Finite Group Databasebeta

← C43×#9915 #24929932

Subgroups — C43×#9915 #24929932

Order 11008.

1044 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#447C211yesmaximal, characteristic
2C43×#2618C211yesmaximal, characteristic, complemented
3C2×C43×#394C211yesmaximal, characteristic, complemented
4C43×#1786C211yesmaximal, characteristic, complemented
5C2×C43×#327C211yesmaximal, characteristic, complemented
6C2×C43×#324C211yesmaximal, characteristic, complemented
7C43×#1294C211yesmaximal, characteristic, complemented
8C23×D4×C43C2211yescharacteristic
9C22×D8×C43—21no—
10C2×#123×C43—21no—
11C2×#121×C43C2211yescharacteristic
12C22×C4⋊C4×C43C2211yescharacteristic
13C22×C22⋊C4×C43—21no—
14C22×C22⋊C4×C43—21no—
15C43×#447—22no—
16C43×#447—22no—
17C2×#102×C43—21no—
18C2×#102×C43—22no—
19C2×C22⋊C8×C43C2211yescharacteristic
20C2×C22⋊C8×C43C2211yescharacteristic
21C43×#398—21no—
22C43×#396—22no—
23C43×#394—21no—
24C43×#394—22no—
25C43×#394—22no—
26C43×#386—21no—
27C43×#380C2211yescharacteristic
28C2×#95×C43C2211yescharacteristic
29C43×#327—22no—
30C43×#324—22no—
31C25×C43—21no—
32C22×D4×C43—21no—
33C22×D4×C43—21no—
34C22×D4×C43—21no—
35C22×D4×C43—21no—
36C22×D4×C43—21no—
37C22×D4×C43—21no—
38C22×D4×C43—44no—
39C22×D4×C43D411yescharacteristic
40C22×D4×C43D412yes—
41C23×C4×C43—21no—
42C23×C4×C43D411yescharacteristic
43C23×C4×C43D411yescharacteristic
44C23×C4×C43C2311yescharacteristic
45C2×D8×C43—24no—
46C2×D8×C43—44no—
47C22×C8×C43—21no—
48C22×C8×C43—21no—
49#123×C43—42no—
50#123×C43—42no—
51#121×C43—21no—
52#121×C43—21no—
53#121×C43—21no—
54#121×C43—21no—
55C2×C4⋊C4×C43—22no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43D411yescharacteristic
63C2×C4⋊C4×C43D412yes—
64C2×C22⋊C4×C43—24no—
65C2×C22⋊C4×C43—24no—
66C2×C22⋊C4×C43—22no—
67C2×C22⋊C4×C43—21no—
68C2×C22⋊C4×C43—21no—
69C2×C22⋊C4×C43—22no—
70C2×C22⋊C4×C43—42no—
71C2×C22⋊C4×C43—44no—
72C2×C22⋊C4×C43—42no—
73#102×C43—24no—
74#102×C43—44no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43—21no—
78C22⋊C8×C43D412yes—
79#95×C43—22no—
80#95×C43—21no—
81#95×C43—21no—
82#95×C43D412yes—
83C24×C43—24no—
84C24×C43—22no—
85C24×C43—21no—
86C24×C43—42no—
87C24×C43—42no—
88C24×C43—42no—
89C24×C43—41no—
90C24×C43—41no—
91C24×C43—41no—
92C24×C43—41no—
93C24×C43—41no—
94C24×C43—41no—
95C24×C43C2×D411yescharacteristic
96C2×D4×C43—24no—
97C2×D4×C43—24no—
98C2×D4×C43—22no—
99C2×D4×C43—21no—
100C2×D4×C43—22no—
101C2×D4×C43—21no—
102C2×D4×C43—44no—
103C2×D4×C43—44no—
104C2×D4×C43—42no—
105C2×D4×C43—42no—
106C2×D4×C43—44no—
107C2×D4×C43—44no—
108C2×D4×C43—41no—
109C2×D4×C43—41no—
110C2×D4×C43—41no—
111C2×D4×C43—41no—
112C2×D4×C43—41no—
113C2×D4×C43—41no—
114C2×D4×C43—41no—
115C2×D4×C43—41no—
116C2×D4×C43—42no—
117C22×C4×C43—21no—
118C22×C4×C43—22no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—42no—
130C22×C4×C43—42no—
131C22×C4×C43—42no—
132C22×C4×C43—42no—
133C22×C4×C43—41no—
134C22×C4×C43—41no—
135C22×C4×C43D812yescomplemented
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43#4111yescharacteristic
142D8×C43—48no—
143C2×C8×C43—22no—
144C2×C8×C43—42no—
145C2×C8×C43—42no—
146C2×C8×C43—41no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—42no—
150C4⋊C4×C43—44no—
151C4⋊C4×C43—41no—
152C4⋊C4×C43—41no—
153C4⋊C4×C43—41no—
154C4⋊C4×C43—41no—
155C22⋊C4×C43—48no—
156C22⋊C4×C43—48no—
157C22⋊C4×C43—44no—
158C22⋊C4×C43—41no—
159C22⋊C4×C43—41no—
160C22⋊C4×C43—41no—
161C22⋊C4×C43—41no—
162C22⋊C4×C43—82no—
163C23×C43—22no—
164C23×C43—22no—
165C23×C43—24no—
166C23×C43—42no—
167C23×C43—44no—
168C23×C43—44no—
169C23×C43—44no—
170C23×C43—44no—
171C23×C43—44no—
172C23×C43—42no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43—42no—
176C23×C43—42no—
177C23×C43—44no—
