Finite Group Databasebeta

← C43×#19913 #24939930

Subgroups — C43×#19913 #24939930

Order 11008.

618 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×#3372C211yesmaximal, characteristic, complemented
2C43×#3364C211yesmaximal, characteristic, complemented
3C43×#3324C211yesmaximal, characteristic
4C43×#3295C211yesmaximal, characteristic
5C43×#1711C211yesmaximal, characteristic, complemented
6C43×#1703C211yesmaximal, characteristic, complemented
7C43×#1702C211yesmaximal, characteristic, complemented
8C43×#1679C211yesmaximal, characteristic, complemented
9C43×#1678C211yesmaximal, characteristic, complemented
10C43×#1644C211yesmaximal, characteristic, complemented
11C43×#1639C211yesmaximal, characteristic
12C43×#1638C211yesmaximal, characteristic, complemented
13C43×#1626C211yesmaximal, characteristic, complemented
14C43×#1590C211yesmaximal, characteristic, complemented
15C8×SD16×C43C211yesmaximal, characteristic, complemented
16C43×#557C2211yescharacteristic, complemented
17C43×#556C2211yescharacteristic
18C43×#554C2211yescharacteristic
19D42×C43C2211yescharacteristic
20C43×#491—21no—
21C43×#488—21no—
22C43×#487C2211yescharacteristic, complemented
23C43×#487C2211yescharacteristic, complemented
24C43×#487C2211yescharacteristic, complemented
25C43×#486C2211yescharacteristic
26C43×#486C2211yescharacteristic
27C43×#486C2211yescharacteristic
28C43×#482—21no—
29C43×#481—21no—
30C43×#479—21no—
31C43×#479—21no—
32C43×#477C2211yescharacteristic, complemented
33C43×#476C2211yescharacteristic
34C43×#474C2211yescharacteristic
35C43×#474C2211yescharacteristic
36C43×#468—21no—
37C43×#465—21no—
38C43×#464—21no—
39C43×#462C2211yescharacteristic, complemented
40C43×#461—21no—
41C43×#461C2211yescharacteristic
42C43×#460C2211yescharacteristic
43C43×#460C2211yescharacteristic
44C43×#450—21no—
45C43×#450—21no—
46C43×#446C2211yescharacteristic, complemented
47C8×Q8×C43C2211yescharacteristic, complemented
48C43×#440—21no—
49C4×Q16×C43—21no—
50C4×SD16×C43C2211yescharacteristic
51C4×SD16×C43C2211yescharacteristic
52C43×#436C2211yescharacteristic
53C8×D4×C43C2211yescharacteristic
54C43×#418—21no—
55C2×#102×C43—21no—
56C43×#334C2211yescharacteristic, complemented
57C43×#334C2211yescharacteristic, complemented
58C43×#333C2211yescharacteristic, complemented
59C43×#332C2211yescharacteristic, complemented
60C43×#332C2211yescharacteristic, complemented
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic, complemented
63C43×Q8⋊C8C2211yescharacteristic, complemented
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic, complemented
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C2×Q16×C43—21no—
70C2×SD16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43D411yescharacteristic
74C2×SD16×C43D411yescharacteristic
75C2×M16×C43—21no—
76C22×C8×C43—21no—
77C4⋊Q8×C43—21no—
78C4⋊Q8×C43C2311yescharacteristic
79C4⋊Q8×C43C2311yescharacteristic
80C4⋊Q8×C43C2311yescharacteristic
81#127×C43C2311yescharacteristic
82#126×C43—41no—
83#125×C43—21no—
84#125×C43—21no—
85#125×C43—41no—
86#124×C43—21no—
87C22⋊Q8×C43—21no—
88C22⋊Q8×C43—21no—
89C22⋊Q8×C43—41no—
90#121×C43—21no—
91#121×C43—21no—
92#120×C43—41no—
93C4×Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43—21no—
96C4×Q8×C43C2311yescharacteristic
97C4×Q8×C43C2311yescharacteristic
98C4×D4×C43—21no—
99C4×D4×C43C2311yescharacteristic
100C4×D4×C43C2311yescharacteristic
101#117×C43—21no—
102C2×C4⋊C4×C43—21no—
103#107×C43—21no—
104#107×C43—21no—
105#107×C43—21no—
106#106×C43—21no—
107#106×C43D411yescharacteristic
108#106×C43D411yescharacteristic
