Finite Group Databasebeta

← C43×#33553 #24953570

Subgroups — C43×#33553 #24953570

Order 11008.

1252 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3537C211yesmaximal, characteristic, complemented
2C43×#3027C211yesmaximal, characteristic, complemented
3C43×#3025C211yesmaximal, characteristic, complemented
4C43×#3021C211yesmaximal, characteristic, complemented
5C43×#2200C214yesmaximal, complemented
6C43×#2196C214yesmaximal, complemented
7C43×#2128C211yesmaximal, characteristic, complemented
8C43×#2122C211yesmaximal, characteristic, complemented
9C43×#2120C211yesmaximal, characteristic, complemented
10C43×#585C2211yescharacteristic, complemented
11C2×AGL(1,ℤ/8)×C43—21no—
12C43×#560—21no—
13C43×#560C2212yescomplemented
14C43×#553—21no—
15C43×#553—21no—
16D42×C43—21no—
17D42×C43—21no—
18D42×C43—21no—
19D42×C43C2212yescomplemented
20C43×#540—21no—
21C43×#538—22no—
22C43×#535—21no—
23C43×#535C2211yescharacteristic
24C43×#535C2211yescharacteristic
25C43×#534—22no—
26C43×#525—21no—
27C43×#525C2211yescharacteristic
28C2×#121×C43—21no—
29C43×#458—21no—
30C43×#458C2212yescomplemented
31C43×B(4,𝔽2)—21no—
32C43×B(4,𝔽2)—22no—
33C43×B(4,𝔽2)C2212yescomplemented
34C43×B(4,𝔽2)C2214yescomplemented
35C43×#454—22no—
36C43×#453C2214yescomplemented
37C43×#421—21no—
38C43×#413C2211yescharacteristic, complemented
39C43×#410—21no—
40C43×#410—21no—
41C43×#410C2211yescharacteristic, complemented
42C43×#410C2211yescharacteristic, complemented
43C43×#353C2214yescomplemented
44C43×#352C2212yescomplemented
45C43×AΣL(1,𝔽16)C2212yescomplemented
46C43×AΣL(1,𝔽16)C2214yescomplemented
472−1+4×C43—21no—
482−1+4×C43—41no—
49H(5,𝔽2)×C43—21no—
50H(5,𝔽2)×C43—21no—
51H(5,𝔽2)×C43—41no—
52H(5,𝔽2)×C43C2312yes—
53C2×#41×C43—21no—
54C2×#41×C43—21no—
55C2×#41×C43—21no—
56C2×#41×C43—42no—
57C2×#41×C43C2311yescharacteristic
58C22×D4×C43—21no—
59C22×D4×C43—22no—
60C22×D4×C43—22no—
61C22×D4×C43—22no—
62C22×D4×C43D411yescharacteristic, complemented
63C22×D4×C43D411yescharacteristic, complemented
64C23×C4×C43D411yescharacteristic, complemented
65AGL(1,ℤ/8)×C43—24no—
66AGL(1,ℤ/8)×C43—42no—
67C2×SD16×C43—41no—
68C2×D8×C43—41no—
69C2×M16×C43—21no—
70#127×C43—21no—
71#127×C43—21no—
72#127×C43—41no—
73#127×C43C2312yes—
74#126×C43—22no—
75#126×C43—22no—
76#125×C43—21no—
77#124×C43—21no—
78#124×C43—41no—
79#124×C43D412yescomplemented
80#123×C43—22no—
81#123×C43—22no—
82#123×C43—22no—
83#123×C43—22no—
84#123×C43—22no—
85#123×C43D411yescharacteristic, complemented
86#123×C43C2311yescharacteristic
87C22⋊Q8×C43—21no—
88C22⋊Q8×C43—41no—
89#121×C43—22no—
90#121×C43—21no—
91#121×C43—21no—
92#121×C43—22no—
93#121×C43—22no—
94#121×C43—21no—
95#121×C43—22no—
96#121×C43—21no—
97#121×C43—21no—
98#121×C43—22no—
99#121×C43—21no—
100#121×C43—21no—
101#121×C43—22no—
102#121×C43—22no—
103#121×C43—22no—
104#121×C43—42no—
105#121×C43—41no—
106#120×C43—22no—
107#120×C43—22no—
108#120×C43—22no—
109#120×C43—21no—
110#120×C43—21no—
111#120×C43—22no—
112#120×C43—22no—
113#120×C43—24no—
114#120×C43D411yescharacteristic, complemented
115#120×C43D412yescomplemented
116#120×C43C2311yescharacteristic
117#120×C43C2312yes—
118C4×D4×C43—22no—
119C4×D4×C43—21no—
120C4×D4×C43—21no—
121C4×D4×C43—21no—
122C4×D4×C43—21no—
