C43C2211yescharacteristic, complemented
28C2×#104×C43—21no—
29C2×#102×C43—21no—
30C2×#99×C43—21no—
31C43×#407C2211yescharacteristic, complemented
32C2×C22⋊C8×C43C2211yescharacteristic, complemented
33C43×#381C2211yescharacteristic, complemented
34C43×#342—21no—
35C43×#340—21no—
36C43×#339—21no—
37C43×#328—21no—
38C43×#327—21no—
39C43×#327—21no—
40C43×#327—21no—
41C43×#324—21no—
42C43×#323—21no—
43C2×#41×C43—21no—
44C2×#41×C43D411yescharacteristic
45C22×D4×C43—21no—
46C22×D4×C43—21no—
47C22×D4×C43—21no—
48C22×D4×C43D411yescharacteristic
49C22×D4×C43D411yescharacteristic
50C23×C4×C43C2311yescharacteristic
51C2×M16×C43—21no—
52C22×C8×C43—21no—
53#127×C43—21no—
54#126×C43—21no—
55#126×C43—21no—
56#126×C43—21no—
57#126×C43—21no—
58#125×C43—21no—
59#125×C43—21no—
60#124×C43—21no—
61#124×C43—21no—
62#124×C43—21no—
63#123×C43—21no—
64#123×C43—21no—
65#123×C43—21no—
66#123×C43—21no—
67#123×C43—21no—
68#123×C43—21no—
69#123×C43—21no—
70#123×C43—21no—
71#123×C43—21no—
72#123×C43—21no—
73#123×C43—21no—
74#123×C43—21no—
75#123×C43—21no—
76#123×C43—21no—
77C22⋊Q8×C43—21no—
78C22⋊Q8×C43—21no—
79C22⋊Q8×C43—21no—
80C22⋊Q8×C43—21no—
81C22⋊Q8×C43—21no—
82C22⋊Q8×C43C2×C411yescharacteristic
83C22⋊Q8×C43D411yescharacteristic
84#121×C43—21no—
85#121×C43—21no—
86#121×C43—21no—
87#121×C43—21no—
88#121×C43—21no—
89#121×C43—21no—
90#121×C43—21no—
91#121×C43—21no—
92#121×C43—21no—
93#121×C43—21no—
94#121×C43—21no—
95#121×C43—21no—
96#121×C43—21no—
97#121×C43—21no—
98#121×C43—21no—
99#121×C43C2×C411yescharacteristic
100#121×C43C2×C411yescharacteristic
101#121×C43C2×C411yescharacteristic
102#121×C43D411yescharacteristic
103#121×C43D411yescharacteristic
104#121×C43D411yescharacteristic
105#120×C43—21no—
106#120×C43—21no—
107#120×C43—21no—
108#120×C43—21no—
109#120×C43—21no—
110#120×C43—21no—
111#120×C43—21no—
112#120×C43—21no—
113C4×D4×C43—21no—
114C4×D4×C43—21no—
115C4×D4×C43—21no—
116C4×D4×C43—21no—
117C4×D4×C43—21no—
118C4×D4×C43—21no—
119C4×D4×C43—21no—
120C4×D4×C43—21no—
121#117×C43—21no—
122#117×C43—42no—
123#117×C43D411yescharacteristic
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43C2×C411yescharacteristic
126C2×C4⋊C4×C43D411yescharacteristic
127C2×C4⋊C4×C43D411yescharacteristic
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43C2×C411yescharacteristic
134C2×C22⋊C4×C43D411yescharacteristic
135C2×C22⋊C4×C43D411yescharacteristic
136C2×C42×C43—21no—
137#104×C43—42no—
138#102×C43—42no—
139#99×C43—42no—
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142C22⋊C8×C43—21no—
143C22⋊C8×C43—21no—
144#95×C43—21no—
145#95×C43—21no—
146C24×C43—21no—
147C24×C43—21no—
148C24×C43C22⋊C411yescharacteristic
149C24×C43C2×D411yescharacteristic
150#41×C43—41no—
151#41×C43—41no—
152#41×C43—82no—
153C2×Q8×C43—21no—
154C2×Q8×C43C22⋊C411yescharacteristic
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—41no—
173C2×D4×C43—41no—
174C2×D4×C43—41no—
175C2×D4×C43—41no—
176C2×D4×C43—82no—
177C2×D4×C43—82no—
178C2×D4×C43—81no—
179C2×D4×C43—81no—
180C2×D4×C43C22⋊C411yescharacteristic
181C2×D4×C43C22⋊C411yescharacteristic
182C2×D4×C43C22⋊C411yescharacteristic
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—41no—
191C22×C4×C43—41no—
192C22×C4×C43—41no—
193C22×C4×C43—41no—
194C22×C4×C43C22⋊C411yescharacteristic
195C22×C4×C43C22⋊C411yescharacteristic
