Finite Group Databasebeta

← C43×#28668 #24948685

Subgroups — C43×#28668 #24948685

Order 11008.

732 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#501C211yesmaximal, characteristic, complemented
2C2×C43×#488C211yesmaximal, characteristic
3C43×#2640C211yesmaximal, characteristic
4C43×#2330C211yesmaximal, characteristic, complemented
5C43×#2068C211yesmaximal, characteristic, complemented
6C43×#2067C211yesmaximal, characteristic
7C43×#2066C211yesmaximal, characteristic, complemented
8C43×#2065C211yesmaximal, characteristic
9C43×#1990C211yesmaximal, characteristic, complemented
10C43×#1959C211yesmaximal, characteristic
11C43×#1928C211yesmaximal, characteristic, complemented
12C43×#1927C211yesmaximal, characteristic, complemented
13C43×#1926C211yesmaximal, characteristic
14C43×#1925C211yesmaximal, characteristic
15C43×#1768C211yesmaximal, characteristic, complemented
16C2×C4⋊Q8×C43C2211yescharacteristic
17C2×#125×C43C2211yescharacteristic
18C2×#124×C43C2211yescharacteristic
19C43×#501—24no—
20C43×#488—24no—
21C2×#107×C43C2211yescharacteristic
22C2×#107×C43C2211yescharacteristic
23C2×#106×C43C2211yescharacteristic
24C2×#106×C43C2211yescharacteristic
25C2×C4⋊C8×C43C2211yescharacteristic
26C2×C4⋊C8×C43C2211yescharacteristic
27C2×#103×C43C2211yescharacteristic
28C2×#103×C43C2211yescharacteristic
29C2×#103×C43C2211yescharacteristic
30C2×#103×C43C2211yescharacteristic
31C2×#102×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#97×C43C2211yescharacteristic
36C2×C4×C8×C43C2211yescharacteristic
37C43×#397—21no—
38C43×#397—21no—
39C43×#393—21no—
40C43×#393—21no—
41C43×#391C2211yescharacteristic
42C43×#391C2211yescharacteristic
43C43×#390C2211yescharacteristic
44C43×#390C2211yescharacteristic
45C43×#389—21no—
46C43×#389—21no—
47C43×#389C2211yescharacteristic
48C43×#389C2211yescharacteristic
49C43×#387—21no—
50C43×#387—21no—
51C43×#384C2211yescharacteristic
52C4×C4⋊C4×C43C2211yescharacteristic
53C4×C4⋊C4×C43C2211yescharacteristic
54C43×#376C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Q8×C43—21no—
62C22×Q8×C43C2311yescharacteristic
63C22×D4×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65C22×C8×C43C2311yescharacteristic
66C22×C8×C43C2311yescharacteristic
67C22×C8×C43C2311yescharacteristic
68C4⋊Q8×C43—22no—
69C4⋊Q8×C43—22no—
70#125×C43—22no—
71#125×C43D414yes—
72#124×C43—22no—
73#124×C43—22no—
74C2×C4⋊C4×C43—21no—
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×C22⋊C4×C43—21no—
93C2×C42×C43—21no—
94C2×C42×C43—21no—
95C2×C42×C43C2311yescharacteristic
96C2×C42×C43C2311yescharacteristic
97C2×C42×C43C2311yescharacteristic
98#107×C43—22no—
99#107×C43—22no—
100#106×C43—22no—
101#106×C43—22no—
102C4⋊C8×C43—22no—
103C4⋊C8×C43—22no—
104#103×C43—22no—
105#103×C43—22no—
106#103×C43—22no—
107#103×C43—22no—
108#102×C43—22no—
109#102×C43—22no—
110#102×C43—22no—
111#102×C43—22no—
112#97×C43—22no—
113C4×C8×C43—22no—
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×C43D411yescharacteristic
123#95×C43D411yescharacteristic
124#95×C43D411yescharacteristic
125#95×C43D411yescharacteristic
126C24×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—42no—
134C2×Q8×C43—81no—
135C2×Q8×C43—81no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×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×C43C2×D411yescharacteristic
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×C43#4112yes—
167C2×C8×C43#4112yes—
168C4⋊C4×C43—24no—
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×C43C2×D412yes—
186C4⋊C4×C43C2×D412yes—
187C22⋊C4×C43—42no—
188C22⋊C4×C43—42no—
189C22⋊C4×C43—81no—
190C22⋊C4×C43—81no—
191C22⋊C4×C43—81no—
192C22⋊C4×C43—81no—
193C42×C43—21no—
194C42×C43—21no—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43—81no—
198C42×C43—81no—
199C42×C43C2×D412yes—