109C4⋊C8×C43—21no—
110C4⋊C8×C43—21no—
111C4⋊C8×C43C2311yescharacteristic
112C4⋊C8×C43C2311yescharacteristic
113C4⋊C8×C43C2311yescharacteristic
114C4⋊C8×C43C2311yescharacteristic
115#103×C43—21no—
116#103×C43—21no—
117#103×C43—21no—
118#103×C43—21no—
119#103×C43—21no—
120#103×C43—21no—
121#103×C43—21no—
122#103×C43—41no—
123#103×C43D411yescharacteristic
124#103×C43D411yescharacteristic
125#102×C43—21no—
126#102×C43—21no—
127#102×C43—21no—
128#102×C43—21no—
129#102×C43—21no—
130#102×C43—21no—
131#102×C43—21no—
132#102×C43—21no—
133#102×C43—21no—
134#102×C43—41no—
135#102×C43D411yescharacteristic
136#102×C43D411yescharacteristic
137C22⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139#97×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C24×C43—41no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—41no—
154C2×D4×C43—41no—
155C2×D4×C43—42no—
156C2×D4×C43—42no—
157C2×D4×C43—81no—
158C2×D4×C43—81no—
159C2×D4×C43C2×D411yescharacteristic
160C2×D4×C43C2×D411yescharacteristic
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—41no—
164Q16×C43—42no—
165SD16×C43—22no—
166SD16×C43—41no—
167SD16×C43—42no—
168SD16×C43—81no—
169SD16×C43—81no—
170M16×C43—81no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—81no—
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
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—21no—
189C4⋊C4×C43—41no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43—41no—
192C4⋊C4×C43—41no—
193C4⋊C4×C43—41no—
194C4⋊C4×C43—41no—
195C4⋊C4×C43C2×D411yescharacteristic
196C4⋊C4×C43C2×D411yescharacteristic
197C4⋊C4×C43C2×D411yescharacteristic
198C4⋊C4×C43C2×D411yescharacteristic
199C22⋊C4×C43—21no—
200C22⋊C4×C43—21no—
201C22⋊C4×C43—41no—
202C22⋊C4×C43—41no—
203C22⋊C4×C43—41no—
204C22⋊C4×C43—41no—
205C42×C43—21no—
206C42×C43—21no—
207C42×C43—41no—
208C42×C43—41no—
209C42×C43C2411yescharacteristic
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—41no—
213C23×C43—82no—
214C23×C43—82no—
215C23×C43—161no—
216Q8×C43—21no—
217Q8×C43—21no—
218Q8×C43—21no—
219Q8×C43—21no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—81no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—81no—
233D4×C43—82no—
234D4×C43—82no—
235D4×C43#13512yes—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
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—161no—
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43H(5,𝔽2)11yescharacteristic
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—41no—
258C8×C43—41no—
259C8×C43—41no—
260C8×C43—41no—
261C8×C43—41no—
262#19913C4311yesmaximal, characteristic, direct product factor, Sylow
263C22×C43—22no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—164no—
273C22×C43D4211yescharacteristic
274C4×C43—21no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43C2×#13511yescharacteristic
285C4×C43#57511yescharacteristic
286C4×C43#57711yescharacteristic
287C4×C43#57711yescharacteristic
288#3372C2×C4311yescharacteristic, complemented
289#3364C2×C4311yescharacteristic, complemented
290#3324C2×C4311yescharacteristic
291#3295C2×C4311yescharacteristic
292#1711C2×C4311yescharacteristic, complemented
293#1703C2×C4311yescharacteristic, complemented
294#1702C2×C4311yescharacteristic, complemented
295#1679C2×C4311yescharacteristic, complemented
296#1678C2×C4311yescharacteristic, complemented
297#1644C2×C4311yescharacteristic, complemented
298#1639C2×C4311yescharacteristic
299#1638C2×C4311yescharacteristic, complemented
300#1626C2×C4311yescharacteristic, complemented
