Finite Group Databasebeta

← C43×#18228 #24938245

Subgroups — C43×#18228 #24938245

Order 11008.

1300 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3537C211yesmaximal, characteristic, complemented
2C43×#3006C211yesmaximal, characteristic, complemented
3C43×#3002C211yesmaximal, characteristic, complemented
4C43×#2615C211yesmaximal, characteristic, complemented
5C43×#1606C212yesmaximal, complemented
6C43×#1601C212yesmaximal, complemented
7C43×#1600C212yesmaximal, complemented
8C43×#1595C212yesmaximal, complemented
9C43×#1519C211yesmaximal, characteristic, complemented
10C43×#1513C211yesmaximal, characteristic, complemented
11C43×#1471C211yesmaximal, characteristic, complemented
12C22×#41×C43C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C43—21no—
14C2×#135×C43—21no—
15C43×#560—22no—
16C43×#553—21no—
17C43×#553—21no—
18D42×C43—22no—
19D42×C43—21no—
20D42×C43—21no—
21C43×#540—21no—
22C43×#538—21no—
23C43×#538C2212yes—
24C43×#535—21no—
25C43×#534—21no—
26C43×#534C2212yes—
27C43×#525C2211yescharacteristic
28C2×#121×C43—21no—
29C2×#121×C43C2211yescharacteristic
30C2×#121×C43C2211yescharacteristic
31C43×#452—21no—
32C43×#451C2211yescharacteristic, complemented
33C43×#450C2211yescharacteristic, complemented
34C43×#449—21no—
35C43×#449—22no—
36C43×#448C2211yescharacteristic, complemented
37C43×#448C2212yescomplemented
38C43×#447C2211yescharacteristic, complemented
39C43×#447C2212yescomplemented
40C43×#417—21no—
41C43×#416—21no—
42C43×#407C2211yescharacteristic, complemented
43C2×C22⋊C8×C43C2211yescharacteristic, complemented
44C43×#393C2212yescomplemented
45C43×#392—22no—
46C43×#392C2212yescomplemented
47C43×#380—21no—
48C43×#380C2211yescharacteristic, complemented
49C43×#328C2212yescomplemented
50C43×#327C2212yescomplemented
51C43×#327C2212yescomplemented
52C43×#327C2212yescomplemented
53C43×#323C2212yescomplemented
54C43×#323C2212yescomplemented
55C2×#41×C43—21no—
56C2×#41×C43—21no—
57C2×#41×C43—21no—
58C2×#41×C43—21no—
59C2×#41×C43—44no—
60C2×#41×C43D411yescharacteristic, complemented
61C22×Q8×C43C2311yescharacteristic
62C22×D4×C43—22no—
63C22×D4×C43—21no—
64C22×D4×C43—21no—
65C22×D4×C43—22no—
66C22×D4×C43—21no—
67C22×D4×C43—22no—
68C22×D4×C43D411yescharacteristic
69C22×D4×C43D412yes—
70C22×D4×C43D411yescharacteristic, complemented
71C22×D4×C43C2311yescharacteristic
72C23×C4×C43—21no—
73C23×C4×C43C2311yescharacteristic
74AGL(1,ℤ/8)×C43—44no—
75#135×C43—44no—
76C2×Q16×C43—21no—
77C2×SD16×C43—21no—
78C2×SD16×C43—21no—
79C2×SD16×C43—22no—
80C2×D8×C43—21no—
81C2×D8×C43—22no—
82C2×M16×C43—21no—
83C22×C8×C43—21no—
84#127×C43—22no—
85#127×C43—21no—
86#126×C43—22no—
87#126×C43—22no—
88#125×C43—21no—
89#124×C43—22no—
90#123×C43—22no—
91#123×C43—21no—
92#123×C43—22no—
93#123×C43—22no—
94#123×C43—22no—
95C22⋊Q8×C43D411yescharacteristic, complemented
96C22⋊Q8×C43C2311yescharacteristic
97#121×C43—22no—
98#121×C43—21no—
99#121×C43—21no—
100#121×C43—22no—
101#121×C43—22no—
102#121×C43—22no—
103#121×C43—22no—
104#121×C43—21no—
105#121×C43—21no—
106#121×C43—21no—
107#121×C43—21no—
108#121×C43—21no—
109#121×C43—21no—
110#121×C43—22no—
111#121×C43—44no—
112#121×C43D412yescomplemented
113#121×C43D411yescharacteristic, complemented
114#121×C43C2312yes—
115#121×C43C2311yescharacteristic
116#120×C43—22no—
117#120×C43—22no—
118#120×C43—22no—
119#120×C43—21no—
120#120×C43—22no—
121#120×C43—22no—
122#120×C43—22no—
123C4×D4×C43—22no—
124C4×D4×C43—21no—
