Finite Group Databasebeta

← C43×#24405 #24944422

Subgroups — C43×#24405 #24944422

Order 11008.

1698 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3484C211yesmaximal, characteristic
2C2×C43×#458C211yesmaximal, characteristic, complemented
3C22×#99×C43C211yesmaximal, characteristic, complemented
4C43×#2412C212yesmaximal, complemented
5C43×#2405C211yesmaximal, characteristic, complemented
6C43×#2044C212yesmaximal, complemented
7C43×#2022C212yesmaximal, complemented
8C43×#1898C212yesmaximal, complemented
9C43×#1890C211yesmaximal, characteristic, complemented
10C43×#1867C211yesmaximal, characteristic, complemented
11C43×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C43C2211yescharacteristic
13C23×D4×C43C2211yescharacteristic
14C43×#546—22no—
15C43×#546—22no—
16D42×C43—22no—
17D42×C43—22no—
18C43×#535—21no—
19C43×#534—21no—
20C43×#534C2212yes—
21C43×#525—21no—
22C2×#123×C43C2211yescharacteristic
23C2×#123×C43C2212yescomplemented
24C2×#123×C43C2211yescharacteristic, complemented
25C2×#120×C43—21no—
26C2×#120×C43C2212yes—
27C43×#518C2211yescharacteristic
28C22×C22⋊C4×C43C2211yescharacteristic, complemented
29C22×C22⋊C4×C43C2212yescomplemented
30C43×#458—24no—
31C2×#99×C43—24no—
32C2×#99×C43C2211yescharacteristic
33C2×#99×C43C2211yescharacteristic
34C2×#99×C43C2212yescomplemented
35C2×#99×C43C2212yescomplemented
36C2×#99×C43C2212yescomplemented
37C43×#397—22no—
38C43×#394—21no—
39C43×#394—21no—
40C43×#394—22no—
41C43×#386—22no—
42C43×#386C2211yescharacteristic
43C43×#386C2211yescharacteristic, complemented
44C43×#386C2212yescomplemented
45C43×#385—21no—
46C43×#385C2212yescomplemented
47C43×#381C2212yescomplemented
48C43×#380—22no—
49C43×#379—21no—
50C43×#379C2211yescharacteristic, complemented
51C43×#342C2212yescomplemented
52C43×#342C2212yescomplemented
53C25×C43D411yescharacteristic
54C25×C43C2311yescharacteristic
55H(5,𝔽2)×C43—22no—
56H(5,𝔽2)×C43—22no—
57H(5,𝔽2)×C43—42no—
58C2×#41×C43—21no—
59C2×#41×C43—22no—
60C22×D4×C43—21no—
61C22×D4×C43—22no—
62C22×D4×C43—22no—
63C22×D4×C43—22no—
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43—22no—
67C22×D4×C43—22no—
68C22×D4×C43—42no—
69C22×D4×C43D411yescharacteristic
70C22×D4×C43D411yescharacteristic
71C22×D4×C43D412yes—
72C22×D4×C43D412yes—
73C22×D4×C43C2312yes—
74C22×D4×C43C2311yescharacteristic
75C22×D4×C43C2311yescharacteristic
76C23×C4×C43—22no—
77C23×C4×C43D411yescharacteristic
78C23×C4×C43C2311yescharacteristic
79C23×C4×C43C2311yescharacteristic
80#127×C43—22no—
81#124×C43—22no—
82#123×C43—22no—
83#123×C43—22no—
84#123×C43—22no—
85#123×C43—22no—
86#123×C43—22no—
87#123×C43—24no—
88#123×C43—42no—
89#123×C43—42no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43—21no—
92#121×C43—21no—
93#121×C43—21no—
94#121×C43—22no—
95#121×C43—22no—
96#121×C43—22no—
97#121×C43—22no—
98#121×C43—22no—
99#121×C43—22no—
100#120×C43—22no—
101#120×C43—22no—
102#120×C43—22no—
103#120×C43—22no—
104#120×C43—22no—
105#120×C43—22no—
106#120×C43—22no—
107#120×C43—22no—