200C42×C43#4112yes—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43C22×D411yescharacteristic
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—84no—
214D4×C43—41no—
215D4×C43—41no—
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—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—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
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#12112yes—
256C2×C4×C43#12112yes—
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C432−1+411yescharacteristic
262C2×C4×C432−1+411yescharacteristic
263C8×C43—22no—
264C8×C43—22no—
265C8×C43—41no—
266C8×C43—41no—
267#28668C4311yesmaximal, characteristic, direct product factor, Sylow
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43C2×#12111yescharacteristic
276C22×C43#53211yescharacteristic
277C22×C43#53611yescharacteristic
278C22×C43#57611yescharacteristic
279C22×C43#57711yescharacteristic
280C22×C43#57711yescharacteristic
281C22×C43#57811yescharacteristic
282C4×C43—22no—
283C4×C43—22no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43—42no—
289C4×C43—42no—
290C4×C43—81no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43—81no—
295C4×C43#54811yescharacteristic
296C4×C43#54811yescharacteristic
297C4×C43#55611yescharacteristic
298C4×C43#55611yescharacteristic
299C2×#501C2×C4311yescharacteristic, complemented
300C2×#488C2×C4311yescharacteristic
301#2640C2×C4311yescharacteristic
302#2330C2×C4311yescharacteristic, complemented
303#2068C2×C4311yescharacteristic, complemented
304#2067C2×C4311yescharacteristic
305#2066C2×C4311yescharacteristic, complemented
306#2065C2×C4311yescharacteristic
307#1990C2×C4311yescharacteristic, complemented
308#1959C2×C4311yescharacteristic
309#1928C2×C4311yescharacteristic, complemented
310#1927C2×C4311yescharacteristic, complemented
311#1926C2×C4311yescharacteristic
312#1925C2×C4311yescharacteristic
313#1768C2×C4311yescharacteristic, complemented
314C2×C43—161no—
315C2×C43#254511yescharacteristic
316C2×C43#304511yescharacteristic
317C2×C43#304611yescharacteristic
318C2×C43#317811yescharacteristic
319C2×C43#317911yescharacteristic
320C2×C43#324311yescharacteristic
321C2×C43#324411yescharacteristic
322C2×C4⋊Q8C22×C4311yescharacteristic
323C2×#125C22×C4311yescharacteristic
324C2×#124C22×C4311yescharacteristic
325#501—24no—
326#488—24no—
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
341C2×#97C22×C4311yescharacteristic
342C2×C4×C8C22×C4311yescharacteristic
343#397—21no—
344#397—21no—
345#393—21no—
346#393—21no—
347#391C22×C4311yescharacteristic
348#391C22×C4311yescharacteristic
349#390C22×C4311yescharacteristic
350#390C22×C4311yescharacteristic
351#389—21no—
352#389—21no—
353#389C22×C4311yescharacteristic
354#389C22×C4311yescharacteristic
355#387—21no—
356#387—21no—
357#384C22×C4311yescharacteristic
358C4×C4⋊C4C22×C4311yescharacteristic
359C4×C4⋊C4C22×C4311yescharacteristic
360#376C22×C4311yescharacteristic
361#340C22×C4311yescharacteristic
362#340C22×C4311yescharacteristic
363#340C22×C4311yescharacteristic
364#340C22×C4311yescharacteristic
365#336C22×C4311yescharacteristic
366#336C22×C4311yescharacteristic
367C43#2866811yescharacteristic, direct product factor, Sylow
368C22×Q8—21no—
369C22×Q8C23×C4311yescharacteristic
370C22×D4C23×C4311yescharacteristic
371C22×C8C23×C4311yescharacteristic
372C22×C8C23×C4311yescharacteristic
373C22×C8C23×C4311yescharacteristic
374C22×C8C23×C4311yescharacteristic
375C4⋊Q8—22no—
376C4⋊Q8—22no—
377#125—22no—
378#125D4×C4314yes—
379#124—22no—
380#124—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4C23×C4311yescharacteristic
389C2×C4⋊C4C23×C4311yescharacteristic
390C2×C4⋊C4C23×C4311yescharacteristic
391C2×C4⋊C4C23×C4311yescharacteristic
392C2×C4⋊C4C23×C4311yescharacteristic
