Finite Group Databasebeta

← C43×#18742 #24938759

Subgroups — C43×#18742 #24938759

Order 11008.

908 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3554C211yesmaximal, characteristic, complemented
2C43×#3246C211yesmaximal, characteristic, complemented
3C43×#3212C211yesmaximal, characteristic, complemented
4C43×#3184C211yesmaximal, characteristic, complemented
5C43×#1653C211yesmaximal, characteristic, complemented
6C43×#1651C211yesmaximal, characteristic, complemented
7C43×#1642C211yesmaximal, characteristic, complemented
8C43×#1640C211yesmaximal, characteristic, complemented
9C43×#1627C211yesmaximal, characteristic, complemented
10C43×#1626C211yesmaximal, characteristic, complemented
11C43×#1621C211yesmaximal, characteristic, complemented
12C43×#1620C211yesmaximal, characteristic, complemented
13C43×#1540C211yesmaximal, characteristic, complemented
14C43×#1485C211yesmaximal, characteristic, complemented
15C43×#1483C211yesmaximal, characteristic, complemented
16C43×#562—22no—
17C43×#559—21no—
18C43×#559C2211yescharacteristic
19C43×#557C2211yescharacteristic
20C43×#554—21no—
21C43×#550C2211yescharacteristic
22D4×Q8×C43C2211yescharacteristic
23C43×#548—21no—
24C43×#547—21no—
25C43×#542—21no—
26C43×#542—21no—
27C43×#540—21no—
28C43×#539—22no—
29C43×#536—21no—
30C43×#533C2211yescharacteristic
31C43×#532C2211yescharacteristic
32C43×#532C2211yescharacteristic
33C43×#529C2211yescharacteristic
34C43×#498C2211yescharacteristic
35C43×#495—21no—
36C43×#493C2211yescharacteristic
37C43×#488—21no—
38C43×#486C2211yescharacteristic
39C43×#486C2211yescharacteristic
40C43×#476—21no—
41C43×#475C2211yescharacteristic
42C43×#475C2211yescharacteristic
43C43×#469—22no—
44C43×#465—21no—
45C43×#465—21no—
46C43×#462C2211yescharacteristic
47C43×#461—21no—
48C43×#461C2211yescharacteristic
49C43×#460C2211yescharacteristic
50C43×#460C2211yescharacteristic
51C43×#460C2211yescharacteristic
52C43×#459C2211yescharacteristic
53C43×#452—21no—
54C43×#449—21no—
55C43×#442—22no—
56C43×#431C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic
58C4×M16×C43C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#331C2211yescharacteristic
62C43×#331C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C43×Q8⋊C8C2211yescharacteristic
67C43×Q8⋊C8C2211yescharacteristic
68C43×Q8⋊C8C2211yescharacteristic
69C43×D4⋊C8C2211yescharacteristic
70C43×D4⋊C8C2211yescharacteristic
71C2×#41×C43—21no—
72C2×#41×C43—21no—
73C2×#41×C43—21no—
74C22×Q8×C43—21no—
75C2×Q16×C43—21no—
76C2×SD16×C43—21no—
77C2×SD16×C43—21no—
78C2×SD16×C43—21no—
79C2×SD16×C43—21no—
80C2×D8×C43—22no—
81C2×D8×C43—21no—
82C2×M16×C43—21no—
83C22×C8×C43—21no—
84C4⋊Q8×C43—21no—
85C4⋊Q8×C43—21no—
86C4⋊Q8×C43D411yescharacteristic
87C4⋊Q8×C43D411yescharacteristic
88C4⋊Q8×C43C2311yescharacteristic
89C4⋊Q8×C43C2311yescharacteristic
90#127×C43—21no—
91#127×C43C2311yescharacteristic
92#127×C43C2311yescharacteristic
93#126×C43—22no—
94#126×C43—21no—
95#125×C43—22no—
96#125×C43—21no—
97#125×C43—21no—
98#125×C43D411yescharacteristic
99#124×C43—22no—
100#124×C43—22no—
101#124×C43—21no—