196C22×C4×C43C22⋊C411yescharacteristic
197C22×C4×C43C22×C411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203M16×C43—41no—
204M16×C43—41no—
205C2×C8×C43—41no—
206C2×C8×C43—41no—
207C2×C8×C43—41no—
208C2×C8×C43—41no—
209C4⋊C4×C43—21no—
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—21no—
222C4⋊C4×C43—22no—
223C4⋊C4×C43—41no—
224C4⋊C4×C43C22⋊C411yescharacteristic
225C4⋊C4×C43C22⋊C411yescharacteristic
226C4⋊C4×C43C22⋊C411yescharacteristic
227C4⋊C4×C43C22⋊C411yescharacteristic
228C22⋊C4×C43—21no—
229C22⋊C4×C43—21no—
230C22⋊C4×C43—21no—
231C22⋊C4×C43—21no—
232C22⋊C4×C43—21no—
233C22⋊C4×C43—21no—
234C22⋊C4×C43—21no—
235C22⋊C4×C43—21no—
236C22⋊C4×C43—21no—
237C22⋊C4×C43—21no—
238C22⋊C4×C43—21no—
239C22⋊C4×C43—21no—
240C22⋊C4×C43—21no—
241C22⋊C4×C43—21no—
242C22⋊C4×C43—21no—
243C22⋊C4×C43—21no—
244C22⋊C4×C43—21no—
245C22⋊C4×C43—21no—
246C22⋊C4×C43—21no—
247C22⋊C4×C43—21no—
248C22⋊C4×C43—22no—
249C22⋊C4×C43—21no—
250C22⋊C4×C43—21no—
251C22⋊C4×C43—21no—
252C22⋊C4×C43—21no—
253C22⋊C4×C43—21no—
254C22⋊C4×C43—41no—
255C22⋊C4×C43—41no—
256C22⋊C4×C43—41no—
257C42×C43—21no—
258C42×C43—21no—
259C42×C43—21no—
260C42×C43—22no—
261C42×C43—41no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—81no—
276C23×C43—81no—
277C23×C43—81no—
278C23×C43—81no—
279C23×C43—81no—
280C23×C43C2×C22⋊C411yescharacteristic
281C23×C43#12011yescharacteristic
282C23×C43#12011yescharacteristic
283Q8×C43—41no—
284Q8×C43—81no—
285D4×C43—41no—
286D4×C43—41no—
287D4×C43—41no—
288D4×C43—42no—
289D4×C43—42no—
290D4×C43—42no—
291D4×C43—41no—
292D4×C43—41no—
293D4×C43—41no—
294D4×C43—41no—
295D4×C43—81no—
296D4×C43—81no—
297D4×C43—81no—
298D4×C43—81no—
299D4×C43—81no—
300D4×C43—81no—
301D4×C43—81no—
302D4×C43—81no—
303D4×C43—81no—
304D4×C43—81no—
305D4×C43—81no—
306D4×C43—81no—
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—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—42no—
327C2×C4×C43—81no—
328C2×C4×C43—81no—
329C2×C4×C43—81no—
330C2×C4×C43—81no—
331C2×C4×C43—81no—
332C2×C4×C43—81no—
333C2×C4×C43—81no—
334C2×C4×C43—81no—
335C2×C4×C43—81no—
336C2×C4×C43—81no—
337C2×C4×C43—81no—
338C2×C4×C43—81no—
339C2×C4×C43C2×C22⋊C411yescharacteristic
340C2×C4×C43C2×C22⋊C411yescharacteristic
341C2×C4×C43#12011yescharacteristic
342C2×C4×C43#12011yescharacteristic
343C8×C43—81no—
344C8×C43—81no—
345#8487C4311yesmaximal, characteristic, direct product factor, Sylow
346C22×C43—21no—
347C22×C43—21no—
348C22×C43—21no—
349C22×C43—21no—
350C22×C43—21no—
351C22×C43—21no—
352C22×C43—21no—
353C22×C43—21no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—161no—
369C22×C43—161no—
370C22×C43—161no—
371C22×C43—162no—
372C22×C43#37911yescharacteristic
373C22×C43B(4,𝔽2)11yescharacteristic
374C22×C43#45811yescharacteristic
375C4×C43—21no—
376C4×C43—21no—
377C4×C43—21no—
378C4×C43—21no—
379C4×C43—41no—
380C4×C43—41no—
381C4×C43—41no—
382C4×C43—41no—
383C4×C43—41no—
384C4×C43—41no—
385C4×C43—41no—
386C4×C43—41no—
387C4×C43—82no—
388C4×C43—161no—
389#3534C2×C4311yescharacteristic
390#1899C2×C4311yescharacteristic, complemented
391#1897C2×C4311yescharacteristic, complemented
392#1875C2×C4311yescharacteristic, complemented
393#1516C2×C4311yescharacteristic, complemented
394#1510C2×C4311yescharacteristic, complemented
395#1468C2×C4311yescharacteristic, complemented
396C2×C43—21no—
