Finite Group Databasebeta

← C43×#20222 #24940239

Subgroups — C43×#20222 #24940239

Order 11008.

642 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3366C211yesmaximal, characteristic, complemented
2C43×#3357C211yesmaximal, characteristic, complemented
3C43×#3354C211yesmaximal, characteristic, complemented
4C43×#3284C211yesmaximal, characteristic, complemented
5C43×#1714C211yesmaximal, characteristic, complemented
6C43×#1697C211yesmaximal, characteristic, complemented
7C43×#1692C211yesmaximal, characteristic, complemented
8C43×#1685C211yesmaximal, characteristic, complemented
9C43×#1675C211yesmaximal, characteristic, complemented
10C43×#1644C211yesmaximal, characteristic, complemented
11C43×#1635C211yesmaximal, characteristic, complemented
12C43×#1631C211yesmaximal, characteristic, complemented
13C43×#1624C211yesmaximal, characteristic, complemented
14C43×#1592C211yesmaximal, characteristic, complemented
15C43×#1581C211yesmaximal, characteristic, complemented
16C2×#135×C43—21no—
17C43×#555C2211yescharacteristic
18C43×#554C2211yescharacteristic
19C43×#550C2211yescharacteristic
20C43×#547C2211yescharacteristic
21C43×#500C2211yescharacteristic
22C43×#498C2211yescharacteristic
23C43×#492C2211yescharacteristic
24C43×#492C2211yescharacteristic
25C43×#490—21no—
26C43×#487C2211yescharacteristic
27C43×#486C2211yescharacteristic
28C43×#485—21no—
29C43×#482—21no—
30C43×#481—21no—
31C43×#480—21no—
32C43×#478—21no—
33C43×#477C2211yescharacteristic
34C43×#476C2211yescharacteristic
35C43×#476C2211yescharacteristic
36C43×#476C2211yescharacteristic
37C43×#474C2211yescharacteristic
38C43×#469—21no—
39C43×#468—21no—
40C43×#465—21no—
41C43×#462C2211yescharacteristic
42C43×#459—21no—
43C43×#459C2211yescharacteristic
44C43×#459C2211yescharacteristic
45C43×#452—21no—
46C43×#449—21no—
47C43×#446C2211yescharacteristic
48C43×#442—21no—
49C4×SD16×C43C2211yescharacteristic
50C4×D8×C43C2211yescharacteristic
51C43×#436C2211yescharacteristic
52C43×#436C2211yescharacteristic
53C8×D4×C43C2211yescharacteristic
54C43×#428—21no—
55C43×#428—21no—
56C43×#335C2211yescharacteristic
57C43×#335C2211yescharacteristic
58C43×#333C2211yescharacteristic
59C43×#333C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×D4⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#41×C43—21no—
68C2×#41×C43—21no—
69#135×C43—44no—
70C2×Q16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—41no—
74C2×SD16×C43D411yescharacteristic
75C2×D8×C43—21no—
76C2×D8×C43—21no—
77C2×D8×C43D411yescharacteristic
78C2×M16×C43—21no—
79C2×M16×C43—21no—
80C22×C8×C43—21no—
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83C4⋊Q8×C43C2311yescharacteristic
84#127×C43—21no—
85#127×C43C2311yescharacteristic
86#125×C43—21no—
87#124×C43—41no—
88#123×C43—41no—
89C22⋊Q8×C43—21no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43—41no—
92#121×C43—21no—
93#121×C43—21no—
94#121×C43—21no—
95#121×C43—21no—
96#121×C43—41no—
97C4×Q8×C43C2311yescharacteristic
98C4×D4×C43—21no—
99C4×D4×C43—21no—
100C4×D4×C43C2311yescharacteristic
101C4×D4×C43C2311yescharacteristic
102C4×D4×C43C2311yescharacteristic
103#117×C43—21no—
104#117×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107#107×C43—21no—
108#107×C43—21no—
109#107×C43—21no—
110#107×C43—21no—
111#107×C43D411yescharacteristic
112#106×C43—21no—
113#106×C43—21no—
114#106×C43—21no—
115#106×C43—21no—
116#106×C43—21no—
117#106×C43D411yescharacteristic
118C4⋊C8×C43—21no—
119C4⋊C8×C43C2311yescharacteristic
120C4⋊C8×C43C2311yescharacteristic
121C4⋊C8×C43C2311yescharacteristic
122C4⋊C8×C43C2311yescharacteristic
123#103×C43—21no—
124#103×C43—21no—
125#103×C43—41no—
126#103×C43D411yescharacteristic
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
137#102×C43D411yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145#41×C43—42no—
146#41×C43—42no—
147#41×C43—81no—
148#41×C43—81no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43C2×D411yescharacteristic
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—41no—
159C2×D4×C43—41no—
160C2×D4×C43C2×D411yescharacteristic
161C2×D4×C43C2×D411yescharacteristic
162C2×D4×C43C2×D411yescharacteristic
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—41no—
167C22×C4×C43—41no—
168C22×C4×C43—41no—
169Q16×C43—42no—
170SD16×C43—22no—
171SD16×C43—42no—
172SD16×C43—81no—
