Finite Group Databasebeta

← C43×#27192 #24947209

Subgroups — C43×#27192 #24947209

Order 11008.

784 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2446C211yesmaximal, characteristic, complemented
2C43×#2354C211yesmaximal, characteristic
3C43×#2096C211yesmaximal, characteristic, complemented
4C43×#2072C211yesmaximal, characteristic, complemented
5C43×#2065C211yesmaximal, characteristic
6C43×#2013C211yesmaximal, characteristic
7C43×#1981C211yesmaximal, characteristic, complemented
8C43×#1968C211yesmaximal, characteristic
9C43×#1927C211yesmaximal, characteristic, complemented
10C43×#1920C211yesmaximal, characteristic, complemented
11C43×#1916C211yesmaximal, characteristic, complemented
12C43×#1880C211yesmaximal, characteristic
13C43×#1877C211yesmaximal, characteristic
14C43×#1877C211yesmaximal, characteristic
15C4×#103×C43C211yesmaximal, characteristic, complemented
16C22×SD16×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C2×C4⋊Q8×C43C2211yescharacteristic
19C2×C4×Q8×C43C2211yescharacteristic
20C2×C4×D4×C43C2211yescharacteristic
21C2×#117×C43—21no—
22C2×#106×C43C2211yescharacteristic
23C2×#106×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×#103×C43C2211yescharacteristic
26C2×#103×C43C2211yescharacteristic
27C2×#103×C43C2211yescharacteristic
28C2×#103×C43C2211yescharacteristic
29C2×#103×C43C2211yescharacteristic
30C2×#103×C43C2211yescharacteristic
31C2×#102×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×C4×C8×C43C2211yescharacteristic
34C43×#400—21no—
35C43×#398—21no—
36C43×#391C2211yescharacteristic
37C43×#391C2211yescharacteristic
38C43×#391C2211yescharacteristic
39C43×#390C2211yescharacteristic
40C43×#390C2211yescharacteristic
41C43×#389C2211yescharacteristic
42C43×#388—21no—
43C43×#388—21no—
44C43×#387—21no—
45C43×#387—21no—
46C43×#384C2211yescharacteristic
47C43×#380—21no—
48C4×C4⋊C4×C43C2211yescharacteristic
49C4×C4⋊C4×C43C2211yescharacteristic
50C4×C4⋊C4×C43C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#336C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Q8×C43C2311yescharacteristic
60C22×Q8×C43C2311yescharacteristic
61C22×D4×C43C2311yescharacteristic
62C23×C4×C43—21no—
63C2×SD16×C43—22no—
64C2×SD16×C43—22no—
65C2×SD16×C43—22no—
66C2×SD16×C43—22no—
67C2×SD16×C43—41no—
68C2×SD16×C43—41no—
69C22×C8×C43C2311yescharacteristic
70C22×C8×C43C2311yescharacteristic
71C22×C8×C43C2311yescharacteristic
72C22×C8×C43C2311yescharacteristic
73C4⋊Q8×C43—22no—
74C4⋊Q8×C43—41no—
75C4×Q8×C43—22no—
76C4×Q8×C43—41no—
77C4×D4×C43—22no—
78C4×D4×C43—22no—
79#117×C43—44no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43—21no—
86C2×C4⋊C4×C43D411yescharacteristic
87C2×C4⋊C4×C43D411yescharacteristic
88C2×C4⋊C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43C2311yescharacteristic
90C2×C4⋊C4×C43C2311yescharacteristic
91C2×C4⋊C4×C43C2311yescharacteristic
92C2×C4⋊C4×C43C2311yescharacteristic
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43—21no—
98C2×C42×C43—21no—
99C2×C42×C43—21no—
100C2×C42×C43—21no—
101C2×C42×C43C2311yescharacteristic
102C2×C42×C43C2311yescharacteristic
103C2×C42×C43C2311yescharacteristic
104#106×C43—22no—
105#106×C43—41no—
106C4⋊C8×C43—41no—
107#103×C43—22no—
108#103×C43—22no—
109#103×C43—22no—
110#103×C43—41no—
111#103×C43—41no—
112#103×C43—41no—
113#102×C43—41no—
114#102×C43—41no—
115C4×C8×C43—41no—
116#95×C43—21no—
117#95×C43—21no—
118#95×C43—21no—
119#95×C43—21no—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43D411yescharacteristic
126#95×C43D411yescharacteristic
127C24×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43#4112yes—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43#4112yes—
146C22×C4×C43—24no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—42no—
155C22×C4×C43—42no—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2411yescharacteristic
163SD16×C43—44no—
164SD16×C43—44no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43#4112yes—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43—42no—
188C4⋊C4×C43—42no—
189C4⋊C4×C43—42no—
190C4⋊C4×C43—42no—
191C4⋊C4×C43—42no—
192C4⋊C4×C43—81no—
193C4⋊C4×C43SD1614yescomplemented
194C4⋊C4×C43#4112yes—
195C22⋊C4×C43—24no—
196C22⋊C4×C43—42no—
197C22⋊C4×C43—42no—
198C22⋊C4×C43—81no—
199C22⋊C4×C43—81no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43—21no—
