Finite Group Databasebeta

← C43×#29158 #24949175

Subgroups — C43×#29158 #24949175

Order 11008.

784 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2851C211yesmaximal, characteristic
2C4×C22⋊Q8×C43C211yesmaximal, characteristic
3C43×#2101C211yesmaximal, characteristic, complemented
4C43×#2097C211yesmaximal, characteristic, complemented
5C43×#2059C211yesmaximal, characteristic, complemented
6C43×#2026C211yesmaximal, characteristic, complemented
7C43×#1920C211yesmaximal, characteristic, complemented
8C43×#1918C211yesmaximal, characteristic, complemented
9C43×#1892C211yesmaximal, characteristic
10C43×#1892C211yesmaximal, characteristic
11C43×#1865C211yesmaximal, characteristic, complemented
12C43×#1863C211yesmaximal, characteristic, complemented
13C43×#1808C211yesmaximal, characteristic
14C43×#1807C211yesmaximal, characteristic
15C2×C43×#336C211yesmaximal, characteristic
16C23×C8×C43C2211yescharacteristic
17C23×C8×C43C2211yescharacteristic
18C2×#125×C43C2211yescharacteristic
19C2×C22⋊Q8×C43C2211yescharacteristic
20C2×C4×Q8×C43C2211yescharacteristic
21C22×C42×C43C2211yescharacteristic
22C2×#107×C43C2211yescharacteristic
23C2×#107×C43C2211yescharacteristic
24C2×#106×C43C2211yescharacteristic
25C2×#106×C43C2211yescharacteristic
26C2×#103×C43C2211yescharacteristic
27C2×#103×C43C2211yescharacteristic
28C2×#103×C43C2211yescharacteristic
29C2×#103×C43C2211yescharacteristic
30C43×#391C2211yescharacteristic
31C43×#389C2211yescharacteristic
32C43×#389C2211yescharacteristic
33C43×#389C2211yescharacteristic
34C43×#387—21no—
35C43×#387—21no—
36C43×#387—21no—
37C43×#385—21no—
38C43×#385—21no—
39C43×#385—21no—
40C43×#382C2211yescharacteristic
41C43×#380C2211yescharacteristic
42C43×#380C2211yescharacteristic
43C43×#380C2211yescharacteristic
44C4×C4⋊C4×C43—21no—
45C4×C4⋊C4×C43C2211yescharacteristic
46C4×C22⋊C4×C43—21no—
47C43×#340C2211yescharacteristic
48C43×#340C2211yescharacteristic
49C43×#340C2211yescharacteristic
50C43×#340C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#336C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Q8×C43C2311yescharacteristic
60C23×C4×C43D411yescharacteristic
61C23×C4×C43D411yescharacteristic
62C23×C4×C43C2311yescharacteristic
63C22×C8×C43—22no—
64C22×C8×C43—22no—
65C22×C8×C43—22no—
66C22×C8×C43—22no—
67C22×C8×C43—41no—
68C22×C8×C43—41no—
69C22×C8×C43C2311yescharacteristic
70C22×C8×C43C2311yescharacteristic
71C22×C8×C43C2311yescharacteristic
72C22×C8×C43C2311yescharacteristic
73#125×C43—41no—
74#125×C43—41no—
75C22⋊Q8×C43—22no—
76C22⋊Q8×C43Q814yes—
77C4×Q8×C43—41no—
78C4×Q8×C43—41no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43—21no—
86C2×C4⋊C4×C43C2311yescharacteristic
87C2×C4⋊C4×C43C2311yescharacteristic
88C2×C4⋊C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43C2311yescharacteristic
90C2×C4⋊C4×C43C2311yescharacteristic
91C2×C4⋊C4×C43C2311yescharacteristic
92C2×C4⋊C4×C43C2311yescharacteristic
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C42×C43—21no—
98C2×C42×C43—21no—
99C2×C42×C43—41no—
100C2×C42×C43—41no—
101C2×C42×C43D411yescharacteristic
102C2×C42×C43D411yescharacteristic
103C2×C42×C43C2311yescharacteristic
104C2×C42×C43C2311yescharacteristic
105#107×C43—22no—
106#107×C43—41no—
107#106×C43—22no—
108#106×C43—41no—
109#103×C43—22no—
110#103×C43—22no—
111#103×C43—41no—
112#103×C43—41no—
113#95×C43—21no—
114#95×C43—21no—
115#95×C43—21no—
116#95×C43—21no—
117#95×C43—21no—
118#95×C43—21no—
119#95×C43—21no—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124C24×C43C2×D411yescharacteristic
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43C2×Q812yes—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—41no—
147C22×C4×C43—41no—
148C22×C4×C43—41no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×Q812yes—
155C22×C4×C43#4112yes—
156C22×C4×C43C2411yescharacteristic
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—44no—
168C2×C8×C43—44no—
169C2×C8×C43#4112yes—
170C2×C8×C43#4112yes—
171C4⋊C4×C43—24no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—42no—
186C4⋊C4×C43—42no—
187C4⋊C4×C43—42no—
188C4⋊C4×C43—42no—
189C4⋊C4×C43—42no—