173SD16×C43—82no—
174D8×C43—41no—
175D8×C43—42no—
176D8×C43—42no—
177M16×C43—42no—
178M16×C43—42no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—42no—
185C2×C8×C43C2×D411yescharacteristic
186C2×C8×C43C2×D411yescharacteristic
187C2×C8×C43C2×D411yescharacteristic
188C2×C8×C43C2×D411yescharacteristic
189C4⋊C4×C43—21no—
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—21no—
206C22⋊C4×C43—41no—
207C22⋊C4×C43—41no—
208C22⋊C4×C43—41no—
209C22⋊C4×C43—41no—
210C22⋊C4×C43—41no—
211C42×C43—21no—
212C42×C43—41no—
213C42×C43C2411yescharacteristic
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—41no—
218Q8×C43—21no—
219Q8×C43—21no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—81no—
223Q8×C43—81no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—81no—
235D4×C43—82no—
236D4×C43—82no—
237D4×C43—161no—
238D4×C43—161no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
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—82no—
254C2×C4×C43—82no—
255C2×C4×C43—161no—
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C8×C43—21no—
260C8×C43—21no—
261C8×C43—21no—
262C8×C43—41no—
263C8×C43—41no—
264C8×C43—41no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43AGL(1,ℤ/8)12yes—
268#20222C4311yesmaximal, characteristic, direct product factor, Sylow
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43D4211yescharacteristic
282C4×C43—21no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43—81no—
289C4×C43—81no—
290C4×C43—81no—
291C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
292C4×C43#57511yescharacteristic
293C4×C43#57711yescharacteristic
294C4×C43#57811yescharacteristic
295#3366C2×C4311yescharacteristic, complemented
296#3357C2×C4311yescharacteristic, complemented
297#3354C2×C4311yescharacteristic, complemented
298#3284C2×C4311yescharacteristic, complemented
299#1714C2×C4311yescharacteristic, complemented
300#1697C2×C4311yescharacteristic, complemented
301#1692C2×C4311yescharacteristic, complemented
302#1685C2×C4311yescharacteristic, complemented
303#1675C2×C4311yescharacteristic, complemented
304#1644C2×C4311yescharacteristic, complemented
305#1635C2×C4311yescharacteristic, complemented
306#1631C2×C4311yescharacteristic, complemented
307#1624C2×C4311yescharacteristic, complemented
308#1592C2×C4311yescharacteristic, complemented
309#1581C2×C4311yescharacteristic, complemented
310C2×C43—81no—
311C2×C43—81no—
312C2×C43—81no—
313C2×C43—161no—
314C2×C43#326911yescharacteristic
315C2×C43#327211yescharacteristic
316C2×C43#328811yescharacteristic
317C2×#135—21no—
318#555C22×C4311yescharacteristic
319#554C22×C4311yescharacteristic
320#550C22×C4311yescharacteristic
321#547C22×C4311yescharacteristic
322#500C22×C4311yescharacteristic
323#498C22×C4311yescharacteristic
324#492C22×C4311yescharacteristic
325#492C22×C4311yescharacteristic
326#490—21no—
327#487C22×C4311yescharacteristic
328#486C22×C4311yescharacteristic
329#485—21no—
330#482—21no—
331#481—21no—
332#480—21no—
333#478—21no—
334#477C22×C4311yescharacteristic
335#476C22×C4311yescharacteristic
336#476C22×C4311yescharacteristic
337#476C22×C4311yescharacteristic
338#474C22×C4311yescharacteristic
339#469—21no—
340#468—21no—
341#465—21no—
342#462C22×C4311yescharacteristic
343#459—21no—
344#459C22×C4311yescharacteristic
345#459C22×C4311yescharacteristic
346#452—21no—
347#449—21no—
348#446C22×C4311yescharacteristic
349#442—21no—
350C4×SD16C22×C4311yescharacteristic
351C4×D8C22×C4311yescharacteristic
352#436C22×C4311yescharacteristic
353#436C22×C4311yescharacteristic
354C8×D4C22×C4311yescharacteristic
355#428—21no—
356#428—21no—
357#335C22×C4311yescharacteristic
358#335C22×C4311yescharacteristic
359#333C22×C4311yescharacteristic
360#333C22×C4311yescharacteristic
361#332C22×C4311yescharacteristic
362#331C22×C4311yescharacteristic
363Q8⋊C8C22×C4311yescharacteristic
364D4⋊C8C22×C4311yescharacteristic
365D4⋊C8C22×C4311yescharacteristic
366D4⋊C8C22×C4311yescharacteristic
367#322C22×C4311yescharacteristic
368C43#2022211yescharacteristic, direct product factor, Sylow
369C2×#41—21no—
370C2×#41—21no—
371#135—44no—
372C2×Q16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—41no—
376C2×SD16D4×C4311yescharacteristic
377C2×D8—21no—
378C2×D8—21no—
379C2×D8D4×C4311yescharacteristic
380C2×M16—21no—
381C2×M16—21no—
382C22×C8—21no—
