Finite Group Databasebeta

← C43×#29267 #24949284

Subgroups — C43×#29267 #24949284

Order 11008.

734 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2331C211yesmaximal, characteristic, complemented
2C43×#2326C211yesmaximal, characteristic
3C43×#2097C211yesmaximal, characteristic, complemented
4C43×#2092C211yesmaximal, characteristic
5C43×#2024C211yesmaximal, characteristic, complemented
6C43×#2023C211yesmaximal, characteristic
7C43×#1983C211yesmaximal, characteristic
8C43×#1983C211yesmaximal, characteristic
9C43×#1948C211yesmaximal, characteristic, complemented
10C43×#1947C211yesmaximal, characteristic, complemented
11C43×#1865C211yesmaximal, characteristic, complemented
12C43×#1864C211yesmaximal, characteristic
13C43×#1863C211yesmaximal, characteristic, complemented
14C43×#1862C211yesmaximal, characteristic
15C43×#1832C211yesmaximal, characteristic, complemented
16C2×C4⋊Q8×C43C2211yescharacteristic
17C2×#124×C43C2211yescharacteristic
18C2×C4×Q8×C43C2211yescharacteristic
19C2×C4×D4×C43C2211yescharacteristic
20C2×#107×C43C2211yescharacteristic
21C2×#107×C43C2211yescharacteristic
22C2×#106×C43C2211yescharacteristic
23C2×#106×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×C4⋊C8×C43C2211yescharacteristic
26C2×#103×C43C2211yescharacteristic
27C2×#103×C43C2211yescharacteristic
28C2×#103×C43C2211yescharacteristic
29C2×#103×C43C2211yescharacteristic
30C2×#102×C43C2211yescharacteristic
31C2×#102×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C43×#391—21no—
35C43×#391—21no—
36C43×#391C2211yescharacteristic
37C43×#390C2211yescharacteristic
38C43×#389C2211yescharacteristic
39C43×#389C2211yescharacteristic
40C43×#388—21no—
41C43×#388—21no—
42C43×#387—21no—
43C43×#387—21no—
44C43×#385—21no—
45C43×#385—21no—
46C43×#384C2211yescharacteristic
47C43×#382C2211yescharacteristic
48C4×C4⋊C4×C43C2211yescharacteristic
49C4×C4⋊C4×C43C2211yescharacteristic
50C43×#376C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#336C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Q8×C43—21no—
60C22×Q8×C43C2311yescharacteristic
61C22×D4×C43C2311yescharacteristic
62C23×C4×C43—21no—
63C22×C8×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65C22×C8×C43C2311yescharacteristic
66C22×C8×C43C2311yescharacteristic
67C4⋊Q8×C43—22no—
68C4⋊Q8×C43—22no—
69#124×C43—22no—
70#124×C43Q814yescomplemented
71C4×Q8×C43—41no—
72C4×Q8×C43—41no—
73C4×D4×C43—41no—
74C4×D4×C43—41no—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43C2311yescharacteristic
82C2×C4⋊C4×C43C2311yescharacteristic
83C2×C4⋊C4×C43C2311yescharacteristic
84C2×C4⋊C4×C43C2311yescharacteristic
85C2×C4⋊C4×C43C2311yescharacteristic
86C2×C4⋊C4×C43C2311yescharacteristic
87C2×C22⋊C4×C43—21no—
88C2×C22⋊C4×C43—21no—
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C42×C43—21no—
93C2×C42×C43—21no—
94C2×C42×C43—21no—
95C2×C42×C43C2311yescharacteristic
96C2×C42×C43C2311yescharacteristic
97C2×C42×C43C2311yescharacteristic
98#107×C43—41no—
99#107×C43—41no—
100#106×C43—41no—
101#106×C43—41no—
102C4⋊C8×C43—22no—
103C4⋊C8×C43—22no—
104#103×C43—22no—
105#103×C43—22no—
106#103×C43—41no—
107#103×C43—41no—
108#102×C43—22no—
109#102×C43—22no—
110#102×C43—41no—
111#102×C43—41no—
112#95×C43—21no—
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×C43D411yescharacteristic
121#95×C43D411yescharacteristic
122#95×C43D411yescharacteristic
123#95×C43D411yescharacteristic
124C24×C43—21no—
125C2×Q8×C43—24no—
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—81no—
132C2×Q8×C43—81no—
133C2×Q8×C43C2×Q812yes—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43C2×Q812yes—
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—21no—
147C22×C4×C43—42no—
148C22×C4×C43—81no—
149C22×C4×C43—81no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
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—21no—
168C2×C8×C43—21no—
169C4⋊C4×C43—24no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
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—42no—
181C4⋊C4×C43—81no—
182C4⋊C4×C43—81no—
183C4⋊C4×C43—81no—
184C4⋊C4×C43—81no—
185C4⋊C4×C43#4112yes—
186C4⋊C4×C43#4112yes—
187C22⋊C4×C43—24no—
188C22⋊C4×C43—24no—
189C22⋊C4×C43—42no—
190C22⋊C4×C43—81no—
191C22⋊C4×C43—81no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43—21no—
195C42×C43—21no—
