Finite Group Databasebeta

← C43×#25446 #24945463

Subgroups — C43×#25446 #24945463

Order 11008.

876 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×#3154C211yesmaximal, characteristic, complemented
2C43×#3069C211yesmaximal, characteristic, complemented
3C43×#3068C211yesmaximal, characteristic, complemented
4C43×#3067C211yesmaximal, characteristic, complemented
5C2×C43×#471C211yesmaximal, characteristic, complemented
6C43×#2957C211yesmaximal, characteristic, complemented
7C43×#2049C211yesmaximal, characteristic, complemented
8C43×#2048C211yesmaximal, characteristic, complemented
9C43×#2009C211yesmaximal, characteristic, complemented
10C43×#2008C211yesmaximal, characteristic, complemented
11C43×#1977C211yesmaximal, characteristic, complemented
12C43×#1953C211yesmaximal, characteristic, complemented
13C43×#1915C211yesmaximal, characteristic, complemented
14C43×#1914C211yesmaximal, characteristic, complemented
15C43×#1757C211yesmaximal, characteristic, complemented
16C43×#575C2211yescharacteristic
17C43×#575C2211yescharacteristic
18C2×#137×C43C2211yescharacteristic
19C2×#137×C43C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
21C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
22C2×#135×C43C2211yescharacteristic
23C22×SD16×C43C2211yescharacteristic
24C43×#568C2211yescharacteristic
25C43×#568C2211yescharacteristic
26C2×#131×C43C2211yescharacteristic
27C43×#536C2211yescharacteristic
28C43×#535C2211yescharacteristic
29C43×#497—21no—
30C43×#496—21no—
31C43×#495—21no—
32C43×#492—21no—
33C43×#473—21no—
34C43×#473—22no—
35C43×#472—21no—
36C43×#472—22no—
37C43×#471—21no—
38C43×#471—21no—
39C43×#471—22no—
40C43×#471—22no—
41C43×#471—22no—
42C43×#471—22no—
43C43×#444—22no—
44C43×#443—22no—
45C43×#430C2211yescharacteristic
46C43×#430C2211yescharacteristic
47C2×#108×C43C2211yescharacteristic
48C2×#108×C43C2211yescharacteristic
49C43×#421C2211yescharacteristic
50C43×#421C2211yescharacteristic
51C43×#419C2211yescharacteristic
52C43×#418C2211yescharacteristic
53C43×#413C2211yescharacteristic
54C43×#413C2211yescharacteristic
55C43×#413C2211yescharacteristic
56C2×#101×C43C2211yescharacteristic
57C2×#101×C43C2211yescharacteristic
58C2×#100×C43C2211yescharacteristic
59C2×#100×C43C2211yescharacteristic
60C43×#410C2211yescharacteristic
61C43×#405C2211yescharacteristic
62C43×#405C2211yescharacteristic
63C43×#344C2211yescharacteristic
64C43×#344C2211yescharacteristic
65C43×#344C2211yescharacteristic
66C43×#344C2211yescharacteristic
67C2×#41×C43C2311yescharacteristic
68C2×#41×C43C2311yescharacteristic
69C2×#41×C43C2311yescharacteristic
70C22×Q8×C43C2311yescharacteristic
71C22×D4×C43C2311yescharacteristic
72#137×C43—21no—
73#137×C43—21no—
74#137×C43—21no—
75#137×C43—21no—
76#137×C43—22no—
77#137×C43—22no—
78#137×C43—41no—
79#137×C43—41no—
80AGL(1,ℤ/8)×C43—21no—
81AGL(1,ℤ/8)×C43—21no—
82AGL(1,ℤ/8)×C43—21no—
83AGL(1,ℤ/8)×C43—21no—