190C4⋊C4×C43—42no—
191C4⋊C4×C43C2×Q812yes—
192C22⋊C4×C43—24no—
193C22⋊C4×C43—42no—
194C22⋊C4×C43—42no—
195C22⋊C4×C43—42no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—41no—
201C42×C43—41no—
202C42×C43—42no—
203C42×C43—42no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43C22⋊Q812yes—
209C23×C43#13512yes—
210C23×C43#13712yes—
211C23×C43C22×D411yescharacteristic
212Q8×C43—22no—
213Q8×C43—22no—
214Q8×C43—41no—
215Q8×C43—41no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—44no—
236C2×C4×C43—44no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43C22⋊Q812yes—
260C2×C4×C43#13512yes—
261C2×C4×C43C22×Q811yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C8×C43—22no—
268C8×C43—22no—
269C8×C43—41no—
270C8×C43—41no—
271#29158C4311yesmaximal, characteristic, direct product factor, Sylow
272C22×C43—22no—
273C22×C43—22no—
274C22×C43—22no—
275C22×C43—22no—
276C22×C43—22no—
277C22×C43—22no—
278C22×C43#47914yes—
279C22×C43C2×C22⋊Q811yescharacteristic
280C22×C43#53211yescharacteristic
281C22×C43#53411yescharacteristic
282C22×C43C2×#13511yescharacteristic
283C22×C43C2×#13511yescharacteristic
284C22×C43C2×#13711yescharacteristic
285C22×C43#57511yescharacteristic
286C4×C43—22no—
287C4×C43—22no—
288C4×C43—42no—
289C4×C43—42no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—81no—
294C4×C43—81no—
295C4×C43—81no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43—81no—
299C4×C43#55111yescharacteristic
300C4×C43#55111yescharacteristic
301C4×C43#55411yescharacteristic
302C4×C43#55411yescharacteristic
303#2851C2×C4311yescharacteristic
304C4×C22⋊Q8C2×C4311yescharacteristic
305#2101C2×C4311yescharacteristic, complemented
306#2097C2×C4311yescharacteristic, complemented
307#2059C2×C4311yescharacteristic, complemented
308#2026C2×C4311yescharacteristic, complemented
309#1920C2×C4311yescharacteristic, complemented
310#1918C2×C4311yescharacteristic, complemented
311#1892C2×C4311yescharacteristic
312#1892C2×C4311yescharacteristic
313#1865C2×C4311yescharacteristic, complemented
314#1863C2×C4311yescharacteristic, complemented
315#1808C2×C4311yescharacteristic
316#1807C2×C4311yescharacteristic
317C2×#336C2×C4311yescharacteristic
318C2×C43—24no—
319C2×C43#256411yescharacteristic
320C2×C43C2×#47911yescharacteristic
321C2×C43#307611yescharacteristic
322C2×C43#316811yescharacteristic
323C2×C43#318111yescharacteristic
324C2×C43#319011yescharacteristic
325C2×C43#319111yescharacteristic
326C23×C8C22×C4311yescharacteristic
327C23×C8C22×C4311yescharacteristic
328C2×#125C22×C4311yescharacteristic
329C2×C22⋊Q8C22×C4311yescharacteristic
330C2×C4×Q8C22×C4311yescharacteristic
331C22×C42C22×C4311yescharacteristic
332C2×#107C22×C4311yescharacteristic
333C2×#107C22×C4311yescharacteristic
334C2×#106C22×C4311yescharacteristic
335C2×#106C22×C4311yescharacteristic
336C2×#103C22×C4311yescharacteristic
337C2×#103C22×C4311yescharacteristic
338C2×#103C22×C4311yescharacteristic
339C2×#103C22×C4311yescharacteristic
340#391C22×C4311yescharacteristic
341#389C22×C4311yescharacteristic
342#389C22×C4311yescharacteristic
343#389C22×C4311yescharacteristic
344#387—21no—
345#387—21no—
346#387—21no—
347#385—21no—
348#385—21no—
349#385—21no—
350#382C22×C4311yescharacteristic
351#380C22×C4311yescharacteristic
352#380C22×C4311yescharacteristic
353#380C22×C4311yescharacteristic
354C4×C4⋊C4—21no—
355C4×C4⋊C4C22×C4311yescharacteristic
356C4×C22⋊C4—21no—
357#340C22×C4311yescharacteristic
358#340C22×C4311yescharacteristic
359#340C22×C4311yescharacteristic
360#340C22×C4311yescharacteristic
361#340C22×C4311yescharacteristic
362#340C22×C4311yescharacteristic
363#340C22×C4311yescharacteristic
364#340C22×C4311yescharacteristic
365#336C22×C4311yescharacteristic
366#336C22×C4311yescharacteristic
367#336C22×C4311yescharacteristic
368#336C22×C4311yescharacteristic
369C43#2915811yescharacteristic, direct product factor, Sylow
370C22×Q8C23×C4311yescharacteristic
371C23×C4D4×C4311yescharacteristic
372C23×C4D4×C4311yescharacteristic
373C23×C4C23×C4311yescharacteristic
374C22×C8—22no—
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—22no—