196C42×C43—42no—
197C42×C43—81no—
198C42×C43—81no—
199C42×C43C2×Q812yes—
200C42×C43#4112yes—
201C23×C43—22no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43C22×D411yescharacteristic
209Q8×C43—22no—
210Q8×C43—22no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—84no—
214D4×C43—22no—
215D4×C43—22no—
216D4×C43—41no—
217D4×C43—41no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—22no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
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—21no—
236C2×C4×C43—21no—
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—84no—
256C2×C4×C43C22⋊Q812yes—
257C2×C4×C43C22⋊Q812yes—
258C2×C4×C43C22×Q811yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43H(5,𝔽2)11yescharacteristic
263C2×C4×C43H(5,𝔽2)11yescharacteristic
264C8×C43—41no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43—41no—
268#29267C4311yesmaximal, characteristic, direct product factor, Sylow
269C22×C43—42no—
270C22×C43—42no—
271C22×C43—42no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43C2×C22⋊Q811yescharacteristic
277C22×C43#52511yescharacteristic
278C22×C43#53511yescharacteristic
279C22×C43#57611yescharacteristic
280C22×C43#57711yescharacteristic
281C22×C43#57711yescharacteristic
282C22×C43#57811yescharacteristic
283C4×C43—22no—
284C4×C43—22no—
285C4×C43—42no—
286C4×C43—41no—
287C4×C43—42no—
288C4×C43—42no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43—81no—
295C4×C43—81no—
296C4×C43#55411yescharacteristic
297C4×C43#55411yescharacteristic
298C4×C43#55911yescharacteristic
299C4×C43#55911yescharacteristic
300#2331C2×C4311yescharacteristic, complemented
301#2326C2×C4311yescharacteristic
302#2097C2×C4311yescharacteristic, complemented
303#2092C2×C4311yescharacteristic
304#2024C2×C4311yescharacteristic, complemented
305#2023C2×C4311yescharacteristic
306#1983C2×C4311yescharacteristic
307#1983C2×C4311yescharacteristic
308#1948C2×C4311yescharacteristic, complemented
309#1947C2×C4311yescharacteristic, complemented
310#1865C2×C4311yescharacteristic, complemented
311#1864C2×C4311yescharacteristic
312#1863C2×C4311yescharacteristic, complemented
313#1862C2×C4311yescharacteristic
314#1832C2×C4311yescharacteristic, complemented
315C2×C43—82no—
316C2×C43#258011yescharacteristic
317C2×C43#308311yescharacteristic
318C2×C43#308411yescharacteristic
319C2×C43#311811yescharacteristic
320C2×C43#312111yescharacteristic
321C2×C43#322411yescharacteristic
322C2×C43#322511yescharacteristic
323C2×C4⋊Q8C22×C4311yescharacteristic
324C2×#124C22×C4311yescharacteristic
325C2×C4×Q8C22×C4311yescharacteristic
326C2×C4×D4C22×C4311yescharacteristic
327C2×#107C22×C4311yescharacteristic
328C2×#107C22×C4311yescharacteristic
329C2×#106C22×C4311yescharacteristic
330C2×#106C22×C4311yescharacteristic
331C2×C4⋊C8C22×C4311yescharacteristic
332C2×C4⋊C8C22×C4311yescharacteristic
333C2×#103C22×C4311yescharacteristic
334C2×#103C22×C4311yescharacteristic
335C2×#103C22×C4311yescharacteristic
336C2×#103C22×C4311yescharacteristic
337C2×#102C22×C4311yescharacteristic
338C2×#102C22×C4311yescharacteristic
339C2×#102C22×C4311yescharacteristic
340C2×#102C22×C4311yescharacteristic
341#391—21no—
342#391—21no—
343#391C22×C4311yescharacteristic
344#390C22×C4311yescharacteristic
345#389C22×C4311yescharacteristic
346#389C22×C4311yescharacteristic
347#388—21no—
348#388—21no—
349#387—21no—
350#387—21no—
351#385—21no—
352#385—21no—
353#384C22×C4311yescharacteristic
354#382C22×C4311yescharacteristic
355C4×C4⋊C4C22×C4311yescharacteristic
356C4×C4⋊C4C22×C4311yescharacteristic
357#376C22×C4311yescharacteristic
358#340C22×C4311yescharacteristic
359#340C22×C4311yescharacteristic
360#340C22×C4311yescharacteristic
361#340C22×C4311yescharacteristic
362#336C22×C4311yescharacteristic
363#336C22×C4311yescharacteristic
364#336C22×C4311yescharacteristic
365#336C22×C4311yescharacteristic
366C43#2926711yescharacteristic, direct product factor, Sylow
367C22×Q8—21no—
368C22×Q8C23×C4311yescharacteristic
369C22×D4C23×C4311yescharacteristic
370C23×C4—21no—
371C22×C8C23×C4311yescharacteristic
372C22×C8C23×C4311yescharacteristic
373C22×C8C23×C4311yescharacteristic
374C22×C8C23×C4311yescharacteristic
375C4⋊Q8—22no—
376C4⋊Q8—22no—
377#124—22no—
378#124Q8×C4314yescomplemented
379C4×Q8—41no—
380C4×Q8—41no—
381C4×D4—41no—
