Finite Group Databasebeta

← C43×#19068 #24939085

Subgroups — C43×#19068 #24939085

Order 11008.

920 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3545C211yesmaximal, characteristic, complemented
2C43×#3219C211yesmaximal, characteristic, complemented
3C43×#3213C211yesmaximal, characteristic, complemented
4C43×#3171C211yesmaximal, characteristic, complemented
5C43×#1664C211yesmaximal, characteristic, complemented
6C43×#1662C211yesmaximal, characteristic, complemented
7C43×#1661C211yesmaximal, characteristic, complemented
8C43×#1659C211yesmaximal, characteristic, complemented
9C43×#1657C211yesmaximal, characteristic, complemented
10C43×#1656C211yesmaximal, characteristic, complemented
11C43×#1656C211yesmaximal, characteristic, complemented
12C43×#1655C211yesmaximal, characteristic, complemented
13C43×#1535C211yesmaximal, characteristic, complemented
14C43×#1529C211yesmaximal, characteristic, complemented
15C43×#1527C211yesmaximal, characteristic, complemented
16C43×#563C2211yescharacteristic
17C43×#562C2211yescharacteristic
18C43×#562C2211yescharacteristic
19C43×H(3,𝔽4)C2211yescharacteristic
20C43×#555—21no—
21C43×#551—21no—
22C43×#551—21no—
23C43×#551—21no—
24C43×#546—21no—
25C43×#546—21no—
26C43×#542—21no—
27C43×#542—21no—
28C43×#538—21no—
29C43×#538—21no—
30C43×#536—21no—
31C43×#534—21no—
32C43×#532C2211yescharacteristic, complemented
33C43×#529C2211yescharacteristic
34C43×#529C2211yescharacteristic
35C2×#124×C43C2211yescharacteristic
36C43×#501C2211yescharacteristic, complemented
37C43×#497C2211yescharacteristic, complemented
38C43×#496C2211yescharacteristic
39C43×#496C2211yescharacteristic, complemented
40C43×#496C2211yescharacteristic, complemented
41C43×#496C2211yescharacteristic, complemented
42C43×#491C2211yescharacteristic, complemented
43C43×#490C2211yescharacteristic, complemented
44C43×#490C2211yescharacteristic, complemented
45C43×#489C2211yescharacteristic
46C43×#489C2211yescharacteristic, complemented
47C43×#489C2211yescharacteristic, complemented
48C43×#469—21no—
49C43×#468—21no—
50C43×#464—21no—
51C43×#463—21no—
52C43×#463—21no—
53C43×#463—21no—
54C43×#452—21no—
55C43×#449—21no—
56C43×#448—21no—
57C43×#447—21no—
58C4×SD16×C43—21no—
59C4×D8×C43—21no—
60C43×#432C2211yescharacteristic, complemented
61C43×#432C2211yescharacteristic, complemented
62C4×M16×C43C2211yescharacteristic, complemented
63C43×#330C2211yescharacteristic, complemented
64C43×#330C2211yescharacteristic, complemented
65C43×#330C2211yescharacteristic, complemented
66C43×#330C2211yescharacteristic, complemented
67C43×#329C2211yescharacteristic
68C43×#329C2211yescharacteristic
69C43×#329C2211yescharacteristic, complemented
70C43×#329C2211yescharacteristic, complemented
71C43×#329C2211yescharacteristic, complemented
72C43×#329C2211yescharacteristic, complemented
73C43×#329C2211yescharacteristic, complemented
74C43×#329C2211yescharacteristic, complemented
75C2×#41×C43—21no—
76C2×#41×C43—21no—
77C22×Q8×C43D411yescharacteristic
78C22×D4×C43—21no—
79C22×D4×C43D411yescharacteristic
80C2×Q16×C43—21no—
81C2×SD16×C43—21no—
82C2×SD16×C43—21no—
83C2×SD16×C43—21no—
84C2×SD16×C43—21no—
85C2×SD16×C43—21no—
86C2×D8×C43—21no—
87C2×D8×C43—21no—
88C2×D8×C43—21no—
89C2×D8×C43—21no—
90C2×M16×C43—21no—
91C4⋊Q8×C43—21no—
92C4⋊Q8×C43—21no—
93C4⋊Q8×C43C2311yescharacteristic
