Finite Group Databasebeta

← C43×#15881 #24935898

Subgroups — C43×#15881 #24935898

Order 11008.

1370 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#125×C43C211yesmaximal, characteristic
2C2×C43×#400C211yesmaximal, characteristic
3C2×C43×#398C211yesmaximal, characteristic
4C2×C43×#382C211yesmaximal, characteristic
5C43×#1445C211yesmaximal, characteristic
6C43×#1442C212yesmaximal
7C43×#1442C212yesmaximal
8C43×#1441C212yesmaximal
9C43×#1436C212yesmaximal
10C43×#1436C211yesmaximal, characteristic
11C43×#1436C211yesmaximal, characteristic
12C2×#125×C43—24no—
13C2×#125×C43—24no—
14C2×#125×C43—24no—
15C22×C4⋊C4×C43C2211yescharacteristic
16C22×C4⋊C4×C43C2212yes—
17C22×C4⋊C4×C43C2211yescharacteristic
18C22×C4⋊C4×C43C2211yescharacteristic
19C22×C4⋊C4×C43C2211yescharacteristic
20C22×C4⋊C4×C43C2211yescharacteristic
21C22×C4⋊C4×C43C2211yescharacteristic
22C22×C4⋊C4×C43C2211yescharacteristic
23C22×C42×C43C2211yescharacteristic
24C22×C42×C43C2211yescharacteristic
25C43×#400—24no—
26C43×#398—24no—
27C43×#382—24no—
28C2×#95×C43C2211yescharacteristic
29C2×#95×C43C2212yes—
30C2×#95×C43C2212yes—
31C2×#95×C43C2211yescharacteristic
32C2×#95×C43C2212yes—
33C2×#95×C43C2212yes—
34C2×#95×C43C2212yes—
35C2×#95×C43C2212yes—
36C2×#95×C43C2212yes—
37C2×#95×C43C2212yes—
38C2×#95×C43C2212yes—
39C2×#95×C43C2212yes—
40C2×#95×C43C2212yes—
41C23×C4×C43C2312yes—
42C23×C4×C43C2312yes—
43C23×C4×C43C2311yescharacteristic
44C23×C4×C43C2311yescharacteristic
45C23×C4×C43C2311yescharacteristic
46C23×C4×C43C2311yescharacteristic
47C23×C4×C43C2311yescharacteristic
48C23×C4×C43C2312yes—
49C23×C4×C43C2312yes—
50C23×C4×C43C2311yescharacteristic
51C23×C4×C43C2311yescharacteristic
52#125×C43—232no—
53C2×C4⋊C4×C43—22no—
54C2×C4⋊C4×C43—22no—
55C2×C4⋊C4×C43—22no—
56C2×C4⋊C4×C43—22no—
57C2×C4⋊C4×C43—22no—
58C2×C4⋊C4×C43—22no—
59C2×C4⋊C4×C43—22no—
60C2×C4⋊C4×C43—22no—
61C2×C4⋊C4×C43—22no—
62C2×C4⋊C4×C43—22no—
63C2×C4⋊C4×C43—22no—
64C2×C4⋊C4×C43—22no—
65C2×C4⋊C4×C43—22no—
66C2×C4⋊C4×C43—22no—
67C2×C4⋊C4×C43—22no—
68C2×C4⋊C4×C43—22no—
69C2×C4⋊C4×C43—22no—
70C2×C4⋊C4×C43—24no—
71C2×C4⋊C4×C43—22no—
72C2×C4⋊C4×C43—24no—
73C2×C4⋊C4×C43—24no—
74C2×C4⋊C4×C43D414yes—
75C2×C4⋊C4×C43D414yes—
76C2×C4⋊C4×C43D414yes—
77C2×C42×C43—22no—
78C2×C42×C43—22no—
79C2×C42×C43—22no—
80C2×C42×C43—22no—
81C2×C42×C43—24no—
82#95×C43—24no—
83#95×C43—24no—
84#95×C43—22no—
85#95×C43—24no—
86#95×C43—22no—
87#95×C43—24no—
88#95×C43—24no—
89#95×C43—24no—
90#95×C43—24no—
91#95×C43—24no—
92#95×C43—24no—
93#95×C43—24no—
94#95×C43—24no—
95C24×C43C2411yescharacteristic
96C22×C4×C43—21no—
97C22×C4×C43—21no—
98C22×C4×C43—22no—
99C22×C4×C43—22no—
100C22×C4×C43—21no—
101C22×C4×C43—21no—
102C22×C4×C43—21no—
103C22×C4×C43—21no—
104C22×C4×C43—21no—
105C22×C4×C43—21no—
106C22×C4×C43—21no—
107C22×C4×C43—21no—
108C22×C4×C43—21no—
109C22×C4×C43—21no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43C2×D412yes—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D412yes—
150C22×C4×C43C2×D412yes—
151C22×C4×C43C2×D412yes—
152C22×C4×C43C2×D412yes—
153C22×C4×C43C2×D412yes—
