Finite Group Databasebeta

← C43×#18705 #24938722

Subgroups — C43×#18705 #24938722

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3546C211yesmaximal, characteristic
2C43×#3252C211yesmaximal, characteristic, complemented
3C43×#3235C211yesmaximal, characteristic, complemented
4C43×#3167C211yesmaximal, characteristic, complemented
5C43×#1654C211yesmaximal, characteristic, complemented
6C43×#1652C211yesmaximal, characteristic, complemented
7C43×#1641C211yesmaximal, characteristic, complemented
8C43×#1639C211yesmaximal, characteristic, complemented
9C43×#1638C211yesmaximal, characteristic, complemented
10C43×#1635C211yesmaximal, characteristic, complemented
11C43×#1631C211yesmaximal, characteristic, complemented
12C43×#1629C211yesmaximal, 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×#533C2211yescharacteristic, complemented
31C43×#532C2211yescharacteristic
32C43×#532C2211yescharacteristic
33C43×#529C2211yescharacteristic
34C43×#501—21no—
35C43×#498C2211yescharacteristic, complemented
36C43×#492C2211yescharacteristic
37C43×#490—21no—
38C43×#487C2211yescharacteristic, complemented
39C43×#486C2211yescharacteristic
40C43×#482—21no—
41C43×#482—21no—
42C43×#479—21no—
43C43×#477C2211yescharacteristic, complemented
44C43×#476C2211yescharacteristic
45C43×#476C2211yescharacteristic
46C43×#476C2211yescharacteristic, complemented
47C43×#474C2211yescharacteristic
48C43×#474C2211yescharacteristic, complemented
49C43×#470—21no—
50C43×#468—21no—
51C43×#465—22no—
52C43×#464—21no—
53C43×#462C2211yescharacteristic, complemented
54C43×#461C2211yescharacteristic
55C4×SD16×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—
75C22×D4×C43—21no—
76C22×D4×C43—21no—
77C2×Q16×C43—21no—
78C2×SD16×C43—22no—
79C2×SD16×C43—21no—
80C2×M16×C43—21no—
81C22×C8×C43—21no—
82C4⋊Q8×C43D411yescharacteristic
83C4⋊Q8×C43C2311yescharacteristic
84C4⋊Q8×C43C2311yescharacteristic
85C4⋊Q8×C43C2311yescharacteristic
86#127×C43—22no—
87#127×C43—21no—
88#127×C43D411yescharacteristic
89#127×C43C2311yescharacteristic
90#126×C43—22no—
91#126×C43—22no—
92#126×C43—21no—
93#125×C43—21no—
94#125×C43D411yescharacteristic
95#124×C43—22no—
96#124×C43—21no—
97#124×C43—21no—
98#124×C43—21no—
99#124×C43D411yescharacteristic
100#123×C43—22no—
101#123×C43—22no—
102#123×C43—21no—
103#123×C43—22no—
104C22⋊Q8×C43—22no—
105C22⋊Q8×C43—21no—
106C22⋊Q8×C43—21no—
107C22⋊Q8×C43—21no—
108C22⋊Q8×C43—21no—
109C22⋊Q8×C43D411yescharacteristic
110#121×C43—22no—
111#121×C43—22no—
112#121×C43—22no—
113#121×C43—22no—
114#121×C43—22no—
115#121×C43—21no—
116#121×C43—22no—
117#121×C43—21no—
118#121×C43—21no—
119#121×C43—21no—
120#121×C43—21no—
121#121×C43—21no—
122#121×C43D411yescharacteristic
123#121×C43D411yescharacteristic
124#121×C43D411yescharacteristic
125#121×C43D412yes—
126#120×C43—22no—
127#120×C43—22no—
128#120×C43—22no—
129#120×C43—22no—
130C4×Q8×C43—21no—
131C4×Q8×C43—21no—
132C4×Q8×C43—21no—
133C4×Q8×C43C2311yescharacteristic
134C4×D4×C43—22no—
135C4×D4×C43—21no—
136C4×D4×C43—21no—
137C4×D4×C43—21no—
138C4×D4×C43—21no—
139C4×D4×C43D412yes—
140C4×D4×C43C2311yescharacteristic
