Finite Group Databasebeta

← C43×#14506 #24934523

Subgroups — C43×#14506 #24934523

Order 11008.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C43C211yesmaximal, characteristic
2C2×C43×#388C212yesmaximal, complemented
3C43×#1445C212yesmaximal, complemented
4C43×#1439C212yesmaximal, complemented
5C43×#1438C211yesmaximal, characteristic
6C43×#1438C211yesmaximal, characteristic
7C43×#1437C212yesmaximal, complemented
8C43×C4⋊#95C212yesmaximal, complemented
9C43×C22⋊#95C212yesmaximal, complemented
10C23×D4×C43C2211yescharacteristic
11C24×C4×C43C2211yescharacteristic
12C2×#123×C43—28no—
13C2×#123×C43C418yescomplemented
14C22×C4⋊C4×C43C2212yes—
15C22×C4⋊C4×C43C2212yes—
16C22×C22⋊C4×C43C2212yes—
17C22×C22⋊C4×C43C2212yes—
18C22×C22⋊C4×C43C2211yescharacteristic
19C22×C22⋊C4×C43C2212yes—
20C22×C22⋊C4×C43C2212yes—
21C22×C22⋊C4×C43C2211yescharacteristic
22C22×C22⋊C4×C43C2211yescharacteristic
23C22×C42×C43C2212yes—
24C43×#388—28no—
25C2×#95×C43C2212yes—
26C2×#95×C43C2212yes—
27C2×#95×C43C2212yes—
28C2×#95×C43C2212yes—
29C2×#95×C43C2212yes—
30C2×#95×C43C2212yes—
31C2×#95×C43C2211yescharacteristic
32C2×#95×C43C2212yes—
33C2×#95×C43C2211yescharacteristic
34C25×C43C2311yescharacteristic
35C25×C43C2311yescharacteristic
36C22×D4×C43—24no—
37C22×D4×C43—42no—
38C22×D4×C43—41no—
39C22×D4×C43—41no—
40C22×D4×C43C2×C414yes—
41C23×C4×C43—24no—
42C23×C4×C43—42no—
43C23×C4×C43—41no—
44C23×C4×C43—41no—
45C23×C4×C43C2×C414yes—
46C23×C4×C43C2312yes—
47C23×C4×C43C2312yes—
48C23×C4×C43C2312yes—
49C23×C4×C43C2311yescharacteristic
50C23×C4×C43C2312yes—
51C23×C4×C43C2312yes—
52C23×C4×C43C2312yes—
53#123×C43—232no—
54C2×C4⋊C4×C43—24no—
55C2×C4⋊C4×C43—24no—
56C2×C4⋊C4×C43—24no—
57C2×C4⋊C4×C43—24no—
58C2×C4⋊C4×C43—42no—
59C2×C4⋊C4×C43C2×C418yes—
60C2×C22⋊C4×C43—24no—
61C2×C22⋊C4×C43—24no—
62C2×C22⋊C4×C43—24no—
63C2×C22⋊C4×C43—24no—
64C2×C22⋊C4×C43—24no—
65C2×C22⋊C4×C43—24no—
66C2×C22⋊C4×C43—24no—
67C2×C22⋊C4×C43—24no—
68C2×C22⋊C4×C43—42no—
69C2×C22⋊C4×C43—42no—
70C2×C22⋊C4×C43—41no—
71C2×C22⋊C4×C43—42no—
72C2×C22⋊C4×C43—42no—
73C2×C22⋊C4×C43—41no—
74C2×C22⋊C4×C43—42no—
75C2×C22⋊C4×C43C2×C418yes—
76C2×C22⋊C4×C43C2×C414yes—
77C2×C22⋊C4×C43D418yes—
78C2×C42×C43—24no—
79C2×C42×C43—24no—
80C2×C42×C43—42no—
81#95×C43—24no—
82#95×C43—24no—
83#95×C43—41no—
84#95×C43—42no—
85#95×C43—42no—
86#95×C43—42no—
87#95×C43—42no—
88#95×C43—42no—
89#95×C43—41no—
90C24×C43—22no—
91C24×C43—22no—
92C24×C43—22no—
93C24×C43—22no—
94C24×C43—21no—
95C24×C43—21no—
96C24×C43—22no—
97C24×C43—22no—
98C24×C43—22no—
99C24×C43—22no—
100C24×C43—22no—
101C24×C43—22no—
102C24×C43—21no—
103C24×C43—21no—
104C24×C43—22no—
105C24×C43C22×C412yes—
106C24×C43C22×C412yes—
107C24×C43C2×D414yes—
108C24×C43C2411yescharacteristic
109C2×D4×C43—28no—
110C2×D4×C43—44no—
111C2×D4×C43—44no—
112C2×D4×C43—48no—
113C2×D4×C43—48no—