382C4×D4—41no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4C23×C4311yescharacteristic
390C2×C4⋊C4C23×C4311yescharacteristic
391C2×C4⋊C4C23×C4311yescharacteristic
392C2×C4⋊C4C23×C4311yescharacteristic
393C2×C4⋊C4C23×C4311yescharacteristic
394C2×C4⋊C4C23×C4311yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42C23×C4311yescharacteristic
404C2×C42C23×C4311yescharacteristic
405C2×C42C23×C4311yescharacteristic
406#107—41no—
407#107—41no—
408#106—41no—
409#106—41no—
410C4⋊C8—22no—
411C4⋊C8—22no—
412#103—22no—
413#103—22no—
414#103—41no—
415#103—41no—
416#102—22no—
417#102—22no—
418#102—41no—
419#102—41no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95D4×C4311yescharacteristic
429#95D4×C4311yescharacteristic
430#95D4×C4311yescharacteristic
431#95D4×C4311yescharacteristic
432C24—21no—
433C2×Q8—24no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—81no—
440C2×Q8—81no—
441C2×Q8C2×Q8×C4312yes—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4C2×Q8×C4312yes—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—42no—
456C22×C4—81no—
457C22×C4—81no—
458C22×C4C2×D4×C4311yescharacteristic
459C22×C4C2×D4×C4311yescharacteristic
460C22×C4C2×D4×C4311yescharacteristic
461C22×C4C2×D4×C4311yescharacteristic
462C22×C4C2×D4×C4311yescharacteristic
463C22×C4C2×D4×C4311yescharacteristic
464C22×C4C24×C4311yescharacteristic
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
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—
477C4⋊C4—24no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—42no—
489C4⋊C4—81no—
490C4⋊C4—81no—
491C4⋊C4—81no—
492C4⋊C4—81no—
493C4⋊C4#41×C4312yes—
494C4⋊C4#41×C4312yes—
495C22⋊C4—24no—
496C22⋊C4—24no—
497C22⋊C4—42no—
498C22⋊C4—81no—
499C22⋊C4—81no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—42no—
505C42—81no—
506C42—81no—
507C42C2×Q8×C4312yes—
508C42#41×C4312yes—
509C23—22no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23C22×D4×C4311yescharacteristic
517Q8—22no—
518Q8—22no—
519Q8—41no—
520Q8—41no—
521Q8—84no—
522D4—22no—
523D4—22no—
524D4—41no—
525D4—41no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
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—41no—
546C2×C4—41no—
547C2×C4—41no—
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—84no—
564C2×C4C22⋊Q8×C4312yes—
565C2×C4C22⋊Q8×C4312yes—
566C2×C4C22×Q8×C4311yescharacteristic
567C2×C4C2×#41×C4311yescharacteristic
568C2×C4C2×#41×C4311yescharacteristic
569C2×C4C2×#41×C4311yescharacteristic
570C2×C4H(5,𝔽2)×C4311yescharacteristic
571C2×C4H(5,𝔽2)×C4311yescharacteristic
572C8—41no—
573C8—41no—
574C8—41no—
575C8—41no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22C2×C22⋊Q8×C4311yescharacteristic
584C22C43×#52511yescharacteristic
585C22C43×#53511yescharacteristic
586C22C43×#57611yescharacteristic
587C22C43×#57711yescharacteristic
588C22C43×#57711yescharacteristic
589C22C43×#57811yescharacteristic
590C4—22no—
591C4—22no—
592C4—42no—
593C4—41no—
594C4—42no—
595C4—42no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4C43×#55411yescharacteristic
604C4C43×#55411yescharacteristic
605C4C43×#55911yescharacteristic
606C4C43×#55911yescharacteristic
607C2—82no—
608C2C43×#258011yescharacteristic
609C2C43×#308311yescharacteristic
610C2C43×#308411yescharacteristic
611C2C43×#311811yescharacteristic
612C2C43×#312111yescharacteristic
613C2C43×#322411yescharacteristic
614C2C43×#322511yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×D4×C43C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C43×#376 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#2331C2semidirect
3. C43×#2097C2semidirect
5. C43×#2024C2semidirect
9. C43×#1948C2semidirect
10. C43×#1947C2semidirect
11. C43×#1865C2semidirect
13. C43×#1863C2semidirect
15. C43×#1832C2semidirect
70. #124×C43Q8semidirect
268. #29267C43direct (N × H)
300. #2331C2×C43semidirect
302. #2097C2×C43semidirect
304. #2024C2×C43semidirect
308. #1948C2×C43semidirect
309. #1947C2×C43semidirect
310. #1865C2×C43semidirect
312. #1863C2×C43semidirect
314. #1832C2×C43semidirect
366. C43#29267direct (N × H)
378. #124Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#23312
C43×#23262
C43×#20972
C43×#20922
C43×#20242
C43×#20232
C43×#19832
C43×#19482
C43×#19472
C43×#18652
C43×#18642
C43×#18632
C43×#18622
C43×#18322
#2926743