Finite Group Databasebeta

← C43×#19030 #24939047

Subgroups — C43×#19030 #24939047

Order 11008.

902 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3559C211yesmaximal, characteristic, complemented
2C43×#3214C211yesmaximal, characteristic, complemented
3C43×#3171C211yesmaximal, characteristic, complemented
4C43×#3142C211yesmaximal, characteristic, complemented
5C43×#1664C212yesmaximal, complemented
6C43×#1662C212yesmaximal, complemented
7C43×#1657C212yesmaximal, complemented
8C43×#1656C212yesmaximal, complemented
9C43×#1529C211yesmaximal, characteristic, complemented
10C43×#1528C211yesmaximal, characteristic, complemented
11C43×#1525C211yesmaximal, characteristic, complemented
12C43×#563C2212yes—
13C43×#562C2212yes—
14C43×#554—21no—
15C43×#553—21no—
16C43×#553—21no—
17C43×#547—22no—
18C43×#547—21no—
19C43×#544—21no—
20C43×#540—21no—
21C43×#539—22no—
22C43×#539—21no—
23C43×#537—21no—
24C43×#532C2211yescharacteristic
25C43×#532C2211yescharacteristic
26C43×#529C2211yescharacteristic
27C2×#125×C43C2211yescharacteristic
28C43×#501C2211yescharacteristic
29C43×#496C2211yescharacteristic
30C43×#496C2212yes—
31C43×#491C2212yes—
32C43×#490C2212yes—
33C43×#490C2211yescharacteristic
34C43×#489C2211yescharacteristic
35C43×#489C2212yes—
36C43×#488—22no—
37C43×#469—21no—
38C43×#468—21no—
39C43×#461—21no—
40C43×#459—21no—
41C43×#449—22no—
42C4×SD16×C43—21no—
43C4×D8×C43—21no—
44C43×#432C2211yescharacteristic
45C43×#417—21no—
46C43×#417—21no—
47C4×M16×C43C2211yescharacteristic
48C4×M16×C43C2211yescharacteristic
49C43×#330C2212yes—
50C43×#330C2212yes—
51C43×#330C2212yes—
52C43×#329C2212yes—
53C43×#329C2212yes—
54C43×#329C2212yes—
55C2×#41×C43—22no—
56C2×#41×C43—21no—
57C2×#41×C43D412yes—
58C2×SD16×C43—21no—
59C2×SD16×C43—22no—
60C2×D8×C43—21no—
61C2×D8×C43—22no—
62C2×M16×C43—21no—
63C2×M16×C43—21no—
64C4⋊Q8×C43—21no—
65C4⋊Q8×C43—22no—
66C4⋊Q8×C43D411yescharacteristic
67C4⋊Q8×C43C2311yescharacteristic
68#127×C43D411yescharacteristic
69#127×C43C2311yescharacteristic
70#126×C43—22no—
71#126×C43—22no—
72#126×C43—21no—
73#125×C43—22no—
74#125×C43—21no—
75#125×C43—21no—
76#125×C43—21no—
77#125×C43D412yes—
78#125×C43C2311yescharacteristic
79#125×C43C2312yes—
80#124×C43—21no—
81#124×C43C2311yescharacteristic
82#124×C43C2312yes—
83#123×C43—22no—
84#123×C43—22no—
85#123×C43—22no—
86#123×C43—22no—
87#123×C43—21no—
88#123×C43—22no—
89#123×C43—22no—
90C22⋊Q8×C43—22no—
91C22⋊Q8×C43—22no—
92C22⋊Q8×C43—22no—
93C22⋊Q8×C43—22no—
94C22⋊Q8×C43—22no—
95C22⋊Q8×C43—22no—
96C22⋊Q8×C43D411yescharacteristic
97#121×C43—22no—
98#121×C43—22no—
99#121×C43—21no—
100#121×C43—21no—
101#121×C43—22no—
102#121×C43—22no—
103#121×C43—21no—
104#121×C43—21no—
105#121×C43—21no—
106#121×C43—21no—
107#121×C43D411yescharacteristic
108C4×Q8×C43D411yescharacteristic
109C4×D4×C43—22no—
110C4×D4×C43—22no—
111C4×D4×C43—21no—
112C4×D4×C43—21no—
113C4×D4×C43—21no—
114C4×D4×C43—21no—
115C4×D4×C43—21no—
116C4×D4×C43—21no—
117C4×D4×C43—21no—
118C4×D4×C43D411yescharacteristic
119#117×C43—21no—
120#117×C43—21no—
121C2×C4⋊C4×C43—22no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43D411yescharacteristic
126C2×C4⋊C4×C43D411yescharacteristic
127C2×C42×C43C2311yescharacteristic
128#107×C43—21no—
129#106×C43—21no—
130C4⋊C8×C43—21no—
131#103×C43—21no—
