Finite Group Databasebeta

← C43×#9916 #24929933

Subgroups — C43×#9916 #24929933

Order 11008.

968 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#448C211yesmaximal, characteristic, complemented
2C43×#2617C211yesmaximal, characteristic
3C2×C43×#393C211yesmaximal, characteristic, complemented
4C43×#1787C211yesmaximal, characteristic, complemented
5C2×C43×#327C211yesmaximal, characteristic, complemented
6C2×C43×#323C211yesmaximal, characteristic, complemented
7C43×#1294C211yesmaximal, characteristic, complemented
8C23×Q8×C43C2211yescharacteristic
9C22×SD16×C43—21no—
10C2×#121×C43C2211yescharacteristic
11C2×#120×C43—21no—
12C22×C22⋊C4×C43—21no—
13C22×C22⋊C4×C43C2211yescharacteristic
14C43×#448—22no—
15C43×#448—22no—
16C2×#103×C43—21no—
17C2×#103×C43—22no—
18C2×C22⋊C8×C43C2211yescharacteristic
19C2×C22⋊C8×C43C2211yescharacteristic
20C43×#397—21no—
21C43×#394—22no—
22C43×#393—22no—
23C43×#393—22no—
24C43×#392—21no—
25C43×#386—21no—
26C43×#380C2211yescharacteristic
27C2×#95×C43—21no—
28C2×#95×C43C2211yescharacteristic
29C43×#327—22no—
30C43×#323—22no—
31C25×C43D411yescharacteristic
32C22×Q8×C43—21no—
33C22×Q8×C43—21no—
34C22×Q8×C43—21no—
35C22×Q8×C43—21no—
36C22×Q8×C43—21no—
37C22×Q8×C43—44no—
38C22×Q8×C43D412yescomplemented
39C22×D4×C43—21no—
40C22×D4×C43—22no—
41C22×D4×C43D411yescharacteristic
42C23×C4×C43—21no—
43C23×C4×C43—21no—
44C23×C4×C43D411yescharacteristic
45C23×C4×C43C2311yescharacteristic
46C2×SD16×C43—24no—
47C2×SD16×C43—44no—
48C22×C8×C43—21no—
49C22×C8×C43—21no—
50#121×C43—21no—
51#121×C43—21no—
52#121×C43—21no—
53#121×C43—21no—
54#120×C43—42no—
55#120×C43—42no—
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C4⋊C4×C43D412yes—
58C2×C22⋊C4×C43—24no—
59C2×C22⋊C4×C43—22no—
60C2×C22⋊C4×C43—21no—
61C2×C22⋊C4×C43—21no—
62C2×C22⋊C4×C43—21no—
63C2×C22⋊C4×C43—21no—
64C2×C22⋊C4×C43—21no—
65C2×C22⋊C4×C43—21no—
66C2×C22⋊C4×C43—21no—
67C2×C22⋊C4×C43—21no—
68C2×C22⋊C4×C43—22no—
69C2×C22⋊C4×C43—44no—
70#103×C43—24no—
71#103×C43—44no—
72C22⋊C8×C43—21no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43—21no—
75C22⋊C8×C43D412yescomplemented
76#95×C43—24no—
77#95×C43—22no—
78#95×C43—21no—
79#95×C43—21no—
80#95×C43D412yescomplemented
81C24×C43—21no—
82C24×C43—21no—
83C24×C43—21no—
84C24×C43—21no—
85C24×C43—21no—
86C24×C43—21no—
87C24×C43—21no—
88C24×C43—42no—
89C24×C43—42no—
90C24×C43SD1612yescomplemented
91C24×C43C2×D411yescharacteristic
92C2×Q8×C43—24no—
93C2×Q8×C43—24no—
94C2×Q8×C43—22no—
95C2×Q8×C43—22no—
96C2×Q8×C43—44no—
97C2×Q8×C43—42no—
98C2×Q8×C43—42no—
99C2×Q8×C43—44no—
100C2×Q8×C43—44no—
101C2×Q8×C43—44no—
102C2×Q8×C43—41no—
103C2×Q8×C43—41no—
104C2×D4×C43—21no—
105C2×D4×C43—21no—
106C2×D4×C43—44no—
107C2×D4×C43—41no—
108C2×D4×C43—41no—
109C2×D4×C43—41no—
110C2×D4×C43—41no—
111C2×D4×C43—41no—
112C2×D4×C43—41no—
113C2×D4×C43—42no—
114C2×D4×C43—82no—
115C2×D4×C43—82no—
116C22×C4×C43—24no—
