Finite Group Databasebeta

← C43×#25949 #24945966

Subgroups — C43×#25949 #24945966

Order 11008.

1202 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3501C211yesmaximal, characteristic, complemented
2C43×#2561C212yesmaximal, complemented
3C43×#2534C211yesmaximal, characteristic
4C43×#2030C212yesmaximal, complemented
5C43×#2029C212yesmaximal, complemented
6C43×#1996C212yesmaximal, complemented
7C43×#1890C212yesmaximal, complemented
8C43×#1889C212yesmaximal
9C4×#99×C43C211yesmaximal, characteristic, complemented
10C43×#554—24no—
11C43×#554—22no—
12D4×Q8×C43—22no—
13C43×#544—21no—
14C43×#543—21no—
15C43×#543C2212yes—
16C43×#533—21no—
17C2×#123×C43C2211yescharacteristic
18C2×C22⋊Q8×C43—21no—
19C2×C22⋊Q8×C43C2212yes—
20C2×#120×C43C2211yescharacteristic
21C43×#518C2212yes—
22C2×C4×D4×C43C2211yescharacteristic
23C22×C22⋊C4×C43C2211yescharacteristic
24C2×#99×C43C2212yes—
25C43×#397—22no—
26C43×#396—21no—
27C43×#394—21no—
28C43×#393—22no—
29C43×#388—24no—
30C43×#388—21no—
31C43×#386—21no—
32C43×#381C2214yes—
33C43×#381C2211yescharacteristic
34C43×#380C2211yescharacteristic
35C43×#379C2214yes—
36C43×#379C2211yescharacteristic
37C4×C22⋊C4×C43C2212yes—
38C43×#342C2214yes—
39C43×#342C2214yes—
40C43×#342C2212yes—
41C25×C43C2311yescharacteristic
42C22×Q8×C43—21no—
43C22×Q8×C43D412yescomplemented
44C22×D4×C43—21no—
45C22×D4×C43C2311yescharacteristic
46C23×C4×C43D411yescharacteristic
47C23×C4×C43C2311yescharacteristic
48C23×C4×C43C2311yescharacteristic
49C4⋊Q8×C43—21no—
50C4⋊Q8×C43—21no—
51C4⋊Q8×C43—24no—
52#125×C43—22no—
53#125×C43—24no—
54#123×C43—24no—
55C22⋊Q8×C43—22no—
56C22⋊Q8×C43—22no—
57C22⋊Q8×C43—24no—
58C22⋊Q8×C43—24no—
59C22⋊Q8×C43—22no—
60C22⋊Q8×C43—22no—
61C22⋊Q8×C43—22no—
62C22⋊Q8×C43—22no—
63C22⋊Q8×C43—22no—
64C22⋊Q8×C43—22no—
65C22⋊Q8×C43—24no—
66C22⋊Q8×C43—24no—
67#120×C43—24no—
68C4×Q8×C43—22no—
69C4×Q8×C43—22no—
70C4×D4×C43—22no—
71C4×D4×C43—22no—
72C4×D4×C43—24no—
73C4×D4×C43—24no—
74#117×C43—22no—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43—22no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43D411yescharacteristic
80C2×C4⋊C4×C43D414yescomplemented
81C2×C4⋊C4×C43D412yescomplemented
82C2×C22⋊C4×C43—22no—
83C2×C22⋊C4×C43—21no—
84C2×C22⋊C4×C43—21no—
85C2×C22⋊C4×C43—22no—
86C2×C22⋊C4×C43—22no—
87C2×C22⋊C4×C43—21no—
88C2×C22⋊C4×C43—21no—
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—24no—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—24no—
93C2×C22⋊C4×C43D411yescharacteristic
94C2×C22⋊C4×C43C2311yescharacteristic
95C2×C22⋊C4×C43C2311yescharacteristic
96C2×C22⋊C4×C43C2314yes—
97C2×C22⋊C4×C43C2311yescharacteristic
98C2×C22⋊C4×C43C2314yes—
99C2×C42×C43—22no—
100C2×C42×C43D411yescharacteristic
101#99×C43—24no—
102#95×C43—22no—
103#95×C43—21no—
104#95×C43—21no—
105#95×C43—24no—
106#95×C43—21no—
107#95×C43—24no—
108C24×C43—22no—
109C24×C43—21no—
110C24×C43—22no—
111C24×C43—22no—
112C24×C43—42no—
113C24×C43—81no—
114C24×C43C2×D411yescharacteristic
115C24×C43C2411yescharacteristic
116C2×Q8×C43—22no—
117C2×Q8×C43—22no—
118C2×Q8×C43—22no—
119C2×Q8×C43—22no—
120C2×Q8×C43—82no—
121C2×Q8×C43—82no—
122C2×D4×C43—22no—
123C2×D4×C43—22no—
124C2×D4×C43—42no—
125C2×D4×C43—42no—
126C2×D4×C43—81no—
127C2×D4×C43#4114yes—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—22no—
133C22×C4×C43—24no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—81no—
140C22×C4×C43—81no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D414yes—
145C22×C4×C43C2×D414yes—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D412yes—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D411yescharacteristic
150C4⋊C4×C43—22no—
151C4⋊C4×C43—24no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—24no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—24no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43—24no—
161C4⋊C4×C43—42no—
162C4⋊C4×C43—81no—
163C22⋊C4×C43—24no—
164C22⋊C4×C43—22no—
165C22⋊C4×C43—24no—
166C22⋊C4×C43—22no—
167C22⋊C4×C43—24no—
168C22⋊C4×C43—24no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—24no—
172C22⋊C4×C43—48no—
173C22⋊C4×C43—42no—