141C4×D4×C43C2311yescharacteristic
142C4×D4×C43C2311yescharacteristic
143#117×C43—21no—
144#117×C43—21no—
145#117×C43—21no—
146C2×C4⋊C4×C43—21no—
147C2×C22⋊C4×C43—22no—
148C2×C42×C43C2311yescharacteristic
149#107×C43—21no—
150#107×C43—21no—
151#107×C43—21no—
152#106×C43—22no—
153#106×C43—21no—
154#106×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—22no—
163#103×C43—21no—
164#103×C43—21no—
165#102×C43—22no—
166#102×C43—21no—
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—
185C2×Q8×C43—21no—
186C2×Q8×C43—21no—
187C2×Q8×C43—21no—
188C2×Q8×C43—21no—
189C2×Q8×C43C2×D411yescharacteristic
190C2×D4×C43—22no—
191C2×D4×C43—22no—
192C2×D4×C43—22no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—21no—
196C2×D4×C43—21no—
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—22no—
202C2×D4×C43—21no—
203C2×D4×C43—81no—
204C2×D4×C43—81no—
205C2×D4×C43—81no—
206C2×D4×C43—81no—
207C2×D4×C43C2×D411yescharacteristic
208C2×D4×C43C2×D411yescharacteristic
209C2×D4×C43C2×D411yescharacteristic
210C2×D4×C43C2×D412yes—
211C22×C4×C43—22no—
212C22×C4×C43—22no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—22no—
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220Q16×C43—81no—
221SD16×C43—44no—
222SD16×C43—81no—
223M16×C43—81no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C2×C8×C43—42no—
231C4⋊C4×C43—22no—
232C4⋊C4×C43—22no—
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—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—41no—
244C4⋊C4×C43—41no—
245C4⋊C4×C43C2×D411yescharacteristic
246C4⋊C4×C43C2×D412yes—
247C4⋊C4×C43C2×D411yescharacteristic
248C4⋊C4×C43C2×D411yescharacteristic
249C4⋊C4×C43C2×D411yescharacteristic
250C22⋊C4×C43—22no—
251C22⋊C4×C43—22no—
252C22⋊C4×C43—22no—
253C22⋊C4×C43—22no—
254C22⋊C4×C43—22no—
255C22⋊C4×C43—21no—
256C22⋊C4×C43—21no—
257C22⋊C4×C43—21no—
258C22⋊C4×C43—21no—
259C22⋊C4×C43—21no—
260C22⋊C4×C43—22no—
261C22⋊C4×C43—22no—
262C22⋊C4×C43—21no—
263C22⋊C4×C43—21no—
264C22⋊C4×C43—21no—
265C22⋊C4×C43—21no—
266C22⋊C4×C43—41no—
267C42×C43—22no—
268C42×C43—21no—
269C42×C43—41no—
270C42×C43C2×D411yescharacteristic
271C42×C43C2×D411yescharacteristic
272C42×C43C2×D411yescharacteristic
273C42×C43C2411yescharacteristic
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—22no—
277C23×C43—21no—
278C23×C43—82no—
279C23×C43—82no—
280C23×C43—82no—
281C23×C43#12011yescharacteristic
282Q8×C43—21no—
283Q8×C43—21no—
284Q8×C43—42no—
285Q8×C43—41no—
286Q8×C43—41no—
287Q8×C43—41no—
288Q8×C43—41no—
289Q8×C43—81no—
290D4×C43—21no—
291D4×C43—21no—
292D4×C43—21no—
293D4×C43—21no—
294D4×C43—21no—
295D4×C43—21no—
296D4×C43—42no—
297D4×C43—41no—
298D4×C43—41no—
299D4×C43—41no—
300D4×C43—41no—
301D4×C43—81no—
302D4×C43—81no—
303D4×C43—81no—
304D4×C43—82no—
305D4×C43—81no—
306D4×C43—81no—
307D4×C43—82no—
308D4×C43—82no—
309D4×C43—82no—
310D4×C43—82no—
311D4×C43—82no—
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—22no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—82no—
332C2×C4×C43—82no—
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—22no—
341C8×C43—41no—
342C8×C43—41no—
343C8×C43—41no—
344C8×C43—41no—
345C8×C43—41no—