123C4×D4×C43—22no—
124C4×D4×C43—42no—
125#117×C43—21no—
126#117×C43—21no—
127#117×C43D411yescharacteristic, complemented
128#117×C43D411yescharacteristic, complemented
129#117×C43D411yescharacteristic, complemented
130C2×C4⋊C4×C43—21no—
131C2×C22⋊C4×C43—22no—
132#104×C43—24no—
133#101×C43—21no—
134#100×C43C2312yes—
135#99×C43—21no—
136#99×C43—21no—
137#99×C43—24no—
138#99×C43—22no—
139#99×C43—22no—
140#99×C43C2312yes—
141#99×C43C2312yes—
142C24×C43—22no—
143C24×C43—21no—
144C24×C43C2×D411yescharacteristic
145C24×C43C2×D412yes—
146#41×C43—22no—
147#41×C43—22no—
148#41×C43—41no—
149#41×C43—41no—
150#41×C43—42no—
151#41×C43—41no—
152#41×C43—41no—
153#41×C43—41no—
154#41×C43—41no—
155#41×C43—41no—
156#41×C43—42no—
157#41×C43—42no—
158#41×C43—42no—
159#41×C43—41no—
160#41×C43—41no—
161#41×C43—41no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—42no—
166C2×Q8×C43C2×D411yescharacteristic
167C2×D4×C43—22no—
168C2×D4×C43—22no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—22no—
172C2×D4×C43—22no—
173C2×D4×C43—22no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—22no—
179C2×D4×C43—22no—
180C2×D4×C43—22no—
181C2×D4×C43—21no—
182C2×D4×C43—22no—
183C2×D4×C43—22no—
184C2×D4×C43—22no—
185C2×D4×C43—21no—
186C2×D4×C43—42no—
187C2×D4×C43—42no—
188C2×D4×C43—42no—
189C2×D4×C43—42no—
190C2×D4×C43—44no—
191C2×D4×C43—41no—
192C2×D4×C43—41no—
193C2×D4×C43—41no—
194C2×D4×C43—41no—
195C2×D4×C43—41no—
196C2×D4×C43—84no—
197C2×D4×C43—84no—
198C2×D4×C43—84no—
199C2×D4×C43—81no—
200C2×D4×C43—81no—
201C2×D4×C43C2×D412yes—
202C2×D4×C43C2×D411yescharacteristic
203C2×D4×C43C2×D411yescharacteristic
204C2×D4×C43C2411yescharacteristic
205C22×C4×C43—22no—
206C22×C4×C43—22no—
207C22×C4×C43—22no—
208C22×C4×C43—22no—
209C22×C4×C43—22no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—41no—
213C22×C4×C43—41no—
214C22×C4×C43—41no—
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219SD16×C43—44no—
220D8×C43—44no—
221M16×C43—22no—
222M16×C43—41no—
223C2×C8×C43—41no—
224C4⋊C4×C43—22no—
225C4⋊C4×C43—22no—
226C4⋊C4×C43—22no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—41no—
233C4⋊C4×C43—41no—
234C4⋊C4×C43—42no—
235C22⋊C4×C43—22no—
236C22⋊C4×C43—22no—
237C22⋊C4×C43—22no—
238C22⋊C4×C43—22no—
239C22⋊C4×C43—22no—
240C22⋊C4×C43—22no—
241C22⋊C4×C43—21no—
242C22⋊C4×C43—22no—
243C22⋊C4×C43—21no—
244C22⋊C4×C43—22no—
245C22⋊C4×C43—21no—
246C22⋊C4×C43—21no—
247C22⋊C4×C43—21no—
248C22⋊C4×C43—22no—
249C22⋊C4×C43—22no—
250C22⋊C4×C43—42no—
251C22⋊C4×C43—42no—
252C22⋊C4×C43—44no—
253C22⋊C4×C43C2×D412yes—
254C22⋊C4×C43C2×D411yescharacteristic
255C22⋊C4×C43C2×D411yescharacteristic
256C42×C43—21no—
257C42×C43—21no—
258C42×C43—41no—
259C42×C43—41no—
260C42×C43C2×D412yes—
261C23×C43—21no—
262C23×C43—22no—
263C23×C43—22no—
264C23×C43—22no—
265C23×C43—22no—
266C23×C43—41no—
267C23×C43—42no—
268C23×C43—41no—
269C23×C43—44no—
270C23×C43—42no—
271C23×C43—81no—
272C23×C43—82no—
273C23×C43—82no—
274C23×C43—82no—
275C23×C43—82no—
276C23×C43#12011yescharacteristic
277C23×C43C22×D411yescharacteristic
278C23×C43C22×D411yescharacteristic
279Q8×C43—22no—
280Q8×C43—41no—
281Q8×C43—41no—
282Q8×C43—41no—
283Q8×C43—41no—
284D4×C43—22no—
285D4×C43—41no—
286D4×C43—41no—
287D4×C43—41no—
288D4×C43—42no—