301#1590C2×C4311yescharacteristic, complemented
302C8×SD16C2×C4311yescharacteristic, complemented
303C2×C43—42no—
304C2×C43—81no—
305C2×C43—161no—
306C2×C43#327511yescharacteristic
307C2×C43#328211yescharacteristic
308C2×C43#329011yescharacteristic
309#557C22×C4311yescharacteristic, complemented
310#556C22×C4311yescharacteristic
311#554C22×C4311yescharacteristic
312D42C22×C4311yescharacteristic
313#491—21no—
314#488—21no—
315#487C22×C4311yescharacteristic, complemented
316#487C22×C4311yescharacteristic, complemented
317#487C22×C4311yescharacteristic, complemented
318#486C22×C4311yescharacteristic
319#486C22×C4311yescharacteristic
320#486C22×C4311yescharacteristic
321#482—21no—
322#481—21no—
323#479—21no—
324#479—21no—
325#477C22×C4311yescharacteristic, complemented
326#476C22×C4311yescharacteristic
327#474C22×C4311yescharacteristic
328#474C22×C4311yescharacteristic
329#468—21no—
330#465—21no—
331#464—21no—
332#462C22×C4311yescharacteristic, complemented
333#461—21no—
334#461C22×C4311yescharacteristic
335#460C22×C4311yescharacteristic
336#460C22×C4311yescharacteristic
337#450—21no—
338#450—21no—
339#446C22×C4311yescharacteristic, complemented
340C8×Q8C22×C4311yescharacteristic, complemented
341#440—21no—
342C4×Q16—21no—
343C4×SD16C22×C4311yescharacteristic
344C4×SD16C22×C4311yescharacteristic
345#436C22×C4311yescharacteristic
346C8×D4C22×C4311yescharacteristic
347#418—21no—
348C2×#102—21no—
349#334C22×C4311yescharacteristic, complemented
350#334C22×C4311yescharacteristic, complemented
351#333C22×C4311yescharacteristic, complemented
352#332C22×C4311yescharacteristic, complemented
353#332C22×C4311yescharacteristic, complemented
354#331C22×C4311yescharacteristic
355Q8⋊C8C22×C4311yescharacteristic, complemented
356Q8⋊C8C22×C4311yescharacteristic, complemented
357D4⋊C8C22×C4311yescharacteristic
358D4⋊C8C22×C4311yescharacteristic
359C82C22×C4311yescharacteristic, complemented
360C43#1991311yescharacteristic, direct product factor, Sylow
361C22×D4—21no—
362C22×D4—21no—
363C2×Q16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16D4×C4311yescharacteristic
368C2×SD16D4×C4311yescharacteristic
369C2×M16—21no—
370C22×C8—21no—
371C4⋊Q8—21no—
372C4⋊Q8C23×C4311yescharacteristic
373C4⋊Q8C23×C4311yescharacteristic
374C4⋊Q8C23×C4311yescharacteristic
375#127C23×C4311yescharacteristic
376#126—41no—
377#125—21no—
378#125—21no—
379#125—41no—
380#124—21no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—41no—
384#121—21no—
385#121—21no—
386#120—41no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8C23×C4311yescharacteristic
391C4×Q8C23×C4311yescharacteristic
392C4×D4—21no—
393C4×D4C23×C4311yescharacteristic
394C4×D4C23×C4311yescharacteristic
395#117—21no—
396C2×C4⋊C4—21no—
397#107—21no—
398#107—21no—
399#107—21no—
400#106—21no—
401#106D4×C4311yescharacteristic
402#106D4×C4311yescharacteristic
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8C23×C4311yescharacteristic
406C4⋊C8C23×C4311yescharacteristic
407C4⋊C8C23×C4311yescharacteristic
408C4⋊C8C23×C4311yescharacteristic
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—41no—
417#103D4×C4311yescharacteristic
418#103D4×C4311yescharacteristic
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—41no—
429#102D4×C4311yescharacteristic
430#102D4×C4311yescharacteristic
431C22⋊C8—21no—
432C22⋊C8—21no—
433#97—21no—
434C4×C8—21no—
435C4×C8C23×C4311yescharacteristic
436C4×C8C23×C4311yescharacteristic
437C4×C8C23×C4311yescharacteristic
438C24—41no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×D4×C4311yescharacteristic