94#127×C43C2311yescharacteristic
95#126×C43—21no—
96#126×C43—21no—
97#126×C43—21no—
98#126×C43—21no—
99#126×C43—21no—
100#126×C43—21no—
101#125×C43C2311yescharacteristic
102#125×C43C2311yescharacteristic
103#124×C43—21no—
104#124×C43—21no—
105#124×C43—21no—
106#124×C43—21no—
107#124×C43—21no—
108#124×C43—21no—
109#124×C43—21no—
110#124×C43—21no—
111#124×C43—21no—
112#124×C43D411yescharacteristic
113#124×C43D411yescharacteristic
114#124×C43C2311yescharacteristic
115#124×C43C2311yescharacteristic
116#124×C43C2311yescharacteristic
117#124×C43C2311yescharacteristic
118#123×C43—21no—
119#123×C43—21no—
120#123×C43—21no—
121#123×C43—21no—
122#123×C43—21no—
123#123×C43—21no—
124#123×C43—21no—
125#123×C43—21no—
126#123×C43—21no—
127#123×C43—21no—
128#123×C43—21no—
129#123×C43—21no—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43—21no—
132C22⋊Q8×C43—21no—
133C22⋊Q8×C43—21no—
134C22⋊Q8×C43—21no—
135C22⋊Q8×C43—21no—
136C22⋊Q8×C43—21no—
137C22⋊Q8×C43—21no—
138C22⋊Q8×C43D411yescharacteristic
139C22⋊Q8×C43D411yescharacteristic
140#121×C43—21no—
141#121×C43—21no—
142#121×C43—21no—
143#121×C43—21no—
144#121×C43—21no—
145#121×C43—21no—
146#121×C43—21no—
147#121×C43—21no—
148#121×C43—21no—
149#121×C43—21no—
150#121×C43D411yescharacteristic
151#121×C43D411yescharacteristic
152#120×C43—21no—
153#120×C43—21no—
154#120×C43—21no—
155#120×C43—21no—
156#120×C43—21no—
157#120×C43—21no—
158C4×Q8×C43D411yescharacteristic
159C4×Q8×C43D411yescharacteristic
160C4×D4×C43—21no—
161C4×D4×C43—21no—
162C4×D4×C43—21no—
163C4×D4×C43—21no—
164C4×D4×C43—21no—
165C4×D4×C43—21no—
166C4×D4×C43—21no—
167C4×D4×C43—21no—
168C4×D4×C43D411yescharacteristic
169C4×D4×C43D411yescharacteristic
170#117×C43—21no—
171#117×C43—21no—
172#117×C43—21no—
173#117×C43—21no—
174#117×C43—21no—
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—21no—
177C2×C22⋊C4×C43—21no—
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C42×C43C2311yescharacteristic
181#107×C43—21no—
182#106×C43—21no—
183C4⋊C8×C43—21no—
184C4⋊C8×C43—21no—
185#103×C43—21no—
186#103×C43—21no—
187#103×C43—21no—
188#103×C43—21no—
189#103×C43—21no—
190#102×C43—21no—
191#102×C43—21no—
192#102×C43—21no—
193#102×C43—21no—
194#102×C43—21no—
195#102×C43—21no—
196#102×C43—21no—
197C22⋊C8×C43—21no—
198C22⋊C8×C43—21no—
199#97×C43C2311yescharacteristic
200#97×C43C2311yescharacteristic
201#97×C43C2311yescharacteristic
202#97×C43C2311yescharacteristic
203#97×C43C2311yescharacteristic
204#97×C43C2311yescharacteristic
205C4×C8×C43—21no—
206C24×C43—21no—
207C24×C43—21no—
208#41×C43—82no—
209#41×C43—81no—
210#41×C43—81no—
211C2×Q8×C43—21no—
212C2×Q8×C43—21no—
213C2×Q8×C43—21no—
214C2×Q8×C43—81no—
215C2×Q8×C43C2×D411yescharacteristic
216C2×Q8×C43C2×D411yescharacteristic
217C2×Q8×C43C2×D411yescharacteristic
218C2×Q8×C43C2×D411yescharacteristic
219C2×D4×C43—21no—
220C2×D4×C43—21no—
221C2×D4×C43—21no—
222C2×D4×C43—21no—
223C2×D4×C43—21no—
224C2×D4×C43—21no—
225C2×D4×C43—21no—
226C2×D4×C43—21no—
227C2×D4×C43—21no—
228C2×D4×C43—21no—
229C2×D4×C43—21no—
230C2×D4×C43—21no—
231C2×D4×C43—21no—
232C2×D4×C43—41no—
233C2×D4×C43—81no—
234C2×D4×C43—82no—
235C2×D4×C43C2×D411yescharacteristic
236C2×D4×C43C2×D411yescharacteristic
237C2×D4×C43C2×D411yescharacteristic
238C2×D4×C43C2×D411yescharacteristic