154C22×C4×C43C2×D412yes—
155C22×C4×C43C2×D412yes—
156C22×C4×C43#4114yes—
157C22×C4×C43#4114yes—
158C22×C4×C43#4114yes—
159C4⋊C4×C43—28no—
160C4⋊C4×C43—28no—
161C4⋊C4×C43—28no—
162C4⋊C4×C43—28no—
163C4⋊C4×C43—28no—
164C4⋊C4×C43—28no—
165C4⋊C4×C43—44no—
166C4⋊C4×C43—48no—
167C42×C43—28no—
168C42×C43—28no—
169C23×C43C22×D411yescharacteristic
170C23×C43C22×D411yescharacteristic
171C23×C43C22×D411yescharacteristic
172C23×C43C2×#4112yes—
173C23×C43C2×#4112yes—
174C23×C43C2×#4112yes—
175C23×C432−1+412yes—
176C23×C432−1+412yes—
177C23×C432−1+412yes—
178C2×C4×C43—22no—
179C2×C4×C43—22no—
180C2×C4×C43—22no—
181C2×C4×C43—22no—
182C2×C4×C43—24no—
183C2×C4×C43—24no—
184C2×C4×C43—24no—
185C2×C4×C43—24no—
186C2×C4×C43—22no—
187C2×C4×C43—22no—
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—22no—
191C2×C4×C43—24no—
192C2×C4×C43—24no—
193C2×C4×C43—22no—
194C2×C4×C43—22no—
195C2×C4×C43—24no—
196C2×C4×C43—24no—
197C2×C4×C43—24no—
198C2×C4×C43—24no—
199C2×C4×C43—24no—
200C2×C4×C43—24no—
201C2×C4×C43—24no—
202C2×C4×C43—24no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43#12014yes—
240C2×C4×C43#12414yes—
241#15881C4311yesmaximal, characteristic, direct product factor, Sylow
242C22×C43C2×#12011yescharacteristic
243C22×C43#52511yescharacteristic
244C22×C43C2×#12411yescharacteristic
245C22×C43#52912yes—
246C22×C43#53211yescharacteristic
247C22×C43#53611yescharacteristic
248C22×C43#53611yescharacteristic
249C22×C43#53611yescharacteristic
250C22×C43#54112yes—
251C22×C43#54112yes—
252C22×C43#54112yes—
253C22×C43#54712yes—
254C22×C43#54712yes—
255C22×C43#54712yes—
256C22×C43#54812yes—
257C22×C43#54812yes—
258C22×C43#54812yes—
259C22×C43#55212yes—
260C22×C43#55212yes—
261C22×C43#55212yes—
262C22×C43#56412yes—
263C4×C43—24no—
264C4×C43—24no—
265C4×C43—42no—
266C4×C43—42no—
267C4×C43—42no—
268C4×C43—42no—
269C4×C43—42no—
270C4×C43—44no—
271C4×C43—44no—
272C4×C43—82no—
273C4×C43—82no—
274C22×#125C2×C4311yescharacteristic
275C2×#400C2×C4311yescharacteristic
276C2×#398C2×C4311yescharacteristic
277C2×#382C2×C4311yescharacteristic
278#1445C2×C4311yescharacteristic
279#1442C2×C4312yes—
280#1442C2×C4312yes—
281#1441C2×C4312yes—
282#1436C2×C4312yes—
283#1436C2×C4311yescharacteristic
284#1436C2×C4311yescharacteristic
285C2×C43#240611yescharacteristic
286C2×C43#243211yescharacteristic
287C2×C43#243611yescharacteristic
288C2×C43#247512yes—
289C2×C43#248912yes—
290C2×C43#251912yes—
291C2×C43#271912yes—
292C2×C43#271912yes—
293C2×C43#271912yes—
294C2×#125—24no—
295C2×#125—24no—
296C2×#125—24no—
297C22×C4⋊C4C22×C4311yescharacteristic
298C22×C4⋊C4C22×C4312yes—
299C22×C4⋊C4C22×C4311yescharacteristic
300C22×C4⋊C4C22×C4311yescharacteristic
301C22×C4⋊C4C22×C4311yescharacteristic
302C22×C4⋊C4C22×C4311yescharacteristic
303C22×C4⋊C4C22×C4311yescharacteristic
304C22×C4⋊C4C22×C4311yescharacteristic
305C22×C42C22×C4311yescharacteristic
306C22×C42C22×C4311yescharacteristic
307#400—24no—
308#398—24no—
309#382—24no—
310C2×#95C22×C4311yescharacteristic
311C2×#95C22×C4312yes—
312C2×#95C22×C4312yes—
313C2×#95C22×C4311yescharacteristic