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C4×D4×C43—21no—
128C4×D4×C43—22no—
129#117×C43—21no—
130#117×C43D411yescharacteristic, complemented
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43D411yescharacteristic
133C2×C4⋊C4×C43D411yescharacteristic, complemented
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—22no—
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—22no—
138C2×C22⋊C4×C43C2312yes—
139#103×C43—21no—
140#103×C43—21no—
141#103×C43—22no—
142#102×C43—21no—
143#102×C43—21no—
144#102×C43—22no—
145C22⋊C8×C43—21no—
146C22⋊C8×C43—21no—
147C22⋊C8×C43C2311yescharacteristic
148C22⋊C8×C43C2311yescharacteristic
149C22⋊C8×C43C2312yes—
150#95×C43—22no—
151#95×C43C2312yes—
152C24×C43—22no—
153C24×C43—21no—
154C24×C43—21no—
155C24×C43C2×D412yes—
156C24×C43C2×D411yescharacteristic
157#41×C43—24no—
158#41×C43—24no—
159#41×C43—42no—
160#41×C43—42no—
161#41×C43—42no—
162#41×C43—42no—
163#41×C43—42no—
164#41×C43—42no—
165#41×C43—42no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43—42no—
169C2×Q8×C43C2×D411yescharacteristic
170C2×D4×C43—22no—
171C2×D4×C43—22no—
172C2×D4×C43—22no—
173C2×D4×C43—22no—
174C2×D4×C43—22no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—22no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—22no—
182C2×D4×C43—22no—
183C2×D4×C43—21no—
184C2×D4×C43—22no—
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—42no—
188C2×D4×C43—42no—
189C2×D4×C43—44no—
190C2×D4×C43—42no—
191C2×D4×C43—42no—
192C2×D4×C43—41no—
193C2×D4×C43—41no—
194C2×D4×C43—42no—
195C2×D4×C43—82no—
196C2×D4×C43—81no—
197C2×D4×C43—81no—
198C2×D4×C43—82no—
199C2×D4×C43—82no—
200C2×D4×C43—82no—
201C2×D4×C43—82no—
202C2×D4×C43—84no—
203C2×D4×C43—82no—
204C2×D4×C43C2×D411yescharacteristic
205C2×D4×C43C2×D412yes—
206C22×C4×C43—24no—
207C22×C4×C43—22no—
208C22×C4×C43—22no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—22no—
213C22×C4×C43—42no—
214C22×C4×C43—42no—
215C22×C4×C43—41no—
216C22×C4×C43—41no—
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D412yes—
223C22×C4×C43C2411yescharacteristic
224Q16×C43—42no—
225SD16×C43—42no—
226SD16×C43—42no—
227SD16×C43—44no—
228D8×C43—42no—
229D8×C43—44no—
230M16×C43—42no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—22no—
234C2×C8×C43—42no—
235C4⋊C4×C43—22no—
236C4⋊C4×C43—22no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—42no—
243C4⋊C4×C43C2×D412yes—
244C4⋊C4×C43C2×D411yescharacteristic
245C4⋊C4×C43C2×D411yescharacteristic
246C22⋊C4×C43—22no—
247C22⋊C4×C43—22no—
248C22⋊C4×C43—22no—
249C22⋊C4×C43—22no—
250C22⋊C4×C43—22no—
251C22⋊C4×C43—22no—
252C22⋊C4×C43—21no—
253C22⋊C4×C43—22no—
254C22⋊C4×C43—22no—
255C22⋊C4×C43—22no—
256C22⋊C4×C43—21no—
257C22⋊C4×C43—21no—
258C22⋊C4×C43—21no—
259C22⋊C4×C43—21no—
260C22⋊C4×C43—44no—
261C22⋊C4×C43—81no—
262C22⋊C4×C43—82no—
263C42×C43—22no—
264C42×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—22no—
270C23×C43—21no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—42no—
279C23×C43—42no—
280C23×C43—42no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—81no—
285C23×C43—81no—
286C23×C43—82no—
287C23×C43—82no—
288C23×C43—82no—
289C23×C43#12011yescharacteristic
290C23×C43#12011yescharacteristic
291C23×C43C22×D411yescharacteristic
292Q8×C43—22no—
293Q8×C43—22no—
294Q8×C43—41no—
295Q8×C43—41no—
296Q8×C43—41no—
297D4×C43—22no—
298D4×C43—22no—
299D4×C43—42no—
300D4×C43—41no—
301D4×C43—41no—
302D4×C43—41no—
303D4×C43—44no—