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—41no—
248C22×C4×C43C2×D411yescharacteristic
249C22×C4×C43C2×D411yescharacteristic
250C22×C4×C43C2×D411yescharacteristic
251Q16×C43—81no—
252SD16×C43—42no—
253SD16×C43—81no—
254SD16×C43—81no—
255SD16×C43—81no—
256SD16×C43—81no—
257D8×C43—42no—
258D8×C43—81no—
259D8×C43—81no—
260D8×C43—81no—
261M16×C43—42no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C2×C8×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43—21no—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—21no—
275C4⋊C4×C43—21no—
276C4⋊C4×C43—21no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43—21no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43—21no—
281C4⋊C4×C43—21no—
282C4⋊C4×C43—21no—
283C4⋊C4×C43—21no—
284C4⋊C4×C43C2×D411yescharacteristic
285C4⋊C4×C43C2×D411yescharacteristic
286C4⋊C4×C43C2×D411yescharacteristic
287C4⋊C4×C43C2×D411yescharacteristic
288C22⋊C4×C43—21no—
289C22⋊C4×C43—21no—
290C22⋊C4×C43—21no—
291C22⋊C4×C43—21no—
292C22⋊C4×C43—21no—
293C22⋊C4×C43—21no—
294C22⋊C4×C43—21no—
295C22⋊C4×C43—21no—
296C22⋊C4×C43—21no—
297C22⋊C4×C43—21no—
298C22⋊C4×C43—21no—
299C22⋊C4×C43—21no—
300C22⋊C4×C43—21no—
301C22⋊C4×C43—21no—
302C22⋊C4×C43—21no—
303C22⋊C4×C43—21no—
304C22⋊C4×C43—21no—
305C22⋊C4×C43—21no—
306C22⋊C4×C43—21no—
307C22⋊C4×C43—21no—
308C22⋊C4×C43—21no—
309C22⋊C4×C43—21no—
310C22⋊C4×C43—21no—
311C22⋊C4×C43—21no—
312C22⋊C4×C43—21no—
313C22⋊C4×C43—21no—
314C22⋊C4×C43—21no—
315C22⋊C4×C43—21no—
316C22⋊C4×C43—41no—
317C22⋊C4×C43—41no—
318C42×C43—21no—
319C42×C43—21no—
320C42×C43—21no—
321C42×C43—21no—
322C42×C43C2×D411yescharacteristic
323C42×C43C2×D411yescharacteristic
324C42×C43C2×D411yescharacteristic
325C42×C43C2411yescharacteristic
326C23×C43—21no—
327C23×C43—21no—
328C23×C43—21no—
329C23×C43—21no—
330C23×C43—42no—
331C23×C43—41no—
332C23×C43—81no—
333C23×C43—81no—
334C23×C43—81no—
335C23×C43—81no—
336C23×C43—81no—
337C23×C43#12011yescharacteristic
338Q8×C43—41no—
339Q8×C43—41no—
340Q8×C43—41no—
341Q8×C43—41no—
342Q8×C43—41no—
343Q8×C43—41no—
344Q8×C43—81no—
345Q8×C43—81no—
346D4×C43—41no—
347D4×C43—41no—
348D4×C43—41no—
349D4×C43—41no—
350D4×C43—41no—
351D4×C43—41no—
352D4×C43—41no—
353D4×C43—41no—
354D4×C43—41no—
355D4×C43—41no—
356D4×C43—42no—
357D4×C43—42no—
358D4×C43—81no—
359D4×C43—81no—
360D4×C43—81no—
361D4×C43—81no—
362D4×C43—81no—
363D4×C43—81no—
364D4×C43—81no—
365D4×C43—81no—
366D4×C43—82no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—21no—
370C2×C4×C43—21no—
371C2×C4×C43—21no—
372C2×C4×C43—21no—
373C2×C4×C43—21no—
374C2×C4×C43—21no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—42no—
379C2×C4×C43—41no—
380C2×C4×C43—81no—
381C2×C4×C43—81no—
382C2×C4×C43—82no—
383C2×C4×C43—81no—
384C2×C4×C43—81no—
385C2×C4×C43—81no—
386C2×C4×C43—81no—
387C2×C4×C43—81no—
388C2×C4×C43#12011yescharacteristic
389C2×C4×C43#12011yescharacteristic
390C2×C4×C43#12011yescharacteristic
391C2×C4×C43C22×D411yescharacteristic
392C2×C4×C43C22×D411yescharacteristic
393C2×C4×C43C22×D411yescharacteristic
394C8×C43—22no—
395C8×C43—41no—
396C8×C43—41no—
397C8×C43—41no—
398C8×C43—41no—
399C8×C43—41no—
400#19068C4311yesmaximal, characteristic, direct product factor, Sylow
401C22×C43—21no—
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—41no—
405C22×C43—41no—
406C22×C43—41no—
407C22×C43—41no—
408C22×C43—41no—