117C22×C4×C43—22no—
118C22×C4×C43—21no—
119C22×C4×C43—22no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—22no—
123C22×C4×C43—21no—
124C22×C4×C43—42no—
125C22×C4×C43—42no—
126C22×C4×C43—42no—
127C22×C4×C43—42no—
128C22×C4×C43—42no—
129C22×C4×C43—41no—
130C22×C4×C43—41no—
131C22×C4×C43—41no—
132C22×C4×C43—41no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43#4111yescharacteristic
139SD16×C43—48no—
140C2×C8×C43—22no—
141C2×C8×C43—42no—
142C2×C8×C43—42no—
143C2×C8×C43—41no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—42no—
147C22⋊C4×C43—44no—
148C22⋊C4×C43—48no—
149C22⋊C4×C43—41no—
150C22⋊C4×C43—41no—
151C22⋊C4×C43—41no—
152C22⋊C4×C43—41no—
153C22⋊C4×C43—41no—
154C22⋊C4×C43—41no—
155C22⋊C4×C43—41no—
156C22⋊C4×C43—41no—
157C22⋊C4×C43—82no—
158C23×C43—22no—
159C23×C43—22no—
160C23×C43—22no—
161C23×C43—22no—
162C23×C43—22no—
163C23×C43—44no—
164C23×C43—42no—
165C23×C43—44no—
166C23×C43—42no—
167C23×C43—41no—
168C23×C43—41no—
169C23×C43—41no—
170C23×C43—42no—
171C23×C43—42no—
172C23×C43—41no—
173C23×C43—41no—
174C23×C43—41no—
175C23×C43—41no—
176C23×C43—42no—
177C23×C43—42no—
178C23×C43—82no—
179C23×C43—82no—
180C23×C43—81no—
181C23×C43—81no—
182C23×C43#12011yescharacteristic
183C23×C43#12011yescharacteristic
184C23×C43#12111yescharacteristic
185C23×C43C2×SD1611yescharacteristic
186C23×C43#13511yescharacteristic
187C23×C43AGL(1,ℤ/8)11yescharacteristic
188C23×C43#13711yescharacteristic
189Q8×C43—24no—
190Q8×C43—24no—
191Q8×C43—42no—
192Q8×C43—44no—
193Q8×C43—44no—
194Q8×C43—42no—
195D4×C43—42no—
196D4×C43—81no—
197D4×C43—88no—
198D4×C43—81no—
199D4×C43—81no—
200D4×C43—81no—
201D4×C43—81no—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
204C2×C4×C43—24no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—42no—
210C2×C4×C43—44no—
211C2×C4×C43—42no—
212C2×C4×C43—44no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—82no—
226C2×C4×C43—82no—
227C2×C4×C43—81no—
228C2×C4×C43#12011yescharacteristic
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12711yescharacteristic
232C8×C43—42no—
233C8×C43—81no—
234#9916C4311yesmaximal, characteristic, direct product factor, Sylow
235C22×C43—22no—
236C22×C43—22no—
237C22×C43—22no—
238C22×C43—22no—
239C22×C43—21no—
240C22×C43—21no—
241C22×C43—21no—
242C22×C43—21no—
243C22×C43—44no—
244C22×C43—44no—
245C22×C43—42no—
246C22×C43—82no—
247C22×C43—82no—
248C22×C43—82no—
249C22×C43—82no—
250C22×C43—81no—
251C22×C43—81no—
252C22×C43—82no—
253C22×C43—82no—
254C22×C43—81no—
255C22×C43—81no—
256C22×C43—81no—
257C22×C43#39211yescharacteristic
258C22×C43#44811yescharacteristic
259C22×C43#44911yescharacteristic
260C22×C43#45011yescharacteristic
261C22×C43#45211yescharacteristic
262C22×C43#45512yes—
263C22×C43B(4,𝔽2)12yes—
264C22×C43#46511yescharacteristic
265C22×C43#46811yescharacteristic
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—44no—