108#120×C43—22no—
109C4×D4×C43—22no—
110C4×D4×C43—22no—
111C4×D4×C43—22no—
112C4×D4×C43—22no—
113#117×C43—21no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—22no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—22no—
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—24no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—22no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—22no—
126C2×C22⋊C4×C43—22no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—22no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43—22no—
135C2×C22⋊C4×C43—42no—
136C2×C22⋊C4×C43D412yes—
137C2×C22⋊C4×C43D412yes—
138C2×C22⋊C4×C43C2312yes—
139C2×C22⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43C2312yes—
142C2×C22⋊C4×C43C2312yes—
143#99×C43—22no—
144#99×C43—24no—
145#99×C43—24no—
146#99×C43—42no—
147#99×C43D414yescomplemented
148#95×C43—22no—
149#95×C43—22no—
150#95×C43—22no—
151#95×C43—21no—
152#95×C43—21no—
153#95×C43—22no—
154C24×C43—21no—
155C24×C43—21no—
156C24×C43—22no—
157C24×C43—21no—
158C24×C43—21no—
159C24×C43—21no—
160C24×C43—22no—
161C24×C43—41no—
162C24×C43—42no—
163C24×C43—42no—
164C24×C43—81no—
165C24×C43—81no—
166C24×C43C2×D411yescharacteristic
167C24×C43C2×D412yes—
168C24×C43C2×D411yescharacteristic
169C24×C43C2×D412yes—
170C24×C43C2×D412yes—
171C24×C43C2×D411yescharacteristic
172C24×C43C2×D411yescharacteristic
173C24×C43C2411yescharacteristic
174#41×C43—44no—
175#41×C43—44no—
176#41×C43—42no—
177#41×C43—42no—
178C2×Q8×C43—21no—
179C2×D4×C43—22no—
180C2×D4×C43—21no—
181C2×D4×C43—22no—
182C2×D4×C43—22no—
183C2×D4×C43—22no—
184C2×D4×C43—22no—
185C2×D4×C43—22no—
186C2×D4×C43—22no—
187C2×D4×C43—22no—
188C2×D4×C43—22no—
189C2×D4×C43—22no—
190C2×D4×C43—22no—
191C2×D4×C43—22no—
192C2×D4×C43—21no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43—22no—
197C2×D4×C43—21no—
198C2×D4×C43—22no—
199C2×D4×C43—22no—
200C2×D4×C43—22no—
201C2×D4×C43—22no—
202C2×D4×C43—22no—
203C2×D4×C43—41no—
204C2×D4×C43—41no—
205C2×D4×C43—44no—
206C2×D4×C43—44no—
207C2×D4×C43—44no—
208C2×D4×C43—44no—
209C2×D4×C43—44no—
210C2×D4×C43—44no—
211C2×D4×C43—42no—
212C2×D4×C43—44no—
213C2×D4×C43—42no—
214C2×D4×C43—82no—
215C2×D4×C43—82no—
216C2×D4×C43—82no—
217C2×D4×C43C2×D412yes—
218C2×D4×C43#4112yes—
219C22×C4×C43—21no—
220C22×C4×C43—22no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—22no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—22no—
227C22×C4×C43—22no—
228C22×C4×C43—21no—
229C22×C4×C43—22no—
230C22×C4×C43—22no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—22no—
237C22×C4×C43—41no—
238C22×C4×C43—44no—
239C22×C4×C43—44no—
240C22×C4×C43—81no—
241C22×C4×C43—82no—
242C22×C4×C43C2×D412yes—
243C22×C4×C43C2×D411yescharacteristic
244C22×C4×C43C2×D411yescharacteristic
245C22×C4×C43C2×D412yes—
246C22×C4×C43C2×D412yes—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—22no—
250C4⋊C4×C43—22no—
251C4⋊C4×C43—44no—
252C4⋊C4×C43—42no—
253C4⋊C4×C43—42no—
254C4⋊C4×C43—82no—
255C22⋊C4×C43—22no—
256C22⋊C4×C43—22no—
