Finite Group Databasebeta

← C43×#28874 #24948891

Subgroups — C43×#28874 #24948891

Order 11008.

722 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2514C211yesmaximal, characteristic, complemented
2C43×#2447C211yesmaximal, characteristic
3C43×#2085C211yesmaximal, characteristic, complemented
4C43×#2067C211yesmaximal, characteristic
5C43×#2056C211yesmaximal, characteristic, complemented
6C43×#2015C211yesmaximal, characteristic
7C43×#1969C211yesmaximal, characteristic, complemented
8C43×#1968C211yesmaximal, characteristic
9C43×#1958C211yesmaximal, characteristic
10C43×#1933C211yesmaximal, characteristic, complemented
11C43×#1933C211yesmaximal, characteristic, complemented
12C43×#1927C211yesmaximal, characteristic, complemented
13C43×#1877C211yesmaximal, characteristic
14C8×C4⋊C4×C43C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic
16C22×Q16×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C2×#124×C43C2211yescharacteristic
19C2×C4×D4×C43C2211yescharacteristic
20C2×#107×C43C2211yescharacteristic
21C2×#106×C43C2211yescharacteristic
22C2×C4⋊C8×C43C2211yescharacteristic
23C2×#103×C43C2211yescharacteristic
24C2×#103×C43C2211yescharacteristic
25C2×#103×C43C2211yescharacteristic
26C2×#103×C43C2211yescharacteristic
27C2×#103×C43C2211yescharacteristic
28C2×#102×C43C2211yescharacteristic
29C2×#102×C43C2211yescharacteristic
30C2×#102×C43C2211yescharacteristic
31C2×C4×C8×C43C2211yescharacteristic
32C2×C4×C8×C43C2211yescharacteristic
33C2×C4×C8×C43C2211yescharacteristic
34C43×#401—21no—
35C43×#400—21no—
36C43×#397—21no—
37C43×#397—21no—
38C43×#391C2211yescharacteristic
39C43×#391C2211yescharacteristic
40C43×#391C2211yescharacteristic
41C43×#391C2211yescharacteristic
42C43×#391C2211yescharacteristic
43C43×#390C2211yescharacteristic
44C43×#389C2211yescharacteristic
45C43×#389C2211yescharacteristic
46C43×#387—21no—
47C43×#385—21no—
48C43×#383—21no—
49C43×#382C2211yescharacteristic
50C43×#381—21no—
51C4×C4⋊C4×C43C2211yescharacteristic
52C4×C4⋊C4×C43C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Q8×C43C2311yescharacteristic
60C22×Q8×C43C2311yescharacteristic
61C22×D4×C43C2311yescharacteristic
62C23×C4×C43—21no—
63C2×Q16×C43—22no—
64C2×Q16×C43—41no—
65C2×Q16×C43—41no—
66C2×SD16×C43—22no—
67C2×SD16×C43—22no—
68C2×SD16×C43—41no—
69C22×C8×C43C2311yescharacteristic
70C22×C8×C43C2311yescharacteristic
71C22×C8×C43C2311yescharacteristic
72C22×C8×C43C2311yescharacteristic
73#124×C43—22no—
74#124×C43—41no—
75C4×D4×C43—22no—
76C4×D4×C43—41no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43D411yescharacteristic
80C2×C4⋊C4×C43D411yescharacteristic
81C2×C4⋊C4×C43C2311yescharacteristic
82C2×C4⋊C4×C43C2311yescharacteristic
83C2×C4⋊C4×C43C2311yescharacteristic
84C2×C4⋊C4×C43C2311yescharacteristic
85C2×C4⋊C4×C43C2311yescharacteristic
86C2×C22⋊C4×C43—21no—
87C2×C22⋊C4×C43—21no—
88C2×C22⋊C4×C43—21no—
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C42×C43—21no—
92C2×C42×C43C2311yescharacteristic
93C2×C42×C43C2311yescharacteristic
94C2×C42×C43C2311yescharacteristic
95#107×C43—41no—
96#106×C43—41no—
97C4⋊C8×C43—22no—
98#103×C43—22no—
99#103×C43—22no—
100#103×C43—22no—
101#103×C43—41no—
102#103×C43—41no—
103#102×C43—22no—
104#102×C43—22no—
105#102×C43—41no—
106C4×C8×C43—22no—
107C4×C8×C43—41no—
108C4×C8×C43—41no—
109#95×C43—21no—
110#95×C43—21no—
111#95×C43—21no—
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×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
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—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43#4112yes—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—42no—
153C22×C4×C43—42no—
154C22×C4×C43—81no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162Q16×C43—44no—
163SD16×C43—44no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43#4112yes—
174C2×C8×C43#4112yes—
175C2×C8×C43#4112yes—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
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—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—42no—
189C4⋊C4×C43—81no—