289D4×C43—41no—
290D4×C43—41no—
291D4×C43—42no—
292D4×C43—42no—
293D4×C43—42no—
294D4×C43—42no—
295D4×C43—44no—
296D4×C43—44no—
297D4×C43—42no—
298D4×C43—42no—
299D4×C43—41no—
300D4×C43—41no—
301D4×C43—41no—
302D4×C43—41no—
303D4×C43—41no—
304D4×C43—81no—
305D4×C43—82no—
306D4×C43—82no—
307D4×C43—82no—
308D4×C43—82no—
309D4×C43—82no—
310D4×C43—82no—
311D4×C43—82no—
312D4×C43—84no—
313D4×C43—164no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—22no—
326C2×C4×C43—21no—
327C2×C4×C43—42no—
328C2×C4×C43—42no—
329C2×C4×C43—42no—
330C2×C4×C43—41no—
331C2×C4×C43—42no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—42no—
336C2×C4×C43—42no—
337C2×C4×C43—81no—
338C2×C4×C43—82no—
339C2×C4×C43—82no—
340C2×C4×C43—82no—
341C2×C4×C43#12011yescharacteristic
342C2×C4×C43#12011yescharacteristic
343C2×C4×C43#12011yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C8×C43—42no—
346#33553C4311yesmaximal, characteristic, direct product factor, Sylow
347C22×C43—22no—
348C22×C43—21no—
349C22×C43—21no—
350C22×C43—21no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—41no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—81no—
365C22×C43—82no—
366C22×C43—82no—
367C22×C43—84no—
368C22×C43—161no—
369C22×C43—164no—
370C22×C43—162no—
371C22×C43C2×#12011yescharacteristic
372C4×C43—21no—
373C4×C43—21no—
374C4×C43—21no—
375C4×C43—42no—
376C4×C43—41no—
377C4×C43—41no—
378C4×C43—42no—
379C4×C43—42no—
380C4×C43—41no—
381C4×C43—82no—
382C4×C43—82no—
383C4×C43B(4,𝔽2)11yescharacteristic
384C4×C43B(4,𝔽2)11yescharacteristic
385#3537C2×C4311yescharacteristic, complemented
386#3027C2×C4311yescharacteristic, complemented
387#3025C2×C4311yescharacteristic, complemented
388#3021C2×C4311yescharacteristic, complemented
389#2200C2×C4314yescomplemented
390#2196C2×C4314yescomplemented
391#2128C2×C4311yescharacteristic, complemented
392#2122C2×C4311yescharacteristic, complemented
393#2120C2×C4311yescharacteristic, complemented
394C2×C43—21no—
395C2×C43—41no—
396C2×C43—41no—
397C2×C43—42no—
398C2×C43—41no—
399C2×C43—82no—
400C2×C43—82no—
401C2×C43—82no—
402C2×C43C2×B(4,𝔽2)11yescharacteristic
403#585C22×C4311yescharacteristic, complemented
404C2×AGL(1,ℤ/8)—21no—
405#560—21no—
406#560C22×C4312yescomplemented
407#553—21no—
408#553—21no—
409D42—21no—
410D42—21no—
411D42—21no—
412D42C22×C4312yescomplemented
413#540—21no—
414#538—22no—
415#535—21no—
416#535C22×C4311yescharacteristic
417#535C22×C4311yescharacteristic
418#534—22no—
419#525—21no—
420#525C22×C4311yescharacteristic
421C2×#121—21no—
422#458—21no—
423#458C22×C4312yescomplemented
424B(4,𝔽2)—21no—
425B(4,𝔽2)—22no—
426B(4,𝔽2)C22×C4312yescomplemented
427B(4,𝔽2)C22×C4314yescomplemented
428#454—22no—
429#453C22×C4314yescomplemented
430#421—21no—
431#413C22×C4311yescharacteristic, complemented
432#410—21no—
433#410—21no—
434#410C22×C4311yescharacteristic, complemented
435#410C22×C4311yescharacteristic, complemented
436#353C22×C4314yescomplemented
437#352C22×C4312yescomplemented
438AΣL(1,𝔽16)C22×C4312yescomplemented
439AΣL(1,𝔽16)C22×C4314yescomplemented
440C43#3355311yescharacteristic, direct product factor, Sylow
4412−1+4—21no—
4422−1+4—41no—
443H(5,𝔽2)—21no—
444H(5,𝔽2)—21no—
445H(5,𝔽2)—41no—
