Finite Group Databasebeta

← C43×#25563 #24945580

Subgroups — C43×#25563 #24945580

Order 11008.

1608 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3490C211yesmaximal, characteristic, complemented
2C43×#2410C212yesmaximal, complemented
3C43×#2405C211yesmaximal, characteristic, complemented
4C43×#2062C211yesmaximal, characteristic, complemented
5C43×#2044C211yesmaximal, characteristic, complemented
6C43×#2029C211yesmaximal, characteristic, complemented
7C43×#2021C211yesmaximal, characteristic, complemented
8C43×#1898C212yesmaximal, complemented
9C43×#1889C212yesmaximal, complemented
10C43×#1867C212yesmaximal, complemented
11C2×C43×#342C211yesmaximal, characteristic, complemented
12C23×D4×C43C2211yescharacteristic
13C43×#551—22no—
14C43×#551—22no—
15C43×#546—22no—
16C43×#546—22no—
17C43×#543C2211yescharacteristic
18C43×#538—21no—
19C43×#538—21no—
20C43×#534C2211yescharacteristic
21C43×#525—21no—
22C43×#525—21no—
23C2×#123×C43—21no—
24C2×#121×C43—22no—
25C2×#120×C43C2212yes—
26C2×#120×C43C2212yes—
27C43×#518C2212yes—
28C22×C22⋊C4×C43C2211yescharacteristic
29C22×C22⋊C4×C43C2212yes—
30C2×#99×C43C2212yes—
31C2×#99×C43C2212yes—
32C43×#394—21no—
33C43×#394—21no—
34C43×#394—22no—
35C43×#392—22no—
36C43×#386—21no—
37C43×#386—22no—
38C43×#386C2212yes—
39C43×#385C2211yescharacteristic
40C43×#385C2212yes—
41C43×#385C2211yescharacteristic
42C43×#379C2211yescharacteristic
43C43×#379C2212yes—
44C43×#379C2211yescharacteristic
45C43×#379C2211yescharacteristic
46C43×#342C2212yes—
47C43×#342C2212yes—
48C43×#342C2212yes—
49C43×#342C2211yescharacteristic
50C43×#342C2211yescharacteristic
51C25×C43C2311yescharacteristic
52C25×C43C2311yescharacteristic
53C2×#41×C43—21no—
54C2×#41×C43—21no—
55C22×D4×C43—22no—
56C22×D4×C43—21no—
57C22×D4×C43—22no—
58C22×D4×C43—21no—
59C22×D4×C43—22no—
60C22×D4×C43—44no—
61C22×D4×C43D412yescomplemented
62C22×D4×C43D412yescomplemented
63C22×D4×C43C2312yes—
64C23×C4×C43—22no—
65C23×C4×C43D411yescharacteristic, complemented
66C23×C4×C43D411yescharacteristic, complemented
67C23×C4×C43C2311yescharacteristic
68#126×C43—22no—
69#126×C43—22no—
70#124×C43—22no—
71#124×C43—22no—
72#123×C43—22no—
73#123×C43—22no—
74#123×C43—22no—
75#123×C43—22no—
76#123×C43—22no—
77#123×C43—44no—
78C22⋊Q8×C43—21no—
79C22⋊Q8×C43—21no—
80C22⋊Q8×C43—21no—
81C22⋊Q8×C43—21no—
82C22⋊Q8×C43—22no—
83C22⋊Q8×C43—22no—
84#121×C43—21no—
85#121×C43—21no—
86#121×C43—22no—
87#121×C43—22no—
88#121×C43—21no—
89#121×C43—21no—
90#121×C43—48no—
91#120×C43—22no—
92#120×C43—22no—
93#120×C43—22no—
94#120×C43—22no—
95#120×C43—22no—
96#120×C43—24no—
97#120×C43—42no—
98C4×D4×C43—22no—
99C4×D4×C43—22no—
100C4×D4×C43—22no—
101C4×D4×C43—22no—
102C4×D4×C43—22no—
103C4×D4×C43—22no—
104#117×C43—21no—
105#117×C43—21no—
106#117×C43—22no—
107C2×C4⋊C4×C43—22no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C22⋊C4×C43—22no—
111C2×C22⋊C4×C43—22no—
112C2×C22⋊C4×C43—22no—
113C2×C22⋊C4×C43—24no—
114C2×C22⋊C4×C43—22no—
115C2×C22⋊C4×C43—22no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—22no—
118C2×C22⋊C4×C43—22no—
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—22no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—42no—