114C22×C4×C43—28no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
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—21no—
141C22×C4×C43—21no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
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—44no—
156C22×C4×C43—44no—
157C22×C4×C43—48no—
158C22×C4×C43—48no—
159C22×C4×C43C22×C414yes—
160C22×C4×C43C22×C412yes—
161C22×C4×C43C22×C414yes—
162C22×C4×C43C2×D414yes—
163C22×C4×C43C2×D414yes—
164C22×C4×C43#4114yes—
165C22×C4×C43#4114yes—
166C4⋊C4×C43—216no—
167C4⋊C4×C43—48no—
168C22⋊C4×C43—216no—
169C22⋊C4×C43—48no—
170C22⋊C4×C43—48no—
171C22⋊C4×C43—44no—
172C22⋊C4×C43—48no—
173C22⋊C4×C43—44no—
174C22⋊C4×C43C22⋊C4116yescomplemented
175C42×C43—48no—
176C23×C43—24no—
177C23×C43—22no—
178C23×C43—22no—
179C23×C43—24no—
180C23×C43—24no—
181C23×C43—24no—
182C23×C43—24no—
183C23×C43—24no—
184C23×C43—24no—
185C23×C43—24no—
186C23×C43—22no—
187C23×C43—24no—
188C23×C43—22no—
189C23×C43—22no—
190C23×C43—24no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—42no—
195C23×C43—41no—
196C23×C43—42no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—42no—
200C23×C43—41no—
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—41no—
212C23×C43—42no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—42no—
216C23×C43—41no—
217C23×C43C2×C22⋊C414yes—
218C23×C43C23×C411yescharacteristic
219C23×C43C22×D412yes—
220C23×C43C2×#4112yes—
221C23×C43C2×#4112yes—
222C23×C43H(5,𝔽2)12yes—
223C23×C43H(5,𝔽2)11yescharacteristic
224C23×C43H(5,𝔽2)11yescharacteristic
225C23×C43H(5,𝔽2)12yes—
226C23×C432−1+412yes—
227D4×C43—416no—
228C2×C4×C43—24no—
229C2×C4×C43—24no—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
232C2×C4×C43—24no—
233C2×C4×C43—24no—
234C2×C4×C43—24no—
235C2×C4×C43—22no—
236C2×C4×C43—24no—
237C2×C4×C43—24no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—24no—
241C2×C4×C43—24no—
242C2×C4×C43—24no—
243C2×C4×C43—24no—
244C2×C4×C43—24no—
245C2×C4×C43—24no—
246C2×C4×C43—416no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—42no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×C4×C43—42no—
258C2×C4×C43—42no—
259C2×C4×C43—42no—
260C2×C4×C43—42no—
261C2×C4×C43—42no—
262C2×C4×C43—42no—
263C2×C4×C43—42no—
264C2×C4×C43—42no—
265C2×C4×C43—42no—
266C2×C4×C43—42no—
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×C43C2×C22⋊C418yes—
276#14506C4311yesmaximal, characteristic, direct product factor, Sylow
277C22×C43—24no—
278C22×C43—28no—
279C22×C43—44no—
280C22×C43—42no—
281C22×C43—42no—
282C22×C43—44no—
283C22×C43—44no—
284C22×C43—44no—
285C22×C43—44no—
286C22×C43—42no—
287C22×C43—44no—
288C22×C43—44no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—82no—
292C22×C43—82no—
293C22×C43—82no—
294C22×C43—82no—
295C22×C43C22×C22⋊C411yescharacteristic
296C22×C43C4×#4112yes—
297C22×C43#51811yescharacteristic