271C4×C43—82no—
272C4×C43—82no—
273C4×C43—81no—
274C4×C43—81no—
275C2×#448C2×C4311yescharacteristic, complemented
276#2617C2×C4311yescharacteristic
277C2×#393C2×C4311yescharacteristic, complemented
278#1787C2×C4311yescharacteristic, complemented
279C2×#327C2×C4311yescharacteristic, complemented
280C2×#323C2×C4311yescharacteristic, complemented
281#1294C2×C4311yescharacteristic, complemented
282C2×C43—21no—
283C2×C43—21no—
284C2×C43—21no—
285C2×C43—21no—
286C2×C43—82no—
287C2×C43—161no—
288C2×C43#160112yes—
289C2×C43#160612yes—
290C2×C43#200011yescharacteristic
291C2×C43#200411yescharacteristic
292C2×C43#202111yescharacteristic
293C23×Q8C22×C4311yescharacteristic
294C22×SD16—21no—
295C2×#121C22×C4311yescharacteristic
296C2×#120—21no—
297C22×C22⋊C4—21no—
298C22×C22⋊C4C22×C4311yescharacteristic
299#448—22no—
300#448—22no—
301C2×#103—21no—
302C2×#103—22no—
303C2×C22⋊C8C22×C4311yescharacteristic
304C2×C22⋊C8C22×C4311yescharacteristic
305#397—21no—
306#394—22no—
307#393—22no—
308#393—22no—
309#392—21no—
310#386—21no—
311#380C22×C4311yescharacteristic
312C2×#95—21no—
313C2×#95C22×C4311yescharacteristic
314#327—22no—
315#323—22no—
316C43#991611yescharacteristic, direct product factor, Sylow
317C25D4×C4311yescharacteristic
318C22×Q8—21no—
319C22×Q8—21no—
320C22×Q8—21no—
321C22×Q8—21no—
322C22×Q8—21no—
323C22×Q8—44no—
324C22×Q8D4×C4312yescomplemented
325C22×D4—21no—
326C22×D4—22no—
327C22×D4D4×C4311yescharacteristic
328C23×C4—21no—
329C23×C4—21no—
330C23×C4D4×C4311yescharacteristic
331C23×C4C23×C4311yescharacteristic
332C2×SD16—24no—
333C2×SD16—44no—
334C22×C8—21no—
335C22×C8—21no—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340#120—42no—
341#120—42no—
342C2×C4⋊C4D4×C4311yescharacteristic
343C2×C4⋊C4D4×C4312yes—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—44no—
356#103—24no—
357#103—44no—
358C22⋊C8—21no—
359C22⋊C8—21no—
360C22⋊C8—21no—
361C22⋊C8D4×C4312yescomplemented
362#95—24no—
363#95—22no—
364#95—21no—
365#95—21no—
366#95D4×C4312yescomplemented
367C24—21no—
368C24—21no—
369C24—21no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—42no—
375C24—42no—
376C24SD16×C4312yescomplemented
377C24C2×D4×C4311yescharacteristic
378C2×Q8—24no—
379C2×Q8—24no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—44no—
383C2×Q8—42no—
384C2×Q8—42no—
385C2×Q8—44no—
386C2×Q8—44no—
387C2×Q8—44no—
388C2×Q8—41no—
389C2×Q8—41no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—42no—
393C2×D4—44no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—82no—
401C2×D4—82no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4C2×D4×C4311yescharacteristic
420C22×C4C2×D4×C4311yescharacteristic
421C22×C4C2×D4×C4311yescharacteristic
422C22×C4C2×D4×C4311yescharacteristic
423C22×C4C2×D4×C4311yescharacteristic
424C22×C4#41×C4311yescharacteristic
425SD16—48no—
426C2×C8—22no—
427C2×C8—42no—
428C2×C8—42no—
