Finite Group Databasebeta

← C43×#18313 #24938330

Subgroups — C43×#18313 #24938330

Order 11008.

910 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×#3455C211yesmaximal, characteristic
2C43×#3230C211yesmaximal, characteristic, complemented
3C43×#3227C211yesmaximal, characteristic, complemented
4C43×#2628C211yesmaximal, characteristic, complemented
5C43×#1618C214yesmaximal, complemented
6C43×#1615C214yesmaximal, complemented
7C43×#1518C211yesmaximal, characteristic, complemented
8C43×#1517C211yesmaximal, characteristic, complemented
9C43×#1458C211yesmaximal, characteristic, complemented
10C43×#542—21no—
11C43×#542—21no—
12C43×#541—21no—
13C43×#540—21no—
14C43×#539—21no—
15C43×#539C2212yes—
16C43×#538—21no—
17C43×#538C2212yes—
18C43×#533C2211yescharacteristic
19C43×#532C2211yescharacteristic
20C2×C4⋊Q8×C43C2211yescharacteristic
21C43×#529—22no—
22C43×#529—22no—
23C43×#525—21no—
24C4×#41×C43—21no—
25C2×#117×C43C2211yescharacteristic
26C43×#500—21no—
27C43×#498—21no—
28C43×#487—21no—
29C43×#486—21no—
30C43×#484C2214yes—
31C43×#481C2214yes—
32C43×#477—22no—
33C43×#476—22no—
34C43×#431C2211yescharacteristic
35C43×#431C2211yescharacteristic
36C43×#400C2212yes—
37C43×#399C2212yes—
38C43×#395—21no—
39C43×#393—21no—
40C43×#389—21no—
41C43×#382C2211yescharacteristic
42C43×#380—21no—
43C43×#328C2214yes—
44C43×#327C2214yes—
45C43×#324C2212yes—
46C43×#323C2212yes—
47C2×#41×C43—21no—
48C22×Q8×C43—21no—
49C23×C4×C43D411yescharacteristic
50C4⋊Q8×C43—21no—
51C4⋊Q8×C43—21no—
52C4⋊Q8×C43—21no—
53C4⋊Q8×C43—21no—
54C4⋊Q8×C43D411yescharacteristic
55C4⋊Q8×C43D411yescharacteristic
56C4⋊Q8×C43D411yescharacteristic
57#127×C43D411yescharacteristic
58#126×C43—22no—
59#126×C43—22no—
60#126×C43—22no—
61#126×C43—22no—
62#125×C43—22no—
63#125×C43—22no—
64#125×C43—21no—
65#124×C43—22no—
66#124×C43—22no—
67#124×C43—21no—
68#123×C43—22no—
69#123×C43—22no—
70#123×C43—22no—
71#123×C43—22no—
72#123×C43—22no—
73C22⋊Q8×C43—21no—
74C22⋊Q8×C43—21no—
75C22⋊Q8×C43—22no—
76C22⋊Q8×C43—22no—
77C22⋊Q8×C43—21no—
78C22⋊Q8×C43C2312yes—
79#121×C43—21no—
80#121×C43—21no—
81#121×C43—22no—
82#121×C43—22no—
83#121×C43—21no—
84#121×C43C2312yes—
85#120×C43—22no—
86C4×Q8×C43—21no—
87C4×Q8×C43—21no—
88C4×Q8×C43—21no—
89C4×Q8×C43D412yes—
90C4×D4×C43—21no—
91C4×D4×C43—21no—
92C4×D4×C43—22no—
93C4×D4×C43—22no—
94C4×D4×C43—22no—
95C4×D4×C43—22no—
96C4×D4×C43—21no—
97C4×D4×C43D412yes—
98#117×C43—22no—
99#117×C43—21no—
100#117×C43—21no—
101#117×C43—21no—
102#117×C43—21no—
103#117×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—22no—
107C2×C4⋊C4×C43D411yescharacteristic
108C2×C4⋊C4×C43C2312yes—
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C22⋊C4×C43—22no—
111C2×C22⋊C4×C43D411yescharacteristic
112C2×C22⋊C4×C43C2311yescharacteristic
113C2×C42×C43—22no—
114C2×C42×C43D411yescharacteristic
115C2×C42×C43C2311yescharacteristic
116#107×C43—24no—
117#106×C43—24no—
118C4⋊C8×C43—21no—
119C4⋊C8×C43—21no—
120#103×C43—24no—
121#102×C43—24no—
122C22⋊C8×C43C2312yes—
123C22⋊C8×C43C2312yes—
124C4×C8×C43—21no—
125C4×C8×C43—21no—
126#95×C43—22no—
127#95×C43—21no—
128#95×C43—22no—
129#95×C43C2312yes—
130C24×C43C2×D411yescharacteristic
131#41×C43—42no—
132#41×C43—42no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—41no—
136C2×Q8×C43—41no—
137C2×Q8×C43—82no—
138C2×Q8×C43C2×D412yes—
139C2×D4×C43—22no—
140C2×D4×C43—22no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—22no—
144C2×D4×C43C2×D412yes—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2411yescharacteristic
160C2×C8×C43—22no—
161C2×C8×C43—22no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43—42no—
181C4⋊C4×C43—82no—
182C4⋊C4×C43C2×D412yes—
183C4⋊C4×C43C2×D412yes—
184C22⋊C4×C43—22no—
185C22⋊C4×C43—22no—