346#18705C4311yesmaximal, characteristic, direct product factor, Sylow
347C22×C43—21no—
348C22×C43—21no—
349C22×C43—21no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—42no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—42no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—42no—
361C22×C43—41no—
362C22×C43—164no—
363C22×C43C2×#12011yescharacteristic
364C4×C43—21no—
365C4×C43—21no—
366C4×C43—21no—
367C4×C43—21no—
368C4×C43—41no—
369C4×C43—42no—
370C4×C43—41no—
371C4×C43—41no—
372C4×C43—41no—
373C4×C43—41no—
374C4×C43—81no—
375C4×C43—81no—
376C4×C43#57611yescharacteristic
377C4×C43#57711yescharacteristic
378C4×C43#57711yescharacteristic
379C4×C43#57711yescharacteristic
380#3546C2×C4311yescharacteristic
381#3252C2×C4311yescharacteristic, complemented
382#3235C2×C4311yescharacteristic, complemented
383#3167C2×C4311yescharacteristic, complemented
384#1654C2×C4311yescharacteristic, complemented
385#1652C2×C4311yescharacteristic, complemented
386#1641C2×C4311yescharacteristic, complemented
387#1639C2×C4311yescharacteristic, complemented
388#1638C2×C4311yescharacteristic, complemented
389#1635C2×C4311yescharacteristic, complemented
390#1631C2×C4311yescharacteristic, complemented
391#1629C2×C4311yescharacteristic, complemented
392#1557C2×C4311yescharacteristic, complemented
393#1494C2×C4311yescharacteristic, complemented
394#1492C2×C4311yescharacteristic, complemented
395C2×C43—41no—
396C2×C43—81no—
397C2×C43—82no—
398C2×C43—81no—
399C2×C43—81no—
400C2×C43#300911yescharacteristic
401C2×C43#301211yescharacteristic
402C2×C43#301811yescharacteristic
403#560—22no—
404#556C22×C4311yescharacteristic
405#553—21no—
406#550—21no—
407#550C22×C4311yescharacteristic
408#547C22×C4311yescharacteristic
409#546—21no—
410#546—21no—
411D42C22×C4311yescharacteristic
412#542—21no—
413#538—22no—
414#537—21no—
415#535—21no—
416#535—21no—
417#533C22×C4311yescharacteristic, complemented
418#532C22×C4311yescharacteristic
419#532C22×C4311yescharacteristic
420#529C22×C4311yescharacteristic
421#501—21no—
422#498C22×C4311yescharacteristic, complemented
423#492C22×C4311yescharacteristic
424#490—21no—
425#487C22×C4311yescharacteristic, complemented
426#486C22×C4311yescharacteristic
427#482—21no—
428#482—21no—
429#479—21no—
430#477C22×C4311yescharacteristic, complemented
431#476C22×C4311yescharacteristic
432#476C22×C4311yescharacteristic
433#476C22×C4311yescharacteristic, complemented
434#474C22×C4311yescharacteristic
435#474C22×C4311yescharacteristic, complemented
436#470—21no—
437#468—21no—
438#465—22no—
439#464—21no—
440#462C22×C4311yescharacteristic, complemented
441#461C22×C4311yescharacteristic
442C4×SD16—22no—
443#432C22×C4311yescharacteristic, complemented
444#423C22×C4311yescharacteristic, complemented
445C2×C4×C8C22×C4311yescharacteristic, complemented
446#332C22×C4311yescharacteristic, complemented
447#332C22×C4311yescharacteristic, complemented
448#331C22×C4311yescharacteristic
449#331C22×C4311yescharacteristic
450Q8⋊C8C22×C4311yescharacteristic, complemented
451Q8⋊C8C22×C4311yescharacteristic, complemented
452D4⋊C8C22×C4311yescharacteristic
