Finite Group Databasebeta

← C43×#24714 #24944731

Subgroups — C43×#24714 #24944731

Order 11008.

746 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
1C2×C43×#477C211yesmaximal, characteristic, complemented
2C2×C43×#433C211yesmaximal, characteristic
3C43×#2628C211yesmaximal, characteristic
4C43×#2323C211yesmaximal, characteristic
5C43×#2076C211yesmaximal, characteristic
6C43×#2075C211yesmaximal, characteristic
7C43×#2036C211yesmaximal, characteristic
8C43×#2035C211yesmaximal, characteristic
9C43×#1988C211yesmaximal, characteristic, complemented
10C43×#1949C211yesmaximal, characteristic, complemented
11C43×#1944C211yesmaximal, characteristic, complemented
12C43×#1942C211yesmaximal, characteristic, complemented
13C43×#1935C211yesmaximal, characteristic, complemented
14C43×#1933C211yesmaximal, characteristic, complemented
15C43×#1805C211yesmaximal, characteristic, complemented
16C2×C4⋊Q8×C43C2211yescharacteristic
17C2×C22⋊Q8×C43C2211yescharacteristic
18C2×C4×Q8×C43C2211yescharacteristic
19C2×#117×C43C2211yescharacteristic
20C43×#477—24no—
21C43×#433—24no—
22C2×#107×C43C2211yescharacteristic
23C2×#107×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C2×#106×C43C2211yescharacteristic
26C2×C4⋊C8×C43C2211yescharacteristic
27C2×C4⋊C8×C43C2211yescharacteristic
28C2×#103×C43C2211yescharacteristic
29C2×#103×C43C2211yescharacteristic
30C2×#103×C43C2211yescharacteristic
31C2×#103×C43C2211yescharacteristic
32C2×C22⋊C8×C43C2211yescharacteristic
33C2×C22⋊C8×C43C2211yescharacteristic
34C2×#97×C43C2211yescharacteristic
35C2×C4×C8×C43C2211yescharacteristic
36C43×#400—21no—
37C43×#399—21no—
38C43×#395—21no—
39C43×#393—21no—
40C43×#391C2211yescharacteristic
41C43×#389—21no—
42C43×#389C2211yescharacteristic
43C43×#389C2211yescharacteristic
44C43×#389C2211yescharacteristic
45C43×#388—21no—
46C43×#388—21no—
47C43×#387—21no—
48C43×#382C2211yescharacteristic
49C43×#380C2211yescharacteristic
50C43×#380C2211yescharacteristic
51C43×#380C2211yescharacteristic
52C4×C4⋊C4×C43C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Q8×C43—21no—
62C22×Q8×C43C2311yescharacteristic
63C23×C4×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65C22×C8×C43C2311yescharacteristic
66C22×C8×C43C2311yescharacteristic
67C22×C8×C43C2311yescharacteristic
68C4⋊Q8×C43—22no—
69C4⋊Q8×C43—22no—
70C22⋊Q8×C43—22no—
71C22⋊Q8×C43—22no—
72C4×Q8×C43—22no—
73C4×Q8×C43—22no—
74#117×C43—22no—
75#117×C43—22no—
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×C43—21no—
82C2×C4⋊C4×C43D411yescharacteristic
83C2×C4⋊C4×C43D411yescharacteristic
84C2×C4⋊C4×C43C2311yescharacteristic
85C2×C4⋊C4×C43C2311yescharacteristic
86C2×C4⋊C4×C43C2311yescharacteristic
87C2×C4⋊C4×C43C2311yescharacteristic
88C2×C4⋊C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43C2311yescharacteristic
90C2×C4⋊C4×C43C2311yescharacteristic
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43D411yescharacteristic
96C2×C22⋊C4×C43D411yescharacteristic
97C2×C42×C43—21no—
98C2×C42×C43—21no—
99C2×C42×C43C2311yescharacteristic
100C2×C42×C43C2311yescharacteristic
101#107×C43—22no—
102#107×C43—22no—
103#107×C43—22no—
104#106×C43—22no—
105C4⋊C8×C43—22no—
106C4⋊C8×C43D414yes—
107#103×C43—22no—
108#103×C43—22no—
109#103×C43—22no—
110#103×C43—22no—
111C22⋊C8×C43—22no—
112C22⋊C8×C43—22no—
113#97×C43—22no—
114C4×C8×C43—22no—
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—
124#95×C43—21no—
125#95×C43—21no—
126C24×C43C2×D411yescharacteristic
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—42no—
133C2×Q8×C43—81no—
134C2×Q8×C43—81no—
135C2×Q8×C43#4112yes—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
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—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C2×C8×C43—21no—
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×C43C2×D412yes—
167C2×C8×C43C2×D412yes—
168C4⋊C4×C43—24no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43—22no—
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—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—42no—
185C4⋊C4×C43—42no—
186C4⋊C4×C43—81no—
187C4⋊C4×C43—81no—
188C4⋊C4×C43—81no—
