Finite Group Databasebeta

← C43×#20274 #24940291

Subgroups — C43×#20274 #24940291

Order 11008.

626 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3397C211yesmaximal, characteristic, complemented
2C43×#3366C211yesmaximal, characteristic, complemented
3C43×#3333C211yesmaximal, characteristic, complemented
4C43×#3304C211yesmaximal, characteristic, complemented
5C43×#1717C211yesmaximal, characteristic, complemented
6C43×#1701C211yesmaximal, characteristic, complemented
7C43×#1698C211yesmaximal, characteristic, complemented
8C43×#1686C211yesmaximal, characteristic, complemented
9C43×#1677C211yesmaximal, characteristic, complemented
10C43×#1643C211yesmaximal, characteristic, complemented
11C43×#1638C211yesmaximal, characteristic, complemented
12C43×#1621C211yesmaximal, characteristic, complemented
13C43×#1621C211yesmaximal, characteristic, complemented
14C43×#1593C211yesmaximal, characteristic, complemented
15C43×#1581C211yesmaximal, characteristic, complemented
16C43×#556C2211yescharacteristic
17C43×#554C2211yescharacteristic
18C43×#550C2211yescharacteristic
19C43×#550C2211yescharacteristic
20C43×#496—21no—
21C43×#493C2211yescharacteristic
22C43×#492C2211yescharacteristic
23C43×#490—21no—
24C43×#487C2211yescharacteristic
25C43×#486C2211yescharacteristic
26C43×#486C2211yescharacteristic
27C43×#486C2211yescharacteristic
28C43×#482—21no—
29C43×#480—21no—
30C43×#478—21no—
31C43×#477C2211yescharacteristic
32C43×#476C2211yescharacteristic
33C43×#475C2211yescharacteristic
34C43×#468—21no—
35C43×#465—21no—
36C43×#463—21no—
37C43×#461C2211yescharacteristic
38C43×#460—21no—
39C43×#460C2211yescharacteristic
40C43×#460C2211yescharacteristic
41C43×#459—21no—
42C43×#459C2211yescharacteristic
43C43×#459C2211yescharacteristic
44C43×#452—21no—
45C43×#452—21no—
46C43×#446C2211yescharacteristic
47C43×#446C2211yescharacteristic
48C43×#442—21no—
49C43×#440—21no—
50C4×Q16×C43C2211yescharacteristic
51C4×D8×C43C2211yescharacteristic
52C43×#436C2211yescharacteristic
53C8×D4×C43C2211yescharacteristic
54C43×#417—21no—
55C43×#416—21no—
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#333C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#331C2211yescharacteristic
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#41×C43—21no—
68C2×#41×C43—21no—
69C2×Q16×C43D411yescharacteristic
70C2×SD16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×D8×C43—21no—
76C2×D8×C43—21no—
77C2×D8×C43—41no—
78C2×D8×C43D411yescharacteristic
79C2×M16×C43—21no—
80C22×C8×C43—21no—
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83#127×C43—21no—
84#127×C43—21no—
85#127×C43C2311yescharacteristic
86#127×C43C2311yescharacteristic
87#126×C43—41no—
88#125×C43—21no—
89#124×C43—21no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43—21no—
92C22⋊Q8×C43—41no—
93#121×C43—21no—
94#121×C43—21no—
95#121×C43—41no—
96#121×C43—41no—
97C4×Q8×C43—21no—
98C4×Q8×C43C2311yescharacteristic
99C4×Q8×C43C2311yescharacteristic
100C4×D4×C43—21no—
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43C2311yescharacteristic
104C4×D4×C43C2311yescharacteristic
105#117×C43—21no—
106C2×C4⋊C4×C43—21no—
107#107×C43—21no—
108#107×C43D411yescharacteristic
109#107×C43D411yescharacteristic
110#106×C43—21no—
111#106×C43—21no—
112C4⋊C8×C43—21no—
113C4⋊C8×C43—21no—
114C4⋊C8×C43C2311yescharacteristic
115C4⋊C8×C43C2311yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118#103×C43—21no—
119#103×C43—21no—
120#103×C43—21no—
121#103×C43—41no—
122#103×C43D411yescharacteristic
123#103×C43D411yescharacteristic
124#102×C43—21no—
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—21no—
135#102×C43D411yescharacteristic
136#102×C43D411yescharacteristic
137C22⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139#97×C43—21no—
140#97×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—42no—
145#41×C43—42no—
146#41×C43—81no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43C2×D411yescharacteristic
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—41no—
159C2×D4×C43—41no—
160C2×D4×C43—41no—
161C2×D4×C43—41no—
162C2×D4×C43C2×D411yescharacteristic
163C2×D4×C43C2×D411yescharacteristic
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—41no—
167C22×C4×C43—41no—
168C22×C4×C43—41no—
169Q16×C43—41no—
170SD16×C43—42no—
171SD16×C43—81no—
172SD16×C43—81no—
173SD16×C43—81no—
174SD16×C43—81no—