132#103×C43—22no—
133#103×C43—22no—
134#103×C43—22no—
135#102×C43—21no—
136#102×C43—22no—
137#102×C43—22no—
138#102×C43—22no—
139#102×C43—21no—
140#102×C43—21no—
141C22⋊C8×C43—21no—
142#97×C43C2311yescharacteristic
143#97×C43C2312yes—
144#97×C43C2311yescharacteristic
145#97×C43C2312yes—
146C4×C8×C43—21no—
147C4×C8×C43—21no—
148#41×C43—44no—
149#41×C43—84no—
150#41×C43—82no—
151C2×Q8×C43—22no—
152C2×Q8×C43—21no—
153C2×Q8×C43C2×D411yescharacteristic
154C2×Q8×C43C2×D412yes—
155C2×D4×C43—22no—
156C2×D4×C43—22no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—22no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—41no—
165C2×D4×C43C2×D411yescharacteristic
166C2×D4×C43C2×D412yes—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—21no—
171C22×C4×C43—22no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—41no—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178SD16×C43—42no—
179SD16×C43—82no—
180D8×C43—42no—
181D8×C43—82no—
182M16×C43—42no—
183M16×C43—42no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—22no—
187C2×C8×C43—22no—
188C4⋊C4×C43—22no—
189C4⋊C4×C43—22no—
190C4⋊C4×C43—22no—
191C4⋊C4×C43—22no—
192C4⋊C4×C43—22no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—22no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—22no—
201C4⋊C4×C43—22no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43C2×D412yes—
207C4⋊C4×C43C2×D412yes—
208C4⋊C4×C43C2×D411yescharacteristic
209C4⋊C4×C43C2×D411yescharacteristic
210C22⋊C4×C43—22no—
211C22⋊C4×C43—22no—
212C22⋊C4×C43—22no—
213C22⋊C4×C43—22no—
214C22⋊C4×C43—22no—
215C22⋊C4×C43—21no—
216C22⋊C4×C43—21no—
217C22⋊C4×C43—21no—
218C22⋊C4×C43—22no—
219C22⋊C4×C43—22no—
220C22⋊C4×C43—21no—
221C22⋊C4×C43—21no—
222C22⋊C4×C43—41no—
223C22⋊C4×C43—41no—
224C42×C43—22no—
225C42×C43—21no—
226C42×C43C2×D411yescharacteristic
227C42×C43C2×D411yescharacteristic
228C42×C43C2×D411yescharacteristic
229C42×C43C2411yescharacteristic
230C23×C43—21no—
231C23×C43—22no—
232C23×C43—41no—
233C23×C43#12011yescharacteristic
234Q8×C43—41no—
235Q8×C43—42no—
236Q8×C43—42no—
237Q8×C43—82no—
238D4×C43—41no—
239D4×C43—42no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—42no—
245D4×C43—44no—
246D4×C43—42no—
247D4×C43—42no—
248D4×C43—81no—
249D4×C43—82no—
250D4×C43—82no—
251D4×C43—82no—
252C2×C4×C43—22no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—22no—
256C2×C4×C43—22no—
257C2×C4×C43—21no—
258C2×C4×C43—22no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—42no—
262C2×C4×C43—42no—
263C2×C4×C43—41no—
264C2×C4×C43—82no—
265C2×C4×C43—81no—
266C2×C4×C43—82no—
267C2×C4×C43—82no—
268C2×C4×C43—82no—
269C2×C4×C43—82no—
270C2×C4×C43#12011yescharacteristic
271C2×C4×C43#12011yescharacteristic
272C2×C4×C43#12011yescharacteristic
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C22×D411yescharacteristic
275C2×C4×C43C22×D411yescharacteristic
276C8×C43—22no—
277C8×C43—42no—
278C8×C43—41no—
279C8×C43—42no—
280#19030C4311yesmaximal, characteristic, direct product factor, Sylow
281C22×C43—21no—
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—41no—
285C22×C43—42no—
286C22×C43—42no—
287C22×C43—41no—
288C22×C43—42no—
289C22×C43—41no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43C2×#12011yescharacteristic
294C4×C43—21no—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—21no—