189C4⋊C4×C43#4112yes—
190C22⋊C4×C43—24no—
191C22⋊C4×C43—22no—
192C22⋊C4×C43—22no—
193C22⋊C4×C43—81no—
194C22⋊C4×C43—81no—
195C22⋊C4×C43—81no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43—42no—
199C42×C43—81no—
200C42×C43C2×D412yes—
201C42×C43#4112yes—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43C22×D411yescharacteristic
210Q8×C43—22no—
211Q8×C43—22no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—84no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
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#12112yes—
257C2×C4×C43#12112yes—
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C432−1+411yescharacteristic
263C2×C4×C432−1+411yescharacteristic
264C8×C43—22no—
265C8×C43—22no—
266C8×C43—41no—
267C8×C43—41no—
268#24714C4311yesmaximal, characteristic, direct product factor, Sylow
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43C2×#12111yescharacteristic
277C22×C43#52511yescharacteristic
278C22×C43#53611yescharacteristic
279C22×C43#57611yescharacteristic
280C22×C43#57711yescharacteristic
281C22×C43#57811yescharacteristic
282C22×C43#57811yescharacteristic
283C4×C43—22no—
284C4×C43—22no—
285C4×C43—42no—
286C4×C43—41no—
287C4×C43—42no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—81no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43—81no—
295C4×C43—81no—
296C4×C43#54711yescharacteristic
297C4×C43#54811yescharacteristic
298C4×C43#55211yescharacteristic
299C4×C43#55611yescharacteristic
300C2×#477C2×C4311yescharacteristic, complemented
301C2×#433C2×C4311yescharacteristic
302#2628C2×C4311yescharacteristic
303#2323C2×C4311yescharacteristic
304#2076C2×C4311yescharacteristic
305#2075C2×C4311yescharacteristic
306#2036C2×C4311yescharacteristic
307#2035C2×C4311yescharacteristic
308#1988C2×C4311yescharacteristic, complemented
309#1949C2×C4311yescharacteristic, complemented
310#1944C2×C4311yescharacteristic, complemented
311#1942C2×C4311yescharacteristic, complemented
312#1935C2×C4311yescharacteristic, complemented
313#1933C2×C4311yescharacteristic, complemented
314#1805C2×C4311yescharacteristic, complemented
315C2×C43—81no—
316C2×C43#241511yescharacteristic
317C2×C43#305911yescharacteristic
318C2×C43#306211yescharacteristic
319C2×C43#312111yescharacteristic
320C2×C43#312411yescharacteristic
321C2×C43#324211yescharacteristic
322C2×C43#324311yescharacteristic
323C2×C4⋊Q8C22×C4311yescharacteristic
324C2×C22⋊Q8C22×C4311yescharacteristic
325C2×C4×Q8C22×C4311yescharacteristic
326C2×#117C22×C4311yescharacteristic
327#477—24no—
328#433—24no—
329C2×#107C22×C4311yescharacteristic
330C2×#107C22×C4311yescharacteristic
331C2×#107C22×C4311yescharacteristic
332C2×#106C22×C4311yescharacteristic
333C2×C4⋊C8C22×C4311yescharacteristic
334C2×C4⋊C8C22×C4311yescharacteristic
335C2×#103C22×C4311yescharacteristic
336C2×#103C22×C4311yescharacteristic
337C2×#103C22×C4311yescharacteristic
338C2×#103C22×C4311yescharacteristic
339C2×C22⋊C8C22×C4311yescharacteristic
340C2×C22⋊C8C22×C4311yescharacteristic
341C2×#97C22×C4311yescharacteristic
342C2×C4×C8C22×C4311yescharacteristic
343#400—21no—
344#399—21no—
345#395—21no—
346#393—21no—
347#391C22×C4311yescharacteristic
348#389—21no—
349#389C22×C4311yescharacteristic
350#389C22×C4311yescharacteristic
351#389C22×C4311yescharacteristic
352#388—21no—
353#388—21no—
354#387—21no—
355#382C22×C4311yescharacteristic
356#380C22×C4311yescharacteristic
357#380C22×C4311yescharacteristic
358#380C22×C4311yescharacteristic
359C4×C4⋊C4C22×C4311yescharacteristic
360#340C22×C4311yescharacteristic
361#340C22×C4311yescharacteristic
362#340C22×C4311yescharacteristic
363#340C22×C4311yescharacteristic
364#340C22×C4311yescharacteristic
365#340C22×C4311yescharacteristic
366#340C22×C4311yescharacteristic
367#340C22×C4311yescharacteristic
368C43#2471411yescharacteristic, direct product factor, Sylow
369C22×Q8—21no—
370C22×Q8C23×C4311yescharacteristic
371C23×C4C23×C4311yescharacteristic
372C22×C8C23×C4311yescharacteristic
373C22×C8C23×C4311yescharacteristic
374C22×C8C23×C4311yescharacteristic
375C22×C8C23×C4311yescharacteristic
376C4⋊Q8—22no—
377C4⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8—22no—