175D8×C43—41no—
176D8×C43—42no—
177D8×C43—81no—
178D8×C43—82no—
179M16×C43—81no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—81no—
186C2×C8×C43C2×D411yescharacteristic
187C2×C8×C43C2×D411yescharacteristic
188C2×C8×C43C2×D411yescharacteristic
189C2×C8×C43C2×D411yescharacteristic
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—41no—
197C4⋊C4×C43—41no—
198C4⋊C4×C43—41no—
199C4⋊C4×C43C2×D411yescharacteristic
200C4⋊C4×C43C2×D411yescharacteristic
201C4⋊C4×C43C2×D411yescharacteristic
202C4⋊C4×C43C2×D411yescharacteristic
203C22⋊C4×C43—21no—
204C22⋊C4×C43—21no—
205C22⋊C4×C43—41no—
206C22⋊C4×C43—41no—
207C22⋊C4×C43—41no—
208C22⋊C4×C43—41no—
209C22⋊C4×C43—41no—
210C42×C43—21no—
211C42×C43—21no—
212C42×C43—41no—
213C42×C43C2411yescharacteristic
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—41no—
217C23×C43—41no—
218Q8×C43—21no—
219Q8×C43—21no—
220Q8×C43—21no—
221Q8×C43—21no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—81no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—81no—
238D4×C43—81no—
239D4×C43—82no—
240D4×C43—82no—
241D4×C43—161no—
242D4×C43—161no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
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—82no—
256C2×C4×C43—82no—
257C2×C4×C43—161no—
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C8×C43—21no—
262C8×C43—21no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43—41no—
268C8×C43—41no—
269C8×C43—41no—
270#20274C4311yesmaximal, characteristic, direct product factor, Sylow
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43D4211yescharacteristic
284C4×C43—21no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43#57511yescharacteristic
294C4×C43#57511yescharacteristic
295C4×C43#57611yescharacteristic
296C4×C43#57711yescharacteristic
297#3397C2×C4311yescharacteristic, complemented
298#3366C2×C4311yescharacteristic, complemented
299#3333C2×C4311yescharacteristic, complemented
300#3304C2×C4311yescharacteristic, complemented
301#1717C2×C4311yescharacteristic, complemented
302#1701C2×C4311yescharacteristic, complemented
303#1698C2×C4311yescharacteristic, complemented
304#1686C2×C4311yescharacteristic, complemented
305#1677C2×C4311yescharacteristic, complemented
306#1643C2×C4311yescharacteristic, complemented
307#1638C2×C4311yescharacteristic, complemented
308#1621C2×C4311yescharacteristic, complemented
309#1621C2×C4311yescharacteristic, complemented
310#1593C2×C4311yescharacteristic, complemented
311#1581C2×C4311yescharacteristic, complemented
312C2×C43—81no—
313C2×C43—81no—
314C2×C43—161no—
315C2×C43—161no—
316C2×C43#327111yescharacteristic
317C2×C43#327311yescharacteristic
318C2×C43#328811yescharacteristic
319#556C22×C4311yescharacteristic
320#554C22×C4311yescharacteristic
321#550C22×C4311yescharacteristic
322#550C22×C4311yescharacteristic
323#496—21no—
324#493C22×C4311yescharacteristic
325#492C22×C4311yescharacteristic
326#490—21no—
327#487C22×C4311yescharacteristic
328#486C22×C4311yescharacteristic
329#486C22×C4311yescharacteristic
330#486C22×C4311yescharacteristic
331#482—21no—
332#480—21no—
333#478—21no—
334#477C22×C4311yescharacteristic
335#476C22×C4311yescharacteristic
336#475C22×C4311yescharacteristic
337#468—21no—
338#465—21no—
339#463—21no—
340#461C22×C4311yescharacteristic
341#460—21no—
342#460C22×C4311yescharacteristic
343#460C22×C4311yescharacteristic
344#459—21no—
345#459C22×C4311yescharacteristic
346#459C22×C4311yescharacteristic
347#452—21no—
348#452—21no—
349#446C22×C4311yescharacteristic
350#446C22×C4311yescharacteristic
351#442—21no—
352#440—21no—
353C4×Q16C22×C4311yescharacteristic
354C4×D8C22×C4311yescharacteristic
355#436C22×C4311yescharacteristic
356C8×D4C22×C4311yescharacteristic
357#417—21no—
358#416—21no—
359#335C22×C4311yescharacteristic
360#334C22×C4311yescharacteristic
361#333C22×C4311yescharacteristic
362#332C22×C4311yescharacteristic
363#331C22×C4311yescharacteristic
364#331C22×C4311yescharacteristic
365Q8⋊C8C22×C4311yescharacteristic
366Q8⋊C8C22×C4311yescharacteristic
367D4⋊C8C22×C4311yescharacteristic
368D4⋊C8C22×C4311yescharacteristic
369#322C22×C4311yescharacteristic
370C43#2027411yescharacteristic, direct product factor, Sylow
371C2×#41—21no—
372C2×#41—21no—
373C2×Q16D4×C4311yescharacteristic
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×D8—21no—
380C2×D8—21no—
381C2×D8—41no—