84AGL(1,ℤ/8)×C43—22no—
85AGL(1,ℤ/8)×C43—22no—
86AGL(1,ℤ/8)×C43—41no—
87AGL(1,ℤ/8)×C43—41no—
88#135×C43—21no—
89#135×C43—21no—
90#135×C43—21no—
91#135×C43—21no—
92#135×C43—41no—
93#135×C43—41no—
94C2×Q16×C43—21no—
95C2×Q16×C43—21no—
96C2×Q16×C43D411yescharacteristic
97C2×SD16×C43—21no—
98C2×SD16×C43—21no—
99C2×SD16×C43—21no—
100C2×SD16×C43—21no—
101C2×SD16×C43—21no—
102C2×SD16×C43—21no—
103C2×SD16×C43—21no—
104C2×SD16×C43—21no—
105C2×SD16×C43—21no—
106C2×SD16×C43—21no—
107C2×SD16×C43D411yescharacteristic
108C2×SD16×C43D411yescharacteristic
109C2×D8×C43—21no—
110C2×D8×C43—21no—
111C2×D8×C43D411yescharacteristic
112#131×C43—22no—
113#131×C43—22no—
114#131×C43—22no—
115#131×C43—22no—
116#131×C43—21no—
117#131×C43—21no—
118#131×C43—21no—
119#131×C43—21no—
120C2×M16×C43—21no—
121C2×M16×C43—41no—
122C2×M16×C43—41no—
123C2×M16×C43C2311yescharacteristic
124C2×M16×C43C2311yescharacteristic
125C2×M16×C43C2311yescharacteristic
126C2×M16×C43C2311yescharacteristic
127C2×M16×C43C2311yescharacteristic
128C2×M16×C43C2311yescharacteristic
129C2×M16×C43C2311yescharacteristic
130C22×C8×C43—21no—
131C22×C8×C43C2311yescharacteristic
132C4⋊Q8×C43—21no—
133#127×C43—21no—
134#124×C43—21no—
135#124×C43—21no—
136#123×C43—22no—
137C22⋊Q8×C43—41no—
138#121×C43—41no—
139#120×C43—22no—
140#117×C43C2311yescharacteristic
141#117×C43C2311yescharacteristic
142#108×C43—22no—
143#108×C43—22no—
144#108×C43—21no—
145#108×C43—21no—
146#108×C43D412yescomplemented
147#108×C43D412yescomplemented
148#104×C43—22no—
149#104×C43—22no—
150#103×C43—41no—
151#102×C43—41no—
152#101×C43—21no—
153#101×C43—21no—
154#101×C43—22no—
155#101×C43—22no—
156#101×C43D412yescomplemented
157#100×C43—21no—
158#100×C43—21no—
159#100×C43—22no—
160#100×C43—22no—
161#100×C43D412yescomplemented
162#99×C43—22no—
163#97×C43—21no—
164#97×C43—21no—
165C4×C8×C43—21no—
166C4×C8×C43—21no—
167C24×C43—21no—
168#41×C43—21no—
169#41×C43—21no—
170#41×C43—21no—
171#41×C43—21no—
172#41×C43—21no—
173#41×C43—21no—
174#41×C43—21no—
175#41×C43—21no—
176#41×C43—21no—
177#41×C43—21no—
178#41×C43—21no—
179#41×C43—21no—
180C2×Q8×C43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43C2×D411yescharacteristic
187C2×Q8×C43C2×D411yescharacteristic
188C2×Q8×C43C2×D411yescharacteristic
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—21no—
197C2×D4×C43—21no—
198C2×D4×C43—42no—
199C2×D4×C43C2×D411yescharacteristic
200C2×D4×C43C2×D411yescharacteristic
201C2×D4×C43C2×D411yescharacteristic
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43C2411yescharacteristic
207Q16×C43—21no—
208Q16×C43—21no—
209Q16×C43—42no—
210Q16×C43—42no—
211Q16×C43—41no—
212Q16×C43—41no—
213SD16×C43—21no—
214SD16×C43—21no—
215SD16×C43—21no—
216SD16×C43—21no—
217SD16×C43—42no—
218SD16×C43—42no—
219SD16×C43—42no—
220SD16×C43—42no—
221SD16×C43—41no—
222SD16×C43—41no—
223SD16×C43—41no—
224SD16×C43—41no—
225SD16×C43—41no—
226SD16×C43—41no—