446H(5,𝔽2)C23×C4312yes—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—42no—
451C2×#41C23×C4311yescharacteristic
452C22×D4—21no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4D4×C4311yescharacteristic, complemented
457C22×D4D4×C4311yescharacteristic, complemented
458C23×C4D4×C4311yescharacteristic, complemented
459AGL(1,ℤ/8)—24no—
460AGL(1,ℤ/8)—42no—
461C2×SD16—41no—
462C2×D8—41no—
463C2×M16—21no—
464#127—21no—
465#127—21no—
466#127—41no—
467#127C23×C4312yes—
468#126—22no—
469#126—22no—
470#125—21no—
471#124—21no—
472#124—41no—
473#124D4×C4312yescomplemented
474#123—22no—
475#123—22no—
476#123—22no—
477#123—22no—
478#123—22no—
479#123D4×C4311yescharacteristic, complemented
480#123C23×C4311yescharacteristic
481C22⋊Q8—21no—
482C22⋊Q8—41no—
483#121—22no—
484#121—21no—
485#121—21no—
486#121—22no—
487#121—22no—
488#121—21no—
489#121—22no—
490#121—21no—
491#121—21no—
492#121—22no—
493#121—21no—
494#121—21no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—42no—
499#121—41no—
500#120—22no—
501#120—22no—
502#120—22no—
503#120—21no—
504#120—21no—
505#120—22no—
506#120—22no—
507#120—24no—
508#120D4×C4311yescharacteristic, complemented
509#120D4×C4312yescomplemented
510#120C23×C4311yescharacteristic
511#120C23×C4312yes—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—22no—
518C4×D4—42no—
519#117—21no—
520#117—21no—
521#117D4×C4311yescharacteristic, complemented
522#117D4×C4311yescharacteristic, complemented
523#117D4×C4311yescharacteristic, complemented
524C2×C4⋊C4—21no—
525C2×C22⋊C4—22no—
526#104—24no—
527#101—21no—
528#100C23×C4312yes—
529#99—21no—
530#99—21no—
531#99—24no—
532#99—22no—
533#99—22no—
534#99C23×C4312yes—
535#99C23×C4312yes—
536C24—22no—
537C24—21no—
538C24C2×D4×C4311yescharacteristic
539C24C2×D4×C4312yes—
540#41—22no—
541#41—22no—
542#41—41no—
543#41—41no—
544#41—42no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—41no—
554#41—41no—
555#41—41no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—42no—
560C2×Q8C2×D4×C4311yescharacteristic
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—44no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—84no—
593C2×D4—84no—
594C2×D4—84no—
595C2×D4C2×D4×C4311yescharacteristic
596C2×D4C2×D4×C4311yescharacteristic
597C2×D4C2×D4×C4312yes—
598C2×D4C24×C4311yescharacteristic
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4C2×D4×C4311yescharacteristic
610C22×C4C2×D4×C4311yescharacteristic
611C22×C4C2×D4×C4311yescharacteristic
612C22×C4C2×D4×C4311yescharacteristic
613SD16—44no—
614D8—44no—
615M16—22no—
616M16—41no—
617C2×C8—41no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—42no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—42no—
645C22⋊C4—44no—
646C22⋊C4—42no—
647C22⋊C4C2×D4×C4312yes—
648C22⋊C4C2×D4×C4311yescharacteristic
649C22⋊C4C2×D4×C4311yescharacteristic
650C42—21no—
651C42—21no—
652C42—41no—
653C42—41no—
654C42C2×D4×C4312yes—
655C23—21no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—41no—
661C23—42no—
662C23—41no—
663C23—44no—
664C23—42no—
665C23—81no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23—82no—
670C23#120×C4311yescharacteristic
671C23C22×D4×C4311yescharacteristic
672C23C22×D4×C4311yescharacteristic
673Q8—22no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—42no—
