Finite Group Databasebeta

← C43×#25697 #24945714

Subgroups — C43×#25697 #24945714

Order 11008.

1030 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3506C211yesmaximal, characteristic
2C43×#3166C211yesmaximal, characteristic, complemented
3C43×#3142C211yesmaximal, characteristic, complemented
4C43×#2566C211yesmaximal, characteristic, complemented
5C43×#2037C212yesmaximal, complemented
6C43×#2037C212yesmaximal, complemented
7C43×#1986C211yesmaximal, characteristic, complemented
8C43×#1980C211yesmaximal, characteristic, complemented
9C43×#1860C212yesmaximal, complemented
10C43×#1859C212yesmaximal, complemented
11C4×#100×C43C211yesmaximal, characteristic, complemented
12C43×#559—22no—
13C43×#556—21no—
14C43×#555—21no—
15C43×#553—22no—
16C43×#550—21no—
17C43×#547—21no—
18C43×#538—22no—
19C43×#535C2212yes—
20C43×#533C2211yescharacteristic
21C43×#532C2211yescharacteristic
22C2×#125×C43C2211yescharacteristic
23C43×#525—22no—
24C43×#520C2212yes—
25C2×C4×D4×C43C2211yescharacteristic
26C43×#501—21no—
27C43×#501—21no—
28C43×#499—22no—
29C43×#491—21no—
30C43×#490—21no—
31C43×#488—22no—
32C43×#428C2212yes—
33C43×#428C2212yes—
34C2×#104×C43C2212yes—
35C2×#104×C43C2212yes—
36C43×#417C2212yes—
37C43×#417C2212yes—
38C2×#100×C43C2212yes—
39C4×M16×C43C2211yescharacteristic
40C4×M16×C43C2211yescharacteristic
41C43×#396—22no—
42C43×#390C2211yescharacteristic
43C43×#390C2211yescharacteristic
44C43×#385—22no—
45C43×#384C2211yescharacteristic
46C43×#382C2211yescharacteristic
47C4×C4⋊C4×C43C2211yescharacteristic
48C43×#343C2212yes—
49C43×#339C2212yes—
50C43×#339C2212yes—
51C2×#41×C43—22no—
52C2×#41×C43C2312yes—
53C22×D4×C43C2311yescharacteristic
54C23×C4×C43D412yes—
55C2×M16×C43C2312yes—
56C2×M16×C43C2312yes—
57C4⋊Q8×C43D411yescharacteristic
58C4⋊Q8×C43D411yescharacteristic
59C4⋊Q8×C43D411yescharacteristic
60#127×C43—22no—
61#127×C43D411yescharacteristic
62#126×C43—24no—
63#125×C43—21no—
64#125×C43—21no—
65#125×C43—21no—
66#125×C43—21no—
67#125×C43D412yes—
68#124×C43—24no—
69#124×C43—22no—
70#124×C43D412yes—
71#123×C43—24no—
72#123×C43—24no—
73C22⋊Q8×C43—22no—
74C22⋊Q8×C43—21no—
75C22⋊Q8×C43—21no—
76#121×C43—22no—
77#121×C43—24no—
78#121×C43—21no—
79#121×C43—21no—
80#121×C43—22no—
81#121×C43—22no—
82#120×C43—24no—
83C4×Q8×C43—22no—
84C4×Q8×C43—21no—
85C4×Q8×C43—21no—
86C4×D4×C43—24no—
87C4×D4×C43—22no—
88C4×D4×C43—24no—
89C4×D4×C43—21no—
90C4×D4×C43—21no—
91C4×D4×C43—21no—
92C4×D4×C43—21no—
93C4×D4×C43—21no—
94C4×D4×C43—21no—
95#117×C43—22no—
96#117×C43—22no—
97#117×C43C2312yes—
98C2×C4⋊C4×C43—22no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—22no—
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C22⋊C4×C43—22no—
107C2×C22⋊C4×C43—22no—
108C2×C22⋊C4×C43D412yes—
109C2×C42×C43C2311yescharacteristic
110C2×C42×C43C2311yescharacteristic
111C2×C42×C43C2311yescharacteristic
112#107×C43—22no—
113#107×C43—22no—
114#106×C43—22no—
115#106×C43—22no—
116#104×C43—24no—
117#104×C43—24no—
118#103×C43—22no—
119#103×C43—22no—
120#102×C43—22no—
121#102×C43—22no—
122#100×C43—24no—
123#97×C43—21no—
124#97×C43—21no—
125C4×C8×C43—21no—
126C4×C8×C43—21no—
127#95×C43—21no—
128#95×C43—22no—
129C24×C43C2×D412yes—
130#41×C43—22no—
131#41×C43—22no—
132#41×C43—22no—
133#41×C43—22no—
134#41×C43—84no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43C2×D412yes—
138C2×D4×C43—24no—
139C2×D4×C43—24no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—22no—
145C2×D4×C43—22no—
146C2×D4×C43—22no—
147C2×D4×C43C2×D412yes—
148C22×C4×C43—24no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—82no—
157C22×C4×C43C2×D412yes—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2411yescharacteristic
161M16×C43—22no—
162M16×C43—22no—
163M16×C43—22no—
164M16×C43#4114yescomplemented
165C2×C8×C43—22no—
166C2×C8×C43—22no—
167C4⋊C4×C43—24no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—22no—
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—41no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43—41no—
185C4⋊C4×C43—82no—
186C4⋊C4×C43C2×D412yes—