257C22⋊C4×C43—22no—
258C22⋊C4×C43—22no—
259C22⋊C4×C43—22no—
260C22⋊C4×C43—22no—
261C22⋊C4×C43—22no—
262C22⋊C4×C43—22no—
263C22⋊C4×C43—22no—
264C22⋊C4×C43—22no—
265C22⋊C4×C43—22no—
266C22⋊C4×C43—22no—
267C22⋊C4×C43—21no—
268C22⋊C4×C43—21no—
269C22⋊C4×C43—22no—
270C22⋊C4×C43—22no—
271C22⋊C4×C43—22no—
272C22⋊C4×C43—44no—
273C22⋊C4×C43—44no—
274C22⋊C4×C43—42no—
275C22⋊C4×C43—42no—
276C22⋊C4×C43—41no—
277C22⋊C4×C43—42no—
278C22⋊C4×C43—41no—
279C22⋊C4×C43—42no—
280C22⋊C4×C43—81no—
281C22⋊C4×C43—81no—
282C22⋊C4×C43—81no—
283C22⋊C4×C43—82no—
284C22⋊C4×C43C2×D414yescomplemented
285C42×C43—22no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—22no—
290C23×C43—22no—
291C23×C43—22no—
292C23×C43—24no—
293C23×C43—21no—
294C23×C43—21no—
295C23×C43—21no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—21no—
299C23×C43—22no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—22no—
303C23×C43—22no—
304C23×C43—42no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43—41no—
308C23×C43—41no—
309C23×C43—42no—
310C23×C43—41no—
311C23×C43—42no—
312C23×C43—42no—
313C23×C43—42no—
314C23×C43—41no—
315C23×C43—41no—
316C23×C43—41no—
317C23×C43—41no—
318C23×C43—42no—
319C23×C43—42no—
320C23×C43—42no—
321C23×C43—42no—
322C23×C43—42no—
323C23×C43—81no—
324C23×C43—81no—
325C23×C43—82no—
326C23×C43—82no—
327C23×C43—84no—
328C23×C43—81no—
329C23×C43—81no—
330C23×C43—84no—
331C23×C43—84no—
332C23×C43#12011yescharacteristic
333C23×C43#12012yes—
334C23×C43#12011yescharacteristic
335C23×C43#12112yes—
336C23×C43C22×D411yescharacteristic
337C23×C43C22×D412yes—
338C23×C43C22×D411yescharacteristic
339C23×C43C2×#4111yescharacteristic
340C23×C43H(5,𝔽2)12yes—
341Q8×C43—42no—
342D4×C43—24no—
343D4×C43—24no—
344D4×C43—44no—
345D4×C43—42no—
346D4×C43—44no—
347D4×C43—44no—
348D4×C43—44no—
349D4×C43—42no—
350D4×C43—42no—
351D4×C43—42no—
352D4×C43—42no—
353D4×C43—42no—
354D4×C43—42no—
355D4×C43—44no—
356D4×C43—82no—
357D4×C43—82no—
358D4×C43—82no—
359D4×C43—82no—
360C2×C4×C43—21no—
361C2×C4×C43—21no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—22no—
365C2×C4×C43—21no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—24no—
369C2×C4×C43—22no—
370C2×C4×C43—22no—
371C2×C4×C43—42no—
372C2×C4×C43—42no—
373C2×C4×C43—44no—
374C2×C4×C43—42no—
375C2×C4×C43—42no—
376C2×C4×C43—42no—
377C2×C4×C43—42no—
378C2×C4×C43—42no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—42no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
386C2×C4×C43—42no—
387C2×C4×C43—42no—
388C2×C4×C43—42no—
389C2×C4×C43—41no—
390C2×C4×C43—41no—
391C2×C4×C43—41no—
392C2×C4×C43—41no—
393C2×C4×C43—41no—
394C2×C4×C43—41no—
395C2×C4×C43—42no—
396C2×C4×C43—42no—
397C2×C4×C43—42no—
398C2×C4×C43—81no—
399C2×C4×C43—81no—
400C2×C4×C43—88no—
401C2×C4×C43#12112yes—
402#24405C4311yesmaximal, characteristic, direct product factor, Sylow
403C22×C43—21no—
404C22×C43—21no—
405C22×C43—22no—
406C22×C43—21no—
407C22×C43—22no—
408C22×C43—21no—
409C22×C43—21no—
410C22×C43—22no—
411C22×C43—22no—
412C22×C43—21no—