227SD16×C43—41no—
228SD16×C43—41no—
229D8×C43—21no—
230D8×C43—21no—
231D8×C43—42no—
232D8×C43—42no—
233D8×C43—41no—
234D8×C43—41no—
235M16×C43—21no—
236M16×C43—21no—
237M16×C43—21no—
238M16×C43—21no—
239M16×C43—21no—
240M16×C43—21no—
241M16×C43—21no—
242M16×C43—21no—
243M16×C43—21no—
244M16×C43—21no—
245M16×C43—42no—
246M16×C43—42no—
247M16×C43—41no—
248M16×C43—41no—
249M16×C43C2×D412yes—
250M16×C43C2×D412yes—
251M16×C43C2×D412yes—
252M16×C43C2×D412yes—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—42no—
261C2×C8×C43—42no—
262C2×C8×C43—41no—
263C2×C8×C43—41no—
264C2×C8×C43C2×D411yescharacteristic
265C2×C8×C43C2×D411yescharacteristic
266C2×C8×C43C2×D411yescharacteristic
267C2×C8×C43C2×D411yescharacteristic
268C2×C8×C43#4111yescharacteristic
269C2×C8×C43#4111yescharacteristic
270C4⋊C4×C43—21no—
271C4⋊C4×C43—21no—
272C4⋊C4×C43—42no—
273C22⋊C4×C43—21no—
274C22⋊C4×C43—42no—
275C22⋊C4×C43—42no—
276C22⋊C4×C43#4112yes—
277C42×C43—21no—
278C42×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—161no—
286C23×C43C2×#4111yescharacteristic
287Q8×C43—21no—
288Q8×C43—21no—
289Q8×C43—21no—
290Q8×C43—21no—
291Q8×C43—21no—
292Q8×C43—21no—
293Q8×C43—41no—
294Q8×C43—41no—
295Q8×C43—41no—
296Q8×C43—41no—
297D4×C43—21no—
298D4×C43—21no—
299D4×C43—21no—
300D4×C43—21no—
301D4×C43—21no—
302D4×C43—21no—
303D4×C43—41no—
304D4×C43—41no—
305D4×C43—41no—
306D4×C43—41no—
307D4×C43—41no—
308D4×C43—41no—
309D4×C43—41no—
310D4×C43—41no—
311D4×C43—41no—
312D4×C43—41no—
313D4×C43—162no—
314C2×C4×C43—21no—
315C2×C4×C43—22no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—41no—
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—41no—
327C2×C4×C43—41no—
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C22×D411yescharacteristic
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C43C2×#4111yescharacteristic
332C2×C4×C43H(5,𝔽2)11yescharacteristic
333C2×C4×C43H(5,𝔽2)11yescharacteristic
334C8×C43—22no—
335C8×C43—22no—
336C8×C43—22no—
337C8×C43—22no—
338C8×C43—41no—
339C8×C43—41no—
340C8×C43—41no—
341C8×C43#12111yescharacteristic
342C8×C43#12111yescharacteristic
343C8×C43#12111yescharacteristic
344C8×C43#12111yescharacteristic
345#25446C4311yesmaximal, characteristic, direct product factor, Sylow
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43—82no—
354C22×C43—81no—
355C22×C43—161no—
356C22×C43—161no—
357C22×C43#53211yescharacteristic
358C22×C43#54611yescharacteristic
359C22×C43#55011yescharacteristic
360C4×C43—42no—
361C4×C43—41no—
362C4×C43—41no—
363C4×C43—41no—
364C4×C43—81no—
365C4×C43—81no—
366C4×C43C2×#12111yescharacteristic
367C4×C43#54011yescharacteristic
368C4×C43D4211yescharacteristic
369C4×C43D4211yescharacteristic
370#3154C2×C4311yescharacteristic, complemented
371#3069C2×C4311yescharacteristic, complemented
372#3068C2×C4311yescharacteristic, complemented
373#3067C2×C4311yescharacteristic, complemented