186C22⋊C4×C43—22no—
187C22⋊C4×C43—22no—
188C22⋊C4×C43—22no—
189C22⋊C4×C43—22no—
190C22⋊C4×C43—21no—
191C22⋊C4×C43—21no—
192C22⋊C4×C43—22no—
193C22⋊C4×C43—21no—
194C22⋊C4×C43—21no—
195C22⋊C4×C43—22no—
196C22⋊C4×C43—22no—
197C22⋊C4×C43—82no—
198C42×C43—22no—
199C42×C43—22no—
200C42×C43—21no—
201C42×C43—22no—
202C42×C43—21no—
203C42×C43C2×D411yescharacteristic
204C42×C43C2×D411yescharacteristic
205C42×C43C2×D411yescharacteristic
206C42×C43C2×D411yescharacteristic
207C23×C43—21no—
208C23×C43—22no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43C22×D411yescharacteristic
214Q8×C43—42no—
215Q8×C43—42no—
216Q8×C43—81no—
217Q8×C43—82no—
218Q8×C43—82no—
219D4×C43—42no—
220D4×C43—42no—
221D4×C43—42no—
222D4×C43—42no—
223D4×C43—81no—
224D4×C43—82no—
225D4×C43—82no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—44no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—82no—
248C2×C4×C43—82no—
249C2×C4×C43#12011yescharacteristic
250C2×C4×C43#12011yescharacteristic
251C2×C4×C43#12011yescharacteristic
252C2×C4×C43#12011yescharacteristic
253C2×C4×C43#13512yes—
254C2×C4×C43#13712yes—
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C8×C43—42no—
258C8×C43—42no—
259#18313C4311yesmaximal, characteristic, direct product factor, Sylow
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—42no—
263C22×C43—41no—
264C22×C43—42no—
265C22×C43—41no—
266C22×C43—42no—
267C22×C43—41no—
268C22×C43—42no—
269C22×C43—81no—
270C22×C43C2×#12011yescharacteristic
271C22×C43C2×#13511yescharacteristic
272C22×C43C2×#13711yescharacteristic
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—41no—
278C4×C43—42no—
279C4×C43—41no—
280C4×C43—42no—
281C4×C43—41no—
282C4×C43—42no—
283C4×C43—82no—
284C4×C43—82no—
285C4×C43#45212yes—
286C4×C43#45212yes—
287#3455C2×C4311yescharacteristic
288#3230C2×C4311yescharacteristic, complemented
289#3227C2×C4311yescharacteristic, complemented
290#2628C2×C4311yescharacteristic, complemented
291#1618C2×C4314yescomplemented
292#1615C2×C4314yescomplemented
293#1518C2×C4311yescharacteristic, complemented
294#1517C2×C4311yescharacteristic, complemented
295#1458C2×C4311yescharacteristic, complemented
296C2×C43—21no—
297C2×C43—21no—
298C2×C43—82no—
299C2×C43—81no—
300C2×C43C2×#45211yescharacteristic
301C2×C43#302111yescharacteristic
302C2×C43#302811yescharacteristic
303#542—21no—
304#542—21no—
305#541—21no—
306#540—21no—
307#539—21no—
308#539C22×C4312yes—
309#538—21no—
310#538C22×C4312yes—
311#533C22×C4311yescharacteristic
312#532C22×C4311yescharacteristic
313C2×C4⋊Q8C22×C4311yescharacteristic
314#529—22no—
315#529—22no—
316#525—21no—
317C4×#41—21no—
318C2×#117C22×C4311yescharacteristic
319#500—21no—
320#498—21no—
321#487—21no—
322#486—21no—
323#484C22×C4314yes—
324#481C22×C4314yes—
325#477—22no—
326#476—22no—
327#431C22×C4311yescharacteristic
328#431C22×C4311yescharacteristic
329#400C22×C4312yes—
330#399C22×C4312yes—
331#395—21no—
332#393—21no—
333#389—21no—
334#382C22×C4311yescharacteristic
335#380—21no—
336#328C22×C4314yes—
337#327C22×C4314yes—
338#324C22×C4312yes—
339#323C22×C4312yes—
340C43#1831311yescharacteristic, direct product factor, Sylow
341C2×#41—21no—
342C22×Q8—21no—
343C23×C4D4×C4311yescharacteristic
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—21no—
347C4⋊Q8—21no—
348C4⋊Q8D4×C4311yescharacteristic
349C4⋊Q8D4×C4311yescharacteristic
350C4⋊Q8D4×C4311yescharacteristic
351#127D4×C4311yescharacteristic
352#126—22no—
353#126—22no—
354#126—22no—
355#126—22no—
356#125—22no—
357#125—22no—
358#125—21no—
359#124—22no—
360#124—22no—
361#124—21no—
362#123—22no—
363#123—22no—
364#123—22no—
365#123—22no—
366#123—22no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—21no—
372C22⋊Q8C23×C4312yes—