453D4⋊C8C22×C4311yescharacteristic
454D4⋊C8C22×C4311yescharacteristic
455D4⋊C8C22×C4311yescharacteristic
456D4⋊C8C22×C4311yescharacteristic, complemented
457D4⋊C8C22×C4311yescharacteristic, complemented
458C43#1870511yescharacteristic, direct product factor, Sylow
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C22×D4—21no—
464C22×D4—21no—
465C2×Q16—21no—
466C2×SD16—22no—
467C2×SD16—21no—
468C2×M16—21no—
469C22×C8—21no—
470C4⋊Q8D4×C4311yescharacteristic
471C4⋊Q8C23×C4311yescharacteristic
472C4⋊Q8C23×C4311yescharacteristic
473C4⋊Q8C23×C4311yescharacteristic
474#127—22no—
475#127—21no—
476#127D4×C4311yescharacteristic
477#127C23×C4311yescharacteristic
478#126—22no—
479#126—22no—
480#126—21no—
481#125—21no—
482#125D4×C4311yescharacteristic
483#124—22no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124D4×C4311yescharacteristic
488#123—22no—
489#123—22no—
490#123—21no—
491#123—22no—
492C22⋊Q8—22no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C4311yescharacteristic
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—21no—
504#121—22no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121D4×C4311yescharacteristic
511#121D4×C4311yescharacteristic
512#121D4×C4311yescharacteristic
513#121D4×C4312yes—
514#120—22no—
515#120—22no—
516#120—22no—
517#120—22no—
518C4×Q8—21no—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×Q8C23×C4311yescharacteristic
522C4×D4—22no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4D4×C4312yes—
528C4×D4C23×C4311yescharacteristic
529C4×D4C23×C4311yescharacteristic
530C4×D4C23×C4311yescharacteristic
531#117—21no—
532#117—21no—
533#117—21no—
534C2×C4⋊C4—21no—
535C2×C22⋊C4—22no—
536C2×C42C23×C4311yescharacteristic
537#107—21no—
538#107—21no—
539#107—21no—
540#106—22no—
541#106—21no—
542#106—21no—
543#106—21no—
544C4⋊C8—21no—
545C4⋊C8C23×C4311yescharacteristic
546C4⋊C8C23×C4311yescharacteristic
547C4⋊C8C23×C4311yescharacteristic
548C4⋊C8C23×C4311yescharacteristic
549#103—21no—
550#103—22no—
551#103—21no—
552#103—21no—
553#102—22no—
554#102—21no—
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559C22⋊C8—21no—
560#97—21no—
561C4×C8—21no—
562C4×C8C23×C4311yescharacteristic
563C4×C8C23×C4311yescharacteristic
564C24—22no—
565#41—81no—
566#41—81no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C4311yescharacteristic
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4C2×D4×C4311yescharacteristic
596C2×D4C2×D4×C4311yescharacteristic
597C2×D4C2×D4×C4311yescharacteristic
598C2×D4C2×D4×C4312yes—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4C2×D4×C4311yescharacteristic
606C22×C4C2×D4×C4311yescharacteristic
607C22×C4C2×D4×C4311yescharacteristic
608Q16—81no—
609SD16—44no—
610SD16—81no—
611M16—81no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—42no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4C2×D4×C4311yescharacteristic
634C4⋊C4C2×D4×C4312yes—
635C4⋊C4C2×D4×C4311yescharacteristic
636C4⋊C4C2×D4×C4311yescharacteristic
637C4⋊C4C2×D4×C4311yescharacteristic
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—41no—
655C42—22no—
656C42—21no—
657C42—41no—