380C4×Q8—22no—
381C4×Q8—22no—
382#117—22no—
383#117—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4D4×C4311yescharacteristic
391C2×C4⋊C4D4×C4311yescharacteristic
392C2×C4⋊C4C23×C4311yescharacteristic
393C2×C4⋊C4C23×C4311yescharacteristic
394C2×C4⋊C4C23×C4311yescharacteristic
395C2×C4⋊C4C23×C4311yescharacteristic
396C2×C4⋊C4C23×C4311yescharacteristic
397C2×C4⋊C4C23×C4311yescharacteristic
398C2×C4⋊C4C23×C4311yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4D4×C4311yescharacteristic
404C2×C22⋊C4D4×C4311yescharacteristic
405C2×C42—21no—
406C2×C42—21no—
407C2×C42C23×C4311yescharacteristic
408C2×C42C23×C4311yescharacteristic
409#107—22no—
410#107—22no—
411#107—22no—
412#106—22no—
413C4⋊C8—22no—
414C4⋊C8D4×C4314yes—
415#103—22no—
416#103—22no—
417#103—22no—
418#103—22no—
419C22⋊C8—22no—
420C22⋊C8—22no—
421#97—22no—
422C4×C8—22no—
423#95—21no—
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—
434C24C2×D4×C4311yescharacteristic
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—42no—
441C2×Q8—81no—
442C2×Q8—81no—
443C2×Q8#41×C4312yes—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4C2×D4×C4311yescharacteristic
459C22×C4C2×D4×C4311yescharacteristic
460C22×C4C2×D4×C4311yescharacteristic
461C22×C4C2×D4×C4311yescharacteristic
462C22×C4C2×D4×C4311yescharacteristic
463C22×C4C24×C4311yescharacteristic
464C2×C8—21no—
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×C8C2×D4×C4312yes—
475C2×C8C2×D4×C4312yes—
476C4⋊C4—24no—
477C4⋊C4—22no—
478C4⋊C4—22no—
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—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—81no—
495C4⋊C4—81no—
496C4⋊C4—81no—
497C4⋊C4#41×C4312yes—
498C22⋊C4—24no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—81no—
502C22⋊C4—81no—
503C22⋊C4—81no—
504C42—21no—
505C42—21no—
506C42—42no—
507C42—81no—
508C42C2×D4×C4312yes—
509C42#41×C4312yes—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23C22×D4×C4311yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522Q8—84no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
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—41no—
564C2×C4#121×C4312yes—
565C2×C4#121×C4312yes—
566C2×C4C22×D4×C4311yescharacteristic
567C2×C4C2×#41×C4311yescharacteristic
568C2×C4C2×#41×C4311yescharacteristic
569C2×C4C2×#41×C4311yescharacteristic
570C2×C42−1+4×C4311yescharacteristic
571C2×C42−1+4×C4311yescharacteristic
572C8—22no—
573C8—22no—
574C8—41no—
575C8—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22C2×#121×C4311yescharacteristic
584C22C43×#52511yescharacteristic
585C22C43×#53611yescharacteristic
586C22C43×#57611yescharacteristic
587C22C43×#57711yescharacteristic
588C22C43×#57811yescharacteristic
589C22C43×#57811yescharacteristic
590C4—22no—
591C4—22no—
592C4—42no—
593C4—41no—
594C4—42no—
595C4—41no—
596C4—41no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4C43×#54711yescharacteristic
604C4C43×#54811yescharacteristic
605C4C43×#55211yescharacteristic
606C4C43×#55611yescharacteristic
607C2—81no—
608C2C43×#241511yescharacteristic
609C2C43×#305911yescharacteristic
610C2C43×#306211yescharacteristic
611C2C43×#312111yescharacteristic
612C2C43×#312411yescharacteristic
613C2C43×#324211yescharacteristic
614C2C43×#324311yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC24×C43C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×#117×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#477C2semidirect
9. C43×#1988C2semidirect
10. C43×#1949C2semidirect
11. C43×#1944C2semidirect
12. C43×#1942C2semidirect
13. C43×#1935C2semidirect
14. C43×#1933C2semidirect
15. C43×#1805C2semidirect
268. #24714C43direct (N × H)
300. C2×#477C2×C43semidirect
308. #1988C2×C43semidirect
309. #1949C2×C43semidirect
310. #1944C2×C43semidirect
311. #1942C2×C43semidirect
312. #1935C2×C43semidirect
313. #1933C2×C43semidirect
314. #1805C2×C43semidirect
368. C43#24714direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4772
C2×C43×#4332
C43×#26282
C43×#23232
C43×#20762
C43×#20752
C43×#20362
C43×#20352
C43×#19882
C43×#19492
C43×#19442
C43×#19422
C43×#19352
C43×#19332
C43×#18052
#2471443