298C22×C43#51811yescharacteristic
299C22×C43#52012yes—
300C22×C43#53512yes—
301C22×C43#53512yes—
302C22×C43#53812yes—
303C22×C43#53912yes—
304C22×C43#54012yes—
305C22×C43#54212yes—
306C22×C43#54612yes—
307C22×C43#54612yes—
308C22×C43#54712yes—
309C22×C43#54712yes—
310C22×C43#55111yescharacteristic
311C22×C43#55312yes—
312C22×C43#55911yescharacteristic
313C22×C43#56011yescharacteristic
314C22×C43#56212yes—
315C22×C43#56311yescharacteristic
316C4×C43—28no—
317C4×C43—44no—
318C4×C43—42no—
319C4×C43—44no—
320C4×C43—44no—
321C4×C43—82no—
322C4×C43—82no—
323C22×#123C2×C4311yescharacteristic
324C2×#388C2×C4312yescomplemented
325#1445C2×C4312yescomplemented
326#1439C2×C4312yescomplemented
327#1438C2×C4311yescharacteristic
328#1438C2×C4311yescharacteristic
329#1437C2×C4312yescomplemented
330C4⋊#95C2×C4312yescomplemented
331C22⋊#95C2×C4312yescomplemented
332C2×C43—44no—
333C2×C43—82no—
334C2×C43#230911yescharacteristic
335C2×C43#233512yes—
336C2×C43#233912yes—
337C2×C43#237411yescharacteristic
338C2×C43#237611yescharacteristic
339C2×C43#270312yes—
340C2×C43#270612yes—
341C2×C43#271012yes—
342C2×C43#271812yes—
343C23×D4C22×C4311yescharacteristic
344C24×C4C22×C4311yescharacteristic
345C2×#123—28no—
346C2×#123C4×C4318yescomplemented
347C22×C4⋊C4C22×C4312yes—
348C22×C4⋊C4C22×C4312yes—
349C22×C22⋊C4C22×C4312yes—
350C22×C22⋊C4C22×C4312yes—
351C22×C22⋊C4C22×C4311yescharacteristic
352C22×C22⋊C4C22×C4312yes—
353C22×C22⋊C4C22×C4312yes—
354C22×C22⋊C4C22×C4311yescharacteristic
355C22×C22⋊C4C22×C4311yescharacteristic
356C22×C42C22×C4312yes—
357#388—28no—
358C2×#95C22×C4312yes—
359C2×#95C22×C4312yes—
360C2×#95C22×C4312yes—
361C2×#95C22×C4312yes—
362C2×#95C22×C4312yes—
363C2×#95C22×C4312yes—
364C2×#95C22×C4311yescharacteristic
365C2×#95C22×C4312yes—
366C2×#95C22×C4311yescharacteristic
367C43#1450611yescharacteristic, direct product factor, Sylow
368C25C23×C4311yescharacteristic
369C25C23×C4311yescharacteristic
370C22×D4—24no—
371C22×D4—42no—
372C22×D4—41no—
373C22×D4—41no—
374C22×D4C2×C4×C4314yes—
375C23×C4—24no—
376C23×C4—42no—
377C23×C4—41no—
378C23×C4—41no—
379C23×C4C2×C4×C4314yes—
380C23×C4C23×C4312yes—
381C23×C4C23×C4312yes—
382C23×C4C23×C4312yes—
383C23×C4C23×C4311yescharacteristic
384C23×C4C23×C4312yes—
385C23×C4C23×C4312yes—
386C23×C4C23×C4312yes—
387#123—232no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4C2×C4×C4318yes—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4C2×C4×C4318yes—
410C2×C22⋊C4C2×C4×C4314yes—
411C2×C22⋊C4D4×C4318yes—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—42no—
415#95—24no—
416#95—24no—
417#95—41no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—41no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24C22×C4×C4312yes—
440C24C22×C4×C4312yes—
441C24C2×D4×C4314yes—
442C24C24×C4311yescharacteristic