126C2×C22⋊C4×C43D411yescharacteristic, complemented
127C2×C22⋊C4×C43D411yescharacteristic, complemented
128C2×C22⋊C4×C43D412yescomplemented
129C2×C22⋊C4×C43D412yescomplemented
130C2×C22⋊C4×C43C2312yes—
131C2×C22⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43C2311yescharacteristic
133C2×C22⋊C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43C2311yescharacteristic
135C2×C22⋊C4×C43C2312yes—
136C2×C22⋊C4×C43C2312yes—
137#99×C43—24no—
138#99×C43—42no—
139#95×C43—22no—
140#95×C43—21no—
141#95×C43—21no—
142#95×C43—22no—
143C24×C43—22no—
144C24×C43—21no—
145C24×C43—21no—
146C24×C43—21no—
147C24×C43—22no—
148C24×C43—22no—
149C24×C43—21no—
150C24×C43—21no—
151C24×C43—42no—
152C24×C43—42no—
153C24×C43—81no—
154C24×C43—81no—
155C24×C43C2×D412yes—
156C24×C43C2×D411yescharacteristic
157C24×C43C2×D412yes—
158C24×C43C2×D412yes—
159C24×C43C2×D411yescharacteristic
160C24×C43C2411yescharacteristic
161#41×C43—82no—
162#41×C43—82no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×D4×C43—28no—
166C2×D4×C43—24no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—22no—
170C2×D4×C43—22no—
171C2×D4×C43—22no—
172C2×D4×C43—22no—
173C2×D4×C43—22no—
174C2×D4×C43—22no—
175C2×D4×C43—22no—
176C2×D4×C43—22no—
177C2×D4×C43—22no—
178C2×D4×C43—22no—
179C2×D4×C43—44no—
180C2×D4×C43—42no—
181C2×D4×C43—44no—
182C2×D4×C43—42no—
183C2×D4×C43—44no—
184C2×D4×C43—44no—
185C2×D4×C43—44no—
186C2×D4×C43—44no—
187C2×D4×C43—42no—
188C2×D4×C43—42no—
189C2×D4×C43—41no—
190C2×D4×C43—41no—
191C2×D4×C43—82no—
192C2×D4×C43—82no—
193C22×C4×C43—22no—
194C22×C4×C43—22no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—22no—
200C22×C4×C43—21no—
201C22×C4×C43—22no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—22no—
205C22×C4×C43—44no—
206C22×C4×C43—42no—
207C22×C4×C43—44no—
208C22×C4×C43—42no—
209C22×C4×C43—81no—
210C22×C4×C43—82no—
211C22×C4×C43C2×D412yes—
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D412yes—
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D412yes—
217C22×C4×C43C2×D411yescharacteristic
218C4⋊C4×C43—22no—
219C4⋊C4×C43—22no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—22no—
225C4⋊C4×C43—22no—
226C4⋊C4×C43—44no—
227C4⋊C4×C43—42no—
228C4⋊C4×C43—42no—
229C22⋊C4×C43—22no—
230C22⋊C4×C43—22no—
231C22⋊C4×C43—22no—
232C22⋊C4×C43—22no—
233C22⋊C4×C43—22no—
234C22⋊C4×C43—22no—
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—22no—
242C22⋊C4×C43—22no—
243C22⋊C4×C43—22no—
244C22⋊C4×C43—22no—
245C22⋊C4×C43—22no—
246C22⋊C4×C43—21no—
247C22⋊C4×C43—22no—
248C22⋊C4×C43—21no—
249C22⋊C4×C43—44no—
250C22⋊C4×C43—44no—
251C22⋊C4×C43—42no—
252C22⋊C4×C43—42no—
253C22⋊C4×C43—42no—
254C22⋊C4×C43—44no—
255C22⋊C4×C43—44no—
256C22⋊C4×C43—81no—
257C22⋊C4×C43—81no—
258C22⋊C4×C43—81no—
259C22⋊C4×C43—82no—
260C22⋊C4×C43#4114yescomplemented
261C42×C43—22no—
262C42×C43—22no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—22no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—24no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—24no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43—41no—
279C23×C43—42no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—42no—