397C2×C43—21no—
398C2×C43—41no—
399C2×C43—41no—
400C2×C43—81no—
401C2×C43—81no—
402C2×C43—81no—
403C2×C43—81no—
404C2×C43#179011yescharacteristic
405C2×C43#179411yescharacteristic
406C2×C43#179511yescharacteristic
407#562—21no—
408#560—21no—
409#553—21no—
410#551—21no—
411#546—21no—
412#546—21no—
413#546—21no—
414D42—21no—
415#540—21no—
416#539—21no—
417#539C4×C4311yescharacteristic, complemented
418#538—21no—
419#538C4×C4311yescharacteristic, complemented
420#537C4×C4311yescharacteristic, complemented
421#534—21no—
422#534C4×C4311yescharacteristic, complemented
423#525C22×C4311yescharacteristic
424C2×#123C22×C4311yescharacteristic
425C2×#121C22×C4311yescharacteristic
426C2×#117C22×C4311yescharacteristic, complemented
427C2×#104—21no—
428C2×#102—21no—
429C2×#99—21no—
430#407C22×C4311yescharacteristic, complemented
431C2×C22⋊C8C22×C4311yescharacteristic, complemented
432#381C22×C4311yescharacteristic, complemented
433#342—21no—
434#340—21no—
435#339—21no—
436#328—21no—
437#327—21no—
438#327—21no—
439#327—21no—
440#324—21no—
441#323—21no—
442C43#848711yescharacteristic, direct product factor, Sylow
443C2×#41—21no—
444C2×#41D4×C4311yescharacteristic
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4D4×C4311yescharacteristic
449C22×D4D4×C4311yescharacteristic
450C23×C4C23×C4311yescharacteristic
451C2×M16—21no—
452C22×C8—21no—
453#127—21no—
454#126—21no—
455#126—21no—
456#126—21no—
457#126—21no—
458#125—21no—
459#125—21no—
460#124—21no—
461#124—21no—
462#124—21no—
463#123—21no—
464#123—21no—
465#123—21no—
466#123—21no—
467#123—21no—
468#123—21no—
469#123—21no—
470#123—21no—
471#123—21no—
472#123—21no—
473#123—21no—
474#123—21no—
475#123—21no—
476#123—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8C2×C4×C4311yescharacteristic
483C22⋊Q8D4×C4311yescharacteristic
484#121—21no—
485#121—21no—
486#121—21no—
487#121—21no—
488#121—21no—
489#121—21no—
490#121—21no—
491#121—21no—
492#121—21no—
493#121—21no—
494#121—21no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121—21no—
499#121C2×C4×C4311yescharacteristic
500#121C2×C4×C4311yescharacteristic
501#121C2×C4×C4311yescharacteristic
502#121D4×C4311yescharacteristic
503#121D4×C4311yescharacteristic
504#121D4×C4311yescharacteristic
505#120—21no—
506#120—21no—
507#120—21no—
508#120—21no—
509#120—21no—
510#120—21no—
511#120—21no—
512#120—21no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521#117—21no—
522#117—42no—
523#117D4×C4311yescharacteristic
524C2×C4⋊C4—21no—
525C2×C4⋊C4C2×C4×C4311yescharacteristic
526C2×C4⋊C4D4×C4311yescharacteristic
527C2×C4⋊C4D4×C4311yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4C2×C4×C4311yescharacteristic
534C2×C22⋊C4D4×C4311yescharacteristic
535C2×C22⋊C4D4×C4311yescharacteristic
536C2×C42—21no—
537#104—42no—
538#102—42no—
539#99—42no—
540C22⋊C8—21no—
541C22⋊C8—21no—
542C22⋊C8—21no—
543C22⋊C8—21no—
544#95—21no—
545#95—21no—
546C24—21no—
547C24—21no—
548C24C22⋊C4×C4311yescharacteristic
549C24C2×D4×C4311yescharacteristic
550#41—41no—
551#41—41no—
552#41—82no—
553C2×Q8—21no—
554C2×Q8C22⋊C4×C4311yescharacteristic
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
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—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—82no—
577C2×D4—82no—
578C2×D4—81no—
579C2×D4—81no—
580C2×D4C22⋊C4×C4311yescharacteristic