658C42C2×D4×C4311yescharacteristic
659C42C2×D4×C4311yescharacteristic
660C42C2×D4×C4311yescharacteristic
661C42C24×C4311yescharacteristic
662C23—21no—
663C23—21no—
664C23—22no—
665C23—21no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23#120×C4311yescharacteristic
670Q8—21no—
671Q8—21no—
672Q8—42no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—81no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—81no—
690D4—81no—
691D4—82no—
692D4—81no—
693D4—81no—
694D4—81no—
695D4—82no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4#120×C4311yescharacteristic
723C2×C4#120×C4311yescharacteristic
724C2×C4#120×C4311yescharacteristic
725C2×C4C22×D4×C4311yescharacteristic
726C2×C4C22×D4×C4311yescharacteristic
727C2×C4C22×D4×C4311yescharacteristic
728C8—22no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C8—41no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—164no—
750C22C2×#120×C4311yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—42no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—81no—
762C4—81no—
763C4C43×#57611yescharacteristic
764C4C43×#57711yescharacteristic
765C4C43×#57711yescharacteristic
766C4C43×#57711yescharacteristic
767C2—41no—
768C2—81no—
769C2—81no—
770C2—82no—
771C2—81no—
772C2C43×#300911yescharacteristic
773C2C43×#301211yescharacteristic
774C2C43×#301811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3546C2
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×#3252C2semidirect
3. C43×#3235C2semidirect
4. C43×#3167C2semidirect
5. C43×#1654C2semidirect
6. C43×#1652C2semidirect
7. C43×#1641C2semidirect
8. C43×#1639C2semidirect
9. C43×#1638C2semidirect
10. C43×#1635C2semidirect
11. C43×#1631C2semidirect
12. C43×#1629C2semidirect
13. C43×#1557C2semidirect
14. C43×#1494C2semidirect
15. C43×#1492C2semidirect
30. C43×#533C22semidirect
35. C43×#498C22semidirect
38. C43×#487C22semidirect
43. C43×#477C22semidirect
46. C43×#476C22semidirect
48. C43×#474C22semidirect
53. C43×#462C22semidirect
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
346. #18705C43direct (N × H)
381. #3252C2×C43semidirect
382. #3235C2×C43semidirect
383. #3167C2×C43semidirect
384. #1654C2×C43semidirect
385. #1652C2×C43semidirect
386. #1641C2×C43semidirect
387. #1639C2×C43semidirect
388. #1638C2×C43semidirect
389. #1635C2×C43semidirect
390. #1631C2×C43semidirect
391. #1629C2×C43semidirect
392. #1557C2×C43semidirect
393. #1494C2×C43semidirect
394. #1492C2×C43semidirect
417. #533C22×C43semidirect
422. #498C22×C43semidirect
425. #487C22×C43semidirect
430. #477C22×C43semidirect
433. #476C22×C43semidirect
435. #474C22×C43semidirect
440. #462C22×C43semidirect
443. #432C22×C43semidirect
444. #423C22×C43semidirect
445. C2×C4×C8C22×C43semidirect
446. #332C22×C43semidirect
447. #332C22×C43semidirect
450. Q8⋊C8C22×C43semidirect
451. Q8⋊C8C22×C43semidirect
456. D4⋊C8C22×C43semidirect
457. D4⋊C8C22×C43semidirect
458. C43#18705direct (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×#32522
C43×#32352
C43×#31672
C43×#16542
C43×#16522
C43×#16412
C43×#16392
C43×#16382
C43×#16352
C43×#16312
C43×#16292
C43×#15572
C43×#14942
C43×#14922
#1870543