284C23×C43—41no—
285C23×C43—42no—
286C23×C43—42no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—42no—
290C23×C43—41no—
291C23×C43—42no—
292C23×C43—42no—
293C23×C43—42no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—42no—
298C23×C43—42no—
299C23×C43—84no—
300C23×C43—84no—
301C23×C43—82no—
302C23×C43—82no—
303C23×C43—82no—
304C23×C43—82no—
305C23×C43#12012yes—
306C23×C43#12011yescharacteristic
307C23×C43#12011yescharacteristic
308C23×C43C22×D411yescharacteristic
309C23×C43C22×D412yes—
310C23×C43C2×#4112yes—
311C23×C43H(5,𝔽2)11yescharacteristic
312C23×C432−1+411yescharacteristic
313Q8×C43—81no—
314Q8×C43—81no—
315D4×C43—44no—
316D4×C43—48no—
317D4×C43—44no—
318D4×C43—42no—
319D4×C43—42no—
320D4×C43—42no—
321D4×C43—42no—
322D4×C43—44no—
323D4×C43—44no—
324D4×C43—82no—
325D4×C43—82no—
326D4×C43—81no—
327D4×C43—81no—
328D4×C43—88no—
329C2×C4×C43—24no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—24no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—42no—
342C2×C4×C43—42no—
343C2×C4×C43—41no—
344C2×C4×C43—42no—
345C2×C4×C43—42no—
346C2×C4×C43—41no—
347C2×C4×C43—42no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—42no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—42no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—42no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—42no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—42no—
363C2×C4×C43—81no—
364C2×C4×C43—81no—
365C2×C4×C43—82no—
366C2×C4×C43—82no—
367C2×C4×C43—88no—
368#25563C4311yesmaximal, characteristic, direct product factor, Sylow
369C22×C43—21no—
370C22×C43—22no—
371C22×C43—21no—
372C22×C43—22no—
373C22×C43—21no—
374C22×C43—21no—
375C22×C43—21no—
376C22×C43—22no—
377C22×C43—21no—
378C22×C43—22no—
379C22×C43—21no—
380C22×C43—22no—
381C22×C43—42no—
382C22×C43—41no—
383C22×C43—41no—
384C22×C43—42no—
385C22×C43—42no—
386C22×C43—44no—
387C22×C43—44no—
388C22×C43—42no—
389C22×C43—42no—
390C22×C43—44no—
391C22×C43—44no—
392C22×C43—42no—
393C22×C43—42no—
394C22×C43—42no—
395C22×C43—42no—
396C22×C43—82no—
397C22×C43—81no—
398C22×C43—81no—
399C22×C43—82no—
400C22×C43—82no—
401C22×C43—82no—
402C22×C43—82no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43—82no—
406C22×C43—81no—
407C22×C43—81no—
408C22×C43B(4,𝔽2)12yes—
409C22×C43C2×#12011yescharacteristic
410C22×C43#53211yescharacteristic
411C22×C43#53711yescharacteristic
412C22×C43#54612yes—
413C22×C43#54712yes—
414C4×C43—44no—
415C4×C43—42no—
416C4×C43—42no—
417C4×C43—41no—
418C4×C43—41no—
419C4×C43—42no—
420C4×C43—41no—
421C4×C43—41no—
422C4×C43—42no—
423C4×C43—81no—
424C4×C43—81no—
425C4×C43—82no—
426#3490C2×C4311yescharacteristic, complemented
427#2410C2×C4312yescomplemented
428#2405C2×C4311yescharacteristic, complemented
429#2062C2×C4311yescharacteristic, complemented
430#2044C2×C4311yescharacteristic, complemented
431#2029C2×C4311yescharacteristic, complemented
432#2021C2×C4311yescharacteristic, complemented
433#1898C2×C4312yescomplemented
434#1889C2×C4312yescomplemented
435#1867C2×C4312yescomplemented
436C2×#342C2×C4311yescharacteristic, complemented
437C2×C43—22no—