190C22⋊C4×C43—42no—
191C22⋊C4×C43—42no—
192C22⋊C4×C43—42no—
193C22⋊C4×C43—42no—
194C22⋊C4×C43—81no—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—21no—
201C42×C43—42no—
202C23×C43—22no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43C22×D411yescharacteristic
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218D4×C43—22no—
219D4×C43—22no—
220D4×C43—41no—
221D4×C43—41no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
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—21no—
237C2×C4×C43—21no—
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×C43—84no—
260C2×C4×C43#13512yes—
261C2×C4×C43#13512yes—
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C2×C4×C43H(5,𝔽2)11yescharacteristic
268C8×C43—22no—
269C8×C43—22no—
270C8×C43—22no—
271C8×C43—41no—
272#28874C4311yesmaximal, characteristic, direct product factor, Sylow
273C22×C43—42no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43#53211yescharacteristic
281C22×C43#54611yescharacteristic
282C22×C43#55011yescharacteristic
283C22×C43C2×#13511yescharacteristic
284C22×C43C2×#13511yescharacteristic
285C22×C43#57711yescharacteristic
286C22×C43#57811yescharacteristic
287C4×C43—22no—
288C4×C43—22no—
289C4×C43—41no—
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—81no—
300C4×C43#52911yescharacteristic
301C4×C43#53811yescharacteristic
302C4×C43#55111yescharacteristic
303C4×C43#55311yescharacteristic
304#2514C2×C4311yescharacteristic, complemented
305#2447C2×C4311yescharacteristic
306#2085C2×C4311yescharacteristic, complemented
307#2067C2×C4311yescharacteristic
308#2056C2×C4311yescharacteristic, complemented
309#2015C2×C4311yescharacteristic
310#1969C2×C4311yescharacteristic, complemented
311#1968C2×C4311yescharacteristic
312#1958C2×C4311yescharacteristic
313#1933C2×C4311yescharacteristic, complemented
314#1933C2×C4311yescharacteristic, complemented
315#1927C2×C4311yescharacteristic, complemented
316#1877C2×C4311yescharacteristic
317C8×C4⋊C4C2×C4311yescharacteristic, complemented
318C4×#102C2×C4311yescharacteristic
319C2×C43—82no—
320C2×C43#255411yescharacteristic
321C2×C43#316811yescharacteristic
322C2×C43#317811yescharacteristic
323C2×C43#329611yescharacteristic
324C2×C43#330211yescharacteristic
325C2×C43#339311yescharacteristic
326C2×C43#339411yescharacteristic
327C22×Q16C22×C4311yescharacteristic
328C22×SD16C22×C4311yescharacteristic
329C2×#124C22×C4311yescharacteristic
330C2×C4×D4C22×C4311yescharacteristic
331C2×#107C22×C4311yescharacteristic
332C2×#106C22×C4311yescharacteristic
333C2×C4⋊C8C22×C4311yescharacteristic
334C2×#103C22×C4311yescharacteristic
335C2×#103C22×C4311yescharacteristic
336C2×#103C22×C4311yescharacteristic
337C2×#103C22×C4311yescharacteristic
338C2×#103C22×C4311yescharacteristic
339C2×#102C22×C4311yescharacteristic
340C2×#102C22×C4311yescharacteristic
341C2×#102C22×C4311yescharacteristic
342C2×C4×C8C22×C4311yescharacteristic
343C2×C4×C8C22×C4311yescharacteristic
344C2×C4×C8C22×C4311yescharacteristic
345#401—21no—
346#400—21no—
347#397—21no—
348#397—21no—
349#391C22×C4311yescharacteristic
350#391C22×C4311yescharacteristic
351#391C22×C4311yescharacteristic
352#391C22×C4311yescharacteristic
353#391C22×C4311yescharacteristic
354#390C22×C4311yescharacteristic
355#389C22×C4311yescharacteristic
356#389C22×C4311yescharacteristic
357#387—21no—
358#385—21no—
359#383—21no—
360#382C22×C4311yescharacteristic
361#381—21no—
362C4×C4⋊C4C22×C4311yescharacteristic
363C4×C4⋊C4C22×C4311yescharacteristic
364#340C22×C4311yescharacteristic
365#340C22×C4311yescharacteristic
366#340C22×C4311yescharacteristic
367#340C22×C4311yescharacteristic
368#336C22×C4311yescharacteristic
369#336C22×C4311yescharacteristic
370C43#2887411yescharacteristic, direct product factor, Sylow
371C22×Q8C23×C4311yescharacteristic
372C22×Q8C23×C4311yescharacteristic
373C22×D4C23×C4311yescharacteristic
374C23×C4—21no—
375C2×Q16—22no—
376C2×Q16—41no—
377C2×Q16—41no—
378C2×SD16—22no—
379C2×SD16—22no—
380C2×SD16—41no—
381C22×C8C23×C4311yescharacteristic
382C22×C8C23×C4311yescharacteristic
383C22×C8C23×C4311yescharacteristic