409C22×C43—41no—
410C22×C43—41no—
411C22×C43—41no—
412C22×C43—41no—
413C22×C43—41no—
414C22×C43—41no—
415C22×C43—41no—
416C22×C43—81no—
417C22×C43—81no—
418C22×C43—81no—
419C22×C43—162no—
420C22×C43—162no—
421C22×C43C2×#12011yescharacteristic
422C4×C43—21no—
423C4×C43—21no—
424C4×C43—21no—
425C4×C43—21no—
426C4×C43—21no—
427C4×C43—21no—
428C4×C43—41no—
429C4×C43—41no—
430C4×C43—41no—
431C4×C43—41no—
432C4×C43—41no—
433C4×C43—41no—
434C4×C43—41no—
435C4×C43—41no—
436C4×C43—81no—
437#3545C2×C4311yescharacteristic, complemented
438#3219C2×C4311yescharacteristic, complemented
439#3213C2×C4311yescharacteristic, complemented
440#3171C2×C4311yescharacteristic, complemented
441#1664C2×C4311yescharacteristic, complemented
442#1662C2×C4311yescharacteristic, complemented
443#1661C2×C4311yescharacteristic, complemented
444#1659C2×C4311yescharacteristic, complemented
445#1657C2×C4311yescharacteristic, complemented
446#1656C2×C4311yescharacteristic, complemented
447#1656C2×C4311yescharacteristic, complemented
448#1655C2×C4311yescharacteristic, complemented
449#1535C2×C4311yescharacteristic, complemented
450#1529C2×C4311yescharacteristic, complemented
451#1527C2×C4311yescharacteristic, complemented
452C2×C43—41no—
453C2×C43—81no—
454C2×C43—81no—
455C2×C43—81no—
456C2×C43—81no—
457C2×C43—161no—
458C2×C43#301811yescharacteristic
459C2×C43#301911yescharacteristic
460C2×C43#302111yescharacteristic
461#563C22×C4311yescharacteristic
462#562C22×C4311yescharacteristic
463#562C22×C4311yescharacteristic
464H(3,𝔽4)C22×C4311yescharacteristic
465#555—21no—
466#551—21no—
467#551—21no—
468#551—21no—
469#546—21no—
470#546—21no—
471#542—21no—
472#542—21no—
473#538—21no—
474#538—21no—
475#536—21no—
476#534—21no—
477#532C22×C4311yescharacteristic, complemented
478#529C22×C4311yescharacteristic
479#529C22×C4311yescharacteristic
480C2×#124C22×C4311yescharacteristic
481#501C22×C4311yescharacteristic, complemented
482#497C22×C4311yescharacteristic, complemented
483#496C22×C4311yescharacteristic
484#496C22×C4311yescharacteristic, complemented
485#496C22×C4311yescharacteristic, complemented
486#496C22×C4311yescharacteristic, complemented
487#491C22×C4311yescharacteristic, complemented
488#490C22×C4311yescharacteristic, complemented
489#490C22×C4311yescharacteristic, complemented
490#489C22×C4311yescharacteristic
491#489C22×C4311yescharacteristic, complemented
492#489C22×C4311yescharacteristic, complemented
493#469—21no—
494#468—21no—
495#464—21no—
496#463—21no—
497#463—21no—
498#463—21no—
499#452—21no—
500#449—21no—
501#448—21no—
502#447—21no—
503C4×SD16—21no—
504C4×D8—21no—
505#432C22×C4311yescharacteristic, complemented
506#432C22×C4311yescharacteristic, complemented
507C4×M16C22×C4311yescharacteristic, complemented
508#330C22×C4311yescharacteristic, complemented
509#330C22×C4311yescharacteristic, complemented
510#330C22×C4311yescharacteristic, complemented
511#330C22×C4311yescharacteristic, complemented
512#329C22×C4311yescharacteristic
513#329C22×C4311yescharacteristic
514#329C22×C4311yescharacteristic, complemented
515#329C22×C4311yescharacteristic, complemented
516#329C22×C4311yescharacteristic, complemented
517#329C22×C4311yescharacteristic, complemented
518#329C22×C4311yescharacteristic, complemented
519#329C22×C4311yescharacteristic, complemented