383C4⋊Q8C23×C4311yescharacteristic
384C4⋊Q8C23×C4311yescharacteristic
385C4⋊Q8C23×C4311yescharacteristic
386#127—21no—
387#127C23×C4311yescharacteristic
388#125—21no—
389#124—41no—
390#123—41no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—41no—
394#121—21no—
395#121—21no—
396#121—21no—
397#121—21no—
398#121—41no—
399C4×Q8C23×C4311yescharacteristic
400C4×D4—21no—
401C4×D4—21no—
402C4×D4C23×C4311yescharacteristic
403C4×D4C23×C4311yescharacteristic
404C4×D4C23×C4311yescharacteristic
405#117—21no—
406#117—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409#107—21no—
410#107—21no—
411#107—21no—
412#107—21no—
413#107D4×C4311yescharacteristic
414#106—21no—
415#106—21no—
416#106—21no—
417#106—21no—
418#106—21no—
419#106D4×C4311yescharacteristic
420C4⋊C8—21no—
421C4⋊C8C23×C4311yescharacteristic
422C4⋊C8C23×C4311yescharacteristic
423C4⋊C8C23×C4311yescharacteristic
424C4⋊C8C23×C4311yescharacteristic
425#103—21no—
426#103—21no—
427#103—41no—
428#103D4×C4311yescharacteristic
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#102D4×C4311yescharacteristic
438#102D4×C4311yescharacteristic
439#102D4×C4311yescharacteristic
440C22⋊C8—21no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443#97—21no—
444C4×C8C23×C4311yescharacteristic
445C4×C8C23×C4311yescharacteristic
446C4×C8C23×C4311yescharacteristic
447#41—42no—
448#41—42no—
449#41—81no—
450#41—81no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8C2×D4×C4311yescharacteristic
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4C2×D4×C4311yescharacteristic
463C2×D4C2×D4×C4311yescharacteristic
464C2×D4C2×D4×C4311yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471Q16—42no—
472SD16—22no—
473SD16—42no—
474SD16—81no—
475SD16—82no—
476D8—41no—
477D8—42no—
478D8—42no—
479M16—42no—
480M16—42no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—42no—
487C2×C8C2×D4×C4311yescharacteristic
488C2×C8C2×D4×C4311yescharacteristic
489C2×C8C2×D4×C4311yescharacteristic
490C2×C8C2×D4×C4311yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4C2×D4×C4311yescharacteristic
502C4⋊C4C2×D4×C4311yescharacteristic
503C4⋊C4C2×D4×C4311yescharacteristic
504C4⋊C4C2×D4×C4311yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C42—21no—
514C42—41no—
515C42C24×C4311yescharacteristic
516C23—21no—
517C23—21no—
518C23—21no—
519C23—41no—
520Q8—21no—
521Q8—21no—
522Q8—41no—
523Q8—41no—
524Q8—81no—
525Q8—81no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—81no—
537D4—82no—
538D4—82no—
539D4—161no—
540D4—161no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—82no—
556C2×C4—82no—
557C2×C4—161no—
558C2×C4C22×D4×C4311yescharacteristic
559C2×C4C22×D4×C4311yescharacteristic
560C2×C4H(5,𝔽2)×C4311yescharacteristic
561C8—21no—
562C8—21no—
563C8—21no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8AGL(1,ℤ/8)×C4312yes—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22D42×C4311yescharacteristic
583C4—21no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
593C4C43×#57511yescharacteristic
594C4C43×#57711yescharacteristic
595C4C43×#57811yescharacteristic
596C2—81no—
597C2—81no—
598C2—81no—
599C2—161no—
600C2C43×#326911yescharacteristic
601C2C43×#327211yescharacteristic
602C2C43×#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×#3366C2semidirect
2. C43×#3357C2semidirect
3. C43×#3354C2semidirect
4. C43×#3284C2semidirect
5. C43×#1714C2semidirect
6. C43×#1697C2semidirect
7. C43×#1692C2semidirect
8. C43×#1685C2semidirect
9. C43×#1675C2semidirect
10. C43×#1644C2semidirect
11. C43×#1635C2semidirect
12. C43×#1631C2semidirect
13. C43×#1624C2semidirect
14. C43×#1592C2semidirect
15. C43×#1581C2semidirect
268. #20222C43direct (N × H)
295. #3366C2×C43semidirect
296. #3357C2×C43semidirect
297. #3354C2×C43semidirect
298. #3284C2×C43semidirect
299. #1714C2×C43semidirect
300. #1697C2×C43semidirect
301. #1692C2×C43semidirect
302. #1685C2×C43semidirect
303. #1675C2×C43semidirect
304. #1644C2×C43semidirect
305. #1635C2×C43semidirect
306. #1631C2×C43semidirect
307. #1624C2×C43semidirect
308. #1592C2×C43semidirect
309. #1581C2×C43semidirect
368. C43#20222direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33662
C43×#33572
C43×#33542
C43×#32842
C43×#17142
C43×#16972
C43×#16922
C43×#16852
C43×#16752
C43×#16442
C43×#16352
C43×#16312
C43×#16242
C43×#15922
C43×#15812
#2022243