174C22⋊C4×C43—41no—
175C22⋊C4×C43—41no—
176C22⋊C4×C43—42no—
177C22⋊C4×C43—42no—
178C22⋊C4×C43—42no—
179C22⋊C4×C43—81no—
180C22⋊C4×C43—84no—
181C42×C43—24no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—82no—
185C23×C43—21no—
186C23×C43—21no—
187C23×C43—24no—
188C23×C43—22no—
189C23×C43—41no—
190C23×C43—41no—
191C23×C43—41no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43—44no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—42no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—44no—
202C23×C43—84no—
203C23×C43—84no—
204C23×C43#12412yes—
205C23×C43C22×D411yescharacteristic
206C23×C43C22×D412yes—
207C23×C43C2×#4112yes—
208C23×C432−1+412yes—
209Q8×C43—44no—
210Q8×C43—82no—
211Q8×C43—82no—
212Q8×C43—82no—
213D4×C43—28no—
214D4×C43—84no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—24no—
219C2×C4×C43—24no—
220C2×C4×C43—21no—
221C2×C4×C43—42no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—44no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—44no—
230C2×C4×C43—44no—
231C2×C4×C43—41no—
232C2×C4×C43—44no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—44no—
242C2×C4×C43—44no—
243C2×C4×C43—81no—
244C2×C4×C43—82no—
245C2×C4×C43—82no—
246C2×C4×C43#12011yescharacteristic
247C2×C4×C43#12011yescharacteristic
248C2×C4×C43#12012yes—
249C2×C4×C43#12412yes—
250#25949C4311yesmaximal, characteristic, direct product factor, Sylow
251C22×C43—21no—
252C22×C43—22no—
253C22×C43—21no—
254C22×C43—22no—
255C22×C43—22no—
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—48no—
260C22×C43—42no—
261C22×C43—42no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—42no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—84no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43C2×#12011yescharacteristic
272C22×C43C2×#12411yescharacteristic
273C22×C43#53611yescharacteristic
274C22×C43#54814yes—
275C4×C43—22no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—22no—
279C4×C43—44no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—44no—
283C4×C43—81no—
284C4×C43—84no—
285C4×C43—81no—
286C4×C43—81no—
287#3501C2×C4311yescharacteristic, complemented
288#2561C2×C4312yescomplemented
289#2534C2×C4311yescharacteristic
290#2030C2×C4312yescomplemented
291#2029C2×C4312yescomplemented
292#1996C2×C4312yescomplemented
293#1890C2×C4312yescomplemented
294#1889C2×C4312yes—
295C4×#99C2×C4311yescharacteristic, complemented
296C2×C43—21no—
297C2×C43—24no—
298C2×C43—21no—
299C2×C43—42no—
300C2×C43—82no—
301C2×C43#243611yescharacteristic
302C2×C43#302511yescharacteristic
303C2×C43#302611yescharacteristic
304#554—24no—
305#554—22no—
306D4×Q8—22no—
307#544—21no—
308#543—21no—
309#543C22×C4312yes—
310#533—21no—
311C2×#123C22×C4311yescharacteristic
312C2×C22⋊Q8—21no—
313C2×C22⋊Q8C22×C4312yes—
314C2×#120C22×C4311yescharacteristic
315#518C22×C4312yes—
316C2×C4×D4C22×C4311yescharacteristic
317C22×C22⋊C4C22×C4311yescharacteristic
318C2×#99C22×C4312yes—
319#397—22no—
320#396—21no—
321#394—21no—
322#393—22no—
323#388—24no—
324#388—21no—
325#386—21no—
326#381C22×C4314yes—
327#381C22×C4311yescharacteristic
328#380C22×C4311yescharacteristic
329#379C22×C4314yes—
330#379C22×C4311yescharacteristic
331C4×C22⋊C4C22×C4312yes—
332#342C22×C4314yes—
333#342C22×C4314yes—
334#342C22×C4312yes—
335C43#2594911yescharacteristic, direct product factor, Sylow
336C25C23×C4311yescharacteristic
337C22×Q8—21no—
338C22×Q8D4×C4312yescomplemented
339C22×D4—21no—
340C22×D4C23×C4311yescharacteristic
341C23×C4D4×C4311yescharacteristic
342C23×C4C23×C4311yescharacteristic
343C23×C4C23×C4311yescharacteristic
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—24no—
347#125—22no—
348#125—24no—
349#123—24no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8—24no—
353C22⋊Q8—24no—
354C22⋊Q8—22no—
355C22⋊Q8—22no—
356C22⋊Q8—22no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360C22⋊Q8—24no—
361C22⋊Q8—24no—
362#120—24no—
363C4×Q8—22no—
364C4×Q8—22no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—24no—
368C4×D4—24no—
369#117—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4D4×C4311yescharacteristic