438C2×C43—21no—
439C2×C43—21no—
440C2×C43—22no—
441C2×C43—22no—
442C2×C43—41no—
443C2×C43—42no—
444C2×C43—82no—
445C2×C43—82no—
446C2×C43#243011yescharacteristic
447C2×C43C2×B(4,𝔽2)11yescharacteristic
448C2×C43#302611yescharacteristic
449C23×D4C22×C4311yescharacteristic
450#551—22no—
451#551—22no—
452#546—22no—
453#546—22no—
454#543C22×C4311yescharacteristic
455#538—21no—
456#538—21no—
457#534C22×C4311yescharacteristic
458#525—21no—
459#525—21no—
460C2×#123—21no—
461C2×#121—22no—
462C2×#120C22×C4312yes—
463C2×#120C22×C4312yes—
464#518C22×C4312yes—
465C22×C22⋊C4C22×C4311yescharacteristic
466C22×C22⋊C4C22×C4312yes—
467C2×#99C22×C4312yes—
468C2×#99C22×C4312yes—
469#394—21no—
470#394—21no—
471#394—22no—
472#392—22no—
473#386—21no—
474#386—22no—
475#386C22×C4312yes—
476#385C22×C4312yes—
477#385C22×C4311yescharacteristic
478#385C22×C4311yescharacteristic
479#379C22×C4311yescharacteristic
480#379C22×C4312yes—
481#379C22×C4311yescharacteristic
482#379C22×C4311yescharacteristic
483#342C22×C4312yes—
484#342C22×C4311yescharacteristic
485#342C22×C4312yes—
486#342C22×C4312yes—
487#342C22×C4311yescharacteristic
488C43#2556311yescharacteristic, direct product factor, Sylow
489C25C23×C4311yescharacteristic
490C25C23×C4311yescharacteristic
491C2×#41—21no—
492C2×#41—21no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—44no—
499C22×D4D4×C4312yescomplemented
500C22×D4D4×C4312yescomplemented
501C22×D4C23×C4312yes—
502C23×C4—22no—
503C23×C4D4×C4311yescharacteristic, complemented
504C23×C4D4×C4311yescharacteristic, complemented
505C23×C4C23×C4311yescharacteristic
506#126—22no—
507#126—22no—
508#124—22no—
509#124—22no—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—22no—
514#123—22no—
515#123—44no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522#121—21no—
523#121—21no—
524#121—22no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—48no—
529#120—22no—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534#120—24no—
535#120—42no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—21no—
543#117—21no—
544#117—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4D4×C4311yescharacteristic, complemented
565C2×C22⋊C4D4×C4311yescharacteristic, complemented
566C2×C22⋊C4D4×C4312yescomplemented
567C2×C22⋊C4D4×C4312yescomplemented
568C2×C22⋊C4C23×C4312yes—
569C2×C22⋊C4C23×C4311yescharacteristic
570C2×C22⋊C4C23×C4311yescharacteristic
571C2×C22⋊C4C23×C4311yescharacteristic
572C2×C22⋊C4C23×C4311yescharacteristic
573C2×C22⋊C4C23×C4312yes—
574C2×C22⋊C4C23×C4312yes—
575#99—24no—
576#99—42no—
577#95—22no—
578#95—21no—
579#95—21no—
580#95—22no—
581C24—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—21no—
589C24—42no—
590C24—42no—
591C24—81no—
592C24—81no—
593C24C2×D4×C4312yes—
594C24C2×D4×C4311yescharacteristic
595C24C2×D4×C4312yes—
596C24C2×D4×C4312yes—
597C24C2×D4×C4311yescharacteristic
598C24C24×C4311yescharacteristic
599#41—82no—
600#41—82no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—82no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—42no—
646C22×C4—44no—
647C22×C4—81no—
648C22×C4—82no—
649C22×C4C2×D4×C4312yes—
650C22×C4C2×D4×C4311yescharacteristic