378C22×C8—41no—
379C22×C8—41no—
380C22×C8C23×C4311yescharacteristic
381C22×C8C23×C4311yescharacteristic
382C22×C8C23×C4311yescharacteristic
383C22×C8C23×C4311yescharacteristic
384#125—41no—
385#125—41no—
386C22⋊Q8—22no—
387C22⋊Q8Q8×C4314yes—
388C4×Q8—41no—
389C4×Q8—41no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4C23×C4311yescharacteristic
398C2×C4⋊C4C23×C4311yescharacteristic
399C2×C4⋊C4C23×C4311yescharacteristic
400C2×C4⋊C4C23×C4311yescharacteristic
401C2×C4⋊C4C23×C4311yescharacteristic
402C2×C4⋊C4C23×C4311yescharacteristic
403C2×C4⋊C4C23×C4311yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—41no—
411C2×C42—41no—
412C2×C42D4×C4311yescharacteristic
413C2×C42D4×C4311yescharacteristic
414C2×C42C23×C4311yescharacteristic
415C2×C42C23×C4311yescharacteristic
416#107—22no—
417#107—41no—
418#106—22no—
419#106—41no—
420#103—22no—
421#103—22no—
422#103—41no—
423#103—41no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435C24C2×D4×C4311yescharacteristic
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8C2×Q8×C4312yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4C2×D4×C4311yescharacteristic
461C22×C4C2×D4×C4311yescharacteristic
462C22×C4C2×D4×C4311yescharacteristic
463C22×C4C2×D4×C4311yescharacteristic
464C22×C4C2×D4×C4311yescharacteristic
465C22×C4C2×Q8×C4312yes—
466C22×C4#41×C4312yes—
467C22×C4C24×C4311yescharacteristic
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—44no—
479C2×C8—44no—
480C2×C8#41×C4312yes—
481C2×C8#41×C4312yes—
482C4⋊C4—24no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4C2×Q8×C4312yes—
503C22⋊C4—24no—
504C22⋊C4—42no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—41no—
512C42—41no—
513C42—42no—
514C42—42no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23C22⋊Q8×C4312yes—
520C23#135×C4312yes—
521C23#137×C4312yes—
522C23C22×D4×C4311yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—41no—
526Q8—41no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—44no—
547C2×C4—44no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4C22⋊Q8×C4312yes—
571C2×C4#135×C4312yes—
572C2×C4C22×Q8×C4311yescharacteristic
573C2×C4C2×#41×C4311yescharacteristic
574C2×C4C2×#41×C4311yescharacteristic
575C2×C4C2×#41×C4311yescharacteristic
576C2×C4H(5,𝔽2)×C4311yescharacteristic
577C2×C4H(5,𝔽2)×C4311yescharacteristic
578C8—22no—
579C8—22no—
580C8—41no—
581C8—41no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—22no—
588C22C43×#47914yes—
589C22C2×C22⋊Q8×C4311yescharacteristic
590C22C43×#53211yescharacteristic
591C22C43×#53411yescharacteristic
592C22C2×#135×C4311yescharacteristic
593C22C2×#135×C4311yescharacteristic
594C22C2×#137×C4311yescharacteristic
595C22C43×#57511yescharacteristic
596C4—22no—
597C4—22no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—42no—
602C4—42no—
603C4—81no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4—81no—
608C4—81no—
609C4C43×#55111yescharacteristic
610C4C43×#55111yescharacteristic
611C4C43×#55411yescharacteristic
612C4C43×#55411yescharacteristic
613C2—24no—
614C2C43×#256411yescharacteristic
615C2C2×C43×#47911yescharacteristic
616C2C43×#307611yescharacteristic
617C2C43×#316811yescharacteristic
618C2C43×#318111yescharacteristic
619C2C43×#319011yescharacteristic
620C2C43×#319111yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC24×C43C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C22×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#2101C2semidirect
4. C43×#2097C2semidirect
5. C43×#2059C2semidirect
6. C43×#2026C2semidirect
7. C43×#1920C2semidirect
8. C43×#1918C2semidirect
11. C43×#1865C2semidirect
12. C43×#1863C2semidirect
271. #29158C43direct (N × H)
305. #2101C2×C43semidirect
306. #2097C2×C43semidirect
307. #2059C2×C43semidirect
308. #2026C2×C43semidirect
309. #1920C2×C43semidirect
310. #1918C2×C43semidirect
313. #1865C2×C43semidirect
314. #1863C2×C43semidirect
369. C43#29158direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#28512
C4×C22⋊Q8×C432
C43×#21012
C43×#20972
C43×#20592
C43×#20262
C43×#19202
C43×#19182
C43×#18922
C43×#18652
C43×#18632
C43×#18082
C43×#18072
C2×C43×#3362
#2915843