375C2×C4⋊C4D4×C4314yescomplemented
376C2×C4⋊C4D4×C4312yescomplemented
377C2×C22⋊C4—22no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4D4×C4311yescharacteristic
389C2×C22⋊C4C23×C4311yescharacteristic
390C2×C22⋊C4C23×C4311yescharacteristic
391C2×C22⋊C4C23×C4314yes—
392C2×C22⋊C4C23×C4311yescharacteristic
393C2×C22⋊C4C23×C4314yes—
394C2×C42—22no—
395C2×C42D4×C4311yescharacteristic
396#99—24no—
397#95—22no—
398#95—21no—
399#95—21no—
400#95—24no—
401#95—21no—
402#95—24no—
403C24—22no—
404C24—21no—
405C24—22no—
406C24—22no—
407C24—42no—
408C24—81no—
409C24C2×D4×C4311yescharacteristic
410C24C24×C4311yescharacteristic
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—82no—
416C2×Q8—82no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—81no—
422C2×D4#41×C4314yes—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—81no—
435C22×C4—81no—
436C22×C4C2×D4×C4311yescharacteristic
437C22×C4C2×D4×C4311yescharacteristic
438C22×C4C2×D4×C4311yescharacteristic
439C22×C4C2×D4×C4314yes—
440C22×C4C2×D4×C4314yes—
441C22×C4C2×D4×C4311yescharacteristic
442C22×C4C2×D4×C4312yes—
443C22×C4C2×D4×C4312yes—
444C22×C4C2×D4×C4311yescharacteristic
445C4⋊C4—22no—
446C4⋊C4—24no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—24no—
450C4⋊C4—22no—
451C4⋊C4—24no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—24no—
456C4⋊C4—42no—
457C4⋊C4—81no—
458C22⋊C4—24no—
459C22⋊C4—24no—
460C22⋊C4—22no—
461C22⋊C4—24no—
462C22⋊C4—22no—
463C22⋊C4—24no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—24no—
467C22⋊C4—48no—
468C22⋊C4—42no—
469C22⋊C4—42no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C22⋊C4—81no—
475C22⋊C4—84no—
476C42—24no—
477C42—21no—
478C42—21no—
479C42—82no—
480C23—21no—
481C23—21no—
482C23—24no—
483C23—22no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—44no—
489C23—41no—
490C23—41no—
491C23—42no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—44no—
497C23—84no—
498C23—84no—
499C23#124×C4312yes—
500C23C22×D4×C4311yescharacteristic
501C23C22×D4×C4312yes—
502C23C2×#41×C4312yes—
503C232−1+4×C4312yes—
504Q8—44no—
505Q8—82no—
506Q8—82no—
507Q8—82no—
508D4—28no—
509D4—84no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—21no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—44no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4—44no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—81no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4#120×C4311yescharacteristic
542C2×C4#120×C4311yescharacteristic
543C2×C4#120×C4312yes—
544C2×C4#124×C4312yes—
545C22—22no—
546C22—21no—
547C22—22no—
548C22—21no—
549C22—22no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—48no—
555C22—42no—
556C22—41no—
557C22—41no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—84no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22C2×#120×C4311yescharacteristic
566C22C2×#124×C4311yescharacteristic
567C22C43×#53611yescharacteristic
568C22C43×#54814yes—
569C4—22no—
570C4—21no—
571C4—21no—
572C4—22no—
573C4—44no—
574C4—41no—
575C4—41no—
576C4—44no—
577C4—81no—
578C4—81no—
579C4—84no—
580C4—81no—
581C2—21no—
582C2—24no—
583C2—21no—
584C2—42no—
585C2—82no—
586C2C43×#243611yescharacteristic
587C2C43×#302511yescharacteristic
588C2C43×#302611yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC24C24×C43
prime radicalC2×#120×C43C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3501C2semidirect
2. C43×#2561C2semidirect
4. C43×#2030C2semidirect
5. C43×#2029C2semidirect
6. C43×#1996C2semidirect
7. C43×#1890C2semidirect
9. C4×#99×C43C2semidirect
43. C22×Q8×C43D4semidirect
80. C2×C4⋊C4×C43D4semidirect
81. C2×C4⋊C4×C43D4semidirect
250. #25949C43direct (N × H)
287. #3501C2×C43semidirect
288. #2561C2×C43semidirect
290. #2030C2×C43semidirect
291. #2029C2×C43semidirect
292. #1996C2×C43semidirect
293. #1890C2×C43semidirect
295. C4×#99C2×C43semidirect
335. C43#25949direct (N × H)
338. C22×Q8D4×C43semidirect
375. C2×C4⋊C4D4×C43semidirect
376. C2×C4⋊C4D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#35012
C43×#25612
C43×#25342
C43×#20302
C43×#20292
C43×#19962
C43×#18902
C43×#18892
C4×#99×C432
#2594943