Finite Group Databasebeta

← C43×#17147 #24937164

Subgroups — C43×#17147 #24937164

Order 11008.

1790 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#397C211yesmaximal, characteristic, complemented
2C2×C43×#392C211yesmaximal, characteristic
3C43×#1443C212yesmaximal, complemented
4C43×#1440C212yesmaximal, complemented
5C43×#1440C211yesmaximal, characteristic, complemented
6C43×#1439C212yesmaximal, complemented
7C43×#1438C212yesmaximal, complemented
8C43×#1438C212yesmaximal, complemented
9C43×#1438C212yesmaximal, complemented
10C23×D4×C43C2211yescharacteristic
11C23×D4×C43C2212yes—
12C22×C4⋊C4×C43C2211yescharacteristic
13C22×C22⋊C4×C43C2212yes—
14C22×C22⋊C4×C43C2212yes—
15C22×C22⋊C4×C43C2212yes—
16C22×C22⋊C4×C43C2212yes—
17C22×C22⋊C4×C43C2212yes—
18C22×C22⋊C4×C43C2211yescharacteristic
19C22×C22⋊C4×C43C2211yescharacteristic
20C22×C22⋊C4×C43C2212yes—
21C22×C22⋊C4×C43C2211yescharacteristic
22C43×#397—24no—
23C43×#392—24no—
24C2×#95×C43C2211yescharacteristic
25C2×#95×C43C2212yes—
26C2×#95×C43C2211yescharacteristic
27C2×#95×C43C2212yes—
28C2×#95×C43C2212yes—
29C2×#95×C43C2212yes—
30C2×#95×C43C2212yes—
31C2×#95×C43C2212yes—
32C2×#95×C43C2212yes—
33C25×C43C2311yescharacteristic
34C25×C43C2312yes—
35C22×D4×C43—24no—
36C22×D4×C43—24no—
37C22×D4×C43—24no—
38C22×D4×C43—22no—
39C22×D4×C43—24no—
40C22×D4×C43—42no—
41C22×D4×C43—42no—
42C22×D4×C43—42no—
43C22×D4×C43—42no—
44C22×D4×C43—41no—
45C22×D4×C43—42no—
46C22×D4×C43—41no—
47C23×C4×C43C2312yes—
48C23×C4×C43C2312yes—
49C23×C4×C43C2312yes—
50C23×C4×C43C2312yes—
51C23×C4×C43C2311yescharacteristic
52C23×C4×C43C2311yescharacteristic
53C23×C4×C43C2312yes—
54C2×C4⋊C4×C43—22no—
55C2×C4⋊C4×C43—41no—
56C2×C4⋊C4×C43—41no—
57C2×C22⋊C4×C43—24no—
58C2×C22⋊C4×C43—24no—
59C2×C22⋊C4×C43—24no—
60C2×C22⋊C4×C43—24no—
61C2×C22⋊C4×C43—41no—
62C2×C22⋊C4×C43—41no—
63C2×C22⋊C4×C43—42no—
64C2×C22⋊C4×C43—42no—
65C2×C22⋊C4×C43—42no—
66C2×C22⋊C4×C43—42no—
67C2×C22⋊C4×C43—42no—
68C2×C22⋊C4×C43—42no—
69C2×C22⋊C4×C43—42no—
70C2×C22⋊C4×C43—42no—
71C2×C22⋊C4×C43—42no—
72C2×C22⋊C4×C43—42no—
73C2×C22⋊C4×C43—42no—
74C2×C22⋊C4×C43—42no—
75C2×C22⋊C4×C43—42no—
76C2×C22⋊C4×C43—41no—
77C2×C22⋊C4×C43—42no—
78C2×C22⋊C4×C43—41no—
79C2×C22⋊C4×C43—42no—
80C2×C22⋊C4×C43—42no—
81C2×C22⋊C4×C43D414yes—
82#95×C43—22no—
83#95×C43—22no—
84#95×C43—24no—
85#95×C43—24no—
86#95×C43—42no—
87#95×C43—42no—
88#95×C43—42no—
89#95×C43—42no—
90#95×C43—42no—
91C24×C43—22no—
92C24×C43—22no—
93C24×C43—22no—
94C24×C43—22no—
95C24×C43—22no—
96C24×C43—22no—
97C24×C43—21no—
98C24×C43—21no—
99C24×C43—22no—
100C24×C43—22no—
101C24×C43—22no—
102C24×C43—22no—
103C24×C43—22no—
104C24×C43—22no—
105C24×C43—22no—
106C24×C43—22no—
107C24×C43—22no—
108C24×C43—22no—
109C24×C43—22no—
110C24×C43—22no—
111C24×C43—22no—
112C24×C43—22no—
113C24×C43C2×D412yes—
114C24×C43#4114yes—
115C24×C43C2411yescharacteristic
116C2×D4×C43—48no—
117C2×D4×C43—44no—
118C2×D4×C43—48no—
119C2×D4×C43—48no—
120C2×D4×C43—48no—
121C2×D4×C43—48no—
122C2×D4×C43—48no—
123C2×D4×C43—48no—
124C2×D4×C43—44no—
125C2×D4×C43—48no—
126C2×D4×C43—48no—