374C2×#471C2×C4311yescharacteristic, complemented
375#2957C2×C4311yescharacteristic, complemented
376#2049C2×C4311yescharacteristic, complemented
377#2048C2×C4311yescharacteristic, complemented
378#2009C2×C4311yescharacteristic, complemented
379#2008C2×C4311yescharacteristic, complemented
380#1977C2×C4311yescharacteristic, complemented
381#1953C2×C4311yescharacteristic, complemented
382#1915C2×C4311yescharacteristic, complemented
383#1914C2×C4311yescharacteristic, complemented
384#1757C2×C4311yescharacteristic, complemented
385C2×C43—21no—
386C2×C43—21no—
387C2×C43—21no—
388C2×C43—81no—
389C2×C43—81no—
390C2×C43—81no—
391C2×C43—161no—
392C2×C43#242811yescharacteristic
393#575C22×C4311yescharacteristic
394#575C22×C4311yescharacteristic
395C2×#137C22×C4311yescharacteristic
396C2×#137C22×C4311yescharacteristic
397C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
398C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
399C2×#135C22×C4311yescharacteristic
400C22×SD16C22×C4311yescharacteristic
401#568C22×C4311yescharacteristic
402#568C22×C4311yescharacteristic
403C2×#131C22×C4311yescharacteristic
404#536C22×C4311yescharacteristic
405#535C22×C4311yescharacteristic
406#497—21no—
407#496—21no—
408#495—21no—
409#492—21no—
410#473—21no—
411#473—22no—
412#472—21no—
413#472—22no—
414#471—21no—
415#471—21no—
416#471—22no—
417#471—22no—
418#471—22no—
419#471—22no—
420#444—22no—
421#443—22no—
422#430C22×C4311yescharacteristic
423#430C22×C4311yescharacteristic
424C2×#108C22×C4311yescharacteristic
425C2×#108C22×C4311yescharacteristic
426#421C22×C4311yescharacteristic
427#421C22×C4311yescharacteristic
428#419C22×C4311yescharacteristic
429#418C22×C4311yescharacteristic
430#413C22×C4311yescharacteristic
431#413C22×C4311yescharacteristic
432#413C22×C4311yescharacteristic
433C2×#101C22×C4311yescharacteristic
434C2×#101C22×C4311yescharacteristic
435C2×#100C22×C4311yescharacteristic
436C2×#100C22×C4311yescharacteristic
437#410C22×C4311yescharacteristic
438#405C22×C4311yescharacteristic
439#405C22×C4311yescharacteristic
440#344C22×C4311yescharacteristic
441#344C22×C4311yescharacteristic
442#344C22×C4311yescharacteristic
443#344C22×C4311yescharacteristic
444C43#2544611yescharacteristic, direct product factor, Sylow
445C2×#41C23×C4311yescharacteristic
446C2×#41C23×C4311yescharacteristic
447C2×#41C23×C4311yescharacteristic
448C22×Q8C23×C4311yescharacteristic
449C22×D4C23×C4311yescharacteristic
450#137—21no—
451#137—21no—
452#137—21no—
453#137—21no—
454#137—22no—
455#137—22no—
456#137—41no—
457#137—41no—
458AGL(1,ℤ/8)—21no—
459AGL(1,ℤ/8)—21no—
460AGL(1,ℤ/8)—21no—
461AGL(1,ℤ/8)—21no—
462AGL(1,ℤ/8)—22no—
463AGL(1,ℤ/8)—22no—
464AGL(1,ℤ/8)—41no—
465AGL(1,ℤ/8)—41no—
466#135—21no—
467#135—21no—
468#135—21no—
469#135—21no—
470#135—41no—
471#135—41no—
472C2×Q16—21no—
473C2×Q16—21no—
474C2×Q16D4×C4311yescharacteristic
475C2×SD16—21no—
476C2×SD16—21no—
477C2×SD16—21no—