413C22×C43—22no—
414C22×C43—21no—
415C22×C43—22no—
416C22×C43—41no—
417C22×C43—41no—
418C22×C43—42no—
419C22×C43—44no—
420C22×C43—42no—
421C22×C43—42no—
422C22×C43—44no—
423C22×C43—42no—
424C22×C43—42no—
425C22×C43—41no—
426C22×C43—41no—
427C22×C43—41no—
428C22×C43—42no—
429C22×C43—41no—
430C22×C43—42no—
431C22×C43—41no—
432C22×C43—42no—
433C22×C43—82no—
434C22×C43—81no—
435C22×C43—81no—
436C22×C43—81no—
437C22×C43—82no—
438C22×C43—84no—
439C22×C43—82no—
440C22×C43—82no—
441C22×C43—81no—
442C22×C43—84no—
443C22×C43—162no—
444C22×C43#45812yescomplemented
445C22×C43C2×#12011yescharacteristic
446C22×C43C2×#12111yescharacteristic
447C22×C43#53411yescharacteristic
448C22×C43D4212yes—
449C22×C43#54612yes—
450C4×C43—22no—
451C4×C43—44no—
452C4×C43—41no—
453C4×C43—42no—
454C4×C43—42no—
455C4×C43—42no—
456C4×C43—81no—
457C4×C43—81no—
458C4×C43—82no—
459C4×C43—81no—
460C4×C43—81no—
461#3484C2×C4311yescharacteristic
462C2×#458C2×C4311yescharacteristic, complemented
463C22×#99C2×C4311yescharacteristic, complemented
464#2412C2×C4312yescomplemented
465#2405C2×C4311yescharacteristic, complemented
466#2044C2×C4312yescomplemented
467#2022C2×C4312yescomplemented
468#1898C2×C4312yescomplemented
469#1890C2×C4311yescharacteristic, complemented
470#1867C2×C4311yescharacteristic, complemented
471#1790C2×C4311yescharacteristic, complemented
472C2×C43—22no—
473C2×C43—21no—
474C2×C43—21no—
475C2×C43—22no—
476C2×C43—22no—
477C2×C43—42no—
478C2×C43—41no—
479C2×C43—42no—
480C2×C43—81no—
481C2×C43—82no—
482C2×C43#241011yescharacteristic
483C2×C43C2×#45811yescharacteristic
484C2×C43#302611yescharacteristic
485C2×H(5,𝔽2)C22×C4311yescharacteristic
486C23×D4C22×C4311yescharacteristic
487#546—22no—
488#546—22no—
489D42—22no—
490D42—22no—
491#535—21no—
492#534—21no—
493#534C22×C4312yes—
494#525—21no—
495C2×#123C22×C4311yescharacteristic
496C2×#123C22×C4312yescomplemented
497C2×#123C22×C4311yescharacteristic, complemented
498C2×#120—21no—
499C2×#120C22×C4312yes—
500#518C22×C4311yescharacteristic
501C22×C22⋊C4C22×C4311yescharacteristic, complemented
502C22×C22⋊C4C22×C4312yescomplemented
503#458—24no—
504C2×#99—24no—
505C2×#99C22×C4311yescharacteristic
506C2×#99C22×C4311yescharacteristic
507C2×#99C22×C4312yescomplemented
508C2×#99C22×C4312yescomplemented
509C2×#99C22×C4312yescomplemented
510#397—22no—
511#394—21no—
512#394—21no—
513#394—22no—
514#386—22no—
515#386C22×C4311yescharacteristic
516#386C22×C4311yescharacteristic, complemented
517#386C22×C4312yescomplemented
518#385—21no—
519#385C22×C4312yescomplemented
520#381C22×C4312yescomplemented
521#380—22no—
522#379—21no—
523#379C22×C4311yescharacteristic, complemented
524#342C22×C4312yescomplemented
525#342C22×C4312yescomplemented
526C43#2440511yescharacteristic, direct product factor, Sylow
527C25D4×C4311yescharacteristic
528C25C23×C4311yescharacteristic
529H(5,𝔽2)—22no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—42no—
532C2×#41—21no—
533C2×#41—22no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—42no—