127C2×D4×C43—44no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43C2×D412yes—
171C22×C4×C43C2×D412yes—
172C22×C4×C43#4114yes—
173C4⋊C4×C43—44no—
174C22⋊C4×C43—44no—
175C22⋊C4×C43—48no—
176C22⋊C4×C43—48no—
177C22⋊C4×C43—48no—
178C22⋊C4×C43—48no—
179C22⋊C4×C43—44no—
180C22⋊C4×C43—48no—
181C22⋊C4×C43—48no—
182C22⋊C4×C43—44no—
183C23×C43—22no—
184C23×C43—22no—
185C23×C43—22no—
186C23×C43—24no—
187C23×C43—24no—
188C23×C43—24no—
189C23×C43—24no—
190C23×C43—24no—
191C23×C43—24no—
192C23×C43—24no—
193C23×C43—24no—
194C23×C43—24no—
195C23×C43—42no—
196C23×C43—42no—
197C23×C43—42no—
198C23×C43—42no—
199C23×C43—42no—
200C23×C43—42no—
201C23×C43—42no—
202C23×C43—42no—
203C23×C43—42no—
204C23×C43—42no—
205C23×C43—42no—
206C23×C43—42no—
207C23×C43—42no—
208C23×C43—42no—
209C23×C43—42no—
210C23×C43—42no—
211C23×C43—42no—
212C23×C43—42no—
213C23×C43—42no—
214C23×C43—42no—
215C23×C43—42no—
216C23×C43—42no—
217C23×C43—41no—
218C23×C43—42no—
219C23×C43—42no—
220C23×C43—42no—
221C23×C43—41no—
222C23×C43—42no—
223C23×C43—42no—
224C23×C43—41no—
225C23×C43—42no—
226C23×C43—42no—
227C23×C43—42no—
228C23×C43—42no—
229C23×C43—42no—
230C23×C43—42no—
231C23×C43—42no—
232C23×C43—42no—
233C23×C43—42no—
234C23×C43—42no—
235C23×C43—42no—
236C23×C43—42no—
237C23×C43—41no—
238C23×C43—42no—
239C23×C43C22×D411yescharacteristic
240C23×C43C2×#4112yes—
241C23×C43C2×#4112yes—
242C23×C43H(5,𝔽2)11yescharacteristic
243C23×C43H(5,𝔽2)11yescharacteristic
244C23×C43H(5,𝔽2)12yes—
245C23×C43H(5,𝔽2)12yes—
246C23×C43H(5,𝔽2)12yes—
247C23×C43H(5,𝔽2)12yes—
248D4×C43—416no—
249D4×C43—432no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—24no—
253C2×C4×C43—24no—
254C2×C4×C43—24no—
255C2×C4×C43—24no—
256C2×C4×C43—24no—
257C2×C4×C43—42no—
258C2×C4×C43—42no—
259C2×C4×C43—42no—
260C2×C4×C43—42no—
261C2×C4×C43—42no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—42no—
266C2×C4×C43—41no—
267C2×C4×C43—42no—
268C2×C4×C43—42no—
269C2×C4×C43—42no—
270C2×C4×C43—42no—
271C2×C4×C43—42no—
272C2×C4×C43—42no—
273C2×C4×C43—42no—
274C2×C4×C43—42no—
275C2×C4×C43—42no—
276C2×C4×C43—42no—
277C2×C4×C43—42no—
278C2×C4×C43—42no—
279C2×C4×C43—42no—
280C2×C4×C43—42no—
281C2×C4×C43—42no—
282C2×C4×C43—42no—
283C2×C4×C43—42no—
284C2×C4×C43—42no—
285C2×C4×C43—42no—
286C2×C4×C43—42no—
287C2×C4×C43—42no—
288C2×C4×C43—42no—
289C2×C4×C43—42no—
290C2×C4×C43—42no—
291C2×C4×C43—42no—
292C2×C4×C43—42no—
293C2×C4×C43—42no—
294C2×C4×C43—42no—
295#17147C4311yesmaximal, characteristic, direct product factor, Sylow
296C22×C43—44no—
297C22×C43—42no—
298C22×C43—44no—
299C22×C43—44no—
300C22×C43—44no—
301C22×C43—44no—
302C22×C43—44no—
303C22×C43—42no—
304C22×C43—44no—
305C22×C43—44no—
306C22×C43—44no—
307C22×C43—42no—
308C22×C43—82no—
309C22×C43—82no—
310C22×C43—82no—
311C22×C43—82no—
312C22×C43—82no—
313C22×C43—82no—
314C22×C43—82no—
315C22×C43—82no—
316C22×C43—82no—
317C22×C43—82no—
318C22×C43—82no—
319C22×C43—82no—
320C22×C43#53411yescharacteristic
321C22×C43#53511yescharacteristic
322C22×C43#53511yescharacteristic
323C22×C43#53812yes—
324C22×C43#53812yes—
325C22×C43#53812yes—
326C22×C43#53812yes—
327C22×C43#54012yes—