187C4⋊C4×C43C2×D412yes—
188C22⋊C4×C43—24no—
189C22⋊C4×C43—24no—
190C22⋊C4×C43—24no—
191C22⋊C4×C43—22no—
192C22⋊C4×C43—22no—
193C22⋊C4×C43—22no—
194C22⋊C4×C43—22no—
195C22⋊C4×C43—22no—
196C22⋊C4×C43—44no—
197C22⋊C4×C43—82no—
198C42×C43—24no—
199C42×C43—22no—
200C42×C43—22no—
201C42×C43—22no—
202C42×C43C2×D411yescharacteristic
203C42×C43C2×D411yescharacteristic
204C42×C43C2×D411yescharacteristic
205C42×C43C2×D411yescharacteristic
206C23×C43—22no—
207C23×C43—22no—
208C23×C43—22no—
209C23×C43—22no—
210C23×C43—42no—
211C23×C43—42no—
212C23×C43C22×D411yescharacteristic
213Q8×C43—22no—
214Q8×C43—22no—
215Q8×C43—42no—
216Q8×C43—81no—
217D4×C43—22no—
218D4×C43—22no—
219D4×C43—42no—
220D4×C43—42no—
221D4×C43—42no—
222D4×C43—42no—
223D4×C43—42no—
224D4×C43—81no—
225D4×C43—84no—
226D4×C43—84no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—44no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—41no—
242C2×C4×C43—42no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—82no—
248C2×C4×C43—84no—
249C2×C4×C43#12011yescharacteristic
250C2×C4×C43#12011yescharacteristic
251C2×C4×C43#12011yescharacteristic
252C2×C4×C43#12011yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C2×#4112yes—
256C2×C4×C432−1+412yes—
257C8×C43—24no—
258C8×C43—42no—
259#25697C4311yesmaximal, characteristic, direct product factor, Sylow
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—44no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—42no—
266C22×C43—42no—
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—82no—
270C22×C43C2×#12011yescharacteristic
271C22×C43#53211yescharacteristic
272C22×C43#53611yescharacteristic
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—42no—
278C4×C43—42no—
279C4×C43—42no—
280C4×C43—42no—
281C4×C43—42no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43#54712yes—
286C4×C43#54812yes—
287#3506C2×C4311yescharacteristic
288#3166C2×C4311yescharacteristic, complemented
289#3142C2×C4311yescharacteristic, complemented
290#2566C2×C4311yescharacteristic, complemented
291#2037C2×C4312yescomplemented
292#2037C2×C4312yescomplemented
293#1986C2×C4311yescharacteristic, complemented
294#1980C2×C4311yescharacteristic, complemented
295#1860C2×C4312yescomplemented
296#1859C2×C4312yescomplemented
297C4×#100C2×C4311yescharacteristic, complemented
298C2×C43—21no—
299C2×C43—21no—
300C2×C43—82no—
301C2×C43—82no—
302C2×C43#243211yescharacteristic
303C2×C43#301811yescharacteristic
304C2×C43#301911yescharacteristic
305#559—22no—
306#556—21no—
307#555—21no—
308#553—22no—
309#550—21no—
310#547—21no—
311#538—22no—
312#535C22×C4312yes—
313#533C22×C4311yescharacteristic
314#532C22×C4311yescharacteristic
315C2×#125C22×C4311yescharacteristic
316#525—22no—
317#520C22×C4312yes—
318C2×C4×D4C22×C4311yescharacteristic
319#501—21no—
320#501—21no—
321#499—22no—
322#491—21no—
323#490—21no—
324#488—22no—
325#428C22×C4312yes—
326#428C22×C4312yes—
327C2×#104C22×C4312yes—
328C2×#104C22×C4312yes—
329#417C22×C4312yes—
330#417C22×C4312yes—
331C2×#100C22×C4312yes—
332C4×M16C22×C4311yescharacteristic
333C4×M16C22×C4311yescharacteristic
334#396—22no—
335#390C22×C4311yescharacteristic
336#390C22×C4311yescharacteristic
337#385—22no—
338#384C22×C4311yescharacteristic
339#382C22×C4311yescharacteristic
340C4×C4⋊C4C22×C4311yescharacteristic
341#343C22×C4312yes—
342#339C22×C4312yes—
343#339C22×C4312yes—
344C43#2569711yescharacteristic, direct product factor, Sylow
345C2×#41—22no—
346C2×#41C23×C4312yes—
347C22×D4C23×C4311yescharacteristic
348C23×C4D4×C4312yes—
349C2×M16C23×C4312yes—
350C2×M16C23×C4312yes—
351C4⋊Q8D4×C4311yescharacteristic
352C4⋊Q8D4×C4311yescharacteristic
353C4⋊Q8D4×C4311yescharacteristic
354#127—22no—
355#127D4×C4311yescharacteristic
356#126—24no—
357#125—21no—
358#125—21no—
359#125—21no—
360#125—21no—
361#125D4×C4312yes—
362#124—24no—
363#124—22no—
364#124D4×C4312yes—
365#123—24no—
366#123—24no—
367C22⋊Q8—22no—
368C22⋊Q8—21no—
369C22⋊Q8—21no—
370#121—22no—
371#121—24no—
372#121—21no—
373#121—21no—
374#121—22no—
375#121—22no—
376#120—24no—