102#124×C43—21no—
103#124×C43—21no—
104#124×C43—21no—
105#124×C43D411yescharacteristic
106#123×C43—22no—
107#123×C43—22no—
108#123×C43—22no—
109#123×C43—22no—
110#123×C43—22no—
111#123×C43—22no—
112#123×C43—21no—
113C22⋊Q8×C43—22no—
114C22⋊Q8×C43—22no—
115C22⋊Q8×C43—22no—
116C22⋊Q8×C43—22no—
117C22⋊Q8×C43—21no—
118C22⋊Q8×C43—22no—
119C22⋊Q8×C43—21no—
120C22⋊Q8×C43D411yescharacteristic
121C22⋊Q8×C43D411yescharacteristic
122C22⋊Q8×C43D411yescharacteristic
123#121×C43—22no—
124#121×C43—22no—
125#121×C43—22no—
126#121×C43—21no—
127#121×C43—21no—
128#121×C43—21no—
129#121×C43—21no—
130#121×C43D411yescharacteristic
131#121×C43D412yes—
132C4×Q8×C43—21no—
133C4×Q8×C43—21no—
134C4×Q8×C43—21no—
135C4×Q8×C43C2311yescharacteristic
136C4×Q8×C43C2311yescharacteristic
137C4×Q8×C43C2311yescharacteristic
138C4×D4×C43—22no—
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×C43D412yes—
148C4×D4×C43C2311yescharacteristic
149#117×C43—21no—
150#117×C43—21no—
151C2×C4⋊C4×C43—22no—
152C2×C42×C43C2311yescharacteristic
153#106×C43—22no—
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—21no—
163#103×C43—21no—
164#103×C43—21no—
165#102×C43—22no—
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
176#41×C43—81no—
177#41×C43—81no—
178#41×C43—81no—
179#41×C43—81no—
180#41×C43—81no—
181#41×C43—81no—
182C2×Q8×C43—22no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—81no—
187C2×Q8×C43—81no—
188C2×Q8×C43C2×D411yescharacteristic
189C2×Q8×C43C2×D411yescharacteristic
190C2×Q8×C43C2×D411yescharacteristic
191C2×D4×C43—22no—
192C2×D4×C43—22no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—22no—
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—41no—
201C2×D4×C43C2×D411yescharacteristic
202C2×D4×C43C2×D412yes—
203C22×C4×C43—22no—
204C22×C4×C43—22no—
205C22×C4×C43—22no—
206C22×C4×C43—21no—
207C22×C4×C43—22no—
208C22×C4×C43—41no—
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212Q16×C43—81no—
213SD16×C43—81no—
214SD16×C43—81no—
215SD16×C43—81no—
216SD16×C43—81no—
217D8×C43—44no—
218D8×C43—81no—
219M16×C43—42no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—81no—
227C4⋊C4×C43—22no—
228C4⋊C4×C43—22no—
229C4⋊C4×C43—22no—
230C4⋊C4×C43—22no—
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—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43C2×D411yescharacteristic
246C4⋊C4×C43C2×D411yescharacteristic
247C4⋊C4×C43C2×D411yescharacteristic
248C4⋊C4×C43C2×D412yes—
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—22no—
259C22⋊C4×C43—22no—
260C22⋊C4×C43—21no—
261C22⋊C4×C43—21no—
262C22⋊C4×C43—21no—
263C22⋊C4×C43—21no—
264C22⋊C4×C43—41no—
265C22⋊C4×C43—41no—
266C42×C43—22no—
267C42×C43—21no—
268C42×C43—21no—
269C42×C43—21no—
270C42×C43C2×D411yescharacteristic
271C42×C43C2×D411yescharacteristic
272C42×C43C2×D411yescharacteristic
273C42×C43C2411yescharacteristic
274C23×C43—21no—
275C23×C43—22no—
276C23×C43—41no—
277C23×C43#12011yescharacteristic
278Q8×C43—21no—
279Q8×C43—21no—
280Q8×C43—21no—
281Q8×C43—21no—
282Q8×C43—21no—
283Q8×C43—21no—
284Q8×C43—41no—
285Q8×C43—41no—
286Q8×C43—41no—
287Q8×C43—41no—