328C22×C43#54012yes—
329C22×C43#54612yes—
330C22×C43#54612yes—
331C22×C43#55111yescharacteristic
332C22×C43#55112yes—
333C22×C43#55312yes—
334C22×C43#55911yescharacteristic
335C22×C43#56011yescharacteristic
336C22×C43#56012yes—
337C22×C43#56012yes—
338C22×C43#56012yes—
339C22×C43#56012yes—
340C22×C43H(3,𝔽4)11yescharacteristic
341C4×C43—42no—
342C4×C43—44no—
343C4×C43—42no—
344C4×C43—82no—
345C4×C43—82no—
346C4×C43—82no—
347C4×C43—82no—
348C2×#397C2×C4311yescharacteristic, complemented
349C2×#392C2×C4311yescharacteristic
350#1443C2×C4312yescomplemented
351#1440C2×C4312yescomplemented
352#1440C2×C4311yescharacteristic, complemented
353#1439C2×C4312yescomplemented
354#1438C2×C4312yescomplemented
355#1438C2×C4312yescomplemented
356#1438C2×C4312yescomplemented
357C2×C43—84no—
358C2×C43—82no—
359C2×C43#268411yescharacteristic
360C2×C43#268512yes—
361C2×C43#270312yes—
362C2×C43#270911yescharacteristic
363C2×C43#274912yes—
364C2×C43#279712yes—
365C2×C43#281511yescharacteristic
366C2×C43#282512yes—
367C2×C43#282812yes—
368C23×D4C22×C4311yescharacteristic
369C23×D4C22×C4312yes—
370C22×C4⋊C4C22×C4311yescharacteristic
371C22×C22⋊C4C22×C4312yes—
372C22×C22⋊C4C22×C4312yes—
373C22×C22⋊C4C22×C4312yes—
374C22×C22⋊C4C22×C4312yes—
375C22×C22⋊C4C22×C4312yes—
376C22×C22⋊C4C22×C4311yescharacteristic
377C22×C22⋊C4C22×C4311yescharacteristic
378C22×C22⋊C4C22×C4312yes—
379C22×C22⋊C4C22×C4311yescharacteristic
380#397—24no—
381#392—24no—
382C2×#95C22×C4311yescharacteristic
383C2×#95C22×C4312yes—
384C2×#95C22×C4311yescharacteristic
385C2×#95C22×C4312yes—
386C2×#95C22×C4312yes—
387C2×#95C22×C4312yes—
388C2×#95C22×C4312yes—
389C2×#95C22×C4312yes—
390C2×#95C22×C4312yes—
391C43#1714711yescharacteristic, direct product factor, Sylow
392C25C23×C4311yescharacteristic
393C25C23×C4312yes—
394C22×D4—24no—
395C22×D4—24no—
396C22×D4—24no—
397C22×D4—22no—
398C22×D4—24no—
399C22×D4—42no—
400C22×D4—42no—
401C22×D4—42no—
402C22×D4—42no—
403C22×D4—42no—
404C22×D4—41no—
405C22×D4—41no—
406C23×C4C23×C4312yes—
407C23×C4C23×C4312yes—
408C23×C4C23×C4312yes—
409C23×C4C23×C4312yes—
410C23×C4C23×C4311yescharacteristic
411C23×C4C23×C4311yescharacteristic
412C23×C4C23×C4312yes—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—41no—
415C2×C4⋊C4—41no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—41no—
421C2×C22⋊C4—41no—
422C2×C22⋊C4—42no—
423C2×C22⋊C4—42no—
424C2×C22⋊C4—42no—
425C2×C22⋊C4—42no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—42no—
428C2×C22⋊C4—42no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4—42no—
432C2×C22⋊C4—42no—
433C2×C22⋊C4—42no—
434C2×C22⋊C4—42no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4—41no—
437C2×C22⋊C4—41no—
438C2×C22⋊C4—42no—
439C2×C22⋊C4—42no—
440C2×C22⋊C4D4×C4314yes—
441#95—22no—
442#95—22no—
443#95—24no—
444#95—24no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95—42no—
449#95—42no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—21no—
457C24—21no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24C2×D4×C4312yes—
473C24#41×C4314yes—
474C24C24×C4311yescharacteristic