683D4—41no—
684D4—41no—
685D4—42no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—44no—
690D4—44no—
691D4—42no—
692D4—42no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704D4—82no—
705D4—82no—
706D4—84no—
707D4—164no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—81no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4—82no—
735C2×C4#120×C4311yescharacteristic
736C2×C4#120×C4311yescharacteristic
737C2×C4#120×C4311yescharacteristic
738C2×C4C22×D4×C4311yescharacteristic
739C8—42no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—41no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—81no—
758C22—82no—
759C22—82no—
760C22—84no—
761C22—164no—
762C22—161no—
763C22—162no—
764C22C2×#120×C4311yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—41no—
774C4—82no—
775C4—82no—
776C4C43×B(4,𝔽2)11yescharacteristic
777C4C43×B(4,𝔽2)11yescharacteristic
778C2—21no—
779C2—41no—
780C2—41no—
781C2—42no—
782C2—41no—
783C2—82no—
784C2—82no—
785C2—82no—
786C2C2×C43×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C43C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C43
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C43 ◁ C2×C4×C43 ◁ C2×#41×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3537C2semidirect
2. C43×#3027C2semidirect
3. C43×#3025C2semidirect
4. C43×#3021C2semidirect
5. C43×#2200C2semidirect
6. C43×#2196C2semidirect
7. C43×#2128C2semidirect
8. C43×#2122C2semidirect
9. C43×#2120C2semidirect
10. C43×#585C22semidirect
13. C43×#560C22semidirect
19. D42×C43C22semidirect
30. C43×#458C22semidirect
33. C43×B(4,𝔽2)C22semidirect
34. C43×B(4,𝔽2)C22semidirect
36. C43×#453C22semidirect
38. C43×#413C22semidirect
41. C43×#410C22semidirect
42. C43×#410C22semidirect
43. C43×#353C22semidirect
44. C43×#352C22semidirect
45. C43×AΣL(1,𝔽16)C22semidirect
46. C43×AΣL(1,𝔽16)C22semidirect
62. C22×D4×C43D4semidirect
63. C22×D4×C43D4semidirect
64. C23×C4×C43D4semidirect
79. #124×C43D4semidirect
85. #123×C43D4semidirect
114. #120×C43D4semidirect
115. #120×C43D4semidirect
127. #117×C43D4semidirect
128. #117×C43D4semidirect
129. #117×C43D4semidirect
346. #33553C43direct (N × H)
385. #3537C2×C43semidirect
386. #3027C2×C43semidirect
387. #3025C2×C43semidirect
388. #3021C2×C43semidirect
389. #2200C2×C43semidirect
390. #2196C2×C43semidirect
391. #2128C2×C43semidirect
392. #2122C2×C43semidirect
393. #2120C2×C43semidirect
403. #585C22×C43semidirect
406. #560C22×C43semidirect
412. D42C22×C43semidirect
423. #458C22×C43semidirect
426. B(4,𝔽2)C22×C43semidirect
427. B(4,𝔽2)C22×C43semidirect
429. #453C22×C43semidirect
431. #413C22×C43semidirect
434. #410C22×C43semidirect
435. #410C22×C43semidirect
436. #353C22×C43semidirect
437. #352C22×C43semidirect
438. AΣL(1,𝔽16)C22×C43semidirect
439. AΣL(1,𝔽16)C22×C43semidirect
440. C43#33553direct (N × H)
456. C22×D4D4×C43semidirect
457. C22×D4D4×C43semidirect
458. C23×C4D4×C43semidirect
473. #124D4×C43semidirect
479. #123D4×C43semidirect
508. #120D4×C43semidirect
509. #120D4×C43semidirect
521. #117D4×C43semidirect
522. #117D4×C43semidirect
523. #117D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#35372
C43×#30272
C43×#30252
C43×#30212
C43×#22002
C43×#21962
C43×#21282
C43×#21222
C43×#21202
#3355343