520C43#1906811yescharacteristic, direct product factor, Sylow
521C2×#41—21no—
522C2×#41—21no—
523C22×Q8D4×C4311yescharacteristic
524C22×D4—21no—
525C22×D4D4×C4311yescharacteristic
526C2×Q16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×SD16—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C2×D8—21no—
536C2×M16—21no—
537C4⋊Q8—21no—
538C4⋊Q8—21no—
539C4⋊Q8C23×C4311yescharacteristic
540#127C23×C4311yescharacteristic
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#125C23×C4311yescharacteristic
548#125C23×C4311yescharacteristic
549#124—21no—
550#124—21no—
551#124—21no—
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#124D4×C4311yescharacteristic
559#124D4×C4311yescharacteristic
560#124C23×C4311yescharacteristic
561#124C23×C4311yescharacteristic
562#124C23×C4311yescharacteristic
563#124C23×C4311yescharacteristic
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573#123—21no—
574#123—21no—
575#123—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8D4×C4311yescharacteristic
585C22⋊Q8D4×C4311yescharacteristic
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121D4×C4311yescharacteristic
597#121D4×C4311yescharacteristic
598#120—21no—
599#120—21no—
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604C4×Q8D4×C4311yescharacteristic
605C4×Q8D4×C4311yescharacteristic
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4D4×C4311yescharacteristic
615C4×D4D4×C4311yescharacteristic
616#117—21no—
617#117—21no—
618#117—21no—
619#117—21no—
620#117—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C42C23×C4311yescharacteristic
627#107—21no—
628#106—21no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#103—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642#102—21no—
643C22⋊C8—21no—
644C22⋊C8—21no—
645#97C23×C4311yescharacteristic
646#97C23×C4311yescharacteristic
647#97C23×C4311yescharacteristic
648#97C23×C4311yescharacteristic
649#97C23×C4311yescharacteristic
650#97C23×C4311yescharacteristic
651C4×C8—21no—
652C24—21no—
653C24—21no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—81no—
661C2×Q8C2×D4×C4311yescharacteristic
662C2×Q8C2×D4×C4311yescharacteristic
663C2×Q8C2×D4×C4311yescharacteristic
664C2×Q8C2×D4×C4311yescharacteristic
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—41no—
679C2×D4—81no—
680C2×D4—82no—
681C2×D4C2×D4×C4311yescharacteristic
682C2×D4C2×D4×C4311yescharacteristic
683C2×D4C2×D4×C4311yescharacteristic
684C2×D4C2×D4×C4311yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—41no—
694C22×C4C2×D4×C4311yescharacteristic
695C22×C4C2×D4×C4311yescharacteristic
696C22×C4C2×D4×C4311yescharacteristic
697Q16—81no—
698SD16—42no—
699SD16—81no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703D8—42no—
704D8—81no—
705D8—81no—
706D8—81no—
707M16—42no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4C2×D4×C4311yescharacteristic
731C4⋊C4C2×D4×C4311yescharacteristic
732C4⋊C4C2×D4×C4311yescharacteristic
733C4⋊C4C2×D4×C4311yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—41no—
763C22⋊C4—41no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42C2×D4×C4311yescharacteristic
769C42C2×D4×C4311yescharacteristic
770C42C2×D4×C4311yescharacteristic
771C42C24×C4311yescharacteristic
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—42no—
777C23—41no—