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—44no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—44no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—44no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4C2×D4×C4312yes—
530C22×C4C2×D4×C4312yes—
531C22×C4#41×C4314yes—
532C4⋊C4—44no—
533C22⋊C4—44no—
534C22⋊C4—48no—
535C22⋊C4—48no—
536C22⋊C4—48no—
537C22⋊C4—48no—
538C22⋊C4—48no—
539C22⋊C4—48no—
540C22⋊C4—44no—
541C22⋊C4—44no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—24no—
546C23—24no—
547C23—24no—
548C23—24no—
549C23—24no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—41no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—41no—
581C23—42no—
582C23—41no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—41no—
597C23—42no—
598C23C22×D4×C4311yescharacteristic
599C23C2×#41×C4312yes—
600C23C2×#41×C4312yes—
601C23H(5,𝔽2)×C4311yescharacteristic
602C23H(5,𝔽2)×C4311yescharacteristic
603C23H(5,𝔽2)×C4312yes—
604C23H(5,𝔽2)×C4312yes—
605C23H(5,𝔽2)×C4312yes—
606C23H(5,𝔽2)×C4312yes—
607D4—416no—
608D4—432no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—42no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C22—44no—
655C22—42no—
656C22—44no—
657C22—44no—
658C22—44no—
659C22—44no—
660C22—42no—
661C22—44no—
662C22—44no—
663C22—44no—
664C22—42no—
665C22—44no—
666C22—82no—
667C22—82no—
668C22—82no—
669C22—82no—
670C22—82no—
671C22—82no—
672C22—82no—
673C22—82no—
674C22—82no—
675C22—82no—
676C22—82no—
677C22—82no—
678C22C43×#53411yescharacteristic
679C22C43×#53511yescharacteristic
680C22C43×#53511yescharacteristic
681C22C43×#53812yes—
682C22C43×#53812yes—
683C22C43×#53812yes—
684C22C43×#53812yes—
685C22C43×#54012yes—
686C22C43×#54012yes—
687C22C43×#54612yes—
688C22C43×#54612yes—
689C22C43×#55111yescharacteristic
690C22C43×#55112yes—
691C22C43×#55312yes—
692C22C43×#55911yescharacteristic
693C22C43×#56012yes—
694C22C43×#56012yes—
695C22C43×#56011yescharacteristic
696C22C43×#56012yes—
697C22C43×#56012yes—
698C22C43×H(3,𝔽4)11yescharacteristic
699C4—42no—
700C4—44no—
701C4—42no—
702C4—82no—
703C4—82no—
704C4—82no—
705C4—82no—
706C2—84no—
707C2—82no—
708C2C43×#268411yescharacteristic
709C2C43×#268512yes—
710C2C43×#270312yes—
711C2C43×#270911yescharacteristic
712C2C43×#274912yes—
713C2C43×#279712yes—
714C2C43×#281511yescharacteristic
715C2C43×#282512yes—
716C2C43×#282812yes—
subgroupG/H
center, socleC24×C43C24
commutator, Frattini, cosocleC24C24×C43
prime radicalC2×C43×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#397C2semidirect
3. C43×#1443C2semidirect
4. C43×#1440C2semidirect
5. C43×#1440C2semidirect
6. C43×#1439C2semidirect
7. C43×#1438C2semidirect
8. C43×#1438C2semidirect
9. C43×#1438C2semidirect
295. #17147C43direct (N × H)
348. C2×#397C2×C43semidirect
350. #1443C2×C43semidirect
351. #1440C2×C43semidirect
352. #1440C2×C43semidirect
353. #1439C2×C43semidirect
354. #1438C2×C43semidirect
355. #1438C2×C43semidirect
356. #1438C2×C43semidirect
391. C43#17147direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#3972
C2×C43×#3922
C43×#14432
C43×#14402
C43×#14392
C43×#14382
#1714743