299C4×C43—41no—
300C4×C43—42no—
301C4×C43—41no—
302C4×C43—42no—
303C4×C43—42no—
304C4×C43—41no—
305C4×C43—81no—
306C4×C43#45412yes—
307#3559C2×C4311yescharacteristic, complemented
308#3214C2×C4311yescharacteristic, complemented
309#3171C2×C4311yescharacteristic, complemented
310#3142C2×C4311yescharacteristic, complemented
311#1664C2×C4312yescomplemented
312#1662C2×C4312yescomplemented
313#1657C2×C4312yescomplemented
314#1656C2×C4312yescomplemented
315#1529C2×C4311yescharacteristic, complemented
316#1528C2×C4311yescharacteristic, complemented
317#1525C2×C4311yescharacteristic, complemented
318C2×C43—41no—
319C2×C43—81no—
320C2×C43—82no—
321C2×C43—161no—
322C2×C43C2×#45411yescharacteristic
323C2×C43#301811yescharacteristic
324C2×C43#301911yescharacteristic
325#563C22×C4312yes—
326#562C22×C4312yes—
327#554—21no—
328#553—21no—
329#553—21no—
330#547—22no—
331#547—21no—
332#544—21no—
333#540—21no—
334#539—22no—
335#539—21no—
336#537—21no—
337#532C22×C4311yescharacteristic
338#532C22×C4311yescharacteristic
339#529C22×C4311yescharacteristic
340C2×#125C22×C4311yescharacteristic
341#501C22×C4311yescharacteristic
342#496C22×C4311yescharacteristic
343#496C22×C4312yes—
344#491C22×C4312yes—
345#490C22×C4312yes—
346#490C22×C4311yescharacteristic
347#489C22×C4311yescharacteristic
348#489C22×C4312yes—
349#488—22no—
350#469—21no—
351#468—21no—
352#461—21no—
353#459—21no—
354#449—22no—
355C4×SD16—21no—
356C4×D8—21no—
357#432C22×C4311yescharacteristic
358#417—21no—
359#417—21no—
360C4×M16C22×C4311yescharacteristic
361C4×M16C22×C4311yescharacteristic
362#330C22×C4312yes—
363#330C22×C4312yes—
364#330C22×C4312yes—
365#329C22×C4312yes—
366#329C22×C4312yes—
367#329C22×C4312yes—
368C43#1903011yescharacteristic, direct product factor, Sylow
369C2×#41—22no—
370C2×#41—21no—
371C2×#41D4×C4312yes—
372C2×SD16—21no—
373C2×SD16—22no—
374C2×D8—21no—
375C2×D8—22no—
376C2×M16—21no—
377C2×M16—21no—
378C4⋊Q8—21no—
379C4⋊Q8—22no—
380C4⋊Q8D4×C4311yescharacteristic
381C4⋊Q8C23×C4311yescharacteristic
382#127D4×C4311yescharacteristic
383#127C23×C4311yescharacteristic
384#126—22no—
385#126—22no—
386#126—21no—
387#125—22no—
388#125—21no—
389#125—21no—
390#125—21no—
391#125D4×C4312yes—
392#125C23×C4312yes—
393#125C23×C4311yescharacteristic
394#124—21no—
395#124C23×C4311yescharacteristic
396#124C23×C4312yes—
397#123—22no—
398#123—22no—
399#123—22no—
400#123—22no—
401#123—21no—
402#123—22no—
403#123—22no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410C22⋊Q8D4×C4311yescharacteristic
411#121—22no—
412#121—22no—
413#121—21no—
414#121—21no—
415#121—22no—
416#121—22no—
417#121—21no—
418#121—21no—
419#121—21no—
420#121—21no—
421#121D4×C4311yescharacteristic
422C4×Q8D4×C4311yescharacteristic
423C4×D4—22no—
424C4×D4—22no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4—21no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4D4×C4311yescharacteristic
433#117—21no—
434#117—21no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4D4×C4311yescharacteristic
440C2×C4⋊C4D4×C4311yescharacteristic
441C2×C42C23×C4311yescharacteristic
442#107—21no—
443#106—21no—
444C4⋊C8—21no—
445#103—21no—
446#103—22no—
447#103—22no—
448#103—22no—
449#102—21no—
450#102—22no—
451#102—22no—
452#102—22no—
453#102—21no—
454#102—21no—