288Q8×C43—81no—
289Q8×C43—82no—
290D4×C43—21no—
291D4×C43—21no—
292D4×C43—42no—
293D4×C43—42no—
294D4×C43—41no—
295D4×C43—41no—
296D4×C43—41no—
297D4×C43—41no—
298D4×C43—41no—
299D4×C43—41no—
300D4×C43—41no—
301D4×C43—41no—
302D4×C43—81no—
303D4×C43—82no—
304D4×C43—82no—
305D4×C43—82no—
306D4×C43—82no—
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—22no—
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—82no—
324C2×C4×C43—82no—
325C2×C4×C43—82no—
326C2×C4×C43—82no—
327C2×C4×C43—82no—
328C2×C4×C43#12011yescharacteristic
329C2×C4×C43#12011yescharacteristic
330C2×C4×C43#12011yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C22×D411yescharacteristic
334C8×C43—22no—
335C8×C43—41no—
336C8×C43—41no—
337C8×C43—41no—
338C8×C43—41no—
339C8×C43—41no—
340#18742C4311yesmaximal, characteristic, direct product factor, Sylow
341C22×C43—21no—
342C22×C43—21no—
343C22×C43—21no—
344C22×C43—41no—
345C22×C43—42no—
346C22×C43—41no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—41no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43C2×#12011yescharacteristic
354C4×C43—21no—
355C4×C43—21no—
356C4×C43—21no—
357C4×C43—21no—
358C4×C43—41no—
359C4×C43—41no—
360C4×C43—41no—
361C4×C43—42no—
362C4×C43—41no—
363C4×C43—41no—
364C4×C43—41no—
365C4×C43—41no—
366C4×C43—81no—
367C4×C43#57611yescharacteristic
368C4×C43#57711yescharacteristic
369C4×C43#57711yescharacteristic
370C4×C43#57711yescharacteristic
371#3554C2×C4311yescharacteristic, complemented
372#3246C2×C4311yescharacteristic, complemented
373#3212C2×C4311yescharacteristic, complemented
374#3184C2×C4311yescharacteristic, complemented
375#1653C2×C4311yescharacteristic, complemented
376#1651C2×C4311yescharacteristic, complemented
377#1642C2×C4311yescharacteristic, complemented
378#1640C2×C4311yescharacteristic, complemented
379#1627C2×C4311yescharacteristic, complemented
380#1626C2×C4311yescharacteristic, complemented
381#1621C2×C4311yescharacteristic, complemented
382#1620C2×C4311yescharacteristic, complemented
383#1540C2×C4311yescharacteristic, complemented
384#1485C2×C4311yescharacteristic, complemented
385#1483C2×C4311yescharacteristic, complemented
386C2×C43—41no—
387C2×C43—81no—
388C2×C43—82no—
389C2×C43—161no—
390C2×C43#301011yescharacteristic
391C2×C43#301211yescharacteristic
392C2×C43#301811yescharacteristic
393#562—22no—
394#559—21no—
395#559C22×C4311yescharacteristic
396#557C22×C4311yescharacteristic
397#554—21no—
398#550C22×C4311yescharacteristic
399D4×Q8C22×C4311yescharacteristic
400#548—21no—
401#547—21no—
402#542—21no—
403#542—21no—
404#540—21no—
405#539—22no—
406#536—21no—
407#533C22×C4311yescharacteristic
408#532C22×C4311yescharacteristic
409#532C22×C4311yescharacteristic
410#529C22×C4311yescharacteristic
411#498C22×C4311yescharacteristic
412#495—21no—
413#493C22×C4311yescharacteristic
414#488—21no—
415#486C22×C4311yescharacteristic
416#486C22×C4311yescharacteristic
417#476—21no—
418#475C22×C4311yescharacteristic
419#475C22×C4311yescharacteristic
420#469—22no—
421#465—21no—
422#465—21no—
423#462C22×C4311yescharacteristic
424#461—21no—