382C2×D8D4×C4311yescharacteristic
383C2×M16—21no—
384C22×C8—21no—
385C4⋊Q8C23×C4311yescharacteristic
386C4⋊Q8C23×C4311yescharacteristic
387#127—21no—
388#127—21no—
389#127C23×C4311yescharacteristic
390#127C23×C4311yescharacteristic
391#126—41no—
392#125—21no—
393#124—21no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8—41no—
397#121—21no—
398#121—21no—
399#121—41no—
400#121—41no—
401C4×Q8—21no—
402C4×Q8C23×C4311yescharacteristic
403C4×Q8C23×C4311yescharacteristic
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4C23×C4311yescharacteristic
408C4×D4C23×C4311yescharacteristic
409#117—21no—
410C2×C4⋊C4—21no—
411#107—21no—
412#107D4×C4311yescharacteristic
413#107D4×C4311yescharacteristic
414#106—21no—
415#106—21no—
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8C23×C4311yescharacteristic
419C4⋊C8C23×C4311yescharacteristic
420C4⋊C8C23×C4311yescharacteristic
421C4⋊C8C23×C4311yescharacteristic
422#103—21no—
423#103—21no—
424#103—21no—
425#103—41no—
426#103D4×C4311yescharacteristic
427#103D4×C4311yescharacteristic
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102D4×C4311yescharacteristic
440#102D4×C4311yescharacteristic
441C22⋊C8—21no—
442C22⋊C8—21no—
443#97—21no—
444#97—21no—
445C4×C8C23×C4311yescharacteristic
446C4×C8C23×C4311yescharacteristic
447C4×C8C23×C4311yescharacteristic
448#41—42no—
449#41—42no—
450#41—81no—
451#41—81no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8C2×D4×C4311yescharacteristic
455C2×Q8C2×D4×C4311yescharacteristic
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4C2×D4×C4311yescharacteristic
467C2×D4C2×D4×C4311yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473Q16—41no—
474SD16—42no—
475SD16—81no—
476SD16—81no—
477SD16—81no—
478SD16—81no—
479D8—41no—
480D8—42no—
481D8—81no—
482D8—82no—
483M16—81no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—81no—
490C2×C8C2×D4×C4311yescharacteristic
491C2×C8C2×D4×C4311yescharacteristic
492C2×C8C2×D4×C4311yescharacteristic
493C2×C8C2×D4×C4311yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4C2×D4×C4311yescharacteristic
504C4⋊C4C2×D4×C4311yescharacteristic
505C4⋊C4C2×D4×C4311yescharacteristic
506C4⋊C4C2×D4×C4311yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C42—21no—
515C42—21no—
516C42—41no—
517C42C24×C4311yescharacteristic
518C23—21no—
519C23—21no—
520C23—41no—
521C23—41no—
522Q8—21no—
523Q8—21no—
524Q8—21no—
525Q8—21no—
526Q8—41no—
527Q8—41no—
528Q8—81no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—81no—
542D4—81no—
543D4—82no—
544D4—82no—
545D4—161no—
546D4—161no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—161no—
562C2×C4C22×D4×C4311yescharacteristic
563C2×C4C22×D4×C4311yescharacteristic
564C2×C4H(5,𝔽2)×C4311yescharacteristic
565C8—21no—
566C8—21no—
567C8—21no—
568C8—21no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22D42×C4311yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—81no—
596C4C43×#57511yescharacteristic
597C4C43×#57511yescharacteristic
598C4C43×#57611yescharacteristic
599C4C43×#57711yescharacteristic
600C2—81no—
601C2—81no—
602C2—161no—
603C2—161no—
604C2C43×#327111yescharacteristic
605C2C43×#327311yescharacteristic
606C2C43×#328811yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
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×#3397C2semidirect
2. C43×#3366C2semidirect
3. C43×#3333C2semidirect
4. C43×#3304C2semidirect
5. C43×#1717C2semidirect
6. C43×#1701C2semidirect
7. C43×#1698C2semidirect
8. C43×#1686C2semidirect
9. C43×#1677C2semidirect
10. C43×#1643C2semidirect
11. C43×#1638C2semidirect
12. C43×#1621C2semidirect
13. C43×#1621C2semidirect
14. C43×#1593C2semidirect
15. C43×#1581C2semidirect
270. #20274C43direct (N × H)
297. #3397C2×C43semidirect
298. #3366C2×C43semidirect
299. #3333C2×C43semidirect
300. #3304C2×C43semidirect
301. #1717C2×C43semidirect
302. #1701C2×C43semidirect
303. #1698C2×C43semidirect
304. #1686C2×C43semidirect
305. #1677C2×C43semidirect
306. #1643C2×C43semidirect
307. #1638C2×C43semidirect
308. #1621C2×C43semidirect
309. #1621C2×C43semidirect
310. #1593C2×C43semidirect
311. #1581C2×C43semidirect
370. C43#20274direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33972
C43×#33662
C43×#33332
C43×#33042
C43×#17172
C43×#17012
C43×#16982
C43×#16862
C43×#16772
C43×#16432
C43×#16382
C43×#16212
C43×#15932
C43×#15812
#2027443