178C23×C43—41no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43—42no—
182C23×C43—42no—
183C23×C43—82no—
184C23×C43—82no—
185C23×C43—82no—
186C23×C43—82no—
187C23×C43—82no—
188C23×C43—81no—
189C23×C43—81no—
190C23×C43—82no—
191C23×C43—81no—
192C23×C43—81no—
193C23×C43#12011yescharacteristic
194C23×C43#12011yescharacteristic
195C23×C43#12111yescharacteristic
196C23×C43C2×D811yescharacteristic
197C23×C43#13511yescharacteristic
198C23×C43AGL(1,ℤ/8)11yescharacteristic
199C23×C43AGL(1,ℤ/8)11yescharacteristic
200D4×C43—24no—
201D4×C43—24no—
202D4×C43—42no—
203D4×C43—44no—
204D4×C43—42no—
205D4×C43—44no—
206D4×C43—42no—
207D4×C43—81no—
208D4×C43—81no—
209D4×C43—81no—
210D4×C43—81no—
211D4×C43—81no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—82no—
238C2×C4×C43—82no—
239C2×C4×C43—81no—
240C2×C4×C43#12011yescharacteristic
241C2×C4×C43#12111yescharacteristic
242C2×C4×C43#12111yescharacteristic
243C2×C4×C43#12711yescharacteristic
244C8×C43—42no—
245C8×C43—81no—
246#9915C4311yesmaximal, characteristic, direct product factor, Sylow
247C22×C43—22no—
248C22×C43—22no—
249C22×C43—22no—
250C22×C43—22no—
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—44no—
256C22×C43—44no—
257C22×C43—44no—
258C22×C43—82no—
259C22×C43—82no—
260C22×C43—84no—
261C22×C43—84no—
262C22×C43—84no—
263C22×C43—84no—
264C22×C43—82no—
265C22×C43—82no—
266C22×C43—82no—
267C22×C43—82no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43#39211yescharacteristic
272C22×C43#44711yescharacteristic
273C22×C43#44711yescharacteristic
274C22×C43#44911yescharacteristic
275C22×C43#44911yescharacteristic
276C22×C43#45412yes—
277C22×C43B(4,𝔽2)12yes—
278C22×C43#46611yescharacteristic
279C22×C43#46911yescharacteristic
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—21no—
284C4×C43—42no—
285C4×C43—82no—
286C4×C43—82no—
287C4×C43—81no—
288C4×C43—81no—
289C2×#447C2×C4311yescharacteristic
290#2618C2×C4311yescharacteristic, complemented
291C2×#394C2×C4311yescharacteristic, complemented
292#1786C2×C4311yescharacteristic, complemented
293C2×#327C2×C4311yescharacteristic, complemented
294C2×#324C2×C4311yescharacteristic, complemented
295#1294C2×C4311yescharacteristic, complemented
296C2×C43—21no—
297C2×C43—21no—
298C2×C43—21no—
299C2×C43—21no—
300C2×C43—84no—
301C2×C43—161no—
302C2×C43#159712yes—
303C2×C43#159812yes—
304C2×C43#199911yescharacteristic
305C2×C43#200311yescharacteristic
306C2×C43#202111yescharacteristic
307C23×D4C22×C4311yescharacteristic
308C22×D8—21no—
309C2×#123—21no—
310C2×#121C22×C4311yescharacteristic
311C22×C4⋊C4C22×C4311yescharacteristic
312C22×C22⋊C4—21no—
313C22×C22⋊C4—21no—
314#447—22no—
315#447—22no—
316C2×#102—21no—
317C2×#102—22no—
318C2×C22⋊C8C22×C4311yescharacteristic
319C2×C22⋊C8C22×C4311yescharacteristic
320#398—21no—
321#396—22no—
322#394—21no—
323#394—22no—
324#394—22no—
325#386—21no—
326#380C22×C4311yescharacteristic
327C2×#95C22×C4311yescharacteristic
328#327—22no—
329#324—22no—
330C43#991511yescharacteristic, direct product factor, Sylow
331C25—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—21no—
337C22×D4—21no—
338C22×D4—44no—
339C22×D4D4×C4311yescharacteristic
340C22×D4D4×C4312yes—
341C23×C4—21no—
342C23×C4D4×C4311yescharacteristic
343C23×C4D4×C4311yescharacteristic
344C23×C4C23×C4311yescharacteristic
345C2×D8—24no—
346C2×D8—44no—
347C22×C8—21no—
348C22×C8—21no—
349#123—42no—
350#123—42no—
351#121—21no—
352#121—21no—
353#121—21no—
354#121—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4D4×C4311yescharacteristic
363C2×C4⋊C4D4×C4312yes—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—42no—
373#102—24no—
374#102—44no—
375C22⋊C8—21no—
376C22⋊C8—21no—
377C22⋊C8—21no—
378C22⋊C8D4×C4312yes—