304D4×C43—42no—
305D4×C43—44no—
306D4×C43—44no—
307D4×C43—42no—
308D4×C43—41no—
309D4×C43—42no—
310D4×C43—41no—
311D4×C43—42no—
312D4×C43—42no—
313D4×C43—81no—
314D4×C43—82no—
315D4×C43—82no—
316D4×C43—81no—
317D4×C43—82no—
318D4×C43—82no—
319D4×C43—82no—
320D4×C43—82no—
321D4×C43—82no—
322D4×C43—88no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—21no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—44no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—44no—
339C2×C4×C43—42no—
340C2×C4×C43—42no—
341C2×C4×C43—42no—
342C2×C4×C43—42no—
343C2×C4×C43—42no—
344C2×C4×C43—81no—
345C2×C4×C43—82no—
346C2×C4×C43—82no—
347C2×C4×C43#12011yescharacteristic
348C2×C4×C43#12011yescharacteristic
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C8×C43—41no—
352C8×C43—41no—
353C8×C43—42no—
354#18228C4311yesmaximal, characteristic, direct product factor, Sylow
355C22×C43—21no—
356C22×C43—21no—
357C22×C43—21no—
358C22×C43—21no—
359C22×C43—21no—
360C22×C43—21no—
361C22×C43—21no—
362C22×C43—21no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—41no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43—41no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—41no—
374C22×C43—42no—
375C22×C43—81no—
376C22×C43—81no—
377C22×C43—82no—
378C22×C43—82no—
379C22×C43—81no—
380C22×C43—81no—
381C22×C43—81no—
382C22×C43—81no—
383C22×C43—162no—
384C22×C43—164no—
385C22×C43C2×#12011yescharacteristic
386C22×C43#57611yescharacteristic
387C22×C43#57711yescharacteristic
388C4×C43—21no—
389C4×C43—21no—
390C4×C43—21no—
391C4×C43—42no—
392C4×C43—41no—
393C4×C43—42no—
394C4×C43—41no—
395C4×C43—42no—
396C4×C43—41no—
397C4×C43—82no—
398C4×C43B(4,𝔽2)12yes—
399#3537C2×C4311yescharacteristic, complemented
400#3006C2×C4311yescharacteristic, complemented
401#3002C2×C4311yescharacteristic, complemented
402#2615C2×C4311yescharacteristic, complemented
403#1606C2×C4312yescomplemented
404#1601C2×C4312yescomplemented
405#1600C2×C4312yescomplemented
406#1595C2×C4312yescomplemented
407#1519C2×C4311yescharacteristic, complemented
408#1513C2×C4311yescharacteristic, complemented
409#1471C2×C4311yescharacteristic, complemented
410C2×C43—21no—
411C2×C43—21no—
412C2×C43—41no—
413C2×C43—41no—
414C2×C43—82no—
415C2×C43—82no—
416C2×C43—82no—
417C2×C43—81no—
418C2×C43#301211yescharacteristic
419C2×C43#301911yescharacteristic
420C2×C43C2×B(4,𝔽2)11yescharacteristic
421C22×#41C22×C4311yescharacteristic, complemented
422C2×AGL(1,ℤ/8)—21no—
423C2×#135—21no—
424#560—22no—
425#553—21no—
426#553—21no—
427D42—22no—
428D42—21no—
429D42—21no—
430#540—21no—
431#538—21no—
432#538C22×C4312yes—
433#535—21no—
434#534—21no—
435#534C22×C4312yes—
436#525C22×C4311yescharacteristic
437C2×#121—21no—
438C2×#121C22×C4311yescharacteristic
439C2×#121C22×C4311yescharacteristic
440#452—21no—
441#451C22×C4311yescharacteristic, complemented
442#450C22×C4311yescharacteristic, complemented
443#449—21no—
444#449—22no—
445#448C22×C4311yescharacteristic, complemented
446#448C22×C4312yescomplemented
447#447C22×C4311yescharacteristic, complemented
448#447C22×C4312yescomplemented
449#417—21no—
450#416—21no—
451#407C22×C4311yescharacteristic, complemented
452C2×C22⋊C8C22×C4311yescharacteristic, complemented
453#393C22×C4312yescomplemented
454#392—22no—
455#392C22×C4312yescomplemented
456#380—21no—
457#380C22×C4311yescharacteristic, complemented
458#328C22×C4312yescomplemented
459#327C22×C4312yescomplemented
460#327C22×C4312yescomplemented