778C23—81no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23#120×C4311yescharacteristic
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—81no—
791Q8—81no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—42no—
803D4—42no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—82no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—82no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4#120×C4311yescharacteristic
835C2×C4#120×C4311yescharacteristic
836C2×C4#120×C4311yescharacteristic
837C2×C4C22×D4×C4311yescharacteristic
838C2×C4C22×D4×C4311yescharacteristic
839C2×C4C22×D4×C4311yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—162no—
865C22—162no—
866C22C2×#120×C4311yescharacteristic
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—81no—
882C2—41no—
883C2—81no—
884C2—81no—
885C2—81no—
886C2—81no—
887C2—161no—
888C2C43×#301811yescharacteristic
889C2C43×#301911yescharacteristic
890C2C43×#302111yescharacteristic
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×#3545C2semidirect
2. C43×#3219C2semidirect
3. C43×#3213C2semidirect
4. C43×#3171C2semidirect
5. C43×#1664C2semidirect
6. C43×#1662C2semidirect
7. C43×#1661C2semidirect
8. C43×#1659C2semidirect
9. C43×#1657C2semidirect
10. C43×#1656C2semidirect
11. C43×#1656C2semidirect
12. C43×#1655C2semidirect
13. C43×#1535C2semidirect
14. C43×#1529C2semidirect
15. C43×#1527C2semidirect
32. C43×#532C22semidirect
36. C43×#501C22semidirect
37. C43×#497C22semidirect
39. C43×#496C22semidirect
40. C43×#496C22semidirect
41. C43×#496C22semidirect
42. C43×#491C22semidirect
43. C43×#490C22semidirect
44. C43×#490C22semidirect
46. C43×#489C22semidirect
47. C43×#489C22semidirect
60. C43×#432C22semidirect
61. C43×#432C22semidirect
62. C4×M16×C43C22semidirect
63. C43×#330C22semidirect
64. C43×#330C22semidirect
65. C43×#330C22semidirect
66. C43×#330C22semidirect
69. C43×#329C22semidirect
70. C43×#329C22semidirect
71. C43×#329C22semidirect
72. C43×#329C22semidirect
73. C43×#329C22semidirect
74. C43×#329C22semidirect
400. #19068C43direct (N × H)
437. #3545C2×C43semidirect
438. #3219C2×C43semidirect
439. #3213C2×C43semidirect
440. #3171C2×C43semidirect
441. #1664C2×C43semidirect
442. #1662C2×C43semidirect
443. #1661C2×C43semidirect
444. #1659C2×C43semidirect
445. #1657C2×C43semidirect
446. #1656C2×C43semidirect
447. #1656C2×C43semidirect
448. #1655C2×C43semidirect
449. #1535C2×C43semidirect
450. #1529C2×C43semidirect
451. #1527C2×C43semidirect
477. #532C22×C43semidirect
481. #501C22×C43semidirect
482. #497C22×C43semidirect
484. #496C22×C43semidirect
485. #496C22×C43semidirect
486. #496C22×C43semidirect
487. #491C22×C43semidirect
488. #490C22×C43semidirect
489. #490C22×C43semidirect
491. #489C22×C43semidirect
492. #489C22×C43semidirect
505. #432C22×C43semidirect
506. #432C22×C43semidirect
507. C4×M16C22×C43semidirect
508. #330C22×C43semidirect
509. #330C22×C43semidirect
510. #330C22×C43semidirect
511. #330C22×C43semidirect
514. #329C22×C43semidirect
515. #329C22×C43semidirect
516. #329C22×C43semidirect
517. #329C22×C43semidirect
518. #329C22×C43semidirect
519. #329C22×C43semidirect
520. C43#19068direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35452
C43×#32192
C43×#32132
C43×#31712
C43×#16642
C43×#16622
C43×#16612
C43×#16592
C43×#16572
C43×#16562
C43×#16552
C43×#15352
C43×#15292
C43×#15272
#1906843