478C2×SD16—21no—
479C2×SD16—21no—
480C2×SD16—21no—
481C2×SD16—21no—
482C2×SD16—21no—
483C2×SD16—21no—
484C2×SD16—21no—
485C2×SD16D4×C4311yescharacteristic
486C2×SD16D4×C4311yescharacteristic
487C2×D8—21no—
488C2×D8—21no—
489C2×D8D4×C4311yescharacteristic
490#131—22no—
491#131—22no—
492#131—22no—
493#131—22no—
494#131—21no—
495#131—21no—
496#131—21no—
497#131—21no—
498C2×M16—21no—
499C2×M16—41no—
500C2×M16—41no—
501C2×M16C23×C4311yescharacteristic
502C2×M16C23×C4311yescharacteristic
503C2×M16C23×C4311yescharacteristic
504C2×M16C23×C4311yescharacteristic
505C2×M16C23×C4311yescharacteristic
506C2×M16C23×C4311yescharacteristic
507C2×M16C23×C4311yescharacteristic
508C22×C8—21no—
509C22×C8C23×C4311yescharacteristic
510C4⋊Q8—21no—
511#127—21no—
512#124—21no—
513#124—21no—
514#123—22no—
515C22⋊Q8—41no—
516#121—41no—
517#120—22no—
518#117C23×C4311yescharacteristic
519#117C23×C4311yescharacteristic
520#108—22no—
521#108—22no—
522#108—21no—
523#108—21no—
524#108D4×C4312yescomplemented
525#108D4×C4312yescomplemented
526#104—22no—
527#104—22no—
528#103—41no—
529#102—41no—
530#101—21no—
531#101—21no—
532#101—22no—
533#101—22no—
534#101D4×C4312yescomplemented
535#100—21no—
536#100—21no—
537#100—22no—
538#100—22no—
539#100D4×C4312yescomplemented
540#99—22no—
541#97—21no—
542#97—21no—
543C4×C8—21no—
544C4×C8—21no—
545C24—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41—21no—
552#41—21no—
553#41—21no—
554#41—21no—
555#41—21no—
556#41—21no—
557#41—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8C2×D4×C4311yescharacteristic
565C2×Q8C2×D4×C4311yescharacteristic
566C2×Q8C2×D4×C4311yescharacteristic
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—42no—
577C2×D4C2×D4×C4311yescharacteristic
578C2×D4C2×D4×C4311yescharacteristic
579C2×D4C2×D4×C4311yescharacteristic
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4C24×C4311yescharacteristic
585Q16—21no—
586Q16—21no—
587Q16—42no—
588Q16—42no—
589Q16—41no—
590Q16—41no—
591SD16—21no—
592SD16—21no—
593SD16—21no—
594SD16—21no—
595SD16—42no—
596SD16—42no—
597SD16—42no—
598SD16—42no—
599SD16—41no—
600SD16—41no—
601SD16—41no—
602SD16—41no—
603SD16—41no—
604SD16—41no—
605SD16—41no—
606SD16—41no—
607D8—21no—
608D8—21no—
609D8—42no—
610D8—42no—
611D8—41no—
612D8—41no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—21no—
618M16—21no—
619M16—21no—
620M16—21no—
621M16—21no—
622M16—21no—
623M16—42no—
624M16—42no—
625M16—41no—
626M16—41no—
627M16C2×D4×C4312yes—
628M16C2×D4×C4312yes—
629M16C2×D4×C4312yes—
630M16C2×D4×C4312yes—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—42no—
639C2×C8—42no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8C2×D4×C4311yescharacteristic
643C2×C8C2×D4×C4311yescharacteristic
644C2×C8C2×D4×C4311yescharacteristic
645C2×C8C2×D4×C4311yescharacteristic
646C2×C8#41×C4311yescharacteristic
647C2×C8#41×C4311yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—42no—