203C42×C43—21no—
204C42×C43—21no—
205C42×C43—21no—
206C42×C43—42no—
207C42×C43—42no—
208C42×C43—42no—
209C23×C43—22no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43C22×D411yescharacteristic
217Q8×C43—22no—
218Q8×C43—22no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—41no—
225D4×C43—22no—
226D4×C43—22no—
227D4×C43—41no—
228D4×C43—41no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—22no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—22no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—48no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43C2×SD1612yes—
267C2×C4×C43C2×SD1612yes—
268C2×C4×C43C2×SD1612yes—
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×C4×C43C2×#4111yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43H(5,𝔽2)11yescharacteristic
274C2×C4×C43H(5,𝔽2)11yescharacteristic
275C8×C43—22no—
276C8×C43—41no—
277C8×C43—41no—
278C8×C43—41no—
279#27192C4311yesmaximal, characteristic, direct product factor, Sylow
280C22×C43—42no—
281C22×C43—42no—
282C22×C43—42no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43#52511yescharacteristic
288C22×C43#54611yescharacteristic
289C22×C43#55011yescharacteristic
290C22×C43C22×SD1611yescharacteristic
291C22×C43#57511yescharacteristic
292C22×C43#57711yescharacteristic
293C22×C43#57811yescharacteristic
294C4×C43—22no—
295C4×C43—22no—
296C4×C43—22no—
297C4×C43—42no—
298C4×C43—41no—
299C4×C43—42no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43—81no—
303C4×C43—81no—
304C4×C43—81no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43#52911yescharacteristic
308C4×C43#54011yescharacteristic
309C4×C43#55111yescharacteristic
310C4×C43#55111yescharacteristic
311#2446C2×C4311yescharacteristic, complemented
312#2354C2×C4311yescharacteristic
313#2096C2×C4311yescharacteristic, complemented
314#2072C2×C4311yescharacteristic, complemented
315#2065C2×C4311yescharacteristic
316#2013C2×C4311yescharacteristic
317#1981C2×C4311yescharacteristic, complemented
318#1968C2×C4311yescharacteristic
319#1927C2×C4311yescharacteristic, complemented
320#1920C2×C4311yescharacteristic, complemented
321#1916C2×C4311yescharacteristic, complemented
322#1880C2×C4311yescharacteristic
323#1877C2×C4311yescharacteristic
324#1877C2×C4311yescharacteristic
325C4×#103C2×C4311yescharacteristic, complemented
326C2×C43—82no—
327C2×C43#247111yescharacteristic
328C2×C43#310111yescharacteristic
329C2×C43#312011yescharacteristic
330C2×C43#329811yescharacteristic
331C2×C43#332111yescharacteristic
332C2×C43#339211yescharacteristic
333C2×C43#340211yescharacteristic
334C22×SD16C22×C4311yescharacteristic
335C22×SD16C22×C4311yescharacteristic
336C2×C4⋊Q8C22×C4311yescharacteristic
337C2×C4×Q8C22×C4311yescharacteristic
338C2×C4×D4C22×C4311yescharacteristic
339C2×#117—21no—
340C2×#106C22×C4311yescharacteristic
341C2×#106C22×C4311yescharacteristic
342C2×C4⋊C8C22×C4311yescharacteristic
343C2×#103C22×C4311yescharacteristic
344C2×#103C22×C4311yescharacteristic
345C2×#103C22×C4311yescharacteristic
346C2×#103C22×C4311yescharacteristic
347C2×#103C22×C4311yescharacteristic
348C2×#103C22×C4311yescharacteristic
349C2×#102C22×C4311yescharacteristic
350C2×#102C22×C4311yescharacteristic
351C2×C4×C8C22×C4311yescharacteristic
352#400—21no—
353#398—21no—
354#391C22×C4311yescharacteristic
355#391C22×C4311yescharacteristic
356#391C22×C4311yescharacteristic
357#390C22×C4311yescharacteristic
358#390C22×C4311yescharacteristic
359#389C22×C4311yescharacteristic
360#388—21no—
361#388—21no—
362#387—21no—
363#387—21no—
364#384C22×C4311yescharacteristic
365#380—21no—
366C4×C4⋊C4C22×C4311yescharacteristic
367C4×C4⋊C4C22×C4311yescharacteristic
368C4×C4⋊C4C22×C4311yescharacteristic
369#340C22×C4311yescharacteristic
370#340C22×C4311yescharacteristic
371#340C22×C4311yescharacteristic
372#340C22×C4311yescharacteristic
373#336C22×C4311yescharacteristic
374#336C22×C4311yescharacteristic
375#336C22×C4311yescharacteristic
376#336C22×C4311yescharacteristic
377C43#2719211yescharacteristic, direct product factor, Sylow
378C22×Q8C23×C4311yescharacteristic
379C22×Q8C23×C4311yescharacteristic
380C22×D4C23×C4311yescharacteristic
381C23×C4—21no—
382C2×SD16—22no—
383C2×SD16—22no—
384C2×SD16—22no—
385C2×SD16—22no—
386C2×SD16—41no—
387C2×SD16—41no—
388C22×C8C23×C4311yescharacteristic