455C22⋊C8—21no—
456#97C23×C4312yes—
457#97C23×C4311yescharacteristic
458#97C23×C4311yescharacteristic
459#97C23×C4312yes—
460C4×C8—21no—
461C4×C8—21no—
462#41—44no—
463#41—84no—
464#41—82no—
465C2×Q8—22no—
466C2×Q8—21no—
467C2×Q8C2×D4×C4311yescharacteristic
468C2×Q8C2×D4×C4312yes—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—41no—
479C2×D4C2×D4×C4311yescharacteristic
480C2×D4C2×D4×C4312yes—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—41no—
489C22×C4C2×D4×C4311yescharacteristic
490C22×C4C2×D4×C4311yescharacteristic
491C22×C4C2×D4×C4311yescharacteristic
492SD16—42no—
493SD16—82no—
494D8—42no—
495D8—82no—
496M16—42no—
497M16—42no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—22no—
501C2×C8—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4C2×D4×C4312yes—
521C4⋊C4C2×D4×C4312yes—
522C4⋊C4C2×D4×C4311yescharacteristic
523C4⋊C4C2×D4×C4311yescharacteristic
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—21no—
536C22⋊C4—41no—
537C22⋊C4—41no—
538C42—22no—
539C42—21no—
540C42C2×D4×C4311yescharacteristic
541C42C2×D4×C4311yescharacteristic
542C42C2×D4×C4311yescharacteristic
543C42C24×C4311yescharacteristic
544C23—21no—
545C23—22no—
546C23—41no—
547C23#120×C4311yescharacteristic
548Q8—41no—
549Q8—42no—
550Q8—42no—
551Q8—82no—
552D4—41no—
553D4—42no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—42no—
559D4—44no—
560D4—42no—
561D4—42no—
562D4—81no—
563D4—82no—
564D4—82no—
565D4—82no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—82no—
579C2×C4—81no—
580C2×C4—82no—
581C2×C4—82no—
582C2×C4—82no—
583C2×C4—82no—
584C2×C4#120×C4311yescharacteristic
585C2×C4#120×C4311yescharacteristic
586C2×C4#120×C4311yescharacteristic
587C2×C4C22×D4×C4311yescharacteristic
588C2×C4C22×D4×C4311yescharacteristic
589C2×C4C22×D4×C4311yescharacteristic
590C8—22no—
591C8—42no—
592C8—41no—
593C8—42no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—41no—
598C22—42no—
599C22—42no—
600C22—41no—
601C22—42no—
602C22—41no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22C2×#120×C4311yescharacteristic
607C4—21no—
608C4—21no—
609C4—21no—
610C4—21no—
611C4—21no—
612C4—41no—
613C4—42no—
614C4—41no—
615C4—42no—
616C4—42no—
617C4—41no—
618C4—81no—
619C4C43×#45412yes—
620C2—41no—
621C2—81no—
622C2—82no—
623C2—161no—
624C2C2×C43×#45411yescharacteristic
625C2C43×#301811yescharacteristic
626C2C43×#301911yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC42C24×C43
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3559C2semidirect
2. C43×#3214C2semidirect
3. C43×#3171C2semidirect
4. C43×#3142C2semidirect
5. C43×#1664C2semidirect
6. C43×#1662C2semidirect
7. C43×#1657C2semidirect
8. C43×#1656C2semidirect
9. C43×#1529C2semidirect
10. C43×#1528C2semidirect
11. C43×#1525C2semidirect
280. #19030C43direct (N × H)
307. #3559C2×C43semidirect
308. #3214C2×C43semidirect
309. #3171C2×C43semidirect
310. #3142C2×C43semidirect
311. #1664C2×C43semidirect
312. #1662C2×C43semidirect
313. #1657C2×C43semidirect
314. #1656C2×C43semidirect
315. #1529C2×C43semidirect
316. #1528C2×C43semidirect
317. #1525C2×C43semidirect
368. C43#19030direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35592
C43×#32142
C43×#31712
C43×#31422
C43×#16642
C43×#16622
C43×#16572
C43×#16562
C43×#15292
C43×#15282
C43×#15252
#1903043