461#327C22×C4312yescomplemented
462#323C22×C4312yescomplemented
463#323C22×C4312yescomplemented
464C43#1822811yescharacteristic, direct product factor, Sylow
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—44no—
470C2×#41D4×C4311yescharacteristic, complemented
471C22×Q8C23×C4311yescharacteristic
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—22no—
478C22×D4D4×C4311yescharacteristic
479C22×D4D4×C4312yes—
480C22×D4D4×C4311yescharacteristic, complemented
481C22×D4C23×C4311yescharacteristic
482C23×C4—21no—
483C23×C4C23×C4311yescharacteristic
484AGL(1,ℤ/8)—44no—
485#135—44no—
486C2×Q16—21no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×D8—21no—
491C2×D8—22no—
492C2×M16—21no—
493C22×C8—21no—
494#127—22no—
495#127—21no—
496#126—22no—
497#126—22no—
498#125—21no—
499#124—22no—
500#123—22no—
501#123—21no—
502#123—22no—
503#123—22no—
504#123—22no—
505C22⋊Q8D4×C4311yescharacteristic, complemented
506C22⋊Q8C23×C4311yescharacteristic
507#121—22no—
508#121—21no—
509#121—21no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—22no—
521#121—44no—
522#121D4×C4312yescomplemented
523#121D4×C4311yescharacteristic, complemented
524#121C23×C4312yes—
525#121C23×C4311yescharacteristic
526#120—22no—
527#120—22no—
528#120—22no—
529#120—21no—
530#120—22no—
531#120—22no—
532#120—22no—
533C4×D4—22no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—22no—
539#117—21no—
540#117D4×C4311yescharacteristic, complemented
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C4311yescharacteristic
543C2×C4⋊C4D4×C4311yescharacteristic, complemented
544C2×C22⋊C4—21no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4C23×C4312yes—
549#103—21no—
550#103—21no—
551#103—22no—
552#102—21no—
553#102—21no—
554#102—22no—
555C22⋊C8—21no—
556C22⋊C8—21no—
557C22⋊C8C23×C4311yescharacteristic
558C22⋊C8C23×C4311yescharacteristic
559C22⋊C8C23×C4312yes—
560#95—22no—
561#95C23×C4312yes—
562C24—22no—
563C24—21no—
564C24—21no—
565C24C2×D4×C4312yes—
566C24C2×D4×C4311yescharacteristic
567#41—24no—
568#41—24no—
569#41—42no—
570#41—42no—
571#41—42no—
572#41—42no—
573#41—42no—
574#41—42no—
575#41—42no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—42no—
579C2×Q8C2×D4×C4311yescharacteristic
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—44no—
605C2×D4—82no—
606C2×D4—82no—
607C2×D4—82no—
608C2×D4—82no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—82no—
612C2×D4—82no—
613C2×D4—84no—
614C2×D4C2×D4×C4311yescharacteristic
615C2×D4C2×D4×C4312yes—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4C2×D4×C4311yescharacteristic
628C22×C4C2×D4×C4311yescharacteristic
629C22×C4C2×D4×C4311yescharacteristic
630C22×C4C2×D4×C4312yes—
631C22×C4C2×D4×C4311yescharacteristic
632C22×C4C2×D4×C4311yescharacteristic
633C22×C4C24×C4311yescharacteristic
634Q16—42no—
635SD16—42no—
636SD16—42no—
637SD16—44no—
638D8—42no—
639D8—44no—
640M16—42no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—42no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4C2×D4×C4312yes—
654C4⋊C4C2×D4×C4311yescharacteristic
655C4⋊C4C2×D4×C4311yescharacteristic
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—44no—
671C22⋊C4—81no—
672C22⋊C4—82no—
673C42—22no—
674C42—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—81no—
695C23—81no—
696C23—82no—
697C23—82no—
698C23—82no—
699C23#120×C4311yescharacteristic
700C23#120×C4311yescharacteristic
701C23C22×D4×C4311yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707D4—22no—