389C22×C8C23×C4311yescharacteristic
390C22×C8C23×C4311yescharacteristic
391C22×C8C23×C4311yescharacteristic
392C4⋊Q8—22no—
393C4⋊Q8—41no—
394C4×Q8—22no—
395C4×Q8—41no—
396C4×D4—22no—
397C4×D4—22no—
398#117—44no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4D4×C4311yescharacteristic
406C2×C4⋊C4D4×C4311yescharacteristic
407C2×C4⋊C4C23×C4311yescharacteristic
408C2×C4⋊C4C23×C4311yescharacteristic
409C2×C4⋊C4C23×C4311yescharacteristic
410C2×C4⋊C4C23×C4311yescharacteristic
411C2×C4⋊C4C23×C4311yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—21no—
420C2×C42C23×C4311yescharacteristic
421C2×C42C23×C4311yescharacteristic
422C2×C42C23×C4311yescharacteristic
423#106—22no—
424#106—41no—
425C4⋊C8—41no—
426#103—22no—
427#103—22no—
428#103—22no—
429#103—41no—
430#103—41no—
431#103—41no—
432#102—41no—
433#102—41no—
434C4×C8—41no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95D4×C4311yescharacteristic
445#95D4×C4311yescharacteristic
446C24—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8#41×C4312yes—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4#41×C4312yes—
465C22×C4—24no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4C2×D4×C4311yescharacteristic
476C22×C4C2×D4×C4311yescharacteristic
477C22×C4C2×D4×C4311yescharacteristic
478C22×C4C2×D4×C4311yescharacteristic
479C22×C4C2×D4×C4311yescharacteristic
480C22×C4C2×D4×C4311yescharacteristic
481C22×C4C24×C4311yescharacteristic
482SD16—44no—
483SD16—44no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8#41×C4312yes—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—41no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—81no—
512C4⋊C4SD16×C4314yescomplemented
513C4⋊C4#41×C4312yes—
514C22⋊C4—24no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—81no—
518C22⋊C4—81no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—42no—
526C42—42no—
527C42—42no—
528C23—22no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23C22×D4×C4311yescharacteristic
536Q8—22no—
537Q8—22no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543Q8—41no—
544D4—22no—
545D4—22no—
546D4—41no—
547D4—41no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—48no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4C2×SD16×C4312yes—
586C2×C4C2×SD16×C4312yes—
587C2×C4C2×SD16×C4312yes—
588C2×C4C2×#41×C4311yescharacteristic
589C2×C4C2×#41×C4311yescharacteristic
590C2×C4C2×#41×C4311yescharacteristic
591C2×C4C2×#41×C4311yescharacteristic
592C2×C4H(5,𝔽2)×C4311yescharacteristic
593C2×C4H(5,𝔽2)×C4311yescharacteristic
594C8—22no—
595C8—41no—
596C8—41no—
597C8—41no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22C43×#52511yescharacteristic
606C22C43×#54611yescharacteristic
607C22C43×#55011yescharacteristic
608C22C22×SD16×C4311yescharacteristic
609C22C43×#57511yescharacteristic
610C22C43×#57711yescharacteristic
611C22C43×#57811yescharacteristic
612C4—22no—
613C4—22no—
614C4—22no—
615C4—42no—
616C4—41no—
617C4—42no—
618C4—41no—
619C4—41no—
620C4—81no—
621C4—81no—
622C4—81no—
623C4—81no—
624C4—81no—
625C4C43×#52911yescharacteristic
626C4C43×#54011yescharacteristic
627C4C43×#55111yescharacteristic
628C4C43×#55111yescharacteristic
629C2—82no—
630C2C43×#247111yescharacteristic
631C2C43×#310111yescharacteristic
632C2C43×#312011yescharacteristic
633C2C43×#329811yescharacteristic
634C2C43×#332111yescharacteristic
635C2C43×#339211yescharacteristic
636C2C43×#340211yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×D4×C43C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C4⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#2446C2semidirect
3. C43×#2096C2semidirect
4. C43×#2072C2semidirect
7. C43×#1981C2semidirect
9. C43×#1927C2semidirect
10. C43×#1920C2semidirect
11. C43×#1916C2semidirect
15. C4×#103×C43C2semidirect
193. C4⋊C4×C43SD16semidirect
279. #27192C43direct (N × H)
311. #2446C2×C43semidirect
313. #2096C2×C43semidirect
314. #2072C2×C43semidirect
317. #1981C2×C43semidirect
319. #1927C2×C43semidirect
320. #1920C2×C43semidirect
321. #1916C2×C43semidirect
325. C4×#103C2×C43semidirect
377. C43#27192direct (N × H)
512. C4⋊C4SD16×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#24462
C43×#23542
C43×#20962
C43×#20722
C43×#20652
C43×#20132
C43×#19812
C43×#19682
C43×#19272
C43×#19202
C43×#19162
C43×#18802
C43×#18772
C4×#103×C432
#2719243