651C22×C4C2×D4×C4312yes—
652C22×C4C2×D4×C4311yescharacteristic
653C22×C4C2×D4×C4311yescharacteristic
654C22×C4C2×D4×C4312yes—
655C22×C4C2×D4×C4311yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—82no—
697C22⋊C4—81no—
698C22⋊C4#41×C4314yescomplemented
699C42—22no—
700C42—22no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—82no—
743C23#120×C4312yes—
744C23#120×C4311yescharacteristic
745C23#120×C4311yescharacteristic
746C23C22×D4×C4311yescharacteristic
747C23C22×D4×C4312yes—
748C23C2×#41×C4312yes—
749C23H(5,𝔽2)×C4311yescharacteristic
750C232−1+4×C4311yescharacteristic
751Q8—81no—
752Q8—81no—
753D4—44no—
754D4—48no—
755D4—44no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—44no—
761D4—44no—
762D4—82no—
763D4—82no—
764D4—81no—
765D4—81no—
766D4—88no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—88no—
806C22—21no—
807C22—21no—
808C22—22no—
809C22—21no—
810C22—22no—
811C22—21no—
812C22—21no—
813C22—22no—
814C22—21no—
815C22—22no—
816C22—21no—
817C22—22no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—81no—
835C22—81no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C43×B(4,𝔽2)12yes—
846C22C2×#120×C4311yescharacteristic
847C22C43×#53211yescharacteristic
848C22C43×#53711yescharacteristic
849C22C43×#54612yes—
850C22C43×#54712yes—
851C4—44no—
852C4—42no—
853C4—42no—
854C4—41no—
855C4—41no—
856C4—42no—
857C4—41no—
858C4—41no—
859C4—42no—
860C4—82no—
861C4—81no—
862C4—81no—
863C2—22no—
864C2—21no—
865C2—21no—
866C2—22no—
867C2—22no—
868C2—41no—
869C2—42no—
870C2—82no—
871C2—82no—
872C2C43×#243011yescharacteristic
873C2C2×C43×B(4,𝔽2)11yescharacteristic
874C2C43×#302611yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC24C24×C43
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C25×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3490C2semidirect
2. C43×#2410C2semidirect
3. C43×#2405C2semidirect
4. C43×#2062C2semidirect
5. C43×#2044C2semidirect
6. C43×#2029C2semidirect
7. C43×#2021C2semidirect
8. C43×#1898C2semidirect
9. C43×#1889C2semidirect
10. C43×#1867C2semidirect
11. C2×C43×#342C2semidirect
61. C22×D4×C43D4semidirect
62. C22×D4×C43D4semidirect
65. C23×C4×C43D4semidirect
66. C23×C4×C43D4semidirect
126. C2×C22⋊C4×C43D4semidirect
127. C2×C22⋊C4×C43D4semidirect
128. C2×C22⋊C4×C43D4semidirect
129. C2×C22⋊C4×C43D4semidirect
260. C22⋊C4×C43#41semidirect
368. #25563C43direct (N × H)
426. #3490C2×C43semidirect
427. #2410C2×C43semidirect
428. #2405C2×C43semidirect
429. #2062C2×C43semidirect
430. #2044C2×C43semidirect
431. #2029C2×C43semidirect
432. #2021C2×C43semidirect
433. #1898C2×C43semidirect
434. #1889C2×C43semidirect
435. #1867C2×C43semidirect
436. C2×#342C2×C43semidirect
488. C43#25563direct (N × H)
499. C22×D4D4×C43semidirect
500. C22×D4D4×C43semidirect
503. C23×C4D4×C43semidirect
504. C23×C4D4×C43semidirect
564. C2×C22⋊C4D4×C43semidirect
565. C2×C22⋊C4D4×C43semidirect
566. C2×C22⋊C4D4×C43semidirect
567. C2×C22⋊C4D4×C43semidirect
698. C22⋊C4#41×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#34902
C43×#24102
C43×#24052
C43×#20622
C43×#20442
C43×#20292
C43×#20212
C43×#18982
C43×#18892
C43×#18672
C2×C43×#3422
#2556343