425#461C22×C4311yescharacteristic
426#460C22×C4311yescharacteristic
427#460C22×C4311yescharacteristic
428#460C22×C4311yescharacteristic
429#459C22×C4311yescharacteristic
430#452—21no—
431#449—21no—
432#442—22no—
433#431C22×C4311yescharacteristic
434C2×C4⋊C8C22×C4311yescharacteristic
435C4×M16C22×C4311yescharacteristic
436#332C22×C4311yescharacteristic
437#332C22×C4311yescharacteristic
438#331C22×C4311yescharacteristic
439#331C22×C4311yescharacteristic
440Q8⋊C8C22×C4311yescharacteristic
441Q8⋊C8C22×C4311yescharacteristic
442Q8⋊C8C22×C4311yescharacteristic
443Q8⋊C8C22×C4311yescharacteristic
444Q8⋊C8C22×C4311yescharacteristic
445Q8⋊C8C22×C4311yescharacteristic
446D4⋊C8C22×C4311yescharacteristic
447D4⋊C8C22×C4311yescharacteristic
448C43#1874211yescharacteristic, direct product factor, Sylow
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C22×Q8—21no—
453C2×Q16—21no—
454C2×SD16—21no—
455C2×SD16—21no—
456C2×SD16—21no—
457C2×SD16—21no—
458C2×D8—22no—
459C2×D8—21no—
460C2×M16—21no—
461C22×C8—21no—
462C4⋊Q8—21no—
463C4⋊Q8—21no—
464C4⋊Q8D4×C4311yescharacteristic
465C4⋊Q8D4×C4311yescharacteristic
466C4⋊Q8C23×C4311yescharacteristic
467C4⋊Q8C23×C4311yescharacteristic
468#127—21no—
469#127C23×C4311yescharacteristic
470#127C23×C4311yescharacteristic
471#126—22no—
472#126—21no—
473#125—22no—
474#125—21no—
475#125—21no—
476#125D4×C4311yescharacteristic
477#124—22no—
478#124—22no—
479#124—21no—
480#124—21no—
481#124—21no—
482#124—21no—
483#124D4×C4311yescharacteristic
484#123—22no—
485#123—22no—
486#123—22no—
487#123—22no—
488#123—22no—
489#123—22no—
490#123—21no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—21no—
496C22⋊Q8—22no—
497C22⋊Q8—21no—
498C22⋊Q8D4×C4311yescharacteristic
499C22⋊Q8D4×C4311yescharacteristic
500C22⋊Q8D4×C4311yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121D4×C4311yescharacteristic
509#121D4×C4312yes—
510C4×Q8—21no—
511C4×Q8—21no—
512C4×Q8—21no—
513C4×Q8C23×C4311yescharacteristic
514C4×Q8C23×C4311yescharacteristic
515C4×Q8C23×C4311yescharacteristic
516C4×D4—22no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4D4×C4312yes—
526C4×D4C23×C4311yescharacteristic
527#117—21no—
528#117—21no—
529C2×C4⋊C4—22no—
530C2×C42C23×C4311yescharacteristic
531#106—22no—
532#106—21no—
533#106—21no—
534C4⋊C8—21no—
535C4⋊C8C23×C4311yescharacteristic
536C4⋊C8C23×C4311yescharacteristic
537C4⋊C8C23×C4311yescharacteristic
538C4⋊C8C23×C4311yescharacteristic
539#103—21no—
540#103—21no—
541#103—21no—
542#103—21no—
543#102—22no—
544#102—22no—
545#102—21no—
546#102—21no—
547#102—21no—
548#102—21no—
549C22⋊C8—21no—
550#97—21no—
551C4×C8—21no—
552C4×C8C23×C4311yescharacteristic
553C4×C8C23×C4311yescharacteristic
554#41—81no—
555#41—81no—
556#41—81no—
557#41—81no—
558#41—81no—
559#41—81no—
560C2×Q8—22no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—81no—
565C2×Q8—81no—
566C2×Q8C2×D4×C4311yescharacteristic
567C2×Q8C2×D4×C4311yescharacteristic
568C2×Q8C2×D4×C4311yescharacteristic
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4C2×D4×C4311yescharacteristic