393C2×C4⋊C4C23×C4311yescharacteristic
394C2×C22⋊C4—21no—
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×C42C23×C4311yescharacteristic
403C2×C42C23×C4311yescharacteristic
404C2×C42C23×C4311yescharacteristic
405#107—22no—
406#107—22no—
407#106—22no—
408#106—22no—
409C4⋊C8—22no—
410C4⋊C8—22no—
411#103—22no—
412#103—22no—
413#103—22no—
414#103—22no—
415#102—22no—
416#102—22no—
417#102—22no—
418#102—22no—
419#97—22no—
420C4×C8—22no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95D4×C4311yescharacteristic
430#95D4×C4311yescharacteristic
431#95D4×C4311yescharacteristic
432#95D4×C4311yescharacteristic
433C24—21no—
434C2×Q8—21no—
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×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4C2×D4×C4311yescharacteristic
457C22×C4C2×D4×C4311yescharacteristic
458C22×C4C2×D4×C4311yescharacteristic
459C22×C4C2×D4×C4311yescharacteristic
460C22×C4C2×D4×C4311yescharacteristic
461C22×C4C2×D4×C4311yescharacteristic
462C22×C4C24×C4311yescharacteristic
463C2×C8—21no—
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#41×C4312yes—
474C2×C8#41×C4312yes—
475C4⋊C4—24no—
476C4⋊C4—24no—
477C4⋊C4—21no—
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—42no—
488C4⋊C4—81no—
489C4⋊C4—81no—
490C4⋊C4—81no—
491C4⋊C4—81no—
492C4⋊C4C2×D4×C4312yes—
493C4⋊C4C2×D4×C4312yes—
494C22⋊C4—42no—
495C22⋊C4—42no—
496C22⋊C4—81no—
497C22⋊C4—81no—
498C22⋊C4—81no—
499C22⋊C4—81no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—81no—
505C42—81no—
506C42C2×D4×C4312yes—
507C42#41×C4312yes—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23C22×D4×C4311yescharacteristic
516Q8—41no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—84no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
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—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#121×C4312yes—
563C2×C4#121×C4312yes—
564C2×C4C22×D4×C4311yescharacteristic
565C2×C4C2×#41×C4311yescharacteristic
566C2×C4C2×#41×C4311yescharacteristic
567C2×C4C2×#41×C4311yescharacteristic
568C2×C42−1+4×C4311yescharacteristic
569C2×C42−1+4×C4311yescharacteristic
570C8—22no—
571C8—22no—
572C8—41no—
573C8—41no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22C2×#121×C4311yescharacteristic
582C22C43×#53211yescharacteristic
583C22C43×#53611yescharacteristic
584C22C43×#57611yescharacteristic
585C22C43×#57711yescharacteristic
586C22C43×#57711yescharacteristic
587C22C43×#57811yescharacteristic
588C4—22no—
589C4—22no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—42no—
595C4—42no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4—81no—
601C4C43×#54811yescharacteristic
602C4C43×#54811yescharacteristic
603C4C43×#55611yescharacteristic
604C4C43×#55611yescharacteristic
605C2—161no—
606C2C43×#254511yescharacteristic
607C2C43×#304511yescharacteristic
608C2C43×#304611yescharacteristic
609C2C43×#317811yescharacteristic
610C2C43×#317911yescharacteristic
611C2C43×#324311yescharacteristic
612C2C43×#324411yescharacteristic
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. C2×C43×#501C2semidirect
4. C43×#2330C2semidirect
5. C43×#2068C2semidirect
7. C43×#2066C2semidirect
9. C43×#1990C2semidirect
11. C43×#1928C2semidirect
12. C43×#1927C2semidirect
15. C43×#1768C2semidirect
267. #28668C43direct (N × H)
299. C2×#501C2×C43semidirect
302. #2330C2×C43semidirect
303. #2068C2×C43semidirect
305. #2066C2×C43semidirect
307. #1990C2×C43semidirect
309. #1928C2×C43semidirect
310. #1927C2×C43semidirect
313. #1768C2×C43semidirect
367. C43#28668direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5012
C2×C43×#4882
C43×#26402
C43×#23302
C43×#20682
C43×#20672
C43×#20662
C43×#20652
C43×#19902
C43×#19592
C43×#19282
C43×#19272
C43×#19262
C43×#19252
C43×#17682
#2866843