443C2×Q8C2×D4×C4311yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—81no—
452C2×D4—81no—
453C2×D4C2×D4×C4311yescharacteristic
454C2×D4C2×D4×C4311yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—41no—
458Q16—42no—
459SD16—22no—
460SD16—41no—
461SD16—42no—
462SD16—81no—
463SD16—81no—
464M16—81no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—81no—
471C2×C8C2×D4×C4311yescharacteristic
472C2×C8C2×D4×C4311yescharacteristic
473C2×C8C2×D4×C4311yescharacteristic
474C2×C8C2×D4×C4311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4C2×D4×C4311yescharacteristic
490C4⋊C4C2×D4×C4311yescharacteristic
491C4⋊C4C2×D4×C4311yescharacteristic
492C4⋊C4C2×D4×C4311yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—21no—
500C42—21no—
501C42—41no—
502C42—41no—
503C42C24×C4311yescharacteristic
504C23—21no—
505C23—21no—
506C23—41no—
507C23—82no—
508C23—82no—
509C23—161no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—81no—
519D4—21no—
520D4—21no—
521D4—21no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—81no—
527D4—82no—
528D4—82no—
529D4#135×C4312yes—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—161no—
544C2×C4C22×D4×C4311yescharacteristic
545C2×C4C22×D4×C4311yescharacteristic
546C2×C4H(5,𝔽2)×C4311yescharacteristic
547C8—21no—
548C8—21no—
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—164no—
566C22D42×C4311yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4C2×#135×C4311yescharacteristic
578C4C43×#57511yescharacteristic
579C4C43×#57711yescharacteristic
580C4C43×#57711yescharacteristic
581C2—42no—
582C2—81no—
583C2—161no—
584C2C43×#327511yescharacteristic
585C2C43×#328211yescharacteristic
586C2C43×#329011yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalD42×C43C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3372C2semidirect
2. C43×#3364C2semidirect
5. C43×#1711C2semidirect
6. C43×#1703C2semidirect
7. C43×#1702C2semidirect
8. C43×#1679C2semidirect
9. C43×#1678C2semidirect
10. C43×#1644C2semidirect
12. C43×#1638C2semidirect
13. C43×#1626C2semidirect
14. C43×#1590C2semidirect
15. C8×SD16×C43C2semidirect
16. C43×#557C22semidirect
22. C43×#487C22semidirect
23. C43×#487C22semidirect
24. C43×#487C22semidirect
32. C43×#477C22semidirect
39. C43×#462C22semidirect
46. C43×#446C22semidirect
47. C8×Q8×C43C22semidirect
56. C43×#334C22semidirect
57. C43×#334C22semidirect
58. C43×#333C22semidirect
59. C43×#332C22semidirect
60. C43×#332C22semidirect
62. C43×Q8⋊C8C22semidirect
63. C43×Q8⋊C8C22semidirect
66. C82×C43C22semidirect
262. #19913C43direct (N × H)
288. #3372C2×C43semidirect
289. #3364C2×C43semidirect
292. #1711C2×C43semidirect
293. #1703C2×C43semidirect
294. #1702C2×C43semidirect
295. #1679C2×C43semidirect
296. #1678C2×C43semidirect
297. #1644C2×C43semidirect
299. #1638C2×C43semidirect
300. #1626C2×C43semidirect
301. #1590C2×C43semidirect
302. C8×SD16C2×C43semidirect
309. #557C22×C43semidirect
315. #487C22×C43semidirect
316. #487C22×C43semidirect
317. #487C22×C43semidirect
325. #477C22×C43semidirect
332. #462C22×C43semidirect
339. #446C22×C43semidirect
340. C8×Q8C22×C43semidirect
349. #334C22×C43semidirect
350. #334C22×C43semidirect
351. #333C22×C43semidirect
352. #332C22×C43semidirect
353. #332C22×C43semidirect
355. Q8⋊C8C22×C43semidirect
356. Q8⋊C8C22×C43semidirect
359. C82C22×C43semidirect
360. C43#19913direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33722
C43×#33642
C43×#33242
C43×#32952
C43×#17112
C43×#17032
C43×#17022
C43×#16792
C43×#16782
C43×#16442
C43×#16392
C43×#16382
C43×#16262
C43×#15902
C8×SD16×C432
#1991343