581C2×D4C22⋊C4×C4311yescharacteristic
582C2×D4C22⋊C4×C4311yescharacteristic
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4C22⋊C4×C4311yescharacteristic
595C22×C4C22⋊C4×C4311yescharacteristic
596C22×C4C22⋊C4×C4311yescharacteristic
597C22×C4C22×C4×C4311yescharacteristic
598C22×C4C2×D4×C4311yescharacteristic
599C22×C4C2×D4×C4311yescharacteristic
600C22×C4C2×D4×C4311yescharacteristic
601C22×C4C2×D4×C4311yescharacteristic
602C22×C4C2×D4×C4311yescharacteristic
603M16—41no—
604M16—41no—
605C2×C8—41no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
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—22no—
623C4⋊C4—41no—
624C4⋊C4C22⋊C4×C4311yescharacteristic
625C4⋊C4C22⋊C4×C4311yescharacteristic
626C4⋊C4C22⋊C4×C4311yescharacteristic
627C4⋊C4C22⋊C4×C4311yescharacteristic
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
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—22no—
654C22⋊C4—41no—
655C22⋊C4—41no—
656C22⋊C4—41no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—22no—
661C42—41no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—81no—
676C23—81no—
677C23—81no—
678C23—81no—
679C23—81no—
680C23C2×C22⋊C4×C4311yescharacteristic
681C23#120×C4311yescharacteristic
682C23#120×C4311yescharacteristic
683Q8—41no—
684Q8—81no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—81no—
696D4—81no—
697D4—81no—
698D4—81no—
699D4—81no—
700D4—81no—
701D4—81no—
702D4—81no—
703D4—81no—
704D4—81no—
705D4—81no—
706D4—81no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—81no—
739C2×C4C2×C22⋊C4×C4311yescharacteristic
740C2×C4C2×C22⋊C4×C4311yescharacteristic
741C2×C4#120×C4311yescharacteristic
742C2×C4#120×C4311yescharacteristic
743C8—81no—
744C8—81no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—81no—
766C22—81no—
767C22—161no—
768C22—161no—
769C22—161no—
770C22—162no—
771C22C43×#37911yescharacteristic
772C22C43×B(4,𝔽2)11yescharacteristic
773C22C43×#45811yescharacteristic
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—82no—
787C4—161no—
788C2—21no—
789C2—21no—
790C2—41no—
791C2—41no—
792C2—81no—
793C2—81no—
794C2—81no—
795C2—81no—
796C2C43×#179011yescharacteristic
797C2C43×#179411yescharacteristic
798C2C43×#179511yescharacteristic
subgroupG/H
center, socleC22×C43#379
commutatorC22×C4C22×C4×C43
Frattini, cosocleC23×C4C23×C43
prime radicalC43×#3534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#1899C2semidirect
3. C43×#1897C2semidirect
4. C43×#1875C2semidirect
5. C43×#1516C2semidirect
6. C43×#1510C2semidirect
7. C43×#1468C2semidirect
18. C43×#539C4semidirect
20. C43×#538C4semidirect
21. C43×#537C4semidirect
23. C43×#534C4semidirect
27. C2×#117×C43C22semidirect
31. C43×#407C22semidirect
32. C2×C22⋊C8×C43C22semidirect
33. C43×#381C22semidirect
345. #8487C43direct (N × H)
390. #1899C2×C43semidirect
391. #1897C2×C43semidirect
392. #1875C2×C43semidirect
393. #1516C2×C43semidirect
394. #1510C2×C43semidirect
395. #1468C2×C43semidirect
417. #539C4×C43semidirect
419. #538C4×C43semidirect
420. #537C4×C43semidirect
422. #534C4×C43semidirect
426. C2×#117C22×C43semidirect
430. #407C22×C43semidirect
431. C2×C22⋊C8C22×C43semidirect
432. #381C22×C43semidirect
442. C43#8487direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35342
C43×#18992
C43×#18972
C43×#18752
C43×#15162
C43×#15102
C43×#14682
#848743