708D4—22no—
709D4—42no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—44no—
714D4—42no—
715D4—44no—
716D4—44no—
717D4—42no—
718D4—41no—
719D4—42no—
720D4—41no—
721D4—42no—
722D4—42no—
723D4—81no—
724D4—82no—
725D4—82no—
726D4—81no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4—82no—
731D4—82no—
732D4—88no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—81no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4#120×C4311yescharacteristic
758C2×C4#120×C4311yescharacteristic
759C2×C4C22×D4×C4311yescharacteristic
760C2×C4C22×D4×C4311yescharacteristic
761C8—41no—
762C8—41no—
763C8—42no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—82no—
787C22—82no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—162no—
793C22—164no—
794C22C2×#120×C4311yescharacteristic
795C22C43×#57611yescharacteristic
796C22C43×#57711yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—41no—
806C4—82no—
807C4C43×B(4,𝔽2)12yes—
808C2—21no—
809C2—21no—
810C2—41no—
811C2—41no—
812C2—82no—
813C2—82no—
814C2—82no—
815C2—81no—
816C2C43×#301211yescharacteristic
817C2C43×#301911yescharacteristic
818C2C2×C43×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
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
1. C43×#3537C2semidirect
2. C43×#3006C2semidirect
3. C43×#3002C2semidirect
4. C43×#2615C2semidirect
5. C43×#1606C2semidirect
6. C43×#1601C2semidirect
7. C43×#1600C2semidirect
8. C43×#1595C2semidirect
9. C43×#1519C2semidirect
10. C43×#1513C2semidirect
11. C43×#1471C2semidirect
12. C22×#41×C43C22semidirect
32. C43×#451C22semidirect
33. C43×#450C22semidirect
36. C43×#448C22semidirect
37. C43×#448C22semidirect
38. C43×#447C22semidirect
39. C43×#447C22semidirect
42. C43×#407C22semidirect
43. C2×C22⋊C8×C43C22semidirect
44. C43×#393C22semidirect
46. C43×#392C22semidirect
48. C43×#380C22semidirect
49. C43×#328C22semidirect
50. C43×#327C22semidirect
51. C43×#327C22semidirect
52. C43×#327C22semidirect
53. C43×#323C22semidirect
54. C43×#323C22semidirect
60. C2×#41×C43D4semidirect
70. C22×D4×C43D4semidirect
95. C22⋊Q8×C43D4semidirect
112. #121×C43D4semidirect
113. #121×C43D4semidirect
130. #117×C43D4semidirect
133. C2×C4⋊C4×C43D4semidirect
354. #18228C43direct (N × H)
399. #3537C2×C43semidirect
400. #3006C2×C43semidirect
401. #3002C2×C43semidirect
402. #2615C2×C43semidirect
403. #1606C2×C43semidirect
404. #1601C2×C43semidirect
405. #1600C2×C43semidirect
406. #1595C2×C43semidirect
407. #1519C2×C43semidirect
408. #1513C2×C43semidirect
409. #1471C2×C43semidirect
421. C22×#41C22×C43semidirect
441. #451C22×C43semidirect
442. #450C22×C43semidirect
445. #448C22×C43semidirect
446. #448C22×C43semidirect
447. #447C22×C43semidirect
448. #447C22×C43semidirect
451. #407C22×C43semidirect
452. C2×C22⋊C8C22×C43semidirect
453. #393C22×C43semidirect
455. #392C22×C43semidirect
457. #380C22×C43semidirect
458. #328C22×C43semidirect
459. #327C22×C43semidirect
460. #327C22×C43semidirect
461. #327C22×C43semidirect
462. #323C22×C43semidirect
463. #323C22×C43semidirect
464. C43#18228direct (N × H)
470. C2×#41D4×C43semidirect
480. C22×D4D4×C43semidirect
505. C22⋊Q8D4×C43semidirect
522. #121D4×C43semidirect
523. #121D4×C43semidirect
540. #117D4×C43semidirect
543. C2×C4⋊C4D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#35372
C43×#30062
C43×#30022
C43×#26152
C43×#16062
C43×#16012
C43×#16002
C43×#15952
C43×#15192
C43×#15132
C43×#14712
#1822843