543C22×D4D4×C4311yescharacteristic
544C22×D4D4×C4311yescharacteristic
545C22×D4D4×C4312yes—
546C22×D4D4×C4312yes—
547C22×D4C23×C4312yes—
548C22×D4C23×C4311yescharacteristic
549C22×D4C23×C4311yescharacteristic
550C23×C4—22no—
551C23×C4D4×C4311yescharacteristic
552C23×C4C23×C4311yescharacteristic
553C23×C4C23×C4311yescharacteristic
554#127—22no—
555#124—22no—
556#123—22no—
557#123—22no—
558#123—22no—
559#123—22no—
560#123—22no—
561#123—24no—
562#123—42no—
563#123—42no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#120—22no—
575#120—22no—
576#120—22no—
577#120—22no—
578#120—22no—
579#120—22no—
580#120—22no—
581#120—22no—
582#120—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587#117—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—22no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4D4×C4312yes—
611C2×C22⋊C4D4×C4312yes—
612C2×C22⋊C4C23×C4312yes—
613C2×C22⋊C4C23×C4311yescharacteristic
614C2×C22⋊C4C23×C4311yescharacteristic
615C2×C22⋊C4C23×C4312yes—
616C2×C22⋊C4C23×C4312yes—
617#99—22no—
618#99—24no—
619#99—24no—
620#99—42no—
621#99D4×C4314yescomplemented
622#95—22no—
623#95—22no—
624#95—22no—
625#95—21no—
626#95—21no—
627#95—22no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—41no—
636C24—42no—
637C24—42no—
638C24—81no—
639C24—81no—
640C24C2×D4×C4311yescharacteristic
641C24C2×D4×C4312yes—
642C24C2×D4×C4311yescharacteristic
643C24C2×D4×C4312yes—
644C24C2×D4×C4312yes—
645C24C2×D4×C4311yescharacteristic
646C24C2×D4×C4311yescharacteristic
647C24C24×C4311yescharacteristic
648#41—44no—
649#41—44no—
650#41—42no—
651#41—42no—
652C2×Q8—21no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4C2×D4×C4312yes—
692C2×D4#41×C4312yes—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—41no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—81no—
715C22×C4—82no—
716C22×C4C2×D4×C4312yes—
717C22×C4C2×D4×C4311yescharacteristic
718C22×C4C2×D4×C4311yescharacteristic
719C22×C4C2×D4×C4312yes—
720C22×C4C2×D4×C4312yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—44no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—82no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—41no—
753C22⋊C4—42no—
754C22⋊C4—81no—
755C22⋊C4—81no—
756C22⋊C4—81no—
757C22⋊C4—82no—
758C22⋊C4C2×D4×C4314yescomplemented
759C42—22no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—24no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—22no—
777C23—22no—
778C23—42no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23—81no—
799C23—82no—
800C23—82no—
801C23—84no—
802C23—81no—
803C23—81no—
804C23—84no—
805C23—84no—
806C23#120×C4311yescharacteristic
807C23#120×C4312yes—
808C23#120×C4311yescharacteristic
809C23#121×C4312yes—
810C23C22×D4×C4311yescharacteristic
811C23C22×D4×C4312yes—
812C23C22×D4×C4311yescharacteristic
813C23C2×#41×C4311yescharacteristic
814C23H(5,𝔽2)×C4312yes—
815Q8—42no—
816D4—24no—
817D4—24no—
818D4—44no—