580C2×D4C2×D4×C4312yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—41no—
587C22×C4C2×D4×C4311yescharacteristic
588C22×C4C2×D4×C4311yescharacteristic
589C22×C4C2×D4×C4311yescharacteristic
590Q16—81no—
591SD16—81no—
592SD16—81no—
593SD16—81no—
594SD16—81no—
595D8—44no—
596D8—81no—
597M16—42no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—81no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
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⋊C4C2×D4×C4311yescharacteristic
624C4⋊C4C2×D4×C4311yescharacteristic
625C4⋊C4C2×D4×C4311yescharacteristic
626C4⋊C4C2×D4×C4312yes—
627C4⋊C4C2×D4×C4311yescharacteristic
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—21no—
642C22⋊C4—41no—
643C22⋊C4—41no—
644C42—22no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42C2×D4×C4311yescharacteristic
649C42C2×D4×C4311yescharacteristic
650C42C2×D4×C4311yescharacteristic
651C42C24×C4311yescharacteristic
652C23—21no—
653C23—22no—
654C23—41no—
655C23#120×C4311yescharacteristic
656Q8—21no—
657Q8—21no—
658Q8—21no—
659Q8—21no—
660Q8—21no—
661Q8—21no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—81no—
667Q8—82no—
668D4—21no—
669D4—21no—
670D4—42no—
671D4—42no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—82no—
681D4—81no—
682D4—82no—
683D4—82no—
684D4—82no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4#120×C4311yescharacteristic
707C2×C4#120×C4311yescharacteristic
708C2×C4#120×C4311yescharacteristic
709C2×C4C22×D4×C4311yescharacteristic
710C2×C4C22×D4×C4311yescharacteristic
711C2×C4C22×D4×C4311yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—41no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22C2×#120×C4311yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4C43×#57611yescharacteristic
745C4C43×#57711yescharacteristic
746C4C43×#57711yescharacteristic
747C4C43×#57711yescharacteristic
748C2—41no—
749C2—81no—
750C2—82no—
751C2—161no—
752C2C43×#301011yescharacteristic
753C2C43×#301211yescharacteristic
754C2C43×#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×#3554C2semidirect
2. C43×#3246C2semidirect
3. C43×#3212C2semidirect
4. C43×#3184C2semidirect
5. C43×#1653C2semidirect
6. C43×#1651C2semidirect
7. C43×#1642C2semidirect
8. C43×#1640C2semidirect
9. C43×#1627C2semidirect
10. C43×#1626C2semidirect
11. C43×#1621C2semidirect
12. C43×#1620C2semidirect
13. C43×#1540C2semidirect
14. C43×#1485C2semidirect
15. C43×#1483C2semidirect
340. #18742C43direct (N × H)
371. #3554C2×C43semidirect
372. #3246C2×C43semidirect
373. #3212C2×C43semidirect
374. #3184C2×C43semidirect
375. #1653C2×C43semidirect
376. #1651C2×C43semidirect
377. #1642C2×C43semidirect
378. #1640C2×C43semidirect
379. #1627C2×C43semidirect
380. #1626C2×C43semidirect
381. #1621C2×C43semidirect
382. #1620C2×C43semidirect
383. #1540C2×C43semidirect
384. #1485C2×C43semidirect
385. #1483C2×C43semidirect
448. C43#18742direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35542
C43×#32462
C43×#32122
C43×#31842
C43×#16532
C43×#16512
C43×#16422
C43×#16402
C43×#16272
C43×#16262
C43×#16212
C43×#16202
C43×#15402
C43×#14852
C43×#14832
#1874243