651C22⋊C4—21no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4#41×C4312yes—
655C42—21no—
656C42—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—161no—
664C23C2×#41×C4311yescharacteristic
665Q8—21no—
666Q8—21no—
667Q8—21no—
668Q8—21no—
669Q8—21no—
670Q8—21no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675D4—21no—
676D4—21no—
677D4—21no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—162no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4C22×D4×C4311yescharacteristic
707C2×C4C22×D4×C4311yescharacteristic
708C2×C4C22×D4×C4311yescharacteristic
709C2×C4C2×#41×C4311yescharacteristic
710C2×C4H(5,𝔽2)×C4311yescharacteristic
711C2×C4H(5,𝔽2)×C4311yescharacteristic
712C8—22no—
713C8—22no—
714C8—22no—
715C8—22no—
716C8—41no—
717C8—41no—
718C8—41no—
719C8#121×C4311yescharacteristic
720C8#121×C4311yescharacteristic
721C8#121×C4311yescharacteristic
722C8#121×C4311yescharacteristic
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—82no—
731C22—81no—
732C22—161no—
733C22—161no—
734C22C43×#53211yescharacteristic
735C22C43×#54611yescharacteristic
736C22C43×#55011yescharacteristic
737C4—42no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—81no—
742C4—81no—
743C4C2×#121×C4311yescharacteristic
744C4C43×#54011yescharacteristic
745C4D42×C4311yescharacteristic
746C4D42×C4311yescharacteristic
747C2—21no—
748C2—21no—
749C2—21no—
750C2—81no—
751C2—81no—
752C2—81no—
753C2—161no—
754C2C43×#242811yescharacteristic
subgroupG/H
center, socleC2×C43#2428
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C43 ◁ C22×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3154C2semidirect
2. C43×#3069C2semidirect
3. C43×#3068C2semidirect
4. C43×#3067C2semidirect
5. C2×C43×#471C2semidirect
6. C43×#2957C2semidirect
7. C43×#2049C2semidirect
8. C43×#2048C2semidirect
9. C43×#2009C2semidirect
10. C43×#2008C2semidirect
11. C43×#1977C2semidirect
12. C43×#1953C2semidirect
13. C43×#1915C2semidirect
14. C43×#1914C2semidirect
15. C43×#1757C2semidirect
146. #108×C43D4semidirect
147. #108×C43D4semidirect
156. #101×C43D4semidirect
161. #100×C43D4semidirect
345. #25446C43direct (N × H)
370. #3154C2×C43semidirect
371. #3069C2×C43semidirect
372. #3068C2×C43semidirect
373. #3067C2×C43semidirect
374. C2×#471C2×C43semidirect
375. #2957C2×C43semidirect
376. #2049C2×C43semidirect
377. #2048C2×C43semidirect
378. #2009C2×C43semidirect
379. #2008C2×C43semidirect
380. #1977C2×C43semidirect
381. #1953C2×C43semidirect
382. #1915C2×C43semidirect
383. #1914C2×C43semidirect
384. #1757C2×C43semidirect
444. C43#25446direct (N × H)
524. #108D4×C43semidirect
525. #108D4×C43semidirect
534. #101D4×C43semidirect
539. #100D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#31542
C43×#30692
C43×#30682
C43×#30672
C2×C43×#4712
C43×#29572
C43×#20492
C43×#20482
C43×#20092
C43×#20082
C43×#19772
C43×#19532
C43×#19152
C43×#19142
C43×#17572
#2544643