384C22×C8C23×C4311yescharacteristic
385#124—22no—
386#124—41no—
387C4×D4—22no—
388C4×D4—41no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4D4×C4311yescharacteristic
392C2×C4⋊C4D4×C4311yescharacteristic
393C2×C4⋊C4C23×C4311yescharacteristic
394C2×C4⋊C4C23×C4311yescharacteristic
395C2×C4⋊C4C23×C4311yescharacteristic
396C2×C4⋊C4C23×C4311yescharacteristic
397C2×C4⋊C4C23×C4311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C42—21no—
404C2×C42C23×C4311yescharacteristic
405C2×C42C23×C4311yescharacteristic
406C2×C42C23×C4311yescharacteristic
407#107—41no—
408#106—41no—
409C4⋊C8—22no—
410#103—22no—
411#103—22no—
412#103—22no—
413#103—41no—
414#103—41no—
415#102—22no—
416#102—22no—
417#102—41no—
418C4×C8—22no—
419C4×C8—41no—
420C4×C8—41no—
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#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95D4×C4311yescharacteristic
437#95D4×C4311yescharacteristic
438C24—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4#41×C4312yes—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—81no—
467C22×C4C2×D4×C4311yescharacteristic
468C22×C4C2×D4×C4311yescharacteristic
469C22×C4C2×D4×C4311yescharacteristic
470C22×C4C2×D4×C4311yescharacteristic
471C22×C4C2×D4×C4311yescharacteristic
472C22×C4C2×D4×C4311yescharacteristic
473C22×C4C24×C4311yescharacteristic
474Q16—44no—
475SD16—44no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8#41×C4312yes—
486C2×C8#41×C4312yes—
487C2×C8#41×C4312yes—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—42no—
501C4⋊C4—81no—
502C22⋊C4—42no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—42no—
506C22⋊C4—81no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—42no—
514C23—22no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23C22×D4×C4311yescharacteristic
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530D4—22no—
531D4—22no—
532D4—41no—
533D4—41no—
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—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
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×C4—41no—
571C2×C4—84no—
572C2×C4#135×C4312yes—
573C2×C4#135×C4312yes—
574C2×C4C2×#41×C4311yescharacteristic
575C2×C4C2×#41×C4311yescharacteristic
576C2×C4C2×#41×C4311yescharacteristic
577C2×C4C2×#41×C4311yescharacteristic
578C2×C4H(5,𝔽2)×C4311yescharacteristic
579C2×C4H(5,𝔽2)×C4311yescharacteristic
580C8—22no—
581C8—22no—
582C8—22no—
583C8—41no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22C43×#53211yescharacteristic
592C22C43×#54611yescharacteristic
593C22C43×#55011yescharacteristic
594C22C2×#135×C4311yescharacteristic
595C22C2×#135×C4311yescharacteristic
596C22C43×#57711yescharacteristic
597C22C43×#57811yescharacteristic
598C4—22no—
599C4—22no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4—81no—
608C4—81no—
609C4—81no—
610C4—81no—
611C4C43×#52911yescharacteristic
612C4C43×#53811yescharacteristic
613C4C43×#55111yescharacteristic
614C4C43×#55311yescharacteristic
615C2—82no—
616C2C43×#255411yescharacteristic
617C2C43×#316811yescharacteristic
618C2C43×#317811yescharacteristic
619C2C43×#329611yescharacteristic
620C2C43×#330211yescharacteristic
621C2C43×#339311yescharacteristic
622C2C43×#339411yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×D4×C43C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C4⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#2514C2semidirect
3. C43×#2085C2semidirect
5. C43×#2056C2semidirect
7. C43×#1969C2semidirect
10. C43×#1933C2semidirect
11. C43×#1933C2semidirect
12. C43×#1927C2semidirect
14. C8×C4⋊C4×C43C2semidirect
272. #28874C43direct (N × H)
304. #2514C2×C43semidirect
306. #2085C2×C43semidirect
308. #2056C2×C43semidirect
310. #1969C2×C43semidirect
313. #1933C2×C43semidirect
314. #1933C2×C43semidirect
315. #1927C2×C43semidirect
317. C8×C4⋊C4C2×C43semidirect
370. C43#28874direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#25142
C43×#24472
C43×#20852
C43×#20672
C43×#20562
C43×#20152
C43×#19692
C43×#19682
C43×#19582
C43×#19332
C43×#19272
C43×#18772
C8×C4⋊C4×C432
C4×#102×C432
#2887443