819D4—42no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—42no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—44no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—82no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—88no—
875C2×C4#121×C4312yes—
876C22—21no—
877C22—22no—
878C22—21no—
879C22—22no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—21no—
887C22—21no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—82no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—82no—
911C22—84no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—162no—
917C22C43×#45812yescomplemented
918C22C2×#120×C4311yescharacteristic
919C22C2×#121×C4311yescharacteristic
920C22C43×#53411yescharacteristic
921C22D42×C4312yes—
922C22C43×#54612yes—
923C4—22no—
924C4—44no—
925C4—41no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—82no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C2—22no—
935C2—21no—
936C2—21no—
937C2—22no—
938C2—22no—
939C2—41no—
940C2—42no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C43×#241011yescharacteristic
945C2C2×C43×#45811yescharacteristic
946C2C43×#302611yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC24C24×C43
prime radicalC43×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C25×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#458C2semidirect
3. C22×#99×C43C2semidirect
4. C43×#2412C2semidirect
5. C43×#2405C2semidirect
6. C43×#2044C2semidirect
7. C43×#2022C2semidirect
8. C43×#1898C2semidirect
9. C43×#1890C2semidirect
10. C43×#1867C2semidirect
11. C43×#1790C2semidirect
23. C2×#123×C43C22semidirect
24. C2×#123×C43C22semidirect
28. C22×C22⋊C4×C43C22semidirect
29. C22×C22⋊C4×C43C22semidirect
34. C2×#99×C43C22semidirect
35. C2×#99×C43C22semidirect
36. C2×#99×C43C22semidirect
43. C43×#386C22semidirect
44. C43×#386C22semidirect
46. C43×#385C22semidirect
47. C43×#381C22semidirect
50. C43×#379C22semidirect
51. C43×#342C22semidirect
52. C43×#342C22semidirect
147. #99×C43D4semidirect
284. C22⋊C4×C43C2×D4semidirect
402. #24405C43direct (N × H)
444. C22×C43#458semidirect
462. C2×#458C2×C43semidirect
463. C22×#99C2×C43semidirect
464. #2412C2×C43semidirect
465. #2405C2×C43semidirect
466. #2044C2×C43semidirect
467. #2022C2×C43semidirect
468. #1898C2×C43semidirect
469. #1890C2×C43semidirect
470. #1867C2×C43semidirect
471. #1790C2×C43semidirect
496. C2×#123C22×C43semidirect
497. C2×#123C22×C43semidirect
501. C22×C22⋊C4C22×C43semidirect
502. C22×C22⋊C4C22×C43semidirect
507. C2×#99C22×C43semidirect
508. C2×#99C22×C43semidirect
509. C2×#99C22×C43semidirect
516. #386C22×C43semidirect
517. #386C22×C43semidirect
519. #385C22×C43semidirect
520. #381C22×C43semidirect
523. #379C22×C43semidirect
524. #342C22×C43semidirect
525. #342C22×C43semidirect
526. C43#24405direct (N × H)
621. #99D4×C43semidirect
758. C22⋊C4C2×D4×C43semidirect
917. C22C43×#458semidirect

Maximal subgroups

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

subgroupindex
C43×#34842
C2×C43×#4582
C22×#99×C432
C43×#24122
C43×#24052
C43×#20442
C43×#20222
C43×#18982
C43×#18902
C43×#18672
C43×#17902
#2440543