429C2×C8—41no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—42no—
433C22⋊C4—48no—
434C22⋊C4—44no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—82no—
444C23—22no—
445C23—22no—
446C23—22no—
447C23—22no—
448C23—22no—
449C23—44no—
450C23—42no—
451C23—44no—
452C23—42no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—42no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—42no—
463C23—42no—
464C23—82no—
465C23—82no—
466C23—81no—
467C23—81no—
468C23#120×C4311yescharacteristic
469C23#120×C4311yescharacteristic
470C23#121×C4311yescharacteristic
471C23C2×SD16×C4311yescharacteristic
472C23#135×C4311yescharacteristic
473C23AGL(1,ℤ/8)×C4311yescharacteristic
474C23#137×C4311yescharacteristic
475Q8—24no—
476Q8—24no—
477Q8—42no—
478Q8—44no—
479Q8—44no—
480Q8—42no—
481D4—42no—
482D4—81no—
483D4—88no—
484D4—81no—
485D4—81no—
486D4—81no—
487D4—81no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—44no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—82no—
512C2×C4—82no—
513C2×C4—81no—
514C2×C4#120×C4311yescharacteristic
515C2×C4#121×C4311yescharacteristic
516C2×C4#121×C4311yescharacteristic
517C2×C4#127×C4311yescharacteristic
518C8—42no—
519C8—81no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—44no—
529C22—44no—
530C22—42no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22—82no—
535C22—81no—
536C22—81no—
537C22—82no—
538C22—82no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22C43×#39211yescharacteristic
543C22C43×#44811yescharacteristic
544C22C43×#44911yescharacteristic
545C22C43×#45011yescharacteristic
546C22C43×#45211yescharacteristic
547C22C43×#45512yes—
548C22C43×B(4,𝔽2)12yes—
549C22C43×#46511yescharacteristic
550C22C43×#46811yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—44no—
556C4—82no—
557C4—82no—
558C4—81no—
559C4—81no—
560C2—21no—
561C2—21no—
562C2—21no—
563C2—21no—
564C2—82no—
565C2—161no—
566C2C43×#160112yes—
567C2C43×#160612yes—
568C2C43×#200011yescharacteristic
569C2C43×#200411yescharacteristic
570C2C43×#202111yescharacteristic
subgroupG/H
center, socleC23×C43#120
commutator, Frattini, cosocleC23×C4C23×C43
prime radicalC43×#2617C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#448C2semidirect
3. C2×C43×#393C2semidirect
4. C43×#1787C2semidirect
5. C2×C43×#327C2semidirect
6. C2×C43×#323C2semidirect
7. C43×#1294C2semidirect
38. C22×Q8×C43D4semidirect
75. C22⋊C8×C43D4semidirect
80. #95×C43D4semidirect
90. C24×C43SD16semidirect
234. #9916C43direct (N × H)
275. C2×#448C2×C43semidirect
277. C2×#393C2×C43semidirect
278. #1787C2×C43semidirect
279. C2×#327C2×C43semidirect
280. C2×#323C2×C43semidirect
281. #1294C2×C43semidirect
316. C43#9916direct (N × H)
324. C22×Q8D4×C43semidirect
361. C22⋊C8D4×C43semidirect
366. #95D4×C43semidirect
376. C24SD16×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4482
C43×#26172
C2×C43×#3932
C43×#17872
C2×C43×#3272
C2×C43×#3232
C43×#12942
#991643