377C4×Q8—22no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×D4—24no—
381C4×D4—22no—
382C4×D4—24no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389#117—22no—
390#117—22no—
391#117C23×C4312yes—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4C23×C4311yescharacteristic
398C2×C4⋊C4C23×C4311yescharacteristic
399C2×C4⋊C4C23×C4311yescharacteristic
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4D4×C4312yes—
403C2×C42C23×C4311yescharacteristic
404C2×C42C23×C4311yescharacteristic
405C2×C42C23×C4311yescharacteristic
406#107—22no—
407#107—22no—
408#106—22no—
409#106—22no—
410#104—24no—
411#104—24no—
412#103—22no—
413#103—22no—
414#102—22no—
415#102—22no—
416#100—24no—
417#97—21no—
418#97—21no—
419C4×C8—21no—
420C4×C8—21no—
421#95—21no—
422#95—22no—
423C24C2×D4×C4312yes—
424#41—22no—
425#41—22no—
426#41—22no—
427#41—22no—
428#41—84no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8C2×D4×C4312yes—
432C2×D4—22no—
433C2×D4—24no—
434C2×D4—24no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4C2×D4×C4312yes—
442C22×C4—21no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—82no—
451C22×C4C2×D4×C4312yes—
452C22×C4C2×D4×C4311yescharacteristic
453C22×C4C2×D4×C4311yescharacteristic
454C22×C4C24×C4311yescharacteristic
455M16—22no—
456M16—22no—
457M16—22no—
458M16#41×C4314yescomplemented
459C2×C8—22no—
460C2×C8—22no—
461C4⋊C4—24no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—22no—
465C4⋊C4—21no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—42no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—82no—
480C4⋊C4C2×D4×C4312yes—
481C4⋊C4C2×D4×C4312yes—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—44no—
491C22⋊C4—82no—
492C42—24no—
493C42—22no—
494C42—22no—
495C42—22no—
496C42C2×D4×C4311yescharacteristic
497C42C2×D4×C4311yescharacteristic
498C42C2×D4×C4311yescharacteristic
499C42C2×D4×C4311yescharacteristic
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—42no—
505C23—42no—
506C23C22×D4×C4311yescharacteristic
507Q8—22no—
508Q8—22no—
509Q8—42no—
510Q8—81no—
511D4—22no—
512D4—22no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—42no—
518D4—81no—
519D4—84no—
520D4—84no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—44no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—84no—
543C2×C4#120×C4311yescharacteristic
544C2×C4#120×C4311yescharacteristic
545C2×C4#120×C4311yescharacteristic
546C2×C4#120×C4311yescharacteristic
547C2×C4C22×D4×C4311yescharacteristic
548C2×C4C22×D4×C4311yescharacteristic
549C2×C4C2×#41×C4312yes—
550C2×C42−1+4×C4312yes—
551C8—24no—
552C8—42no—
553C22—21no—
554C22—21no—
555C22—44no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—82no—
563C22C2×#120×C4311yescharacteristic
564C22C43×#53211yescharacteristic
565C22C43×#53611yescharacteristic
566C4—21no—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—42no—
571C4—42no—
572C4—42no—
573C4—42no—
574C4—42no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4C43×#54712yes—
579C4C43×#54812yes—
580C2—21no—
581C2—21no—
582C2—82no—
583C2—82no—
584C2C43×#243211yescharacteristic
585C2C43×#301811yescharacteristic
586C2C43×#301911yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#3506C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#3166C2semidirect
3. C43×#3142C2semidirect
4. C43×#2566C2semidirect
5. C43×#2037C2semidirect
6. C43×#2037C2semidirect
7. C43×#1986C2semidirect
8. C43×#1980C2semidirect
9. C43×#1860C2semidirect
10. C43×#1859C2semidirect
11. C4×#100×C43C2semidirect
164. M16×C43#41semidirect
259. #25697C43direct (N × H)
288. #3166C2×C43semidirect
289. #3142C2×C43semidirect
290. #2566C2×C43semidirect
291. #2037C2×C43semidirect
292. #2037C2×C43semidirect
293. #1986C2×C43semidirect
294. #1980C2×C43semidirect
295. #1860C2×C43semidirect
296. #1859C2×C43semidirect
297. C4×#100C2×C43semidirect
344. C43#25697direct (N × H)
458. M16#41×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#35062
C43×#31662
C43×#31422
C43×#25662
C43×#20372
C43×#19862
C43×#19802
C43×#18602
C43×#18592
C4×#100×C432
#2569743