443C2×D4—28no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4C22×C4×C4314yes—
494C22×C4C22×C4×C4312yes—
495C22×C4C22×C4×C4314yes—
496C22×C4C2×D4×C4314yes—
497C22×C4C2×D4×C4314yes—
498C22×C4#41×C4314yes—
499C22×C4#41×C4314yes—
500C4⋊C4—216no—
501C4⋊C4—48no—
502C22⋊C4—216no—
503C22⋊C4—44no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C22⋊C4—48no—
507C22⋊C4—44no—
508C22⋊C4C22⋊C4×C43116yescomplemented
509C42—48no—
510C23—24no—
511C23—22no—
512C23—22no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—24no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—41no—
548C23—41no—
549C23—42no—
550C23—41no—
551C23C2×C22⋊C4×C4314yes—
552C23C23×C4×C4311yescharacteristic
553C23C22×D4×C4312yes—
554C23C2×#41×C4312yes—
555C23C2×#41×C4312yes—
556C23H(5,𝔽2)×C4312yes—
557C23H(5,𝔽2)×C4311yescharacteristic
558C23H(5,𝔽2)×C4311yescharacteristic
559C23H(5,𝔽2)×C4312yes—
560C232−1+4×C4312yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—416no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4C2×C22⋊C4×C4318yes—
610C22—28no—
611C22—24no—
612C22—44no—
613C22—42no—
614C22—42no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22C22×C22⋊C4×C4311yescharacteristic
629C22C4×#41×C4312yes—
630C22C43×#51811yescharacteristic
631C22C43×#51811yescharacteristic
632C22C43×#52012yes—
633C22C43×#53512yes—
634C22C43×#53512yes—
635C22C43×#53812yes—
636C22C43×#53912yes—
637C22C43×#54012yes—
638C22C43×#54212yes—
639C22C43×#54612yes—
640C22C43×#54612yes—
641C22C43×#54712yes—
642C22C43×#54712yes—
643C22C43×#55111yescharacteristic
644C22C43×#55312yes—
645C22C43×#55911yescharacteristic
646C22C43×#56011yescharacteristic
647C22C43×#56212yes—
648C22C43×#56311yescharacteristic
649C4—28no—
650C4—44no—
651C4—44no—
652C4—44no—
653C4—42no—
654C4—82no—
655C4—82no—
656C2—44no—
657C2—82no—
658C2C43×#230911yescharacteristic
659C2C43×#233512yes—
660C2C43×#233912yes—
661C2C43×#237411yescharacteristic
662C2C43×#237611yescharacteristic
663C2C43×#270312yes—
664C2C43×#270612yes—
665C2C43×#271012yes—
666C2C43×#271812yes—
subgroupG/H
center, socleC24×C43C24
commutatorC23C23×C4×C43
Frattini, cosocleC24C24×C43
prime radicalC23×D4×C43C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#388C2semidirect
3. C43×#1445C2semidirect
4. C43×#1439C2semidirect
7. C43×#1437C2semidirect
8. C43×C4⋊#95C2semidirect
9. C43×C22⋊#95C2semidirect
13. C2×#123×C43C4semidirect
174. C22⋊C4×C43C22⋊C4semidirect
276. #14506C43direct (N × H)
324. C2×#388C2×C43semidirect
325. #1445C2×C43semidirect
326. #1439C2×C43semidirect
329. #1437C2×C43semidirect
330. C4⋊#95C2×C43semidirect
331. C22⋊#95C2×C43semidirect
346. C2×#123C4×C43semidirect
367. C43#14506direct (N × H)
508. C22⋊C4C22⋊C4×C43semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C432
C2×C43×#3882
C43×#14452
C43×#14392
C43×#14382
C43×#14372
C43×C4⋊#952
C43×C22⋊#952
#1450643