379#95—22no—
380#95—21no—
381#95—21no—
382#95D4×C4312yes—
383C24—24no—
384C24—22no—
385C24—21no—
386C24—42no—
387C24—42no—
388C24—42no—
389C24—41no—
390C24—41no—
391C24—41no—
392C24—41no—
393C24—41no—
394C24—41no—
395C24C2×D4×C4311yescharacteristic
396C2×D4—24no—
397C2×D4—24no—
398C2×D4—22no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—21no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—44no—
406C2×D4—44no—
407C2×D4—44no—
408C2×D4—44no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4D8×C4312yescomplemented
436C22×C4C2×D4×C4311yescharacteristic
437C22×C4C2×D4×C4311yescharacteristic
438C22×C4C2×D4×C4311yescharacteristic
439C22×C4C2×D4×C4311yescharacteristic
440C22×C4C2×D4×C4311yescharacteristic
441C22×C4#41×C4311yescharacteristic
442D8—48no—
443C2×C8—22no—
444C2×C8—42no—
445C2×C8—42no—
446C2×C8—41no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—42no—
450C4⋊C4—44no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C22⋊C4—48no—
456C22⋊C4—44no—
457C22⋊C4—48no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—41no—
462C22⋊C4—82no—
463C23—22no—
464C23—22no—
465C23—24no—
466C23—42no—
467C23—44no—
468C23—44no—
469C23—44no—
470C23—44no—
471C23—44no—
472C23—42no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—44no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—42no—
482C23—42no—
483C23—82no—
484C23—82no—
485C23—82no—
486C23—82no—
487C23—82no—
488C23—81no—
489C23—81no—
490C23—82no—
491C23—81no—
492C23—81no—
493C23#120×C4311yescharacteristic
494C23#120×C4311yescharacteristic
495C23#121×C4311yescharacteristic
496C23C2×D8×C4311yescharacteristic
497C23#135×C4311yescharacteristic
498C23AGL(1,ℤ/8)×C4311yescharacteristic
499C23AGL(1,ℤ/8)×C4311yescharacteristic
500D4—24no—
501D4—24no—
502D4—42no—
503D4—44no—
504D4—42no—
505D4—44no—
506D4—42no—
507D4—81no—
508D4—81no—
509D4—81no—
510D4—81no—
511D4—81no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4—81no—
540C2×C4#120×C4311yescharacteristic
541C2×C4#121×C4311yescharacteristic
542C2×C4#121×C4311yescharacteristic
543C2×C4#127×C4311yescharacteristic
544C8—42no—
545C8—81no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—44no—
555C22—44no—
556C22—44no—
557C22—82no—
558C22—82no—
559C22—84no—
560C22—84no—
561C22—84no—
562C22—84no—
563C22—82no—
564C22—82no—
565C22—82no—
566C22—82no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22C43×#39211yescharacteristic
571C22C43×#44711yescharacteristic
572C22C43×#44711yescharacteristic
573C22C43×#44911yescharacteristic
574C22C43×#44911yescharacteristic
575C22C43×#45412yes—
576C22C43×B(4,𝔽2)12yes—
577C22C43×#46611yescharacteristic
578C22C43×#46911yescharacteristic
579C4—21no—
580C4—21no—
581C4—21no—
582C4—21no—
583C4—42no—
584C4—82no—
585C4—82no—
586C4—81no—
587C4—81no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—84no—
593C2—161no—
594C2C43×#159712yes—
595C2C43×#159812yes—
596C2C43×#199911yescharacteristic
597C2C43×#200311yescharacteristic
598C2C43×#202111yescharacteristic
subgroupG/H
center, socleC23×C43#120
commutator, Frattini, cosocleC23×C4C23×C43
prime radicalC2×C43×#447C2
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
2. C43×#2618C2semidirect
3. C2×C43×#394C2semidirect
4. C43×#1786C2semidirect
5. C2×C43×#327C2semidirect
6. C2×C43×#324C2semidirect
7. C43×#1294C2semidirect
135. C22×C4×C43D8semidirect
246. #9915C43direct (N × H)
290. #2618C2×C43semidirect
291. C2×#394C2×C43semidirect
292. #1786C2×C43semidirect
293. C2×#327C2×C43semidirect
294. C2×#324C2×C43semidirect
295. #1294C2×C43semidirect
330. C43#9915direct (N × H)
435. C22×C4D8×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4472
C43×#26182
C2×C43×#3942
C43×#17862
C2×C43×#3272
C2×C43×#3242
C43×#12942
#991543