373#121—21no—
374#121—21no—
375#121—22no—
376#121—22no—
377#121—21no—
378#121C23×C4312yes—
379#120—22no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8D4×C4312yes—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—21no—
391C4×D4D4×C4312yes—
392#117—22no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4D4×C4311yescharacteristic
402C2×C4⋊C4C23×C4312yes—
403C2×C4⋊C4C23×C4311yescharacteristic
404C2×C22⋊C4—22no—
405C2×C22⋊C4D4×C4311yescharacteristic
406C2×C22⋊C4C23×C4311yescharacteristic
407C2×C42—22no—
408C2×C42D4×C4311yescharacteristic
409C2×C42C23×C4311yescharacteristic
410#107—24no—
411#106—24no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414#103—24no—
415#102—24no—
416C22⋊C8C23×C4312yes—
417C22⋊C8C23×C4312yes—
418C4×C8—21no—
419C4×C8—21no—
420#95—22no—
421#95—21no—
422#95—22no—
423#95C23×C4312yes—
424C24C2×D4×C4311yescharacteristic
425#41—42no—
426#41—42no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—82no—
432C2×Q8C2×D4×C4312yes—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4C2×D4×C4312yes—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4C2×D4×C4311yescharacteristic
449C22×C4C2×D4×C4311yescharacteristic
450C22×C4C2×D4×C4311yescharacteristic
451C22×C4C2×D4×C4311yescharacteristic
452C22×C4C2×D4×C4311yescharacteristic
453C22×C4C24×C4311yescharacteristic
454C2×C8—22no—
455C2×C8—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—42no—
475C4⋊C4—82no—
476C4⋊C4C2×D4×C4312yes—
477C4⋊C4C2×D4×C4312yes—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—22no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—22no—
491C22⋊C4—82no—
492C42—22no—
493C42—22no—
494C42—21no—
495C42—22no—
496C42—21no—
497C42C2×D4×C4311yescharacteristic
498C42C2×D4×C4311yescharacteristic
499C42C2×D4×C4311yescharacteristic
500C42C2×D4×C4311yescharacteristic
501C23—21no—
502C23—22no—
503C23—21no—
504C23—21no—
505C23—41no—
506C23—41no—
507C23C22×D4×C4311yescharacteristic
508Q8—42no—
509Q8—42no—
510Q8—81no—
511Q8—82no—
512Q8—82no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—81no—
518D4—82no—
519D4—82no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4#120×C4311yescharacteristic
544C2×C4#120×C4311yescharacteristic
545C2×C4#120×C4311yescharacteristic
546C2×C4#120×C4311yescharacteristic
547C2×C4#135×C4312yes—
548C2×C4#137×C4312yes—
549C2×C4C22×D4×C4311yescharacteristic
550C2×C4C22×D4×C4311yescharacteristic
551C8—42no—
552C8—42no—
553C22—21no—
554C22—21no—
555C22—42no—
556C22—41no—
557C22—42no—
558C22—42no—
559C22—41no—
560C22—42no—
561C22—41no—
562C22—81no—
563C22C2×#120×C4311yescharacteristic
564C22C2×#135×C4311yescharacteristic
565C22C2×#137×C4311yescharacteristic
566C4—21no—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—41no—
571C4—42no—
572C4—41no—
573C4—42no—
574C4—41no—
575C4—42no—
576C4—82no—
577C4—82no—
578C4C43×#45212yes—
579C4C43×#45212yes—
580C2—21no—
581C2—21no—
582C2—81no—
583C2—82no—
584C2C2×C43×#45211yescharacteristic
585C2C43×#302111yescharacteristic
586C2C43×#302811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#3455C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#3230C2semidirect
3. C43×#3227C2semidirect
4. C43×#2628C2semidirect
5. C43×#1618C2semidirect
6. C43×#1615C2semidirect
7. C43×#1518C2semidirect
8. C43×#1517C2semidirect
9. C43×#1458C2semidirect
259. #18313C43direct (N × H)
288. #3230C2×C43semidirect
289. #3227C2×C43semidirect
290. #2628C2×C43semidirect
291. #1618C2×C43semidirect
292. #1615C2×C43semidirect
293. #1518C2×C43semidirect
294. #1517C2×C43semidirect
295. #1458C2×C43semidirect
340. C43#18313direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#34552
C43×#32302
C43×#32272
C43×#26282
C43×#16182
C43×#16152
C43×#15182
C43×#15172
C43×#14582
#1831343