314C2×#95C22×C4312yes—
315C2×#95C22×C4312yes—
316C2×#95C22×C4312yes—
317C2×#95C22×C4312yes—
318C2×#95C22×C4312yes—
319C2×#95C22×C4312yes—
320C2×#95C22×C4312yes—
321C2×#95C22×C4312yes—
322C2×#95C22×C4312yes—
323C43#1588111yescharacteristic, direct product factor, Sylow
324C23×C4C23×C4312yes—
325C23×C4C23×C4312yes—
326C23×C4C23×C4311yescharacteristic
327C23×C4C23×C4311yescharacteristic
328C23×C4C23×C4311yescharacteristic
329C23×C4C23×C4311yescharacteristic
330C23×C4C23×C4311yescharacteristic
331C23×C4C23×C4312yes—
332C23×C4C23×C4312yes—
333C23×C4C23×C4311yescharacteristic
334C23×C4C23×C4311yescharacteristic
335#125—232no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4D4×C4314yes—
358C2×C4⋊C4D4×C4314yes—
359C2×C4⋊C4D4×C4314yes—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—24no—
365#95—24no—
366#95—24no—
367#95—22no—
368#95—24no—
369#95—22no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—24no—
378C24C24×C4311yescharacteristic
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4C2×D4×C4312yes—
431C22×C4C2×D4×C4312yes—
432C22×C4C2×D4×C4312yes—
433C22×C4C2×D4×C4312yes—
434C22×C4C2×D4×C4312yes—
435C22×C4C2×D4×C4312yes—
436C22×C4C2×D4×C4312yes—
437C22×C4C2×D4×C4312yes—
438C22×C4C2×D4×C4312yes—
439C22×C4#41×C4314yes—
440C22×C4#41×C4314yes—
441C22×C4#41×C4314yes—
442C4⋊C4—28no—
443C4⋊C4—28no—
444C4⋊C4—28no—
445C4⋊C4—28no—
446C4⋊C4—28no—
447C4⋊C4—28no—
448C4⋊C4—44no—
449C4⋊C4—48no—
450C42—28no—
451C42—28no—
452C23C22×D4×C4311yescharacteristic
453C23C22×D4×C4311yescharacteristic
454C23C22×D4×C4311yescharacteristic
455C23C2×#41×C4312yes—
456C23C2×#41×C4312yes—
457C23C2×#41×C4312yes—
458C232−1+4×C4312yes—
459C232−1+4×C4312yes—
460C232−1+4×C4312yes—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4#120×C4314yes—
523C2×C4#124×C4314yes—
524C22C2×#120×C4311yescharacteristic
525C22C43×#52511yescharacteristic
526C22C2×#124×C4311yescharacteristic
527C22C43×#52912yes—
528C22C43×#53211yescharacteristic
529C22C43×#53611yescharacteristic
530C22C43×#53611yescharacteristic
531C22C43×#53611yescharacteristic
532C22C43×#54112yes—
533C22C43×#54112yes—
534C22C43×#54112yes—
535C22C43×#54712yes—
536C22C43×#54712yes—
537C22C43×#54712yes—
538C22C43×#54812yes—
539C22C43×#54812yes—
540C22C43×#54812yes—
541C22C43×#55212yes—
542C22C43×#55212yes—
543C22C43×#55212yes—
544C22C43×#56412yes—
545C4—24no—
546C4—24no—
547C4—42no—
548C4—42no—
549C4—42no—
550C4—42no—
551C4—42no—
552C4—44no—
553C4—44no—
554C4—82no—
555C4—82no—
556C2C43×#240611yescharacteristic
557C2C43×#243211yescharacteristic
558C2C43×#243611yescharacteristic
559C2C43×#247512yes—
560C2C43×#248912yes—
561C2C43×#251912yes—
562C2C43×#271912yes—
563C2C43×#271912yes—
564C2C43×#271912yes—
subgroupG/H
center, socle, prime radicalC24×C43C24
commutator, Frattini, cosocleC24C24×C43
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
241. #15881C43direct (N × H)
323. C43#15881direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#125×C432
C2×C43×#4002
C2×C43×#3982
C2×C43×#3822
C43×#14452
C43×#14422
C43×#14412
C43×#14362
#1588143